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Electrochemical
Techniques in
Corrosion Science
and Engineering
Robert G. Kelly and
John R. Scully
University of Virginia
Charlottesville, Virginia, U.S.A.
David W. Shoesmith
University of Western Ontario
London, Ontario, Canada
Rudolph G. Buchheit
The Ohio State University
Columbus, Ohio, U.S.A.
Marcel Dekker, Inc.
New York • Basel
TM
Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.
ISBN: 0-8247-9917-8
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Current printing (last digit):
10 9 8 7 6 5 4 3 2 1
PRINTED IN THE UNITED STATES OF AMERICA
CORROSION TECHNOLOGY
Editor
Philip A. Schweitzer, P.E.
Consultant
York, Pennsylvania
1. Corrosion and Corrosion Protection Handbook: Second Edition,
Revised and Expanded, edited by Philip A. Schweitzer
2. Corrosion Resistant Coatings Technology, Ichiro Suzuki
3. Corrosion Resistance of Elastomers, Philip A. Schweitzer
4. Corrosion Resistance Tables: Metals, Nonmetals, Coatings, Mortars, Plastics, Elastomers and Linings, and Fabrics: Third Edition,
Revised and Expanded (Parts A and B), Philip A. Schweitzer
5. Corrosion-Resistant Piping Systems, Philip A. Schweitzer
6. Corrosion Resistance of Zinc and Zinc Alloys, Frank C. Porter
7. Corrosion of Ceramics, Ronald A. McCauley
8. Corrosion Mechanisms in Theory and Practice, edited by P.
Marcus and J. Oudar
9. Corrosion Resistance of Stainless Steels, C. P. Dillon
10. Corrosion Resistance Tables: Metals, Nonmetals, Coatings, Mortars, Plastics, Elastomers and Linings, and Fabrics: Fourth Edition,
Revised and Expanded (Parts A, B, and C), Philip A. Schweitzer
11. Corrosion Engineering Handbook, edited by Philip A. Schweitzer
12. Atmospheric Degradation and Corrosion Control, Philip A.
Schweitzer
13. Mechanical and Corrosion-Resistant Properties of Plastics and
Elastomers, Philip A. Schweitzer
14. Environmental Degradation of Metals, U. K. Chatterjee, S. K. Bose,
and S. K. Roy
15. Environmental Effects on Engineered Materials, edited by Russell
H. Jones
16. Corrosion-Resistant Linings and Coatings, Philip A. Schweitzer
17. Corrosion Mechanisms in Theory and Practice: Second Edition,
Revised and Expanded, edited by Philippe Marcus
18. Electrochemical Techniques in Corrosion Science and
Engineering, Robert G. Kelly, John R. Scully, David W. Shoesmith,
and Rudolph G. Buchheit
19. Metallic Materials: Physical, Mechanical, and Corrosion Properties,
Philip A. Schweitzer
ADDITIONAL VOLUMES IN PREPARATION
Preface
Corrosion science and engineering have benefited tremendously from the explosion in the use of electrochemical methods that can probe the thermodynamic
and kinetic aspects of corrosion, including the rate of corrosion. These methods
have proved of great utility to corrosion engineers and scientists in predicting
the performance of materials and devising corrosion mitigation strategies, understanding the effects of changes in process and environment conditions, and assessing the accuracy of corrosion monitoring techniques. Enhanced prevention
and understanding of corrosion has been achieved over the past several decades
by applying these methods in both the laboratory and field. Electrochemical methods for corrosion, when used properly, have distinct advantages over exposure
techniques. Some of these advantages are speed, nondestructiveness, high resolution, and ability to provide mechanistic information. Unfortunately, few engineers
and scientists tasked with corrosion problems have been trained in electrochemical fundamentals and their application to corrosion phenomena.
The goal of this book is to present a framework for understanding the principles of electrochemistry and the methods derived from these principles in a
clear manner and ready-to-apply format. The book emphasizes practical fundamentals that make it possible to determine whether electrochemical techniques
are of use for a given problem, choose the correct electrochemical method, and
intelligently interpret the results, including the limitations of the methods and
analyses.
Chapter 1 provides an introduction to some of the basic terms and concepts
of electrochemistry and corrosion and provides a detailed overview of the remainder of the book. Chapter 2 provides an overview of the important thermodynamic
and kinetic parameters of relevance to corrosion electrochemistry. Chapter 3 focuses on what might be viewed as an aberration from normal dissolution kinetics:
passivity. This aberration—or “peculiar condition,” as Faraday referred to it—
is critical to the use of stainless steels, aluminum alloys, and all the so-called
corrosion resistant alloys (CRAs).
iii
iv
Preface
Chapter 4 describes how the electrical nature of corrosion reactions allows
the interface to be modeled as an electrical circuit, as well as how this electrical
circuit can be used to obtain information on corrosion rates. Chapter 5 focuses
on how to characterize flow and how to include its effects in the test procedure.
Chapter 6 describes the origins of the observed distributions in space and time
of the reaction rate. Chapter 7 describes the applications of electrochemical measurements to predictive corrosion models, emphasizing their use in the long-term
prediction of corrosion behavior of metallic packages for high-level nuclear
waste. Chapter 8 outlines the electrochemical methods that have been applied to
develop and test the effectiveness of surface treatments for metals and alloys.
The final chapter gives experimental procedures that can be used to illustrate the
principles described.
“Electrochemical techniques, when conducted intelligently and interpreted
knowledgeably, are valuable tools for solving, understanding, and preventing corrosion problems.” This has been the mantra of a short course on electrochemical
methods applied to corrosion that has been conducted annually since 1984. The
overall goal of the course is to provide practicing corrosion engineers with an
introduction to the use of electrochemical techniques. This book, based on the
lectures and laboratories of that short course, shows how to use electrochemical
methods to understand corrosion phenomena and solve corrosion problems.
ACKNOWLEDGMENTS
More than 50 people have contributed to the success of the course that spawned
this book. These include both faculty members and graduate student assistants
who have taken to heart the desire to constantly improve the quality of the instruction. The father of the short course is Pat Moran (U.S. Naval Academy). He not
only designed the original course but also served as a mentor for many graduate
students in corrosion, including two of the authors of this book. The graduate
students listed below have made critical contributions to the experiments described in Chapter 8. The written experimental procedures reflect only a small
portion of the time they devoted to designing these labs and making them work
during the course. Their influence permeates the book.
The course has enjoyed outstanding support from our sponsors throughout
its history. The local sections of NACE International (Baltimore/Washington
from 1985–1990; Old Dominion from 1991–present) provided advertising support and their good name. Perkin-Elmer Instruments provided excellent equipment and outstanding technical support from the start. Their steadfast assistance
was instrumental in the success of the course.
Preface
v
Many of the figures in Chapters 1 through 5 were created by Jean Reese,
who was also critical in the organization of the short course, and the Center for
Electrochemical Science and Engineering at the University of Virginia.
The patience and pleasant persistence of the team at Marcel Dekker, Inc.,
especially Rita Lazazzaro and Eric Stannard, have been instrumental in making
this book a reality. Most importantly, we acknowledge our families, who made
all the work worthwhile.
Bob Baboian
Bill Eggers
Gary Greczek
Robert G. Kelly
Lecturers
Jerry Kruger
Chip Lee
Pat Moran
Geoff Prentice
Chris Brodrick
Sean Brossia
Noah Budiansky
Brendan Coffey
Brian Connolly
Kevin Cooper
Lisa DeJong
Ron Dombro
Susan Ehrlich
Michelle Gaudett
Steve Golledge
Lab Instructors
Ron Holser
Sudesh Kannan
Robert G. Kelly
Karen Ferrer
Jason Lee
Scott Lillard
Daryl Little
Greg Makar
Lysle Montes
Leigh Ann Pauly
Jeff Poirier
John R. Scully
David W. Shoesmith
Theresa Simpson
Glenn Stoner
Sheldon Pride
James Scanlon
Louie Scribner
Steve Smith
Chris Streinz
Doug Wall
Chris Weyant
Jackie Williams
Todd Wilson
Steve Yu
Robert G. Kelly
John R. Scully
David W. Shoesmith
Rudolph G. Buchheit
Contents
Preface
iii
Chapter 1
Introduction
Robert G. Kelly
Chapter 2
Electrochemical Thermodynamics and Kinetics of
Relevance to Corrosion
Robert G. Kelly
1
9
Chapter 3
Passivity and Localized Corrosion
Robert G. Kelly
Chapter 4
The Polarization Resistance Method for Determination of
Instantaneous Corrosion Rates
John R. Scully
125
The Influence of Mass Transport on Electrochemical
Processes
John R. Scully
151
Chapter 5
55
Chapter 6
Current and Potential Distributions in Corrosion
John R. Scully
Chapter 7
Development of Corrosion Models Based on
Electrochemical Measurements
David W. Shoesmith
205
The Use of Electrochemical Techniques in the Study of
Surface Treatments for Metals and Alloys
Rudolph G. Buchheit
257
Chapter 8
175
vii
viii
Chapter 9
Index
Contents
Experimental Procedures
Robert G. Kelly and John R. Scully
361
423
1
Introduction
Corrosion can be defined as the deterioration of a material’s properties due to
its interaction with its environmnet. The demands for long-term performance of
engineering structures over a wide size scale continue to increase. As microelectronic structures decrease in size, smaller amounts of dissolution on interconnects
in integrated circuits can lead to the failure of large computer systems. The longterm storage of nuclear waste may represent man’s most compelling engineering
challenge: containment of high-level radioactive material for thousands of years.
In both cases, as well as in many in between, the corrosion engineer has a primary
responsibility to provide guidance throughout the design, construction, and life
process in terms of material selection, environment alteration, and life prediction.
Over the past thirty years, the use of electrochemical methods for probing corrosion processes has increased to the point where they represent an indispensable
set of tools. The overarching goal of this book is to provide the foundation for
corrosion engineers to use electrochemical techniques as part of the tool kit they
apply to corrosion concerns.
This introduction briefly reviews topics that underlie the remainder of the
book. Most of these topics will be familiar from high school or college chemistry.
Nonetheless, the topics are generally given short shrift in standard chemistry
syllabi, so their importance with respect to corrosion is emphasized here.
I.
CHEMICAL VS. ELECTROCHEMICAL REACTIONS
Chemical reactions are those in which elements are added or removed from a
chemical species. Purely chemical reactions are those in which none of the species undergoes a change in its valence, i.e., no species is either oxidized or reduced. Electrochemical rections are chemical reactions in which not only may
elements be added or removed from a chemical species but also at least one
species undergoes a change in the number of valence electrons. For example, the
precipitation of iron hydroxide, Fe(OH) 2, is a pure chemical reaction:
1
2
Chapter 1
Fe 2⫹ ⫹ 2OH ⫺ → Fe(OH) 2
(1)
None of the atoms involved have changed its valence; the iron and oxygen are
still in the divalent state, and the hydrogen is still univalent. One way to produce
the ferrous ion needed in the above reaction is via the oxidation of metallic (zero
valent) iron:
Fe → Fe 2⫹ ⫹ 2e ⫺
(2)
In order for this reaction to occur, the two electrons produced must be consumed
in a reduction reaction such as the reduction of dissolved oxygen:
O 2 ⫹ 2H 2 O ⫹ 4e ⫺ → 4OH ⫺
(3)
If the two reactions are not widely physically separated on a metal surface, the
chemical reaction between the hydroxide and ferrous ions can produce a solid
on the surface. Thus chemical and electrochemical reactions can be (and often
are) coupled. 1 The electrochemical methods described in this book can be used
to study directly the wide range of reactions in which electrons are transferred.
In addition, some chemical reactions can also be studied indirectly using electrochemical methods.
The vast majority of engineering materials dissolve via electrochemical
reactions. Chemical processes are often important, but the dissolution of metallic
materials requires an oxidation of the metallic element in order to render it soluble
in a liquid phase. In fact, there are four requirements for corrosion: an anode
(where oxidation of the metal occurs), a cathode (where reduction of a different
species occurs), an electrolytic path for ionic conduction between the two reaction
sites, and an electrical path for electron conduction between the reaction sites.
These requirements are illustrated schematically in Fig. 1.
All successful corrosion control processes affect one or more of these requirements. For example, the use of oxygen scavengers affects the cathodic reaction rate possible. Isolating dissimilar metals with insulating materials attempts
to remove the electrical path. Most organic coatings serve to inhibit the formation
of an electrolytic path. Thus, when evaluating a corrosion process or proposed
mitigation method, a first-pass analysis of the effects of it on the four requirements can serve to structure one’s thinking.
A simple calculation demonstrates the tremendous power of electrochemical reaction rate measurements due to their sensitivity and dynamic range. Dissolution current densities of 10 nA/cm 2 are not tremendously difficult to measure.
1
Bard and Faulkner (1) is an excellent source of information on the intricacies of such coupling.
Introduction
3
Figure 1 Schematic diagram of four requirements for corrosion. Note that the anode
and cathode can be on the same piece of material.
A metal corroding at this rate would lose 100 nm of thickness per year.2 On the
other end of the spectrum, measurements of reaction rates of several to hundreds
of A/cm 2 are needed in some transient studies of localized corrosion. A dissolution rate of 100 A/cm 2 corresponds to a penetration rate of 1 km/s. Fortunately
for modern society, such penetration rates last in practice for far less than one
second! Thus modern instrumentation allows the measurement of dissolution
rates over more than 10 orders of magnitude with accuracy on the order of a few
percent.
The issues of accuracy and precision are often controversial in discussions
of corrosion electrochemistry. Analytical electrochemists can achieve high accuracy and precision through the strict control of variables such as temperature,
solution composition, surface condition, and mass transport. Throughout this
book, the effects of these and other variables on corrosion processes are highlighted. Unfortunately, in practice, close control of such important parameters is
often impossible. In addition, corrosion systems are generally time-varying in
practice, further complicating reproducibility. This situation can be disturbing
for physical scientists new to electrochemical corrosion measurements who are
used to more control and thus more reproducibility in instrumental measurements.
2
In most applications, this would be considered outstanding corrosion resistance, but for a nuclear
waste storage vessel needing 100,000 years of service, the corrosion allowance would need to be
at least 10 cm.
4
Chapter 1
Nonetheless, they become more comfortable with experience, as they realize that
in most cases, getting the first digit in the corrosion rate right is both a necessary
and a sufficient condition for job security.
II. FARADAY’S LAWS OF ELECTROLYSIS
In the early 1800s, Michael Faraday performed superb quantitative experimental
studies of electrochemical reactions. He was able to demonstrate that electrochemical reactions follow all normal chemical stoichiometric relations and in
addition follow certain stoichiometric rules related to charge. These additional
rules are now known as Faraday’s laws. They can be written as follows:
Faraday’s First Law: The mass, m, of an element discharged at an electrode is directly proportional to the amount of electrical charge, Q, passed through
the electrode.
Faraday’s Second Law: If the same amount of electrical charge, Q, is
passed through several electrodes, the mass, m, of an element discharged at each
will be directly proportional to both the atomic mass of the element and the
number of moles of electrons, z, required to discharge one mole of the element
from whatever material is being discharged at the electrode. Another way of
stating this law is that the masses of the substances reacting at the electrodes are
in direct ratio to their equivalent masses.
The charge carried by one mole of electrons is known as 1 faraday (symbol
F ). The faraday is related to other electrical units because the charge on a single
electron is 1.6 ⫻ 10 ⫺19 C/electron. Multiplying the electronic charge by the Avogadro number 6.02 ⫻ 10 23 electrons/mole electrons tells us that 1 F equals 96,485
C.
These empirical laws of electrolysis are critical to corrosion as they allow
electrical quantities (charge and current, its time derivative) to be related to mass
changes and material loss rates. These laws form the basis for the calculations
referenced above concerning the power of electrochemical corrosion measurements to predict corrosion rates. The original experiments of Faraday used only
elements, but his ideas have been extended to electrochemical reactions involving
compounds and ions.
By combining the principles of Faraday with an electrochemical reaction
of known stoichiometry permits us to write Faraday’s laws of electrolysis as a
single equation that relates the charge density (charge/area), q, to the mass loss
(per unit area), ∆m:
∆m ⫽
q(AM)
nF
(4)
Introduction
5
Taking the time derivative of the equation allows the mass loss rate to be related
to the dissolution current density:
˙ ⫽
m
i(AM)
nFρ
(5)
In many cases, a penetration rate, in units of length/time, is more useful in design.
The inclusion of corrosion allowances in a structure requires an assumption of
uniform penetration rate. The most common engineering unit of penetration rate
is the mil per year (mpy). One mil of penetration equates to a loss in thickness
of 0.0001″. Corrosion rates of less than 1 mpy are generally considered to be
excellent to outstanding, although such adjectives are highly dependent on the
details of the engineering scenario. A rule of thumb is that 1µA/cm 2 is approximately equivalent to 0.5 mpy for a wide range of structural materials, including
ferrous, nickel-, aluminum-, and copper-based alloys. For more extract calculations, the following formula can be used:
mpy ⫽
129(AM)(i)
nρ
(6)
where
mpy
AM
i
ρ
n
⫽
⫽
⫽
⫽
⫽
penetration rate (mils per year)
atomic mass (g)
corrosion current density (mA/cm 2)
density (g/cm 3)
number of electrons lost per atom oxidized
Throughout the text, distinctions are made between current, i.e., the rate of a
reaction, and current density, i.e., the area-specific reaction rate. The combination
of Faraday’s laws described above involves current density rather than current.
The current, usually symbolized with a capital I, has units of amperes and represents an electrical flux. The current density, usually symbolized with a lower
case i, has units of amperes per unit area, e.g., A/cm 2. Under a given set of
conditions (i.e., potential, metal and solution composition, temperature, etc.), the
current density is fixed. Thus, although doubling the area of the electrode will
double the measured current, the current density will remain unchanged.
The most direct example of the importance of differentiating between i and
I is in the application of the conservation of charge to corrosion. In this case,
the conservation of charge means that in a isolated system,3 all electrons that are
liberated in oxidation reactions (at anodes must be consumed in reduction reac3
Isolated means that there are no external sources or sinks of electrons.
6
Chapter 1
tions (at cathodes). In terms of charge, the total anodic charge must equal the
total cathodic charge (each in coulombs):
冱Q ⫽ 冱Q
a
i
(7)
c
j
Taking the time derivative converts the law to a rate expression:
冱I ⫽ 冱I
a
i
(8)
c
j
For each reaction, the current density is the current for that reaction divided by
the area over which it occurs:
ii ⫽
Ii
Ai
(9)
Thus combining these expressions demonstrates that only in the cases in which
the areas on which the anodic and cathodic reactions occur are equal can the
anodic and cathodic current densities be equal:
冱i A ⫽ 冱i A
a
i
a
c
c
(10)
j
In other cases, a push-me-pull-you situation arises; the faster (as defined by the
current density) reaction cannot produce current any faster than the slower reaction can consume it. Corrosion engineers use this principle in several ways including sacrificial anodes and corrosion inhibitors. Examples can be found throughout
the text.
III. OVERVIEW OF THE REMAINDER OF THIS BOOK
A.
What Is Covered
This book consists of nine chapters. The second chapter provides an overview
of the important thermodynamic and kinetic parameters of relevance to corrosion
electrochemistry. This foundation is used in the third chapter to focus on what
might be viewed as an aberration from normal dissolution kinetics, passivity.
This aberration, or ‘‘peculiar condition’’ as Faraday called it, is critical to the
use of stainless steels, aluminum alloys, and all of the so-called corrosion resistant
alloys (CRAs). The spatially discrete failure of passivity leads to localized corrosion, one of the most insidious and expensive forms of environmental attack.
Chapter 4 explores the use of the electrical nature of corrosion reactions to model
the interface as an electrical circuit, allowing measurement methods originating
in electrical engineering to be applied to nondestructive corrosion evaluation and
Introduction
7
inspection. Convective flow of the environment can have substantial effects on
corrosion processes. The fifth chapter focuses on how to characterize flow and
how to include its effects in test procedures. In many systems, there are distributions in space and time of the reaction rate due to distributions in the electrochemical potential. The origins of such distributions and their effects on measurements
and interpretations are explored in the sixth chapter of the book. Chapter 7 describes the applications of electrochemical measurements to predictive corrosion
models, emphasizing their use in the long-term prediction of the corrosion behavior of metallic packages for high-level nuclear waste. Chapter 8 outlines how
electrochemical methods have been applied to develop and test the effectiveness
of surface treatments for metals and alloys. The final chapter contains descriptions
of experimental procedures that can be used to illustrate the principles described.
Throughout the book, example from the literature are provided in order to ground
the discussions and to provide the interested reader with access to more in-depth
discussions of certain topics.
B. What Is Not Covered
We have chosen to focus this text on the use of electrochemical techniques. Thus
there are many important areas in corrosion engineering that are excluded. For
example, space constraints prevent any direct coverage of environment-assisted
cracking, although some of the concepts considered in localized corrosion can
be easily extended to the conditions inside occluded cracks. Details of corrosion
mechanisms are not described. Fundamental corrosion information is provided
only to the extent necessary to understand the origin of signals measured by
the electrochemical methods under consideration. Similarly, nonelectrochemical
methods are not described in any detail. In general, high-temperature gaseous
oxidation does not involve a liquid phase and thus falls outside the purview of
this book.
C. Importance of the Motto
The motto found in the front of this book was coined by Pat Moran, currently
Chairman of the Department of Mechanical Engineering at the U.S. Naval Academy and the Ph.D. advisor of two of the authors (RGK, JRS). It includes the key
elements in electrochemical testing that will be emphasized throughout this book.
In order to conduct tests intelligently, one needs to perform the tests in a relevant
environment, on a relevant material surface, under relevant experimental conditions. Although this advice sounds obvious, there is always a tension between
the proper choices for experimental parameters for accurate simulations and the
proper choices for experimental convenience. Such tradeoffs must be carefully
8
Chapter 1
considered. In order to interpret knowledgeably one must be well-read in the
appropriate literature, bring one’s engineering experience to bear on the results,
and use complementary methods for data verification wherever possible. The
power of electrochemical methods is substantial as long as their limitations are
kept in mind.
REFERENCE
1. A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications. John Wiley, New York, 1980.
2
Electrochemical Thermodynamics
and Kinetics of Relevance
to Corrosion
I.
ELECTROCHEMICAL THERMODYNAMICS
A. Utility of Thermodynamics in Electrochemistry
Thermodynamic considerations in electrochemistry allow the determination of
whether a reaction can occur spontaneously, i.e., without the input of external
energy. If metal dissolution is unfavorable thermodynamically in a given set of
circumstances, the job of the corrosion engineer is generally done. For example,
copper will not corrode in pure, deoxygenated water at any pH. Although this
example is one of the few in which corrosion can be excluded on thermodynamic
grounds, the use of such principles can be used to understand the effects of some
variables on corrosion tendencies. In addition, thermodynamics provides the basis
for many of the electrochemical measurements made in corrosion science and
engineering.
The three goals of the thermodynamic section are (1) to relate the thermodynamics of corrosion-related electrochemistry to concepts with which the reader
may be familiar, (2) to describe the need for and characteristics of reference
electrodes, and (3) to describe the origin, use, and limitations of electrochemical
phase diagrams (a.k.a., E-pH or Pourbaix diagrams).
B. Relation of ⌬G to Er
All processes in nature that occur spontaneously have a Gibbs free energy change
(∆G) associated with them that is negative. A negative free energy change indicates that the stability of the products is greater than that of the reactants. The
nature of the process determines the components of the free energy change that
contribute.
9
10
Chapter 2
In electrochemistry, the ∆G is related to the change in the energy of charge
as it passes through the potential difference (Er) at the metal/solution interface
by the relation
∆G ⫽ ⫺nFEr
(1)
where ∆G is the free energy change, n is the number of electrons transferred in
the reaction, and Er is the reversible potential differences across the interface.
This equation relates the amount of energy required to move a charge of nF
reversibly through a potential difference Er. If the energy change is negative, no
external source of energy is required; the reaction will proceed spontaneously,
just as a ball will roll spontaneously down a hill.
One can think of the reversible (i.e., equilibrium) potential for a reaction
across an interface as a battery with a value of Er , as shown schematically in
Fig. 1. Thus, at equilibrium, our metal/solution interface can be modeled as a
battery. Because the system is at equilibrium, no net reaction is occurring under
these conditions.
Each electrochemical reaction has its own reversible potential, just as each
element has its own melting temperature. A list of these reversible potentials
under standard conditions is called an electromotive (emf ) series.
Figure 1 Schematic of an equilibrium metal–solution interface as battery with a voltage
of magnitude Er.
Electrochemical Thermodynamics and Corrosion
11
Table 1 Partial List of Standard
Electrochemical Potentials
Reaction
Au3⫹ ⫹ 3e⫺ ⫽ Au
Cl2 ⫹ 2e⫺ ⫽ 2Cl⫺
O2 ⫹ 4H⫹ ⫹ 4e⫺ ⫽ 2H2O
Cu2 ⫹ 2e⫺ ⫽ Cu
2H⫹ ⫹2e⫺ ⫽ H2
Ni2⫹ ⫹ 2e⫺ ⫽ Ni
Fe2⫹ ⫹ 2e⫺ ⫽ Fe
Zn2⫹ ⫹ 2e⫺ ⫽ Zn
A13⫹ ⫹ 3e⫺ ⫽ A1
Mg2⫹ ⫹ 2e⫺ ⫽ Mg
Na⫹ ⫹ e⫺ ⫽ Na
Standard Potential
(V vs. NHE)
1.42
1.36
1.229
0.34
0.000
⫺0.23
⫺0.44
⫺0.763
⫺1.706
⫺2.375
⫺2.712
Two aspects of Table 1 are important. The “standard conditions” are 298
K and all reactants and products are at unity activity.* The second key is the
selection of the hydrogen reaction as having a standard reversible potential of
0.0 V. The table allows the first use of thermodynamics in corrosion. For a metal
in a 1 M solution of its salt, the table allows one to predict the electrochemical
potential below (i.e., more negative) which net dissolution is impossible. For
example, at ⫹0.337 V(NHE), copper will not dissolve to cuprous ion if the solution is 1 M in Cu2⫹. In fact, at more negative potentials, there will be a tendency
at the metal/solution interface to reduce the cuprous ions to copper metal on the
surface.
The concept of interfacial potential difference can be a major stumbling
block for those new to electrochemistry. The measurement of voltage and its
analogy to pressure in fluid flow is reasonable, but the reference point of zero
volts and the sign conventions can be confusing. Moran and Gileadi wrote an
excellent article on these topics to which the interested reader is referred (1). The
key issues are summarized here.
Measurements of voltages within electrical circuits are familiar to many.
One connects the lead from the positive terminal of the voltmeter to the point
in the circuit of interest, and the lead from the negative terminal of the voltmeter
to the point known as the ground. The ground is often in some way connected
* In most cases in corrosion, we ignore activity coefficients. Thus activity and concentration are used
interchangeably. Strictly, this approach is flawed, but the lack of information concerning the values
of activity coefficients in most cases makes it necessary.
12
Chapter 2
electrically to the earth. In an ideal world, all grounds are the same voltage and
are interchangeable. In electrochemical measurements, the idea of a ground as a
reference point is more complicated.
Consider Fig. 2. In Fig. 2a, the connections for a standard measurement
of voltage in an electrical circuit are shown. In Fig. 2b, the connections for an
electrochemical measurement are started; connecting the lead from the positive
terminal of the voltmeter to the electrode of interest is straightforward, but what
is to be done with the negative lead? We need the electrochemical equilivalent
of a ground. Despite many attempts, it has proved impossible to measure the
Figure 2 (a) Connections to measure potential difference in an electrical circuit. (b)
Impossibility of measuring the potential across an electrochemical interface without introducing a second interface.
Electrochemical Thermodynamics and Corrosion
13
Figure 3 Inclusion of a second interface allows combined voltage of the two interfaces
to be measured with a voltmeter.
potential across an electrochemical interface without introducing another electrochemical interface as shown in Fig. 3.
C. Reference Electrodes
By introducing another electrochemical interface, it would seem that the problem
of measurement has been doubled. In fact, if the additional interface is at thermodynamic equilibrium, then the practical problem of measurement is solved. By
maintaining a reaction in equilibrium at the interface, the potential across it is
constant (and calculable). Thus any changes in the measurement of the potential
between the two interfaces can be attributed to the electrode of interest (typically
referred to as the working electrode).
Theoretically, any of the reactions shown in Table 1 could be used as reference electrodes (along with many others). Many years ago, the hydrogen reaction
was selected as the reaction to which a value of zero volts is ascribed. Thus the
standard for all reference electrodes is the hydrogen electrode in which a Pt (or
other catalytic but corrosion-free surface) is exposed to a pH 0 solution saturated
with hydrogen gas at room temperature. Its value is zero as the reaction is at
equilibrium in a 1 M solution of the ion of interest (H⫹) with the other reactant
at unit activity (a partial pressure of 1 atm for H2, generally achieved by bubbling
hydrogen gas into the solution). It is sometimes called the standard hydrogen
14
Chapter 2
electrode (SHE) or the normal hydrogen electrode (NHE). Thus voltages of other
electrodes referred to this electrode are labeled in V(SHE) or V(NHE).
The perfect reference electrode (RE) is one for which the value depends
solely on the concentration of one species, is in thermodynamic equilibrium, does
not contaminate the solution of interest, is cheap to acquire, and is easy to maintain. Although the NHE electrode has a value of zero volts, it has some practical
disadvantages. Chief among these is the need to maintain a source of hydrogen
gas. Ever since the Hindenburg, many individuals have shied away from routinely
having large volumes of hydrogen in close proximity to possible ignition sources.
Fortunately, many more practical RE have been developed and are commercially
available.
Most RE have the components shown in Fig. 4. In order to maintain the
RE at equilibrium, a glass or polymeric body separates the inner, or fill, solution
from the test environment. The ionic communication with the test solution needed
is controlled, often through a porous frit. The electrode interface itself is often
composed of a metal coated with a metal salt. This arrangement often leads to
a robust equilibrium condition; as long as some metal salt is present on the electrode surface, the potential of the RE is independent of the amount of salt. The
composition of the fill solution is important in maintaining the RE at equilibrium.
A large variety of reference electrodes has been reviewed by Ives and Janz
Figure 4 Components of typical commercial reference electrode: (a) electrical connection, (b) metal–metal salt electrode, (c) filling solution that maintains electrode interface
equilibrium, (d) glass or polymeric electrode body, (e) porous frit.
Electrochemical Thermodynamics and Corrosion
15
(2). There are commercial suppliers for many of these. Three of the most commonly used in aqueous solutions are the saturated calomel electrode (SCE), the
Ag/AgCl electrode, and the Hg/Hg2SO4 electrode. For soil, concrete, and other
partially aqueous systems, other RE have been found to be better suited.
Selection of the type of RE is determined in large part by the composition
of the fill solution. The fill solution can have two major effects on the electrochemical measurement. Along with the metal electrode, it controls the value of
the RE potential. In addition it is generally concentrated (i.e., on the order to 0.5
to 5 M salt). Thus it can act as a source for ionic contamination of the test solution.
Because the most popular reference electrodes contain chloride ion, a known
aggressive species, this contamination source must be considered carefully. The
rate at which the fill solution contaminates the solution (and vice versa) is strongly
dependent on the leak rate of the frit. If the frit (or valve) prevented all movement
of ionic species, then the RE would not function as a complete electrical circuit,
which is required to allow a potential to be measured. Thus frits are generally
designed to leak at rates on the order of 1µL/h.
A simple calculation shows the effects of such a leak rate. Consider a 0.5
1L test solution volume having 4 µL/h of 4 M Cl⫺ added (the KCl concentration
in a saturated calomel electrode). In a 24 h test the initial Cl⫺-free solution will
develop a concentration of 7.7 ⫻ 10⫺5 M Cl⫺. Although low, this concentration
will lead to pitting in many alloys (3), confounding interpretation of the results.
A second effect of filling solution leakage into the bulk solution involves the
cations that are released. In the case of the SCE, there is a small concentration
of Hg2⫹ that makes its way into the bulk. Once in the bulk solution, the mercurous
ions can be deposited electrochemically onto any surface at a potential below
the reversible potential for Hg deposition. This deposition of metallic mercury
can cause dramatic changes in the surface behavior.
Whereas the discussion of filling solution leakage has focused on the effects
of the filling solution leaking out, there can also be effects of the bulk solution
leaking into the reference electrode. Some compounds can foul the metal–
solution interface within the RE or displace/convert the metal salt. The important
effect of such processes is the disturbance of the equilibium at the interface,
rendering our assumption of constant interfacial potential in the RE invalid. Unfortunately no warning signal is emitted from the RE under these conditions.
Periodic checking of the RE to a laboratory standard is the only means of ensuring
valid measurements.
In some cases, the physical size of a reference electrode can be important
when space is constrained either in a laboratory cell or in a field monitoring
application. The success of microdevices for monitoring environmental, physiological, and corrosivity variables has been greatly impeded by the lack of a robust,
inexpensive RE. As discussed in Chapter 5, a RE placed too close to a surface
can affect the current distribution and lead to erroneous potential measurements.
16
Chapter 2
Rules of thumb are discussed in Chapter 5 that allow minimization of this
problem.
Care and feeding of the RE is often neglected. Nonetheless, due to the
nature of electrochemical potential measurements, confidence in one’s reference
electrode is critical. To maintain such confidence, establish a laboratory reference
reference electrode. This standard can be most easily established by purchasing
an extra reference electrode of choice and placing it in a two-necked flask containing the same solution that is used as the filling solution within the RE. For
example, at UVa we have a “lab standard SCE” that is exposed to a saturated
solution of KCl. On a regular basis, the RE to be used in an experiment can be
compared to the lab standard. Be sure to clean the outer surface of the to-betested RE before immersion in the two-necked flask. If the value of the potential
difference between the two nominally identical RE is steady and small (e.g.,
⬍ 3 mV), the tested RE passes. For high-precision meaurements, the difference
measured can be used to correct the measured potentials in the experiment. Periodic refurbishment of RE used in experiments according to the manufacturer’s
instructions is also good practice and will keep RE cost under control.
Protection of the lab standard is clearly of paramount importance. Use of
the lab standard for any measurement in a real cell is considered a capital offense
in our center. Every year or so the lab standard is introduced into experimental
service and replaced with a new lab standard.
Independent of the RE chosen for a measurement, there is often a need to
convert the measured values to a difference reference scale. For example, although the measurements may have been made with an SCE, the investigator
may want to make a comparison with thermodynamic data that are referenced
to NHE. The most foolproof means of conversion is the number line. Even the
most algebraically challenged can use a number line flawlessly to convert readings from one scale to another. Figure 5 shows a number line containing the most
common RE.
An example will serve to illustrate the use of the number line. If a measure-
Figure 5 Number line for conversion of electrode potentials among different reference
electrode scales.
Electrochemical Thermodynamics and Corrosion
17
ment of the potential of steel in seawater shows that it is ⫺0.5 V(SCE), what is
the potential on the NHE scale? On the Cu/CuSO4 scale? By placing a tick at
the measured value (see arrows) we can see that the measured value would be
⫺0.259 V(NHE) and ⫺0.68 V(Cu/CuSO4).
D. Nernst Equation
As electrochemical reactions are, at their heart, chemical reactions, their thermodynamics depend on the concentrations of the species involved, as well as the
temperature. The Nernst equation describes this dependence. Derivations of the
Nernst equation are available in many standard texts (4–6). For our purposes, it
will be simply stated that for a reaction described by
aRd ⫹ mH⫹ ⫹ ne⫺ ⫽ bOx ⫹ cH2O
(2)
The reversible potential can be calculated according to
E r ⫽ Eo ⫺
RT {Ox}b {H2O}c
ln
nF {Rd}a {H⫹}m
(3)
where Er ⫽ reversible potential (V), Eo ⫽ standard reversible potential (i.e., Er
for unit activity of all reactants/products), and {i} j ⫽ activity of species i, raised
to the stoichiometric coefficient j.
The standard reversible potential is that listed in the EMF series of Table
1 and represents a special case of the Nernst equation in which the second term
is zero. The influence of the solution composition manifests itself through the
logarithmic term. The ratio of activities of the products and reactants influences
the potential above which the reaction is thermodynamically favorted toward
oxidation (and conversely, below which reduction is favored). By convention,
all solids are considered to be at unit activity. Activities of gases are equal to
their fugacity (or less strictly, their partial pressure).
Note that the effects of solution composition on Er are fairly weak as they
appear in the logarithm term. Thus an order of magnitude change in the concentration of oxidized form (i.e., Ox in the equation above), while keeping the concentration of the reduced form constant, changes the reversible potential by RT/nF
(typically 30 to 60 mV). Although small, these changes can be important in corrosion situations. Figure 6 shows a graphical representation of the Nernst equation.
E.
Pourbaix Diagrams
In 1945, Marcel Pourbaix submitted a Ph.D. dissertation entitled “Thermodynamics in dilute solutions: graphical representation of the role of pH and potential.”
It was initially rejected, or so the legend goes. Fortunately for corrosion scientists
18
Chapter 2
Figure 6 Semilogarithmic plot of Nernst equation showing dependence of reversible
potential on ratio of activities of oxidized and reduced species for cases in which both
stoichiometric coefficients are unity.
and engineers everywhere, Pourbaix continued his development of graphical representations of electrochemical thermodynamics. The work of the institute that
M. Pourbaix founded continues through both additions and updates to his Atlas
of Electrochemical Equilibria in Aqueous Solution, a must-have for all corrosionists (7). These diagrams are to electrochemistry what temperature–composition phrase diagrams are to materials science. In both cases, the plots identify
the phases that have the lowest Gibbs free energy for various values of the external variables. In this way the spontaneous directions of all reactions can be determined.
Pourbaix diagrams are plots of (reversible) potential vs. pH for elements
in pure water. They consist of regions of stability defined by lines as borders.
Three types of lines exist on Pourbaix diagrams. Horizontal lines describe reactions that are dependent only on potential (e.g., Fe ⫽ Fe2⫹ ⫹ 2e⫺). Vertical lines
describe reactions that are dependent only on pH (e.g., Fe2⫹ ⫹ 2OH⫺ ⫽ Fe(OH)2).
Angled lines correspond to reactions that depend on both potential and pH (e.g.,
O2 ⫹ 4H⫹ ⫹ 4e⫺ ⫽ 2H2O).
The most simple Pourbaix diagram is that for water shown in Fig. 7. All
Pourbaix diagrams contain the two lines that bound the regions of stability for
water, known as the reversible hydrogen and reversible oxygen lines, and labeled
as “a” and “b,” respectively. For corrosionists the importance of these lines should
not be underestimated. As noted in the introduction, for metal dissolution to occur, a reduction reaction must occur. In aqueous solution, the most common reduction reactions are the reduction of dissolved oxygen and the reduction of water
Electrochemical Thermodynamics and Corrosion
Figure 7
‘‘b.’’
19
E–pH (Pourbaix) diagram for water. Water is stable between lines ‘‘a’’ and
(also known as hydrogen evolution). Lines “a” and “b” define the regions of pH
and potential where these two cathodic reactions can occur. The lines are dotted
as an indication that all the species in the reaction are dissolved rather than solid.
Oxygen can be reduced only at potentials below the line “b,” conditions for which
the oxygen reduction reaction (ORR),
20
Chapter 2
O2 ⫹ 4H⫹ ⫹ 4e⫺ → 2H2O
(4)
is favored to proceed as written. Similarly, the reduction of water can only occur
at potentials more negative than line “a,” under which conditions the hydrogen
evolution reaction (HER),
2H2O ⫹ 2e⫺ → H2 ⫹ 2OH⫺
(5)
is favored to proceed as written. When the metal surface is at a potential where
one or both of these reactions can occur, the possibility of corrosion exists as
long as the metal dissolution reaction is thermodynamically favorable. For example, the reversible potential for copper metal oxidation reaction is above line “a”
for all pH. Thus, in the absence of oxygen, metallic copper is thermodynamically
favored in pure water over all dissolved or other solid copper species. The Pourbaix diagram can be used to illustrate why gold is useful for wedding bands as
shown in Fig. 8. As (generally) marriage is considered to be permanent state, the
selection of gold is fortuitous; the reversible potential for the oxidation of pure
gold is above the oxygen line for all pH. Thus gold is absolutely stable at room
temperature in pure water. If only all marriages were.
The Nernst equations for ORR and HER are simplified due to their dependence only on pH, which is itself the negative logarithm of the activity of H⫹:
For ORR:
Er ⫽ 1.23 ⫺ 0.059pH
(6)
For HER:
Er ⫽ ⫺0.059pH
(7)
As with all Pourbaix diagrams, the potential scale is referenced to NHE. Thus,
line “a” at pH 0 (i.e., 1 M H⫹) has a value of 0 V(NHE), and line “b” at pH 0
has a value of 1.23 V (NHE).
A slightly more complicated diagram is that for Al as shown in Fig. 9.
Many valve metals have such fairly simple E–pH diagrams. Lines “a” and “b”
are present, as always. The solid lines represent three reactions: oxidation of Al
metal to Al3⫹, the equilibrium between Al3⫹ and Al2O3, and the equilibrium between AlO2 and Al2O3. The latter two are purely chemical reactions, so there
is no potential dependence. The oxidation of Al at low pH does not involve water,
whereas it does at higher pH.
At low pH:
Al → Al3⫹ ⫹ 3e⫺
(8)
At high pH:
Al ⫹ 2H2O → AlO2⫺ ⫹ 4H⫹ ⫹ 3e⫺
(9)
The involvement of both electrons and hydrogen ion in the high pH reaction
explains the slope of the line. Because both reactions involve at least one solid
species, the lines are solid, by convention. The diagram in Fig. 9a assumes that
the concentration of all dissolved species except H⫹ and O2 is 10⫺6 M. Such
simplified diagrams have pedagogical uses, but the dependence of the Nernst
Electrochemical Thermodynamics and Corrosion
21
Figure 8 E–pH diagram for Au. Note that Au is stable at all pH in pure water at room
temperature, as the reversible potential for Au oxidation is greater than the reversible
potential for oxygen reduction (line ‘‘b’’).
22
Chapter 2
Figure 9 (a) Simplified E–pH diagram for Al, which is typical of many valve metals
such as Ti, W, and Zn. Al is expected to show amphoteric behavior, i.e., corrode at both
high and low pH, because soluble species are more stable than metallic Al under such
conditions. (b) E–pH diagram for Al showing effects of dissolved ion concentration on
the boundaries of the phase diagram. Numbers next to boundary lines are the logarithms
of the concentration of the species involved.
equation on concentration must generally be considered. A more extensive E–
pH diagram for Al is shown in Figure 1-9b.
The Pourbaix diagram for Cu represents one of the more complicated sets
of E–pH behavior as shown in Fig. 10. All three kinds of lines are possible due
to the large number of reactions to be considered. Nonetheless, the same principles apply to the diagrams as for the more simple Pourbaix diagrams. The Atlas
(7) and the literature continue to refine and extend the E–pH concept for a concise
graphical approach to electrochemical equilibria. Some current issues in this regard include:
1. Higher Temperature
All of the diagrams in Pourbaix’s original atlas were calculated for room temperature. To develop Pourbaix diagrams under higher temperature conditions, several
aspects need to be considered. Not only does the temperature affect the logarith-
Electrochemical Thermodynamics and Corrosion
23
Figure 10 E–pH diagram for Cu showing all three types of lines along with the effects
of dissolved copper concentration.
mic term but also the effects on the standard potentials (including the effect on
the NHE) must be included. In recent years there has been increasing work for
high-temperature conditions in pure water driven by the need for nuclear reactor
materials (8–10).
2. Metastable Species
Metastable species (such as thiosulfate, S2O32⫺) have been shown to be important
in some corrosion scenarios (11–13). Such species are not represented on stan-
24
Chapter 2
dard Pourbaix diagrams. For example, Marcus (14,15) has published diagrams
that consider metastable sulfur species. The most significant challenge in these
studies is the determination of accurate thermodynamic data.
3. Alloys
Alloys represent special problems for E–pH diagrams. Overlaying of the diagrams for the individual elements has shown some, albeit limited, promise (16).
The problem may indicate that the effects of alloying are manifested more in
the kinetics than in the thermodynamics of corrosion and electrochemistry. For
example, passivity of pure iron in acid is not predicted from E–pH diagrams; it
is a kinetic effect.
F.
Applications
Despite the limitations inherent in E–pH diagrams, the approach can be extremely
useful in understanding and overcoming corrosion problems in solutions more
complicated than pure water. Two examples illustrate the power of this approach.
Figure 11 shows an E–pH diagram developed by Silverman (17,18). This
diagram differs from that in the Atlas (7) in the use of more recent, more accurate
thermodynamic data for the species involved, including several titanium chloride
species expected because of the presence of several molar chloride, and because
it was calculated for a temperature of 75°C. The conditions represent a process
stream in which Grade 2 Ti was exposed to acidic chloride solutions containing
an organic molecule that had acid–base and thermodynamic properties very similar to those of aspartic acid. There was concern that the Grade 2 Ti might corrode
at sufficiently low pH, but the critical pH was unknown. Although details are
available in the original work (17,18), the key results can be seen in Fig. 11, in
which the corrosion potentials (Ecorr) measured for several possible process solutions are indicated. The open symbols are for conditions in which the thermodynamics predict dominance of TiO2, suggesting that low corrosion rates are likely,
whereas the solid symbols are in a region in which Ti3⫹ dominates, indicating
the likely absence of any protective film. The E–pH diagram indicates a threshold
pH of approximately zero, below which corrosion rates would be expected to
increase rapidly. Short-term (two-day) experiments were conducted. For solutions of pH 0.05 and greater, corrosion rates of ⬍ 1 mpy were observed, whereas
for pH values of ⫺0.55 and ⫺0.9, penetration rates of 20 and 100 mpy, respectively, were measured. By taking into account complexation and using the best
thermodynamic data avilable, Silverman showed that a rapid assessment of process limitations can be made and handed off to the production line.
A second example of the utility of E–pH diagrams comes from the work
of Walter at the University of Wollongong in Australia. Hot-dipped Al–Zn-
Electrochemical Thermodynamics and Corrosion
25
Figure 11 E–pH diagram for Ti developed by Silverman for 75°C and 10 M Cl⫺. Symbols represent measured Ecorr of Grade 2 Ti alloy in a simulated process solution. Solid
symbols indicate conditions that led to rapid corrosion (⬎ 20 mpy), whereas open symbols
represent conditions that led to very low corrosion rates (⬍⬍ 1 mpy).
coated steel is widely used for fences and roofs after painting. Their expected
service life is in the 20 to 30 year range. Unfortunately, in some geographical
locations, so-called “bleedthrough rusting” occurred in which rust stains appeared
(i.e., “bled through”) coatings in only a few years. The hot-dipped coatings were
designed to be sacrificial to the steel, but failure analyses showed that although
the metallized coatings were still present, the underlying steel had corroded at
defects. Figure 12 shows a photograph of such a system after service in the field.
Walter used Pourbaix diagrams in order to assess what types of environmental
conditions could lead to such a phenomenon.
26
Chapter 2
Figure 12 Photomicrograph of bleedthrough rust phenomenon. Red areas represent corroded steel that was not protected by the hot-dipped Al-Zn coating. (From Ref. 22.)
Figure 13 Simplified E–pH for Zn. (From Ref. 22.)
Electrochemical Thermodynamics and Corrosion
27
To approach the problem, the complex system was modeled as a galvanic
couple amongst pure Al, pure Zn, and pure Fe. Figure 13 shows the E–pH diagram for Zn. Qualitatively, it is similar to the Al diagram shown in Fig. 9. Figure
14 shows an overlay of the E–pH diagrams for Al, Zn, and Fe. In order for
material to function as a sacrificial anode, it must remain active/unfilmed. In fact,
prevention of passivation of Al anodes continues to be an area of interest for
marine applications owing to its many advantages over conventional zinc anodes.
Careful inspection of Fig. 14 shows that there exists a narrow region of potential
and pH in which both Al and Zn would be expected to (possibly) form protective
films, but in which metallic Fe is thermodynamically unstable. In these neutral,
but oxidizing, solutions, it would be expected that the hot-dipped Al–Zn would
not provide sacrificial protection to the steel.
II. ELECTROCHEMICAL KINETICS
A. Types of Electrochemical Cells
1. Driving and Driven Cells
The kinetics of electrochemical reactions at a metal–solution can best be studied
when the electrode of interest is part of an electrochemical system or cell. The
polarity of electrochemistry conventions can be confusing, but the application of
a few simple rules can alleviate much of the uncertainty. Electrochemical cells are
two-terminal devices that can be classified as either driving or driven according to
their function. A driving electrochemical cell is a power producer, converting
chemical energy into electrical power. In some cases this power can be used
externally to the cell. A driven electrochemical cell is a power consumer. When
used to power an electrical device, a battery is a driving system. When a battery
is being recharged, it becomes a driven system. Corrosion systems in the absence
of external influence are short-circuited, driving systems.
Consider the driving system shown in Fig. 15a. A battery is connected to
a resistor. Convention states that positive current (defined as the flow of positive
charge) leaves the positive terminal of a discharging battery and enters the positive terminal of a resistor.* A voltmeter would read a positive value if its positive
lead were connected to the positive end of the resistor (or battery) and its negative
lead attached to the negative side of the resistor.
Now consider just the battery in Fig. 15b. It is acting as a driving system.
The positive electrode is called the cathode and the negative electrode is the
anode. Four rules can be used to assist in determining polarity and the location
of the different reactions.
* Of course, it is now known that electrons are the charge carriers and hence their flow is in the
opposite direction of conventional current.
28
Chapter 2
Figure 14 Overlay of Pourbaix diagrams for Al, Fe, and Zn, showing that there exists
a region of potential and pH within which Al and Zn would be expected to form solid
films (i.e., passivate) and lose their ability to corrode sacrificially and protect the steel.
(From Ref. 22.)
Rule
Rule
Rule
Rule
1:
2:
3:
4:
Gain of electrons is reduction.
Reduction always occurs at the cathode.
Loss of electrons is oxidation.
Oxidation always occurs at the anode.
These rules applied to Fig. 15b imply that the reduction reaction (at the cathode)
produces positive current (i.e., it consumes electrons), whereas the oxidation reaction (at the anode) consumes positive current. The resistor is blissfully unaware
of these goings on. It simply removes some of the energy from the electrons for
its own purposes, such as running a watch, calculator, or laptop computer. In the
case of a driving system, the cathode is at a potential more positive than the
anode.
In Fig. 15c, the resistor has been replaced by an electrochemical cell. This
cell could be a recharging battery or a corrosion cell that is being studied electrochemically. In either case, it will be a driven system. The driving is being done
by the battery just discussed, or a power supply, or a potentiostat (more on this
option below). Nonetheless, replacing the resistor with an electrochemical cell
does nothing to change the polarity of the driven system. The electrode on the
Electrochemical Thermodynamics and Corrosion
29
Figure 15 Types of electrical/electrochemical cell with polarity conventions shown:
(a) power supply driving a resistor, (b) battery driving resistor, (c) power supply recharging
a driven battery, (d) corrosion cell as a nearly short-circuited driving system. The resistance represents the electrical resistance in the metal between anode and cathode sites.
left is at a more positive potential than the electrode on the right, allowing positive
current to continue to pass through the cell. Consider the electrode on the left.
Positive current enters it from the electrical lead and leads it into the solution.
Electrons must be being liberated by a reaction at the interface and moving into
the lead. Thus an electrochemical oxidation is occurring on that positive electrode, making it an anode. Similarly, electrochemical reduction occurs on the
opposite electrode, making it a cathode. Note that in the case of the driven cell,
the anode is positive whereas the cathode is negative, opposite the case of the
driving cell. Test your understanding by using these concepts to determine if the
terminals in your car battery are labeled correctly under both charge and discharge. See the footnote below* for the answer.
A corrosion cell is represented in this manner as shown in Fig. 15d. It is
a driving cell, but one that is short-circuited. The anodic and cathodic reactions
occur on the same metal surface. If the sites at which the two reactions occur
could be physically separated, then the cathodic reactions would be occurring at
a higher potential than the anodic reactions.
* The labels on your car battery (or any other rechargeable battery) are always correct. During use
(discharge), the positive terminal is the cathode and the negative terminal is the anode; it is a driving
system. During recharge, the positive terminal is the anode and the negative terminal is the cathode;
it is a driven system.
30
Chapter 2
Figure 16 Terminal connections for operational amplifier. Vcc represent the positive and
negative power supplies needed. The input terminals are labeled as ‘‘⫺’’ and ‘‘⫹’’.
2. Potentiostats
In most electrochemical measurements of corrosion kinetics a potentiostat is
used. This description will cover the rudimentary operation of a potentiostat using
the concept of an ideal operational amplifier (op amp) as a basis. An op amp is
a three-terminal device as shown in Fig. 16 with two input terminals and one
output terminal. A perfect op amp follows five basic rules (19):
1.
2.
3.
4.
5.
When the voltage difference ∆V (⫽ V⫹ ⫺ V⫺ ) is zero, the output voltage Vout (relative to ground) is zero. That is, a perfect device acts as a
differential amplifier.
When a small ∆V is applied between the input terminals, the output
voltage tends towards plus or minus infinity depending upon the polarity of ∆V. That is, the gain of a perfect op amp is infinite.
The current between the two input terminals is zero because the resistance (impedance) between them is infinite. That is, the input impedance is infinite.
The output current depends only on the output voltage and the resistance (impedance) of the load. That is, the output impedance is zero.
If ∆V undergoes changes, the output voltage follows these changes
exactly. That is, the bandwidth of a perfect device is infinite.
Fig. 17 shows how such an ideal op amp can be configured as a potentiostat
and connected to an electrochemical cell to study kinetics. First consider the
electrochemical cell in the schematic. Unlike the cells discussed above, this cell
has three electrodes. The working elecrode (WE) represents the interface of inter-
Electrochemical Thermodynamics and Corrosion
31
Figure 17 Configuration of op amp to function as a potentiostat. The desired Vin is set
by the experimenter via the voltage divider on the left, which consists of a battery and a
variable resistor. The path of the current is shown, indicating that no current passes through
the RE.
est; the reference electrode (RE) has been introduced earlier in Chapter 2 and
acts as our standard for potential measurements. The counter electrode (CE) is
an additional interface whose sole purpose is to act as an anode or a cathode
(electron sink or source) for our driven electrochemical cell via reactions that
occur on its surface. In order to study the corrosion kinetics of the WE, the
potential of the WE is controlled with respect to the RE at a constant value, and
the reaction rate (i.e., current density) under those conditions is determined. A
series of potentials may be studied in order to determine the effect of changes
in potential on the corrosion rate, for example.
The potentiostat accomplishes this feat by simply following the five rules.
If the ∆V between the RE and the WE is not Vin (set by the battery and variable
resistor), the output voltage will be nonzero until ∆V goes to zero. The application
of a Vout other than zero allows current to pass through the ammeter, through the
CE interface, through the solution, through the WE interface, and to electrical
ground. This current path is shown in Fig. 17. Because of the infinite input impedance of the assumed perfect negative input (see Rule 3), no current passes through
the RE, allowing it to remain at equilibrium and to serve as a potential standard.
If the current needed to maintain Vin changes because of alterations in conditions
at the WE surface (e.g., formation of a film), then Vout changes instantaneously
to accommodate. By changing the polarity and magnitude of Vin, the kinetic behavior of an interface in terms of the i–E relationship over a wide range of potential can be determined. Of course, the effects of external variables such as temperature, solution composition, and solution flow can also be studied under constant
electrochemical conditions.
32
Chapter 2
The WE and CE combination represents a driven electrochemical cell. The
presence of the RE allows the separation of the applied potential into a controlled
portion (between the RE and the WE) and a controlling portion (between the RE
and the CE). The voltage between the RE and the CE is changed by the potentiostat in order the keep the controlled portion at the desired value. Consider the
application of a potential Vin to the WE that is more positive than its rest potential,
Vrest, with respect to RE. By definition, polarization of the WE anodically (i.e.,
in a positive direction) would lead to an anodic current through the WE–solution
interface and a release of electrons to the external circuit. These electrons would
be transported by the potentiostat to the CE. A reduction reaction would occur
at the CE–solution interface facilitated by a more negative potential across it.
The circuit would be completed by ionic conduction through the solution.
For simplicity, assume that the WE and the CE are identical and therefore,
in the absence of external polarization, have the same interfacial potential. As
shown in Fig. 18a, application of a potential that encourages oxidation on the
WE surface would cause reduction on the CE surface. The WE potential would
Figure 18 Number lines representing change in the potential of the WE and CE under
conditions of (a) anodic polarization of the WE and (b) cathodic polarization of the WE.
The extent of the polarization of each is determined by the kinetics of the reactions occurring.
Electrochemical Thermodynamics and Corrosion
33
become more positive, and the CE potential would become more negative. The
current passing through the WE at a given level of polarization (Vin ⫺ Vrest) is a
measure of the reaction kinetics at the WE–solution interface. The amount of
polarization of the CE would depend on its kinetics. Changing the polarity of Vin
⫺ Vrest would result in changes in interfacial potentials in the directions shown
in Fig. 18b.
B. Tafel Behavior and Evans Diagrams
Consider the electrochemical system shown in Fig. 19 consisting of three Pt–
solution interfaces in room-temperature solutions. The middle chamber is separated from the outer chambers by a porous membrane that limits mass transport,
allowing the solutions to remain at different pH. Chamber A represents a NHE
reference electrode: the pH is zero and hydrogen gas is present at 1 atm. At this
Pt–solution interface, the HER reaction is in thermodynamic equilibrium. A
Figure 19 Three-compartment cell for studies of the kinetics of the hydrogen evolution
reaction on Pt. The lines between the chambers prevent mixing but allow ionic conduction.
34
Chapter 2
nearly identical situation exists in chamber B; the only difference is that the
solution is at pH 2. Both chambers are deaerated (thus removing the reduction
of dissolved oxygen as a possibility). In chamber C, a Pt wire is immersed in a
pH 2 solution. The presence or absence of oxygen or hydrogen gas is immaterial
in chamber C, as will be discussed below. The WE wire in chamber B is connected to the positive terminal of a voltmeter, whereas the RE wire in chamber
A is connected to the negative terminal. The WE can also be connected (via a
switch) to a variable current source that is connected to the CE wire in chamber
C through an ammeter.
With the switch open, the potential measured by the high-impedence* voltmeter would be ⫺0.118 V. This value can be calculated from the Nernst equation.
The reversible potential of the Pt wire in chamber A would be zero relative to
NHE as it is itself an NHE, the reversible potential of the WE in chamber B
would be
EWE ⫽ ⫺0.059 pH ⫽ ⫺0.059(2) ⫽ ⫺0.118 V (NHE)
(10)
As long as the two electrodes are in equilibrium (i.e., no current is passing through
the interfaces), the reversible potentials will follow the Nernst equation.
The variable current source can be used to supply electrons to the WE at
a constant current of 100 µA/cm2. The source of these electrons is an oxidation
reaction occurring at the CE–solution interface. The most likely is water oxidation,
2H2O → O2 ⫹ 4H⫹ ⫹ 4e⫺
(11)
also known as oxygen evolution. According to the Nernst equation, the potential
of the CE must be at least 1.05 V(NHE)† for this reaction to occur. At the WE,
water reduction occurs, producing hydrogen gas at the prescribed rate (which is
about 1 nanomole of hydrogen per second ⫽ about 600 trillion hydrogen atoms
per second). To give this net rate of hydrogen production, the interfacial potential
of the WE must move in the negative direction. Assume that it does so by 100
mV, so that the potential of the WE becomes ⫺0.218 V(NHE). Increasing the
applied cathodic current by an order of magnitude 1 mA leads to another 100
mV movement in potential more negative, so that the WE potential becomes
⫺0.318 V(NHE). Continued measurements result in the plot of Fig. 20.
Figure 20a is a plot of the data on semilogarithmic axes; the potential is
on a linear scale, whereas the current is on a logarithmic scale. The data form a
straight line with a slope of b, referred to as the Tafel slope, in honor of Henrik
Tafel, who studied the HER in the early 1900s (20). The data shown have a Tafel
* If the voltmeter did not have a high impedance (resistance) between its terminals, current would
pass between the WE and RE, polarizing both and rendering the RE a useless standard for potential.
†
Er,02 ⫽ 1.23 ⫺ 0.059 pH ⫽ 1.05 V(NHE).
Electrochemical Thermodynamics and Corrosion
35
Figure 20 Schematic results from apparatus in Fig. 19: (a) cathodic polarization data
in terms of current, (b) normalized polarization data assuming an area of 10 cm2. Also
included is an extrapolation of the data to Er in order to determine io.
slope of 100 mV/decade, a value in the middle of the 30–200 mV/decade range
typical of such slopes. As was noted previously, current densities are generally
of more interest than currents, so the data in Fig. 20b represent an area correction
assuming an area of 10 cm2. Note that the Tafel slope is independent of the
electrode area.
36
Chapter 2
Included in Fig. 20b is an extrapolation of the data to lower applied current
densities back to the reversible potential for the WE (⫺0.118 V(NHE)). At the
reversible potential, no net reaction occurs; the system is in thermodynamic equilibrium. Nonetheless, this equilibrium is a dynamic one. Both hydrogen evolution
and hydrogen oxidation are occurring on the Pt surface, albeit at the same rate
so that no net production or consumption of hydrogen occurs. It is somewhat
analogous to the idle rate of an engine; there is no net movement, but the automobile is ready to go as soon as the gear is engaged. In the case of electrochemistry,
engaging the gear is achieved by applying a potential or current. The electrochemical analogue to the idle rate is referred to as the exchange current density, i0.
For the data in Fig. 20, the exchange current density for the hydrogen reaction
is 10⫺6 A/cm2. Current densities for electrochemical reactions usually range between 10⫺2 and 10⫺12 A/cm2.
The difference between the potential applied and the reversible potential
for a reaction is known as the overpotential. It represents the driving force for
the kinetics of the reaction. Anodic overpotentials are associated with oxidation
reactions, and cathodic overpotentials are associated with reduction reactions.
The relationship between the overpotential and the reaction rate defines the kinetics. Mathematical relationships exist for many instances, but in corrosion situations, the data are generally experimentally derived.
During this polarization of the WE, qualitatively similar effects have occured on the CE as shown in Fig. 21, which includes the data from Fig. 20a.
The current passing through the CE must be the same as that passing through
the WE in order to satisfy the conservation of charge. As mentioned above, oxidation of water occurs on the CE surface in order to change the electronic condition
to ionic conduction.* The Tafel slope for this reaction is shown as 50 mV/decade
for illustration purposes. Thus, for every 100 mV of polarization of the WE with
respect to the RE, the CE is polarized 50 mV in the opposite direction. Note that
the difference in potential between the WE and the CE is termed the cell voltage.
One rating for potentiostats is the maximum cell voltage (called the compliance
voltage) that can be applied and is usually in the range of 10 to 100 V.
Consider now the dissolution of iron by replacing the Pt WE with an Fe
wire and adding 1 M Fe2⫹ to the solution in chamber B (via dissolution of FeSO4,
for example), as shown in Fig. 22. Calculation of the reversible potential for iron
dissolution indicates that it would be the same as the standard reversible potential,
⫺0.44 V (NHE), as the ferrous ion is at unit activity. We will assume that only
iron oxidation/reduction can occur in this cell. Changing the polarity of the variable voltage supply allows removal of electrons from the WE, forcing net oxidation to occur there and net reduction to occur on the Pt CE in chamber C. Figure
* The description of an interface acting as a transducer from ionic to electronic conduction is due
to Eliezer Gileadi.
Electrochemical Thermodynamics and Corrosion
37
Figure 21 Polarization data for both the CE and the WE for the experiment discussed
in Fig. 19 and 20. In order to allow net reduction to occur on WE, net oxidation must
occur on the CE at the same rate (i.e., current).
23a shows illustrative data for the WE. A Tafel slope of 100 mV is calculated,
and an exchange current density for iron dissolution is found to be 10⫺7 A/cm2.
The anodic kinetics of the iron dissolution reaction are thus determined. Faraday’s
laws can be used to show that a dissolution rate of 100 µA/cm2 (⫽0.1 mA/cm2
⫽ 10⫺4 A/cm2) represents a penetration rate of 46 mpy.
In Fig. 23b, the cell voltage as a function of applied current density for
our illustrative example is shown. At zero applied current density, the cell voltage
38
Chapter 2
Figure 22 Three-compartment cell for studies of the kinetics of iron dissolution in acid.
is the difference between reversible potentials. During anodic polarization of the
WE, the cell voltage actually decreases. In other words, a controlled short-circuiting of the two electrodes occurs. At an applied current of 3 ⫻ 10⫺4 A/cm2 the
cell voltage is zero. The potential of both the WE and the CE is ⫺0.13 V(NHE).
As discussed below, this condition represents a galvanic coupling between the
Pt CE and the Fe WE. In order to polarize the WE above ⫺0.13 V(NHE), the
voltage supply must do electrical work, and the magnitude of the cell voltage
increases.
Throughout this discussion, the behavior of the RE has been ignored. One
might question how the RE maintains its standard value with applied voltages
and currents everywhere else. In a well-built instrumental arrangement, the impedance of the electrical connection to the RE (i.e., the input impedance of the
voltmeter) is so high that the current passing through the RE is truly negligible
(⬍⬍ 1 nA). Very high impedance voltage measuring devices used in commercial
potentiostats are known as electrometers, with input impedances of 1013 Ω or
more. Thus, with a voltage between the CE and the RE of the 100 V, the current
through the RE is 10 pA. Assuming a Tafel slope of 100 mV/decade and an
exchange current density of 10⫺11 A/cm2 (both worst-case conditions for a RE),
the RE would be polarized 10 mV, which would be a significant problem. In
Electrochemical Thermodynamics and Corrosion
39
Figure 23 Schematic results from apparatus in Fig. 22. (a) Anodic polarization data
normalized for the exposed area; (b) cell voltage (VCE-VWE) as a function of applied current
density.
40
Chapter 2
Figure 24 Schematic polarization data for oxygen reduction reaction (ORR) in neutral
(pH 7.2) solution. Diffusion-limited current density (iL) is present due to mass transport
limitations on dissolved oxygen.
practice, exchange current densities are closer to mA/cm2, so pA currents have
no effect on the RE potential. Nonetheless, keeping the possibility of such effects
in mind is important.
A final example of electrochemical kinetics will consider a return of the
Pt WE from before but now exposed to a neutral (pH 7.2) solution into which
oxygen is bubbled. The kinetics of the oxygen reduction reaction (ORR) will be
studied. The data generated might appear as shown in Fig. 24. The reversible
potential for the ORR in pH 7 solution, according to the Nernst equation, is
EORR,pH2 ⫽ 1.23 ⫺0.059pH ⫽ 1.23 ⫺ 0.059(7.2) ⫽ ⫹0.80 V(NHE).
(12)
As before, polarization in the cathodic direction yields a straight line on the semi-
Electrochemical Thermodynamics and Corrosion
41
logarithmic scales at low overpotentials (i.e., within 200 mV of the reversible
potential). At more negative potentials, a region of potential-independent kinetics
appears. As discussed in detail in Chapter 5, this behavior represents a diffusionlimited current density. The rate of oxygen reduction under these conditions is
controlled by the rate at which dissolved oxygen diffuses to the Pt surface, not
by the potential across the interface. Transport of oxygen and electrochemical
reduction occur in series, so the slowest step controls the rate. At low overpotentials, diffusion is rapid compared to the electrochemical reaction rate, so a potential dependence is observed.
Many corrosion systems are controlled by diffusion limitations on oxygen
because of its low solubility in aqueous solution (0.25 mM at room temperature).
The diffusion-limited current density, iL, can be described mathematically by
iL ⫽
Kcb
δ
(13)
where K ⫽ constant that includes the diffusion coefficient of oxygen, cb ⫽ bulk
concentration of oxygen, and δ ⫽ diffusion layer thickness.
The diffusion layer thickness is controlled by the hydrodynamics (fluid
flow). Although more details on mass transfer effects are discussed in Chapter
5, it is worthwhile to point out here that the diffusion-limited current density is
independent of the substrate material.
C. Polarization Curves
Metallic corrosion occurs because of the coupling of two different electrochemical reactions on the material surface. If, as assumed in the discussion of iron
dissolution kinetics above, only iron oxidation and reduction were possible, the
conservation of charge would require that in the absence of external polarization,
the iron be in thermodynamic equilibrium. Under those conditions, no net dissolution would occur. In real systems, that assumption is invalid, and metallic dissolution occurs with regularity, keeping corrosionists employed and off the street.
Return to the Fe dissolution experiment discussed above, altering the solution to contain 5 µM M Fe2⫹. In addition, allow hydrogen evolution to occur on
the iron surface with an exchange current density of 10⫺5 A/cm2, whereas the
exchange current density for the iron reaction is 10⫺6 A/cm2. Assume that both
reactions have Tafel slopes of 100 mV/decade. These conditions are illustrated
graphically in the Evans diagram, named in honor of its creator, U. R. Evans,
shown in Fig. 25. The lines represent the reaction kinetics of the two reactions
considered.
The corrosion rate of the iron can be directly predicted from the Evans
diagram by considering two facts:
42
Chapter 2
Figure 25 Evans diagram for Fe in acid showing use of conservation of charge to determine Ecorr and corrosion rate (icorr), given complete knowledge of the kinetic parameters
involved.
1.
2.
Measurement of a material immersed in solution gives a single potential value at any instant. Thus all reactions must be occurring at the
same potential.
The conservation of charge demands that under rest conditions (the
absence of any applied potential or current), all of the electrons produced in oxidation reactions must be consumed in reduction reactions.
The two facts imply that the rest, or corrosion, potential (Ecorr) of the system must
be ⫺0.25 V(NHE) as this is the only potential at which the rates of two reactions
are identical. The common rate of the two reactions, known as the corrosion rate,
icorr, is approximately 3 mA/cm2. Thus iron is dissolving at 3 mA/cm2 and hydro-
Electrochemical Thermodynamics and Corrosion
43
gen is being evolved on the iron surface at 3 mA/cm2. These data could be used
to predict the long-term performance of iron in this environment if they were
representative of the steady state conditions. This example is an illustration of
the application of mixed potential theory, the framework that underlies virtually
all electrochemical corrosion science.
Given sufficient quantitative information about the electrochemical processes occurring, mixed potential theory can be used to predict a corrosion rate.
Unfortunately, in the vast majority of cases, there are few data that can be applied
with any confidence. In general, experimental measurements must be made that
can be interpreted in terms of mixed potential theory. The most common of these
measurements in electrochemical corrosion engineering is the polarization curve.
The data discussed in Figs. 20 through 24 represent the type of data in a
polarization curve: combinations of potential and applied current density. Figure
26 shows a complete polarization curve for the iron in acid systems for which
the Evans diagram is shown in Fig. 25. The Evans lines are included as dotted
lines in the figure. The difference between the Evans diagram and the polarization
curve is that the polarization curve data display applied current densities, whereas
the Evans diagram displays the reaction rates in terms of current densities.
The applied current density is the difference between the total anodic and
the total cathodic current densities (reaction rates) at a given potential:
iapp ⫽ ia ⫺ | ic |
(14)
using the convention in which the cathodic current density is defined as negative.
At the corrosion potential (Ecorr), the anodic and cathodic rates are exactly equal;
thus the applied current density is zero. No external device is needed to supply
or remove electrons from the reactions; all of the electrons generated by oxidation
reactions (iron dissolution in the case under consideration) are consumed by reduction reactions (HER) on the same metal surface. Note that the corrosion rate
is not zero; it is simply not directly measurable because of the presence of the
HER on the same surface. The logarithm of zero is negative infinity. As this is
tough to plot on finite-sized paper, the applied current density forms a sharp point
as the electronics of the current converter output a large negative voltage to the
recording device.
Imposing an anodic current density on the iron with an external device
results in the generation of the anodic branch of the polarization curve. Increasing
the applied anodic current decreases the reduction reaction rate as the surface is
polarized in the positive direction. At small anodic current densities, the HER
current density is still an appreciable fraction of the anodic current density. Under
these conditions the applied current density is less than anodic current density.
For example, at a potential of ⫺0.225 V(NHE), ic is 2 ⫻ 10⫺3 A/cm2, iapp is 6
⫻ 10⫺3 A/cm2, and ia is 8 ⫻ 10⫺3 A/cm2. At sufficiently large anodic current
densities (e.g., 10⫺2 A/cm2 in Fig. 26), the cathodic reaction is insignificant rela-
44
Chapter 2
Figure 26 Polarization curve that would result for Evans diagram of Fig. 25. The Evans
lines are included as well.
tive to the anodic current density, so the applied current density is virtually equal
to the anodic current density. Measurements under these conditions allow the
Tafel slope to be determined. The development of the cathodic branch of the
polarization curve can be described in a qualitiatively similar manner.
The impossibility of a direct measurement of corrosion rate using electrochemical testing would seem to be discouraging. Application of mixed potential
theory allows determination of the corrosion rate using a method known as Tafel
extrapolation.
D.
Tafel Extrapolation
The Evans lines in Fig. 26 are key to the method of Tafel extrapolation. At
potentials well away from the corrosion potential, the applied current density
Electrochemical Thermodynamics and Corrosion
45
reflects the kinetics of only one of the reactions. Extrapolating the linear portions
of the polarization curve found at potentials well away from Ecorr leads to an
intersection at Ecorr. This intersection corresponds to icorr, the corrosion rate. Assuming uniform dissolution across the surface, Faraday’s laws can be used to
convert it to penetration rate for engineering design. Note that extrapolation to
the reversible potentials can, in theory, be used to determine the exchange current
densities for the two reactions.
1. Analysis Issues
The logarithmic nature of the current density axis amplifies errors in extrapolation. A poor selection of the slope to be used can change the corrosion current
density calculated by a factor of 5 to 10. Two rules of thumb should be applied
when using Tafel extrapolation. For an accurate extrapolation, at least one of the
branches of the polarization curve should exhibit Tafel (i.e., linear on semilogarithmic scale) over at least one decade of current density. In addition, the extrapolation should start at least 50 to 100 mV away from Ecorr. These two rules improve
the accuracy of manual extrapolations.
Commercial corrosion electrochemistry software applies nonlinear least
squares fitting to fit the entire polarization curve, which can improve accuracy.
Nonetheless users are wise to check periodically the software-generated corrosion
rates with manual fits. Not all computation algorithms are created equally robust
against noise and other realities of corrosion measurements. In addition, the use
of Tafel extrapolation invokes the implicit assumption that the dissolution is uniformly spread over the entire specimen surface. Figure 27 shows a polarization
curve for which it might be tempting to apply Tafel extrapolation, ignoring the
portion of the anodic region very close to Ecorr. In actuality this polarization curve
represents a system in which pitting is occurring at Ecorr. The area over which
the anodic current is distributed is much less than 5% of the total area. Using
Tafel extrapolation on these data would lead to highly erroneous conclusions.
More on the interpretation of polarization curves in passive systems undergoing
localized corrosion is presented in Chapter 3.
There are several factors that can lead to non-Tafel behavior. Diffusion
limitations on a reaction have already been introduced and can be seen in the
cathodic portion of Fig. 27. Ohmic losses in solution can lead to a curvature of
the Tafel region, leading to erroneously high estimations of corrosion rate if not
compensated for properly. The effects of the presence of a buffer in solution can
also lead to odd-looking polarization behavior that does not lend itself to direct
Tafel extrapolation.
2. Interpretation Issues
The generation and analysis of polarization curve data has become increasingly
straightforward with the increasing computerization of electrochemical instru-
46
Chapter 2
Figure 27 Example of real polarization data illustrating problems associated with analysis of limited or false Tafel regions.
mentation. Nonetheless the interpretation of the data can be a tremendous challenge. Rarely do polarization curves look as classic as those presented here. Thus
several cautions regarding interpretation should be added to those presented concerning data analysis.
The assumption of a steady-state system has been implicit throughout all
of the discussion of polarization curves. Note the difference between steady state
and equilibrium. No corroding system can be in equilibrium; if it were, it would
not be corroding. Corrosion is a nonequilibrium process that may occur at steady
state. Steady state corrosion occurs when the rate of corrosion does not change
with time. Knowledge that a given system is and will remain in steady state is
of great value. In many cases steady state is only approached and never achieved.
No universally agreed upon rule exists concerning a means to establish whether
an elecrochemical system has achieved a steady state. The most popular means
of monitoring the approach to steady state of a corrosion system is the measurement of the corrosion potential with time. Generally, the Ecorr changes most rapidly at the beginning of immersion. As the conditions at the metal/solution inter-
Electrochemical Thermodynamics and Corrosion
47
Figure 28 Polarization curves on Pt and Fe in alkaline sulfide solution at 65°C illustrating danger of interpreting all anodic current as due to metal dissolution. Above approximately ⫺0.7 V(SCE), the anodic current on both Pt and Fe is dominated by sulfide oxidation.
face approach steady state, the time-rate of change in Ecorr decreases. A reasonable
criterion for steady state would be a change of less than 5 mV in Ecorr over a 10
minute period.
An additional interpretation issue involves the presence of oxidation reactions that are not metal dissolution. Figure 28 shows polarization curves generated
for platinum and iron in an alkaline sulfide solution (21). The platinum data
show the electrochemistry of the solution species; sulfide is oxidized above ⫺0.8
V(SCE). Sulfide is also oxidized on the iron surface, its oxidation dominating the
anodic current density on iron above a potential of approximately ⫺0.7 V(SCE).
Without the data from the platinum polarization scan, the increase in current on
the iron could be mistakenly interpreted as increased iron dissolution. The more
complex the solution in which the corrosion occurs, the more likely that it contains one or more electroactive species. Polarization scans on platinum can be
invaluable in this regard.
Finally, even the most skilled interpretation of electrochemical data is akin
to the best photograph in that it contains only a portion of the information avail-
48
Chapter 2
able. Correlation of electrochemical measurements to as many varied measurements as possible is good practice. Whereas electrochemical measurements may
be the most rapid, they are also the most susceptible to variations in conditions.
Corrosion rate estimations based on Tafel extrapolation should be compared to
weight loss measurements whenever possible. Often decisions need to be made
regarding material selection in a narrow time window that precludes such information. In these cases, postselection weight loss measurements in the actual environment are invaluable checks on the applicability of the electrochemically derived corrosion rates.
E.
Polarization Curve Measurements for Galvanic
Corrosion Prediction
One example of the application of polarization curves in a predictive manner
involves their use in galvanic corrosion. Galvanic corrosion occurs when two
dissimilar metals are in electrical and ionic contact as is schematically shown in
Fig. 29. Galvanic corrosion is used to advantage in sacrificial anodes of zinc in
seawater and magnesium in home water heaters. It slows corrosion of millions
of tons of structural materials. The darker side of galvanic corrosion is that it
also causes major failures by the accelerated dissolution of materials that are
accidentally linked electrically to more noble materials.
Galvanic series are well known to many. These listings of corrosion potentials for materials (generally structural alloys) in a given environment are often
Figure 29 Schematic of galvanic corrosion arrangement.
Electrochemical Thermodynamics and Corrosion
49
used to avoid damaging combinations. One example is shown in Fig. 30 for
materials in seawater. Conventional corrosion engineering would suggest
avoiding combinations with widely different corrosion potentials, such as Ti and
Al alloys. If this combination of alloys were electrically in contact in seawater,
the galvanic series would predict that the corrosion rate of the Al alloy would
increase, whereas that of the Ti alloy would decrease. The galvanic series does
not allow even an estimation of the changes in the corrosion rates. The magnitude
of the potential differences does not always correlate with the changes in corrosion rate, nor can the effects of anode-to-cathode area ratio (a key parameter in
galvanic corrosion) be predicted accurately. There is no direct correlation between the value of the corrosion potential of different materials and their relative
corrosion rates, even when exposed to the same environment. Polarization curves
allow generation not only of the galvanic series in the environment of interest
but also information on the effects of area ratio on the changes in corrosion rate
of both materials.
Consider the two materials whose polarization curves are shown in Fig.
31. Both the polarization curves and the Evans lines are shown for both materials.
Material 1 is the more noble material (i.e., it has a more positive Ecorr) and has
a lower circuit corrosion rate when it is uncoupled. If the surface area of the two
materials is the same and the materials are coupled, then the two material–solution interfaces must come to the same potential. In a manner identical to that used
for the example of iron in acid used to introduce Evans diagrams, the potential and
current at which this condition is met can be found by applying the conservation
of charge to the sysytem:
∑ IA ⫽ ∑ IC
(15)
Note that it is the currents, not the current densities, that are involved in the
statement of charge conservation.
The intersection of the total anodic and total cathodic lines is at the (Ecouple,
icouple) pair. The Ecouple represents the potential measured (vs. a RE) for the case
of the two metals in electrical contact in the test environment. The potential of
the more noble material (Metal 1) has been moved from its own circuit Ecorr in
the negative direction, which would generally lead to a lower dissolution rate.
The potential of the more active material (Metal 2) has been moved from its
open circuit Ecorr in the positive direction, which would generally lead to a higher
dissolution rate.
The open circuit Ecorr values for each metal are the entries in the traditional
galvanic series. Kinetic information is also available via analysis of the polarization curves. The icouple can be used to calculate the increased corrosion rate of
Metal 2. Because of the coupling to Metal 1, the dissoultion rate has increased
from icorr,2 to icouple. The rate has increased because the cathodic kinetics on Metal
1 must now be satisfied. In addition to determining the increase in the corrosion
50
Chapter 2
Figure 30 Partial list of galvanic series in seawater. (From H.P. Hack, Metals Handbook, Vol. 13, Corrosion, 9th ed., ASM, Metals Park, OH, p. 234, 1987.)
Electrochemical Thermodynamics and Corrosion
51
Figure 31 Polarization curves of Metals 1 and 2 that are to be analyzed for their behavior in a galvanic couple.
rate of Metal 2, the decrease in the corrosion rate of Metal 1 can also be estimated
by extrapolating the Metal 1 anodic line to Ecouple. Recall that the Evans lines
describe the reaction rate as a function of the interfacial potential independent
of the means by which that potential is achieved. Thus the application of a sacrificial anode (Metal 2) serves to reduce the corrosion rate of Metal 1. The predictive ability of corrosion electrochemistry can be used to investigate the effect
of changing the relative areas of Metal 1 and Metal 2, i.e., changing the cathodeto-anode area ratio. In Fig. 32 the polarization data are reconfigured with the
assumption of two different area ratios: in part (a) the anode area is 10 cm2 and
the cathode area 1 cm2, whereas in part (b) the cathode area is considered to be
10 cm2 and the anode area 1 cm2. Note that no additional experiments are needed
to perform this analysis, as all the unit-area data are applicable.
Experience shows that increasing the cathode-to-anode area ratio increases
the rate of consumption of the anode and decreases the corrosion rate of the
cathode, but the galvanic series alone would not allow a quantitative analysis of
these effects. Inspection of Fig. 32 reveals that the abscissa has been changed to
current from current density. When dealing with unequal areas, such a transfor-
52
Chapter 2
Figure 32 Shift in polarization curves on a current basis for cases in which (a) the
anode area is considered to be 10 cm2 and the cathode area 1 cm2, (b) the cathode area
is considered to be 10 cm2 and the anode area 1 cm2.
Electrochemical Thermodynamics and Corrosion
53
mation is needed, as it is currents that must be balanced rather than current densities. In the case of Fig. 32a, the increase in the area of the anode leads to a
decrease in Ecouple relative to the equal area case. Two other effects can also be
noted. The corrosion rate of the cathodes (Metal 1) has decreased (the interfacial
potential is more negative, reducing the driving force for oxidation). In addition,
the dissolution rate of the anode (Metal 2) has also decreased. The anodic current
is higher, but the area-averaged dissolution rate is lower once the increased area
is taken into account (by moving from the Ecouple, Icouple point to the point on the
Metal 2 unit area line at Ecouple).
This paradox of lowering both corrosion rates can be understood by considering the accounting of the electrons. By simply increasing the anode area, the
number of electrons per second (i.e., the anodic current) that is produced is increased at all potentials more positive than the open circuit Ecorr of Metal 2. To
accommodate this increased production, the cathodic reaction on Metal 1 must
increase the rate at which it consumes electrons (i.e., the cathodic current). Increased cathodic current can only be achieved by moving the system to more
negative potentials. The more negative the potential, the lower the dissolution
rate of both materials.
The converse situation regarding area ratio is shown in Fig. 32b, in which
the area of the cathode has increased by a factor of 10 relative to the anode. The
effect on Ecouple and the corrosion rate of both materials is opposite that of increasing the area of the anode, although the Icouple has increased in both cases, (a and
b). From Fig. 32b the widsom of avoiding large cathode-to-anode area ratios is
clear. Not only is the corrosion rate of the material to be protected higher the
higher the ratio but also the dissolution rate of the anode material is higher. Because of the impossibility of producing and/or maintaining pinhole-free coatings,
noble metal coatings are generally avoided. The gold-plated electrical connectors
used in the electronics industry are an exception. The gold plating is deposited
onto copper layers that are connected into circuit boards. Problems have indeed
developed in some atmospheric environments in which thin moisture layers lead
to galvanic corrosion of the copper and resulting loss of electrical continuity
between the connector and the electrical device.
REFERENCES
1. P. J. Moran, E. Gileadi. J. Chem. Educ. 66, 912 (1989).
2. D. J. G. Ives, J. G. Janz, eds. Reference Electrodes: Theory and Practice. Academic
Press, New York (1961).
3. Z. Szklarska-Smialowska. Pitting Corrosion of Metals. NACE International, Houston, 203 (1986).
4. A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications. John Wiley, New York, 50 (1980).
54
Chapter 2
5. P. W. Atkins, Physical Chemistry, 2nd ed., W. H. Freeman and Co., San Francisco,
1982, p. 355.
6. E. Gileadi. Electrode Kinetics for Chemists, Chemical Engineers, and Materials Scientists. VCH, New York, 19 (1993).
7. M. Pourbaix. Atlas of Electrochemical Equilibria in Aqueous Solutions. NACE International, Houston (1974).
8. J. B. Lee. Corrosion, 37, 467 (1981).
9. J. T. Atkinson. In: Equilibrium Diagrams. Proc. Int. Symp. Electrochem. Soc. (R. P.
Frankenthal, J. Kruger, eds.) Electrochemical Society, Pennington, NJ, 175 (1984).
10. L. B. Kriksunov, D. D. Macdonald. Corrosion 53, 605 (1997).
11. A. Garner, Corrosion 41, 587 (1985).
12. S. J. Mulford, D. Tromans. Corrosion 44, 891 (1988).
13. D. B. Wells, J. Stewart, R. Davidson. Corrosion Sci. 33, 39 (1992).
14. P. Marcus, E. Protopopoff. J. Electrochem. Soc. 144, 1586 (1997).
15. P. Marcus, E. Protopopoff. J. Electrochem. Soc. 140, 1571 (1993).
16. E. D. Verink, Jr. In: Electrochemical Techniques for Corrosion Engineering (R.
Baboian, ed.). NACE International, Houston, 101 (1986).
17. D. Silverman. Corrosion 38, 541 (1982).
18. D. C. Silverman. In: Electrochemical Techniques for Corrosion Engineering (R.
Baboian, ed.). NACE International, Houston, 117 (1986).
19. E. Gileadi, E. Kirowa-Eisner, J. Penciner. Interfacial Electrochemistry: An Experimental Approach. Addison-Wesley, Reading, MA, 151 (1975).
20. H. Tafel. Z. Physik. Chem. 50, 641 (1905).
21. S. Kannan, R. G. Kelly. Corrosion Sci. 38, 1051 (1996).
22. G. Walter, personal communication (1999).
3
Passivity and Localized Corrosion
The objectives of this chapter are to provide a basic explanation of the chemical
and physical processes involved in localized corrosion and to explain the test
techniques that are commonly used to determine the resistance of alloys to localized corrosion.
I.
INTRODUCTION
While localized corrosion occurs in many forms, the results are the same: the
accelerated loss of material at discrete sites on a material’s surface. The amount
of metal lost would usually be considered insignificant if uniformly distributed
across the entire surface. However, since current density is important in assessing
penetration rates, the same amount of material lost, when confined to a discrete
site, can result in perforation or other failure. More than one-third of the corrosion
failures in a major chemical plant were due to localized corrosion (including
stress-corrosion cracking) (1). One can usually design around uniform corrosion,
by the choice of alloy, by the application of a corrosion control program, or by
the inclusion of a corrosion allowance. Localized corrosion often appears to have
a stochastic (or purely random) nature. Thus it is very difficult to design a structure with a corrosion allowance for localized corrosion. Another difficulty with
localized corrosion is that associated with its detection and monitoring under
service conditions. Since the vast majority of the surface is unaffected, thickness
monitoring is generally unhelpful. In addition, many forms of localized corrosion
occur in areas that are difficult to access such as at flanges and under deposits.
Another important aspect of localized corrosion is the fact that it most often
occurs in highly alloyed materials that were chosen specifically for their corrosion
resistance.
The same aspects of localized corrosion that make it such an engineering
nuisance also make it difficult to study. Since it has a stochastic nature, Murphy’s
law applies, and the sample never seems to pit at the time or in the place that
55
56
Chapter 3
suits the experimenter and his or her apparatus. The existence of an incubation
time, during which no measurable attack occurs, can also make such studies very
time-consuming. The sensitivity of the phenomenon to seemingly small changes
in environmental, metallurgical, and experimental conditions adds to the confusion.
The phenomenology of localized corrosion helps to define certain requirements for localized corrosion that can be expressed in terms of the concepts
already discussed in Chapter 2. In order for localized corrosion to occur, there
must be a spatial variation in the electrochemical or metallurgical conditions.
The occurrence of discrete sites of attack demonstrates that passivity must be
able to coexist on the same surface with active regions. In fact, this is one of the
scientifically interesting aspects of localized corrosion. Under “normal” circumstances, one would expect that a surface would either be completely passive or
completely active, not a mixture of the two. Finally, there is a physical separation
of the anodic and cathodic reaction sites during localized corrosion. In order to
understand localized corrosion and thus how to test for resistance to localized
corrosion, we must understand each of these aspects and their interrelations.
A.
Chapter Overview
The goal of this chapter is to provide a basic understanding of the processes
involved in localized corrosion in terms of what has been covered in Chapters
1 and 2. In addition, the different test techniques that are used to determine the
resistance of alloys to pitting and crevice corrosion will be reviewed and discussed.
The first section briefly introduces the concepts behind passivity. The ability of the material to passivate in an environment is a necessary condition for
localized corrosion. While volumes have been written on the subject (2,3), this
section provides the basic framework for understanding how passivity develops
and how it can be characterized electrochemically. The next section discusses the
breakdown of passivity that leads to localized corrosion. A basic understanding of
the underlying causes of localized corrosion aids in understanding currently used
tests as well as in the design of new tests. More details of the phenomenology
of the different types of localized corrosion are presented, including the electrochemical manifestations of this phenomenology. The final section discusses the
various test techniques that can be used both to characterize the resistance of
material to localized corrosion and to understand the factors that control it. A
description of the manner in which each test is performed is followed by a discussion of why each works as well as its advantages, disadvantages, and limitations.
From this discussion, the parameters of the test that can be modified by a user
to make it more applicable to an individual case of interest will become clear.
Owing to space constraints, stress-corrosion cracking (SCC) will not be
Passivity and Localized Corrosion
57
treated as a specific subject in this chapter. However, information that impacts
SCC will be highlighted. While we will concentrate on pitting and crevice corrosion, the basic phenomenology presented is applicable to other forms of localized
corrosion including integranular attack, weld- or heat-affected zone attack, and
exfoliation. While each of these has particular details that are unique (e.g., exfoliation occurs in wrought, precipitation-hardened aluminum alloys), much of the
basic approach to understanding the process is the same. The main differences
are the origin of the heterogeneity that leads to the localized attack and the details
of the electrochemistry. Since the focus of this chapter is to introduce electrochemical techniques rather than a study of corrosion, we will concentrate on
pitting and crevice corrosion as generic examples.
II. PASSIVITY
Passivity is the origin of the utility of all corrosion resistant alloys (CRAs). While
passivity can be defined in a number of ways, two have become generally accepted:
1. A metal is passive if it substantially resists corrosion in an environment
where there is a large thermodynamic driving force for its oxidation
(also known as thick film passivity). The Evans diagram for this type
of behavior is shown in Fig. 1.
Figure 1 Schematic Evans diagram for a material that exhibits thick film passivity.
58
Chapter 3
2.
A metal is passive if, on increasing its potential to more positive values,
the rate of dissolution decreases, exhibiting low rates at high potentials
(also known as thin film passivity). The anodic Evans diagram for this
type of behavior is shown in Fig. 2.
Examples of material–solution combinations that fall within the first definition are Pb in H 2 SO 4 and Mg or Al in water. These materials can be considered
to have very high (near infinite) anodic Tafel slopes in these solutions. Thus large
increases in potential do not cause significant increases in dissolution rate. On
the other hand, metal–solution combinations such as nickel, molybdenum, or
chromium in sulfuric acid would be classified as passive according to the second
criterion. For these materials, the Tafel slope can be thought of as having a strong
potential dependence. At potentials in the vicinity of the reversible (equilibrium)
potential, the Tafel slope is similar to that of the materials discussed in Chapter
2, with values on the order of 40 to 100 mV/decade. The Tafel slope increases
Figure 2 Typical anodic dissolution behavior of an active–passive metal. E PP ⫽ primary
passivation potential, i crit ⫽ critical anodic current density, and i pass ⫽ passive current density. (After Ref. 71.)
Passivity and Localized Corrosion
59
Figure 3 Faraday’s experiments on the passivity of Fe. In dilute nitric acid, Fe corrodes
at a high rate. In concentrated nitric acid, the reaction rate slows to almost zero. Upon a
return to dilute acid, the reaction rate remains low, i.e., it is passive, until the surface is
disturbed, at which point it begins to corrode at a high rate again. (After Ref. 21.)
dramatically near E pp , approaching infinity after a short range of potential in
which it is actually negative.
Kier first observed the passivity of Fe in 1790. A set of experiments by
Michael Faraday have become a standard method for demonstrating the phenomena involved. In this experiment, shown in Fig. 3, a piece of Fe is placed in dilute
(⬃30%) nitric acid. It dissolves at a high rate, with simultaneous generation of
NO 2 by the reduction of nitrate. Placing the same specimen in more concentrated
(70%) HNO 3 results in only a momentary reaction followed by no observable
reaction. Upon moving the sample back into the dilute acid, no increase in rate
occurs until the sample is scratched. Beginning at the point of the scratch and
quickly engulfing the entire surface, the dissolution increases to a high rate again.
One would normally expect that placing the sample into the concentrated
acid would cause the reaction to occur even faster than in the dilute acid, based
upon Le Chaˆtlier’s principle. In addition, one would not expect that exposure to
the concentrated acid would alter the behavior of the Fe in the dilute acid, but
it does. This alteration was called “passivity” by Scho¨enbien in 1836. The electrochemical explanation of the Faraday experiment is discussed below. While a large
body of literature exists concerning the underlying mechanisms, for our purposes
only a brief review of the fundamental origins will be required.
A. Origins of Passivity
Thick film passivity (i.e., protection of a metal surface by a film of visible thickness) can be due either to oxide formation or salt film precipitation. Salt film
60
Chapter 3
precipitation can in some cases be either a precursor for a thin passive film (4)
or provide adequate protection alone. For example, Mg passivates in fluoridecontaining solutions by the precipitation of MgF 2 , which forms an effective barrier coating. Precipitation of FeSO 4 as a precursor to Fe 2 O 3 has been observed
for Fe in acid (4). In addition, Beck showed that Ti initially passivates via precipitation of TiCl 3 in HCl (5), while Carraza and Galvele have (6) postulated a similar
mechanism for Type 304 SS in acidic chloride solutions. Mayne and Menter (7)
showed that the passive film on Fe in 0.1 N Na 2 HPO 4 consists of ferric oxide
with particles of FePO 4 embedded within it, showing that in some cases, mixed
thick film and thin film passivity can occur.
While thick film passivity has been documented and understood for many
years, the difficulties in studying thin film passivity were daunting. It took many
years to determine that indeed a film was responsible for the effect, as these films
are so thin that they are invisible to the eye (i.e., transparent to radiation in the
visible region). Two main types of theories were developed in order to explain
the phenomena observed: theories based upon the idea of adsorption reducing
the corrosion rate, and theories based upon the formation of a new phase, an
oxide of the base metal, on the surface. In all cases, an increased barrier to dissolution results upon the increase in potential. This increased kinetic barrier upon
anodic polarization contrasts with the exponentially decreased barrier which develops during anodic polarization of an active material.
B.
Electrochemical Phenomenology
Independent of the mechanism of passivity, its electrochemical manifestations
can be best understood on the basis of mixed potential theory presented in Chapter
2. A schematic Evans diagram for a passivating metal is shown in Fig. 4. If there
are no strong oxidizing agents in the solution, the corrosion potential is E corr , and
the metal corrodes uniformly in a film-free condition. As the potential is raised
in this active region (either by the application of an external current or by the
introduction of oxidizing species into the environment), the dissolution rate of
the metal increases until a potential of E pp is reached. Above this passivation
potential, a dramatic decrease in the dissolution rate occurs. Further increases in
potential usually have little effect on the passive current density, i pass . In some
cases, the difference between the critical anodic current density for passivation,
i crit , and i pass can be over four orders of magnitude. As shown in Chapter 1, these
current densities are directly related to the dissolution rate of the material. In
solutions without aggressive species such as Cl ⫺, further increases in potential
will eventually lead to an increase in the current due to a combination of oxygen
evolution and transpassive dissolution of the passivating film for most metals.
For the valve metals (e.g., aluminum, tantalum, lead, titanium), certain solutions
Passivity and Localized Corrosion
61
Figure 4 Schematic Evans diagram for a material that undergoes an active–passive
transition. Important parameters that characterize this behavior are indicated.
will allow a thick, insulating oxide film to grow on which oxygen evolution does
not occur. Under these conditions, anodization occurs. The electrochemical parameters that characterize passivity (E pp , E t , i crit , and i pass) depend upon both the
metal and the environment to which it is exposed.
In order to determine the corrosion state of an active–passive system, the
position of the corrosion potential relative to E pp must be determined. According
to Fig. 4, if E corr is below E pp , the material will undergo uniform dissolution under
film-free conditions. If E corr is above E pp but below E t , the material will be passive
and will dissolve at its passive current density, which is often on the order of
0.01 mpy. Corrosion-resistant alloys are designed to operate under such conditions. For situations in which E corr is above E t , the material will dissolve transpassively, i.e., uniformly.
As discussed in detail in Chapter 2, the corrosion potential is determined
by the intersection of the sum of the anodic Evans lines and the sum of the
cathodic Evans lines. For active–passive materials, the only new wrinkle is the
increased complexity of the anodic line. Since the anodic line is not single-valued
with respect to current density, three distinct cases can be considered. In all cases,
the condition ∑ I a ⫽ ∑ I c determines the position of the corrosion potential, and
the condition i app ⫽ i a ⫺ i c determines the appearance of the polarization curve
62
Chapter 3
for each case. Thus the nature and kinetics of the cathodic reaction(s) are critical
in determining the corrosion state and rate of dissolution of an active–passive
material.
Under reducing conditions (e.g., in acids such as HCl), the predominant
cathodic reaction is hydrogen evolution as shown in Fig. 5. This combination
results in a polarization curve in which all of the parameters characterizing passivity can be measured as shown in Fig. 5. If a material were to be used under these
conditions, nothing would be gained from its ability to passivate.
In the presence of oxidizing species (such as dissolved oxygen), some metals and alloys spontaneously passivate and thus exhibit no active region in the
polarization curve, as shown in Fig. 6. The oxidizer adds an additional cathodic
reaction to the Evans diagram and causes the intersection of the total anodic and
total cathodic lines to occur in the passive region (i.e., E corr is above E pp ). The
polarization curve shows none of the characteristics of an active–passive transition. The open circuit dissolution rate under these conditions is the passive current
density, which is often on the order of 0.1 µA/cm 2 or less. The increased costs
involved in using CRAs can be justified by their low dissolution rate under such
oxidizing conditions. A comparison of dissolution rates for a material with the
same anodic Tafel slope, E o , and i o demonstrates a reduction in corrosion rate
Figure 5 Schematic Evans diagram and resulting potential-controlled polarization curve
for a material that undergoes an active–passive transition and is in a reducing solution.
The heavy line represents the applied currents required to polarize the sample.
Passivity and Localized Corrosion
63
Figure 6 Schematic Evans diagram and resulting potential-controlled polarization curve
for a material that undergoes an active–passive transition and is in an oxidizing solution.
The heavy line represents the applied currents required to polarize the sample. If the sample did not undergo an active–passive transition, it would corrode at a much higher rate
in this solution, as is indicated by the intersection of the dotted line and the cathodic curve.
by many orders of magnitude.
Examples of materials whose “active nose” is hidden are stainless steel in
dilute aerated acid and carbon steel in alkaline solution containing strong oxidizers. In the case of materials that are passive only in the presence of oxidizers
stronger than water, removal of those oxidizers (e.g., by deaeration in the case
of oxygen) reveals the presence of the active–passive transition as shown in Fig.
7. Note the lower E corr after deaeration. Oxidizers are not always good; if the
oxidizing power of the solution raises the potential too much, transpassive dissolution or pitting (if an aggressive species is present) can occur.
For the case shown in Fig. 8, the anodic and cathodic Evans lines intersect
at three points. The polarization curve for this situation appears unusual, although
it is fairly commonly observed with CRAs. At low potentials, the curve is identical to that shown in Fig. 5. However, just above the active–passive transition,
another E corr appears followed by a “loop” and yet a third E corr before the passive
region is observed. The direction (anodic or cathodic) of the applied current density for each region shown in the polarization curve of Fig. 8 is indicated, showing
that the loop consists of cathodic current. The origin of the cathodic loop is the
64
Chapter 3
Figure 7 Polarization curves for carbon steel in pH 11.5 solution at 65°C containing
10 g/L Na 2 S, 1 g/L catechol under (a) deaerated and (b) aerated conditions. Upon aeration,
quinones are formed, which act as strong oxidizing agents. Note the higher E corr of the
steel under aerated conditions. (Data courtesy of S. Kannan, University of Virginia.)
fact that at these potentials, the rate of the cathodic reaction is greater than the
passive current density. Thus the net current is cathodic over that range of potential. An example of this behavior is seen in Fig. 9 (8). Generally, either the uppermost or lowermost E corr is the most stable, and the material exhibits that corrosion
potential spontaneously.
Such cathodic loop behavior is often observed on the reverse scans of polarization curves in which pitting does not occur as shown in Fig. 10 (9). During
the initial anodic scan, the oxide is thickening and the anodic line is moving to
the left. Thus, upon the return scan, the unchanged cathodic line now intersects
the anodic line at several places, leading to the appearance of cathodic loops.
Cathodic loops do not pose fundamental problems; they merely conceal the passive current density at potentials near the active–passive transition.
The cathodic reaction kinetics thus play an important role in determining
the corrosion state for an active–passive material. The introduction of additional
cathodic reactions to an environment or the change in the kinetics of one already
present can dramatically affect the state of the material’s surface. Figure 11 shows
Passivity and Localized Corrosion
65
Figure 8 Schematic Evans diagram and potential-controlled polarization curve for a
material/environment combination that exhibits a cathodic loop. Note that the direction
of the applied current changes three times in traversing the curve.
schematically the effects of changes in the kinetics of a single cathodic reaction
(modeled as changes in the exchange current density). From the different corrosion potentials established, one can see the key role of cathodic reaction kinetics
in establishing the corrosion state of active–passive metals.
Based upon the above descriptions, the Faraday experiment can now be
explained. Figure 5 shows the polarization curve and Evans diagram for a passivating metal in a reducing acid such as dilute H 2 SO 4 . Figure 12 shows the Evans
diagram for this case. The anodic curve in the Evans diagram is independent of
the acid (to a first approximation). In the dilute acid, the rate of reduction of
nitric acid is not higher than i crit , so the sample does not passivate, but the presence
of the nitric acid reduction as an additional cathodic reaction raises the potential
above what it would be if hydrogen evolution were dominant. With the concentrated nitric acid, not only is the E r raised, but also the i dl increases owing to the
higher concentration, so i crit and E pp are exceeded, and the sample passivates.
Upon returning the passivated sample to the dilute acid, the nitric acid reduction
is able to maintain the passivity because only a small current is necessary. However, when bare surface is exposed, the passivation process must start again, and
soon the passive film is undermined, as the entire surface subsequently dissolves
at the high rate, since the low nitric acid concentration is insufficient to raise the
E corr above E pp .
66
Chapter 3
Figure 9 Polarization curve of carbon steel in deaerated, pH 13.5 solution at 65°C.
Sample was initially held potentiostatically at ⫺1.2 V(SCE) for 30 min before initiation
of the potentiodynamic scan in the anodic direction at 0.5 m V/s. The cathodic loop results
from the fact that the passive current density is only 1 µA/cm 2, which is less than the
diffusion-limited current density for oxygen reduction for the 0.5 ppm of dissolved oxygen
present. (From Ref. 8.)
The i dl of the cathodic reaction can be of critical importance in the passivation of a material. The effects of increasing i dl by increasing solution velocity
are shown in Fig. 13a for both passivating and nonpassivating metals. The Evans
diagram in Fig. 13b shows that for both types of materials, the corrosion potential
and corrosion rate initially increase with increasing velocity. However, for the
passivating metal, a critical velocity is reached at which the i crit is exceeded and
the sample passivates (i.e., the dissolution rate decreases dramatically). Higher
velocities have no effect on the corrosion rate. For the nonpassivating metal, the
increased cathodic reaction rate increases the corrosion rate until the sample is
under complete activation control. It should be stressed that these velocities are
at much lower values than those under which erosion corrosion occurs.
1. Galvanic Couples
The presence of galvanic couples can affect passivity in three ways (two of which
are bad), as demonstrated in Fig. 14: (1) increasing the potential of the active–
Passivity and Localized Corrosion
67
Figure 10 Polarization curve for Type 302 stainless steel in 0.5% HCl. Note the presence of a cathodic loop on the return scan due to the greatly reduced passive current
density. Also, note the lowered critical current density on the reverse scan due to incomplete activation of the surface. (From Ref. 9.)
passive material so that passivity can occur for conditions under which it otherwise would not, (2) increasing the potential of the active–passive material to the
point that localized corrosion can occur, and (3) decreasing the potential of the
previously spontaneously passive material so that passivity cannot be maintained
and active dissolution occurs on the (previously) passive metal. In case 1 the
cathodic material must be able to deliver a cathodic current density higher than
the i crit of the active–passive material. Case 2 is similar to the case discussed
above in which the cathodic reaction raises the corrosion potential above E t ,
leading to transpassive corrosion. If an aggressive species such as chloride ion
is present, the dissolution can become nonuniform. This phenomenon will be
discussed in greater detail in the section on localized corrosion. Though rare,
case 3 is an example of a sacrificial anode that is causing, rather than solving,
problems. While the idea of cathodic protection by galvanic coupling might be
appealing, in the schematic shown this would lead to rapid uniform dissolution
of the cathode (active–passive) material. Thus galvanic couples involving active–
passive materials must be considered carefully.
68
Chapter 3
Figure 11 Schematic Evans diagram illustrating the effect of a change in the cathodic
reaction kinetics on the corrosion conditions. Case 1 would be representative of Fig. 5.
Case 3 would lead to the polarization behavior described in Fig. 6. Case 2 would lead to
the polarization behavior shown in Fig. 8. (After Ref. 71.)
Figure 12 Schematic Evans diagrams for the three conditions of the Faraday experiment.
Passivity and Localized Corrosion
69
(a)
(b)
Figure 13 (a) Effect of fluid velocity on the electrochemical behavior of both active–
passive and nonactive–passive materials. (b) Effect of fluid velocity on corrosion rate of
these materials. (After Ref. 71.)
2. Anodic Protection
Corrosion control using external polarization usually operates by reducing the
driving force for the metal dissolution reaction, as in cathodic protection. For
passivating metals, an alternative is to reduce the kinetics of the dissolution process by raising the potential. This is known as anodic protection and has been
70
Chapter 3
Figure 14 Evans diagrams for active–passive metal when coupled to (a) a metal that
holds E corr in a passive region, (b) a metal that holds E corr above pitting or transpassive
potential, and (c) a metal that causes a passive–active transition.
applied with success in the pulp and paper industry, particularly for the mitigation
of stress-corrosion cracking. The operating principles are shown in Figs. 15 and
16. Recall that i app ⫽ i a ⫺ i c . Therefore at E corr , i app ⫽ 0, by definition. In order
to polarize the surface to E i , i appi must be applied:
E c requires i app,c ⫽ 10,000 µA/cm 2 (cathodic)
E 3 requires i app3 ⫽ 0.9 µA/cm 2 (anodic)
E 4 requires i app4 ⫽ 1.0 µA/cm 2 (anodic)
At E 4 , the sample is dissolving at 1 µA/cm 2. In order to protect cathodically
the structure to the same dissolution rate, the potential must be E c . To polarize
the surface to Ec would require 10,000 µA/cm 2, a value five orders of magnitude
Passivity and Localized Corrosion
71
Figure 15 Applied current densities required for different applied potentials for an active–passive material in acid. If there is a dissolution rate of 1 µA/cm 2, cathodic protection
to E c would require an applied current density of 10,000 µA/cm 2, while anodic protection
to E 4 would require only 1 µA/cm 2. (After Ref. 21.)
Figure 16 Schematic diagram showing protection range and optimum potential for anodically protecting an active–passive metal. (After Ref. 21.)
72
Chapter 3
higher than that required for anodic protection. Since current costs money, there
are cases when it is cheaper to use anodic protection.
One must be wary of the use of anodic protection, in that any area that is
not polarized completely into the passive region will dissolve at a high rate. The
optimum protection range is shown in Fig. 16. Therefore anodic protection is
more susceptible to the presence of crevices, deposits, or poor placement of polarizing electrodes than is cathodic protection. If a component is cathodically under
protected, the maximum rate at which the unprotected area corrodes is the “normal” open circuit corrosion rate; in anodic protection, underprotection results in
high rate dissolution of the unprotected area and can therefore can lead to unexpected career changes. Understanding the manner in which current from an anodic protection system is distributed across a surface is important in such installations. The issues involved in current distribution are discussed in detail in Chapter
4.
Figure 17 Fracture mechanics data plotted as log apparent crack velocity vs. stress
intensity. Each point represents the exposure of a single specimen. The specimens were
immersed in a simulated impregnation zone liquor at 115°C for 151 days. No crack propagation was observed at anodic protection potentials (⫺730 mV SCE ). (From Ref. 10.)
Passivity and Localized Corrosion
73
Singbeil and Garner (10) showed that the use of anodic protection can
prevent stress-corrosion cracking in the pressure vessel steels exposed to alkaline
solutions used in digesters in the pulp and paper industry, as shown in Fig. 17.
The 200 mV anodic polarization placed the material above the active–passive
transition where cracking had been shown to occur (10).
III. LOCALIZED CORROSION
Localized corrosion is the direct result of the breakdown of passivity at discrete
sites on the material surface. As was stated above, once passivity is established on
a surface, one might expect either that it would remain passive or that a complete
activation of the surface would occur. However, what is often observed in practice
is the appearance of discrete areas of attack that begin to corrode actively while
the vast majority of the surface remains passive. These isolated regions of attack
are more than mere annoyances; the local penetration rates can be on the order
of 10 mpy or higher, leading to rapid perforation of any reasonably sized container. Since the original intent in using passive materials (e.g., CRAs) in any
application is to exploit their low dissolution rates, localized corrosion can be a
major operational problem.
This section provides a basic explanation of the underlying physical processes that control localized corrosion in order to lay the foundation for an understanding of the tests that are discussed in the next section. The manifestations
of these physical processes through electrochemically measurable quantities are
then discussed. Some generalized phenomenology is presented through illustrative examples from the literature. Full mechanistic understanding of localized
corrosion has not yet been achieved. Information on the various models proposed
can be found in review articles (11,12) and corrosion texts (13,14).
While there are a variety of types of localized corrosion phenomena (e.g.,
crevice corrosion, pitting, intergranular attack, stress-corrosion cracking, filiform
corrosion), they share a number of common features. Foremost among these is
the development of an extremely aggressive solution locally which causes highrate localized attack. It is becoming increasingly clear that much can be understood about the different types of localized corrosion by considering them as
manifestations of the same set of basic phenomena (15–17). For example, pitting
can be viewed as crevice corrosion on a smaller scale, with either micropores or
surface heterogeneities acting to form the crevice.
A. Important Physical Processes
The important physical processes that control localized corrosion do so through
their impact on three key aspects: (1) the development of a local solution chemis-
74
Chapter 3
try that is sufficiently aggressive to destroy passivity, (2) the physical separation
and ionic/electrical communication of anodic and cathodic sites, and (3) the stability of the high-rate dissolution. For localized corrosion to occur, the local conditions
must become substantially more aggressive than those across the majority of the
surface. While some controversy remains, it is generally accepted that during the
growth of a localized corrosion site, a highly aggressive solution develops in which
the material undergoes active dissolution. Mears and Evans (18) originally proposed the development of what has become known as the critical crevice solution
(CCS) (19–22). Oldfield and Sutton (19,20) were the first to construct a mathematical model based upon the CCS concept formulated by Fontana and Greene (21),
and it is in this context that the important physical processes will be discussed.
While the Fontana and Greene model was developed specifically for crevice
corrosion of stainless steel in neutral halide solutions, it has been traditionally
accepted as qualitatively describing the phenomena that occur during the initiation and propagation in most alloys, with minor modifications. The model identifies four stages in the crevice corrosion of stainless steel in neutral Cl ⫺ solution
as shown in Fig. 18. In the first stage, the model predicts that the alloy will
dissolve stoichiometrically, with Fe, Ni, and Cr entering the solution in proportion
to their presence in the alloy. This dissolution occurs over the entire surface and
constitutes the passive current. The cathodic reaction (oxygen reduction) also
occurs both inside and outside the crevice. However, owing to the restricted diffusion to the occluded site, oxygen becomes depleted inside the crevice, and the
physical separation of anode and cathode develops that is necessary for localized
corrosion to occur. This marks the beginning of stage II. As the passive dissolution of the alloy continues, the accumulation of cations inside the crevice (due
to the production of Fe 2⫹, Cr 3⫹, Ni 2⫹ by dissolution and the mass transport restrictions inherent in the geometry) is balanced by the electromigration of Cl ⫺ into
the crevice from the bulk solution. Chloride dominates the anion migration into
the crevice owing to its high mobility and concentration compared to other
anions. The Cl ⫺ forms complexes with the metal ions, which are then quickly
hydrolyzed. This hydrolysis lowers the pH of the crevice through the production
of hydrogen ion. As the pH drops, the passive current in the crevice increases,
which acts to increase the amount of Cl ⫺ migration, which increases the amount
of hydrolysis, leading to further decreases in pH. The limited concentration of
OH ⫺ (0.1 µM at neutral pH) in the bulk prevents its migration into the crevice
from having a substantial effect on the local pH. Due to the large stability constant
for Cr 3⫹ hydrolysis (23), it is generally thought that this reaction path determines
the final occluded site pH for stainless steels.
The self-sustaining nature of the process leads to a drastic reduction in the
stability of the passive film. Stage III is characterized by the breakdown of the
passive film due to the attainment of what has become known as the critical crevice
solution. This solution has a low pH [typically 1 or less (23)] and a high Cl ⫺
Passivity and Localized Corrosion
75
Figure 18 Schematic of Fontana and Greene model for crevice corrosion initiation of
stainless steels in aerated Cl ⫺ solution. (After Ref. 21.)
concentration [typically on the order of several M (24)] that results from the continual ingress of Cl ⫺ into the crevice. These concentrated solutions form in the localized corrosion site even if the bulk solution Cl ⫺ concentration is low. Stainless
steel is not able to remain passive in this solution and begins to dissolve actively.
In stage IV, propagation is stabilized owing to the large cathode-to-anode area ratio
that exists. The large freely exposed surface acts as a large cathode (with oxygen
reduction supplying the current), while the creviced area acts as an anode.
76
Chapter 3
Both calculations and measurements have indicated that it is possible to
develop very concentrated metal chloride solutions within occluded sites. For
example, stainless steel pits would be expected to contain 5 N Cl ⫺, 4 N Fe 2⫹,
1 N Cr 3⫹, 0.5 Ni 2⫹, and 0.007 N Na ⫹ and have a pH of 0.5. The low sodium ion
concentration develops as the Na ⫹ migrates out of the crevice due to the electric
field but is not replaced by any reaction in the crevice. Recent measurements
(24) of active crevice sites on Type 316L stainless steel showed the following
concentrations: 2.9M Fe 2⫹, 0.77 M Cr 3⫹, 0.24 M Ni 2⫹, and 0.06 M Mn 2⫹. As was
stated above, stainless steel will not remain passive in such a solution and can
dissolve at a high rate. The autocatalytic nature of the process stabilizes the environment by exceeding the rate at which diffusion can disperse the concentrated
solution. Initial dissolution rates of the order of 1 A/cm 2 (⬇ 440 in./yr) can be
reached.
In order for these rates to be maintained, the anodic dissolution current
must be balanced with a cathodic current according to ∑ I a ⫽ ∑ I c . The cathodic
current comes from reduction reaction(s) occurring on the outer surface of the
sample. Since this has a large surface area associated with it, it is a classic galvanic corrosion problem of large cathode and small anode. In this case, they are
on the same surface, as shown in Fig. 19. However, as the pit deepens, it becomes
more and more isolated from the outside environment, both chemically and in
terms of potential control. There are three limitations on the dissolution rate at
a localized corrosion site: (1) diffusional effects at the cathode (e.g., increases
in the boundary layer thickness with time limits the cathodic current), (2) salt
film precipitation at the anode (i.e., exceeding the solubility of the metal salts
causes a porous film to form across which some of the driving force drops), and
(3) ohmic effects in the solution between anode and cathode. Together these
decrease the steady-state penetration rates to values of between 0.5 and 10 mm/
yr. Figure 20 shows how each of these effects can act to limit the pit dissolution
rate in terms of Evans diagrams. Figures 21 and 22 show data for pit depth deter-
Figure 19 Location of anodic and cathodic reactions in pitting, showing the “galvanic”
nature of the process.
Passivity and Localized Corrosion
77
Figure 20 Evans diagrams showing limitations to pit growth: (a) diffusion limitation
at cathode, (b) salt film formation at anode, and (c) IR limitations between anode and
cathode.
mined from long-term exposures of alloys to seawater. The pitting rate can be
crudely estimated from the slope of the curves. In the cases shown of copper and
two aluminum alloys in seawater, the rate of pit propagation falls off dramatically
after the first year. Such behavior is typical in localized corrosion, due to the
effects discussed above, which limit the local current density.
The propagation of localized corrosion thus becomes an issue of stability.
For the localized corrosion site to exist, the CCS must be maintained locally.
However, the solution inside the localized corrosion site is constantly diffusing
away. The higher the concentrations required in the CCS, the larger the Fickian
driving force. In order to maintain the CCS within the localized corrosion site,
the anodic reactions inside the localized corrosion site must occur at a high rate
and must be balanced by cathodic reactions either inside or outside the localized
corrosion site. Any process that upsets this balance will cause the diffusion of
78
Chapter 3
Figure 21 Pit penetration as a function of time for pure copper exposed to natural seawater. The pit penetration rate can be estimated from the slope of the line. While the
initial pit penetration rate is rapid, it decreases substantially after the first year. (Data from
C. R. Southwell, J. D. Bultman, A. L. Alexander, Materials Performance, 15 (1976).)
CCS to dominate and the localized corrosion site to repassivate. In studying the
localized corrosion test techniques, these three aspects of localized corrosion, the
CCS, the separation of anode and cathode, and the stability of these processes,
should be kept in mind.
The initiation of localized corrosion is one of its most important and least
understood aspects. While theories of initiation abound (10–15), a full under-
Figure 22 Maximum pitting depth as a function of time for (a) AA3003-H14 and (b)
AA6061-T6 exposed to natural seawater at Halifax, Nova Scotia. The pit penetration rate
can be estimated from the slope of the line. While the initial pit penetration rate is rapid,
it decreases substantially after the first year. (Data from H. P. Godard et al., The Corrosion
of Light Metals, John Wiley, New York (1967).
Passivity and Localized Corrosion
(a)
(b)
79
80
Chapter 3
standing of the atomistics of the process(es) involved has remained elusive. The
model described above has a number of drawbacks and shortcomings. In engineering terms, propagation of localized corrosion sites is often considered more
problematic, though there are situations where even very small pits constitute
failure (e.g., interconnections on integrated circuits).
B.
Electrochemical Phenomenology
Armed with an understanding of the underlying physical processes, the electrochemical phenomenology of localized corrosion can be better understood. Figure
23 shows three schematic polarization curves for a metal in an environment in
which it spontaneously passivates and (1) can be anodized, (2) transpassively
dissolves at higher potentials, and (3) pits upon further anodic polarization. We
have discussed cases 1 and 2 in the section on passivity. For case 3, the region
of passivity extends from E corr to a potential labeled E bd at which point the current
increases dramatically at higher potentials.
Inspection of the specimen surface at the points labeled “a” and “b” on
curves 2 and 3 would show the difference in the physical processes causing the
identical current densities to be measured. In the case of curve 2, the surface
would have undergone uniform dissolution; in some cases, the dissolution is so
slight that it is imperceptible without magnification. In the case of curve 3, the
Figure 23 Schematic polarization curve for metal that spontaneously passivates but pits
upon anodic polarization. A hysteresis loop, which can appear during a reverse scan, is
shown ending at Erp. One dotted line shows behavior for anodizing conditions, while the
other shows transpassive dissolution.
Passivity and Localized Corrosion
81
vast majority of the surface would appear unaffected as well. However, one or
more areas would have suffered severe localized attack. Note that without physical inspection of the surface, determination of the origins of the applied currents
cannot be made.
The dotted lines in Fig. 23 show the applied current densities observed if,
after reaching points a and b respectively, the direction of the potential scan is
reversed. In both cases, a hysteresis loop is generated. For case 2, a negative
loop occurs, i.e., the current densities in the passive region on the reverse scan
are less than those on the forward scan at the same potential. For case 3, a positive
hysteresis develops. In both cases, the current eventually changes polarity (note
the new “E corr’s”). Inspection of the two surfaces would reveal that while the case
2 surface remains virtually unaffected, the localized corrosion sites on the case
3 surface will have increased in size dramatically.
The physical origins behind the negative hysteresis of case 2 lie in the
effect of passive film thickness on potential and subsequent dissolution rate. Passive films grow thicker at higher potentials and after longer times at a constant
potential. As the potential of the material of case 2 is scanned anodically, its film
thickens and becomes more protective. If the scan were stopped at any potential
and held, the current would decrease with time. However, in the experiment
shown, the potential is constantly being increased until the vertex current density
(point a) is reached. On the reverse scan, the currents are lower at all potentials
because of the thickened passive film. The effect can also be understood by assuming that at the end of the forward scan, the surface with the thickened film
has an anodic Evans line that is displaced to lower current densities compared
to the Evans line for the forward scan. Assuming no change in the kinetics of
the reduction reaction, the applied currents will be lower and the potential at
which ∑ I a ⫽ ∑ I c is also more positive, as shown in Fig. 24.
The physical origins behind the positive hysteresis of case 3 lie in the connection among the CCS, the stability of localized corrosion sites, and the competition between diffusion and dissolution at localized corrosion sites. As was discussed in the section on localized corrosion phenomenology, CRAs will actively
corrode only in aggressive, concentrated solutions. These concentrated solutions
can be generated locally by hydrolysis of dissolution products, but there will be
a large Fickian driving force to disperse them. An open pit is subject to hemispherical diffusion that is quite rapid. In order to maintain the aggressive CCS,
the dissolution rate and subsequent hydrolysis must be able to overcome the diffusional processes even as the pit grows. At high applied potentials (near point b
on curve 3), the local dissolution rate can be quite high (ca. A/cm 2), the diffusion
is overwhelmed and an aggressive solution is maintained. During the initial portion of the reverse scan, the driving force for dissolution is decreasing, but the
CCS has not had sufficient time to diffuse away. As the reverse scan continues,
the driving force for dissolution continues to decrease, and eventually the CCS
82
Chapter 3
Figure 24 Schematic Evans diagram and polarization curve illustrating the origin of
the negative hysteresis observed upon cyclic polarization for materials that do not pit.
Line a represents the (unchanging) cathodic Evans line. Line b represents the anodic Evans
line during the anodically directed polarization, while line c represents the anodic Evans
line for the material after its passive film has thickened because of the anodic polarization.
The higher corrosion potential observed for the return scan (E corr (back)) is due to the
slowing of the anodic dissolution kinetics.
cannot be maintained against diffusion. At this point, the localized corrosion site
repassivates, and the anodic current falls. Throughout the scan, the areas on the
surface that were not dissolving at high rate were having the passive films covering them thicken, as in case 2. Thus the E rp is a convolution of the loss of the
critical crevice solution from the localized corrosion site and the raising of the
E corr of the surrounding passive surface due to a decrease in anodic kinetics.
From polarization curves of the type shown in case 3, three important parameters can be determined: E corr , E bd , and E rp . In the literature there exists a
nearly infinite number of variations of nomenclature, many of which are shown
in Table 2. The interpretation of cyclic polarization curves has been and continues
to be a subject of great controversy. The classic interpretation of case 3 would
be that the potential of a material must exceed E bd for new pits (or localized
corrosion sites) to nucleate, but that at potentials between E bd and E rp , existing
pits can propagate. At potentials below E rp , all localized corrosion sites repassivate. Thus, from a design or material selection perspective, a material will perform well if its E corr is kept below E rp . This criterion can be met by environment
Passivity and Localized Corrosion
83
Table 1 Partial List of Terminology Used to Define
Characteristic Pitting Potentials
Symbol
Name
Eb
Ec
Ei
E p , E pit
E np
E cp
Ez
Breakdown potential, breakthrough potential
Critical potential
Initiation potential
Pitting potential
Nucleation potential
Critical pitting potential
Potential of pit precursor
E prot
E rp
Eu
Protection potential
Repassivation potential
Unique pitting potential
treatment (e.g., the removal of oxidizers) and/or cathodic protection. More discussion of the controversy surrounding the interpretation of cyclic polarization
data can be found in Section IV.B.3, p. 104.
Two other aspects of electrochemical phenomenology associated with localized corrosion should be appreciated before we discuss individual test techniques: common observations during potentiostatic testing and common observations during open circuit testing. Careful interpretation of these tests can provide
useful information on the processes that control localized corrosion.
Three cases of potentiostatic testing can be considered: potentiostatic holds
above E bd , potentiostatic holds between E bd and E rp , and potentiostatic holds between E rp and E corr . In these tests, the applied current is measured versus time.
Generally, at potentials above the E bd found in potentiodynamic scans, large initial current will be observed, which is due to a combination of double layer charging, passive film growth, and pit initiation. The current will then decay before
increasing in an erratic manner to values on the order of 1 to 10 mA/cm 2 (higher
for higher potentials above E bd ). These currents represent both the propagation
of the first pits and the initiation of new pits. The erratic nature of the currents
is due to the repeated birth and death of pits. Deconvolution of the signal into
components for individual pits is not possible without deterministic laws for initiation and propagation.
For potentiostatic holds between E rp and E bd , the current vs. time signal
will typically look like Fig. 25a. After the initial decay from a high current, there
will be an incubation time during which the current will remain low (e.g., on the
order of 1 µA/cm 2 or less for stainless steels in neutral solution). Often, transient
bursts of current will be observed. These currents are due to the initiation and
84
Chapter 3
Figure 25 Current versus time behavior for Type 302 stainless steel in 1,000 ppm NaCl
at (a) a potential between its repassivation and breakdown potentials, and (b) at a potential
below its repassivation potential. Note the existence of an incubation time before stable
localized corrosion occurs in (a). The small, short-lived current spikes during the first
400 s are due to the formation and repassivation of metastable pits, which can also be
observed in (b), although they are of a smaller magnitude.
Passivity and Localized Corrosion
85
short-term propagation of metastable pits. The only difference between these pits
and the stable pits is that the metastable ones repassivate in a short time (1 to
20 s, typically). If the test were interrupted at time t* and the surface inspected,
a series of small pits would be observed. The number would be less than or equal
to the number of transients, as some of the repassivated metastable pits may
reinitiate (e.g., if they are located at an inclusion stringer). Eventually, the current
will increase as shown and stable pitting will commence. One or more metastable
pits will stabilize (possibly by the formation of deposits of corrosion products
from previous metastable pitting activity), the current will increase to values on
the order of mA/cm 2, and the pits will propagate. For potentiostatic holds below
E rp , the currents will remain low, though metastable pitting activity may still
occur, with the peak currents for each pit being smaller, as shown in Fig. 25b.
Due to their separation in time, it is possible to analyze the metastable pit
transients in terms of the electrochemical processes occurring. If each transient
is considered to be from a single, hemispherical pit, the dissolution current density
in that pit can be calculated:
i diss ⫽
I peak
A pit
A pit ⫽ πr 2pit
r pit ⫽
冢 冣
3V pit
4π
1/3
t
V pit ⫽
(EW) ∫ t 0peak I(t) dt
Fρ
where I peak is the peak current of the transient, EW and ρ are the equivalent weight
and density of the material, F is Faraday’s constant, and the integral of I(t) is
the charge passed during the transient. In addition to the assumption of a hemispherical geometry, these calculations assume that all of the dissolution is electrochemical and that all of the cathodic reaction supporting the anodic dissolution
occurs on the counter electrode (i.e., no reduction reactions take place within the
pit or on the boldly exposed surface). Such calculations on actual data (see the
laboratory experiments associated with this chapter) demonstrate that the dissolution current density inside pits can reach the order of A/cm 2. By studying how
these current densities are affected by potential, solution, alloy composition, and
other experimental variables, insights into the factors that control the stabilization
of pitting for any given material can be gained.
Upon immersion of CRAs into solution, their E corr’s tend to rise with time
as shown in Fig. 26. This rise in potential occurs as the passive film thickens or
otherwise improves, moving the anodic Evans line to lower current densities.
These circumstances lead to a rise in E corr , in an analogous manner to the higher
E corr observed during a return scan of the transpassively dissolved material (Fig.
24). In a solution containing aggressive species, this rise in potential can eventually result in the E corr exceeding the critical potential for localized attack, as shown
in Fig. 26. Once localized corrosion can occur, a new Evans diagram must be
considered. Figure 27 shows the Evans diagram for an initiated localized corrosion site. The cathodic line is that for the reduction of oxygen on the boldly
86
Chapter 3
Figure 26 Corrosion potential vs. time for Type 410 stainless steel in 0.5 M NaCl ⫹
0.01 M H 2 O 2 . The breakdown potential is indicated by the dotted line. Once this potential
is exceeded, the potential falls as stable, localized corrosion begins to propagate.
exposed, nonlocally corroding surface. The anodic line is that for the dissolution
of material in an aggressive CCS. Note that the abscissa is in terms of current
rather than current density, since we must take area effects into account. At all
times, the sum of the anodic currents must equal the sum of the cathodic currents.
In the presence of the newly initiated pit, the new corrosion potential is lower.
Our observation is a drop in the E corr . If this is a metastable pit and it repassivates,
the potential will rise again as the anodic line for the pit returns to its previously
passive condition. This change can be viewed as an increase in Tafel slope. Once
completely repassivated, the E corr has regained its prepit initiation value. This
process can be repeated at other sites on the surface, leading to a series of corrosion potential excursions as shown in Fig. 27 (line c). These transients will be
discussed in more detail in the section on electrochemical noise.
Passivity and Localized Corrosion
87
Figure 27 Schematic (a) Evans diagram and (b) corrosion potential vs. time behavior
for localized corrosion stabilization. Line a on the Evans diagram represents the electrochemical behavior of the material before localized corrosion initiates, while line b represents the electrochemical behavior of the material in the localized corrosion site. Due to
the low Tafel slope of the active site, the corrosion potential of the passive surface/localized corrosion site falls. If repassivation occurs, the anodic behavior reverts back to line
a, and the corrosion potential increases again (line c). If repassivation does not occur, the
corrosion potential will remain low (line d).
IV. TEST TECHNIQUES
The ultimate goal of any corrosion test technique is the ability to quantitatively
predict rate of corrosion attack, whether it be uniform dissolution, pitting, intergranular corrosion, or stress-corrosion cracking. This objective has been achieved
for uniform corrosion in most instances as discussed in Chapters 1 and 2. However, the complexity of localized corrosion has prevented the achievement of this
goal. Instead, the test techniques generally are used as a means of ranking the
resistance of alloys to a particular type of attack. A second goal of many test
programs is the study of the effects of changes in environmental variables due,
for example, to intentional changes in chemical process conditions or transients.
Often, the tests are conducted in specified environments. Extrapolation of
the results obtained under those conditions to others is fraught with uncertainty.
Electrochemical testing can usually be performed in the solution of interest, making the results more applicable. Nevertheless, a common theme throughout this
book is the need for the user of electrochemical tests to ensure that both the
environment and the material surface are relevant to the corrosion problem of
interest.
This section will focus on explaining the electrochemical bases for two
generic types of testing: accelerated coupon testing and electrochemical testing.
88
Chapter 3
Several accelerated coupon tests described in ASTM standards will serve as examples of the use of chemical potentiostats as accelerating agents. The bulk of
the section will focus on electrochemical testing. Some of the problems involved
in sample preparation for electrochemical testing for localized corrosion will be
discussed first. Electrochemical potentiokinetic reactivation (EPR) testing for the
quantitative analysis of susceptibility of stainless steels to intergranular attack
will be reviewed and compared to ASTM accelerated coupon tests. The issues
surrounding the use of cyclic polarization for determining resistance to pitting
will be discussed. Several applications of potentiostatic testing to localized corrosion studies will be presented, along with two examples of the use of galvanostatic
testing. Finally, a review of the present understanding of the basis and utility of
electrochemical noise measurements for localized corrosion will be presented.
A.
Accelerated Coupon Testing
The use of highly aggressive environments and elevated temperatures for the
accelerated testing of materials has a long and successful history in the ranking
of the relative resistance of materials to localized corrosion. Numerous ASTM
standards have been developed that fall within this classification. This section
will review four tests that are representative of this type: the ferric chloride test
for pitting and crevice corrosion in stainless steels, the Huey and Streicher tests
for the susceptibility to intergranular corrosion in stainless steels, and the
NAMLT test for intergranular corrosion in aluminum alloys.
1. Chemical Potentiostats
All four of these accelerated tests rely on the introduction of a redox couple into
the solution that serves to poise the potential of the specimen surface in a region
where localized attack will commence if and only if the material is susceptible.
This redox couple is termed a chemical potentiostat. Figure 28 shows an Evans
diagram for a generic chemical potentiostat that would test if a material is susceptible to pitting in that solution. In the absence of the redox couple O/R, the open
circuit potential of the material would be E corr (1), and the material would not
undergo localized attack. Upon introduction of O/R, the corrosion potential for
a material that is resistant to localized attack would rise to E corr (2), since the
kinetics of both the oxidation and the reduction reaction of O/R are faster than
the other reactions present. Thus the kinetics of O/R would dominate the criterion
for establishing the corrosion potential. A resistant material would remain passive
under these conditions as its pitting potential is much higher. The open circuit
potential of a less resistant material, whose pitting potential is at or below the
reversible potential for O/R, would rise up towards the E r (O/R) until it exceeded
Passivity and Localized Corrosion
89
Figure 28 Schematic Evans diagrams and polarization curves for a material in a solution
containing a redox couple that acts as a chemical potentiostat. The i o used in the Evans
diagram for the O/R redox couple is that relevant to the material of interest. In the absence
of the redox couple, the material obtains E corr1 . In the presence of the redox couple, the
material obtains E corr2 . If E corr2 is above the pitting potential, the material will be rapidly
attacked.
the material pitting potential. At that point, pitting would commence, and the
potential would fall, as was discussed above for Fig. 27. The presence of the
O/R redox couple would accelerate the attack by providing a fast cathodic reaction on the passive surface.
The choice of the redox couple for an accelerated test will depend on factors
such as its thermodynamics and kinetics, its compatibility with other accelerating
factors (e.g., temperature, aggressive anion concentration), and its ease of use.
Rarely is the relevance of the redox couple to the service environment of interest
considered.
90
Chapter 3
2. Ferric Chloride Test
Described in ASTM G 48 (25), this type of test for stainless steels (including
Ni-base alloys containing a large amount of Cr) involves exposure of the material
to a highly oxidizing, highly acidic, concentrated metal chloride solution. Briefly,
a material is exposed to a 10 wt% FeCl 3⋅6H 2 O solution for a relatively short time
(24 to 72 hours) at either ambient or elevated (usually 50°C) temperature. At the
end of the test, the sample is examined for weight loss and localized attack. If
pitting and crevice corrosion are of concern, artificial crevices can be applied by
the use of Teflon blocks held tightly to the sample surface by rubber bands,
though a superior method for forming a crevice is discussed below.
The chemical potentiostat in this test is the ferric salt that forms a Fe 3⫹ /
2⫹
Fe redox couple with a potential of approximately ⫹0.45 V(SCE). The high
concentration of ferric ion (0.4 M) allows the couple to provide a large current
without an appreciable change in potential (approaching an ideally nonpolarizable
electrode). The cathodic reaction (reduction of ferric to ferrous ion) occurs on
the boldly exposed passive surface. The high potential in turn increases the probability of exceeding the pitting potential on a given material, especially in such
a concentrated Cl ⫺ solution (and even more so if the test temperature is raised
to 50°C). Other accelerating factors include the high chloride concentration (1.2
M) and the low pH of the solution (typically about 1.3), which inhibits repassivation and lowers the stability of the passive film. Thus the ferric chloride test is
a test of the resistance of an alloy to propagation of localized corrosion for most
alloys, since their pitting potentials are well below ⫹0.45 V(SCE) in this solution.
However, more highly alloyed materials can resist initiation in this solution, and
thus the time of the test is often extended to a period of many days.
This very popular test does have a number of drawbacks. Very few industries operate in 10 wt% FeCl 3 (thankfully). Thus the relation of the results of this
test to performance in real service environments that are profoundly different is
questionable, and in fact, a number of cases where reversals in alloy ranking has
occurred have been documented. Part of the problem lies in the use of Fe 3⫹ to
act as the chemical potentiostat. Inside pits in stainless steels, it is well established
that anaerobic conditions exist, and thus the concentration of ferric ion is small,
though the concentration of ferrous (Fe 2⫹) can be very high. For Ni-base materials, the use of an iron-base solution is also of questionable value. In addition, the
effects of other alloying elements in determining the chemistry of the localized
corrosion site are not addressed with this type of test. The fact that crevice corrosion can occur in such an aggressive solution indicates that the accumulation of
other types of compounds at the localized corrosion site is of importance. Despite
these limitations, the FeCl 3 test will continue to be an important tool in alloy
development and screening for historical, if for no other, reasons.
A variety of modifications can be made to the ferric chloride test and still
Passivity and Localized Corrosion
91
fall within the spirit of the method. The exposure time and temperature can be
altered, as can the surface finish. Since surface finish can have important impact
on the localized corrosion behavior by providing occluded sites and, in some
cases, surface area for cathodic reactions, it is important that this be chosen with
care.
Since crevice corrosion can occur under more mild conditions than pitting,
it often limits the operating envelope for highly alloyed materials. Thus a variety
of exposure tests for crevice corrosion resistance have been developed. The most
important part of a testing program for crevice corrosion is the ability to inflict
a tight, reproducible crevice. Many designs have been tried, but the multiple
crevice assembly, shown in Fig. 29 and discussed in detail by Kearns (26), has
emerged as the crevice former of choice. This nonmetallic (usually Teflon or
Delrin) segmented washer addresses a number of issues in crevice corrosion
testing. Since each washer contains 20 individual crevice formers, a large number
of potential crevice sites can be tested simultaneously, allowing a statistically
significant number of sites to be evaluated on a small number of specimens. For
example, triplicate specimens would provide three specimens ⫻ 20 sites per
washer ⫻ 2 washers per specimen ⫽ 120 sites. The wealth of information that
can result from such a test, in terms of initiation probability and depth of attack,
allows a great deal to be learned about the service limitations of a material. In
addition, the use of torque wrenches allows a reproducible force to be applied
and thus reproducible crevice dimensions to be realized. Finally, the low cost
and ease of application makes this arrangement amenable to large scale testing.
Other designs do exist, and may be more applicable in certain situations.
For example, O-rings or Tygon  tubes may provide a more realistic crevice arrangement for material in pipe form. Dissimilar metal–metal crevices may be
more appropriate in some circumstances (24,27), and such arrangements can be
easily fabricated as well. One of the major advantages of crevice corrosion testing
using crevice formers is that acceleration of the process can often be accomplished by applying a tighter crevice than would be expected to exist in service
(this is another advantage of nonmetallic deformable crevice formers). The tighter
the crevice gap, the more severe the problem. Solution ingress will always occur
at practical gaps by capillary action. To accelerate the process further, daily increases in temperature of 5°C, with periodic inspection for initiation, can result
in the determination of the critical crevice temperature.
3. Intergranular Corrosion Tests
Intergranular attack occurs due to a difference in the metallurgical condition of
the material at (or near) the grain boundaries. Exposure solutions that magnify
the differences in corrosion resistance between the grain boundary areas and the
92
Figure 29 Details of multiple crevice washer (not to scale).
Chapter 3
Passivity and Localized Corrosion
93
bulk grain are therefore useful in evaluating the extent to which sensitization has
occurred. The more that is known about the metallurgy behind the sensitization,
the more efficient can be the test designed. Due to differences in the metallurgy
and the effects of hot and cold work on the distribution of the precipitates at the
grain boundaries, separate tests must be developed for different alloys and even
for cast and wrought materials of the same composition.
Over the years, a number of standard practices have developed to evaluate
the susceptibility of austenitic stainless steels to intergranular attack, especially
as the result of heat treatment and welding. The most popular have been compiled
into ASTM standard A262. The oxalic acid test (Practice A) is an excellent
screening test and is discussed below under galvanostatic testing. The accelerated
coupon tests (Practices B through E) are aimed at evaluating the degree of sensitization in more detail with a more severe test. They vary in the details of their
solution composition, test temperature, and length. These tests include the
Streicher test (ferric sulfate–sulfuric acid) and the Huey test (boiling nitric acid).
Each has applicability to the detection of susceptibility among certain classes of
alloys, since each attacks different types of precipitates (or the depleted areas
adjacent to the precipitates).
The Huey and Streicher tests rely on the effect of a material’s Cr content
on its electrochemical behavior in acid. Figure 30 shows polarization curves for
two materials in acid, one representing the unsensitized grain interiors containing
18% Cr and the other representing the sensitized grain boundary material containing 10% (less than the 13% required for “stainless” behavior). Both tests rely
on the differences between the passive behavior of sensitized and unsensitized
material, the main electrochemical difference being the potentials to which the
materials are driven by the respective chemical potentiostats (Fe 3⫹ /Fe 2⫹ for the
Streicher, NO 3⫺ /NO for the Huey). The corrosion potentials in the Streicher test
reach approximately ⫹0.6 V(SCE), while those in the Huey test reach ⫹0.75 to
⫹1.0 V(SCE). The sensitized material has dissolution rates two orders of magnitude higher than the unsensitized material. Since this attack is focused at the
grain boundaries, the grains eventually fall out, and substantial weight losses can
be observed for sensitized products. The advantages and disadvantages of the
different sensitization tests are reviewed by Streicher (28).
Another good example of the importance of understanding the metallurgy
involved is the use of ASTM G-67 for IGA resistance of the 5XXX series alloys
(Al–Mg and Al–Mg–Mn) known as the NAMLT test. It is known that the precipitation of AlMg, an intermetallic compound, leads to the susceptibility of these
alloys. The AlMg precipitate is anodic to the base material and is thus susceptible
to removal. By exposing the alloy to nitric acid (which acts as the chemical
potentiostat), the AlMg is quickly removed while the base metal remains passive.
The more precipitates present, the higher the weight loss in the 24 hour exposure
to concentrated (70%) nitric acid, with losses on the order of 50 mg/cm 2 possible
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Chapter 3
Figure 30 Schematic polarization curves illustrating the origins of the ability of the
oxalic etch test and acid ferric sulfate test to differentiate sensitized (represented by the
Fe-10Cr-10Ni) from unsensitized (represented by the Fe-18Cr-10Ni) material.
resulting from grain fallout. This high mass loss occurs when the precipitates
form a continuous path around the grains. It should be noted that electrochemical
measurements of grain fallout are impossible, since no charge is passed that accounts for the material lost.
Each practice indicates its limitations, and these are important to keep in
mind. As with all accelerated tests, what is actually tested is the resistance of
these alloys to IGA in the specific test environment. One must be very careful
to be sure that these results correlate with longer term exposures to the field
environment of interest. In addition, these tests are only useful for evaluating the
susceptibility of these alloys to IGA, not to pitting or general corrosion or SCC.
Passivity and Localized Corrosion
95
Finally, it is difficult to quantify many of these tests to compare alloys whose
resistance is intermediate. That is, these tests are excellent at weeding out very
good material from very bad material, but provide no means by which the infinite
shades of grey can be fairly ranked. Electrochemical tests such as the EPR test
described below fill such a need.
B. Electrochemical Testing
The main advantage of electrochemical testing is the opportunity to investigate
corrosion phenomena in the solution of interest rather than in a more aggressive
and probably less relevant environment. In addition, a great deal of information
can be gained about the dependence of the phenomena on external variables in
a short time. Finally, the determination of critical potentials for initiation and
propagation of localized corrosion can be useful in design decisions. For example,
the use of mixed potential theory can allow the prediction of the protection (either
anodic or cathodic) criteria, as well as galvanic couples to avoid. However, misinterpretation of electrochemical test results occurs regularly; this section has been
designed to explain the commonly used tests and possible interpretation pitfalls.
1. Specimen Mounting
Probably the main problem with electrochemical testing for localized corrosion
resistance is sample mounting. It can be extremely difficult to mount a sample
with an insulated electrical contact and a controlled surface area without introducing a crevice at the sample–mount interface as shown in Fig. 31. Since crevice
corrosion will occur at lower potentials than pitting, the sample invariably begins
to be attacked at the crevice, leading to an underestimation of the resistance of
the sample to pitting. Some may argue that for the same reason, this type of
testing is not overly conservative, as in service, one wants to know the potential
at which any localized corrosion can occur, not just pitting. The drawback is that
most crevices formed during sample preparation are not reproducible either in
position or geometry, making comparisons extremely difficult. In addition, there
may be applications where crevice corrosion is not the limiting performance factor, but pitting is. Such testing would lead one to choose a more resistant (and
therefore expensive) alloy than one would actually need.
A number of solutions have been suggested for sample mounting, including
the use of “knife-edge” PTFE washers, other mounting compounds and procedures, the use of wire loops, and flag geometries. All of these have their limitations, and one must choose the most appropriate for the particular alloy–environment combination. The knife-edge PTFE washer (as shown in Fig. 32) has been
used successfully in a number of applications in which a tight seal can be formed
that prevents ingress of any electrolyte. The success of this approach is closely
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Chapter 3
Figure 31 Schematic of crevice formed at mount–sample interface. Mounting material
is used to insulate the electrical contact to the sample.
related to the quality of the surface finish both in terms of its fineness (i.e., final
polishing step particle size) and its uniformity. One large scratch can allow capillary action to draw electrolyte into an otherwise impervious crevice and start the
sample down the slippery slope to crevice corrosion. This intolerance of polishing
faults is the prime reason for the failings of this type of approach. In addition,
due to the cost of the PTFE washers, many experimenters tend to try to reuse
them. This recycling works occasionally, though unpredictably. The knife-edge
PTFE washer is actually a second generation of the Stern–Makrides approach
Passivity and Localized Corrosion
97
Figure 32 Schematic of cross section of arrangement used with knife-edge PTFE
washer for definition of sample area. A represents the PTFE washer, B represents the
sample, C represents the assembly, including the backing plate that generally is screwed
against the sample to press it against the PTFE washer, and D represents the insulated
electrical contact.
(Fig. 33) in which a cylinder of PTFE is forced onto the top of a generally cylindrical sample. The Stern-Makrides washer suffers from same problems as does
the knife-edge, but to a greater degree due to the larger surface area involved.
One example of the effect of crevices is shown in Fig. 34 for a solution
in which propagating crevice corrosion will not occur. In this case, the higher
passive current densities are observed for the insulating materials that perform
poorly. In a Cl ⫺-containing solution, this would translate into a lower E bd . As
can be seen from Fig. 34, some mounting materials perform well in this solution,
though it should be pointed out that this is not so for other solutions. For example,
the alkyd varnish is used in electroplating to mask off areas. While it works well
in acid solutions, it performs very poorly in neutral or basic solutions, especially
on materials with passive films such as stainless steel. One mounting compound
that has been found to work well is a mixture of five parts of Armstrong A-12
adhesive to 1 part of T-146 hardener by weight.1 After mixing well, the epoxy
1
Armstrong Products Co., Argonne Road, Warsaw, IA.
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Chapter 3
Figure 33 Schematic of cross section of Stern–Makrides arrangement. A represents the
glass tube which protects the threaded rod, which acts as an electrical contact. A is pressed
onto B, a machined PTFE cylinder that seals against the sample C.
can be poured over the previously well-cleaned sample. After setting overnight,
the sample can be polished and used in electrochemical studies. It has been used
successfully for stainless steel, Ni-base alloys, magnesium, aluminum, and steel
at room temperature. It has been found to degrade in propylene carbonate–water
mixtures. Other mounting compounds have also been found to form very good
seals, such as the Interlux 404 base/414 Reactor combination.2
Qvarfort (29) developed a cell in which the creviced area of the sample is
continuously washed with deionized water in order to prevent the development
of the critical crevice solution. As shown schematically in Fig. 35, the purified
water enters the creviced area via a groove machined in the cell base. In order
to disperse the flow throughout the occluded region, a fine porosity filter paper
ring is placed between the groove and the specimen. The water flow rate is typically 4 to 5 mL/h. Thus dilution of the solution inside the cell should not be an
issue in most electrochemical testing (e.g., after 4 h, a 1 M NaCl solution will
become a 0.98 M solution). Named the Avesta cell for Qvarfort’s employer, this
approach has been used to study pitting and intergranular corrosion at tempera2
Courtlauds Coatings, Inc., Morris Avenue, Union, NJ.
Passivity and Localized Corrosion
99
Figure 34 Potentiostatic anodic polarization curves of a Fe 10% Cr 10% Ni alloy in
a 1 N H 2 SO 4 solution at 25°C as a function of electrode mounting technique. (From Greene
et al., France, and Wilde.)
tures up to 100°C (29,30). Avesta has not copyrighted the design and has made
it generally available to the corrosion community.
If mounting cannot be accomplished, two other approaches can be used.
The first is the use of a wire loop electrode, as shown in Fig. 36. Bo¨ehni (31)
has used this approach to study pitting without the complications of crevice corrosion. This approach works extremely well if one can obtain the material in wire
form, though there is always the concern of metallurgical differences between
material in wire form and that in plate or tube form, which is more likely to be
used in actual applications. A related approach is the use of a flag electrode
configuration, as shown in Fig. 36b. This design works well with plate material
by minimizing the shaft size and thereby minimizing any effects of the waterline.
If localized corrosion at the waterline continues to be a problem, deaeration of
the air space above the solution can be of help as well. However, edge attack
can be an issue, particularly in wrought products.
2. EPR Testing
Sensitization of stainless steel can occur owing to improper heat treatment, welding, or long-term exposure in service to elevated temperatures (28). While there
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Chapter 3
Figure 35 Schematic diagram of the Avesta cell. Note that some details such as the
thermometer have been omitted. (From Ref. 29.)
are a number of exposure tests to evaluate sensitization, as discussed above, none
of these allows a quantitative comparison of the degree of sensitization (DOS),
especially for lightly sensitized materials. Electrochemical potentiokinetic reactivation (EPR) tests have been developed as rapid nondestructive tools for assessing the DOS of stainless steels. All types of EPR testing involve polarization of
a sample (which could be, for example, the wall of a pipe in a chemical plant)
in a solution of deaerated sulfuric acid containing a depassivator (KSCN). Sensi-
Passivity and Localized Corrosion
(a)
101
(b)
Figure 36 (a) Wire loop and (b) flag sample configurations used to prevent crevice
corrosion during electrochemical testing.
tized grain boundaries will activate to a stronger degree than unsensitized boundaries, and therefore a greater current will be measured. The magnitude of the
current is a quantitative measure of the DOS. The single loop (SL-EPR) test (32)
is shown schematically in Fig. 37. After allowing the sample (previously polished
to a 1 µm finish) to establish a steady-state E corr , the potential is stepped into the
passive region and then scanned in the cathodic direction. The passive–active
transition involves the passage of a certain amount of charge. This charge is then
normalized to the grain boundary area to establish a P a value (a measure of DOS):
Pa ⫽
Q
GBA
where:
P a ⫽ degree of sensitization
Q ⫽ charge passed during test
GBA ⫽ grain boundary area ⫽ A s [5.09544 ⫻ 10 ⫺3 exp(0.34696X )
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Chapter 3
Figure 37 Schematic SL-EPR polarization curve. (From Ref. 32.)
A s ⫽ specimen surface area
X ⫽ ASTM micrograin size number [per ASTM Practice E 112 (33)].
The grain interiors will have a characteristic charge density associated with their
passive–active transition. Unsensitized material will exhibit this low value of P a .
Sensitized grain boundaries will activate more vigorously, resulting in higher
currents and therefore larger amounts of charge passed. However, since the
amount of grain boundary area will have a direct influence on the amount of
charge passed, it is important to take this into account when comparing materials
that have been exposed to different heat treatments.
The SL-EPR test was pioneered by Clark (32). Figure 38 shows the results
from an extensive study by Majidi and Streicher (32) that compared the results
of SL-EPR testing to those from the ASTM ferric sulfate test. One can see that
at low levels of sensitization, the SL-EPR test is much more discriminating,
though for severely sensitized steel, the electrochemical test results saturate.
Since it is usually more important to find low levels of sensitization, EPR tests
are becoming increasingly popular.
An improvement on the SL-EPR test is the double loop, or DL-EPR, test,
which is shown schematically in Fig. 39. In this test, the potential is first scanned
in the anodic direction from E corr to a point in the middle of the passive region
before the scan is reversed. The ratio of the two peak current densities, L/I a , is
used as the degree of sensitization indicator. During the anodic sweep, the entire
surface is active and contributes to the peak current. During the reactivation
sweep, only the sensitized grain boundaries contribute to the passive–active transition. Thus in unsensitized specimens there is a small I r , and therefore a small
ratio, while in heavily sensitized specimens, I r approaches I a , as shown in
Passivity and Localized Corrosion
103
Figure 38 Comparison of data from SL-EPR, acid ferric sulfate, and oxalic acid etch
test for seven separate heats of Type 304 and 304L stainless steel. Note that for low levels
of sensitization, the SL-EPR can quantitatively distinguish among degrees of sensitization.
At higher levels, the coupon exposure tests are more discriminating. (From Ref. 32.)
Fig. 40. The advantages of the DL-EPR are (1) only a 100 grit finish is necessary,
as the anodic sweep “cleans” the surface, (2) intragrain pitting does not affect
the ratio, and (3) no measurement of either surface area or grain size is necessary.
The anodic sweep essentially gives an internal calibration for the method. Majidi
and Streicher have shown excellent correlation between SL- and DL-EPR tests
for Type 304 SS (32). DOS values measured by EPR have been included in
models of intergranular SCC of sensitized stainless steel (34,35).
The EPR technique has been used for other alloys as well, including cast
(36) and wrought (37,38) duplex stainless, as well as Ni-base alloys (39). Lee
(38) used DL-EPR testing to determine the minimum amount of Ti and/or Nb
required to render Type 430 SS immune from intergranular attack. In some cases,
the details of the experimental method (i.e., solution temperature, KCNS and
H 2 SO 4 concentrations, scan range) must be modified to differentiate best the
levels of sensitization of interest. For example, Scully and Kelly doubled the
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Figure 39 Schematic diagram of the double loop (DL) EPR test. Sensitization is evaluated from the current ratio, I r /I a .
KCNS concentration and increased the peak potential for their study of sensitization of duplex alloy 2205 (40).
Intergranular stress-corrosion cracking (IG-SCC) can occur in some sensitized materials when placed under tensile stress. Thus DL-EPR has been used to
study the effects of aging time on the susceptibility of Alloy 600 to IGSCC, as
shown in Fig. 41 (39). This work also shows the need to modify the experimental
parameters of the test to achieve optimal correlation for alloys other than Type
304SS, in this case lowering the KCNS concentration and the temperature while
raising the peak potential and the scan rate.
3. Cyclic Potentiodynamic Polarization
The most common electrochemical test for localized corrosion susceptibility is
cyclic potentiodynamic polarization. As was discussed briefly in the section on
the electrochemical phenomenology of localized corrosion, this test involves polarizing the material from its open circuit potential (or slightly below) anodically
until a predetermined current density (known as the vertex current density) is
achieved, at which point the potential is scanned back until the current reverses
polarity, as shown in Fig. 42. The curve is generally analyzed in terms of the
breakdown (E bd ) and repassivation potentials (E rp). Very often, metastable pits
are apparent by transient bursts of anodic current. The peaks in current shown
in Fig. 42 for a potentiodynamic scan are due to the same processes as those
shown in Fig. 25 for a potentiostatic hold.
Passivity and Localized Corrosion
105
Figure 40 Double loop EPR data for Type 304 stainless steel heated at 600°C for 100
h (solid line) and 1 h (dotted line). The extremely sharp active–passive transition at ⫺0.5
V(SCE) is due to ohmic drop effects. Note the much larger i r for the sensitized (100 h)
material. (Data courtesy of M. A. Gaudett, University of Virginia.)
Controversy concerning the interpretation of cyclic polarization curves has
raged for many years. Of particular interest is which (if either) of the two potentials can be used for material selection and mitigation strategy decisions. The
classic interpretation is that a material’s potential must exceed E bd in order to
initiate pits, but if flaws were introduced into the surface in any way, they could
propagate at all potentials above E rp . Thus E rp could be used in design as a protection potential.
There are those who feel that there are not two distinct potentials. These
workers propose that, when measured correctly, E bd and E rp are one and the same.
In standard testing, the nucleation of pits occurs at E rp , but owing to the time
necessary for pits to become established, the probability that pits will repassivate,
and the finite potential scan rate used, pits do not cause a dramatic increase in
the current until E bd . This explanation would rationalize the often-observed effect
that increasing the scan rate increases E bd but not E rp . If E rp is properly measured,
these workers feel that it can be used as a go–no go potential for applications,
i.e., if the potential of the alloy is always below E rp , then pitting cannot occur.
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Chapter 3
Figure 41 Comparison in normalized condition between the results of EPR tests and
S IGSCC of Alloy 600 aged at 700°C. (From Ref. 39.)
The E rp could be an important design parameter for engineering structures
if it can be shown to be a material property like yield strength, for example. If
the E rp were known accurately, preventing localized corrosion would be possible
by maintaining the potential of the structure below that value, either by chemical
treatments designed to lower the E corr or via external polarization (cathodic protection). The difficulty has been in determining if a proper method exists for measuring E rp . Since the early 1970s, there has been disagreement concerning the utility
of E rp , since it was shown to depend upon the maximum current density used in
the forward scan, as shown in the result of Wilde in Fig. 43. However, a recent
evaluation of both the literature and long-term experiments by Sridhar and Cragnolino (41) and Sridhar and Dunn (42) have clarified the situation somewhat.
Sridhar and Cragnolino (41) showed that the repassivation potential decreased with increasing pit depth for shallow pits but became independent of the
degree of attack for deep pits, as shown in Fig. 44. Sridhar and Cragnolino (41)
showed that for Alloy 825 and Type 316L SS, E rp became independent of charge
passed above 10 C/cm 2. This charge density corresponded to a maximum pit
depth of about 100 µm (42). In Wilde’s work (43), the charge density passed
was less than 0.7 C/cm 2 in all cases studied. Such charge densities are typical
Passivity and Localized Corrosion
107
Figure 42 Cyclic polarization curve for Type 302 stainless steel in 1,000 ppm NaCl.
Note the definition of the breakdown and repassivation potentials, the vertex current density, and the appearance of metastable pits.
Figure 43 Cyclic polarization behavior of 430 stainless steel in 1 M NaCl, demonstrating the striking effect of pit propagation on E prot . (From Ref. 43.)
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Chapter 3
Figure 44a A compendium of repassivation potential versus charge density data from
the literature for various Ni–Fe–Cr–Mo alloys in Cl ⫺ solutions. Some of the charge densities were calculated from the data provided in the original references. (From Ref. 41.)
of results using the standard cyclic polarization method. Not surprisingly, a dependence of E rp on vertex current density or pit depth has been observed by a
number of workers (44–46) using low charge densities, as would be expected
from Fig. 44. Those workers who have used larger localized corrosion charge
densities to determine E rp have observed its independence of charge passed.
Important evidence supporting the application of E rp is the long-term potentiostatic data of Dunn and Sridhar (47), in which potentiostatic holds of alloy
825 in 1000 ppm Cl ⫺ at 95°C have been performed for up to 18 months. They
found that the repassivation potential determined for deep pits at short times
corresponded well to the potential below which localized attack did not occur
over long times. Localized attack did occur only 10 mV above the highest observed repassivation potential.
A third approach to critical localized corrosion potentials is emerging in
which no single critical potential is accepted as a material property. In this school
of thought, E rp is the potential at which pits will most probably (in a statistical
sense) repassivate. However, pit initiation and propagation can occur below this
Passivity and Localized Corrosion
109
Figure 44b Effect of charge density on the repassivation potential for pitting and crevice corrosion.
Figure 44c Effect of applied potential on the initiation and repassivation of localized
corrosion in Alloy 825 in 1,000 ppm Cl ⫺ at 95°C.
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Chapter 3
potential. The probabilities that a pit will initiate or propagate decrease as the
potential of the surface decreases below E rp . In most applications, the most probable E rp is usable as a guide for material selection or process alteration. However,
in critical applications, a more statistical approach is needed. For example, even
a 1 µm pit will cause a failure of a connection on an integrated circuit, and thus
pits that form at this size are considered failures. Such pits can occur at potentials
below E rp .
Shibata and Takeyama (48) and Williams et al. (49) have applied such
statistical arguments to pitting of stainless steel. In order to develop these models,
a large amount of data that can be treated as an ensemble must be gathered. In
other words, variations in results from test to test are expected, even for nominally
identical tests. This variation is used to develop the cumulative probability curve
for pitting under a certain set of conditions. Both groups used multiple specimen
testing apparatus to gather up to 12 data points for critical potentials and metastable pit nucleation rates simultaneously. The results for one set of 30 tests is shown
in Fig. 45. This shows that the breakdown potential, E bd , follows a distribution.
Thus, for this alloy–environment combination, there is a 20% chance that the
breakdown potential of commercial 304 SS will be below ⫹160 mV(SCE) in
1000 ppm NaCl. The argument is that there was nothing wrong with those tests
Figure 45 Cumulative distributions of pitting breakdown potentials for the commercial
purity (CP), high sulphur (HiS), and high purity (HiP) 304L steels. (From Ref. 50.)
Passivity and Localized Corrosion
111
whose E bd was less than ⫹ 160 mV(SCE), but that the variation reflects the stochastic nature of the pitting process. Such information could then be used to
estimate component lifetimes, which could then be used to make design decisions
based upon the consequences of a failure. For example, a 30% chance of perforation may be acceptable for an easily shut down and repaired vessel if it allows
a cheaper alloy to be used, but such a probability would not be acceptable for a
critical component in an inaccessible submersible. Fujimoto et al. (51) have also
recently applied this type of approach to the initiation of crevice corrosion.
4. Potentiostatic Testing
While long-term potentiostatic tests can be useful, they are extremely time-consuming and expensive. Potentiostaircase tests can be performed in lieu of potentiodynamic tests, though at equivalent potential scan rates, the results should be
identical. In addition, the time frames involved are usually still very short compared to the projected life. Thus a number of approaches have been developed
for accelerating the process of initiation in order to determine the potential below
which initiated sites will repassivate (i.e., E rp).
Mechanical scratching is favored by some as a means by which a bare
surface can be created. In this technique, one is ascribing no importance to (or
taking any engineering credit for) initiation time. The surface is held at a constant
potential and then a portion of it is scratched, usually with a diamond-tipped
point. The current is monitored with time. For potentials below E rp , the surface
will repassivate rather rapidly, as shown in Fig. 46. Just above E rp , the surface
Figure 46 Schematic of applied current density vs. time observed for mechanical
scratching of a surface exposed to a solution above and below its repassivation potential.
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Chapter 3
will try to repassivate, but it will fail, and the current will eventually increase.
The closer the potential to E rp , the longer is the time before the current increases.
Thus, in most cases, the E rp measured by this method is not conservative, as usually
no more than 10 minutes is spent at any one potential. If one had waited long
enough at the potential used just before the measured E rp , localized corrosion
might have occurred. However, this does not denigrate its utility as a screening
test. One problem with scratching tests of this type is the dependence on the weight
of the scratch. For hand scratching, the E rp decreases with increasing damage. A
mechanical system improves the reproducibility. A more damning problem concerns the site of pitting. In many (if not most) cases, pitting occurs in practice at
inclusions or second phase particles of one type or another. Such inclusions are
usually present at small volume fractions, so the probability of hitting one (or
more) with a fine diamond tip is extremely small. Thus this approach can lead to
erroneously high values of E rp that reflect the pitting susceptibility of the matrix
material but ignore the susceptibility of the weakest link, the inclusions.
A second method of producing a bare surface is what has become known
as the electrochemical scratch. In this technique, the entire exposed surface is
activated by a large positive voltage excursion that is followed by a voltage step
back to (or towards) E corr . In this way, any likely pitting sites are initiated, and
the test measures the ability of the material to resist propagation and to repassivate. One version of the test (see Fig. 47) involves a step to ⫹2 V for 3 s followed
by a step back to E corr , during which time the current is monitored. The potential
is held there for 5 minutes before it is again stepped to ⫹2 V for 3 s to reinitiate
localized corrosion. At this point, the potential is stepped back to a potential 50
mV above E corr and the current is monitored for 5 minutes. The process is repeated
until the current does not decay upon the step in the negative direction. In this
way, an estimate of E rp can be made, with better estimates resulting from the use
of smaller increments in the test potential (i.e., 25 mV instead of 50 mV). Sridhar
et al. (41,42,47) used a variation of this technique to determine the repassivation
potentials discussed previously. They found excellent correlation from these tests
and the long-term performance of materials. Tsujikawa and coworkers (52,53)
have also used repassivation potentials measured via potentiostatic tests that focused on the stability of the localized corrosion process (i.e., measured the conditions under which a material would repassivate once activated and allowed to
grow).
Temperature has been used in conjunction with electrochemical control to
quantify the resistance of materials to localized corrosion. Kearns (26) has reviewed the different critical temperature tests in some detail. Electrochemical
critical temperature testing consists of holding a material exposed to a solution
of interest potentiostatically at a potential in its passive region while increasing
the temperature of the solution either intermittently (54) or continuously (55).
An example of the results of the latter type of testing is shown in Fig. 48. In this
Passivity and Localized Corrosion
113
Figure 47 Schematic E app (t) and I app (t) for the electrochemical scratch test. Once the
return potential exceeds E rp , the current increases. The size of the step (50 mV in this
case) will define the uncertainty of the measurement of E rp .
case, a localized corrosion site is stabilized and the current increases dramatically.
Parameters of importance in such testing include the potential at which the sample
is held, the rate of temperature increase, and the criterion for the current that
establishes the critical temperature. This method allows a quantitative ranking
of a wide variety of alloys by a single parameter that can be related to actual
process conditions.
5. Galvanostatic Testing
The vast majority of electrochemical testing involves controlling the potential of
the working electrode and measuring the applied current required. This bias has
development for two main reasons: (1) the easier applicability of critical potentials, rather than critical current densities in mitigation strategies, (2) the exponential dependence of dissolution rate on potential. There are situations in which
galvanostatic tests (in which a constant applied current is maintained) can be more
discriminating. These are most often coupled with post-test visual examination of
the specimen. The posttest examination allows a determination of the sites from
which the current was emitted in cases where the polarization behavior itself is
114
Chapter 3
Figure 48 Plot of breakdown and repassivation potentials vs. temperature for different
steel grades in 1 M NaCl. Filled symbols for breakdown and open symbols for repassivation potentials. (From Ref. 30.)
not discriminating. Galvanostatic tests also require less advanced equipment than
potentiostatic tests.
The most widely-used galvanostatic test is Practice A of ASTM A262, the
oxalic etch test. In this screening test for sensitization of stainless steels, an applied anodic current density of 1 A/cm 2 polarizes the specimen to high potentials
for 1.5 min in 10% oxalic acid. Posttest examination reveals whether the charge
passed went to uniform dissolution or localized attack along the grain boundaries.
Unsensitized materials show a “step” structure in which the individual grains are
uniformly dissolved. As shown in the cross section, the different grains dissolve
at different rates owing to the dependence of the kinetic parameters on crystallographic orientation. Slightly sensitized materials have localized attack of some
grain boundary areas superimposed on the uniform dissolution, while heavily
sensitized materials have entire grains circled. This test allows a rapid estimation
of sensitization with a minimum of equipment.
A second example of the utility of galvanostatic testing is from an investigation of surface treatments and alloying on the dealloying of aluminum bronzes.
Kelly and Scully (56) used a 150 µA/cm 2 applied anodic current density for
7 days in simulated ocean water followed by cross-sectional metallography to
differentiate the susceptibilities of five aluminum- and nickel–aluminum–
Passivity and Localized Corrosion
115
bronzes. They found that the test led to dealloying morphologies and relative
susceptibilities that correlated well to those developed in natural seawater over
36 months, though the depths of attack were less.
6. Electrochemical Noise
Recently, electrochemical noise has been promoted as a tool for both corrosion
science and corrosion engineering. The basics behind the concept for localized
corrosion have already been outlined above; by monitoring the galvanic current
between two nominally identical electrodes, or by monitoring the corrosion potential of a single electrode carefully, metastable pitting can be detected. The
localization of the dissolution inherent in localized corrosion implies a separation
of the anodic and cathodic reactions that constitute the corrosion couple. This
physical separation of reactions distinguishes localized corrosion from uniform
corrosion, in which it is traditionally thought that the anodic and cathodic sites
are in very close proximity to one another. The majority of the anodic (oxidative
dissolution) reaction occurs inside the localized corrosion site, while the majority
of the cathodic (reduction) reaction occurs on the boldly exposed surface. Thus
a galvanic couple is created (see Fig. 19). The spatial separation of the processes
necessitates the passage of current between the two sites. This passage of current
leads to the various electrochemical noise signals measured.
Under open circuit conditions, bursts of dissolution at localized corrosion
sites require the generation of bursts of cathodic current from the surrounding
boldly exposed surface. This increased demand typically causes a decrease in the
measured open circuit potential (see Fig. 49). Localized corrosion sites are typically very small (⬍100 µm in diameter). However, the current densities inside
these cavities during transient bursts can be on the order of 1 A/cm 2. These rates
are possible because of the extremely aggressive environments that develop inside localized corrosion sites. Thus, even though the sites are geometrically small,
they can influence the electrochemical potential of the much larger boldly exposed surface on which the kinetics are far slower. This difference in relative
current densities on separated anodes and cathodes is what accounts for the ability
to detect the electrochemical noise associated with localized corrosion. When the
potential of the surface is controlled with an external device, the same burst of
dissolution requires the device to supply a burst of current, which can be recorded
(see Fig. 25). Usually, these bursts are transient, with temporary repassivation
of the localized corrosion site occurring and allowing the system to return to the
previous steady-state condition. On a metal surface of appreciable size (⬎1 cm 2),
there can be many localized corrosion sites. They will usually propagate individually, so that a series of current (or potential) fluctuations are observed because
of the summation of the signals from the individual sites. These fluctuations are
referred to as electrochemical noise. Since electrochemical noise can often be
116
Chapter 3
Figure 49 Electrochemical time series of galvanically coupled AA2024-T3 (ST) in
1 M NaCl. No deaeration and 0.01 cm 2 exposure area. (a) Current and (b) open circuit
potential. The horizontal dashed lines represent the mean pitting (top) and transition (bottom) potentials of high purity Al at this Cl ⫺ concentration. (Data courtesy of Sheldon T.
Prude, University of Virginia.)
Passivity and Localized Corrosion
117
observed under open circuit conditions, it has been hailed as the only truly noninvasive electrochemical method. An example of electrochemical noise associated with the pitting of stainless steel is shown in Fig. 50.
Changes in the noise signal are often taken as indications that conditions
are favorable for pit initiation to occur. Thus, if one is monitoring corrosion of a
material in a process stream, corrective action can be taken. The disadvantage of
noise monitoring is that it does not give sufficient information about what level
of metastable pitting is acceptable. For example, there may be literally millions of
metastable pits forming and repassivating in a vessel wall, but only one needs to
penetrate completely. It is impossible to differentiate between conditions that will
allow this and those in which the extent of pitting is negligible. In addition, the
noise from crevice corrosion is often extremely hard to detect owing to the
shielding associated with its formation. Experience and correlations with coupon
exposures are critical factors in the use of noise for localized corrosion monitoring.
One way to divide the types of electrochemical noise is by the manner in
which it is collected. Potential noise refers to measurements of the open circuit
potential of an electrode versus either a reference electrode or a nominally identical electrode. While measurements with a conventional reference electrode have
the advantage of being relatable to thermodynamic conditions, these reference
electrodes have their own noise associated with them that could complicate analysis. In addition, the application of noise monitoring to field conditions would be
Figure 50 Electrochemical noise (spontaneous potential and current fluctuations) associated with the metastable pitting of austenitic stainless steel. (From Ref. 57.)
118
Chapter 3
much more attractive if maintenance of the reference electrode were not required.
Since typically the fluctuations of the signal are the most important aspect, rather
than the absolute value of the potential, the use of an electrode nominally identical
to the working electrode has become popular. Current noise can occur with two
types of experimental arrangements. In one, measurements are made of the current that passes between two nominally identical electrodes that are exposed to
the same environment and connected through a zero resistance ammeter (ZRA).
The fluctuations in this coupling current are due to each electrode becoming more
or less anodic with respect to the other as a function of time. The initiation, shortterm propagation, and repassivation of a pit on one electrode, while the other
remains passive, is one example. A second situation in which current noise can
be generated is during a potentiostatic experiment in which the current necessary
to hold the interfacial potential constant fluctuates. The origin of these fluctuations is the same as those in the ZRA arrangement, but in this case it is the
potentiostat that supplies the current, and the transients are only of one polarity
(since the potentiostat never “pits”). All types of measurements of electrochemical noise described have been used to study corrosion processes. Most field applications have involved a three-electrode probe system. Two electrodes are connected via a ZRA and the current noise is measured. The potential of this couple
is then measured against the third electrode in order to monitor the potential noise
associated with the same processes. This approach has been found useful in that
it allows an additional correlation (between the two types of noise measurements)
to be made.
7. Analysis Methods and Precautions
Analysis methods for electrochemical noise data can be separated into three categories, (1) deterministic, (2) statistical, and (3) spectral. Deterministic methods
involve the use of mixed potential theory to explain the oscillations that occur.
For example, if the ZRA current increases suddenly while the potential difference
between the two current electrodes and the potential electrode increases, localized
corrosion has likely initiated on one of the current electrodes. A common pitfall
in such a measurement is that if a nominally identical “reference” electrode is
used, it could pit as well, leading to no change in potential versus the coupled
electrodes. Due to the need for careful interpretation, deterministic methods are
not widely used.
Statistical methods are the most popular techniques for EN analysis. The
potential difference and coupling current signals are monitored with time. The
signals are then treated as statistical fluctuations about a mean level. Amplitudes
are calculated as the standard deviations root-mean-square (rms) of the variance
according to (for the potential noise)
Passivity and Localized Corrosion
σE ⫽
119
√
∑ i (E i) 2
N⫺1
By taking the ratio of the standard deviation of the potential signal to that of the
coupling current signal, a parameter with the units of resistance (or Ω-cm 2 when
corrected for area) can be calculated. This ratio has been termed the noise resistance, R n , by Eden and Rothwell (57) and has been found to correlate to the
polarization resistance, R p , to be discussed in Chapter 4. Localized corrosion
indices have also been proposed (58), though none have been sufficiently correlated with other measurements to allow generalizations to be made.
Spectral analysis of EN generally uses the fast Fourier transform (FFT) or
other algorithm to convert the signal from the time domain to the frequency
domain. This transformation displays the frequency content of the signal, i.e.,
the amount of the signal power as a function of frequency. Generally, EN of
interest to corrosion studies has most of its power in the range of 0.01 to 1 Hz.
A typical FFT spectrum for potential noise is shown in Fig. 51 for carbon steel
pitting. As with the pitting index, a number of workers have published correlations between parameters describing the FFT spectra and localized corrosion behavior, but the correlations are not extendable to other systems.
Correlations between noise measurements and corrosion processes have
been reported for uniform corrosion as well as pitting, crevice corrosion, and
stress corrosion cracking in individual systems. Dawson et al. (59) found that
the ratio of the root-mean-square (rms) amplitudes of the potential and current
noise (which they termed the noise resistance, R n) correlated well with both the
polarization resistance determined by conventional methods and by weight loss
of steel in acid. By using different solution compositions, different types of attack
were created, and they found qualitative differences between the electrochemical
noise signatures for uniform, pitting, and crevice corrosion. A number of workers
have correlated noise measurements to the occurrence of localized corrosion.
Pitting has been the most studied, with applications with steels (60), stainless
steels in Cl ⫺ (61–63), and aluminum alloys (64,65). Crevice corrosion of stainless
steel has also received some attention, especially in differentiating it from pitting
(61). A number of applications of noise to stress corrosion cracking have been
published (66–69). For example, the group at Harwell Lab in the UK has shown
that current noise can be correlated with the nucleation and growth of stresscorrosion cracks in stainless steel exposed to thiosulfate at room temperature (67)
as well as in BWR conditions (pure water, 288°C) (68). Newman et al. (69)
correlated electrochemical noise with acoustic emission and discontinuous crack
growth in brass exposed to nitrite solution. Eden et al. (66) correlated the shape,
frequency, and magnitude of both current and potential noise of steel exposed
to CO/CO 2 solutions with the observed cracking. Loto and Cottis (70) found that
120
Chapter 3
Figure 51 Fast Fourier transform of the potential noise from two nominally identical
carbon steel electrodes exposed to 0.2 M HCl ⫹ 0.5 M NaCl ⫹ 0.15 M NaNO 2 . (Data
courtesy of J. Yuan, M. Inman, T. Lunt, J. Hudson, University of Virginia.)
not only did the amplitude of the potential noise increase during the cracking of
aluminum alloy 7075 in chloride solution, but also the standard deviation calculated from the noise signal increased as well.
In the absence of a fundamentally based theory of electrochemical noise
that has been thoroughly tested, the utility of the technique should be demonstrated on a case-by-case basis. For example, the reliance upon purely empirical
correlations leaves open the possibility of changes in some process variable causing changes in the noise signal but not in the corrosion process or vice versa. Of
utmost importance is the correlation of noise data to other measurements such
as conventional electrochemical measurements and coupon testing. Recently,
Huet and Bertocci (72) have made important progress in putting noise resistance
measurements on a firmer theoretical basis.
Passivity and Localized Corrosion
V.
121
SUMMARY AND CONCLUSIONS
The goals of this chapter were (1) to provide an introduction to the science behind
passivity and its breakdown, (2) to furnish a framework for understanding the
conditions under which localized corrosion occurs and how external variables
affect it, (3) to give a brief overview of the accelerated coupon exposure tests
used to determine localized corrosion susceptibility, including the reasons why
each works, and (4) critically to introduce a variety of electrochemical techniques
that can provide important information concerning localized corrosion susceptibility if they are used correctly. None of the methods discussed is perfect or a
panacea, but when they are used judiciously and in combination with each other,
a better picture of the localized corrosion process can be gained, even in complicated solutions. This allows for better informed decisions on alloy selection, process alteration, or failure analysis. While prediction of localized penetration rate
remains a goal of electrochemical testing, recent applications of statistics to the
process appear promising.
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4
The Polarization Resistance
Method for Determination of
Instantaneous Corrosion Rates
OVERVIEW
The polarization resistance method utilized for determination of instantaneous
corrosion rates of metals is reviewed. The fundamental assumptions in electrode
kinetics that govern the technique are restated. Error-producing factors such as
high excitation voltage amplitude, insufficiently slow scan rate or inadequate polarization hold period, high solution resistance, presence of competing reduction–
oxidation reactions, and nonuniform current and potential distributions are discussed with the goal of defining conditions and circumstances where these complicating factors are important.
I.
INTRODUCTION
A variety of methods such as electrical resistance, gravimetric-based mass loss,
quartz crystal microbalance-based mass loss, electrochemical, and solution analysis methods enable the determination of the corrosion rates of metals. The polarization resistance method, based on electrochemical concepts, enables determination of instantaneous interfacial reaction rates such as corrosion rates and
exchange current densities from a single experiment. In contrast, electrical resistance change, gravimetric and quartz crystal microbalance mass loss, as well as
solution analysis for metallic cations all provide historical or integrated mass loss
information from corrosion that has occurred over some period of time. Therefore
instantaneous rates cannot be determined from a single measurement using these
other methods. Instead, the derivative of multiple measurements over time provides rate information.
125
126
Chapter 4
II. POLARIZATION RESISTANCE METHOD
A.
Review of the Governing Electrode Kinetics
in Corrosion Processes
The following relationship is experimentally observed between applied electrochemical current density and potential for a corroding electrode in the absence
of competing reduction–oxidation reactions (1,2). The applicability of this relationship relies on the presence of a single charge transfer controlled cathodic
reaction and a single charge transfer controlled anodic reaction.
冢 冤
i app ⫽ i corr exp
冥
冤
冥冣
2.3(E ⫺ E corr )
⫺2.3(E ⫺ E corr )
⫺ exp
βa
βc
(1)
where β a and β c are the anodic and cathodic Tafel parameters (∂E/∂ log i app )
given by the slopes of the polarization curves in the anodic and cathodic Tafel
regimes, respectively. E-log(i app ) data govern by such kinetics are shown in Fig. 1.
E corr is the corrosion potential. E is an applied potential such that E ⫺ E corr is ∆E,
and i corr is the corrosion current density. This relationship provides the basis for
the electrochemical polarization technique as applied to a corroding electrode at
its corrosion potential.
Figure 1 E–log(i app ) data for hypothetical corroding interfaces with R p ⫽ 100 and 10,000
ohm-cm2 and β a ⫽ β c ⫽ 60 mV/decade. The two cases produce corrosion current densities
of 130.4 and 1.3 µA/cm2, respectively. The Tafel slope is obtained from E–log(i app ) data at
high overpotential. The open circuit potential is arbitrarily selected to be 0 mV.
The Polarization Resistance Method
127
B. The Derivation of the Polarization Resistance
Many investigators have experimentally observed that i app was approximately linearly related to applied potential within a few millivolts of polarization from E corr
(3). Stern and Geary simplified the kinetic expression to provide an approximation to the charge transfer controlled reaction kinetics given by Eq. (1) for the
case of small overpotentials with respect to E corr (4–6). Equation (1) can be mathematically linearized by taking its series expansion (e.g., e x ⫽ 1 ⫹ x ⫹ x 2 /2! ⫹ x 3 /
3! ⫹ x 4 /4! . . .) and by neglecting higher terms when ∆E/β ⬍ 0.1. This simplified
relationship has the form
R p (ohm ⫺ cm2) ⫽
冤∆i∆E 冥
app
⫽
(E⫺E corr )→0
冢
β aβ c
2.3i corr (β a ⫹ β c)
冣
(2)
Rearranging, we obtain
i corr ⫽
冢
冣
β aβ c
1
B
⫽
(2.3R p ) β a ⫹ β c
Rp
(3)
where R p is the polarization resistance given by (∂E/∂i) at t ⫽ ∞, ∆E ⫽ 0 (ohmcm2 ), and B is a proportionality constant. Note that R p in units of ohms is obtained
from E–I data if current is not normalized by electrode area. Such data must be
multiplied by electrode area to yield R p (ohm-cm2 ). If electrode area is doubled
then the measured R p value in ohms is halved, but R p (ohm-cm2 ) would be the
same since the electrode area is doubled. This gives the result that corrosion rate
per unit area is independent of electrode surface area. However, the working
electrode area must be known to calculate corrosion rate. Note also that the proportionality constant, B, is dominated by the smaller of the two anodic and cathodic Tafel slopes, if unequal. Therefore cathodic mass transport control such
that β c → ∞ results in B ⫽ β a /2.3. Similarly, anodic mass transport control results
in B ⫽ β c /2.3 (7). Knowledge of R p , β a , and β c enables direct determination of
the corrosion rate at any instant in time using Eq. (3) (4–9). i app is often approximately linear with potential within ⫾5 to 10 mV of E corr, as in Fig. 2. The slope
of this plot is ∆E/∆i. When determined from a tangent to the E–i curve at E corr
as shown in Fig. 2, it defines the polarization resistance. Consequently, this
method is often called the linear polarization method (LPR). The slope is independent of the degree of linearity (3), although the extent of the approximately linear
E–i region can vary considerably among corroding systems, as will be discussed
below.
The fact that the corrosion rate is inversely proportional to the polarization
resistance is clearly seen by Eq. (3). Taking the logarithm of this equation, it is
seen that log i corr versus log R p is linear with a slope of ⫺1 and has the intercept
log B 3.
128
Chapter 4
(a)
(b)
Figure 2 Hypothetical E–i polarization resistance data for hypothetical corroding interfaces with R p ⫽ 100, 1000, and 10,000 ohms (assumed 1 cm2 ) and β a ⫽ β c ⫽ 60 mV/
decade. The three cases produce corrosion current densities of 130.4, 13.0, and 1.3 µA/
cm2, respectively. Plots (a) and (b) of the same data provide different current scales to
indicate the nonlinearity in each case. Plot (c) shows the linear relationship between
log(R p ) and log(i corr). (From Ref. 8.)
The Polarization Resistance Method
129
(c)
log(R p ) ⫽ log B ⫺ log(i corr )
(4)
Stern and Wiesert (8) confirmed such a relationship over a six-order-of-magnitude change in corrosion rate for corroding systems or exchange current density
for reduction–oxidation systems*, as is illustrated in Fig. 2(c).
* This review focuses on corroding systems. However, the concept of polarization resistance applies
equally well to reduction–oxidation systems. Here, the exchange current density, i o, may be calculated from the polarization resistance, where R is the ideal gas constant, T is the temperature, and
α a and α c are the anodic
R p (ohm-cm2 ) ⫽
冤∆E∆i 冥
⫽
(E⫺E rev )→0
冢
冣
RT
i o F(α a ⫹ α c )
and cathodic multistep electron transfer coefficients, respectively, for the reduction–oxidation process.
130
C.
Chapter 4
Time Domain Methods for Determining
the Polarization Resistance
ASTM standards D-2776 (9) and G-59 (10) describe standard procedures for
conducting polarization resistance measurements. Potentiodynamic (11), potential step, and current-step methods (12,13) have all been described to determine
the linear E–i behavior of an electrode near E corr. The current step method has
been cited to be faster than potentiodynamic methods and less susceptible to
errors associated with drift in E corr. This issue will be discussed below. Regardless
of the method used, independent determination of β a and β c is still required.
Alternative techniques exploit nonlinearity at larger overpotentials. Note
that nonlinearity invalidates Eq. (3). However, the nonlinearity, if treated properly, can enable determination of β a and β c without excessive polarization. The
Oldham–Mansfeld method calculates i corr from nonlinear E vs. i app data obtained
within ⫾30 mV of E corr without the need for high overpotential determination of
β a and β c (14). Computerized curve fitting can exploit nonlinearity to calculate
β a and β c from low overpotential data, avoiding the destructive nature of large
overpotentials (15). The Mansfeld technique substitutes Eq. (3) into Eq. (1), eliminating i corr (15). β a and β c are determined from the best fit of the resulting expression containing β a and β c as unknowns to a nonlinear plot of ∆E vs. 2.3i app R p.
R p is determined in the usual way from the slope of a linear tangent to the E vs.
i app data at E corr. i corr is subsequently determined from Eq. (3) for known values
of R p, β a, and β c. In this technique, elimination of i corr enables determination of
only two unknowns by fitting. Advancements in computerization enables a fit to
Eq. (1), but this requires simultaneous determination of three unknowns. Consequently, extremely high quality E–log(i) data that is corrected for ohmic voltage
error and does not contain other sources of overpotential (i.e., mass transport
overpotentials) is required.
D.
Electrochemical Impedance Methods for Determination
of Polarization Resistance
The complications and sources of error associated with the polarization resistance
method are more readily explained and understood after introducing electrical
equivalent circuit parameters to represent and simulate the corroding electrochemical interface (1,16–20). The impedance method is a straightforward approach for analyzing such a circuit. The electrochemical impedance method is
conducted in the frequency domain. However, insight is provided into complications with time domain methods given the duality of frequency and time domain
phenomena. The simplest form of such a model is shown in Fig. 3a. The three
parameters (R p, R s, and C dl ) that approximate a corroding electrochemical inter-
The Polarization Resistance Method
131
(a)
(b)
Figure 3 Electrical equivalent circuit model commonly used to represent an electrochemical interface undergoing corrosion. R p is the polarization resistance, C dl is the double
layer capacitance, R ct is the charge transfer resistance in the absence of mass transport and
reaction intermediates, R D is the diffusional resistance, and R S is the solution resistance. (a)
R p ⫽ R ct when there are no mass transport limitations and electrochemical reactions involve no absorbed intermediates and nearly instantaneous charge transfer control prevails.
(b) R p ⫽ R D ⫹ R ct in the case of mass transport limitations.
132
Chapter 4
face are shown. Here R s is the solution resistance, and C dl is the double-layer
capacitance that arises whenever an electrochemical interface exists. The algebraic sum of R s and R p is measured when a dc measurement is performed (e.g.,
zero ac frequency, long hold time during potential or current step, or slow scan
rate approaching zero). This is because impedance associated with a capacitor
approaches infinity as frequency approaches zero, and parallel electrical circuit
elements are dominated by the element with the smallest impedance. Therefore
the sum of R s and R p is measured at zero frequency. The true corrosion rate will
be underestimated when R s is appreciable. Conversely, any experiment conducted
at too fast a voltage scan rate (short time, or too high an ac frequency) causes
the algebraic sum of the ohmic resistance and the resultant frequency-dependent
parallel impedance of the parallel resistive–capacitive network to be measured.
This value will be lower than the sum of R p and R s determined at an infinitely
slow scan rate or frequency because current leaks through the parallel capacitive
element at higher scan rate owing to its low impedance at high frequency. This
will usually result in an overestimation of the true corrosion rate. These complications in scan rate or current-step hold time can be overcome or at least detected
more easily by using the electrochemical impedance method (1,16,20).
ASTM standard G 106 provides a standard practice for verification of algorithm and equipment for electrochemical impedance measurements (20). The
standard also contains an appendix reviewing the technique. Typically a smallamplitude sinusoidal potential perturbation is applied to the working electrode
at a number of discrete frequencies, ω. At each one of these frequencies, the
resulting current waveform will exhibit a sinusoidal response that is out of phase
with the applied potential signal by an amount depending upon the circuit parameters of the corroding interface and has a current amplitude that is inversely proportional to the impedance of interface. This electrochemical impedance, Z(ω), is
the frequency-dependent proportionality factor that acts as a transfer function by
establishing a relationship between the excitation voltage signal and the current
response of the electrochemical system:
Z(ω) ⫽
E(ω)
i(ω)
(5)
where E ⫽ the time-varying voltage across the circuit, E ⫽ E o sin(ωt), i ⫽ the
time-varying current density through the circuit, i ⫽ i o sin(ωt ⫹ θ), Z(ω) ⫽ the
impedance (ohm-cm2 ), and t ⫽ time (s).
Z(ω) is a complex-valued vector quantity with real and imaginary components whose values are frequency dependent:
Z(ω) ⫽ Z′(ω) ⫹ jZ″(ω)
(6)
The Polarization Resistance Method
133
Figure 4 Cartesian coordinate system with imaginary j notation depicting an impedance
vector |Z| and its real and imaginary components Z ′ and Z ″ as well as phase angle θ.
where Z′(ω) ⫽ the real component of impedance, Z′(ω) ⫽ |Z(ω)|cos(θ), Z″(ω)
⫽ the imaginary component of impedance where Z″(ω) ⫽ |Z(ω)|sin(θ), j 2 ⫽ the
square of the imaginary number, or ⫺1, |Z(ω)| ⫽ the impedance magnitude,
where |Z(ω)| ⫽ (Z′(ω)2 ⫹ Z ″(ω)2 )1/2, and the phase angle (θ) ⫽ tan⫺1 Z″(ω)/
Z ′(ω). An example of an impedance Z(ω) vector with real and imaginary (capacitive) components is shown in the complex plane plot in Fig. 4. The impedance
vector indicated changes as a function of ω and is illustrated at a single frequency
here.
The electrochemical impedance is a fundamental characteristic of the electrochemical system it describes. A knowledge of the frequency dependence of
impedance for a corroding system enables a determination of an appropriate
equivalent electrical circuit describing that system. Such a circuit is typically
constructed from resistors and capacitors. Table 1 shows the transfer functions
Table 1 Linear Circuit Elements
Commonly Used in Electrochemical
Impedance
Circuit component
Resistor (R)
Capacitor (C)
Inductor (L)
Impedance
Z(ω) ⫽ R
Z(ω) ⫽ ⫺1/jωC
Z(ω) ⫽ jωL
134
Chapter 4
for resistors, capacitors, and inductors. The capacitor can be a double layer capacitance, C dl, alone, or a double layer capacitance and a pseudo-capacitance, C θ,
associated with an adsorbed intermediate, where q F is the charge to form a fractional surface coverage, of such an intermediate.
CT ⫽
冢 冣 冢 冣冢 冣
dq
dE
⫽
T
dt
dE
dq T
dt
⫽
T
dq T
dE
(7)
where C dl ⫽ dq dl /dE and C θ ⫽ dq F /dE. Figure 3a illustrates a simple equivalent
electrical circuit model commonly used to represent an actively corroding metal.
The following expression describes the impedance for that system:
Z(ω) ⫽ R s ⫹
Rp
(1 ⫹ ω2R 2pC 2 )
⫺
jωCR 2p
(1 ⫹ ω2R 2pC 2 )
(8)
where ω ⫽ 2πf, the frequency of the applied signal (rad/s), f ⫽ the frequency
of the applied signal (Hz), C ⫽ the interfacial capacitance (F/cm2 ). The complex
plane, Bode magnitude, and phase plots resulting from a circuit such as is shown
in Fig. 3a and described by Eq. (8) are shown for three different values of R p in
Fig. 5. It can be seen that at very low frequencies,
Z ω→0 (ω) ⫽ R s ⫹ R p
(9)
while at very high frequencies,
Z ω→∞ (ω) ⫽ R s
(10)
Thus the determination of R p is attainable in media of high resistivity because
R p can be mathematically separated from R s by taking the difference between
Z(ω) obtained at low and high ω (R p ⫽ Z ω→0 ⫺ Z ω→∞ ). In other words, determination of R p can be achieved by subtracting the results of Eq. (10) from the results
of Eq. (9). This is a particularly useful approach if R s is nearly the same value
as R p, as shown in Fig. 6. This situation may result from either low conductivity
environments or placement of the reference electrode far away from the working
electrode. Note that corrosion rate determination in Eq. (3) requires knowledge
of β a and β c, which are not obtained in the impedance experiment.
It should be noted that the presence of diffusion controlled corrosion processes does not invalidate the EIS method but does require extra precaution. In
the case of a finite diffusional impedance added in series with the usual charge
transfer parallel resistance shown in Fig. 3b, the frequency-dependent diffusional
impedance can be described as (21)
The Polarization Resistance Method
135
Figure 5 Nyquist, Bode magnitude and Bode phase angle plots for hypothetical corroding interfaces with R p ⫽ 10, 100, or 1,000 ohms, C dl ⫽ 100 µF, and R s ⫽ 10 ohms using
the electrical equivalent circuit model of Fig. 3a.
Z D (ω) ⫽ R D
( j ωs)
冤tanh√
√( j ωs) 冥
(11)
Here, s ⫽ l 2eff /D, where l eff is the actual finite diffusion length and D is the diffusivity of the diffusing species. The value of Z D (ω) approaches R D as ω → 0. The
low frequency required to obtain R D depends on the value of s. The larger the
value of s, the lower the frequency required. Therefore R p, defined in Eq. (9) as
[∆E/∆i app] as ω → 0, becomes the sum of the charge transfer controlled, R ct and
136
Chapter 4
Figure 6 Nyquist, Bode magnitude and Bode phase angle plots for hypothetical corroding interfaces with R p ⫽ 100 ohms, C dl ⫽ 100 µF, and R s ⫽ 1, 10, or 100 ohms using
the electrical equivalent circuit model of Fig. 3a.
diffusion controlled, R D, contributions to the polarization resistance, assuming
that R D ⫹ R ct ⬎⬎ R s.
R p ⫽ R ct ⫹ R D
(12)
A very low frequency or scan rate may be required to obtain R p under such
circumstances, as is illustrated in Fig. 7. Here an l eff of 0.1 cm and a D ⫽ 10⫺5
cm2 /s require that a frequency below 0.1 mHz be implemented to obtain R p.
The Polarization Resistance Method
137
Figure 7 Nyquist, Bode magnitude and Bode phase angle plots for hypothetical corroding interfaces with R ct ⫽ 100 ohms, R d ⫽ 1000 ohms, C dl ⫽ 100 µF, R s ⫽ 10 ohms,
l eff ⫽ 0.1 cm, and D ⫽ 10⫺5, 10⫺6, and 10⫺7 cm2 /s using the electrical equivalent circuit
model of Fig. 3b.
E.
Complications with Polarization Resistance
Measurement by the Linear Polarization Method
Error-producing complications related to the polarization resistance method and
possible remedies are reported in the literature (14,15,22–27). The most common
errors involve (1) invalidation of the results through oxidation of some other
electroactive species besides the corroding metal in question, (2) a change in the
open-circuit or corrosion potential during the time taken to perform the measurement, (3) use of ∆E that is too large, invalidating the assumption of a linear
relationship between i app and E required by Eq. (2) (i.e., ∆E/β ⬍ 0.1), (4) too
138
Chapter 4
fast a voltage scan rate or insufficient potential hold time, (5) ohmic solution
resistance, and (6) current and potential distributions.
F.
Oxidation or Reduction of Some Other
Electroactive Species
If the E corr of the corroding system is close to the reversible electrode potential of
either the anodic or the cathodic reactions, as well as near the reversible electrode
potential of any other redox process, then the corrosion rate will likely be overestimated. This situation can be experimentally ascertained by the use of any noncorroding, readily polarizable electrode, such as platinum, gold, or high-density
graphite. These materials will assume a “redox” potential that is governed by the
dominant parallel reduction–oxidation processes occurring in the system. If the
corrosion potential of the corroding metal is very close to the “redox” potential
of such an electrode, then E corr may be close to a reversible electrode potential.
The error in estimation of the corrosion rate depends on the exchange current
density for the redox process, i corr, β a, β c, and the difference in potentials between
E corr and the reversible electrode potential in question (27). A cyclic voltammogram on the platinum electrode may reveal the approximate reaction rate of any
parallel redox process over the potential range of interest.
G.
Deviations from Linearity Near the Open
Circuit Potential
Deviations from linearity have been discussed in the literature (27–29). At issue
is the question of when the range of ∆E is small enough so that the higher terms
in the series expansion of Eq. (1) can be reasonably neglected. This requires
that ∆E/β ⬍⬍ 1. Clearly, the extent of the E–i region, where Eq. (2) is a good
approximation of Eq. (1), depends on the values of the Tafel parameters β a and
β c. An approximately linear region can be restricted to ⫾2 mV for low values
of β a and β c and can be greater than 60 mV for high values. This curvature has
been described mathematically by (27)
冢 冣
冢
冣
∂ 2i
1
1
⫽ i corr
⫹
2
2
∂E
(β a /2.3)
(β c /2.3)2
(13)
Therefore, the extent of the curvature will depend on i corr, which itself depends
on B/R p and is inversely proportional to the squares of β a and β c. Hence the
curvature will be greater for smaller R p, as indicated in Figs. 2 and 8, and smaller
values of β a and β c. Obviously, the linear regions will differ for anodic versus
cathodic polarization for differing values of β a and β c. Of course, the polarization
resistance is always properly obtained from the tangent of the E–i data in the
The Polarization Resistance Method
139
Figure 8 Second derivative of E–i data (d 2i/dE 2 ) versus (β a ⫹ β c ) for i corr ⫽ 1.305,
13.05, and 130.5 µA/cm2, indicating that the curvature of E–i data is a function of corrosion rate and Tafel parameters.
vicinity of E corr. Stated another way, there will always be finite curvature associated with the true governing electrode kinetic expression given by Eq. (1) when
plotted as E vs. i, as is shown in Fig. 2. Since the E–i behavior of the corroding
electrode will have a finite, albeit small, curvature, the presence of persistent
linearity over a significant potential range may be a clue that ohmic voltage controls E–i behavior (27).
A second related issue is the asymmetry in the E–i response near E corr for
different values of β a and β c. Corrosion involves a cathodic electron transfer
reaction that is different from the metal oxidation reaction. Therefore there is no
fundamental reason why β a and β c should be equal, and they should be expected
to differ. The extent of their difference defines the degree of asymmetry. Asymmetry matters because the extent of the region where Eq. (2) is a good approximation of Eq. (1) then differs for anodic and cathodic polarization (29). The errors
in assuming ⫾10 mV linearity using both the tangent to the E–i data at E corr and
for ⫹10 or ⫺10 mV potentiostatic polarizations have been defined for different
Tafel slopes (30).
H. Voltage Scan Rate, AC Frequency or Hold Time
During Potential or Current Step
Capacitive effects cause hysteresis in small amplitude cyclic voltammogram current density–potential plots (16,31–34). Hysteresis in the current density-applied
potential plot is brought about by combinations of high voltage scan rate, large
140
Chapter 4
interfacial capacitances, and large polarization resistances. High capacitance multiplied by a rapid voltage scan rate causes a high capacitive current, which results
in the hysteresis in cyclic E–i data. Attempting to determine R p at too fast a scan
rate can underestimate its true value as shown by Macdonald (31), leading to an
overestimation of the corrosion rate. This error can be minimized by determining
the polarization resistance at a slow scan rate, or extrapolating the results at several different slow scan rates to zero scan rate (31). Alternatively, one may take
two or more current density measurements from potentiostatic data after long
time periods near E corr to minimize scan rate effects. However, cyclic voltammograms, potential steps, and current steps all represent the Fourier synthesis of
sine waves, and therefore all require that adequate time be taken to perform each
measurement, as will be shown below. This required time period depends on the
R pC time constant of the electrochemical interface for an electrode that does not
involve mass transport controlled reactions.
The maximum scan rate allowed to obtain accurate measurement of the
polarization resistance has been addressed in the literature (35). The governing
principles are best understood through the concepts of impedance and the Bode
magnitude plot for the simplified circuit shown in Fig. 5. Here the maximum
applied frequency allowed to obtain R s ⫹ R p from the low frequency plateau can
be approximated by
f max ⬍ f bp ⫽
1
2πC(R s ⫹ R p )
(14)
where f bp ⫽ an approximation of the lower breakpoint frequency (Hz) and f max
⫽ the maximum test frequency (Hz). Thus it can be seen from Eq. (14) that
increasing values of C, R sol, or R p dictate that a lower f max is required to obtain
R p ⫹ R sol at Z ω→0 accurately (see Fig. 5). Capacitances may become larger than
that expected from the double-layer capacitance alone in the presence of adsorption psuedo-capacitance. Such a psuedo-capacitance may be caused by an adsorbed intermediate with some fractional monolayer coverage. Corrosion of steel
in concrete can complicate LPR measurements owing to very large apparent capacitances that may in fact represent mass transport control of oxygen reduction.
One way that R p may be increased is by passivity. Another is by diffusion controlled corrosion such that R p ⫽ R CT ⫹ R D. A 1 mHz frequency is typically chosen
as a reasonable initial choice of f max, but it is obvious from Eq. (14) that either
lower or higher frequencies may be required depending upon the circumstances.
Since the magnitudes of C, R s, and R p are not known explicitly, a priori, prudence
dictates that f max be selected as one tenth of the estimated f bp. Mansfeld and Kendig
proposed that f max determined by the impedance method defines the maximum
voltage scan rate (V max ) for the potentiodynamic method (22). This derivation is
The Polarization Resistance Method
141
based on the assumption that the maximum voltage scan rate should not exceed
the maximum rate of change of voltage with time during the sinusoidal voltage
excitation at f max:
V max ⫽
π∆E pp f max
(15)
10
Here ∆E pp is the peak-to-peak voltage excitation. Therefore V max is 0.16 mV/s
assuming a 10 mV peak-to-peak amplitude, for the equivalent circuit shown in
Fig. 2 with R p ⫽ 1000 Ω, R sol ⫽ 10 Ω, and C ⫽ 1000 µF. If ∆E is ⫾5 mV, then
the time required for one complete cyclic voltammogram at such a potential
sweep rate is 125 seconds. However, for a slowly corroding electrode with the
R sol ⫹ R p ⫽ 10,010 Ω, V max becomes 0.0157 mV/s and the time required is 1250
seconds. Similarly, a frequency above the high-frequency breakpoint must be
applied to obtain R s :
f hf ⱖ
1
2πCR s
(16)
Typically, f app must be in the KHz range to determine R s.
In separate but parallel efforts Gabrielli (32), Macdonald (31), and Townley
(33) each discussed the choice of voltage scan rates for accurate R p determination
from small-amplitude cyclic voltammograms.
In these equations a ⫽ R s ⫹ R p, b ⫽ R sR pC, t is time, v ⫽ sweep rate, and
τ ⫽ 1/R sC ⫹ 1/R pC. Time in Eq. (19) can be equated to the sweep rate since t
⫽ ∆E pp /v. All three equations include a term that is independent of voltage scan
rate and a second term that depends on voltage scan rate. The scan-rate-dependent
term becomes negligible at low scan rates. Macdonald (31) and Townley (33)
separately derived the current response of the standard three-element electrical
equivalent circuit (Fig. 3a) to a small-amplitude triangular voltage excitation
冢
冣冢
1
1
2R p
⫽
⫹
R app R s ⫹ R p
R s (R s ⫹ R p )
1
(1 ⫹ e a∆Epp /vb )
冣
(17)
(e.g., a potential sweep at fixed scan rate). The E–i response of this circuit to
the triangular voltage excitation
冢
1
2R 2pC
1
⫽
⫹
Rd Rs ⫹ Rp
∆E(R s ⫹ R p ) 2
冣冢
冣
(e a∆Epp/vb ⫺ 1)
(e a∆Epp /vb ⫹ 1)
v
(18)
142
Chapter 4
is shown to be a complex function of circuit elements, ∆E pp, and the voltage
sweep rate. The results predict an
冢
冣
Rp
1
1
⫽
⫹
e⫺t/τ
R meas R s ⫹ R p
R s (R s ⫹ R p )
(19)
increase in current hysteresis and deviation of R meas from R p ⫹ R s at high scan
rates, as is shown in Fig. 9a. Figures 9b and c show actual experimental results
from a Cu–Ni alloy in flowing seawater. Macdonald characterized the E–i response by the diagonal resistance, R d, the apparent resistance determined from
the tangent to the curve at the end of the sweep before the forward and reverse
sweeps reversal, R app, and the hysteresis current. Townley (33) obtained R meas,
which is similar to the tangent resistance, R app. A plot of experimental 1/R d and
1/R app data versus scan rate is shown in Fig. 9c for the Cu–Ni system. Macdonald
(31) and Townley (33) both deduced that it is possible to determine R p ⫹ R s
from the tangent to the E–i curve at the end of both the forward and reverse
sweeps at much higher scan rates than predicted by Eq. 15. The ideal scan rate
maxima are shown in Figs. 10a and b for the same circuit parameters as examined
above (i.e., R s ⫽ 10 ohms, R p ⫽ 1000 ohms, and C ⫽ 10⫺3 F). Specifically, it
is shown that 1/R meas and 1/R app approach the value 1/(R s ⫹ R p ) at scan rates as
high as 100 mV/s when the slope of the E–i plot is carefully taken at the very
end of the forward or reverse voltage scan. However, accurate determination of
1/(R s ⫹ R p ) from experimental 1/R d values still requires a scan rate below 1 mV/
s, which is in agreement with the predictions from Eq. 15. Unfortunately, the
experimental case of Cu–Ni in seawater shows that a much lower scan rate is
required in a real system (Figs. 9b and c). This problem is discussed further
below.
The equivalence of R app to (R s ⫹ R p ) at fast scan rates must be treated with
caution in real corroding systems. Such an equivalence is only true for ideal fast
charge transfer controlled corrosion processes and ideal double layer capacitances. The presence of either mass transport control or an adsorption pseudocapacitance caused by an adsorbed intermediate that participates in the corrosion
process may complicate the results and the ability to use faster scan rates. The
roles of adsorbed intermediates and mass transport in corrosion may not be observed at fast scan rates because the surface coverage and diffusional boundary
layer does not have time to react and adjust to a very fast change in voltage. R ct
(Fig. 3b) is determined instead of R p. Unfortunately, a sufficiently fast scan rate
that “freezes in” an intermediate coverage may result in large capacitive currents
as well as R app and R d values far below R p. Indeed, Macdonald observed that an
accurate value of R s ⫹ R p was, in fact, not obtained from R app or R d values determined at fast scan rates for a corroding copper–nickel alloy in flowing seawater
(Figs. 9b and c) (31). In contrast, a model like that of Fig. 3a for an ideal R pC
The Polarization Resistance Method
143
(a)
Figure 9 (a) Small-amplitude cyclic voltammograms depicting the E–i response for an
electrical equivalent circuit of Fig. 3 with R p ⫽ 1000 ohms, C dl ⫽ 1000 µF, and R s ⫽ 10
ohms when triangle voltage excitation waveform is applied to a corroding interface at
various scan rates indicated. All results are for the circuit parameters listed above. (b)
Experimental results for 90:10 Cu–Ni in flowing seawater showing cyclic voltammograms
versus voltage scan rate. (c) Reciprocal values of R d and R app versus scan rate from experimental data for 90:10 Cu–Ni in seawater. (D. D. Macdonald. J. Electrochem. Soc. 125
(1978):1443. Reproduced by permission of the Electrochemical Society, Inc.)
144
Chapter 4
(b)
Figure 9 Continued
interface and Eqs. (17–19) suggest that 4–20 mV/s scan rates would be more
than slow enough to obtain an R app value that approaches R p. Experimentally, this
is not the case, as the corrosion rate would be overestimated from such data. In
this system, O 2 reduction is mass transport controlled at the OCP of the Cu–Ni
alloy, and adsorbed intermediates may also exist.
Jones and Greene (38) proposed that a current step method was attractive
because of measurement speed and ability to contend with OCP drift during the
time taken to conduct the measurement. For negligible R s, it has been shown that
the potential transient during a current step is given by
E app ⫽ E corr ⫹ i app R p (1 ⫺ exp⫺t/RpC )
(20)
The Polarization Resistance Method
145
(c)
When t ⱖ 4R pC, E app reaches 98% of its value achieved at infinite time. Therefore
the polarization resistance condition is reached when t ⱖ 4R pC, or ∆E/i app ⫽ R p.
The time required to reach this condition is about 4 s for R p ⫽ 1000 Ω, R s ⫽
10 Ω, and C ⫽ 1000 µF. However, the time required for a slowly corroding
electrode with R p ⫽ 10,000 Ω is about 40 s. Thus in comparison to polarization
scans at the voltage scan rates predicted from Eq. (15), the time required for a
single current step to approach steady state is much less than the time required
to complete a low-amplitude cyclic voltammogram, given exactly the same electrical equivalent circuit parameters. It has also been argued that the measurement
of overvoltages at selected times, after a series of small current steps, produces
∆E vs. i app plots that develop linear slopes approximating the steady state conditions after incomplete short periods of decay (38).
Lastly it should be noted that the time or scan rate issue equally plagues
time as well as frequency domain methods for obtaining R p, since in the time
domain measurement, the triangle waveform is simply the Fourier synthesis of
a series of sinusoidal signal functions. However, voltage sweep, potential step,
and impedance methods should all yield the same value of R p when all the scan
146
Chapter 4
(a)
(b)
Figure 10 Relationship between measured R app, R d, and R meas and scan rate using Eqs.
(17), (18), and (19) for the circuit model of Fig. 3a with R P ⫽ 1000 ohms, C dl ⫽ 1000
µF, and R s ⫽ 10 ohms The true impedance of the system at the limit of zero scan rate
is R s ⫹ R p. The true impedance of the system at infinite scan rate is R s . (a) Linear scale.
(b) Logarithmic scale.
The Polarization Resistance Method
147
rate and AC frequency precautions given above are taken into consideration. This
has been demonstrated by Syrett (39) in a study that produced R p values that
were independent of voltage excitation waveform.
I.
Effect of Solution Resistance
Another frequently encountered complication is the need to correct polarization
data for errors that arise from the contribution of solution resistance, R s. Solution
resistance contributes to a voltage error as well as a scan rate error (2). Since
the applied potential is increased by an ohmic voltage component, an apparent
value of polarization resistance is obtained that overestimates R p by an amount
equal to R s. Consequently, the corrosion rate is underestimated.
J. Nonuniform Current and Potential Distributions
to Polarization Resistance Probes
A dimensionless parameter known as the Wagner number is useful for qualitatively predicting whether a current distribution will be uniform or nonuniform
(2,40,41). This parameter helps to answer the question, Which current distribution
applies to my cell: primary, secondary or tertiary?
The Wagner parameter, W, is the ratio of the kinetic resistance to the ohmic
resistance. The Wagner parameter is the ratio of the true polarization slope given
by the partial derivative, ∂E true /∂i app, evaluated at the overpotential of interest at
constant pressure, temperature, and concentration, divided by the characteristic
length and the solution resistance (2,40).
W⫽
冢 冣冢 冣
κ
L
∂E
∂i
(21)
where κ (or 1/ρ) is the specific solution conductivity (ohm-cm)⫺1 and L is a
characteristic length (cm) or the dimension of “irregularity.” Its value marks the
transition from the primary to the secondary current distribution. When the
Wagner number is much less than one, the ohmic component dominates, and
current and potential distributions are governed primarily by cell geometry. When
it is much larger than one, the kinetic component dominates and the resistance
of the interface primarily governs the current flow from counterelectrode to working electrode. In practice, the primary current distribution is said to exist when
W ⬍ 0.1 and the secondary current distribution exists if W ⬎ 102. We can take the
partial derivative, ∂E/∂i, of any analytical expression describing the interfacial
148
Chapter 4
potential E true as a function of i app or obtain a polarization slope, R p, from experimental E vs. i app data. The partial derivative, ∂E/∂i, has the units of Ω-cm2. The
solution resistance expressed in the same units is (κ/L). The resulting Wagner
number in the low overpotential region where the linear E–i approximation is
valid is
W⫽
Rp
Rs
(22)
Thus the experimenter interested in estimating the current distribution regime
pertinent to their polarization cell can estimate whether the primary or secondary
current distribution applies from knowledge of R p and R s. The corrosion engineer
can use this information in the following way. If the primary current distribution
applies (W ⬍ 0.1), then current distributions are likely to be very nonuniform
unless an ideal cell geometry leading to a uniform primary current distribution
is used. Otherwise, errors in polarization resistance and other kinetic parameters
are likely, because the electrode area actually undergoing polarization differs
from the total area. Low scan rate data still gives R p ⫹ R s, but the area required
to compute a true R p value is uncertain.
Errors in polarization resistance from nonuniform primary or secondary
current distributions have been documented (42). Data presented in the literature
show examples of the extent of such errors (43). Positioning of the reference
electrode at the center, at the edge, and at infinity with respect to the disk-shaped
working electrode altered the apparent polarization resistance value by some
amount relative to the true value. Placement at the edge is typical of flushmounted probes. The source of difference between R p and R eff with position lies
in that no single R s value applies for all electrode positions. In other words, there
is in fact a nonuniform ohmic potential drop over the disk. There can be large
errors depending on reference electrode position (center, infinity, edge), conductivity, and resistance (43). When solution conductivity, κ, and R eff are increased,
the Wagner number becomes larger, indicating a more uniform current distribution and minimization of this source of error. Similarly, counter and reference
electrode placement in low conductivity can alter solution resistance values and
apparent polarization resistance values (44).
III. SUMMARY
The polarization resistance method, when performed properly, enables reliable
determinations of instantaneous corrosion rates (45). Possible sources of error
include violating linearity, high solution resistance, fast scan rates or inadequate
The Polarization Resistance Method
149
hold times, parallel redox reactions, and nonuniform current and potential distributions.
REFERENCES
1. J. O’M. Bockris, A. K. N. Reddy. Modern Electrochemistry 2. New York, Plenum
Press, 1970.
2. E. Gileadi. Electrode Kinetics for Chemists, Chemical Engineers and Materials Scientists. VCH, 1993.
3. D. A. Jones. Principles and Prevention of Corrosion. New York, Macmillan, 1992.
4. M. Stern, R. M. Roth. J. Electrochem. Soc. 104 (1957):390.
5. M. Stern, A. L. Geary. J. Electrochem. Soc. 105 (1958):638.
6. M. Stern, A. L. Geary. J. Electrochem. Soc. 104 (1957):56.
7. I. Epelboin, C. Gabrielli, M. Keddam, H. Takenouti. In: Electrochemical Corrosion
Testing, STP 727 (F. Mansfeld and U. Bertocci, eds.). ASTM, 1981, p. 150.
8. M. Stern, E. D. Weisert. Experimental observations on the relation between polarization resistance and corrosion rate. ASTM Proceedings 59, American Society for
Testing and Materials, 1959, p. 1280.
9. Test methods for corrosivity of water in the absence of heat transfer (electrical methods), D Annual Book of ASTM Standards 03.02, ASTM, pp. 2776–2779.
10. Standard practice for conducting potentiodynamic polarization resistance measurements. ASTM Standard G-59, ASTM Annual/Book of Standards, ASTM.
11. F. Mansfeld. In: Electrochemical Techniques for Corrosion (R. Baboian, ed.). Houston, TX, NACE, 1977, p. 18.
12. D. A. Jones, N. D. Greene. Corrosion 22 (1966):198.
13. D. A. Jones. Corrosion 39 (1983):444.
14. K. B. Oldham, F. Mansfeld. Corros. Sci. 13 (1973):813.
15. F. Mansfeld. J. Electrochem. Soc. 120 (1973):515.
16. D. D. MacDonald, M. C. H. McKubre. In: Electrochemical Corrosion Testing, STP
727 (F. Mansfeld and U. Bertocci, eds.). ASTM, 1981, p. 110.
17. A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications. John Wiley, 1980.
18. F. Mansfeld. Corrosion 36(5) (1981):301.
19. F. Mansfeld, M. W. Kendig, S. Tsai. Corrosion 38 (1982):570.
20. Practice for verification of algorithm and equipment for electrochemical impedance
measurements. G 106 Annual Book of ASTM Standards 03.02, ASTM.
21. D. R. Franceschetti, J. R. Macdonald. Electroanal. Chem. 101 (1979):307.
22. F. Mansfeld, M. Kendig. Corrosion 37(9) (1981):556.
23. R. Bandy, D. A. Jones. Corrosion 32 (1976):126.
24. M. J. Danielson. Corrosion 36(No. 4) (1980):174.
25. J. C. Reeve, G. Bech-Nielsen. Corros. Sci. 13 (1973):351.
26. L. M. Callow, J. A. Richardson, J. L. Dawson. Br. Corrosion J. 11 (1976):132.
27. F. Mansfeld, K. B. Oldham. Corrosion Sci. 27 (1971):434.
150
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
Chapter 4
S. Barnartt. Corros. Science 9 (1969):148.
R. L. Leroy. Corrosion 29 (1973):272.
F. Mansfeld. Corrosion 29 (1973):397.
D. D. MacDonald. J. Electrochem. Soc. 125 (1978):1443.
C. Gabrielli, M. Keddam, H. Takenouti, V. Kirk, F. Bourelier. Electrochem. Acta
24 (1979):61.
D. W. Townley. Corrosion 47 (1991):737.
D. D. Macdonald. J. Electrochem. Soc. 125 (1979):1977.
F. Mansfeld, M. Kendig. Corrosion 37 (1981):545.
S. R. Taylor, E. Gileadi. Corrosion 51 (1995):664.
K. Videm, R. Myrdal. Corrosion 53 (1997):734.
D. A. Jones, N. D. Greene. Corrosion 22 (1966):198.
B. Syrett, D. D. MacDonald. Corrosion 35 (1979):505.
J. Newman. Electrochemical Systems. Englewood Cliffs, NJ, Prentice Hall, 1973.
C. Wagner. J. Electrochem. Soc. 101 (1959):225.
W. C. Ehrhardt. In: The Measurement and Correction of Electrolyte Resistance in
Electrochemical Cells. ASTM STP 1056 (Scribner, Taylor, eds.), (1990), pp. 5–26.
K. Nisancioglu. Corrosion J. 43 (1987):258.
M. A. Pech-Canul, A. A. Sagues, P. Castro. Corrosion J. 54(8) (1998):663.
J. R. Scully. Corrosion 56(2) (2000):199.
5
The Influence of Mass Transport
on Electrochemical Processes
I.
INTRODUCTION
In order to make a valid assessment of the thermodynamic tendency for corrosion
to occur, the chemical potentials of all relevant species that participate in the
reaction and their concentrations, as well as the system temperature and pressure,
must be known. While thermodynamic prediction methods (i.e., Pourbaix diagrams) can be used to determine whether an electrochemical reaction can occur,
information on electrochemical reaction rates is not provided.
The information required to predict electrochemical reaction rates (i.e., experimentally determined by Evans diagrams, electrochemical impedance, etc.)
depends upon whether the reaction is controlled by the rate of charge transfer or
by mass transport. Charge transfer controlled processes are usually not affected
by solution velocity or agitation. On the other hand, mass transport controlled
processes are strongly influenced by the solution velocity and agitation. The influence of fluid velocity on corrosion rates and/or the rates of electrochemical
reactions is complex. To understand these effects requires an understanding of
mixed potential theory in combination with hydrodynamic concepts.
In this chapter you will learn that proper assessment of mass transport controlled corrosion reactions requires knowledge of the concentration distribution
of the reacting species in solution, certain properties of the electrolyte, and the
geometry of the system. A rigorous calculation of mass transport controlled reaction rates requires detailed information concerning these parameters. Fortunately,
many of the governing equations have been solved for several well-defined geometries.
This chapter is divided into two sections. The first will present some of
the basic phenomenological observations regarding solution velocity effects and
provide a framework for explaining them using mixed potential electrochemical
theory. The concept of the limiting current density will be introduced. The second
151
152
Chapter 5
section will review the mass transport correlations developed for the rotating disk
and cylinder electrodes as well as the pipe and impinging jet geometries. Lastly,
the effect of the fluid shear stress on protective surface films will be discussed.
The emphasis of the chapter is on single-phase liquid systems. In cases where
solid particles or bubbles interact with metallic surfaces to produce mechanical
and electrochemical damage, the procedures discussed below must be modified
or adjusted to account for these effects.
II. PHENOMENOLOGICAL OBSERVATIONS
Figure 1 qualitatively summarizes some of the effects of solution velocity on
various mass transport controlled corrosion situations (1). The corrosion rate of
bare metals is often observed to increase with solution velocity but becomes fixed
at high solution velocities. This is an example of a situation where the cathodic
reaction is under mass transport control until high solution velocities are reached.
The anodic reaction is charge transfer controlled. At high velocity, both anodic
and cathodic reactions are charge transfer controlled. The Evans diagram of Fig.
2 illustrates this phenomenon. Recall that the corrosion rate at open circuit (the
corrosion potential) is defined by the point on the Evans diagram where the anodic
and cathodic reaction rates are equal. By examining this point on the Evans diagram as a function of velocity, the trend shown in Fig. 1 can be established. It
must be recognized that either the cathodic or anodic reaction can be the ratelimiting step in the overall corrosion process. The corrosion rate of many nonpassivating metals and alloys in neutral solutions is often determined by mass transport control of the cathodic reaction. One classic example of a mass transport
controlled cathodic reaction is the oxygen reduction reaction on steel in aerated
neutral sodium chloride solution (2,3). Here the low bulk oxygen concentration
in room temperature aqueous solutions (typically 8 ppm ⫽ 0.25 mM/liter) limits
the cathodic reaction rate on cathodically polarized structures. However, the supply of oxygen from the bulk solution to the reacting interface is enhanced by
fluid flow. At fixed intermediate cathodic potentials the mass transport controlled
reaction rate (vertical cathodic reaction line in Fig. 2) will continue to increase
with increasing flow rate until charge transfer control is established. The transition to a velocity-independent cathodic reaction rate signifies the change from
mass to charge transfer control.
It is useful now to describe the origins of the shape of the anodic and
cathodic E–log i behaviors shown in Fig. 2. Note that the anodic reaction is linear
on the E–log i plot because it is charge transfer controlled and follows Tafel
behavior discussed in Chapter 2. The cathodic reaction is under ‘‘mixed’’
mass transport control (charge transfer control at low overpotential and mass
transport control at high overpotential) and can be described by Eq. (1), which
Influence of Mass Transport
153
Figure 1 Phenomenological observations concerning the influence of solution velocity
on metal corrosion rates.
can account for the vertical reaction line. The vertical line indicates that the mass
transport controlled cathodic reaction rate is independent of applied potential. In
this potential regime, the interfacial cathodic reaction rate is fast enough that the
reacting species is depleted at the reacting surface. In order to maintain the reaction rate, diffusion of the reacting species through the electrolyte becomes the
kinetic limitation. The cathodic reaction may be under ‘‘mixed’’ charged transfer
154
Chapter 5
Figure 2 Evans diagram illustrating the influence of solution velocity on corrosion rate
for a cathodic reaction under ‘‘mixed’’ charge transfer–mass transport control. The anodic
reaction shown is charge transfer controlled.
mass transport or full mass transport control for many realistic corrosion situations, particularly if the cathodic reaction is O 2 reduction. The polarization behavior associated with mixed control can be described mathematically by the algebraic sum of the cathodic Tafel equation and the expression for mass transport
control. The reaction becomes completely diffusion controlled at the limiting
current density, i L:
η c ⫽ ⫺β c log
冢冣
冢
i ca
2.3RT
i
log 1 ⫺ ca
⫹
io
nF
iL
冣
(1)
where
i ca ⫽ the true cathodic current density
i L ⫽ the limiting current density defined by Fick’s first law at steady state
n ⫽ the number of electrons consumed to complete the reduction reaction a
single time
β c ⫽ the cathodic Tafel slope
i o ⫽ the exchange current density for the cathodic half cell reaction
and R, T, and F have their usual meanings.
Influence of Mass Transport
155
As i app approaches i L, the cathodic overpotential, η c , becomes very large
and the cathodic reaction rate becomes independent of overpotential. For a completely mass transport limited cathodic reaction, the concentration of the reacting
specie in solution, C b , approached zero at the electrode interface and i corr ⫽ i L .
This is shown at V1 and V2 in Fig. 2. The limiting current density is increased
by increasing solution stirring or rotation rate, ω, in the case of a rotating cylinder
or disk electrode. The corrosion rate would be increased.
An analogous situation can exist for the case of a charge transfer controlled
cathodic reaction and a mass transport controlled anodic reaction. This can also
account for a corrosion rate that increases with solution velocity but is independent of velocity at high velocities, as shown in Fig. 1. One example of a system
exhibiting this behavior is rapidly corroding Fe in concentrated H 2 SO 4 . Slightly
soluble FeSO 4 is precipitated and lowers the corrosion rate as it thickens to account for anodic mass transport control at low solution velocities (Fig. 3) (4,5).
At extremely high velocities the reaction may become charge transfer controlled
when bare Fe is exposed. This may occur as a result of elimination of the deposited sulfate deposit by rapid transport of dissolved FeSO 4 away from the interfacial region. Once all of the precipitated layer is removed, the anodic reaction rate
cannot be increased further by additional stirring, and the anodic reaction rate,
Figure 3 Evans diagram illustrating the influence of solution velocity on corrosion rate
for an anodic reaction under ‘‘mixed’’ charge transfer–mass transport control. The cathodic reaction shown is charge transfer controlled. Ecorr and icorr at V1 is shown.
156
Chapter 5
and therefore the corrosion rate, becomes independent of velocity. It is useful
now to describe the corresponding origins of the shape of the anodic and cathodic
reaction lines on the Evans diagrams of Fig. 3. Note that the cathodic reaction
is linear on the E–log i plot because it is charge transfer controlled and follows
the Tafel behavior as discussed in Chapter 2. The anodic reaction is under mixed
mass transport and charge transport control and can be described by and equations
similar to that given by Eq. (1).
For passivating alloys, corrosion rate may at first be increased with velocity
until the critical potential for passivation (e.g., the primary passive potential, E pp)
is exceeded. At this point the alloy becomes passivated, and the corrosion rate
is much lower until extremely high shear stresses produce erosion corrosion (Fig.
1). An example of this is Fe–18Cr–8Ni alloys in concentrated H 2 SO 4 ⫹ HNO 3
mixtures at elevated temperatures (1). Figure 4 provides an electrochemical description of this phenomenon using mixed potential theory. This Evans diagram
illustrates an anodic reaction for an electrode that can be passivated above E pp
and a mass transport controlled cathodic reaction. Again, the interception of the
anodic and cathodic reaction rates defines the corrosion potential.
A protective film may be physically removed at still greater velocities by
high shear stresses. In fact, some Cu alloys have good corrosion resistance in
seawater that is attributed to the formation of a protective oxychloride film. It
has been theorized that high fluid velocities produce shear stresses that alter or
Figure 4 Evans diagram illustrating the influence of solution velocity on corrosion rate
for a passivating electrode exhibiting an active–passive transition. The cathodic reaction
shown is under ‘‘mixed’’ charge transfer–mass transport control.
Influence of Mass Transport
157
strip off these films (5). Such behavior should be characterized by an abrupt
increase in corrosion rate at a certain critical flow velocity. Such behavior has
been observed for 316 stainless steel in a molten salt mixture at 493°C (7).
III. THEORETICAL ORIGINS OF THE LIMITING
CURRENT DENSITY
Now let us discuss the origins of the limiting current density i L introduced above
and how it is affected by solution velocity. Recall that when the cathodic reaction
is nearly mass transport limited, the concentration of the reacting specie (C s)
approaches zero at the electrode surface (Fig. 5). However, at a distance far away
from the reacting electrode, the bulk concentration (C b) is unaffected by the depletion of this reactant at the electrode surface. Near the electrode surface the concentration profile decreases with time and eventually reaches zero at the electrode
surface. In this situation, the limiting c.d. defines the maximum rate at which the
reaction can take place. The actual concentration profile is given by a curved line
in Fig. 5, but for simplicity we will assume it to be a straight line as represented
here by the dashed line. The distance from the electrode to the position where
the dashed line crosses a horizontal line representing the bulk concentration defines the Nernst diffusion layer thickness, δ. δ is approximately 0.05 cm in un-
Figure 5 Schematic plot of cathodic specie concentration profile for a mass transport
controlled cathodic reaction with the electrode–solution interface at the far left. The solid
line represents the actual concentration profile. The dashed line from C s to C b represents
an approximating linear concentration gradient. Its interception with the horizontal line
representing C b defines an approximation of the mass transport boundary layer.
158
Chapter 5
stirred solution and 0.01 cm in lightly stirred solution. However, our objective
will be to determine it precisely. The mass transport controlled reaction rate is
given by Fick’s first law under steady-state conditions. For the case of one-dimensional mass transport (8) this gives
J ⫽ ⫺D ∗
∆C
(moles/cm 2 ⫻ s)
δd
(2)
where D is the diffusion coefficient for the reacting species and J is the flux.
∆C ⫽ C b ⫺ C s , where C b and C s are the bulk and surface concentrations, respectively. The negative sign indicates that transport is in the direction of the negative
of the concentration gradient for the cathodic reaction. In terms of electrochemical current density Eq. (2) may be rewritten as
i L (µA/cm 2) ⫽ ⫺JnF ⫽ ⫺nFD ∗
Cb ⫺ Cs
δ
(3)
where F ⫽ 96,487 coulombs/equivalent and n ⫽ equivalent/mole or the number
of electrons transferred when the half cell reaction is completed a single time.
In the case of anodic mass transport limitation, the concentration C s becomes the
saturation concentration for the sparingly soluble corrosion product forming on
the metal surface. Note that the limiting current density in both cases is independent of the exact electrode material (of course, this is only true over a range of
potentials where neither charge transfer control nor mixed control can be maintained). Can you think of a situation in which the properties of the electrode
material might influence δ d? (Hint: For a diffusion boundary layer established
across a material-specific porous suface film.)
Either anodic or cathodic mass transport limited corrosion may be observed
in numerous corrosion systems. Such phenomena may be simulated and investigated in the laboratory by establishing experimental conditions that match those
in the field application. This is accomplished by equating i L or δ d in the laboratory
to the same values present in the field. In this way the effect of fluid velocity or
mass flow rate on the corrosion rate may be investigated. Similarly, the hydrodynamic conditions in the field must be matched by those in the laboratory. Procedures for establishing such correlations between field and laboratory measurements are described below.
IV. USE OF MASS TRANSPORT CORRELATIONS
FOR UNDERSTANDING MASS TRANSPORT
CONTROLLED CORROSION
The corrosion engineer concerned with mass transport controlled corrosion is
interested in determining the limiting current density for a variety of geometries
Influence of Mass Transport
159
and flow situations. Hundreds of mass transport correlations exist in the literature
for various systems of interest to the corrosion engineer (4,9). For convenience
most mass transport solutions are expressed in terms of dimensionless parameters. In this section we briefly review the typical dimensionless parameters utilized in the correlations presented below.
At low velocities between the metal and the solution, the solution flow is
laminar, while at high velocities it is turbulent. The transition velocity depends
on the geometry, flow rate, liquid viscosity, and surface roughness. The Reynolds
number accounts for these effects and predicts the transition from laminar to fluid
turbulent flow. The Reynolds number is the ratio of convective to viscous forces
in the fluid. For pipes experiencing flow parallel to the centerline of the pipe
(4,8):
Re ⫽
V∗d
(unitless)
ν
(4)
where V is the solution velocity (cm/s), d is a characteristic length (cm), and ν
is the kinematic viscosity (cm 2 /s). The kinematic viscosity is equal to the fluid
viscosity (µ) divided by its density (ρ). For rotating cylinders and disks an angular
velocity terms is used instead, where V ⫽ rω. Here r is the radius of the disk
or cylinder and ω is the rotation rate in units of radians per second. This results
in a Reynolds number expression for the disk (4):
Re ⫽
r2 ω
(unitless)
ν
(5)
The precise transition from laminar to turbulent flow occurs at different values
of Re depending on geometry. Even in turbulent flow there exists a thin laminar
hydrodynamic sublayer of thickness δ h near the metal surface. If mass transport
is also occurring at the surface, there will be a diffusional boundary layer of
thickness δ d . δ h is a function of ν while δ d is a function of D. The Schmidt
number quantifies a relationship between these two parameters:
Sc ⫽
ν
(unitless)
D
(6)
For high Sc numbers a thin diffusion layer will be produced, and it will develop
rapidly, since diffusional transport is slow.
The mass transfer coefficient, K, is defined as the ratio of the mass transport
controlled reaction rate to the concentration driving force. The concentration driving force will depend on both turbulent and bulk convection. Bulk convection
depends on molecular diffusivity, while the turbulent component depends on
‘‘eddy’’ diffusivity (4). The mass transfer coefficient considers the combination
of the two transport mechanisms, empirically.
160
Chapter 5
K⫽
rate of reaction
concentration driving force
(7)
The concentration driving force is usually expressed as ∆C, and the limiting c.d.
(J ⫽ i L /nF, where J is given in units of moles/cm 2-s) describes the rate of reaction, under mass transport control.
K⫽
J
∆C
(8)
Hence K can be determined by measuring J at different fixed ∆C values. Mass
transfer rates are defined by the Sherwood number (Sh), which is given by (4)
Sh ⫽
iLd
Kd
⫽
D
nFD ∆C
(9)
where d is a characteristic dimension and D is the diffusion coefficient for the
reacting species. However, dimensionless analysis shows that Sh is also a function of Re and Sc. These correlations are of the form (4,7,9)
Sh ⫽ constant Re x Sc y
(10)
where x often varies from 0.3 to 1 and y is about 0.33. Substitution of this expression for Sh into Eq. (9) and rearrangement shows that the limiting c.d. is given
by the following expression for many mass transport correlations:
i L ⫽ constant
nFD ∆C x y
Re Sc
d
(11)
Here x and y will vary with the exact geometry.
It is worth mentioning again that not all reactions will exhibit complete
mass transport control at all potentials. Complete mass transport control will only
occur for extremely fast (reversible) charge transfer reactions and very slow mass
transport rates. Charge transfer reactions occurring only at moderate rates will
by under mixed control over a certain range of potentials. Here the total cathodic
current density, i total , will be equal to a combination of activation controlled current density and mass transport limiting current density. i total is given as
1
1
1
⫽ ⫹
i total i ac i L
(12)
Here i ac is the activation controlled current density occurring when transport to
the interface is very fast. To clarify this equation, consider the two processes
(activation and diffusion) to occur sequentially in the overall reaction sequence.
Since they occur in series, the slowest rate will dominate the overall total rate.
Influence of Mass Transport
V.
161
MASS TRANSPORT CORRELATIONS FOR SELECTED
GEOMETRIES OF INTEREST
This section describes selected mass transport correlations for laboratory devices
such as the rotating disk and cylinder. These mass transport correlations may be
used in order to establish the same mass transport conditions (diffusional boundary layer thicknesses) as those obtained in a pipe or under impinging flow. Essentially, the experimenter may vary the rotation rate and geometry of the cylinder
or disk to ‘‘dial in’’ the same mass transport conditions as obtained in the field for
pipes or impinging jets. The user should also verify that the same hydrodynamic
conditions also exist through use of Reynolds numbers, as shown above.
A. The Rotating Disk Electrode
The rotating disk electrode (RDE) is an important system in electrochemistry.
Axial followed by radial flow across the disk brings fresh solution to all points
across the disk (Fig. 6). The surface is therefore uniformly accessible to reacting
species. The RDE operates under laminar flow for Re ⬍ 1.7 ⫻ 10 5. Flow is
turbulent above 3.5 ⫻ 10 5 and is transitional in between (4). Thus the system is
less practical for the study of corrosion under turbulent conditions but enjoys
widespread use in research electrochemistry. For the rotating disk electrode, the
laminar mass transport correlation obtained in the literature is given by Levich
(10):
Sh ⫽ 0.621 Re 0.5 Sc 0.33
Figure 6 Cross-sectional view of the rotating disk electrode.
(13)
162
Chapter 5
Recall that the limiting current density is given by
i L ⫽ nF ∆CK
(14)
and that K is given by
D
d
(15)
nFD ∆C
Sh
d
(16)
K ⫽ Sh ∗
so that
iL ⫽
or that
i L ⫽ 0.621
nFd ∆C 0.5 0.33
Re Sc
d
(17)
Moreover, it is easy to show that the limiting current density is expressed entirely
in terms of readily obtained parameters: D, ∆C ⫽ C b ⫺ C s , ω, and ν. Recall that
C s ⫽ 0 when the limiting c.d. is reached, yielding
i L ⫽ 0.621 nFD 2/3 C b ν ⫺1/6 ω 1/2
(18)
Data is shown in Figs. 7a and 7b for oxygen reduction on carbon steel in room
temperature 0.6M NaCl. i L increases with ω 0.5 as predicted. Hence if the corrosion
rate is determined by the mass transport of oxygen to the disk surface to support
oxygen reduction, then the corrosion rate will increase as a function of the rotation
rate, ω, raised to the 0.5 power and linearly with dissolved oxygen concentration.
The diffusion boundary layer thickness, δ d , may be calculated from Fick’s first
law after i L is determined. Recall that δ ⫽ nFDC b /i L for one dimensional diffusion
at the steady state. This leads to the following expression for the diffusional
boundary layer thickness:
δ d ⫽ 1.61 D 1/3 ν 1/6 ω ⫺1/2
(19)
The boundary layer thickness decreases with increasing rotation rate as expected.
Figure 7 (a) Cathodic polarization data for a low carbon steel rotating disk electrode
in 0.6 M NaCl with ambient aeration. Oxygen reduction limiting current densities are
shown for the indicated rotation rates. (b) Plot of experimental limiting current density
versus square root of the rotation rate, showing the experimental and predicted linear
behavior.
Influence of Mass Transport
(a)
(b)
163
164
B.
Chapter 5
The Rotating Cylinder Electrode
The rotating cylinder electrode (Fig. 8) is operated in the turbulent flow regime
at Re ⬎ 200, although flow can be complicated with vortexing until much higher
Re, where true turbulence develops (4). A Re number ⬎200 is readily achieved
at modest rotation rates and cylinder diameters. Therefore the cylinder can be
(a)
Figure 8 The rotating cylinder electrode. (a) Electrode specimen and mandrel shown
as partially disassembled. (b) Typical laboratory setup for the RDE. (From Ref. 3.)
Influence of Mass Transport
165
(b)
readily utilized by the corrosion engineer to simulate flowing corrosion conditions
in turbulent pipes. For the smooth rotating cylinder electrode, the mass transport
correlation is given by Eisenberg (11). However, surface roughening increases
mass transport.
Sh ⫽ 0.079 Re 0.7 Sc 0.36
(20)
This correlation is valid within the following range: 1000 ⬍ Re ⬍ 100,000 and
835 ⬍ Sc ⬍ 11,490. Recalling that the limiting current density is given by
i l ⫽ nF ∆CK
(21)
and that K is given by
K ⫽ Sh ∗
D
d
(22)
166
Chapter 5
it is easy to show that the limiting current density can be expressed entirely in
terms of very accesible parameters: D, ∆C, d, V, and ν, again, assuming that
C s ⫽ 0:
i l ⫽ 0.079 nFC b (V) 0.7 (D) 0.64 (ν) ⫺0.34 (d) ⫺0.3
(23)
If the characteristic dimension is taken as the radius of the cylinder, r (recall that
V ⫽ rω), throughout the calculation where d ⫽ 2r we have
i l ⫽ 0.064 nFC b (ω) 0.7 (D) 0.64 (ν) ⫺0.34 (r) 0.4
(24)
Hence if the corrosion rate is determined by the mass transport of cathodic reactant to the cylinder surface, then the corrosion rate will increase as a function
of the rotation rate raised to the 0.7 power and linearly with dissolved reactant
concentration. Increasing the velocity by a factor of ten increases the corrosion
rate by a factor of five. Figure 9a shows the cathodic polarization results obtained
on a Ni-Cr-Mo-V alloy steel at five different rotation rates. Figure 9b illustrates
that excellent agreement is obtained between the predicted limiting c.d. for oxygen reduction and those obtained experimentally. Silverman (12) has shown that
the velocity of the rotating cylinder necessary to match the mass transport conditions for pipe flow, assuming the Eisenberg correlation applies, is given by
V cyl ⫽ 0.11845
冢冢 冣 冢 冣
ρ
ν
0.25
冣
d 0.429
cyl
Sc ⫺0.0857 V 1.25
pipe
d 0.179
pipe
Useful velocity conversions in order to have equality of mass transport conditions
between the rotating cylinder and the annulus and impinging jet are also reported
by Silverman (12).
C.
Flow in a Circular Tube or Pipe
Flow in circular tubes is of interest to many corrosion engineers. A large number
of correlations exist for mass transport due to turbulent flow in a smooth straight
pipe (4,9). The flow is transitionally turbulent at Re ⬃ 2 ⫻ 10 3 and is fully
turbulent at Re ⬃ 10 5 (4). The most frequently used expression for turbulent
conditions at a straight tube wall is that given by Chilton and Colburn using the
analogy from heat transfer (13):
Figure 9 (a) Cathodic polarization data for a Ni-Cr-Mo-V alloy steel rotating cylinder
electrode in seawater with ambient aeration. Oxygen reduction limiting current densities
are shown for the indicated rotation rates. (b) Plot of experimental limiting current density
versus predicted limiting current density according to the Eisenberg correlation for selected rotation rates on different alloys. (From Ref. 3.)
Influence of Mass Transport
(a)
(b)
167
168
Chapter 5
Sh ⫽ 0.023 Re 0.8 Sc 0.33
(26)
Recalling that the limiting current density is given by
i l ⫽ nF ∆CK
(27)
and that K is given by
K ⫽ Sh ∗
D
d
(28)
it is easy to show that the limiting current density is expressed entirely in terms
of very familiar parameters: D, ∆C, d, V, and ν, where d is the pipe diameter:
i l ⫽ 0.023 nFC b (V) 0.8 (D) 0.67 (ν) ⫺0.47 (d) ⫺0.2
(29)
Hence, if the corrosion rate is determined by the mass transport of cathodic reactant to the pipe surface, then the corrosion rate will increase as a function of the
solution velocity raised to the 0.8 power and linearly with the dissolved reactant
concentration. Note that at the same fluid velocity and reactant concentration,
the limiting c.d. and hence the corrosion rate will be greater for pipes of smaller
diameter. A similar relationship was proposed by Harriot and Hamilton (14) and
applied by various investigators concerned with anodic mass transport controlled
corrosion of ferrous piping materials (5,15).
Sh ⫽ 0.0096 Re 0.913 Sc 0.346
(30)
It is logical to expect that enhanced mass transfer will occur at pipe entrances. Berger and Hae found the following relationship, where L is the length
or distance from the entrance (4,16):
Sh ⫽ 0.276 Re 0.583 Sc 0.33
d 0.33
L
(31)
The establishment of nonentrance conditions was found to be a function of Reynolds number and flow regime (4,16). Expressions have also been utilized to describe the ‘‘average’’ limiting current density in the rectangular flow channel
with plane parallel electrodes imbedded in opposite sides. Under laminar flow
conditions, the current, potential, and concentration distributions have been calculated correlations and are reported in the literature (9). The complication with
mass transport controlled processes in the rectangular channel is that the limiting
c.d. is the greatest at the leading edge and varies with distance from the leading
edge.
Influence of Mass Transport
169
D. Flow from an Impingment Jet
If the incoming flow from a nozzle is at 90° to a planar metallic surface, then
the flow impinges onto the metal surface and moves radially outward. The flow
is redirected from being perpendicular to the planar surface to radial parallel to
the surface. Mass transport solutions to this situation have been proposed and in
general depend upon the ratio of vertical distance to nozzle diameter (H/d) and
the radial position on the plate (x/d) as shown in Fig. 10. Chin and Tsang (4,17)
showed that, for H/d between 0.2 and 6 and x/d between 0.1 and 1,
Sh ⫽ 1.12 Re Sc
0.5
0.33
冢冣
H
d
⫺0.057
(32)
for turbulent Reynolds numbers between 4000 and 16,000. Patrick proposed that
mass transport in the wall jet region decreases with radial distance (4). The wall
jet region begins at ⬃three to five nozzle diameters, and the following mass
Figure 10 Schematic of the impinging fluid jet geometry showing various flow regions.
170
Chapter 5
transport expression was found for 5120 ⬍ Re ⱕ 13498; 8 ⱕ x/d ⬍ 17; 5 ⬍
h/d ⬍ 20 (4):
Sh ⫽ 1.14 Re
0.82
冢冣
x
d
⫺1.05
(33)
VI. THE CRITICAL SHEAR STRESS AS A MEANS
TO SIMULATE THE EFFECTS OF FLUID FLOW
IN CORROSION
For many years corrosion engineers have recognized that velocity controlled corrosion processes were significantly influenced by the gradient of the fluid velocity
(creating a shear stress) as well as the reacting species concentration gradient
with respect to the electrode surface instead of the absolute value of these parameters (7). These points are confirmed from consideration of two pipes of different
diameters with the same fluid velocity. Clearly there will be different pressure
drops and velocity gradients and therefore different shear stresses and mass
transfer rates. A difference in velocity gradient occurs because of the boundary
condition that the solution velocity approaches zero at the metal surface.
Recall that the shear stress experienced by the metal surface is proportional
to the gradient of fluid velocity with respect to the perpendicular distance away
from the surface and the solution viscosity (8). This gradient will be larger
for smaller diameter pipes operating at the same average velocity as larger
pipes.
The mass transport correlations developed in the previous section are valid
if the process controlling the corrosion rate is strictly the transport of a reacting
specie to the electrode surface with no other influencing factors. On the other
hand, it is possible to have a situation where fluid momentum transfer at the
surface controls the corrosion rate. The shear stress induced by the fluid flow
can strip off protective corrosion products or remove a protective corrosion-inhibiting film. Here the total metal loss rate is defined by the bare metal anodic reaction rate after mechanical stripping of the protective layer as well as by other
factors such as purely mechanical erosion. The ‘‘critical shear stress’’ is the stress
at which protective films are removed (6). However, it has been argued that even
in cases of mass transport controlled corrosion it is useful to equate shear stresses
in the laboratory to those in the field. This equality produces similar velocity
gradients, similar hydrodynamic conditions, and thus similar Sherwood numbers,
which contain mass transport coefficients. Hence, mass transfer can be linked to
shear stress (12,15) as Silverman has reviewed relationships between mass transfer coefficients and wall shear stresses for the rotating cylinder, pipe, annulus,
Influence of Mass Transport
171
and jet impingement (13). Indeed, Efird and coworkers recently found that shear
stress was a useful correlating hydrodynamic parameter for the corrosion of steel
under jet impingment (18). However, a shear mechanism of corrosion acceleration, per se, was not endorsed.
Hence it is useful for a variety of reasons to determine the shear stress
on the electrode surface and to determine its variation with solution velocity.
Laboratory tests must be able to apply the same shear stress as is obtained in the
field (15). The idea then is to design the laboratory test so that the shear stress
in the laboratory matches that present in the field application:
τ lab ⫽ τ field
(34)
However, it should be noted that equality of shear stresses in lab and field
will not produce exact equality of mass transport coefficients owing to different
dependencies on flow velocity, as shown below (15). Clearly, the flow regimes
must be the same in the laboratory and in the field (e.g., both laminar or both
turbulent).
A. The Rotating Disk Electrode
Flow is not uniform across the RDE. At high speeds the edges may be in turbulent flow, and the shear stress should vary with radial position. An average
velocity or Re number value must be used in order to characterize flow. Consequently, the RDE is not favored for studying corrosion controlled by shear
stresses.
B. The Rotating Cylinder Electrode
The rotating cylinder electrode utilized a specimen with a fixed diameter. Consequently, all points on the surface are exposed to the same surface velocity (excluding surface roughness effects). The RCE can be used to simulate flowing conditions present in other geometries if flow in those geometries is tangential to the
electrode surface by using in the appropriate rotation rate. The surface shear
stress* for the rotating cylinder is given as (15)
τ (kg/m-s2) ⫽ constant
f
ρ ω2 r2
2
(35)
where f is the friction factor. The Re number and the surface roughness are important factors in determining the surface shear stress. For a smooth cylinder, f/2 is
* kg/m-s2 is equivalent to N/m2 or Pa, which is a shear stress term.
172
Chapter 5
equal to 0.079 Re ⫺0.30 (19). Substitution of this relationship gives the following
expression for shear stress:
τ (kg/m-s2) ⫽ 0.079 Re ⫺0.30 ρ ω 2 r 2
⫽ 0.079
冢
冣
2r 2 ω ρ
µ
⫺0.30
(36)
ρ ω2 r2
Rearranging yields
τ ⫽ 0.064 (r 1.4) (ω 1.7) (ρ 0.7) (µ 0.3)
(37)
where the shear stress is given in terms of the fluid density, ρ, the angular velocity,
ω, the fluid viscosity, µ, and the cylinder radius, r. Note that the shear stress will
increase as a function of the rotation rate raised to the 1.7 power. In contrast,
the limiting current density increases with velocity raised to the 0.7 power for
the RCE.
C.
Flow in a Circular Pipe
The shear stress for flow in a pipe is given by the following expression, where
all terms have their usual meaning (12,15,19):
τ⫽
f
ρ V2
2
(38)
here the friction factor for a smooth tube is given by (19):
f ⫽ 0.079 Re ⫺0.25
(39)
for 2.3 ⫻ 10 ⱕ Re ⱕ 10 , or for Re ⱖ 10 , then (19):
3
5
5
f ⫽ 0.046 Re ⫺0.2
(40)
for Re ⱖ 10 . The former case yields the following relationship:
5
τ ⫽ 0.040 (V) 1.75 (µ) 0.25 (d) ⫺.25 (ρ) .75
(41)
It was shown above that the limiting c.d. increases with velocity raised to the
0.8 power and the pipe diameter raised to the ⫺0.2 power for piping corrosion
rates that are controlled by mass transport. In contrast, it is evident that the shear
stress increases with the fluid velocity raised to the 1.75 power and the pipe
diameter raised to the ⫺0.2 power. Thus equality of shear stress does not give
equality of mass transfer rates. In both cases corrosion is enhanced in pipes of
smaller diameter for the same solution velocity. Such a relationship can be rationalized based on the effect of pipe diameter on the thickness of the mass transport
and hydrodynamic boundary layers for a given fixed geometry. Cameron and
Chiu (19) have derived similar expressions for defining the rotating cylinder rotation rate required to match the shear stress in a pipe for the case of velocity-
Influence of Mass Transport
173
influenced corrosion. In their derivation, pipe flow is defined in terms of volumetric flow rate. This form may be more convenient to the corrosion engineer.
An alternative version of the same expression describing flow-induced
shear stresses for a circular pipe operating in the turbulent flow regime is described by the relation (6)
τ
冢
冣
force
fv2ρ
⫽
unit area
2gc
(42)
where g is a dimensional constant ⫽ 32.17 lb.-ft/(lb. force-s2) and all other terms
have their usual meanings. It is also evident from this expression that the shear
stress increases with the fluid velocity raised to the 1.8 power and the pipe diameter raised to the ⫺0.2 power, as shown above. Thus the shear stress is higher in
smaller diameter pipes.
D. Impingment Jet
If the incoming flow from a nozzle is at right angles to a planar metallic surface,
the flow impinges onto the metal surface and moves radially outward. The flow
is redirected from being perpendicular to the planar surface to radial parallel to
the surface at a distance of three to five nozzle diameters (wall jet region). The
shear stress for the ‘‘wall jet’’ beyond the stagnation point has been given by
Giralt and Trass (20,21) for x/d ⬎ ⬃2-3 and Reynolds numbers in the range
2.4 ⫻ 10 4 ⬍ Re ⬍ 1.25 ⫻ 10 5 (12):
τ ⫽ 0.0447 ρ V 2 Re ⫺0.182
冢冣
x
d
⫺2.0
(43)
Here as before, the diameter of the nozzle is d, and x is the distance from the
centerline of the jet as shown in Fig. 10.
E.
Other Geometries
Silverman has defined a number of useful expressions that allow one to utilize
the rotating cylinder method with a variety of practical geometries (12,15). Both
shear stresses and mass transfer coefficients are included in the derivations described (12). Table 1 in NACE standard TM-0270-72 summarized the various
features of experimental systems for studying flow induced corrosion (22).
VII. CORROSION AND EROSION
Many practical situations exist in which metal loss occurs from both erosion of
a nonelectrochemical nature and corrosion phenomena. The question arises as to
appropriate test methods. One suggestion has been to duplicate the test conditions
174
Chapter 5
discussed above using the Sherwood number–Reynolds number correlations to
calculate mass transfer coefficients (12). These calculated coefficients may then
be compared to experimentally determined coefficients derived from mass loss.
In this case of cavitation-induced corrosion, an ASTM standard exists that places
the metal test specimen at the end of a vibrating transducer to generate bubble
collapse in aqueous solutions (7,23).
REFERENCES
1. M. G. Fontana, N. D. Greene. Corrosion Engineering. McGraw-Hill, 18–21 (1978).
2. J. R. Scully, H. P. Hack, D. G. Tipton. Corrosion J. 42(8), 462–469 (1986).
3. R. Guanti, H. P. Hack. Determination of the best hydrodynamic parameter for modelling flow on cathodically polarized surfaces. Corrosion 1987, Paper No. 267, NACE,
Houston, TX (1987).
4. B. Poulson. Corrosion Sci. 23(4), (1983).
5. B. T. Ellison, W. R. Schmeal. J. Electrochem. Soc. 125, 524 (1978).
6. K. D. Efird. Corrosion J. 33(1), 3 (1977).
7. S. W. Dean. Materials Performance 29(9), 61 (1990).
8. R. B. Bird, W. E. Stewart, E. N. Lightfoot. Transport Phenomena. John Wiley
(1960).
9. J. R. Selman, C. W. Tobias. In: Advances in Chemical Engineering 10, 212 (1978).
10. V. G. Levich. Physico-Chemical Hydrodynamics. Prentice-Hall, Englewood Cliffs,
NJ (1962).
11. M. Eisenberg, C. W. Tobias, C. R. Wilke. J. Electrochem. Soc. 101(6) (1954).
12. D Silverman. Corrosion J. 42–49 (1988).
13. T. H. Chilton, A. P. Colburn. Ind. Eng. Chem. 26, 1183 (1934).
14. P. Harriot, R. M. Hamilton. Chem. Eng. Sci. 20, 1023 (1965).
15. D. Silverman. Corrosion 1983, Paper No. 258, NACE, Houston, TX (1983).
16. T. K. Ross, D. H. Jones. J. Appl. Chem. 12, 314 (1962).
17. D. T. Chin, C. H. Tsang. J. Electrochem. Soc. 1461, 125 (1978).
18. K. D. Efird, E. J. Wright, J. A. Boros, T. G. Hailey. Corrosion, 992 (1993).
19. G. R. Cameron, A. S. Chiu. Electrochemical techniques for corrosion inhibitor studies. In: Electrochemical Techniques for Corrosion Engineering (R. Baboian, ed.),
183–189, NACE (1986).
20. F. Giralt, D. Trass. Can. J. Chem. Eng. 53, 505 (1975).
21. F. Giralt, D. Trass. Can. J. Chem. Eng. 54, 148 (1976).
22. Guidelines for conducting controlled velocity laboratory corrosion experiments.
NACE Standard TM-0270-72.
23. ASTM Standard G-32. Standard method for cavitation erosion using vibratory apparatus. ASTM Volume 03.02, Wear and Erosion; Metal Corrosion, ASTM, Philadelphia, PA (1993).
6
Current and Potential Distributions
in Corrosion
I.
INTRODUCTION
A. Empirical Observations
Current and potential distributions are of great interest in cases where the anode
and cathode are separated as in the case of cathodic protection, bimetal galvanic
corrosion, pitting corrosion, crevice corrosion, stress corrosion, and local galvanic
corrosion caused by the presence of inclusions, precipitate phases, or any other
kind of surface heterogeneity (1–6). Moreover, current and potential distributions
are of interest in laboratory or field two- and three-electrode polarization cells
where errors in the measurement of electrode kinetics and polarization resistance
may occur due to nonuniformity in current and potential distributions (1). In all
of these situations, it is of great interest to understand the local electrochemical
potential at the electrode interface (i.e., across the double layer), the local current
density, and the possible errors in kinetic parameters (e.g., polarization resistance,
Tafel slopes, etc.). On the other hand, current and potential distributions are not
of great interest to the corrosion engineer in the case of freely corroding metals
uniformly corroding, since local anodic and cathodic reactions occur at equal
rates on the same surface, and balancing ionic current flow between anodes and
cathodes occurs on a very local basis.
Let us begin with two common observations involving separated anodes
and cathodes. The cathodic protection level obtained on metallic surfaces is often
noted to vary with position. The metal is usually less well protected as the distance of the metal surface from the sacrificial or impressed current anode increases. Alternatively, the structure may be overprotected at positions close to
the anode, leading to potentially embrittling hydrogen production. Similarly, it
is well known that it is more difficult to plate metals electrolytically or “throw”
current into corners or recesses, while exposed edges may receive a thicker plating deposit. The main explanation for this behavior is that the aqueous solution
175
176
Chapter 6
Table 1
at 20°C
Resistivities of Some Metallic and Ionic Conductors
Conductor
Copper wire
Seawater
Soil
Resistivity (ohm-cm)
Conductivity (ohm-cm)⫺1
1.72 ⫻ 10⫺6
25
2500
0.58 ⫻ 106
0.04
0.0004
has a finite ionic conductivity, especially compared to the electrical conductivity
of the metal. Note the significant differences in resistivity of metallic copper
compared to seawater and soil as shown in Table 1.
The finite conductivity of aqueous solutions leads to an ohmic voltage
“loss” or drop in the aqueous solution when ionic current flows between separated
anodes and cathodes. This voltage drop consumes some of the total voltage driving force otherwise available to increase the overpotential at the electrode surface.
Note that there may be other causes of local variations in electrochemical current
and potential. For instance, the concentrations of reacting species in solution may
vary locally, leading to local differences in conductivity and/or reaction rates.
However, the main cause of current distributions is the separation (distance) between anodes and cathodes, irregular cell geometry, in combination with the finite
conductivity of the electrolyte. These factors all affect the local overpotential
that is achieved at the electrode surface of interest and ultimately affect the local
galvanic corrosion rate or the cathodic protection level.
B.
The Effect of Ohmic Resistance on Twoand Three-Electrode Cells
Finite electrolyte conductivities and ionic current flow lead to ohmic voltage
components in electrochemical cells. It is constructive at this point to review the
effects of ohmic voltage contributions to driven and driving cells in the case of
uniform current distributions. It will be shown that for each type of cell, the
ohmic resistance lowers the true overpotential at the electrode interface for a
fixed cell voltage even in the case of a uniform current distribution at all points
on the electrode.
The most typical cell arrangement for the corrosion engineer involves a
three-electrode configuration with working, reference, and counter electrodes, as
shown in Fig. 1. If we wish to polarize the working electrode to some applied
potential, E app, differing from the mixed potential, E corr, in the presence of a finite
solution resistance between our reference and working electrodes, then E app is
given by the following equation, where the terms have the same meanings as
developed in earlier chapters:
Current and Potential Distributions
177
Figure 1 Influence of IR voltage error on E app in a three-electrode polarization cell. E app
is increased for both anodic and cathodic polarization. A larger E app than theoretical must
be applied to achieve the same true overpotential, η true . The resistors between the working
electrode (WE), reference electrode (RE), and counter electrode (CE) signify the finite
solution conductivity.
E app ⫽ η true ⫹ iR Ω ⫹ E corr
(1)
Obviously, the E app is increased by a finite value for nonzero R Ω values.
Note that the potential applied is greater than it would be in the absence of iR Ω
voltage for a fixed current density, but the true overpotential is less than it would
otherwise be at fixed E app. Said another way, a greater E app must be applied to
obtain the true overpotential desired. Recall that the applied overpotential is the
sum of the true overpotential and the iR Ω voltage drop (the product of the current
density and the solution resistance) (2). The greater the product of these terms,
the greater the chance that the true surface overpotential differs from the applied
overpotential.
η app ⫽ η true ⫹ iR Ω
(2)
Here η true ⫽ E true ⫺ E corr, and the product of I (A/cm ) and R Ω (ohm-cm ) produces
volts. Note that E true is the exact local potential across the metal–solution interface
2
2
178
Chapter 6
(i.e., the double layer measured with respect to a reference electrode) and not
the potential of the metal itself. The engineer has only the option of controlling
E app, and consequently η app, which equals E app ⫺ E corr. Hence if iR Ω varies spatially
over the surface, then it follows that E true must vary spatially as well, even though
the engineer maintains a single E app. iR Ω does not effect an anodic reaction and
a cathodic reaction occurring on the same surface at equal and opposite rates.
Therefore electrode geometry does not affect the uniform corrosion rate of a homogeneous metal or alloy, or electroless metal plating.
Similarly, for a galvanic couple (driving system) between two materials,
A and B, of differing E corr , the difference in E corr values between A and B must
equal the overpotentials on both the anode and the cathode as well as any IR
voltage which is present.1
E Acorr ⫺ E Bcorr ⫽ ∑η anode ⫹ |∑η anode| ⫹ IR Ω
(3)
From this equation it can been seen that as the ohmic resistance increases,
the remaining voltage driving force available to increase the overpotentials of
the anode or cathode is diminished. Consequently smaller total current, I, flows
through the cell. This is shown in Fig. 2, where in the absence of a finite R Ω
there is a single galvanic couple potential. A similar argument can be developed
for the case of a driven two-electrode system.
C.
Verification of Spatially Varying True Overpotentials
So far, we have discussed the effects of ohmic resistance for cells with completely
uniform current distributions. That is, the distance, geometry, and ionic resistivity
governed R Ω term was assumed to be the same at all positions on the electrode
surface. Consider the hypothetical cell in Fig. 3. Note that the top working electrode has the shape of a half-sinusoidal wave and is consequently further away
from the flat counterelectrode at one position and closer at another. Therefore
the solution path length varies, producing a large “effective” R Ω at the position
where the separation distance is greatest. Even though the same applied potential
(E app ) on the working electrode may be “dialed in” from the potentiostat, using
a reference electrode located at a fixed distance from the bottom flat electrode
shown in Fig. 3, the true overpotential at the surface may differ owing to the
position-dependent differences in R Ω. It is apparent from Eq. (1) that the local
value of η true must be less for a given E app if the product of i local and R Ω is greater,
locally, at positions where the distance between the two electrodes is greater.
In the case of a nonpolarizable cell (e.g., small or zero η true at any current
1
In the case of galvanic corrosion, total current, I, is used instead of current density, i. The galvanic
current associated with the anode must equal that from the cathode, or i*A area A ⫽ i*B area B. In order
for the last term in Eq. (3) to yield volts, R Ω must have units of ohms.
Current and Potential Distributions
179
(a)
(b)
Figure 2 Influence of IR voltage error on galvanic corrosion. Increasing IR voltage
error decreases the extent of anodic polarization of the anode and cathodic polarization
of the cathode.
180
Chapter 6
Figure 3 Sinusoidal two-electrode cell with insulating boundaries. In the primary current distribution, all current flow occurs at the peak in the sinusoid. For increasing ratios
of R p /R Ω, the current uniformity increases.
density, I ), the ohmic resistance, R Ω will have controlling influence on the current
distribution. For polarizable cells (e.g., η true large at any current density, I ) the
effect of ohmic resistance may be negligible, as η true is the dominant term in Eq.
(1). This point will be developed and discussed further below.
D.
Rules Used to Describe Isopotential and Current Lines
It is useful now to describe a few rules pertinent to current and potential distributions prior to discussing specific geometries (1).
1. Current lines are perpendicular to “isopotential lines” otherwise known
as equipotential lines, which are lines of constant potential in two dimensions or
surfaces of constant potential in three dimensions. Current lines do not terminate
at insulating surfaces.
2. Isopotential lines or surfaces are perpendicular to insulator material
surfaces because current cannot flow into the insulator.
Current and Potential Distributions
181
3. Isopotential lines are parallel to the electrode surfaces for what is
known as the primary current distribution (no interfacial electrode polarization,
or zero polarization resistance). Said another way, the solution adjacent to an
electrode surface is an equipotential surface (1). This primary current distribution
applies to the case of extremely fast electrochemical reactions (e.g., nonpolarizable electrode reactions). This current distribution situation is only of interest
to the corrosion engineer in cases where high current densities might be flowing
(i.e., in relatively nonpolarizable cells).
4. Isopotential lines may vary with electrode position for the secondary
and tertiary current and potential distributions, where interfacial polarization of
various types is considered. The variation of local true potential across the electrochemical interface with electrode position is of great interest in galvanic corrosion, cathodic protection, etc., since this true potential drives electrochemical
reactions.
These rules for the case of a flat electrode with an insulating edge at various
angles are shown in Fig. 4. Note that the lines of constant potential or isopotential
lines (solid) are perpendicular to the dotted lines, indicating the path taken by
the current in the solution. The current density is greatest at positions where the
current lines are crowded close together. The primary current distribution is a
function of angle greater than or less than 90°. At angles greater than 90° between
insulator and electrode, the primary current density approaches infinity. At angles
Figure 4 Primary current distribution rules applied to the case of a flush mounted electrode with an insulating edge of various angles.
182
Chapter 6
less than 90° it approaches zero. Potential gradients are greatest where isopotential lines of widely different values are closest together. It will be shown below
that the local current density is a function of the potential gradient. So, in order
to proceed in understanding current distribution effects in corrosion, we must
review the factors governing the magnitude of local current densities.
E.
Theoretical Considerations Concerning
Current Distributions
Ions can be transported through an electrochemical solution by three mechanisms.
These are migration, diffusion, and convection. Electroneutrality must be maintained. The movement of ions in a solution gives rise to the flow of charge, or
an ionic current. Migration is the movement of ions under the influence of an
electric field. Diffusion is the movement of ions as driven by a concentration
gradient, and convection is the movement due to fluid flow. In combination these
terms produce differential equations with nonlinear boundary conditions (1).
Neglecting transport due to convection, or the existence of concentration
gradients (these are valid assumptions for the bulk of the solution, far from surface boundary layers where concentrations might vary), the equations describing
current flow in an electrolyte containing cations and anions reduce to the familiar
Ohm’s law. Unidirectional current between two parallel plates can be described
by (1)
κ∆E
i⫽⫺
l
(4)
where i is the current density (amps/cm 2 ), κ is the solution conductivity in units
of ohms⫺1 cm⫺1, ∆E/l ⫽ E 1 ⫺ E 2 /l is the difference in potentials between any
two isopotential lines separated by a distance, l, in one dimension, V/cm. The
more general expression for one-dimensional current density is given by
i ⫽ ⫺κ∇E
(5)
where ∇E is the gradient of the potential (a scalar quantity), so that in Cartesian
coordinates ∇E ⫽ ∂E/∂x ⫹ ∂E/∂y ⫹ ∂E/∂y.2 Hence the local current density
will depend upon the gradient of potential in the solution. Note that the potential
gradient in the metal itself will be close to zero for current densities typical in
electrochemistry, since the high metallic conductivity precludes the possibility of
potential gradients within the metal. (In extremely long pipelines, the resistance
through the metal itself may come into play.) However, the potential gradient in
solution can be considerable. Note the form of the equation above. It is similar
2
It is also recognized that the divergence of the gradient in potential is zero, or ∇ 2E ⫽ 0. This means
that ∂ 2E/∂x 2 ⫹ ∂ 2E/∂y 2 ⫹ ∂ 2E/∂ 2 ⫽ 0.
Current and Potential Distributions
183
to that describing the steady-state flux of a diffusing species discussed in Chapter 4 (J ss ⫽ Ddc/dx), which states that the flux is proportional to the concentration
gradient times a term describing the mobility or ease of motion of the diffusing
species, D. In the case of migration, κ, the solution conductivity is the ease of
motion term.
The notion of a potential and therefore a current distribution through a
solution between two electrodes can be illustrated by the following examples.
We can apply these rules and the equations given above to describe the
iR Ω voltage associated with a rectangular “box” or prism-shaped cell. In this cell,
the working and counterelectrodes are exposed on opposite parallel walls (Fig.
5), and the side walls are insulators. Ohm’s law can be applied to describe the
IR Ω voltage across this cell if we apply a voltage between the WE and CE.
κ∆E
i⫽⫺
l
(6)
The negative sign indicates that positive ions flow in the direction of the negative
potential gradient. Note that the current density and current is the same at all
positions across this cell, since the voltage gradient is linear across the cell (assuming that the conductivity is also the same at all positions).
The total current is (1)
I ⫽ iA ⫽ ⫺
Aκ∆E
l
(7)
Rearranging this expression to solve for the ohmic voltage V IR3 and integrating
from x ⫽ 0 to 1 where l is the total length of the cell yields
(Il)
⫽ ⫺IR Ω
V IR ⫽ ⫺
(Aκ)
(8)
where R Ω ⫽ l/Aκ, is given in units of ohms. As expected, the total ohmic voltage
across the cell is influenced by I ⫽ I/A, l, the cell length, and is inversely proportional to solution conductivity, κ. This equation essentially is Ohm’s law. The
electrode area normalized resistance (ohm-cm 2 ) in such a cell is a linear function
of the distance, l, and inversely proportional to the conductivity.
3
In this chapter, E is used to represent any potential measurement that can be made versus a reference
electrode. E app and E corr are measured relative to some reference electrode scale. The potential difference ∆E can also be measured at any two points in the electrolyte between separated anodes and
cathodes. Two reference electrodes connected between a high impedance voltameter can make this
measurement. Alternatively, the potential between the reference electrode and anode or cathode
may be determined at any two points. ∆E is determined by taking the difference, which in this case
eliminates the reference potential scale. V IR is an absolute ohmic voltage (not referenced to any
scale).
184
Chapter 6
(a)
(b)
Figure 5 (a) Calculation of the local current density for flat parallel electrodes in a
prismatic cell. (b) The ohmic voltage is shown to be a linear function of the distance from
the working electrode. (From Ref. 6.)
RΩ ⫽
l
κ
(9)
If a reference electrode is inserted at a finite distance, l, from the working electrode, then the effective IR drop between WE and RE that contributes to error
between η app and η true as given in Eq. (2) (6) is only the amount indicated by iR Ω
(Fig. 5b). Note that multiplication of Eq. (9) by the current density (amperes/
cm 2 ) produces the correct units for voltage (volts). This is the amount by which
the true potential of the interface differs from the applied potential, as indicated
by Eq. (2).
Current and Potential Distributions
185
The same derivation can also be developed for two concentric cylinders
(1). Consider a cylinder of inner radius r i, outer radius r o, and a height of H
(Fig. 6a). In this case the current distribution and thus the potential distribution
will be completely homogeneous with regard to circumferential position on each
concentric cylinder. The potential in solution and value of local current density
will both vary radially, however.
Ohm’s law for unidirectional current flow can be written in cylindrical
coordinates as (1)
i ⫽ ⫺κ
冢 冣
∂E
∂r
(10)
Multiplying by electrode area produces (1)
I ⫽ 2πrHi ⫽ ⫺2πrHκ
冢 冣
∂E
∂r
(11)
(a)
Figure 6 (a) Annular cell made from two concentric cylinders of height H, inner radius
r i, and outer radius r o. (b) The ohmic voltage is a logarithmic function of radial distance.
(c) Equipotential lines are concentric even in the primary current distribution. Note that
the current density is greater on the inner electrode than on the outer electrode by an
amount equal to the ratio of areas of the inner and outer electrodes. (From Ref. 1.)
186
(b)
(c)
Figure 6 Continued
Chapter 6
Current and Potential Distributions
187
Rearranging this expression in terms of ∂E and integrating from r i to r o yields
the ohmic voltage of the annular cell (1):
V IR ⫽
冢 冣 冢冣
I
r
ln o
2πHκ
ri
(12)
Hence different isopotential lines of constant voltage increments in solution (actually cylindrical isopotential surfaces in 3D) vary logarithmically with respect to
radial distance. Figure 6b illustrates the radial potential distribution as a function
of radial distance. The isopotential lines and current lines are indicated in Fig. 6c
looking down on such a cell. Note that the current density is greater on the inner cylinder in agreement with the logarithmic increase in the potential gradient,
∂E/∂r, at the inner cylinder. The solution resistance (ohm-cm 2 ) is given by the
following expression for r i ⬍ r ⬍ r o:
RΩ ⫽
冢冣 冢冣
r
r
ln
κ
ri
(13)
A simple rearrangement of this expression gives the solution resistance for a
reference electrode placed a distance d ⫽ r ⫺ r i away from the inner cylinder
with the outer cylinder at infinity (6).
F.
Variation of Solution Resistance with Reference
Electrode Position for Three Geometries
The variation of solution resistance with the distance, d, from the working electrode surface for three ideal electrode geometries, all with a uniform current distribution in the case of strictly one-dimensional migration or current flow (orthogonal to a planar electrode and radial to a cylindrical or spherical electrode,
ignoring edge effects), is given below (6). These geometries include a flat working electrode in the parallel plate–rectangular cell arrangement, a cylinder, and
a sphere. (See Table 2.) The expressions for solution resistance derive from the
equations given above. Note again that the units of (ohm-cm 2 ) produce an ohmic
voltage drop (volts) when multiplied by current density (A/cm 2 ). The motivation
for using ohmic resistances in this form is that a corrosion engineer is always
interested in current normalized to electrode area or current density.
G.
Classification of Current Distribution Problems
Current distribution problems are often categorized according to the process that
limits or determines the current and potential distribution (1,6).
188
Table 2
Distance
Chapter 6
Solution Ohmic Resistance Versus Reference Electrode
Working electrode geometry
RΩ vs. WE–RE distance (Ω-cm2)
Planar
RΩ ⫽
d
κ
Cylindrical
RΩ ⫽
冢冣 冢 冣
(15)
Spherical
RΩ ⫽
冢 冣冢 冣
(16)
(14)
d
r
ln l ⫹
κ
r
d
κ
r
r⫹d
1. The primary current distribution: The current distribution is determined solely by the potential field in the solution. Hence the solution conductivity
and geometry are the only factors considered, and the potential across the electrochemical interface is assumed to be negligible, such as when the electrode reactions are extremely fast (i.e., a nonpolarizable electrode).
2. The secondary current distribution: Both ohmic factors and charge
transfer controlled overpotential kinetic effects are considered. The potential
across the electrochemical interface can vary with position on the electrode.
3. The tertiary current distribution: Ohmic factors, charge transfer
controlled overpotential effects, and mass transport are considered. Concentration
gradients can produce concentration overpotentials. The potential across the electrochemical interface can vary with position on the electrode.
Many analytical numerical solutions appear in the literature for category
1 and 2, but few appear for 3 owing to its complexity (1). Consider for example
the two-electrode half-sinusoidal cell shown in Fig. 3 with the irregular geometry
(7). The current distribution can be described by replacing the solution and interfacial elements with resistors. For case 1, only solution resistances appear, and
the resulting current density is extremely nonuniform. However, as the interfaces
are replaced by larger and larger resistors to simulate slower charge transfer and
mass transport, the current distribution becomes more uniform. This occurs
primarily if the resistance of the interface is larger than the resistance of the
solution. The resistance of the solution itself can be thought of as being determined by the specific resistivity of the electrolyte multiplied by the path length
taken by the current and divided by the cross-sectional area for current flow.
When the potential-dependent interfacial resistance becomes much larger than
the solution resistance, the current will tend to spread out to minimize the cell
voltage. This occurs because the incremental decrease in iR Ω voltage, brought
Current and Potential Distributions
189
about by minimizing the current path length by having all the current “crowd”
the geometrically close electrode position, is more than offset by the much larger
local true overpotential that results from crowding too much current to one area
of the electrode. By plotting local current density divided by the average current
density (i.e., total current/total area), the degree of nonuniformity can be seen
as a function of electrode position (7).
H. Use of the Wagner Polarization Parameter to Estimate
Qualitatively the Uniformity of Current Distribution
A dimensionless parameter known as the Wagner number is useful for qualitatively predicting whether a current distribution will be uniform or nonuniform
(1,6,7). This parameter helps to answer the question, Which current distribution
applies to my cell, primary, secondary, or tertiary?
The Wagner parameter may be thought of as the ratio of the kinetic resistance to the ohmic resistance. Hence when the Wagner number approaches numbers less than one, the ohmic component dominates the current distribution characteristics, and when it is much larger than one, the kinetic component dominates.
In practice, the primary current distribution is said to exist when W ⬍ 0.1, and
the secondary current distribution exists if W ⬎ 10 (6). The Wagner parameter
is the ratio of the true polarization slope, ∂E true /∂i (evaluated at the overpotential
of interest) divided by the characteristic length and the solution resistance (1,6).
W⫽
冢冣冢 冣
κ
L
∂E
∂i
(17)
where κ (or 1/ρ) is the specific solution conductivity (ohm-cm)⫺1 and L is a
characteristic length (cm), or the dimension of “irregularity.” We can take the
partial derivative, ∂E/∂I, of any analytical expression describing the interfacial
potential E true as a function of I or obtain a polarization slope, R p, from experimental E vs. I data. Such a slope can be evaluated at the average current density or
at any pertinent applied current density. The partial derivative, ∂E/∂i has the
units of Ω-cm 2. The solution resistance expressed in the same units is (κ/L). The
resulting Wagner number is
W⫽
Rp
RΩ
(18)
Thus the experimenter interested in estimating the current distribution “case”
pertinent to their polarization cell can estimate whether the primary or secondary
current distribution applies from knowledge of R p and R Ω.
The resulting Wagner numbers for various analytical expressions are shown
190
Chapter 6
Table 3 Wagner Polarization Number Determination
Current
distribution
Overpotential–current relationship
E ⫽ f(i)
Primary
Secondary
Secondary
...
E ⫽ Bi (linear)
E ⫽ B′ln(i/icorr) (Tafel)
Tertiary
E ⫽ [RT/nF]ln(l ⫺ i/il) (diffusion)
Polarization ∂E/∂i
resistance term
Wagner number
...
B
B′/i
κ/L
κB/L
κB′/iL
(RT/nF) ⋅
冢 冣
1
il ⫺ i
κRT/[nF(il ⫺ i)L]
in Table 3 for a number of current-overpotential cases. Note that a slightly different solution has been suggested.
The corrosion engineer can use this information in the following way. If
the primary current distribution applies (W ⬍ 0.1), then current distributions are
likely to be nonuniform unless one of the ideal cell geometries leading to uniform
primary current distributions (discussed in Table 2) is used. In the former case,
errors in polarization resistance and kinetic parameters are likely. In the latter
case, η app must still be corrected for iR Ω, using the relationships given in Eq. (2)
but the value of VIR will be the same at all positions along the electrode surface.
II. CURRENT DISTRIBUTIONS FOR SELECTED
GEOMETRIES OF INTEREST
Primary, secondary, and tertiary current distributions have been defined for selected geometries that are of practical interest to the corrosion engineer (2–6).
A.
Current and Potential Distributions for the Rotating
Cylinder Electrode
The rotating cylinder electrode with a concentric cylindrical counterelectrode is
an ideal geometry for minimizing nonuniformity in current distribution. The current density will be completely uniform at all vertical positions around the full
circumference of the inner cylinder, assuming little surface roughness (Fig. 6C)
in the primary, secondary, and tertiary current distributions. However, this is only
true for concentric cylinders that are of infinite length. For cylindrical samples
of finite length, the current density will be greater at the top and bottom edges
of the cylinders, except in the case of the tertiary current distribution. Here the
current density will be nearly uniform at all locations.
Current and Potential Distributions
191
B. Current and Potential Distributions for the Rotating
Disk Electrode
The rotating disk electrode will have a uniform tertiary current distribution but
an extremely nonuniform primary current distribution with the current density at
the electrode edge approaching infinity (8–12). For a disk electrode of radius r o,
embedded in an infinite insulating plane with the counterelectrode far away, the
primary current distribution is given by
i local
0.5
⫽
i avg
(1 ⫺ (r/r o )) 1/2
(19)
Since the isopotential lines are close together near the electrode edge, the gradient
of the potential will be greater, and it follows from this that the local current
density will be greater. This behavior is illustrated in Figs. 7a and b (1). In the
secondary case, the current density will be greater at the electrode edge but not
infinite. Figure 7c maps i local /i avg for various values of inverse Wagner numbers,
J ⫽ 1/W (1).
It is clear from the analysis of a disk electrode that when the electrode and
insulator reside in the same plane (i.e., a flush mounted disk or plate), the primary
current distribution is infinite at the electrode edge (13). Alternatively, the primary current distribution at the edge is zero if the angle between the insulator
and the edge is less than 90°. The primary current distribution is not zero or infinite only when the angle is exactly 90°. This is shown in Fig. 4.
C. Current and Potential Distribution for the Flow
Channel with Parallel Plates
The flow channel with parallel plates (Fig. 8a) will behave like the disk electrode
in that it will have a uniform or nearly uniform tertiary current distribution but
an extremely nonuniform primary current distribution (1,3,14–17). The tertiary
current distribution may also be nonuniform if the reacting species is depleted
at positions downstream from its upstream or leading edge. In the primary and
secondary cases, the current density will be much greater at all electrode edges.
Since the isopotential lines will bend so that they are closer together near the
electrode edge, the gradient of the potential will be greater, and it follows from
this that the local current density will be greater near such edges. A primary
current distribution for two parallel plates of length L, mounted flush within insulating planes that are separated by a distance much greater than the plate length,
has been given (3) by
i local
1
⫽
i avg
π[(x/L) ⫺ (x/L) 2] 1/2
(20)
192
Chapter 6
(a)
(b)
Figure 7 (a) Rotating disk electrode, flush mounted into an insulating plane. (b) Current
distributions for primary, secondary, and tertiary cases as a function of radial position r/
r o. (c) Variation of i local /i avg as a function of r/r o for various values of the reciprocal Wagner
number (J ⫽ 1/W) for the case of linear polarization kinetics on the disk electrode. (From
Refs. 1 and 9.)
Current and Potential Distributions
193
(c)
Here x is the distance along the plate starting at one of its edges. The distribution
is very nonuniform, as it is infinite at the edges and only 64% of the average in
the center of the electrode plate (3).
It should be mentioned that errors in both kinetic parameters and polarization resistance result from nonuniform primary or secondary current distributions
during such measurements (3). Figure 9 shows examples of the extent of such
errors (18). In this figure, R eff is the “measured” polarization resistance from linear
polarization or EIS corrected for the apparent value of R Ω determined from current interruption or high-frequency impedance. R p is the “true” value of the polarization resistance. The source of difference between R p and R eff lies in that no
single R Ω value applies for all electrode positions. That is, there is a nonuniform
potential drop. Depending on reference electrode position (center, infinity, edge),
there are large errors that represent the differences between R eff and the true R p.
These errors decrease as R eff, r o, or conductivity κ or their combination become
large (Fig. 9). When these parameters are large, the Wagner number becomes
large, indicating a more uniform current distribution and minimization of this
error.
194
Chapter 6
(a)
(b)
Figure 8 (a) Flow channel electrodes, flush mounted parallel to each other in insulating
planes. (b) Current distributions for primary, secondary, and tertiary cases. (From Ref. 1.)
D.
Two Parallel Cylinders
It is common in corrosion laboratories and in field corrosion monitoring probes
to immerse two vertical rods parallel to one another in an electrolyte. In the lab,
one of the rods consists of a high-density graphite counterelectrode while the
other is a working electrode. A reference electrode may be placed in between
the two rods. In the field, polarization resistance or electrochemical noise measurements are often made between two nominally identical rods that both consist
of the material of interest. The primary current distribution is nonuniform with
respect to circumferential position about each electrode when the distance between the two rods is small in comparison to the radius of the rod, Fig. 10a (16).
Again, the value of R Ω varies from where the rods face each other to where they
Current and Potential Distributions
195
Figure 9 Calculated error in polarization resistance measured, R eff, compared to true
polarization resistance, R p, on a disk electrode with the reference electrode at the center,
edge, and infinity as a function of conductivity, κ, disk radius, r o, and R eff. (From Ref. 18.)
face away from each other. Therefore no single value of R Ω can properly correct
polarization data. Alternatively, when the distance of separation between the rods
is great compared to their radius, then the local current becomes more uniform.
Essentially, all of the current will not crowd to the portions of the surfaces facing
each other when the distance required to spread out onto the rod surfaces facing
away is small compared to the distance of rod separation, Fig. 10b (16). The
transition from one regime to the other depends on the Wagner number.
E.
Microelectrode Disk
The microelectrode disk embedded in an insulating planar surface is a useful
arrangement for accessing high current densities without excessive ohmic resistances in low-conductivity environments. The reference electrode should be
placed far away. The solution resistance expression for a spherical electrode can
then be used, because ionic migration is hemispherical to an isolated disk in a flat
insulating plane for a counterelectrode located at infinity. The ohmic resistance to
a sphere has been given above in Table 2. In the limiting case, for large values
of d (d/r ⬎⬎ 1), when the reference electrode is placed far away from the microelectrode disk, is (6)
196
Chapter 6
(a)
(b)
Figure 10 (a) Equipotential and current lines for two parallel cylinders in the primary
current distribution. (b) i local /i avg as a function of electrode separation and angular position
around the cylindrical electrodes. 0 degrees represents the horizontal position between the
two electrodes. (From Ref. 16.)
RΩ ⫽
ro
κ
(21)
Here r o is the radius of the microelectrode disk. Note that R Ω has been normalized
to surface area, i.e., has units of Ω-cm 2. When this resistance is multiplied by
current density, an ohmic voltage drop is determined. Note that the area normalized resistance decreases as the electrode disk is made smaller (6). Thus small
Current and Potential Distributions
197
electrodes enable higher current densities to be accessed in low-conductivity environments.
III. CASE STUDIES
The geometries discussed above are relevant to laboratory scale experimental
cells. The geometries discussed below are more appropriate for situations encountered in industry or practical application involving galvanic corrosion, cathodic
protection, or field corrosion probes.
A. Polarization into a Recess or Crevice
A common situation of interest is the cathodic polarization of a recess or crevice.
A related industrial geometry is a field probe electrode that is immersed under
a film of electrolyte (18,19). This later case is similar to a crevice consisting of
an insulator on one face and a metallic electrode on the opposite, parallel face.
In the thin film situation, the insulator is the air–electrolyte interface. Nisancioglu
and Pickering have independently modeled this situation (20–22). Nisancioglu
considered a secondary current distribution solution for a metal embedded in an
insulating plane of length L c ⫺ L m (20) (Fig. 11A). The current and potential
distribution is considered only in the x direction, because x is much greater than
the crevice gap, h. The boundary conditions were as follows. There exists a current balance: the sum of all current in the walls equals the sum of all current in
the solution. The local current density in the electrolyte in the horizontal direction,
x, is ix, where ix ⫽ ⫺κ dE/dx such that dE/dx ⫽ 0 at x ⫽ 0, the end of the recess.
The reaction kinetics are linear and uniform at all crevice sites, and there is no
change in solution chemistry. It can be shown that the reciprocal of the Wagner
polarization parameter, J, is given by (20)
J⫽
L2m
κh(∂η/∂i)
(22)
As J approaches infinity (∂η/∂i approaching zero, or κ approaching zero), the
primary current distribution is reached, and the current density is infinite at
x/L m → 1. The current density is zero at all other x. As J approaches zero,
the current distribution is uniform. In this expression, the polarization resistance
∂η/∂i is assumed to be position- and potential-independent. The true interfacial
potential and local current distributions are given by
E(x) ⫽ E(s)
and
cosh(J 0.5x/L m )
cosh(J 0.5 )
(23)
198
Chapter 6
(a)
(b)
Figure 11 (a) Recess geometry where h is the crevice gap and x is the distance from
the bottom of the recess. (b) i local /i avg for x/L m. (From Ref. 20.)
Current and Potential Distributions
199
J 0.5 cosh(J 0.5x/L m )
sinh(J 0.5 )
(24)
i local ⫽ i(avg)
where E(s) is the potential at the entrance to the crevice so that E ⫽ E(s) at
x ⫽ L m. The current distribution for linear electrode kinetics (polarization resistance ⫽ ∂η/∂i), assuming various values of J (Fig. 11b) is shown below. Note that
lowering either the solution conductivity or the polarization resistance produces a
less uniform current distribution with greater current densities at the mouth of
the recess (for homogeneous electrode kinetics).
Ateya and Pickering have been concerned with the cathodic polarization
of a crevice or recess (21,22). Note that while the term crack has been used, the
crack half-angle is zero, which is not realistic for actual cracks. They focus on
the situation where the external surface is either anodically or cathodically polarized for various metals. Active/passive electrodes and actively corroding metals
have both been considered in these analyses.
B. Current and Potential Distributions at the Entrance
to a Circular Pipe
The entrance to a circular pipe is an important engineering geometry. It is often
necessary to attempt to protect cathodically the I.D. of the pipe using an anode
located at the pipe entrance. The question arises as to how far the cathodic current
can be “thrown” down the length of pipe. The engineer may also be confronted
with a situation where he must choose between overprotecting the tube entrance
with the undesirable possibility of hydrogen embrittlement versus the consequences of inadequately protecting the pipe I.D. at greater distances away. (An
example of this type of arrangement is the cathodic protection of heat exchanger
tube-sheets with an anode placed inside the water box at the end of the tube
bundle.) Cathodic disbondment of any protective coatings on the structure near
the anode may also be of concern.
Recall that the Wagner number depends on the solution conductivity, characteristic length, as well as the interfacial electrode characteristics. A solution
has been given for the primary current distribution where the entire interior pipe
surface (radius r o ) is uniformly cathodically protected to i w and the pipe interface
is considered to be nonpolarizable (16). The IR drop down the pipe to a distance,
L, can be calculated so that the maximum tolerable potential drop from the entrance to the far end is known:
V IR ⫽
i w L2
r oκ
(25)
Again, the problem with such a primary current distribution solution is that the
pipe–solution interface is assumed to be an equipotential surface. Instead, we
200
Chapter 6
would like to know how the interfacial potential varies with distance down the
pipe.
Therefore let us instead consider the more practical case of the tertiary
current distribution. Based on the dependency of the Wagner number on polarization slope, we would predict that a pipe cathodically protected to a current density
near its mass transport limited cathodic current density would have a more uniform current distribution than a pipe operating under charge transfer control. Of
course the cathodic current density cannot exceed the mass transport limited value
at any location on the pipe, as said in Chapter 4. Consider a tube that is cathodically protected at its entrance with a zinc anode in neutral seawater (4). Since
the oxygen reduction reaction is mass transport limited, the Wagner number is
large for the cathodically protected pipe (Fig. 12a), and a relatively uniform current distribution is predicted. However, if the solution conductivity is lowered,
the current distribution will become less uniform. Finite element calculations and
experimental confirmations (Fig. 12b) confirm the “qualitative” results of the
Wagner number (4).
Consider, on the other hand, a galvanic couple between a tube (Cu-Ni) and
a tube-sheet (Monel 400) where the reaction kinetics for both alloys are under
charge transfer control (4). Here the Wagner number would be slightly greater
than one. The resulting current distribution would be much less uniform, and the
galvanic interaction would cease at the short distance away from the tube-sheet
of a few tube diameters (Figs. 13a and b). However, after a corrosion film forms
on the tube anode material, the anodic polarization slope becomes quite large,
and the current is “thrown” further down the tube. Hence time effects can become
very important.
C.
Local Electrochemical Sites: Pits, Precipitates,
or Inclusions
The current and potential distributions between pits, precipitates, and inclusions
and the surrounding matrix are of great practical interest given that most materials
are not microstructurally homogeneous and that pitting is a common issue for
passive materials exposed to halides. The conductivity, potential differences, and
polarization characteristics determine how far away the matrix will experience
a galvanic interaction with the local site. Most solutions consider either the matrix
or the local site to be nonpolarizable and thus to create an equipotential surface.
Levich and Frumkin examined a disk-shaped cathode inclusion (23). Newman
examined the same case except that the inclusion was considered to be the anode
(24). Newman et al. examined the current and potential distribution in a hemispherical pit (25). An interesting variation of this issue is the question of the
anodic polarization of an Al matrix by the presence of a cathodic precipitate
phase. Cu-containing precipitate phases are common in age-hardened Al alloys
Current and Potential Distributions
201
(a)
(b)
Figure 12 (a) Tube-tubesheet arrangement showing qualitative effect of Wagner number. (b) Finite element model predictions, analytical model predictions, and experimental
verifications for 70-30 Cu-Ni tube coupled to anode grade zinc at the mouth of the tube
in quiescent seawater. (From Ref. 4.)
202
(a)
(b)
Chapter 6
Current and Potential Distributions
203
Figure 14 Potential distribution at the surface of the Al matrix near a theta phase precipitate assuming a nonpolarizable cathode site (Al 2Cu precipitate), polarizable passive Al
matrix, and a dilute acidic solution. The effect of precipitate size is shown. (From Ref. 26.)
and they are well known to induce pitting. The extent of anodic polarization of
the matrix to the more noble potential of the Cu-rich precipitate was of interest
(26). The precipitate was assumed to be nonpolarizable, which was reasonable
considering that fast cathodic reactions are possible on Cu-rich precipitates (26).
The matrix was assumed to be polarizable, which also was reasonable considering
that the matrix was passivated by Al 2O 3 prior to breakdown. The outcome was
the extent of cathodic polarization of the matrix as a function of solution conductivity, the radius of the precipitate particle, the polarization resistance of the matrix, and the open circuit potentials of the matrix and particles. The size of the
theta phase (Al 2Cu) particles governed the extent of anodic polarization of the
adjacent matrix in a dilute acidic solution as shown in Fig. 14. Metastable pitting
was observed only near precipitates, confirming the importance of local potentials.
Figure 13 Tube-tubesheet arrangement similar to Fig. 12 showing time effects on 9010 Cu-Ni coupled to Monel 400 tubesheet in flowing seawater. The strong time effect on
the potential distribution arises from a changing E corr for the Monel 400 and increased
kinetic resistance for the 90-10 Cu-Ni as oxide films thicken near the tube entrance. (From
Ref. 4.)
204
Chapter 6
Electrode roughness call also cause variations in current distributions (28).
Penetration of current into pores may be limited if the solution resistance of pores
is large relative to the polarization resistance.
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21. Ateya and Pickering. J. Electrochem. Soc. 122, 1018, (1975).
22. Ateya and Pickering. Corros. Science 37, 1443 (1995).
23. B. Levich, A. Frumkin. Acta Physiochimica U.R.S.S. 18, 325 (1943).
24. J. Newman. In: Advances in Localized Corrosion (H. Isaacs, U. Bertocci, J. Kruger,
S. Smialowska, eds.). NACE 9, Houston, TX, 1990, p. 227.
25. J. Newman, D. N. Hanson, K. Vetter. Electrochmica Acta 22, 829 (1977).
26. J. R. Scully. In: Critical Factors in Localized Corrosion (G. S. Frankel, R. Newman,
eds.). ECS PV 92-9, 1991, p. 144.
27. J. R. Scully, D. E. Peebles, A. D. Romig, Jr., D. R. Frear, C. R. Hills. Met. Trans.
A, 22A, 2429 (1991).
28. C. B. Diem, B. Newman, M. E. Orazem. J. Electrochem. Soc. 135, 2524 (1988).
7
Development of Corrosion Models
Based on Electrochemical
Measurements
I.
INTRODUCTION
Models to predict materials performance in industrial applications, or to assess
the environmental consequences of some industrial activity, are a major immediate need. The requirement for such models is driven by environmental concerns,
such as a desire to avoid groundwater contamination, and industrial concerns
such as the necessity of reducing costs by extending plant lifetimes and operating
efficiencies. Since many materials corrosion and mineral dissolution processes
are electrochemical in nature, electrochemical techniques are commonly used in
the study and development of solutions to these problems.
In many cases, the approach used has been mechanistically or empirically
qualitative, with the primary purpose of developing immediate solutions to pressing environmental problems, or of improving plant maintenance and operating
schedules and procedures. However, the need to preempt costly outages, extend
plant lifetimes, or perform environmental assessments is leading to efforts to
develop predictive models. The primary emphasis in this chapter is the development of such models and how electrochemical methods can be used in the process.
The problem and the required solution will dictate the experimental and
modeling approach adopted. Many trade-offs driven by the need to balance economical operation against public/personnel safety must be made. When cost is
the predominant driving force, engineering expediency leading to short-term solutions based only on qualitative assurances often dominate. Models for plant
behavior must be based on accurate and realistic data to avoid unnecessary and
costly shutdowns due to overly conservative predictions. Often, in this context,
accurately measured but empirical data may be more valuable than a fundamen205
206
Chapter 7
tal scientific understanding of the corrosion process. By contrast, when public/
personnel safety is the primary concern, a more rigorous scientific and technical
approach, one leading to longer term generic solutions, may be necessary, but
inadequate databases can be compensated for by conservative model assumptions.
Figure 1 attempts to define the key stages in the development of corrosion
models. Irrespective of whether the key concern is safety or operating efficiency,
the steps involved in model development are common up to the point where data
reliability must be accounted for (stage 8). At this juncture, the approaches deviate. When public/personnel safety is the key issue, one would adopt conservative
assumptions (stage 9A) to cover the uncertainties that will inevitably permeate
one’s model. If plant efficiency is the key issue, then at this juncture it is necessary
to refine one’s data input by a combination of further experimentation and the
careful consideration of information from plant inspection records (stage 9B).
Figure 1 General modeling scheme.
Models Based on Electrochemical Measurements
207
Within this scheme, the application of electrochemical methods will be key
in the determination of mechanism (stage 5) and the measurement of important
modeling parameters (stage 6). It will be clear that the relevance of the latter is
seriously reduced if the former is not addressed. This is because the influence
of the simplifying assumptions that are always required in modeling would be
unknown, and hence unquantifiable, if made in ignorance of a mechanistic understanding. Obviously, electrochemical methods also play a key role in the materials selection process (stage 2), but their discussion in this context is only briefly
addressed toward the end of this chapter.
Most of the examples used in this chapter emphasize assessment models
that can afford to incorporate conservative assumptions. Most deal with the environmental issue of nuclear waste disposal. This emphasis should not be taken to
suggest that the literature is not replete with many other examples of valuable
corrosion models. It is hoped that this chapter will encourage the reader to search
for them.
II. THE EVOLUTION OF THE CORROSION PROCESS
Corrosion occurs when a material is exposed to an environment in which it is
thermodynamically unstable. Generally, but not exclusively, materials degradation occurs under oxidizing conditions. Figure 2 illustrates the electrochemical
driving force for corrosion under oxidizing conditions; it is defined as the difference between the equilibrium potential of the material in the environment of
interest, E eM/Mn⫹, and the redox potential of the environment, E eOx/Red. Evolution of
the corrosion process with time could cause these potentials to change; i.e., the
e
n⫹
driving force for corrosion would not necessarily remain constant. Thus EM/M
would increase if dissolved corrosion product deposit with a more positive equilibrium potential, E eMOx/M, accumulated on the surface of the corroding material.
A decrease in E eOx/Red would occur if available oxidant was consumed with time.
Determining the evolution of the corrosion process with time may require
a significant amount of research, but at least a preliminary mechanistic understanding of the corrosion process is required before the development of a model
to predict corrosion behavior can commence. Such preliminary understanding
can be gained from a knowledge of the system corrosion potential, E CORR, and
how it changes with time.
The corrosion potential, E CORR, adopted by the system will be dictated by
the relative kinetics of the anodic material degradation process and the cathodic
reduction kinetics of the oxidant. While E CORR yields no quantitative information
on the rate of the overall corrosion process, its value, and how it changes with
time, is a good qualitative indication of the balance in corrosion kinetics and
their evolution with time. Thus a knowledge of E CORR and its comparison to ther-
208
Chapter 7
Figure 2 Electrochemical driving force for corrosion.
modynamic expectations (embodied in potential E e –pH diagrams) provides a
convenient reference point in model development. Also, the value of E CORR and
its proximity to breakdown (E B ) and repassivation potentials (E R ) is a key reference point in determining the probability of occurrence of localized corrosion
processes.
A preliminary knowledge of which reaction steps could be key in determining the overall corrosion rate can be assessed by measurements of E CORR as a
function of important system parameters, e.g., oxidant concentration, solution
composition, temperature. The proximity of E CORR to either E eM/Mn⫹ or E eOx/Red can
indicate which of the two half-reactions may be rate determining. This is illustrated in Fig. 3A, which shows an Evans diagram for the combination of a fast
anodic reaction coupled to a slow cathodic one. The corrosion of iron or carbon
steel in aerated neutral solution would be an example of such a combination. The
anodic reaction requires only a small overpotential (η ⫽ E eM/Mn⫹ ⫺ E CORR ) to
sustain the corrosion current, I CORR, compared to the much larger overpotential
required to sustain the cathodic reaction at this current. The anodic reaction would
Models Based on Electrochemical Measurements
209
(A)
(B)
Figure 3 (A) Evans diagram illustrating the change in I CORR and E CORR for the increase
in rate (from 1 to 2) of a fast anodic reaction coupled to a slow cathodic reaction. (B)
Evans diagram for the same combination, illustrating the influence of a change in rate of
the slow cathodic reaction (from 1 to 2).
be termed the potential-determining one. A change in the rate of the anodic reaction (line 1 to line 2 in Fig. 3A) exerts little influence on the corrosion rate but
a measurable effect on E CORR, whereas the opposite is true for a change in the
cathodic reaction rate (line 1 to line 2 in Fig. 3B).
For many corroding systems, such a distinct separation in kinetics is not
so readily obvious, but for those for which such a condition prevails, preliminary
knowledge of this kind may greatly simplify the form of any predictive model
210
Chapter 7
that might be developed. For the above example one might choose to model
only the rate-determining cathodic half-reaction. If the corrosion process does
not evolve with time, then the development of a corrosion model would be unnecessary, and a straightforward measurement of corrosion rate would suffice. However, for more complex situations, a knowledge of how the corrosion process
evolves with time is essential to the development of a model. Again, a preliminary
understanding of what parameters may dictate this temporal evolution can be
obtained from E CORR measurements.
In an environment with a constant redox condition (e.g., permanently aerated and/or constant pH), a condition not uncommon in industrial and environmental situations, E CORR could shift in the positive direction for a number of reasons. Incongruent dissolution of an alloy could lead to surface ennoblement.
Alternatively, as corrosion progresses, the formation of a corrosion product deposit could polarize (i.e., increase the overpotential, η, for) the anodic reaction
as illustrated in the Evans diagram of Fig. 4. Polarization in this manner may be
due to the introduction of anodic concentration polarization in the deposit as the
rate of transport of dissolved metal species away from the corroding surface becomes steadily inhibited by the thickening of the surface deposit; i.e., the anodic
half-reaction becomes transport controlled.
The introduction of transport effects due to the formation of corrosion product deposits would not necessarily be confined to one half-reaction. It is likely
that transport of the oxidant to the corrosion site would also be polarized. Such
an effect, coupled possibly to a consumption of the oxidant in the bulk environment, would make the evolution in E CORR with time much more difficult to inter-
Figure 4 Evans diagram for the coupling of a fast anodic reaction to a slow cathodic
reaction, illustrating the influence of the formation of a corrosion product deposit.
Models Based on Electrochemical Measurements
211
Figure 5 Evans diagram illustrating the influence on I CORR and E CORR of a corrosion
product deposit that affects both the anodic and cathodic half-reactions. The solid lines
are for no deposit; the dashed lines illustrate the changes in the presence of the deposit.
pret, as illustrated in the Evans diagram of Fig. 5. The shift in E CORR anticipated
due to anodic concentration polarization would be offset by a similar effect of
the deposit on the cathodic half reaction. While its behavior may not be mechanistically definitive, the evolution of E CORR with time does provide a qualitative template upon which to base the development of a corrosion model.
An example is shown in Fig. 6 for UO 2 (nuclear fuel) in the near neutral
to slightly alkaline environment anticipated in a Canadian nuclear waste disposal
vault. The E CORR –time plot is schematic but is representative of that obtained in
many laboratory experiments and is anticipated under waste disposal conditions.
The reaction sequence was demonstrated for corrosion conditions by analyzing the surface composition of the fuel [using x-ray photoelectron spectroscopy
(XPS)] as a function of the E CORR achieved (1). The observed onset of surface
oxidation around ⫺0.3 V (vs. SCE) obviously matches thermodynamic expectations, as is indicated by the equilibrium stability zones (bottom right in Fig. 6)
for various oxidized uranium phases. The equilibrium potential for an aerated
solution environment is shown in the top right corner. The difference between
upper and lower shaded areas defines the thermodynamic driving force for the
corrosion process (as described in Fig. 2). In this case, E CORR does not achieve
a value conveniently close to either equilibrium potential, and the question of
overall rate control cannot easily be decided. While the change in fuel surface
composition as the steady-state E CORR value (E CORR ) SS is approached may be instructive, any model used to predict long-term fuel behavior under permanent
disposal conditions must focus predominantly on the oxidative dissolution of
212
Chapter 7
Figure 6 Schematic showing the evolution of E CORR and the reactions occurring with
time for the oxidation of nuclear fuel (UO 2 ) in neutral noncomplexing solution. The lines
marked by uranium phases show the equilibrium potentials for the formation of discrete
phases: E eO2 /H2 O is the system redox potential for these conditions.
the oxidized fuel and the accumulation of corrosion product deposits (secondary
phases); e.g., UO 3 ⋅ 2H 2O on the fuel surface. Once accumulated, these corrosion
product deposits could maintain oxidizing conditions at the UO 2 fuel surface for
a very long time even if all available oxidant is consumed; hence, E eO2 /H2O falls
considerably. As indicated in the figure, a fall in E CORR of ⬃300 mV from the
steady-state value would be required before a UO 3 ⋅ 2H 2O deposit would become
thermodynamically unstable. In the absence of oxidant, its removal to expose the
underlying UO 2 surface would proceed by a chemical dissolution process in neutral solutions. This would be expected to be very slow. A combination of cyclic
voltammetry and photothermal deflection spectroscopy was used to demonstrate
that the onset of oxidation was accompanied by the onset of dissolution around
⫺0.3 V, Fig. 7 (2). This knowledge of when dissolution commences/ceases is a
key modeling parameter, since it provides a measured criterion for fuel stability.
III. DETERMINATION OF THE RATES OF CORROSION
REACTIONS
Corrosion can be considered as a galvanic cell in which an anodic and cathodic
half-reaction couple to yield the overall corrosion reaction, Fig. 8. The overall
reaction proceeds at a rate I CORR (⫽ I A ⫽ |I C |) at the corrosion potential, E CORR.
Models Based on Electrochemical Measurements
213
Figure 7 Electrochemical photothermal deflection spectroscopy experiment (0.5 mol ⋅
dm⫺3 Na 2SO 4; pH ⫽ 10.5, 20 mV⋅s⫺1 ), illustrating the detection of the onset of dissolution
of nuclear fuel (UO 2 ); (A) voltammetric response for scans to various anodic potential
limits; (B) and (C) probe beam deflection for each scan. The deflection of the probe beam
is proportional to the dissolved uranium concentration, and deflection of the probe beam
towards the electrode surface is an indication that dissolution is occurring (Reprinted from
Ref. 2 with permission from Elsevier Science S.A.)
214
Chapter 7
Figure 8 Current–potential relationship for a corrosion process, showing the separation
of the anodic and cathodic half-reactions by polarization to positive and negative potentials, respectively.
However, since this corrosion reaction is short-circuited on the corroding surface,
no current will flow in any external measuring circuit. Consequently, a direct
electrochemical measurement of the corrosion current (convertible to corrosion
rate by the application of Faraday’s law) cannot be made. Despite this limitation, electrochemical techniques can be used to decouple the two half-reactions,
thereby enabling each to be separately and quantitatively studied. This involves
the determination of the current–potential relationships for each half-reaction.
Subsequently, the behavior under electrochemically unperturbed (open-circuit or
natural corrosion) conditions can be reconstructed by extrapolation of these relationships to E CORR.
A.
Active Corrosion Conditions
This process of electrochemically “deconstructing” the corrosion reaction provides a convenient experimental methodology for investigating active corrosion
conditions and is illustrated schematically in Fig. 8. Each half-reaction should
obey Butler–Volmer kinetics, in which the current increases exponentially [posi-
Models Based on Electrochemical Measurements
215
tively (anodic) or negatively (cathodic)] with applied potential. For a sufficiently
large applied potential the two half-reactions are totally decoupled, and the individual Tafel relationships,
log|I | ⫽ log I CORR ⫾ b(E CORR ⫺ E APPLIED)
(1)
can be determined. Extrapolation of these relationships to E CORR (as illustrated
in Fig. 8) then allows a determination of I CORR.
This approach is experimentally intrusive, since large currents leading to
irreversible surface damage can be sustained, particularly when recording the
anodic relationship. By restricting the potential perturbation from E CORR to ⬃ ⫾10
mV, such damage can be minimized and the current measured in the linear region
around E CORR (i.e., within the box in Fig. 8). This linear current–potential region
arises because the exponential terms in the Butler–Volmer equation can be linearized for such small values of E CORR ⫺ E APPLIED. Under these conditions, the two
half-reactions are only partially decoupled, and the measured current contains
contributions from both. Techniques that utilize this approach to determine a
charge transfer resistance (inversely proportional to I CORR ) are linear polarization
(LP) and electrochemical impedance spectroscopy (EIS).
Despite the obvious advantage of these minimal perturbation techniques,
their application requires a knowledge of Tafel slopes in order to convert the
measured charge transfer resistances into corrosion currents/rates. In many applications, the use of LP and EIS is difficult or impossible, a modeling approach
based on Tafel relationships is more appropriately or more easily applied. Their
determination, however, is not always as simple as would initially appear. The
currents that must be used in Tafel analyses are steady-state values free of contributions from solution transport. Also, if large currents are measured in resistive
media [e.g., in dilute solutions with a high resistance, R S, or on electrodes with
a substantial bulk resistance, R B (e.g., UO 2 )], then the curves must be corrected
for the distortion caused by IR S and/or IR B effects. Providing R S (and/or R B ) is
known, this second correction is readily made, and most modern electrochemical
equipment is capable of making this correction using either a current interrupt
or a feedback methodology.
The elimination of transport effects is not so readily achieved. One relatively
simple procedure is to measure currents (Im ) as a function of electrode angular
velocity (ω) using a rotating disc electrode. Currents free of diffusive transport
effects (Ik ) can then be obtained by application of the Koutecky–Levich equation,
⫺1
⫺1/2
I⫺1
m ⫽ I k ⫹ Bω
(2)
where B is a constant. An example would be the anodic dissolution of Cu in strong
chloride solutions, which has been shown to proceed via the two steps (2,3)
Cu ⫹ Cl⫺ s CuCl ad ⫹ e (surface)
(3)
216
Chapter 7
Figure 9 Use of the Koutecky–Levich equation to correct for diffusive transport effects
on the anodic dissolution of Cu in 1 mol ⋅ dm⫺3 NaCl recorded on a rotating disk electrode.
CuCl ad ⫹ Cl⫺ s Cu(Cl) 2⫺
(bulk)
(4)
followed by the slow transport step,
Cu(Cl) 2⫺ (surface) → Cu(Cl) 2⫺ (bulk)
(5)
The fit to the Koutecky–Levich equation, Fig. 9, demonstrates that the anodic dissolution of Cu occurs under mass-transport control, and extrapolation of
these fits to ω⫺1/2 ⫽ 0 yields kinetically controlled currents, I k, free from transport
effects and appropriately used in Tafel plots.
The Tafel expressions for both the anodic and the cathodic reaction can be
directly incorporated into a mixed potential model. In modeling terms, a Tafel
relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction (E e ), and the exchange current density (I 0 ), where
the latter can be easily expressed as a rate constant, k. An attempt to illustrate
this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride
solutions as an example. The equilibrium potential is calculated from the Nernst
equation; e.g., for the O 2 reduction reaction,
(E e )c ⫽ (E o )c ⫺
[OH⫺]4
RT
ᐉn
nF
p O2
(6)
As indicated in the figure, extrapolation of one or both of the Tafel lines to E CORR
yields the condition
Models Based on Electrochemical Measurements
217
Figure 10 Schematic Tafel relationships showing the key parameters, E e, I 0, and b,
which define them. The sets of lines indicate the expected influence of concentration on
the anodic and cathodic reactions.
log I A ⫽ log|I C| ⫽ log I CORR
(7)
and hence a value of the corrosion rate.
Also shown in Fig. 10 are additional lines indicating the influence of O 2
and Cl⫺ concentrations on the Tafel relationships. The lines allow the determination of reaction orders with respect to these reaction participants and yield the
following expressions for the anodic and cathodic Tafel lines:
I A ⫽ n AFk A[Cl⫺ ]2 exp{b A (E ⫺ (E e )A)}
(8)
I C ⫽ n CFk C[O 2 ] exp{⫺b C (E ⫺ (E )C)}
(9)
e
where n A and n C are the number of electrons involved in the anodic and cathodic
reactions.
Implicit in these relationships is that both the anodic and the cathodic halfreactions are polarized far from their equilibrium potentials (i.e., E ⫺ E e is large)
and hence are irreversible. For the O 2 reduction reaction this is inevitably so, but
for reactive metals like Cu (and Fe, Zn) this may not be so.
This fact, and the more complicated two-step nature of the anodic reaction
[via steps (3) and (4)], could be incorporated into the Tafel relationship to yield
218
Chapter 7
I A ⫽ n AF(k A )f[Cl⫺ ]2 exp{b A (E ⫺ (E e )A)} ⫺ (kb)2[CuCl2⫺]
(10)
where (k b ) 2 is the rate constant for the reverse of reaction (4) and (k A ) f is a composite rate constant,
(k A ) f ⫽
(k f ) 1
(k b )1(k f ) 2
(11)
with (k f ) 1 and (k b ) 1 being the forward and reverse electrochemical rate constants
for reaction (3), and (k f ) 2 the forward rate constant for the chemical reaction (4).
Obviously, the use of Eq. (10) as opposed to Eq. (8) would require a more detailed
quantitative knowledge of the anodic reaction. A more extensive discussion of
the details of this corrosion process has been given elsewhere (5).
It is worth emphasizing that the reaction orders measured for the individual
half-reactions are not necessarily the same as those for the overall corrosion reaction. Manipulation of Eqs. (7) and (8) to yield an expression for I CORR predicts
a reaction order (nO2 ) with respect to O 2 (assuming [Cl⫺ ] constant) given by
nO2 ⫽ b C (b A ⫹ b C )⫺1
(12)
i.e., the reaction order is determined by the Tafel slopes. Only when b A ⬍⬍ b C
will n O2 → 1. Under these circumstances the cathodic half-reaction would be
extremely polarized and totally rate determining [see Fig. 3 (A and B)]. The other
extreme (b A ⬎⬎ b C ) would, of course, yield a corrosion rate independent of O 2
concentration, since the anodic reaction would be rate determining. This latter
condition might be expected for the corrosion of passive metals or those whose
corrosion is severely hindered by the presence of a corrosion product deposit.
Relationships such as that in Eq. (12) offer convenient means of testing the
validity of mixed potential models by comparing electrochemically determined
parameters (in this case, a reaction order based on measured Tafel slopes) to
values measured by other means. One such example would be the corrosion of
UO 2 (nuclear fuel) in aerated neutral solutions containing added carbonate (6).
In the presence of carbonate, corrosion product deposits are avoided, since the
UO22⫹ corrosion product is solubilized by complexation with the carbonate. Measured Tafel slopes yield a predicted reaction order of nO2 ⫽ 0.67 with respect to
O 2 for the overall corrosion reaction:
UO 2 ⫹ O 2 ⫹ 2CO32⫺ ⫹ 2H 2O s UO 2 (CO 3 )22⫺ ⫹ 4OH⫺
(13)
This value is in excellent agreement with the range of values (0.69 to 0.74) measured in chemical dissolution experiments.
The determination of a Tafel slope for O 2 reduction illustrates some of the
difficulties encountered in determining a value of this parameter and emphasizes
the need for a thorough understanding of the reaction mechanism if the develop-
Models Based on Electrochemical Measurements
219
Figure 11 Transport- and IR-compensated O 2 reduction currents as a function of potential recorded on nuclear fuel (UO 2 ) in 0.1 mol ⋅ dm⫺3 NaClO 4 (pH ⫽ 9.5). The electrode
was cathodically reduced before the experiment. (1) Data recorded from the most negative
to the most positive potential, showing the behavior on a reduced UO 2 surface. (2) Data
recorded from the most positive to the most negative potential after corrosion in aerated
solution, illustrating the behavior on an oxidized UO2⫹x surface.
ment of a justified model is to be achieved. The kinetics for this reaction change
with the composition of the corroding surface. For example, O 2 reduction on UO 2
surfaces is accelerated if the surface is preoxidized as would be the case for the
corrosion of UO 2 under oxidizing conditions. This is illustrated in Fig. 11, which
shows the O 2 reduction current on reduced (UO 2 ) and oxidized (UO 2⫹x ) surfaces.
Not only is the current higher on the oxidized surface, but also the slope of the
Tafel plot changes with potential, since the degree of oxidation of the surface (x
in UO 2⫹x ) changes with potential. The appropriate data to use in a model for UO 2
220
Chapter 7
Figure 12 Schematic illustrating the mechanism of cathodic reduction of O 2 at donor–
acceptor (U IV /U V ) sites on UO 2 (nuclear fuel).
corrosion is that recorded on the oxidized surface in the potential range ⫺0.2 to
⫺0.4 V; i.e., closest to the natural corrosion conditions prevailing at E CORR. This
behavior is attributable to the fact that the breaking of the OEO bond during
O 2 reduction on oxide surfaces requires catalysis by mixed oxidation states available in the surface of the oxide (7,8). This is illustrated in the schematic mechanism for O 2 reduction on UO 2 shown in Fig. 12. The presence of oxides on metal
surfaces can similarly distort O 2 cathodic kinetics (9–11), making it difficult to
specify a Tafel relationship.
In some situations the determination of Tafel relationships for anodic and
cathodic reactions is extremely difficult and may be impossible. However, this
does not necessarily disqualify the use of electrochemical methods to provide a
database of corrosion rates for use in models. An example would be the determination of nuclear fuel (UO 2 ) corrosion rates in radiolytically decomposed water.
In this case, the determination of Tafel slopes for the anodic dissolution of UO 2
in neutral to slightly alkaline solutions is achievable, as illustrated in Fig. 13 (6),
which shows a series of such plots for solutions containing various amounts of
dissolved carbonate. However, the cathodic half-reaction is the reduction of oxidants produced by the radiolytic decomposition of water. Depending on the nature
of the radiation (α, β, γ), a range of reactive oxidants (predominantly OH°/O 2⫺
for γ/β-radiation, and H 2O 2 /O 2 for α-radiation) is produced in relatively small
concentrations (12) at the radiation dose rates expected in fuel storage and disposal conditions. For γ-radiolysis, the extremely reactive radical species (OH°,
O 2⫺ ) appear to react with the fuel surface under diffusion controlled conditions.
This dominance of diffusion control and the low concentrations make it impossible to determine a cathodic Tafel relationship. Alpha radiolysis is a high linear
energy transfer form of radiation that deposits all its energy in a layer of solution
⬃25 µm thick adjacent to the fuel surface, a situation for which it is again impossible to measure a Tafel relationship.
However, a measurement of E CORR in these environments is relatively simple. To obtain E CORR as a function of γ-radiation dose rate it is simply necessary to
Models Based on Electrochemical Measurements
221
Figure 13 Electrochemically determined anodic dissolution currents recorded on a rotating nuclear fuel (UO 2 ) disk (ω ⫽ 16.7 Hz) in 0.1 mol ⋅ dm⫺3 NaClO 4 (pH ⫽ 9.5)
containing various amounts of carbonate; (䊐) 0.005 mol ⋅ dm⫺3; (䉱) 0.01; (⫻) 0.05; (䊊)
0.1. Line 1 is the line that would fit the dissolution currents recorded with no carbonate
present. Line 2 is a line of the same slope as line 1 shifted up two orders of magnitude
in current.
conduct the measurement in a γ-cell (13). For measurements in α-radiolyticallydecomposed water, the electrode is brought within 25 µm of a gold-plated αsource using a thin-layer electrochemical cell arrangement. Figure 14 shows the
key electrode-source gap area of such a cell and illustrates the key reactions and
features involved in this measurement. Since diffusive loss of oxidants from the
periphery of the gap is possible (J O2, J H2O2 ), it is necessary to model this geometric
arrangement using finite difference methods and radiolysis codes to obtain a relationship between E CORR and radiolytic oxidant concentration (14). This involves
solving the radial reaction-diffusion equation
222
Chapter 7
Figure 14 Schematic of the thin-layer electrochemical cell used to measure the influence of alpha radiolysis of water on the corrosion of nuclear fuel (UO 2 ).
冦 冧
∂c i D i ∂
∂c
⫽
r i
∂t
r ∂r
∂r
(14)
for the many species, i, involved. Subsequently, an extrapolation of the anodic
Tafel relationship to individual E CORR values measured in the above manner can
be used to produce a database of corrosion rates as a function of radiolytic oxidant
concentration. This procedure is illustrated schematically in Fig. 15. As illustrated
Figure 15 Procedure used to obtain a database of nuclear fuel (UO 2 ) corrosion rates
(currents) (B) from a Tafel relationship for the anodic dissolution currents for UO 2 and
a series of E CORR values measured in radiolytically decomposed solutions (A).
Models Based on Electrochemical Measurements
223
Figure 16 Illustration of the procedure used to evaluate fuel corrosion performance in
a nuclear waste vault: (A) fuel corrosion rate as a function of radiation dose rate [from
(B) in Figure 15]; (B) calculated radiation dose rate decay curve; (C) fuel corrosion rates
as a function of time in a waste vault. The dashed line indicates that there is a limit to
the acceptable extrapolation of rates determined electrochemically.
in Fig. 16, this database of rates can then be used with the easily calculable
radiation decay characteristics of the fuel to predict the evolution of fuel corrosion
rate as a function of time in a waste disposal vault.
B. Influence of Corrosion Product Deposits
Inevitably, corrosion is not a process that proceeds by straightforward, uncomplicated active dissolution, especially over extended exposure periods. Reactive materials (e.g., Fe, carbon steel, Cu, UO 2 ) corroding in neutral to slightly alkaline
solutions (4 ⬍ pH ⬍ 9) when oxide/hydroxide solubilities are low, tend to accumulate corrosion product deposits.
224
Chapter 7
These deposits will form at a rate determined by the material corrosion rate
and the solubility of the deposit in the exposure environment. Predicting their
rate of thickening and their ability to attenuate the corrosion rate of the substrate
material could be a complicated procedure. The process involves at least one
moving boundary (the material/deposit interface) and a knowledge of the evolution of deposit morphology, especially its porosity, as a function of increasing
thickness. Also, the chemistry within the pores of a deposit is likely to differ
from that of the general exposure environment and to involve diffusion gradients
of various species such as dissolved metal cations, cathodic reagents (e.g., O 2 ),
and pH. A detailed discussion of these features is beyond the scope of this chapter,
but it is worth noting that a steady-state condition can evolve with extended
exposure (15,16), and that key properties, such as porosity, would then be approximately constant.
For the sake of this discussion, it is assumed that the deposit is electrically
insulating. This limits the available anodic and cathodic sites to the material surface at the base of the pores. If it is assumed that steady-state conditions exist
within the deposit, then the only film parameter that changes as corrosion progresses will be its thickness. Ideally, the deposit can be considered to contain a
uniform distribution of cylindrical pores, each of radius r i and length l with the
latter equivalent to the thickness of the film. The cross-sectional area of the pores
will be ∑πr 2i, their volume ∑πr 2il, and the total volume of the deposit including
pores, lA.
If the geometric surface area of the film is A, the total porosity of the deposit
(ε) will be given by
ε⫽
πr 2i
冱A
(15)
i
Consequently, the fraction of the fuel surface area exposed at the base of the
pores is equal to ε. Since corrosion is confined to this exposed area, the rates of
the interfacial anodic and cathodic reactions [i.e., Eqs. (7) and (8)] must be multiplied by this factor, ε, to account for the reduction in effective cross-sectional
area. Figure 17 shows a schematic representation of this model.
This idealized model does not capture all of the essential details of corrosion deposits. As indicated in Fig. 17, the influence of local chemistry within the
deposit (especially pH effects) is likely to separate the corrosion site (at the
material/deposit interface) from the site at which the deposit forms (deposit/
environment interface). Consequently, diffusion processes within the porous deposit must be involved if corrosion is to be sustained. Under simple steady-state
conditions, diffusion can be treated simply using the Nernst diffusion layer approach; i.e., the flux, J, of a species dissolving in a pore will be given by
Models Based on Electrochemical Measurements
225
Figure 17 Schematic of an idealized corrosion product deposit on a corroding surface;
l is the pore length, ε A the fracture of the surface area exposed to the corrosion environment; (1 ⫺ ε A) is the fraction of the surface blocked by corrosion product deposit.
J ⫽ D eff
∆c
∆c
⬃ D eff
∆x
l
(16)
where ∆c is the difference in species concentration over the length of the pore,
and the effective diffusion coefficient, D eff, is the solution diffusion coefficient
(D) attenuated by the porosity (D eff ⫽ εD). If we now accept a more general
model, in which the corrosion product deposit is considered as a tortuous but
continuous network of interconnected pores, Fig. 18, then the diffusion path
length can be significantly greater than the film thickness, and the effective diffusion coefficient must be modified by a tortuosity factor (τ); i.e.,
D eff ⫽ ετD
(17)
226
Chapter 7
Figure 18 Schematic showing a corrosion product deposit composed of interconnected
tortuous pores illustrating that the diffusion path length of dissolved species or dissolved
oxidant through the deposit is greater than the thickness of the deposit.
Thus the key parameters influencing the corrosion rate under deposits will
be the deposit porosity, which determines the available surface area of material
for corrosion, and the deposit tortuosity, which along with porosity will modify
the fluxes of diffusing species within pores. Readers interested in a more extensive discussion are referred to other sources (17). Here we concentrate on a brief
discussion of electrochemical methods of investigating the properties of deposits
as a basis for eventual modeling.
A primary methodology for investigating such processes is impedance
spectroscopy (EIS). The interpretation of EIS data using equivalent circuits can
yield a substantial amount of information on the properties of evolving films,
and many detailed studies have been published (18,19). Here we attempt only
to capture the essential features of such analyses. It should be noted before proceeding that, as with many electrochemical techniques, EIS records only a general
surface response and does not yield site-specific information. For the present
application, this means that EIS may successfully detect low-impedance pathways associated with pores but cannot differentiate easily between a large number
of narrow pores and a small number of larger ones; i.e., it cannot on its own
provide an accurate measure of deposit porosity. Microscope, metallographic and
mercury porosimetry (20) measurements are necessary complements.
Figure 19 (A to E) shows a collection of potential EIS responses and possi-
Models Based on Electrochemical Measurements
227
Figure 19 Schematic Bode plots from EIS measurements and equivalent circuits that
could be used to fit them for various possible corrosion product deposit structures: (A)
nonporous deposit (passive film); (B) deposit with minor narrow faults such as grain
boundaries or minor fractures; (C) deposit with discrete narrow pores; (D) deposit with
discrete pores wide enough to support a diffusive response (to the a.c. perturbation) within
the deposit; (E) deposit with partial pore blockage by a hydrated deposit: (1) oxide capacitance; (2) oxide resistance; (3) bulk solution resistance; (4) interfacial capacitance; (5)
polarization resistance; (6) pore resistance; (7) Warburg impedance; (8) capacitance of a
hydrated deposit.
228
Figure 19 Continued
Chapter 7
Models Based on Electrochemical Measurements
229
ble equivalent circuits that could be used to interpret them in terms of deposit
properties. The key features in the spectra illustrating the influence of the deposit
on the corrosion process are to be found at the low-frequency ends of the spectra.
For a nonporous deposit, the response and simple parallel circuit shown in Fig.
19A would be expected. Since R F ⬃ 10 6 ohm ⋅ cm⫺2, the deposit effectively acts
as a capacitor. Such a deposit is unlikely, and a system yielding this kind of response can be considered passive, since corrosion at the material/deposit interface
could only be sustained by film dissolution/corrosion at the oxide/solution interface. Passivity is dealt with in the next section.
Deposits with extremely low porosities or an interconnected network of
fine crystalline grain boundaries would be expected to show some loss of phase
shift at low frequencies (i.e., a less than fully capacitative response) as the real
resistance of the flaws becomes detectable, Fig. 19B. The value of R F obtained
is inversely proportional to the corrosion rate.
Eventually, as pores increase in size, additional equivalent circuit elements
are required to account for the detection of these pores as discrete time constants
in the low frequency end of the spectrum, Fig. 19C. As frequencies are scanned
to lower values in recording the EIS spectrum, the frequency at which the decrease in phase shift (i.e., a decrease in absolute value of the phase angle) commences provides an indication of either the number density of fine pores or the
dimensions of a smaller number of larger pores. The value of the pore resistance
(R PORE ) is a more direct indication of pore dimension. The interfacial capaci-
230
Chapter 7
tance (C I ) approaches values anticipated for the double-layer capacitance at the
material/solution interface but could be significantly increased if adsorbed intermediates are involved in the interfacial corrosion process [e.g., Fe(OH) ads in carbon steel corrosion or (UO 2HCO 3 ) ads in nuclear fuel corrosion]. The interfacial
resistance, R I, is the system polarization resistance and is inversely related to the
corrosion rate. Since both anodic and cathodic reactions occur at the base of
pores in the deposit, R I cannot distinguish which of these two reactions is of
overriding importance in determining the corrosion rate. An attempt to separate
the response of these reactions using EIS has been published (21).
For wider pores it becomes possible to detect the influence of diffusive
transport within the pores. Under these circumstances, the use of the Warburg
impedance (Z w ) is required to fit the data, where
Z w ⫽ σω⫺1/2 (1 ⫺ j )
(18)
and σ (ohm s 1/2 ) is the Warburg impedance coefficient. When diffusion is the
dominant (rate controlling) process, the log |Z| vs. log f (frequency) plot will
approach a slope of ⫺0.5 and a phase angle (θ) of ⫺45 degrees as ω → 0.
Inevitably, diffusion is not totally dominant, and control of the corrosion process
at the base of the pore will be partially controlled by interfacial kinetics. For this
situation, the slope of log |Z| against log f will change with frequency in the rage
0 to ⫺0.5, and θ will change with frequency over the range 0 to ⫺45 degrees,
as illustrated in Fig. 19D.
The final section of Fig. 19, E, shows the EIS response anticipated if the
accumulation of hydrated deposits were to partially reseal the pores. These deposits tend to act like a capacitor, C H. Such an EIS response would be anticipated
in complex environments (e.g., ones containing a number of anions) or in pores
with complex chemistry (e.g., containing large gradients in pH and/or metal cation complexants). It is clear from the Bode plots in Fig. 19 that distinguishing
between possible behaviors is not simple.
Many of these approaches have been used in mixed potential models to
predict the behavior of copper nuclear waste containers in a compacted clay environment (22), and to predict the corrosion rate of nuclear fuel inside these containers once they have failed and water allowed to contact the nuclear fuel (UO 2 )
wasteform (6). The container is lined with a carbon shell liner to give it mechanical integrity. Consequently, when the container floods with water on failure,* two
corrosion processes are possible, corrosion of the UO 2 wasteform (conservatively
assumed to be unprotected by the Zircalloy cladding within which it is encapsulated) and corrosion of the carbon steel liner. The reaction scheme underlying
* This is an example of a conservative assumption permissible in such a performance assessment
model. In reality, a narrow aperture failure in the copper shell would allow only a very slow entry
of water into the container.
Models Based on Electrochemical Measurements
231
this model is shown in Fig. 20. The two interfacial corrosion processes are linked
by the aqueous environment, a scenario that introduces the possibility that each
corrosion process can interfere with the other. Interconnecting diffusion processes
makes a wide range of adsorption, desorption, solution redox, and precipitation
processes possible (6). Fuel corrosion will be driven by the alpha radiolytic production of the oxidants H 2O 2 and O 2 and carbon steel corrosion by reaction with
water. A key potential interaction that could suppress fuel corrosion is the scavenging of the radiolytic oxidants (H 2O 2, O 2 ) by Fe 2⫹ formed by carbon steel corrosion reactions (k 4, k 5 ).
The model solves a set of 10-one-dimensional reaction–diffusion equations
2⫺
for the ten key species involved in corrosion processes [UO2⫹
2 , UO 2(CO 3 ) 2 ,
2⫹
II
IV
2⫹
UO 3 ⋅ 2H 2O, CO2⫺
,
O
,
H
O
,
Fe
,
(Fe
)
,
(U
)
,
(UO
)
],
2
2 2
ppt
ppt
3
2 ads
ε
冦
冧 冱R
∂
∂c
∂c i
⫽
τεD i i ⫹ ε
∂t
∂x
∂x
10
j
(19)
j⫽1
where Rj represents the chemical reactions occurring in the system; the diffusion
coefficient, Di, is modified to take into account that the species will, on occasion,
be diffusing within the porous corrosion product layers on the two corroding
surfaces. The boundary conditions within this model are the electrochemical expressions, similar in form to those shown in Eqs. (8) and (9) above, for those
species involved in anodic and cathodic reactions at the fuel and carbon steel
surfaces.
The fuel corrosion rate is given by
I CORR ⫽
冱I
Anod
⫽ IUO2⫹
⫹ I UO2 (CO3)2⫺
2
2
(20)
i
The two anodic reactions on the fuel surface are
kA
UO2 → UO22⫹ ⫹ 2e
kB
2⫺
UO2 ⫹ 2CO2⫺
3 → UO 2 (CO 3 ) 2 ⫹ 2e
(21)
(22)
The fuel corrosion potential, E CORR, is computed from the relationship
∑I Anod ⫹ ∑I Cath ⫽ 0
(23)
which applies only at E CORR and can be expanded to yield
⫹ IUO2(CO3 )2⫺
⫹ (IH2O2 )A} ⫹ (IO2 ⫹ (I H2O2 )C} ⫽ 0
{I UO2⫹
2
2
(24)
An anodic and cathodic current is included for H 2O 2 since electrochemical
experiments indicate that this species may be catalytically decomposed by the
fuel surface:
232
Chapter 7
Figure 20 The reaction scheme considered for nuclear fuel (UO 2 ) corrosion inside a
failed (flooded) carbon-steel-lined nuclear waste container.
Models Based on Electrochemical Measurements
233
Figure 21 Schematic illustrating the one-dimensional array of layers considered in the
mixed potential model of nuclear fuel corrosion in a failed (flooded) nuclear waste container.
2H 2O 2 → O2 ⫹ 2H 2O
(25)
The diffusion–reaction equations are solved using finite-difference techniques
employing a multilayer spatial grid to account for the corrosion product deposits
present on the fuel and carbon steel surfaces, Fig. 21. For further details the
reader is referred to more extensive discussions published elsewhere (6,23).
Other examples of such mixed potential models include that developed by
Macdonald and Urquidi-Macdonald to predict water radiolysis effects in thin
condensed water layers on metal surfaces (24), and the models of Marsh and
Taylor (25), and Kolar and King (22) to predict the corrosion of carbon steel and
copper waste containers surrounded by a low permeability material such as clay.
C. Passive Conditions
Most modern industrial materials are designed to be passive; i.e., covered by an
adherent, chemically inert, and pore-free oxide that is highly insoluble in aqueous
solutions and hence dissolves at an extremely slow rate. Examples would be
modern stainless steels, nickel-chromium-molybdenum, and titanium alloys. The
concept of passivity is often defined by reference to the polarization curve for
metals and alloys in aggressive acidic solutions, Fig. 22. This curve defines the
potential regions within which the alloy would be expected to corrode actively
or passively.
In the passive region, values of the passive corrosion rate could be obtained
from a polarization curve, though there is no guarantee that it would represent
234
Figure 22
regions.
Chapter 7
Schematic anodic polarization curve indicating active and passive corrosion
the true passive corrosion rate under steady-state conditions. A more reliable
value could be obtained by potentiostating the material in the passive region and
recording the passive current only after steady-state conditions were achieved.
In this manner the transient changes in film composition and/or defect density
induced by rapidly enforced film growth are complete, and the film is more representative of that expected under natural corrosion conditions. In these applications
there is no need to model the corrosion processes. However, for the specialized
application of nuclear waste disposal, when maintenance of passivity over 10 5
years is required, it is necessary to consider how passivity may evolve over long
time periods, especially when changes in exposure environment (e.g., salinity
and temperature) may change. Under these circumstances, passive corrosion may
not be as simple a process as initially envisaged.
An example would be the long term passive corrosion of titanium. Over
observable time periods the passive oxide film on titanium grows via either a
direct logarithmic or an inverse logarithmic growth law (24,25). Under these
conditions, the rapid development of an electric field in the oxide would prevent
the ionic conduction (of Ti 4⫹ and/or O 2⫺ ) necessary to sustain film growth. To
all intents and purposes, film growth would effectively stop. However, crystallization, a process that seems inevitable over long exposure periods, would introduce
a high density of grain boundaries along which ionic conduction to sustain film
growth could be facilitated. Under these conditions, passive film growth is effectively the same as the thickening of a corrosion product deposit, as was discussed
above. A difference between the two processes might be that, in the case of
Models Based on Electrochemical Measurements
235
passive film growth, the original pore-free passive layer could survive as a thin
barrier layer of constant thickness, while film growth led to a thickening of an
outer recrystallized layer. This is the commonly accepted view of passivity (26).
If these conditions prevailed, the electric field in the barrier layer would remain
constant and, assuming the recrystallized layer exerted no retarding influence on
continued growth, a linear film growth process (and hence a constant corrosion
rate) would be maintained. This scenario is represented in Fig. 23A.
A second possibility is that a linear corrosion rate could also be maintained
by the finite dissolution rate of the film in the environment. For this situation,
the rate of film thickening would eventually be counterbalanced by the rate of
film dissolution, leading to both a constant film thickness and a constant corrosion
Figure 23 Various reaction scenarios for the passive corrosion of titanium alloys: (A)
linear oxide film growth due to film recrystallization; (B) linear film growth kinetics maintained by film dissolution.
236
Chapter 7
rate, Fig. 23B. A complication with this second process is that film growth and
dissolution may not proceed uniformly across the surface and that a transition
from slow passive film growth to a more rapid growth of a corrosion product
deposit could occur. If the dual exposure of metal and oxide occurs, then the
galvanic coupling of metal dissolution and oxide dissolution may become possible, a process likely to be facilitated by the development of local acidity within
these local pores, Fig. 17. Such processes are well documented for reactive metals
such as Fe and carbon steel (27), and they help to explain the thick film formation
in situations such as the development of tubercles in water pipe systems (28).
While theoretically possible with metals like titanium, such a process is only
likely under reducing acidic conditions and will not be considered further here.
The direct electrochemical measurement of such low corrosion rates is difficult and limited in accuracy. However, electrochemical techniques can be used
to establish a database against which to validate rates determined by more conventional methods (such as weight change measurements) applied after long exposure times. Blackwood et al. (29) used a combination of anodic polarization
scans and open circuit potential measurements to determine the dissolution rates
of passive films on titanium in acidic and alkaline solutions. An oxide film was
first grown by applying an anodic potential scan to a preset anodic limit (generally
3.0 V), Fig. 24, curve 1. Subsequently, the electrode was switched to open-circuit
and a portion of the oxide allowed to chemically dissolve. Then a second anodic
Figure 24 Schematic polarization curve showing the anodic film reformation technique
for determining passive oxide dissolution rates; (1) original anodic polarization scan to
grow the oxide film; (2) second anodic polarization scan to regrow the oxide dissolved
on open circuit. Q F is the charge lost in open-circuit dissolution between the two scans.
Models Based on Electrochemical Measurements
237
scan was performed from the open-circuit potential attained to the same anodic
limit, Fig. 24, curve 2. The charged passed in reforming the oxide (Q F in Fig.
24) is a direct measure of the amount of film dissolved on open circuit. This
charge divided by the time spent on open circuit yields a value for the passive
film dissolution rate. Since these authors also determined a pH dependence for
the oxide dissolution process, it was then possible to extrapolate these rates to
more neutral environments. A comparison of these extrapolated rates to those
obtained by other nonelectrochemical techniques yielded a gratifyingly close
agreement, thereby strengthening the justification for the use of the latter values
in corrosion models.
Based on measurements of this kind, the lifetimes of titanium nuclear waste
containers under Canadian waste disposal conditions have been modeled (30).
Since these conditions are expected to be anoxic, the passive corrosion of titanium
will be driven by a very slow reaction with water, leading to the possibility of
hydrogen adsorption into the metal:
Ti ⫹ 2H 2O → TiO2 ⫹ 2H
→ TiO2 ⫹ fH(2H) abs ⫹ (1 ⫺ fH)H2
(26)
where f H is the fractional efficiency for H absorption into the metal, the remaining
fraction being lost to the environment as evolved H 2. Hydrogen absorbed in this
fashion will precipitate in the metal as titanium hydrides (TiHx (1 ⬍ x ⬍ 2))
and, once a critical hydrogen level is achieved, render the material potentially
susceptible to hydrogen-induced cracking (HIC).
Since these hydrides are thermodynamically stable in the metal, the passive
oxide can only be considered as a transport barrier, not as an absolute barrier.
Various electrochemical techniques including EIS and photoelectrochemical
measurements have been used to identify the mechanism by which the TiO 2 may
be rendered permeable to hydrogen, and to identify the conditions under which
absorption is observable (31). These determinations show that H absorption into
the TiO 2 (and hence potentially into the metal) occurs under reducing conditions
when redox transformations (Ti IV → Ti III ) in the oxide commence. However, the
key measurement, if H absorption is to be coupled to passive corrosion, is that
of the absorption efficiency.
A measurement of f H can be achieved electrochemically (32). Under galvanostatic (constant current) cathodic conditions, the fractional efficiency of hydrogen absorption is the ratio of the amount of hydrogen produced electrochemically
to the amount absorbed by the metal, as is illustrated in Fig. 25. While this appears
to be a very simple direct measurement, it has the normal problems associated
with an accelerated electrochemical measurement, including the need to demonstrate that the parameter measured electrochemically will retain the same value
under the much slower natural corrosion conditions.
238
Chapter 7
Figure 25 Schematic illustrating the galvanostatic method of determining the hydrogen
absorption efficiency of titanium.
Using a constant corrosion rate multiplied by the adsorption efficiency measured as described above, the rate of hydrogen absorption into the metal was
calculated, and susceptibility to HIC was assumed to be established once a critical
hydrogen concentration (H C ) was reached. A more detailed discussion of this
simple conservative model, including a description of the determination of H C
from mechanical experiments, is described elsewhere (33). The conservatism in
the model arises from the assumption that all the hydrogen absorbed is retained
by the metal rather than released by oxidation as the corrosion process proceeds
through the metal. As was emphasized in the introduction, such a conservatism
is acceptable in a model where safety is the primary requirement. The approach
described would be too conservative for an industrial service model.
D.
Localized Corrosion Processes
When one is dealing with localized corrosion processes, the tendency is experimentally to determine or model whether a particular process can occur in a specific environment; i.e., to determine the susceptibility. Such procedures are invaluable in materials selection, and the use of electrochemical methods is an
integral part of these efforts. However, in some environments it is injudicious to
assume that localized corrosion will not occur. One example would be SCC in
nuclear reactor heat exchangers and other components. In other applications, the
need to minimize materials costs leads to the selection of materials for which
there is no guarantee of immunity to localized corrosion. For such applications
there is a strong need for models that will predict how fast such processes will
propagate once they are initiated and what kind and extent of damage will accumulate.
Models Based on Electrochemical Measurements
239
Local corrosion sites are typified by (1) local chemistries that are commonly
only loosely related to the bulk exposure environment, (2) the separation of anodic and cathodic sites, and (3) the localization of corrosion damage sites (i.e.,
within pits, crevices, and cracks). Since, within a local corrosion site, the reactive
surface area to available solution volume can be very large, extreme environments
(in terms of concentration, concentration gradients, pH) are often encountered.
For the same geometric reasons, these environments are difficult to characterize.
Extremely high corrosion current densities can be sustained within the local site
by the presence of much lower cathodic current densities over a much larger
available surface area outside the corrosion site. Finally, the existence of ionic
and concentration gradients between the local corrosion site and the external
environment introduces complex transport scenarios.
Many models exist to predict the conditions within these sites (e.g., 34,35).
However, if the primary need is to determine the extent of corrosion damage (e.g.,
the depth of corrosion penetration), these models are not sufficient. Generally,
electrochemical techniques contain no spatial information, since the current measured is the sum of currents from all individual corrosion sites. In the case of
pitting, this limitation is being slowly erased as scanning techniques capable of
spatial resolution are being developed. However, the ability to resolve local corrosion sites within fixed occluded areas such as cracks and crevices remains minimal.
The generally applied electrochemical procedure to predict when localized
corrosion can initiate is to compare the system corrosion potential (E CORR ) with
the breakdown (E B ) and/or repassivation potential (E R ) measured in a polarization experiment. This procedure is illustrated schematically in Fig. 26 for pitting
or crevice corrosion. The shaded areas associated with E B and E R indicate the
range of values (usually normally distributed) associated with these two parameters. Defining these distributions is a major need in reducing the uncertainties
inherent in predicting the probability of occurrence of localized corrosion. A good
example of the electrochemical and statistical approaches to achieve this goal
has recently been published by Kehler et al. (36). An example of a polarization
curve to record E B and E R for the Ni-Cr-Mo alloy C-276 in high-temperature
saline solution is shown in Fig. 27 (37).
Figure 26 shows that known values of E B and E R, coupled to a knowledge
of how E CORR evolves with exposure time, allow the specification of the duration
of the period of propagation of localized corrosion. The difference between the
two periods A and B is a measure of the uncertainty in the duration of propagation
due to the distribution in the repassivation potential. The use of E R, as opposed
to E B, to specify the period of localized corrosion is conservative, and the efficacy
of relying on this parameter in safety assessment models has been demonstrated
by Sridhar et al. (38). These authors also showed that the value of E R decreases
as the extent of corrosion damage sustained during the propagation period in-
240
Chapter 7
Figure 26 Illustration of the period of propagation of localized corrosion (pitting) as
defined by the relative values of E CORR and the breakdown (E B ) and repassivation potentials
(E R ). The shaded areas associated with E B and E R illustrate the uncertainties in the values
of these two parameters.
Figure 27 Anodic polarization scan recorded on a creviced specimen of the Ni-Cr-Mo
alloy C276 in 0.59 mol ⋅ dm⫺3 NaCl at 150°C at a scan rate of 0.8 mV ⋅ s⫺1.
Models Based on Electrochemical Measurements
241
creases. This highlights the dangers inherent in relying on E R values measured
under dynamic polarization conditions. More appropriately, the time should be
taken to measure these values potentiostatically over a sufficient time period that
they are uninfluenced by the extent of localized corrosion damage.
Attempts to determine the extent of corrosion damage during the propagation period are also fraught with difficulties. A substantial amount of evidence
exists to show that electrochemically grown pits obey the empirical growth law
d ⫽ kt n
(27)
where d is the maximum depth of penetration, k is a pit growth constant, and the
time exponent n empirically incorporates the penetration limiting features of the
localized process (38, and references therein). The maximum pit depth is the key
depth determining first failure. Simple theoretical developments show that this
relationship does represent pit growth under either diffusion or IR control (40).
A source of doubt in such analyses is whether the depths of the pits grown
electrochemically are representative of those expected under natural conditions
and therefore appropriate to extrapolate to longer times in predictive models. The
data shown for pitting of carbon steel, sketched in Fig. 28, show that they are
not. Clearly, growth is accelerated under potentiostatic electrochemical conditions, and the extrapolation of pit depths seriously overestimates the predicted
pit depths after long exposure times. This is not surprising, since the use of a
Figure 28 Illustration of the problems encountered when trying to produce a database
of pit depths in an accelerated electrochemical experiment. The shaded area shows the
range of pit depths on naturally corroded steel specimens in a range of soil types. (1)
Predicted pit depth evolution based on potentiostatically grown pits. (Data schematically
reproduced from Ref. 50.)
242
Chapter 7
potentiostat will override the natural stifling features inherent in pit growth by
allowing no limit on the pits’ demand for sustaining current. As emphasized by
Shoesmith et al. (41) and Laycock and Newman (42), limitations on the supply
of current by the external cathodic reaction and chemical/geometric features
within the pit can lead to the stifling/repassivation of pits at shallower depths
than would be predicted based on electrochemical measurements. For this reason
care must be taken in using the depths of electrochemically grown pits in predictive models. Consequently, whenever possible, models to predict the evolution
of pit depths have relied on the statistical evaluation of naturally grown pit populations (43–45). Unfortunately, such extensive databases are not commonly available.
For the stochastic process of pitting, this limitation on the application of
electrochemical methods is difficult to avoid. For crevice corrosion, however,
the localized corrosion sites are confined within a well-defined occluded site and
hence are more easily simulated in an electrochemical experiment. By coupling
an artifically creviced electrode through a zero resistance ammeter to a large
planar counterelectrode of the same material, it is possible electrochemically to
monitor the propagation of crevice corrosion without the use of a potentiostat.
By making the coupled cathode area much bigger than the creviced area, the
small anode/large cathode characteristic of a natural crevice is achieved. Also,
the influence of the available cathodic area on the crevice corrosion process can
be simulated by varying the anode-to-cathode ratio. If a reference electrode is
included in the same cell and connected via a high-impedance voltameter to the
creviced electrode, it is possible simultaneously to monitor both the crevice potential and the crevice current. If these electrodes are sealed into a pressure vessel,
experiments of this kind can be conducted at high temperatures (up to ⬃270°C)
of industrial relevance (13).
For some materials (e.g., nickel alloys), the current is a direct measure of
the rate of crevice propagation. For systems such as titanium alloys, however,
internal cathodic reactions are also possible, as is illustrated in Fig. 29. This
figure shows schematically the important electrochemical and chemical reactions
occurring within the creviced area and on the coupled counterelectrode. This
system will be used to illustrate the information that can be obtained from this
galvanic coupling technique and how it can then be used directly in the development of models.
Once crevice propagation is underway, the reduction of O 2 on the coupled
cathode drives metal dissolution, which only occurs within the acidified occluded
area of the crevice. Hydrolysis of dissolved cations leads to the formation of a
TiO 2 ⋅ 2H 2O deposit that tightens the crevice, and to the generation of protons,
which further suppress the pH. As a consequence, the metal dissolution is further
accelerated by proton reduction within the crevice, leading to both the evolution
of hydrogen and the absorption of hydrogen into the metal. This absorbed hydro-
Models Based on Electrochemical Measurements
243
Figure 29 Schematic showing the important electrochemical/chemical reactions occurring inside a creviced titanium electrode and on a Ti cathode coupled to the creviced
electrode through a zero resistance ammeter.
gen leads to the precipitation of titanium hydrides. The key feature of the proton
reduction reaction is that the current generated is short-circuited within the crevice. Hence this internal contribution to crevice propagation is undetectable electrochemically; i.e., it does not contribute to the current measured by the ammeter
(Fig. 29). This dual cathode response introduces a second potential failure mode
for Ti under crevice conditions. The first is, of course, penetration of the wall
thickness by metal dissolution. This second mode is hydrogen-induced cracking
as a consequence of H absorption and TiHx formation in the presence of tensile
stresses.
Figure 30 shows the general form of the crevice current (I C ), creviced electrode potential (E C ), and the potential of a planar electrode (E P ) monitored in the
same experiment for comparison. The form of these parameters represents the
behavior observed for experiments conducted within a sealed pressure vessel
containing a fixed charge of oxygen. Consequently, an experiment conducted at
constant temperature will capture the crevice behavior from initiation, through
propagation, to repassivation as the O 2 within the vessel is consumed. Initiation
is indicated by a separation between E p and E C as E C drops accompanied by the
onset of I C. As propagation proceeds, E C remains low as expected for active
crevice conditions, while I C increases as crevice propagation spreads within the
crevice and then falls as the available O 2 is consumed. E p remains positive, while
244
Chapter 7
Figure 30 The general form of the crevice current (I C ), crevice potential (E C ), and
planar electrode potential (E P ) measured using a galvanic coupling technique. (A) Range
of planar electrode (corrosion) potentials (E P ) measured for passive corrosion under oxidizing conditions; (B) range of E P values measured for passive corrosion under anoxic
conditions; (C) range of crevice potentials (E C ) measured during active crevice propagation.
passive oxidizing conditions prevail on the planar electrode, but begins to fall
as O 2 is depleted. The onset of repassivation is marked by a fall in I C to zero
and an equalizing of the E C and E p values. This equalization often involves a
slight rise in E C as I C approaches zero. In the example shown, repassivation does
not occur until all available O 2 is consumed and passive reducing conditions
are established. For more crevice-resistant materials, such as Ti-12, on which
propagation is limited by materials properties, E C rises to meet E p while passive
oxidizing conditions still prevail.
Many features and much mechanistic detail on crevice corrosion can be
determined using this technique (46). Here the discussion is concentrated on the
Models Based on Electrochemical Measurements
245
determination of those parameters that will enable us to develop a predictive
model for the crevice corrosion process.
Since I C is a measure of the rate of crevice propagation supported by O 2
reduction on the coupled cathode, the total amount of O 2 consumed (Q C ) can be
found from
冮I
t
QC ⫽
tI
C
⋅ dt
(28)
where t 1 is the time of initiation. To determine the total crevice propagation rate
we must also determine the rate of internally supported propagation (i.e., by H⫹
reduction). This rate cannot be monitored continuously in the electrochemical
experiment and must be determined from weight change (W) measurements on
a series of specimens from experiments of different duration. A parameter g ⫽
W/Q C can be defined as the ratio of the total extent of crevice propagation to
that supported only by O 2 reduction, from which the total rate of propagation
(R CC ) can be evaluated,
冮R
t
W ⫽ gQ C ⫽
tI
CC
⋅ dt
(29)
The parameter g has been determined, from this kind of investigation, to be ⬃5
and constant; i.e., ⬃80% of propagation is supported internally by proton reduction (47) under rapid propagation conditions. Since only the internal cathodic
reaction supports hydrogen absorption, the rate of hydrogen absorption (R HA ) can
be defined by
R HA ⫽ f H (R CC ⫺ I C ) ⫽ f hI C
W ⫺ QC
QC
(30)
where f h is the fraction of the hydrogen produced that is absorbed by the metal.
This efficiency was determined by measuring the hydrogen content of the crevice
volumetrically after vacuum degassing and found to be ⬃0.15 and independent
of propagation rate (32,33). Since this value was obtained by postexamination
of the crevice, it is an overall efficiency and may disguise a variation in efficiency
as propagation proceeds.
Since metallographic examination of the crevice shows the hydrogen concentrates within a surface hydride layer within the crevice (32,33), continuing
propagation will oxidatively dissolve this layer as well as promote absorption.
Consequently, we would expect the hydrogen concentration to achieve a steadystate value as propagation progresses, and eventual failure will be by wall penetration, not HIC. Thus it is necessary to connect the extent of propagation (Q C, W)
to the maximum depth of wall penetration (P w ). This can be done using metallographic and image analysis techniques (48) for a series of crevices that have
246
Chapter 7
Figure 31 Maximum penetration depths measured on Ti-2 specimens crevice corroded
in 0.27 mol ⋅ dm⫺3 NaCl at 100°C (䊐) and 150°C(1 ) for various amounts of oxygen consumed.
propagated for different durations (t) and hence extent (Q C ). Figure 31 shows the
relationship between P W and Q C determined for two temperatures. The interesting
feature is that while the propagation rate is much faster at 150°C than at 100°C,
the depth of penetration is independent of this rate and apparently dependent
only on the amount of O 2 consumed. This greatly simplifies the eventual model
development, since only one damage function (P w vs. Q C ) is required.
The electrochemical and supplementary procedures described above have
been used to develop a model to predict the extent of corrosion damage sustained
by Canadian nuclear waste containers constructed from different titanium alloys.
As noted in Fig. 1, before model development can begin it is necessary to specify
the exposure environment and how it will evolve with time. As shown schematically in Fig. 32, within a waste vault the temperatures will be initially high but
will decrease with time as the heat-producing radioactivity within the fuel decays.
Also, the initially high O 2 concentration, trapped within the vault on sealing, will
decrease with time as it is consumed by the corrosion process and/or scavenged
by oxidizable minerals or organics in the backfill materials compacted around
the container. As a consequence of this evolution in environmental conditions,
two distinct periods can be defined (Fig. 32): an early warm oxidizing period
lasting, at most, up to a few hundred years, and a longer term cool nonoxidizing period, which would prevail indefinitely. Intuitively therefore, crevice corrosion would be most likely to initiate and propagate using the warm oxidizing
period, but to repassivate eventually as cooler nonoxidizing conditions are established.
Models Based on Electrochemical Measurements
247
Figure 32 Expected evolution of the key environmental parameters within a Canadian
nuclear waste vault. The shaded area for temperature illustrates the distribution of waste
container cooling profiles within the waste vault. The two profiles for decaying O 2 concentration represent the range of estimated profiles for [O 2 ] being consumed by reaction with
minerals and organic matter within the vault.
To capture this evolution in a model requires that relationships between
propagation rate (R CC or I C ) and O 2 concentration and temperature be determined.
This can be achieved in the galvanic coupling experiment by activating a crevice
and then changing the O 2 concentration or temperature and recording I C as a
function of these two parameters. The results of such experiments have been
published elsewhere (49), and the relationship for O 2 concentration is shown in
Fig. 33. Once O 2 reaches a sufficiently low concentration, I C drops to zero; i.e.,
repassivation occurs. This enables us to specify a repassivation criterion based
on a critical O 2 concentration ([O 2 ] P ) as noted in the figure. A similar dependence
of I C (and hence R CC ) on temperature was determined.
Based on this information and these relationships a model framework can
now be developed, Fig. 34. The four primary inputs to the model are the crevice
propagation rate as a function of O 2 concentration and temperature (A and B),
a knowledge of the time-evolution of temperature and oxygen concentration
within the waste vault (C), and a transport model for the flux of O 2 to the container
248
Chapter 7
Figure 33 Crevice current (I C ) recorded on a creviced Ti-2 electrode in 0.27 mol ⋅ dm⫺3
NaCl (95°C) as the volume fraction of O 2 in the pressure vessel was changed. This volume
fraction could easily be converted to a dissolved concentration: [O 2 ] p is the volume fraction
when the crevice repassivated.
surface (D). This last input is necessary since the container would be placed in
a compacted clay environment through which diffusive transport of O 2 would be
very slow (D eff ⫽ 10⫺7 cm 2 ⋅ s⫺1 ). One arbitrary feature of the model is that the
creviced area and anode-to-cathode area would have to be specified.
The combination of these inputs would lead to a prediction of the rate of
crevice propagation with time, and using [O 2 ] CRIT, a repassivation time could be
specified (E). Integration of this relationship yields a measure of the total extent
of crevice propagation as a function of time (F). Then, using the experimentally
Figure 34 The steps involved in determining the depth of container wall penetration
under Canadian nuclear waste disposal conditions using data obtained in an electrochemical galvanic coupling experiment. (A) Crevice propagation rate (R′CC ⬀I C ) as a function of
temperature (T ); (B) R CC as a function of O 2 concentration [O 2 ]; (C) calculated evolution
of container surface temperatures and vault O 2 concentrations with time in the vault; (D)
flux of O 2 (J O 2 ) to the container surface as a function of time; (E) predicted evolution of
R CC up to the time of repassivation (i.e., at [O 2 ] p ); (F) total extent of crevice corrosion
damage expressed as the total amount of O 2 consumed (Q) up to the time of repassivation;
(G) experimentally determined maximum depth of wall penetration (P w ) as a function of
O 2 consumed (Q); (H) predicted maximum value of P w up to the time of repassivation
(t p ).
Models Based on Electrochemical Measurements
249
250
Chapter 7
determined damage function (P w as a function of the amount of O 2 consumed)
(G), the extent of wall penetration as a function of exposure time can be calculated
(H). Comparison of this depth of penetration [(P w ) max ] to the available corrosion
allowance is then a measure of the extent of container damage.
The modeling scheme outlined in Fig. 34 indicates only one path to failure:
penetration by loss of wall thickness. However, propagation is accompanied by
absorption of hydrogen into the alloy, and even though repassivation may eventually occur, the material is left with an increased inventory of hydrogen. While
propagation persists, metallographic examination of corroded specimens show
that the majority of absorbed hydrogen resides in a surface hydride layer (33).
Once repassivation has occurred, this inventory of hydrogen will diffuse into the
metal at a rate determined by temperature. Thus, under the eventually prevailing
passive corrosion conditions, there are two sources for the accumulation of hydrogen in the bulk of the material, as illustrated in Fig. 35.
The maximum inventory of hydrogen absorbed during crevice propagation
could be calculated by integration of Eq. (30), and all the terms in this equation
can be evaluated from data gathered in galvanic coupling experiments. However
this is likely to overestimate significantly the hydrogen content of the crevice
corroded specimen, since it does not account for the fraction of the surface hydride redissolved as crevice propagation continues. Consequently, a direct experimental measurement of hydrogen content (by vacuum degrassing and volumetric
analysis) provides a more accurate measure.
Figure 35 Schematic showing the process of hydrogen absorption into titanium under
passive corrosion conditions after a period of crevice corrosion.
Models Based on Electrochemical Measurements
251
What is clear from these analyses is that the avoidance of crevice corrosion
will delay eventual container failure significantly, irrespective of whether it occurs by wall penetration or by HIC. With this is mind, the galvanic coupling
technique (along with the associated analytical methods outlined above) can be
used to compare qualitatively the crevice corrosion performance of a series of
titanium alloys. Figs. 36A and B compare the parameter (I C, E C, E p ) values ob-
Figure 36 Values of the parameters, I C (crevice current), E C (crevice potential), and E p
(planar potential) recorded in galvanic coupling experiments at 125°C in 0.27 mol ⋅ dm⫺3
NaCl: (A) Ti-2 (commercially pure alloy); (B) Ti-12 (0.8 wt% Ni ⫹ 0.3 wt% Mo).
252
Chapter 7
tained for Ti-2 and Ti-12 (containing 0.8 wt% Ni and 0.3 wt% Mo to resist
crevice corrosion). As expected for Ti-2, propagation proceeds at high currents
until available O 2 is consumed, and repassivation is only observed once passive
reducing conditions [E p ⬃ ⫺500 mV (see Fig. 30)] are established. By contrast,
propagation on Ti-12 progresses at much lower currents, and repassivation occurs
while oxidizing conditions still prevail [E p ⬃ 100 mV (see Fig. 30)]. Based on
the results from this galvanic coupling technique, the crevice corrosion resistance
of a series of alpha titanium alloys is summarized in Fig. 37 (Ti-16 contains
⬃0.06 wt% Pd). A more extensive discussion of the results of these experiments
is given elsewhere (46).
This understanding provides not only a basis for materials selection (improved resistance to crevice corrosion must be balanced against materials costs)
but also a basis for predicting the possible loss of wall thickness for a range of
Figure 37 Schematic illustrating the improvement in crevice corrosion behavior as the
composition and microstructure of a series of α-Ti alloys are changed.
Models Based on Electrochemical Measurements
253
materials due to an early period of crevice propagation. Again, more extensive
discussions are given elsewhere (30).
IV. SUMMARY
A general scheme for the development of corrosion models based on electrochemical principles has been described, and a number of examples for active, passive,
and localized corrosion has been given. This chapter is by no means comprehensive, and a search of the scientific and technical literature will unearth many
additional examples. The value in using electrochemical methods both to develop
understanding of the corrosion process and to measure the values of specific
modeling parameters is obvious. However, their application alone would not provide all the elements and parameter values required for the development of corrosion models, so the use of supplementary techniques is necessary. It is necessary
also to keep in mind that electrochemical techniques inevitably accelerate the
corrosion process one is interested in. Consequently, the scaling of electrochemically determined parameter values to the rates and time periods of interest in the
corrosion process to be modeled should be undertaken carefully and with a full
knowledge of the limitations involved.
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8
The Use of Electrochemical
Techniques in the Study of Surface
Treatments for Metals and Alloys
I.
OVERVIEW
Electrochemical methods are used in many different ways to assess the effectiveness of corrosion inhibitors and coatings for metals and alloys. In this chapter,
several important cleaning, inhibition, and coating technologies are described
including passivation, conversion coating, anodizing, and organic coating. The
use of electrochemical methods for determining the effectiveness of these corrosion protection methods is the focus of this discussion. Methods based on the
use of DC polarization and electrochemical impedance are presented. Electrochemical impedance spectroscopy (EIS) has matured greatly over the past 20
years as a tool in corrosion protection research and has proved to be one of the
most useful electrochemical characterization techniques presently available. This
chapter concludes with a presentation of some of the newest electrochemical
measurement techniques. These techniques have developed in research laboratories over the past 10 years. They hold promise for the study of coatings and
corrosion inhibition but have only been applied on a selective basis so far.
II. DESCALING AND PASSIVATION OF STEELS
AND STAINLESS STEELS
A. Overview of Descaling and Passivation
Steels and stainless steels develop oxides scales during hotworking, annealing,
or welding that lower corrosion resistance or paint adhesion. Scales are removed
using chemical means, mechanical means, or combinations of both. Within the
trade, chemical descaling is often referred to as pickling. In the case of stainless
257
258
Chapter 8
and semistainless alloys, additional chemical treatments, commonly referred to
as passivation processes, are used to ensure maximum resistance to pitting and
crevice corrosion by enriching the adherent oxide film with Cr (1), and preferentially dissolving inclusions that serve as pit initiators (2).
Pickling of carbon and alloy steels is usually carried out in sulfuric acid
solutions ranging in concentration from 3 to 40%, depending on the alloy type
and product form (3,4). Baths are operated at 60° to 100°C, and processing times
range from tens of seconds to 30 minutes or more. Contact times greater than
30 minutes are not common as the risk for surface etching increases. Steel rod
and wire are often pickled using a 1 to 20 s immersion in hot hydrochloric acid
solutions with concentrations of 6 to 15% by weight at temperatures of 75° to
95°C, or chloride additions to sulfuric acid baths are sometimes used to accelerate
the descaling action (5). Other acid cleaning treatments are used to remove not
only oxide scale but also dirt, oils, and other contaminants from the steel surface.
The use of mineral acids such as phosphoric acid is common in this regard (6).
For structures too large for treatment by immersion, pickling pastes have been
developed (7).
The more corrosion resistant 300 and 400 series stainless steels are normally pickled in nitric acid, or HF-accelerated nitric acid mixtures. Solutions are
operated at temperatures ranging from 70° to 90°C, and contact times of 2 to 20
minutes are typical (3).
B.
Traditional Techniques to Assess Effectiveness of
Descaling and Passivation
Most descaling and passivation processes for steels were developed prior to the
widespread use of electrochemical techniques. As a result, a variety of visual
and chemical tests are widely used for determining the surface cleanliness. Chemical tests have also been established to verify the presence of a robust oxide film
on austenitic and ferritic stainlesses (8). These methods are very simple to conduct in a manufacturing environment, but they are qualitative in nature and rely
strongly on the judgment of the inspector. Outside of the laboratory, electrochemical methods have not been widely used to evaluate cleanliness of carbon and
alloy steels after pickling. Nevertheless, they are well suited for this purpose and
have been examined in considerable detail in laboratory studies.
C.
Electrochemical Techniques for Assessing
Effectiveness of Descaling and Passivation
Austenitic stainless steels are generally regarded as being spontaneously passive
in aerated, near-neutral aqueous solutions, but surface treatment has a significant
Study of Surface Treatments
259
Figure 1 Surface finish versus pitting potential for 316 stainless steel subject to various
surface treatments. (From G. E. Coates. Materials Perf., Aug. 1990, p. 61.)
effect on pitting and crevice corrosion resistance. Figure 1 shows a compilation
of pitting potentials for various surface treatments on 316 stainless steel (9). This
figure illustrates the beneficial effects of polishing and chemical treatment on the
resistance to localized corrosion and suggests that measurement of pitting potential is a good electrochemically derived parameter for assessing surface cleanliness.
In principle, rinsing austenitic stainlesses in aerated water after pickling
should be sufficient to induce passivation most of the time. But further treatment
by dipping in nitric acid or nitric–hydrofluoric acid mixtures is common practice
because it decontaminates the surface, further stabilizes the passive film, and
ensures passivity (10). Acid dipping helps remove contamination in the alloy’s
surface such as slag inclusions from welding and residual iron from machining
and grinding. Surface roughness, MnS inclusions, oxide inclusions and Crdepleted surfaces will also serve to destabilize passivity. In service, these factors
lead to unexpected red rusting, pitting, and crevice corrosion. In laboratory tests,
260
Chapter 8
these effects increase the metastable pitting rate, lower the pitting potential, lower
the critical pitting temperature, and lower the resistance to crevice corrosion, as
has been shown in several studies discussed below.
Suter et al. have developed a microelectrochemical cell that uses glass capillaries drawn down to tens of micrometers in diameter (11–14) (Fig. 2). Capillary
ends can be precisely positioned on an alloy surface enabling electrochemical
measurements to be made at microstructurally relevant length scales. Using this
technique, the effect of MnS inclusions on the pitting activity of stainless steels
has been studied directly. When smaller and smaller capillaries are used to measure polarization curves, the pitting potential is observed to increase substantially.
In a 0.003% S austenitic stainless steel the pitting potential, E pit , in 1 M NaCl
increases from about ⫹0.300 to V sce to a value more positive than the oxygen
evolution potential when the capillary tip diameter was reduced from 100 to 50
µm (Fig. 3). The increase in E pit occurs because as the cell size decreases, the
number of inclusions sampled decreases, thereby reducing the number of defect
sites available for pit initiation. This finding is in agreement with conventional
understanding articulated by Crolet, who states that the effectiveness of a given
Figure 2 Schematic illustration of the experimental apparatus for the microcapillary
electrochemical cell. (From T. Suter, T. Peter, H. Bohni. Mater. Sci. Forum, 192–194,
25 (1995).)
Study of Surface Treatments
261
Figure 3 Potentiodynamic polarization curves from a 0.003% S austentic stainless steel
measured in 1 M NaCl with capillaries of differing size. (From T. Suter, T. Peter, H.
Bohni. Mater. Sci. Forum, 192–194, 25 (1995).)
passivation treatment is determined to a large extent by the effectiveness of MnS
inclusion removal (10).
Other researchers have investigated the effects of Cr enrichment in the
oxide film during nitric acid passivation (15–17). Cr enrichment during passivation has been observed in XPS measurements. However, on the basis of electrochemical measurements, it is not clear that Cr enrichment has as profound an
effect on pitting resistance as the removal of inclusions. Hultquist examined the
effect of nitric and nitric–hydrochloric acid passivation on pitting and crevice
corrosion of Mo-bearing 316 stainlesses. XPS showed that the various passivation
treatments examined resulted in Cr⫹Fe⫹Ni ratios in the oxide of 40 to 60%.
Stepwise potentiodynamic polarization of samples with artificial crevices showed
that the crevice corrosion initiation potential scaled linearly with oxide film Cr
content. Conversely, the E pit measured on boldly exposed surfaces did not scale
with the oxide film Cr content, which led the authors to conclude that Cr enrichment is more important in determining crevice corrosion resistance and that inclusion removal is more important in determining pitting resistance.
Wallinder et al. examined passivation of 316L using electrochemical impedance spectroscopy (EIS), potentiodynamic polarization, and x-ray photoelectron spectroscopy (XPS) techniques to examine the relationships between corrosion resistance and surface chemistry after passivation treatments (17). The
262
Chapter 8
effects of variables including contact time, temperature, HNO 3 concentration, and
surface finish on surface composition and electrochemical behavior in 0.5%
H 2 SO 4 solutions were systematically studied. EIS measurements showed that
passivated surfaces exhibited a single but broadly dispersed time constant that
was modeled using a parallel constant phase element (CPE)–resistor network in
series with a solution resistance. The magnitude of the film resistance and the
capacitance extracted from the CPE showed regular dependencies on variables
such as surface finish, acid concentration, and passivation time. Film thicknesses
were estimated from capacitance measurements, and thickness values were compared to those derived from XPS data. Findings from this study led the authors
to conclude that improved corrosion resistance was due to a high Cr content and
increased thickness in the passive film.
Hong et al. examined the effect of nitric acid passivation on type 430 ferritic
stainless steel using potentiodynamic polarization, EIS, and Auger electron spectroscopy (AES) (18). Passivation treatments were carried out on wet polished
surfaces by immersion for 60 minutes in nitric acid solutions ranging from 1 to
61% at 50°C. Pitting potential and the magnitude of the total impedance were
positively correlated with surface Cr concentration. In response to this study,
Figure 4 Metastable pitting rate (λ) for 316 stainless steel in 1 M NaCl solution as a
function of potential for untreated samples and samples passivated with 20% or 50% nitric
acid for 1 hour. (From J. S. Noh, N. J. Laycock, W. Gao, D. B. Wells. Corrosion Sci.
42, 2069 (2000).)
Study of Surface Treatments
263
Crolet remarked that causality does not always follow from correlation of results
from electrochemical tests and results from surface analysis (19). Strictly speaking, the effect of inclusion removal on pitting potential cannot be distinguished
from effects due to Cr surface enrichment.
Noh et al. characterized pitting potentials and metastable pitting transients
collected during potentiodynamic polarization of passivated 316 stainless steel
immersed in deaerated 1 M NaCl solutions at 70°C (20). Passivation treatments
were carried out for 1 hour at ambient temperatures on surfaces polished to 600
grit in HNO 3 solutions ranging in concentration from 0.65 to 25 wt%. MnS inclusions were removed to certain extents at all concentrations of HNO 3 , but the Cr
concentration in the surface film, measured as a Cr: Fe peak height ratio by XPS,
achieved a maximum at about 25%. This peak height ratio was about four to five
times that measured on the grit polished but unpassivated sample. A maximum
in E pit was also recorded on samples passivated in the 25 wt% solution, suggesting
a relation to the oxide film Cr content, though it was also pointed out that the
correlation between E pit and Cr: Fe ratio is not a linear one, suggesting the influence of other factors, such as inclusions, in determining E pit . Nitric acid passivation was shown to decrease metastable pitting rates and decrease the probability
of a metastable pit becoming stable. Figure 4 shows the metastable pitting rate
as a function of applied potential in 1 M NaCl solution. These results were interpreted as indicating a reduction in the number of available pitting sites due to
the passivation treatment.
III. INHIBITION BY SOLUBLE CHROMATE
A. Overview of Chromate Inhibition
The various simple chromate anions including chromate, CrO 42⫺, dichromate,
Cr 2 O 72⫺, and bichromate, HCrO 4⫺, have all been reported to be potent corrosion
inhibitors when they are present as soluble species in solution. Chromate is an
effective inhibitor for Al, Fe, Mg, Cd, Sn, and many other metals and alloys.
The specific form of the anion present in solution depends on its concentration
and solution pH (21). Because evidence of corrosion inhibition has been detected
over very wide ranges of soluble Cr(VI) ion concentration and pH, each of these
species appears to possess inhibiting properties.
Recently, the mechanism of corrosion protection by soluble chromate inhibitors has been the subject of active research, which has attempted to understand and replicate its inhibiting functions with less toxic chemical substances. In
this section, some recent findings on chromate corrosion inhibition are reviewed,
particularly as they pertain to corrosion of light metals, with a focus on the use
of techniques that are useful for studying mechanisms of inhibition.
264
Chapter 8
Chromates are particularly effective inhibitors, and there appear to be several components to inhibition. Chromate in solution inhibits metal dissolution
and oxygen reduction reactions. It also slows metastable pitting, the transition
to stable pitting, and, when present in sufficient concentration, the growth stage
of pitting and crevice corrosion.
Electrochemical techniques alone cannot reveal all the relevant aspects of
chromate inhibition, and key characterization experiments involving surface analysis, solution analysis, or other techniques are required to help understand inhibition. For this reason, several useful nonelectrochemical techniques are also discussed. These techniques provide a means for examining the effects of inhibition
under free corrosion conditions where electrochemical methods are not well
suited for measuring corrosion rate.
B.
Chromates and Anodic Inhibition
In polarization experiments using solutions containing mixtures of chromates and
attacking ions like chloride, evidence for anodic inhibition of aluminum by chromates is derived from elevation of the pitting potential and reduction in passive
current density (22–24). In these solutions, the pitting potential will depend on
alloy type, pH, and degree of aeration. Most significantly though, the pitting
potential depends on the chromate:chloride activity ratio (Fig. 5). Data from
Kaesche for aerated near-neutral solutions suggest that the pitting potential begins
to be ennobled when the chromate:chloride ratio exceeds about 0.1 to 1.0 (23).
Bohni and Uhlig have reported pitting inhibition efficiencies that are based on
complete suppression of pitting and are therefore somewhat more conservative
because greater chromate: chloride ratios are indicated (22).
1. Effect of Chromates on Metastable Pitting
In near-neutral dilute chloride solutions, concentrations of chromate, less than
those suggested by Kaesche, have been observed to increase the pitting potential.
Figure 6a shows anodic polarization curves from high purity Al wire loop electrodes in deaerated 1.0 mM chloride solutions (25). Additions of 25 to 50 µM
of sodium chromate were shown to elevate the pitting potential by hundreds of
millivolts and reduce the passive current density by about a factor of 2.
This elevation was attributed to the effect of chromate on metastable pitting.
Figure 6b shows plots or current density versus time for high purity Al wire loop
electrodes potentiostatically polarized to ⫺0.500 V sce in the same solutions as
those shown in Fig. 6a. As the chromate concentration is increased from 0 to 25
µM, and then from 25 to 50 µM, the metastable pit nucleation rate (events per
unit time) diminishes, as does the magnitude of individual events (event peak
current). The presence of chromate appears to decrease the metastable pit growth
Study of Surface Treatments
265
(a)
(b)
Figure 5 (a) Minimum activity of NaNO 3 or Na 2 CrO 4 required to inhibit pitting in
99.99% Al in aerated NaCl solutions. (b) Dependence of the pitting potential of Al on
the chloride : chromate ratio. (From (a) H. Bohni, H. H. Uhlig. J. Electrochem. Soc. 119,
906 (1969). (b) H. Kaesche. Localized Corrosion III, p. 516, NACE, Houston, TX (1971).)
rate and the apparent pit current density compared to chromate-free chloride solutions. These factors combine to decrease the probability that metastable pits will
stabilize to form propagating pits.
The use of the wire loop electrode technique is important in these studies,
as it is one means of ensuring against crevice attack that might compromise the
integrity of the experimental findings. In such experiments, the working electrode
266
Chapter 8
(a)
(b)
Figure 6 (a) Anodic polarization curves showing the effect of CrO 42⫺ on the pitting
potential of pure Al wire loop electrodes in deaerated 1 mM NaCl solution. (b) Time
records show in the effect of CrO 42⫺ on metastable pitting activity during potentiostatic
polarization at ⫺0.500 V sce in 1 mM NaCl solution. The inset shows the cumulative number of metastable pitting events shown as events/cm 2 versus exposure time. (From S. T.
Pride, J. R. Scully, J. L. Hudson. J. Electrochem. Soc. 141, 3028 (1994).)
Study of Surface Treatments
267
consists of a thin wire loop, a portion of which is immersed below the level of
the electrolyte. There is no gasket or seal required, and the opportunity for crevice
formation is minimized. Care is taken to avoid plastically deforming the wire,
which may localize dissolution. While it is possible to use a straight wire electrode, the presence of a cut end may be a region of high plastic deformation or
have asperities or recesses that may affect the electrochemical response. The
looped wire configuration exposes only the length of the wire, which is much
more nearly all in the same surface condition. Local effects at the water line,
where the loop is submerged, may develop, especially in aerated solutions where
a differential aeration cell may occur. Solution deaeration may be used to minimize this effect, but if deaeration is accomplished by bubbling a gas into the
electrolyte, care must be taken to isolate the electrode from ripples on the solution
surface that may cause variations in the submerged electrode area.
2. Pit Growth in Thin Films
The thin film pitting technique has been used to examine the influence of chromate on pit growth kinetics. Thin film pitting is a nonelectrochemical technique
for assessing pit growth kinetics in thin film metallizations. In films that are
sufficiently thin (1000 nm or less), pits initiate, very rapidly penetrate to the inert
substrate under the metallization, and then propagate radially outward. Pit growth
can be recorded by measuring the rate of change of the pit radius, dr/dt, using
a video recording system (Fig. 7a and b). Pit depth is fixed by the film thickness,
and pitting propagates in a two-dimensional fashion. Knowing the thin film thickness and the pit wall velocity, Faraday’s law can be used to make a nonelectrochemical determination of pit dissolution kinetics:
i⫽
ρnF dr
⋅
M dt
(1)
In this expression, i is current density, ρ is density, n is the number of electron
equivalents per mole of dissolved metal, M is the atomic weight of the metal, F
is Faraday’s constant, r is pit radius, and t is time. The advantage of this technique
is that a direct determination of the dissolution kinetics is obtained. A direct
determination of this type is not possible by electrochemical methods, in which
the current recorded is a net current representing the difference between the anodic and the cathodic reaction rates. In fact, a comparison of this nonelectrochemical growth rate determination with a comparable electrochemical growth rate
determination shows that the partial cathodic current due to proton reduction in
a growing pit in Al is about 15% of the total anodic current (26).
In experiments aimed at measuring pit and crevice growth kinetics, chromate is not a potent anodic inhibitor (27). The growth of film pits in Al films
is not slowed unless high chromate:chloride ratios exist. The addition of 0.05
268
Chapter 8
(a)
(b)
Figure 7 (a) Schematic drawing of the thin film pit experimental apparatus. (b) An
optical micrograph of a 2D thin film pit growing in an Al film at ⫺0.450 V sce in aerated
1.0 M NaCl solution. (From A. Sehgal, D. Lu, G. S. Frankel. J. Electrochem. Soc. 145,
2834 (1998).)
Study of Surface Treatments
269
M Na 2 Cr 2 O 7 to aerated 1.0 M NaCl solution has virtually no effect on the pit
polarization curve compared to a dichromate-free solution. Additions of 0.5
M Na 2 Cr 2 O 7 increase the repassivation potential by about 90 mV, while a 2.0
M Na 2 Cr 2 O 7 addition nearly stops pit propagation. The concentrations of dichromate required to inhibit thin film pit growth are consistent with those proposed
by Kaesche (23) but are much greater than those required to slow metastable
pitting in bulk Al samples.
3. Pit Growth in Metal Foils
The foil penetration technique is another nonelectrochemical technique for assessing the growth stage of pitting and intergranular corrosion (24). In this technique, metal foils with thicknesses ranging from 50 to 200 µm are exposed to
an attacking electrolyte in a cell configuration like that shown in Fig. 8a and b.
The sample is exposed to solution through a gasketed port that prevents crevice
corrosion. The sample may also be made the working electrode (WE) in a threeelectrode cell configuration for potential- or current-controlled experiments. A
detection circuit is incorporated into the cell design to record the time at which
the sample is perforated by localized corrosion. The detection scheme involves
the use of a metal foil (e.g., Cu) separated from the back side of the WE electrode
metal foil by wettable filter paper. The WE and Cu electrode are connected, and
the Cu foil is held at ⫹12 V with respect to the WE. During the experiment, the
resistance is measured between the WE and the Cu foil. The measurement circuit
is open when the paper is dry, but it closes when corrosion perforates the WE
and wets the filter paper with electrolyte. Once the circuit is closed, the time is
recorded, and an accurate determination of the time required to penetrate the WE
is made. Using this technique, penetration times can be collected in experiments
where the environmental conditions or the WE thickness is varied in a systematic
fashion.
Hunkeler and Bohni used this approach to show that pit growth in Al foils
occurred under ohmic control (24). It was also shown that nitrate and chromate
inhibitors, added to the electrolyte after pit initiation, inhibited pit growth kinetics; though the effect due to chromate additions was small. Several other inhibitors added to solution increased pit growth kinetics, since their primary influence
was in decreasing the solution resistance.
More recently, this technique has been used to examine the effect of dichromate additions on the stable growth of pitting and intergranular corrosion in highstrength Al alloys (28). Figure 8c shows the average foil penetration time for 220
µm thick 2024-T3 (Al-4.4Cu-1.5Mg-.06 Mn) foils potentiostatically polarized to
⫺0.550 V sce in oxygen-sparged 1.0 M NaCl solution containing different concentrations of dichromate. In these experiments the 2024-T3 foils were polarized
0.3 V above the pitting potential for a few seconds to initiate pit growth and
270
(a)
(b)
(c)
Chapter 8
Study of Surface Treatments
271
ensure that the time to penetrate that was recorded reflected the pit propagation
only. These data show that there is no increase in the penetration time for dichromate additions up to 0.1 M. A 1.0 M addition of dichromate about doubled the
penetration time, showing that the anodic inhibition localized kinetics is modest
and requires about a 1:1 ratio of dichromate to chloride, as was suggested by
the data of Kaesche (23).
4. Pit and Crevice Growth Studies with Artificial Crevice
Electrodes
Artificial pits and crevice electrodes can be formed by embedding wires or thin
foils in an insulating material leaving an exposed wire or foil edge. As the wire
or foil dissolves and the interface recedes, a one-dimensional pit or crevice forms.
Normally, the entire interfacial area is active, which facilitates determination of
dissolution rates, and pit or crevice current density. Modeling the effects of mass
transfer are straightforward as the pit or crevice grows only in one dimension.
If a transparent mounting medium is used, the recession rate of the wire or foil
can be measured optically to make a nonelectrochemical determination of the
dissolution rate possible.
These techniques have been used to study pitting reaction control mechanisms in stainless steel (29,30), iron (31), and nickel (32). The effect of bulk
solution flow on pit dissolution rates for Fe, Ti, and Al have also been made
(33). Interrogation of artificial crevice chemistries by x-ray absorption techniques
has also been reported (30,34,35).
Artificial crevice electrodes have been used to study the effect of dichromate on active dissolution of aluminum. In these experiments, 50 µm thick commercially pure Al foils were placed between thin plastic sheets and mounted in
epoxy. This assembly was fixed against a square cell that accommodated counter
and reference electrodes and a trap that allowed for H 2 gas collection. A schematic
illustration of this cell and electrode is shown in Fig. 9 (36). Crevice corrosion
growth experiments were conducted in aerated 0.1 M NaCl solution with additions of either 0.01 or 0.1 M Na 2 Cr 2 O 7 . Artificial crevice growth experiments
were conducted under potentiostatic polarization at potentials ranging from 0 to
Figure 8 (a) Schematic illustration of the experimental apparatus used in the foil penetration technique. (b) A schematic of the detection circuit used to determine the time of
penetration of the sample foil. (c) Average foil penetration times from replicate experiments for a 216 µm thick 2024-T3 foil potentiostatically polarized to ⫺0.550 V sce in actively oxygenated 1.0 M NaCl solutions containing different concentrations of dichromate
ion. The bars represent one standard deviation. (From A. Sehgal, G. S. Frankel, B. Zoofan,
S. Rokhlin. J. Electrochem. Soc. 147, 140 (2000).)
272
Chapter 8
Figure 9 A schematic illustration of the artificial crevice cell. (From E. Akiyama, G.
S. Frankel. J. Electrochem. Soc. 146, 4095 (1999).)
1 V sce for 2 hour time intervals. In these experiments, it is possible to analyze
the following charge balance:
Qnet ⫽ Qanodic ⫺ Qcathodic ⫽ Qanodic ⫺ (Q H2 ⫹ Q chromate)
(2)
Here, Q net is the charge supplied by the potentiostat during the course of the
experiment. Q anodic is the charge evolved by metal dissolution. This is determined
using Faraday’s law and measurement of the volume of foil dissolved during
the experiment. Q cathodic consists of two components Q H2 , cathodic charge due to
hydrogen reduction, which is determined by gas collection, and Q chromate , the
charge due to chromate-to-chromic reduction. The analysis assumes that oxygen
reduction does not contribute significantly to Q cathodic , Q net , Q anodic , and Q H2 , which
are all determined by direct measurement, while Q chromate can be estimated by
difference. This allows experiments to be systematically characterized to assess
any possible inhibiting effect due to the presence of chromate.
Figure 10 shows the effect of applied potential in the range of 0.0 to ⫹1.0
V sce on the various charge components in 0.1 M NaCl solution and 0.1 M NaCl
solutions with additions of 0.01 and 0.1 M Na 2 Cr 2 O 7 (28). The data for charge
components are scattered but do not indicate a strong inhibiting effect due to the
addition of dichromate to solution. With increasing dichromate concentration,
the total cathodic charge increased, presumably due to an increased contribution
from dichromate reduction. In a related fashion, the total anodic charge also appeared to increase with increasing dichromate concentration. Analysis of the crevice solution conductivity during ohmically limited crevice growth showed that
Study of Surface Treatments
273
Figure 10 The effect of applied potential on the various charge components arising
from electrochemical activity in artificial crevice experiments conducted for different dichromate concentrations and different dichromate : chloride concentration ratios: (a) 0.1
M NaCl. (b) 0.1 M NaCl plus 0.01 M Na 2 Cr 2 O 7 , (c) 0.1 M NaCl plus 0.1 M Na 2 Cr 2 O 7 .
(From E. Akiyama, G. S. Frankel. J. Electrochem. Soc. 146, 4095 (1999).)
274
Chapter 8
the crevice solution conductivity was not a simple function of the bulk solution
dichromate concentration. As a result, a systematic effect of increased solution
conductivity on Q anodic is not evident.
Dichromate does not function as an anodic inhibitor during crevice propagation in these experiments. Dichromate is not expected to be an inhibitor at the
applied potentials used here, but estimates of the potential drop place the bottom
of the crevice at a potential ranging from ⫺0.5 to ⫺0.8 V sce . In this potential
range, anodic inhibition might be expected, provided the chromate: chloride ratio
is sufficiently large.
Kendig has argued that in experiments conducted under potential control,
the cathodic reaction is displaced to the counter electrode (37). This may allow
more acidic conditions to develop on the electrode surface than might be expected
under natural conditions where the cathodic reaction must be supported on the
corroding surface. Crevice pH values are normally observed to be in the 3 to 4
range for crevices in Al alloy samples immersed in a bulk environment and can
become slightly alkaline if they are isolated from a bulk environment. Kendig
has speculated that in potential controlled experiments, the pH is much lower if
there is no cathodic activity in the crevice. Chromate anions become increasingly
protonated with decreasing pH. For total dissolved chromium concentrations in
the millimolar range, Cr 6⫹ is present predominantly as fully protonated H 2 CrO 4 .
In 10 mM chromic acid solutions at pH 2, an 1100 Al sample polarized to ⫺0.500
V sce exhibits a dissolution current that is about 1% of that measured in a chromic
acid-free solution. In pH 1 solutions, the current ratio increases to about 10%,
and at pH 0, it is 100%. Although the chloride–chromate ratio in these experiments was not held constant, these results suggest that part of the loss in inhibition
efficiency with decreasing pH is attributable to increased speciation of Cr 6⫹ to
noninhibiting H 2 CrO 4 .
Overall, these results indicate that chromates inhibit corrosion by elevating
the pitting potential on aluminum with respect to the corrosion potential, which
decreases the probability for the formation of stable pits. In general a chromate
chloride concentration ratio in excess of 0.1 is necessary to observe significant
anodic inhibition.
C.
Chromates and Cathodic Inhibition
Chromates are excellent inhibitors of oxygen reduction in near neutral and alkaline solutions. In these environments, they can stifle corrosion by suppressing
this cathodic partial reaction. The inhibition mechanism appears to involve reduction of Cr(VI) to Cr(III) at a metal surface and formation of Cr(III)-O-substrate
metal bonds (38). This surface complex is likely to be substitutionally inert and
a good blocker of oxygen reduction sites, as suggested by the exceedingly small
water exchange rate constant for the first coordination sphere of Cr 3⫹ (39).
Study of Surface Treatments
275
1. Chromate Inhibition and Cathodic Polarization
Chromate is a very powerful cathodic inhibitor even at low chromate: chloride
ratios. In cathodic polarization curves collected for 2024-T3 in a base solution
of oxygen-sparged 1.0 M Na 2 Cr 2 O 7 , the oxygen reduction reaction rate is reduced by about an order of magnitude (at ⫺0.800V sce) by the addition of 10 ⫺5
M Na 2 Cr 2 O 7 (28) (Fig. 11). In similar experiments where 0.3% H 2 O 2 was added
as a cathodic depolarizer, 10 ⫺4 M dichromate additions had no effect on the oxygen reduction reaction rate, but additions of 10 ⫺3 M chromate reduced the cathodic reaction rate by an order of magnitude. The results of these experiments
show that chromate inhibits the cathodic reaction at chromate: chloride concentration ratios of 10 ⫺5. This value is much lower than the 0.1 to 1.0 ratio required
to observe increases in the pitting potential during anodic polarization experiments (23). The curves in Fig. 11 also suggest that hydrogen and water reduction
are inhibited at the lowest measured potentials. Sometimes the cathodic polarization response of Al alloys is compromised by cathodic corrosion In Cu-bearing
alloys this may lead to Cu surface enrichment and enhancements in the cathodic
kinetics. However, the data of Fig. 11 suggest that dichromate is potent enough
to inhibit cathodic kinetics and suppress cathodic corrosion even at very large
cathodic overpotentials.
2. The Split Cell and Related Experiments
The split cell is similar to the classic differential aeration cell (40). Corrosion
kinetics are studied by measuring the current flowing between two physically
separated working electrodes. The electrodes may reside in the same cell exposed
to the same electrolyte (single cell), or they may be segregated in different compartments separated by a porous frit that allows ionic conduction but restricts
mixing of the cell contents (split cell). Current flow between the two electrodes
can be measured using a zero resistance ammeter. The potential difference between electrodes, or between an electrode and a reference electrode, may be made
using a high impedance voltmeter. A schematic illustration of these cell arrangements are show in Fig. 12 (41). In experiments conducted with dissimilar electrode materials, one electrode will be become the net anode, while the other will
become the net cathode. By properly pairing electrode materials and area ratios
it is possible to simulate the galvanic interactions among microstructural elements
in heterogeneous alloys and examine the action of chromates on local anodic and
cathodic regions. In the split cell arrangement, the environments may be varied
to examine separately the effect of solution chemistry on the anodic or cathodic
parts of a corrosion process.
Ramsey et al. used split cell experiments to study the effect of chromates
on inhibition of the anodic and cathodic reactions using Cu, Al, and Al alloy
2024-T3 in near-neutral chloride solutions (41). Split cell experiments involving
Figure 11 Cathodic polarization curves on 2024-T3 in actively oxygen-sparged 1 M
NaCl solution with (a) dichromate additions and (b) 0.3 vol% peroxide and dichromate
additions. (From A. Sehgal, G. S. Frankel, B. Zoofan, S. Rokhlin. J. Electrochem. Soc.
147, 140 (2000).)
276
Study of Surface Treatments
277
Figure 12 Schematics of single- and split-cell apparatus. (Courtesy of W. J. Clark,
J. D. Ramsey, R. L. McCreery, G. S. Frankel, Ohio State University.)
Al and Cu electrodes strongly segregated anodic and cathodic reactions. And
although they are idealized models of microstructural features in Al–Cu alloys
(42), they are relevant to microgalvanic coupling in high-strength Al alloys. Figure 13 shows plots of galvanic couple current and couple potential versus time
showing the effect of 50 mM K 2 Cr 2 O 7 additions (0.1 M chromate) to aerated
100 mM NaCl solutions (41). When dichromate is added to the cell compartment
containing the Al (or Al alloy 2024), there is no detectable reduction in the galvanic current flowing, and only a very small change in the couple potential is
observed. Since the cathodic reaction proceeds unimpeded in the other compartment of the cell, this result suggests that there is very little effect of dichromate
on the anodic reaction, consistent with Kaesche’s findings (23). However, when
dichromate is added to the cell compartment containing the Cu, which supports
oxygen reduction, there is a sharp transient increase in the couple current followed by a rapid decrease to low steady-state values. This is attributed to chromate reduction to insoluble Cr(OH) 3 , which forms an insulating film on the Cu
electrode surface and restricts the reduction reaction and limits the couple current.
This shows that the overall corrosion process is under cathodic reaction control
and that dichromate is a potent cathodic inhibitor at this concentration ratio.
3. Rotating Disk Electrode (RDE) Experiments
Corrosion of Al alloys often occurs under conditions in which the primary cathodic reaction is oxygen reduction. In cathodic polarization experiments, this
reaction appears to be under mass-transfer control at potentials near the open
278
Chapter 8
Figure 13 Behavior of a split cell containing a Cu electrode in one compartment and
either Al or 2024-T3 in the other. Both compartments were open to air but not actively
aerated. K 2 Cr 2 O 7 was added as indicated to a total chromate content of 5 mM. (From W.
J. Clark, J. D. Ramsey, R. L. McCreery, G. S. Frankel. J. Electrochem. Soc., in review,
June, 2001.)
circuit potential of many engineering alloys. The rotating ring disk electrode approach enables study of transport controlled reactions under well controlled experimental conditions and has been used to separate direct and indirect effects
of chromate on the suppression of oxygen reduction on Al alloys (43).
The RDE consists of a disk electrode embedded in an insulating rod material as shown in Fig. 14 (44). The composite electrode can be rotated about its
axis, which causes electrolyte to be drawn up against, and forced outwards across,
the face of the metal disk electrode, as shown in Fig. 15 (45). The convection
and diffusion equations that describe solution flow in this situation have been
rigorously established making this experimental approach a powerful one for the
study of the effects of forced convection of electrochemical reactions.
Study of Surface Treatments
279
Figure 14 Schematic illustration of the composite electrode used in RDE experiments.
(From A. J. Bard, L. E. Faulkner. Electrochemical Methods: Fundamentals and Applications. 2d ed. John Wiley, New York, 2001, p. 335.)
In the present case, the Levich equation describes the reaction rate for a
mass-transfer limited reaction in an RDE experiment. The Levich equation is
i l ⫽ 0.62nFAD O2/3 ω 1/2 ν ⫺1/6 C*O
(3)
The limiting reaction rate expressed as a current density depends on the electrode
area, A, angular velocity, ω, the kinematic viscosity, ν, the concentration of reactant in solution, C*
o and its diffusion coefficient, D o .
Figure 16 shows the steady-state limiting current density, i lim , for the oxygen reduction reaction (ORR) on pure Al, pure Cu, and an intermetallic compound phase in Al alloy 2024-T3 whose stoichiometry is Al 20 Cu 2(Mn,Fe) 3 after
exposure to a sulfate–chloride solution for 2 hours (43). The steady-state i lim
values for the Cu-bearing materials match the predictions of the Levich equation,
while those for Al do not. Reactions that are controlled by mass transport in the
solution phase should be independent of electrode material type. Clearly, this is
not the case for Al, which suggests that some other process is rate controlling.
280
Chapter 8
Figure 15 Representation of steady-state electrolyte flow past the electrode disk in RDE
experiments. (From A. J. Bard, L. E. Faulkner. Electrochemical Methods: Fundamentals
and Applications, 2d ed. John Wiley, New York, 2001, p. 337.)
Figure 16 Limiting current densities for oxygen reduction on rotating disks for pure
Cu, Al 20 Cu 2(Mn,Fe)3 , and pure Al in 0.1 M Na 2 SO 4 ⫹ 0.005 M NaCl under ambient
aeration. The Levich prediction assumes a dissolved oxygen concentration of 6 ppm (1.8 ⫻
10 ⫺4 M). (From G. O. Ilevbare, J. R. Scully. Corrosion 57, 134 (2001).)
Study of Surface Treatments
281
In this case, it is likely that electron transfer is sluggish through the Al oxide
film on the pure Al electrode, and this limits the rate at which the ORR can be
sustained. The high ORR rate on the Cu-bearing materials was attributed to corrosion and surface roughening that increased the area capable of supporting the
ORR. In the case of the intermetallic compound, dealloying may also have contributed to the increase in active surface area.
A different situation is observed when these same materials are exposed
to a chromate-bearing sulfate–chloride solution prior to RDE measurement. In
this case, transport-limited ORR rates were lower than the Levich prediction, but
not as low as the ORR rates on pure Al, as shown in Fig. 17. RDE measurements
of the ORR on Au, which is not susceptible to roughening in chromate–sulfate–
chloride solutions, showed no change due to prior exposure. On the basis of these
results, chromate appeared to suppress corrosion during the pretreatment phase,
thereby limiting the extent of surface roughening and any increase in active surface area. The important finding from these studies for Al–Cu alloys is that the
limitation in surface roughening of Cu-bearing intermetallics in Al–Cu alloys
limits the development of large catalytically active surface to support the ORR.
This in turn contributes to improved resistance to corrosion.
Figure 17 Limiting current densities for oxygen reduction on rotating disks for pure Cu,
Al 20 Cu 2(Mn,Fe)3 , and pure Al in 0.1 M Na 2 SO 4 ⫹ 0.005 M NaCl ⫹ 0.0062 M Na 2 CrO 4 ⫹
0.0038 M H 2 CrO 4 at pH 6 under ambient aeration. The Levich prediction assumes a dissolved oxygen concentration of 6 ppm (1.8 ⫻ 10 ⫺4 M). (From G. O. Ilevbare, J. R. Scully.
Corrosion 57, 134 (2001).)
282
Chapter 8
IV. CONVERSION COATINGS
A.
Overview of Conversion Coatings
Conversion coatings are formed on metal surfaces to enhance adhesion of subsequently applied paints and adhesives and to provide temporary or modest permanent increases in corrosion resistance. In the broadest sense, conversion coatings
can be divided into three categories: chromate conversion coatings, phosphate
conversion coatings, and a less well-defined and still emerging class of environmentally friendly conversion coatings that contain little or no phosphate or chromate. Conversion coatings are usually formed by immersing or spraying an aqueous solution that activates a metal surface, dissolves any existing surface oxide,
and replaces it with a thin mixed metal oxide coating.
In terms of processing, conversion coatings are distinct from anodized coatings because no externally applied voltage or current is needed to the substrate
to accomplish coating formation. In terms of properties, conversion coatings are
distinct from anodized coatings because they are much less corrosion resistant
and much more susceptible to inadequate coverage or improper coating formation
due to substrate composition and metallurgical heterogeneity. Conversion coatings are usually much softer than anodized coatings, especially when they are
first formed.
Conversion coating thicknesses range from 0.1 to nearly 10 µm. Most commonly, they are in the 1 to 2 µm range. The coatings may be largely amorphous
or polycrystalline. They do not possess regular arrays of pores and are not generally known to have a duplex structure (inner barrier layer and outer porous layer)
like anodized coatings.
Chromate conversion coatings are used widely on aluminum alloys as a
pretreatment for painting, though in some applications, where noncondensing
atmospheric exposure is expected, they may be used as the primary means of
corrosion protection. Chromate conversion coatings are used on magnesium, cadmium, and zinc, and on galvanized steel to suppress the formation of white
rust.
Phosphate conversion coatings have long been used in the automotive industry to prepare steel surfaces for painting. Owing to the increasing use of aluminum in automobiles and the desire to maintain simple and cost-effective surface
finishing facilities, phosphate conversion is now being used to prepare Al alloy
sheet for painting. A detailed review on chromate and phosphate conversion coatings can be found in Ref. 46.
Phosphate conversion coatings are formed on metal surfaces by immersion
in aqueous phosphate solutions. These coatings are primarily intended to promote
the adhesion of subsequently applied paints. Phosphate coatings typically consist
of a compact mass of hydrated metal phosphate crystallites; M 3 (PO 4) 2 nH 2 O.
They differ from CCCs in that they are crystalline, do not attempt to provide
Study of Surface Treatments
283
complete surface coverage of the metal, and provide lower levels of corrosion
resistance.
Chromate- and phosphate-free coating chemistries are currently the subject
of intensive research and development. Chromates are toxic and carcinogenic to
humans. Phosphate discharged into aquatic environments leads to accelerated
eutrophication. The challenge for environmentally friendly replacement coating
chemistries is to duplicate the ease of application and high performance of chromate and phosphate coatings without using or producing hazardous chemical
substances. Reviews on the status of Cr-free coatings development can be found
in Refs. 47–50.
For many years, evaluation of conversion coatings was carried out using
cabinet exposure testing (51) or spot testing (52). Over the past 20 years, and
especially since the introduction of electrochemical impedance spectroscopy to
corrosion research, electrochemical techniques have been used with increasing
regularity to assess corrosion resistance of conversion coatings. Phosphate coatings are not usually as corrosion resistant as chromate coatings, but electrochemical techniques are used to estimate the extent of phosphate surface coverage. As
the use of electrochemical techniques has increased, effort has been directed towards characterizing the corrosion behavior of traditional chromate-based coatings using modern electrochemical methods to establish a performance baseline
defined in terms of results from electrochemical experiments.
B. Electrochemical Testing of Conversion Coatings
1. Anodic Polarization
In general, small passive current densities and increases in pitting potential are
regarded as evidence for anodic inhibition in anodic polarization experiments.
However, in aerated chloride solutions, chromate conversion coated alloys do
not exhibit strong reductions in passive current or elevations in pitting potential.
In fact, it is not uncommon for conversion coated aluminum alloys to exhibit no
passive region at all in aerated solutions with chloride concentrations greater than
0.1 M. This has been interpreted as a lack of anodic inhibition by CCCs. However,
test electrode areas are usually on the order of square centimeters and contain
many metallurgical and surface defects that readily initiate pits. Given that pitting
is a defect-dominated process, pits will initiate at the weakest site no matter how
robust the remainder of the coating. In this sense, anodic polarization measures
only the strength of the weakest point in the sample. This is unlike cabinet exposure testing, or electrochemical impedance methods, where the evaluation more
or less accounts for the behavior of the entire sample surface.
The effect of defect mediation of coating breakdown in anodic polarization
experiments can be observed in polarization experiments conducted with arrays
284
Chapter 8
Figure 18 Effect of immersion time on CCC breakdown distributions determined in
0.5 M NaCl solution. CCCs formed on high purity Al wire electrodes. (From W. Zhang,
B. Hurley, R. G. Buchheit. J. Electrochem Soc., submitted, June, 2001.)
of small, nominally identical electrodes. Figure 18 shows distributions of pitting
potentials measured in 0.5 M NaCl solution on 500 µm diameter Al electrodes
arranged in an array (53). Entire arrays were chromate conversion coated for
different lengths of time, removed, aged in air for 24 hours, and then immersed
in 0.5 M NaCl and polarized potentiodynamically until pitting was detected. This
plot shows that as the immersion time in the conversion coating bath increases,
the distribution of the pitting potential shifts to more positive potentials, clearly
indicating anodic inhibition. These pitting potential distributions reflect the behavior of large area measurements, where some regions of the surface break down
more readily than others.
For phosphate coatings, anodic polarization techniques have been used to
assess the uncoated metal surface area. Integration of metal oxidation peaks in
the i–V curves from cyclic voltammetry and comparison to integrated peak areas
determined from reference samples with known surface coverages give such indications (54–56). However, the metal oxidation process and the interpretation of
the electrochemical response may be significantly altered by the fact that metal
dissolution occurs at the bases of pores, where local chemistry may differ significantly compared to the bulk. Polarization resistance measurements have also been
explored as a means for determining the exposed surface area (57). In the proper
Study of Surface Treatments
285
environment, the corrosion rate of the metal will be proportional to the exposed
area. This approach has the advantage that the coated surface is never driven
very far from its steady-state open circuit potential and that the coating is not
heavily damaged during the measurement.
2. Cathodic Polarization
Conversion coatings are electronically resistive and do not support reduction reactions that depend on electron transfer through the coating. In near-neutral aqueous solutions oxygen reduction is transport limited on bare metals and occurs at
a rate of about 10 ⫺5 A/cm 2. For an intact conversion coating, oxygen reduction
occurs under mixed reaction control at much lower rates, and it is a straightforward matter to distinguish between bare and conversion coated surfaces on the
basis of cathodic polarization. Defective or damaged conversion coatings will
support reduction reactions at higher rates, and it is possible to rank the corrosion
resistance of certain types of conversion coatings on the basis of their ability
to inhibit oxygen reduction. In many conversion coatings, the only meaningful
component of corrosion resistance is the ability to inhibit the cathodic portion
of the corrosion process.
For phosphate coatings, the magnitude of the limiting current density is
used as a measure of exposed surface area (58). Like anodic polarization methods
though, this method must be used with care, as chemistry changes and restricted
transport occurs in pore spaces where the reduction reaction occurs. Alkaline
dissolution of the phosphate coating may also occur after extended cathodic polarization, which damages the coating and increases the exposed metal area.
3. Tests for Self-Healing
One of the most noteworthy components of chromate coating corrosion protection
is active corrosion protection or self-healing. Self-healing refers to the ability of
a coating to resist localized corrosion in locations where it has suffered minor
amounts of mechanical or chemical damage; or where the original coating did not
form completely. It has long been speculated that chromium–chromate coatings
possess this property, because they can leach chromate into an attacking solution,
which is transported to the site of attack to stifle corrosion. The self-healing effect
appears to be very pronounced for primer paint coatings containing high fractions
of sparingly soluble chromate pigment, but the effect also seems to be present
in chromate conversion coatings (CCCs).
A simple cell, termed the simulated scratch cell, has been devised that can
check for the key elements in the self-healing of CCCs (59). This cell, shown
in Fig. 19, consists of two metal surfaces, normally several square centimeters
in area, opposing one another and separated by several millimeters. One metal
surface is conversion coated, while the other is left bare to simulate a defect or
286
(a)
(b)
Chapter 8
Study of Surface Treatments
287
“scratch.” The two metal surfaces are separated by a gap of several millimeters,
which is filled with an attacking electrolyte like a dilute chloride solution. The
cell may be equipped with a counter and reference electrode and either the coated
or defect sides of the cell can be interrogated using electrochemical methods.
Using this cell constructed with bare and conversion coated 2024-T3 and
filled with a solution of 0.1 M NaCl, an accelerated chromium–chromate conversion coating was examined for evidence of self-healing (59). Over a span of 48
hours, the polarization of the originally bare surface was found to increase by
two orders of magnitude, while the pitting potential increased 60 mV. Raman
spectroscopy on the surface showed that CCC-like chromate products had formed
near pits. In ex situ solution chemistry determinations, chromate release was verified by placing a droplet of solution on a conversion coated surface. Over a 48
hour period, a chromate concentration of 35 ppm was found to have developed.
All together, these results confirmed anecdotal reports of self-healing derived
from the performance of scribed conversion coated panels in cabinet exposure
testing.
Simulated scratch cells have been used to show that hydrotalcite conversion
coatings containing Ce(VI) can also be self-healing (60). Conversion coatings
were made by first forming a hydrotalcite coating on 2024-T3 and 6061-T6 substrates and then immersing the coated substrates in a solution consisting of 10
g/L Ce(NO 3) 3 ⫹ 3 mL/L 30 vol% H 2 O 2 . The alkaline conditions of the coating
induced precipitation of sparingly soluble Ce(VI) hydrated oxides. Simulated
scratch cells were constructed using this coating and a bare 2024-T3 sample as
the scratch. The gap solution in these experiments was 0.5 M NaCl. Bare surfaces
were exposed in the simulated scratch cell and then tested for changes in corrosion resistance ex situ in a 0.05 M NaCl solution. Results from these experiments
and other comparative experiments are shown in Fig. 20. The plot shows that
the corrosion resistance of the bare surface exposed to the Ce sealed hydrotalcite
coating exhibited a much greater corrosion resistance than a sample exposed to
Ce coating containing primarily Ce(III) or a sample exposed to another uncoated
alloy surface. Solution analysis showed that Ce was released by Ce(IV) coatings,
and that Ce precipitated on the bare surface, primarily at Cu-rich inclusions in
the alloy.
Evidence for self-healing is not detected in identical experiments with lanthanum sealed hydrotalcite coatings. La does not have a soluble tetravalent oxide
Figure 19 (a) Cross section schematic of the simulated scratch cell. (b) Photograph of
an artificial scratch cell modified to make in situ electrochemical measurements to test
for self-healing by conversion coatings. (From Zhao, McCreery, Frankel. J. Electrochem.
Soc. 145, 2258 (1998).)
288
Chapter 8
Figure 20 Coating resistance versus time for bare 2024-T3 surfaces exposed to Ce
sealed hydrotalcite, a Ce(III) conversion coating, and bare 2024-T3 in the simulated
scratch cell. R c was determined ex situ during immersion in 0.05 M NaCl solution. The
plot indicates an elevated resistance to corrosion for the sample exposed to the Ce sealed
hydrotalcite coating. (From S. B. Mamidipally, P. Schmutz, R. G. Buchheit. Corrosion,
58, 3, 2001.)
like Ce. Therefore, once it is precipitated on the hydrotalcite surface, it is not
easily released to aid in self-healing. Overall, these results show that self-healing
is not limited to chromate conversion coatings.
C.
Electrochemical Impedance Spectroscopy (EIS)
1. Overview of the Technique
EIS has become an important method of characterizing inorganic coating of all
types and the basis of the technique is briefly introduced here. For details on EIS
measurements, hardware, data analysis, data presentation, and applications the
reader is referred to the materials presented in Refs. 61–64.
EIS uses small periodic signals to perturb an electrode surface and measure
an electrochemical response that can be analyzed to gain information on corrosion
mechanisms and corrosion kinetics. In corrosion experiments, it is common to
apply a 10 to 50 mV sinusoidal voltage signal to a corroding electrode interface
and measure the resulting current signal occurring at the same excitation frequency. The voltage and current signals are related by the impedance in a form
that is analogous to Ohm’s law:
Z(ω) ⫽
V(ω)
I(ω)
(4)
The term Z(ω) is known as the complex impedance and accounts for the relationship between the amplitudes of the voltage and current signals as well as the
phase shift between them. The measurement is spectroscopic because the com-
Study of Surface Treatments
289
plex impedance is measured over a domain of discrete frequencies. For corrosion
studies, the high-frequency end of the measurement domain is determined by the
frequency required to short the interfacial capacitance. Under these conditions,
only the cell solution resistance will be contained in the complex impedance. For
bare metals, conversion coated metals, the interfacial capacitance is shorted at
frequencies ranging from 5 to 20 kHz. For anodized coatings, excitation frequencies of 50 to 100 kHz may be required. The coating capacitance for organic
coatings cannot be shorted at frequencies accessible to EIS measurement systems,
which is normally about 100 kHz for commercial EIS systems. As the frequency
is lowered, interfacial resistances and reactances will contribute to the complex
impedance. Electrochemical and diffusional processes associated with corrosion
are detected at frequencies between about 10 and 10 ⫺6 Hz. However, it is rare
that measurements are made below about 10 ⫺3 Hz owing to the instability of
corroding metal surfaces.
EIS measurements on corroding surfaces are usually made using two or
three electrode cell configurations. A potentiostat is used to control the potential
between the working and reference electrodes and measure the current flow between the counter and working electrodes. A frequency generator is required to
provide the periodic excitation signal. An impedance analyzer is also required
to measure the complex impedance. Frequency response analyzers or lock-in amplifiers may be used for this purpose. Integrated systems that contain all the necessary electronic hardware for conducting EIS measurements are commercially
available. The measurement hardware is controlled by a personal computer,
which runs software that coordinates the execution of the experiment, logs the
data, and provides graphical and numerical analysis of the EIS spectra.
In corrosion studies, EIS data are graphically presented in complex plane
plots and Bode plots. Examples of these plots are shown in Fig. 21 (65). In
complex plane plots, the complex impedance at each frequency is located according to its real and imaginary components. At each frequency, the magnitude
of the complex impedance is equal to the length of the vector drawn to the point
from the plot origin. The phase angle is defined as the angle the impedance magnitude vector makes with the real axis. Capacitive responses, like those associated
with intact barrier coatings, are represented by straight or nearly straight lines
that fall along the imaginary axis. Charge transfer processes, like those associated
with pitting, usually trace out partial or complete semicircular arcs in the complex
plane. Diffusional processes take on a variety of forms depending on the precise
nature of the process. In severely pitted conversion coated samples, diffusion is
characterized by a tail extending from the right-hand side of a semicircular arc.
In Bode plots the log of the impedance magnitude and the phase angle
are plotted versus the log of the applied frequency. Capacitive responses are
characterized by regions of the curve that take on slopes of about ⫺1 in the Bode
magnitude plot and have phase angles approaching ⫺90 degrees. Charge transfer
290
Chapter 8
(a)
(b)
Figure 21 Common graphical representations of EIS data in corrosion studies. (a) Complex plane plot. (b) Bode magnitude and Bode phase angle plots. (From Gamry, EIS Manual, pp. 2–3, 2–5.)
processes have sigmoidally shaped Bode magnitude plots. At the highest and
lowest measured frequencies the impedance is primarily resistive in nature, and
the Bode magnitude plots are flat. These two regions are separated at intermediate
frequencies by a region, where the capacitive response of the electrode is predominant. In Bode phase angle plots, the phase angle is near 0° at high and low
frequencies and is near ⫺90° at intermediate frequencies. At the lowest measured
frequencies where diffusional processes tend to dominate the impedance response, the Bode magnitude often increases slowly with decreasing frequency
and takes on an ω ⫺1/2 to ω ⫺1/4 frequency dependence.
2. EIS and Conversion Coatings
Historically, conversion coatings have been evaluated by exposure testing, usually in a 5% salt fog. Corrosion resistance of conversion coated panels is deter-
Study of Surface Treatments
291
mined by visual inspection after some predetermined exposure period. Usually
the extent of corrosion damage is evaluated against some established metric such
as number of pits per unit area visible to the unaided eye. Coated samples are
normally given a pass or a fail ranking. This type of test is simple and is relevant
to certain types of service conditions. It can also be very useful for process in
quality control. However, exposure durations of 100 to 1000 hours may be required for discriminating results to develop, and the results are based on visual
inspection, which is subjective. During exposure, samples will fade, stain, pit,
and form corrosion product deposits. A means of quantifying the distribution of
corrosion type and intensity has not been widely accepted. Normally, it is a simple
matter to distinguish between coatings that provide little corrosion protection
from those that offer superior protection. However, no good scheme has arisen
to distinguish among coatings of intermediate (but useful) corrosion protection
that fail the salt spray test but provide substantially different levels of corrosion
resistance.
For these reasons, EIS has been explored as an alternative proof test for
evaluation of conversion coatings. In these tests, conversion coated surfaces are
exposed to an aggressive electrolyte for some period of time during which coating
damage will accumulate. An impedance spectrum is collected and evaluated using a suitable equivalent circuit model and complex nonlinear last-squares fitting.
EIS has several advantages for evaluations of conversion coatings. First,
it is a small-signal technique, and the electrode is never polarized very far away
from its corrosion potential as the measurement is made. Second, EIS can be
very quantitative as it yields both kinetic and mechanistic information about the
corrosion process taking place on the sample. The interfacial capacitance can be
shorted at frequencies as low as 10 kHz. As a result, meaningful characterizations
of the corrosion response can often be obtained from spectra collected between
10 kHz and 10 mHz. This can be completed in a matter of minutes with currently
available commercial measuring equipment. Although nearly all conversion coatings yield a nondiscriminating capacitive response immediately upon immersion
in an aggressive solution (e.g., 0.5 M NaCl), pitting damage will begin to occur
in a number of hours. As a result, discriminating results can be obtained in less
then one day using EIS, whereas several days or more are required for exposure
testing.
3. Equivalent Circuit Analysis
Equivalent circuit analysis is well suited for analysis of EIS measurements of
conversion coatings and is the primary method for interpreting EIS spectra from
conversion coated metal surfaces. A widely accepted generalized equivalent circuit model for the EIS response of pitted conversion coatings is shown in Fig.
22a (66,67). Several related models discussed below are also shown. In the gener-
292
Chapter 8
Figure 22 Equivalent circuit models for conversion coatings. (a) Generalized model
for pitting conversion coated surfaces, adapted from Ref. (b) Model for a barrier conversion coating. (c) Model for the early stages of CCC breakdown.
alized model, R p and C p refer to the specific resistance and capacitance of the
conversion coating. R pit and C pit refer to the pit resistance and capacitance. The
element labeled W is present to account for any diffusional processes, such as
those that may be present in severely degraded coatings, or coatings that are
naturally porous. When a conversion coating with good barrier properties degrades, the fraction of the surface area covered by pits, F, increases. This shorts
the impedance associated with the conversion coating.
For coatings with no pitting, the generalized model must be amended to
account for that fact that all current must flow through the barrier coating. The
coating resistivity, R p , is on the order of 100 to 1000 MΩ ⋅ cm 2 and behaves
essentially as an open circuit under near-DC conditions (f ⫽ 0). The EIS response
over the typically measured frequency domain is that of a constant phase element
(CPE) in series with a solution resistance (Fig. 22b).
A CPE is a nonphysical circuit element whose characteristic is a constant
phase shift over a wide range of frequencies. The impedance of this element is
(68)
Z CPE (ω) ⫽
1
C( jω) α
(5)
Study of Surface Treatments
293
On a complex plane plot, a CPE exhibits a straight line whose angle is π/2 ⋅ α
(1 ⬍ α ⬍ ⫺1) with respect to the real axis. In a Bode magnitude plot a straight
line response like that of a capacitor is obtained. The slope deviates from an ideal
value of ⫺1 as α decreases below 1.
As exposure time to an aggressive environment increases, conversion coating begins to break down. The conversion coating impedance is shorted by pits,
which typically have smaller resistivities and larger specific capacitances than
the intact conversion coating. In the early stages of coating breakdown, diffusion
in pits, represented in the generalized model, is not significant. Usually, a single
time constant EIS response is observed. In this case, the measured capacitance
consists of contributions from the coating and the pits:
C c ⫽ C p (1 ⫺ F ) ⫹ C pit (F)
(6)
where C c is the composite capacitance and the other symbols refer to elements
described in the generalized model. This composite capacitance is usually nonideal and can be modeled in an equivalent circuit using a CPE (Fig. 22c). For
pitting conversion coatings, α, which is a measure of nonideality in the capacitance, typically ranges from 0.7 to 0.95.
The composite resistance, R c , is
1
(1 ⫺ F )
F
⫽
⫹
Rc
Rp
R pit
(7)
Since R p ⬎⬎ R pit
1
F
⬇
R c R pit
(8)
This leads to a very simple single time constant model that accounts for
the EIS response for conversion coatings in the early stages of breakdown (Fig.
22c).
For coatings that are inherently porous, or have suffered extensive pitting,
the generalized model in Fig. 22a describes the EIS response. Degraded conversion coatings often exhibit one or two time constants in addition to a diffusional
impedance.
A common way to rank the performance of coatings is to compute the
total impedance from equivalent circuit modeling or to use the magnitude of the
impedance at the DC limit. So while the EIS response becomes increasingly
complicated as pitting initiates and propagates, the magnitude of the impedance
typically falls with increasing exposure time. Table 1 give typical values of the
total impedance of various coated and passivated substrates.
294
Chapter 8
Table 1 Coating Resistance Ranges for Various
Surface Treatments and Substrates
Coating
Bare Al alloys
Sputter-deposited high purity Al
Poor conversion coatings
Good conversion coatings
Sealed anodized coatings
Painted surfaces
“Coating Resistance”
MΩ ⋅ cm 2
0.005
0.5–1.0
0.1–1.0
1–5
10
⬎10
4. Continuum Reaction Analysis
The continuum reaction approach has been used to examine film formation on
Al under modestly anodizing conditions (69). In the continuum reaction approach, the entire electrochemical reaction mechanism is written explicitly. Rate
equations for the various steps in the electrochemical process are developed.
Changes in surface coverages that affect the mechanism are usually accounted for
using appropriate adsorption isotherms. Diffusional, migrational, and convective
components of mass transfer are expressed in terms of diffusivities, solution conductivies, and viscous properties. A comprehensive description of the various
elements in the reaction mechanism are defined and subject to mass and charge
balance. An overall rate equation describing the behavior of the net current response is then constructed and linearized to eliminate exponential terms. Polarization dependencies are incorporated for activation controlled and electromigration
controlled processes. A term describing a periodic (usually sinusoidal) voltage
perturbation is inserted into the equation, and the expression is rearranged to
extract the impedance transfer function, which is now defined in terms of kinetic
and physical parameters rather than a network of equivalent passive circuit elements. This approach has been used best in analyzing dissolution and passivation
in well-behaved systems such as iron in sulfuric acid (70–72). Continuum reaction analysis is a very powerful method for understanding the contributions of
faradaic reactions, adsorption, passivation, and transport to the EIS response.
However, developing the transfer function requires precise knowledge of the corrosion process. Ancillary data such as reaction rate constants and transport characteristics are also required to construct a comprehensive and meaningful expression for the impedance function. Often these data do not exist in sufficient detail.
For these reasons, the continuum reaction approach has not been widely used in
the analysis of EIS data for conversion coated surfaces.
Study of Surface Treatments
295
5. Nonparametric Analysis
The total equivalent resistance of a corroding surface may be estimated by integration of the imaginary component of the impedance over the measured frequency domain according to
ω hi
2
Rc ⫽
π
冮 Z″ (ω)d ln ω
(9)
ω lo
where Z″(ω) is the imaginary component of the impedance, and ω is the radial
frequency (2πf ). ω hi and ω lo refer to the limits of the frequency range used in
the experiment.
This expression was originally used to estimate the polarization resistance
for actively corroding metals whose impedance response was a well-behaved
semicircular arc in the complex plane (73), but can be used in certain situations
to estimate the equivalent resistance of conversion coated metal surfaces. Equation (9) is derived from the Kramers–Kronig transforms and subject to the conditions that limit their use (74–78). These conditions include
Causality: The measured response is due only to the applied perturbation
and does not contain contributions from spurious sources.
Linearity: The relation between the applied perturbation and the measured
response is linear.
Stability: The system is stable to the extent that it returns to its original
condition after the perturbation is removed.
Finiteness of the impedance function: The impedance must be finite valued
at f → 0 and f → ∞, and the impedance must be continuous and finite
valued at intermediate frequencies.
This method of estimating R c is useful when it can be applied, since the
determination is not based on any presumed model of the corrosion damage process or any of the assumptions that come with assignment of an equivalent circuit
model. This method is particularly helpful when there is more than one time
constant in the spectrum, or the impedance spectrum is particularly complicated.
Caution is warranted however. This method of estimation can be in serious error
for samples with large capacitance-dominated low-frequency impedances. As a
general rule, for this estimation method to be reasonably accurate, the impedance
function must exhibit a clear DC limit, or a diffusional response that can be
modeled by a constant phase element in equivalent circuit analysis (75).
D. Use of EIS for Evaluation of Conversion Coatings:
Examples
EIS is very sensitive to the conversion coating breakdown process, and changes
in coating corrosion protection can be recognized in graphical representations of
296
Chapter 8
the data; the accumulation of damage can be tracked using equivalent circuit
modeling. However, standardized methods for evaluating conversion coatings by
EIS do not yet exist.
Intact barrier conversion coatings behave as capacitors that yield distinctive
Bode plots. An example of this is shown in Fig. 23 for Ce/Mo passivated Al
6061-T6 exposed to 0.5 M NaCl solution (79). At high frequencies, the interfacial
capacitance is shorted, and only the solution resistance is measured. At frequencies below about 10 4 Hz, a pure capacitive response is obtained. This is characterized by a large negative phase shift in the Bode phase angle plot and a straight line
with a slope of about ⫺1 in the Bode magnitude plot. These are the indications
of high corrosion resistance. This coating is particularly resistant under these
conditions, and does not exhibit signs of breakdown after exposures as long as
30 days.
Passivation of Al alloys surfaces in Ce, La, and Y chloride solutions might
be expected to produce similar levels of corrosion protection because they all
belong to the lanthanide series in the periodic table and share similar chemical
characteristics. Examination of surfaces passivated in solutions of each of these
salts shows that this is not the case. Figure 24 shows Bode plots for Al 6061-
Figure 23 Bode plots for Ce/Mo passivated 6061-T6 exposed to 0.5 M NaCl solution.
Curve 1, 6 h; curve 2, 1 d; curve 3, 7 d; curve 4, 14 d; curve 5, 30 d. This plot illustrates
the EIS response of a very protective conversion coating. (From F. Mansfeld, V. Wang,
H. Shih. J. Electrochem. Soc. 138, L74 (1991).)
(a)
(b)
Figure 24 Bode magnitude plots for CeCl 3-, LaCl 3-, and YCl 3-passivated 6061-T6 exposed to 0.5 M NaCl solution. (a) CeCl 3-passivated samples exposed for 7 d (curve 1),
15 d (curve 2), and 60 d (curve 3). (b) LaCl 3-passivated sample (curve 1), YCl 3-passivated
sample (curve 2), and bare alloy (curve 3). (From H. Shih, F. Mansfeld. p. 180, ASTM
STP 1134, ASTM, Philadelphia, PA (1992).)
297
298
Chapter 8
T6 passivated in CeCl 3 (Fig. 24a) and LaCl 3 and YCl 3 (Fig. 24b), which were
then exposed to 0.5 M NaCl solution (80). The CeCl 3-passivated samples exhibit
capacitive behavior. These coatings are not as corrosion resistant as those shown
in Fig. 23 and begin to exhibit a low-frequency breakpoint (phase angle ⫽ 45°)
just above 10 mHz in some cases. The LaCl 3- and YCl 3-passivated samples have
much smaller capacitive regions across the frequency domain and distinct-low
frequency breakpoints, which result in well-defined DC limits in the magnitude
of the impedance. Overall, these DC limits are one to two orders of magnitude
smaller than the impedance of the CeCl 3-passivated surfaces measured at the
same frequency. This type of EIS response is characteristic of modest levels of
corrosion protection, easily distinguished from the response of more corrosion
resistant coatings.
Using the generalized equivalent circuit model for conversion coated surfaces shown in Fig. 22, it is possible to track the time-dependent changes in the
resistances and capacitances of the intact coating and evolving pits. Figure 25
shows representative Bode plots for CeCl 3-passivated and bare Al 7075-T6 immersed in 0.5 M NaCl solution (81). Spectra like these were collected over 35
(a)
Figure 25 (a) Bode plot for CeCl 3-treated 7075-T6 during immersion in 0.5 M NaCl
solution. (b) Results of the equivalent circuit modeling of the EIS data from Fig. 25 using
the generalized equivalent circuit model in Figure 22a. (From F. Mansfeld, S. Lin. S. Kim.
H. Shih. Corrosion 45, 615 (1989).)
Study of Surface Treatments
299
(b)
(c)
days and analyzed using the generalized equivalent circuit model. Figure 25b
shows the variation in coating and pit resistances versus time, and Fig. 25c shows
the variation in coating and pit capacitances. For the CeCl 3-passivated sample,
the coating resistance R p is more or less constant over the course of the experiment. Pitting damage does accumulate, but the total pitted area never exceeds a
300
Chapter 8
few parts per thousand and does not contribute to any increase in R p . After 25
days, a new low frequency time constant appears indicating the appearance of
pits. In this case, owing to the small pit area fraction, pit resistance does decrease
as pit area increases. For the uncoated sample, the total resistance is comparatively low, and pitting initiates very early in the experiment.
Capacitance is also a sensitive indicator of the onset of pitting. In Fig. 25c
a significant pit capacitance increase is detected at 25 days, at the onset of pitting.
Capacitance increases dramatically at the outset of the exposure period for the
unprotected sample as widespread pitting progresses. Capacitance measurements
in particular are good early indicators of pitting in conversion coated samples
because increases in sample capacitance usually precede any visual indication of
pitting.
E.
Relation Between EIS and Salt Spray Exposure
The use of EIS for evaluating conversion coatings has grown considerably since
the late 1980s. EIS methods clearly enable conversion coated metals to be evaluated more quickly and quantitatively than exposure test methods such as salt
spray. As a research tool, EIS provides important information on corrosion kinetics and mechanisms. EIS-based coating evaluations also appear to be significant
from a practical perspective, as they give indications of corrosion resistance that
appear to scale with those provided by exposure testing.
To understand more completely the relationship between coating corrosion
resistance determined by EIS and that determined by salt spray, 33 different conversion coatings applied to five different Al alloy substrates were evaluated by
both methods (82). The data were then evaluated to determine if a correlation
existed. A variety of chromate and chromate-free coatings were included in the
evaluation representing a wide range in corrosion resistance (83). Coatings were
applied to cast 356 (Al-7.0Si), 2024-T3 (Al-4.4Cu-1.5Mg-0.6Mn), 3003 (Al1.2Mn), 6061-T6 (Al-1.0Si-0.6Mg), and 7075-T6 (Al-5.6Zn-2.5Mg-1.6Cu). Salt
spray testing was carried out in accordance with ASTM B117 (84), which directs
that coated samples be exposed in a chamber to a 5% salt fog at 95°F. Five
replicate samples from each unique coating–substrate combination were evaluated. The samples were visually inspected for evidence of corrosion after 24, 48,
96, and 168 hours. Based on the inspection, samples were assigned a fail ranking
if five or more isolated pits were identified. Otherwise, the samples were given
a pass ranking.
For the EIS evaluation, samples were exposed to an aerated 0.5 M NaCl
solution for 24 h under free corrosion conditions. During this time, some amount
of corrosion damage occurred that normally manifested itself as pitting. Replicate
EIS spectra were collected from each sample between 10 kHz and 10 mHz using
a 10 mV sinusoidal voltage perturbation. During the 24 h exposure period, sam-
Study of Surface Treatments
301
ples pitted to greater or lesser extent determined by the protectiveness of the
coating. The EIS spectra were fitted to the equivalent circuit model in Fig. 22c,
which describes the EIS response of a small number of small area pits on an
otherwise passive surface. The model was able to fit the EIS data well except
for organically sealed paintlike coatings that gave a strongly capacitive response,
and coatings with little corrosion resistance where the EIS response was dominated by diffusional impedance. Numeric parameters describing the spectra were
the solution resistance, the coating resistance, R c , and the magnitude of the impedance and exponent term from the CPE.
A qualitative sensitivity analysis indicated that R c scaled best with the salt
spray pass–fail data. For each sample–coating combination, the average R c value
was treated as an independent random variable, and the fraction of the five replicate samples that earned a passing rating in salt spray was treated as the relative
dependent variable. The mean rank method was then used to develop a probabilistic description of the tendency for a given substrate–coating combination to exhibit a passing salt spray result (85,86). From the paired EIS and salt spray data,
graphical depictions of the relationship between R c and the probability of achieving a passing salt spray result were constructed. Figure 26 shows a plot of the
cumulative passing frequency (CPF), which is the measure of the tendency to
pass the salt spray test, versus R c measured by EIS for coatings applied to 2024-
Figure 26 Plot of the CPF versus R c for chromate and chromate-free conversion coatings on 2024-T3 substrates. (From R. G. Buchheit, M. Cunningham, H. Jensen, M. W.
Kendig, M. A. Martinez. Corrosion 54, 61 (1998).)
302
Chapter 8
T3 substrates (82). In general, as R c increases, the chances of achieving a passing
result in salt spray increase, as might be expected. Individual panels must either
pass or fail, so a CPF of 80% or greater applied to five panels suggests that more
than four of the five panels would pass the test, or essentially five panels would
pass. Therefore samples with R c values corresponding to a CPF of 80% or greater
are expected to exhibit passing behavior in salt spray testing at the proper inspection interval. Table 1 shows the R c values corresponding to the 80% CPF for the
five different alloys examined in this study, showing that these values range from
2 to 20 MΩ ⋅ cm 2. The threshold R c value for 2024-T3 is about 2.4 MΩ ⋅ cm 2,
which agrees well with a threshold value of 2 MΩ ⋅ cm 2, which has been suggested as a critical value for achieving a salt spray result in another study (87).
Figure 26 also shows that there is a set of data that exhibit R c values that
range from 0.01 to 0.5 MΩ ⋅ cm 2, but have a 0% CPF at 168 h. This suggests
that EIS has the ability to discriminate quantitatively among coating performances with more sensitivity than salt spray testing. While these coatings do not
perform well in ASTM B117 salt spray, these differences in corrosion protection
may be important to know for other applications or environments.
Overall, this analysis suggests that results from EIS do give indications of
coating corrosion resistance that scale with the indications of salt spray testing
in many cases. EIS also provides some important advantages including greater
discriminating power, a more quantitative description of corrosion protection,
and a more rapid measurement.
V.
ANODIZED SURFACES
A.
Overview of Anodization
Anodization involves thickening of oxide layers on metals through application
of a voltage or current to a metal surface that is immersed in a suitable electrolyte.
Anodization is used to improve the corrosion resistance, abrasion resistance, paint
adhesion, and adhesive bonding characteristics of Al, Mg, Ti, and their alloys.
Anodizing can be accomplished in a range of solutions. The use of nitric, phosphoric, chromic, and sulfuric oxalic acids is common. Anodic oxide films are
divided into two categories: (1) thin barrier layers with high dielectric strength
and (2) thick duplex films, which consists of an inner barrier layer and a thick
porous outer layer (88,89).
The growth of barrier layers on Al occurs under conditions where oxide
film dissolution is negligible. Film growth has been described quantitatively by
a high field conduction model involving transport of both Al 3⫹ cations and O 2⫺
or OH ⫺ anions (90,91). Al 3⫹ cations are transported to the film/electrolyte interface, react with water, and participate in film growth. O 2⫺ and OH ⫺ anions are
Study of Surface Treatments
303
transported to the film/substrate interface where they react with the metal substrate to contribute to film growth. The film growth constant for Al is generally
˚ /V (92). Anions present in the anodizing
reported to be in the range of 12 to 14 A
solution may also be incorporated into the barrier film and affect its subsequent
electronic and barrier properties (93–95).
The thickness of structure of anodized layers depends on the solution chemistry and the magnitude of the current or voltage that is applied. Anodized layer
thicknesses range from about 5 to 50 µm depending on the substrate type and
anodization conditions. Anodized surfaces often possess excellent corrosion resistance. Further increases in corrosion resistance can be imparted by the use of
various sealing treatments that plug pores in the layer by precipitation, or react
with the pore walls. Electrochemical methods are well suited for studying the
corrosion resistance of anodized surfaces and anodized and sealed surfaces. In
particular, electrochemical impedance spectroscopy (EIS) is well suited for determining the characteristics of anodized layers and the effects of sealants and
their breakdown in aggressive environments.
Porous-type coatings exhibit a duplex structure consisting of an inner barrier layer and a crystalline outer layer that consists of a regularly spaced array
of pores in certain cases. As with barrier film formation, Al 3⫹ cation and O 2⫺
and OH ⫺ anion transport occurs during anodization, but in this case Al 3⫹ is
ejected into solution instead of participating in film formation. The Al 3⫹ then
reprecipitates on the previously existing barrier layer leading to the formation of
a porous outer layer (89,96).
During anodization, it is possible to monitor current or voltage and relate
these to coating characteristics. Figure 27 is a schematic illustration of the voltage
versus time response and representative cross sections of porous films, which
form on aluminum in sulfuric acid solution (97). Initially, sample voltage increases rapidly, and a barrier film consisting of amorphous aluminum oxide and
perhaps some excess aluminum ions is formed. At later stages, a porous outer
layer consisting of interpenetrating oxide and voids forms, resulting in a bilayered
or duplex structure. This outer layer thickens to a terminal value that is established
by solution chemistry applied current and voltage and the material.
Porous coatings may be sealed to improve their properties. Sealing involves
precipitation of solids in the intercrystalline spaces or regular pores that exist in
porous coatings. Sealing is accomplished by contacting coatings with steam, water vapor, or boiling water. A wide range of inorganic sealing solutions are
known. Noteworthy among these are chromates, silicates and nickelous solutions.
Organic sealing solutions include triethanolamine and tannins. Coatings may also
be sealed with a range of lacquers, waxes and oils. Wernick et al. review in some
detail the sealing of anodic coatings on aluminum, and further details can be
obtained in their review (46).
304
Chapter 8
Figure 27 Schematic illustration of the film formation morphology across the anodization voltage–time response for Al in sulfuric acid. In this environment, porous anodic
films form. (From J. De Laet, H. Terryn, J. Vereecken. Electrochim Acta 41, 7/8, 1151
(1996).)
B.
Measurement Methods
1. Single-Frequency Admittance Measurements
Single-frequency admittance measurements, sometimes reported as capacitance
and dissipation factor measurements, can be made on anodized surfaces at frequencies between 0.5 and 50 kHz. At these frequencies, electrochemical processes with time constants ranging from about 10 ⫺3 to 10 ⫺6 s can be detected in
the admittance response, and it is generally agreed that pore filling due to sealing
can be studied effectively using admittance techniques. Various interpretations
of the admittance of anodic films, particularly in the 1 to 10 kHz regime, have
been developed.
The admittance in this region is modeled using either a film capacitance
in series with the solution resistance or a parallel resistance and capacitance,
which is in series with the solution resistance. This is treated as a parallel R–C
combination whose magnitude, expressed as an impedance, is given by
Study of Surface Treatments
|Z | ⫽
冷冢
冣冷 冢
ZR ZC
ZR ⫹ ZC
⫽
305
R2
1 ⫹ (ωRC ) 2
冣
1/2
(10)
The loss factor, δ, which is a comparative measure of the resistive and reactive
components of the admittance, is also used to characterize the response
tan δ ⫽
ZR
R
⫽
⫽ ωRC
Z C (ωC ) ⫺1
(11)
Admittance measurements were used extensively prior to the widespread
use of impedance spectroscopy in the 1980s. Capacitance bridge methods are
typically used, though this limits the lower bound on the measured frequency to
several hundred hertz. Corrosion processes, whose time constants are normally
measured at or below 1 Hz, cannot be directly interrogated with this method.
There are two general interpretations for the admittance characteristics of
barrier anodic films (98). The first interpretation is based on film conduction
mechanisms, either electronic or ionic, and the influence of solution ions on the
oxide film lattice defect structure on conduction behavior. The second is based
on the behavior of preexisting defects in anodic films and the effects of attacking
or passivating solutions.
Pryor and coworkers used capacitance bridge methods to determine admittance characteristics at single frequencies ranging from 1 to 100 kHz associated
with the interaction of electrolytes with passive and barrier anodic films on aluminum. Results were interpreted in the context of changes, occurring prior to the
onset of localized corrosion, in bulk conduction characteristics associated with
oxide film thickness changes, or changes in the defect structure that affected
˚ anodic barrier
conduction mechanism (99–101). For example, exposure of 260 A
films on aluminum to 1.0 M sodium chloride solution resulted in a decrease in
the resistance at 1 kHz, but no change at 100 kHz, indicating a decrease in film
ionic resistance, but no change in film electronic resistance. A substitution of
Cl ⫺ for O 2⫺ in the anodic film oxide lattice, which increased the concentration
of n-type carriers in the film, contributed to conduction at lower frequencies but
not at higher frequencies. F ⫺ and OH ⫺ were also thought to induce similar effects
though formation of a crystalline oxyfluoride phase in fluoride solution, which
complicated the interpretation of the data. Exposure of anodic films to sulfate
solutions induced no change in either the ionic or the electronic resistivity of
anodic films. It was proposed that the sulfate anion does not exchange with oxide
ions in the lattice of the film and did not affect the charge carrier concentration.
Measurements made while films were thinned by chemical dissolution in chromate solutions produced variations in admittance that were used to characterize
film electrical properties as a function of film depth.
306
Chapter 8
The admittance response at 1 kHz has also been interpreted in terms of the
behavior at residual defects in anodic films. This interpretation is based on electron optical characterization, which shows that anodic films contain a distribution of preexisting defects associated with substrate inclusions and mechanical
flaws (96,102). In aggressive environments, pits nucleate from these defects and
propagate into the metal substrate. In this model, pits are distinct from anodic
film flaws, and both can contribute to the measured admittance. Measurements
of anodic films exposed to chloride solutions showed that the dissipation factor increased with time, but the capacitance remained nearly constant. Under
these conditions, pit propagation at a flaw led to a pit area increase, which increased the resistive component of the admittance, resulting in an increased dissipation factor, but no increase in the capacitance. Measurements at 100 kHz
were reflective of the electric double layer and not the components of the oxide
film.
During exposure to chromate solutions, defects in the anodic film heal, and
there is some thinning of the barrier layer. Under these conditions, the characteristic response in a 1 kHz admittance measurement is a slight increase in the capacitance and dissipation factor. An anodic film with an intentional defect will show
an increase in capacitance due to flaw healing.
Single-frequency or limited-frequency range capacity measurements have
been used to collect information about the time dependence in the resistive and
reactive characteristics of anodic films (103).
2. EIS
EIS is well suited for characterizing anodized films and has been used to study
the formation and characteristics of barrier and duplex coatings. EIS has also
been used widely to study the sealing of anodized films. As with conversion
coatings, equivalent circuit modeling is a powerful tool for analyzing EIS spectra
obtained from anodized surfaces. Barrier layers formed early in the anodization
process behave much like intact passive layers in EIS measurements. The response obtained is that of an imperfect capacitor or CPE. An example of CPE
behavior for a barrier film is given in Fig. 28, which shows Bode magnitude and
phase angle plots for a barrier layer on Al formed by galvanostatic polarization
in ammonium tartarate (97). It is evident from the phase angle information that
even a CPE does not fully represent barrier layer behavior. The two minima in
the phase angle data are due to two time constants, which may originate with a
duplex film or from the presence of residual flaws (96).
Figure 28 also shows data from a duplex film consisting of an inner barrier
layer and an unsealed outer porous layer. Superposition of this data set with a
data set from a sample with the barrier layer only suggests that the resistance of
Study of Surface Treatments
307
Figure 28 EIS spectra of the porous film formed at 360 s in 20% sulfuric acid at a
current density of 400 A/m 2, and a barrier film formed in 3% ammonium tartarate at a
current density of 88 A/m 2. (From J. DeLaet. H. Terryn, J. Vereecken. Electrochim. Acta
41, 1155 (1996).)
308
Chapter 8
the porous layer is very small. As a result, neither the resistance nor the capacitance of the porous layer can be detected in the EIS response.
C.
Sealing of Anodic Films
Porous anodic films can be sealed by immersion in aqueous solutions to increase
the protection of the underlying substrate. For anodized coatings on Al alloys,
sealing can be accomplished by immersion in boiling water or hot or cold metal
salt solutions. Contact times are usually on the order of tens of minutes. Sealing
of porous anodic films on Al in boiling water involves the formation of hydrated
oxide material in the topmost regions of the pores that results in plugging. With
time, the new deposit may crystallize, and the void space in the intermediate
layer of the coating reorganizes. Admittance measurements can be used to track
changes in coatings due to sealing, but EIS measurements are usually more informative because they are conducted over a larger frequency range, which enables
changes in the porous layer to be distinguished from changes occurring in the
barrier layer.
Figure 29a shows a cross section of a pore and an explicit equivalent circuit
model superimposed on it (104). In this model, the EIS response of the barrier
layer is represented by the parallel combination of the barrier layer resistance
and capacitance. The pore walls are also represented by a parallel resistance and
capacitance, which is in series with the barrier layer R–C network. The pore
solution resistance and bulk solution resistances are represented as indicated.
Sealing does not involve any electrochemical reactions, so parameters representing faradaic processes are not required. In unsealed coatings, only the impedance
of the barrier layer is significant, and the model reduces to the R–C combination
associated with the barrier layer. As sealing progresses and the pores plug,
changes in the EIS response can be accounted for using a parallel R–C combination that accounts for the contributions of the pore walls and pore solution resistance (Fig. 29b). In some cases, porous layer capacitance is small compared to
the resistance, and its contribution to the EIS response is negligible. This results
in a further simplification of the equivalent circuit model (Fig. 29c). In this case,
the sealed anodized layer exhibits single-time-constant barrier behavior.
Figure 30 shows Bode magnitude and Bode phase angle plots for EIS measurements of a 5 µm thick porous coating sealed in hot water for various lengths
of time (104). These measurements were interrupted, meaning that the sample
was removed from the sealing bath and placed into cold water (20°C) for measurement and then returned to the sealing bath for further treatment. The unsealed
coating exhibits a single-time-constant response due to the capacitance of the
barrier layer. As sealing proceeds, a second time constant emerges at high frequencies owing to processes associated with surface film precipitation and pore
plugging. Figure 31 shows variation in the characteristic coating resistances and
Study of Surface Treatments
(a)
309
(b)
(c)
Figure 29 (a) Explicit equivalent circuit model for an unsealed porous anodized film
superimposed on a single pore cross section. (b) A simplified equivalent circuit model
representing the impedance response from the barrier and porous layer. In this case, RH
and CH represent the impedance of the porous layer. (c) The equivalent circuit model for
a fully sealed layer, which yields only a single time-constant barrier response. (From J.
L. Dawson, G. E. Thompson, M. B. H. Ahmadun. p. 255, ASTM STP 1188, ASTM,
Philadelphia, PA (1993).)
capacitances as a function of sealing time over the course of 5 minutes (104).
R s increases initially and then stabilizes owing to the formation of a precipitated
alumina layer on top of the porous coating. After an induction period, R H increases and C H decreases. The increase in resistance of the porous layer is due
to shrinking of the pore volume and filling with a more resistive gel material.
C H decreases owing to the same geometric change in pore volume and the displacement of water (ε ⫽ 80) with a lower dielectric constant hydrated alumina
get (ε → 10). The induction time observed in these experiments is believed to
represent the length of time required to exceed the solubility product for the porefilling gel. In many cases R B and C B do not change with sealing, because the
barrier layer does not thin or thicken, and compositional and structural changes
310
Chapter 8
(a)
(b)
Figure 30 Bode magnitude and phase angle plots of a 5 µm thick sulfuric acid anodized
film subject to sealing in hot water. Measurements were made on an interrupted basis in
cold water. Immersion times are (1) 0 s, (2) 30 s, (3) 60 s, (4) 90 s, (5) 120 s, (6) 180 s,
(7) 300 s, (From J. L. Dawson, G. E. Thompson, M. B. H. Ahmadun. p. 255. ASTM STP
1188. ASTM, Philadelphia, PA (1993).)
Study of Surface Treatments
311
(a)
(b)
(c)
(d)
(e)
Figure 31 Time-dependent changes in equivalent circuit model element values due to
interrupted sealing. (a) Solution resistance, R s , (b) porous layer resistance, R H , (c) porous
layer capacitance, C H , (d) barrier layer resistance, R b , (e) barrier layer capacitance, C b .
(From J. L. Dawson, G. E. Thompson, M. B. H. Ahmadun. p. 255, ASTM STP 1188,
ASTM, Philadelphia, PA (1993).)
do not occur that alter the electrical resistivity or dielectric properties of the layer.
In this example, R B decreases and C B increases, indicating barrier film thinning.
This leads to an overall decrease in the impedance of the film, which seems
contrary to the primary intent of sealing. This observation has been interpreted
as thinning due to attack by acid from the anodizing bath trapped in the pore
volume. It has also been suggested that these measurements are sensitive to the
gel formation process and that the known improvement in corrosion resistance
312
Chapter 8
by sealing is achieved when this gel crystallizes after the sample is removed from
the sealing bath.
D.
Breakdown of Anodic Films
Breakdown of anodic films is yet another phenomenon for which EIS is well
suited. Equivalent circuit analysis has been used to analyze EIS spectra from
corroding anodized surfaces. While changes in anodic films due to sealing are
detected at higher frequencies, pitting is detected at lower frequencies. Film
breakdown leads to substrate dissolution, and equivalent circuit models must be
amended to account for the faradaic processes associated with localized corrosion.
For the case of breakdown of sealed anodized surfaces, two closely related
equivalent circuit models exist (105,106). Figure 32a shows a representation of
a duplex surface film in which the outer layer has broken down to expose the
inner barrier layer. This type of model represents passivated pits, or defect sites
that may have formed some type of protective layer that differs from that on
other portions of the surface (107,108). The fractional area of the intact surface
is denoted by θ and the defective area by 1 ⫺ θ. The corresponding equivalent
circuit model is also shown in Fig. 32a. In this model, one leg of the circuit
accounts for the impedance response through the intact duplex film and is represented by two R–C networks arranged in series. The subscripts L1 and L2 refer
to the individual layers in the duplex film. Each parameter is normalized by the
surface coverage term θ. The second leg of the circuit accounts for the impedance
response of the defective area. R b and C b are the barrier layer resistance and
capacitance, and R Ω,por is the solution resistance in the defects. The resistance of
the bulk solution is denoted by R Ω . Each of these terms is normalized by the
sample defect area (1 ⫺ θ). Simulated Bode magnitude and phase angle plots
for this equivalent model are shown in Fig. 32b. In the high-frequency regions
denoted by 1, 2, and 3, the effect of decreasing surface coverage of the intact
film is evident. As the intact area falls, the magnitude of the capacitive impedance
decreases, and the resistive plateau associated with the outer layer resistance is
Figure 32 (a) The equivalent circuit model and physical model for a passive pit in a
duplex film. EC and IC refer to electronic conductor and ionic conductor, respectively,
in the physical model. (b) Simulated Bode plots of the equivalent circuit in (a), where
R Ω,por is equal to zero. Simulation parameters are R L2 ⫽ 10 5 Ω, C L2 ⫽ 10 ⫺9 F, C L1 ⫽ 5 ⫻
10 ⫺7 F, R sol ⫽ 20 Ω, and θ ⫽ (1) 1, (2) 0.95, (3) 0.5, R L1 /θ ⫽ (4) 10 8 Ω, (5) 10 7 Ω, (6)
10 6 Ω. (From (a) K. Juttner, W. J. Lorenz, W. Paatsch. Corrosion Sci. 29, 279 (1989).
(b) J. Hitzig, K. Juttner, W. J. Lorenz, W. Paatsch. J. Electrochem. Soc. 133, 887 (1986).)
Study of Surface Treatments
(a)
(b)
313
314
Chapter 8
resolved less distinctly. Eventually, the solution resistance is resolved at the highest frequencies. At low frequencies denoted by 4, 5, and 6, the effect of decreasing
the barrier layer resistance for a fixed surface coverage θ is shown. As R b decreases from 10 8 to 10 6 ohms, a low-frequency plateau becomes evident, and the
DC limit of the impedance decreases in direct relation to R b . In this example,
R Ω,por is assumed to be zero.
Actively pitting surfaces are represented by analogous physical and equivalent circuit models shown in Fig. 33a. The main difference in these models is
that the substrate is exposed at the base of the pits and active dissolution is occurring. The area-specific capacitance and resistance take on values consistent
with metal dissolution, e.g., tens of µF/cm 2 for the double layer capacitance, C dl ,
and 10 2 to 10 3 ohm ⋅ cm 2 for faradaic resistance Z SR . Simulated Bode magnitude
and phase angle plots for increasing defect area, and for the case where R Ω,por is
zero, are shown in Fig. 33b. As the defect area increases, the impedance in the
high-frequency capacitive region decreases, and the resistive plateau associated
with the porous layer resistance is less clearly resolved. Although Z SR is taken
to be 10 5 ohms in this example, the DC limit associated with this impedance
ranges from about 5 ⫻ 10 7 ohms to 10 6 ohms due to defect area normalization.
Overall as the defect area increases, the DC limit decreases, making this parameter useful for the evaluation of pitting damage.
The essential characteristics of the EIS response from simulated Bode plots
can be detected in spectra collected from real anodized samples (109). Figure 34
shows Bode plots from chromic acid anodized and sulfuric acid anodized surfaces
exposed to aerated 0.5 M NaCl for various lengths of time. As predicted by the
simulated spectra, the main changes in the Bode magnitude plot due to pitting
occur at frequencies below about 1 Hz. The effects of pitting on the Bode phase
angle plot are detectable as frequencies as high as 10 4 Hz for unsealed sulfuric
acid anodized surfaces.
To track the progression of corrosion damage accumulation on anodized
surfaces it is often desirable to use more simplified analysis approaches, especially when many replicate samples are to be examined. Since the effects of
sealing are confined to the highest measured frequencies and those due to corro-
Figure 33 (a) The equivalent circuit model and physical model for an active pit in a
duplex film. EC and IC refer to electronic conductor and ionic conductor, respectively,
in the physical model. (b) Simulated Bode plots of the equivalent circuit in (a) where
R Ω.por is equal to zero. Simulation parameters are R L2 ⫽ 10 5 Ω, C L2 ⫽ 10 ⫺9 F, R L1 ⫽ 10 25
Ω, C L1 ⫽ 5 ⫻ 10 ⫺7 F Z SR ⫽ 10 5 Ω, C dl ⫽ 3 ⫻ 10 ⫺5 F, R sol ⫽ 20 Ω, and θ ⫽ (1) 1, (2)
0.999, (3) 0.99, (4) 0.92. (From (a) K. Juttner, W. J. Lorenz, W. Paatsch. Corrosion Sci.
29, 279 (1989). (b) J. Hitzig, K. Juttner, W. J. Lorenz, W. Paatsch. J. Electrochem. Soc.
133, 887 (1986).)
Study of Surface Treatments
(a)
(b)
315
316
Chapter 8
Figure 34 Bode plots of EIS data determined in aerated 0.5 M NaCl solution for sealed
and unsealed sulfuric acid anodized Al alloy 2024. (From F. Mansfeld, M. W. Kendig.
Corrosion 41, 490 (1985).)
Study of Surface Treatments
317
sion at low frequencies, it is possible to use the DC limit in the impedance spectra
to assess corrosion damage.
There are indications that the magnitude of the DC limit measured in an
impedance experiment correlates with the performance of anodized surfaces in
cabinet exposure tests. On this basis, it is possible to define a damage function,
D, as the logarithm of the ratio of the impedance, taken at 0.1 Hz at zero exposure
time, to that at some exposure time, t (109).
D ⫽ log
冷
Z0
Zt
(12)
0.1Hz
At this frequency, the magnitude of the impedance will decrease with increasing
exposure time, so the damage function should increase with time. In principle,
this measurement could be made using a single-frequency admittance-type approach, but collection of the spectrum at higher frequencies than 0.1 Hz can be
made with little additional measurement time penalty.
VI. ORGANIC COATINGS
A. Overview of Organic Coatings
There is a wide range of organic coatings and adhesives that are applied to metals
for corrosion protection. Organic coatings provide barrier protection by isolating
the metal substrate from the environment, and they do not support electron transfer well because the are very resistive. As a result, electrochemical activity is all
but impossible on undegraded organic coatings. Some coatings contain active
inhibitors, like sparingly soluble chromate pigments. Chromate leached into an
attacking electrolyte is transported to coating defects, where it acts to stifle corrosion. Such coatings are said to be actively protecting or self-healing.
Many electrochemical methods are of limited utility for studying the processes leading to organic coating degradation. In the early stages of coating breakdown, the interfacial impedance is exceedingly large and cannot be measured by
a potentiostat. However, as the coating degradation process proceeds, the interfacial impedance falls to levels that can be effectively measured by EIS. For this
reason, EIS has been particularly effective for quantitatively evaluating the progress of organic coating degradation and metallic corrosion that occurs as a result.
It is convenient to consider the corrosion of polymer coated metals as a
process that consists of several distinct stages:
Defect formation
Uptake and transport of water through the coating
318
Chapter 8
Coating–substrate decohesion and formation of a condensed electrolyte at
the interface
Substrate corrosion
Defects may exist in the coating as a result of imperfections arising at the time
of coating application. These defects may include entrained dust, dirt, moisture,
oil or grease, lack of surface coverage, or lack of adhesion on the substrate.
Mechanical defects may occur owing to abrasion or impact. Chemical defects
may arise by exposure to acids or solvents. Defects may also arise from elevated
temperature exposure or exposure to light (UV damage). The defect structure in
an organic coating system is important because it determines the course of subsequent corrosion damage. The second stage in the degradation process is water
uptake and transport. Water uptake is aided by a molecular level defect specific
to organic coatings commonly known as pore space. Pore space generally refers
to open space between polymer chains or molecules in the polymer film. In many
coatings, this pore space allows the uptake and transport of water and ions that
leads to coating degradation and corrosion. Pore space is a natural consequence
of coating curing and is usually unavoidable, though some polymer coatings have
very low water permeabilities. In aggressive environments, electrolyte may penetrate through defects and result in the loss of adhesion. Loss of adhesion may
spread laterally from a defect site. Alternatively, loss of adhesion may occur
under mechanically intact coatings when electrolyte condenses at the metal-film
interface to form a blister. Once an aggressive electrolyte has made contact with
the metallic substrate, corrosion is likely.
B.
Measurement Methods
1. Direct Current (DC) Electrochemical Methods
DC electrochemical methods are not well suited for characterizing the breakdown
of polymer coated metals for several reasons. First, coating breakdown is defect
mediated; the results from measurement to measurement are irreproducible. Measurements of a surface-averaged response are much more suitable for this reason
(e.g., EIS or exposure test methods). Second, organic coatings are electrically
resistive, and high potential drops develop across organic films when DC voltages
are applied to the interface. This reduces the driving force for electrochemical
reactions at the coating–metal interface. Often the extent of this potential drop
is uncharacterized, which clouds the interpretation of the resulting data. Third,
as with all large signal DC measurements, application of a large polarization
drives the electrode far from the steady state and from the conditions under which
corrosion naturally occurs. Additionally, application of high potentials may also
lead to irreversible changes in the polymer structure, especially if dielectric breakdown is induced.
Study of Surface Treatments
319
2. EIS
EIS is considerably more effective for the study of organic coating breakdown.
It is sensitive to each of the four main stages of the coating breakdown process,
and it can also be used in situ. Degradation of organic coatings occurs over the
span of days and months (or longer) and is slow compared to the typical impedance
spectrum collection times. As a result, EIS measurements can be used to measure
changes in organic coating degradation in real time. Typically, the overall process
of coating degradation and corrosion is analyzed using an equivalent circuit modeling approach, but first it is important to address instrument limitations.
Instrument limitations must be considered in the measurement of organic
coatings because their resistivities are large, 10 12 Ω ⋅ cm or more. The input
resistance of common potentiostats is usually not more than 10 11 to 10 12 ohms,
and if the cell resistance approaches or exceeds the input resistance of the potentiostat, a significant fraction of the applied signal will pass across the input impedance and not the cell impedance. In these cases the collected data do not reflect
just the impedance of the electrochemical interface, which is a fundamental assumption in almost all data analyses. In fact, the potentiostat input impedance
in parallel with the stray capacitance associated with the potentiostat measuring
leads will be obtained.
Measurement leads used to connect to the electrochemical cell contribute
measured capacitance. Lead capacitance between the potentiostat and the electrometer is normally accounted for in the potentiostat calibration, but stray capacitance associated with the leads and connections to the cell may not. Moreover,
this capacitance may change with time: the leads age, and the connections become
oxidized. Uncompensated capacitance may also exist within the measurement
circuitry of the potentiostat itself. These uncompensated capacitances impose a
practical lower limit on the coating capacitance that can be measured.
A convenient check for the input impedance and stray capacitance can be
obtained by making an impedance measurement with the leads not connected to
anything. The resulting data can be analyzed to estimate the input impedance
and the stray capacitance using a parallel R–C network or by graphical analysis
of the Bode magnitude plot. The Bode magnitude plot is especially useful because
it graphically illustrates the measurement limitations of an EIS system in the
lower frequency regions. Figure 35 is a Bode magnitude plot of just such a measurement made with commercial equipment. Analysis of the data using an equivalent circuit model consisting of a parallel combination of the input resistance and
the stray capacitance indicates an input resistance of 2 ⫻ 10 9 ohms and a stray
capacitance of 2 ⫻ 10 ⫺10 F.
Measurement of calibrated capacitors can also be used to determine instrument limitations. Figure 36 shows a plot of the variation in measured capacitance
versus known capacitance for a commercial impedance analyzer system (110).
320
Chapter 8
Figure 35 Bode magnitude plot for a “leads unconnected” measurement with a commercial electrochemical impedance system. Analysis of the data enable an estimate of the
potentiostat input impedance (2 ⫻ 10 9 Ω) and the stray capacitance (2 ⫻ 10 ⫺10 F).
The empirically derived error from all sources in the measured capacitance is
greater than 10% for capacitances less than about 1 nF. Therefore acceptable
determinations of coating capacitance can only be made for capacitances greater
than about 1 nF. One simple strategy for increasing the measured coating capacitance above a measurement sensitivity threshold is to increase the electrode area.
Using estimates for the relative permittivity and coating thickness, it is possible
Figure 36 Error in the observed capacitance as a function of the value of the known
capacitance. This illustrates the limit of an impedance measurement system. (From M.
Kendig, J. Scully. Corrosion 46, 23 (1990).)
Study of Surface Treatments
321
to estimate the electrode area required to bring the coating capacitance into a
measurable range. If the expression for coating capacitance is
C⫽
εε 0 A
t
(13)
and the relative permittivity for organic coatings ranges from 3 to 4, to obtain
nanofarad sensitivity the electrode area must be
A ⬎ 10 ⫺9
冢 冣
t
⬎ 4000t
εε o
(14)
where t is the coating thickness in cm, ε is the relative permittivity of the coating,
and ε o is the permittivity constant. For a 10 µm thick coating, an electrode area
of 4 cm 2 is sufficient to exceed sensitivity constraints. However, for a 500 µm
coating (20 mils), an electrode area of 200 cm 2 is necessary.
C. Coating Degradation
1. Defects in Coatings
The range of unintentional defects that can be present in polymer coatings was
listed earlier. However, polymer coatings often contain intentionally added solid
particulate in the form of fillers, pigments, and extenders. These solid particles
may constitute defects in some cases. An example of the inorganic particulate
distribution in an automotive paint is shown in Fig. 37. This figure shows a mixture of intentionally added metal flake and unwanted dirt and dust. The extent
to which these particulates constitute breakdown-initiating defects can be determined from EIS measurements conducted shortly after immersion in an aggressive electrolyte. The most protective coatings exhibit purely capacitive behavior
and retain that behavior for long periods of time during exposure to near neutral
molar chloride solutions. The presence of serious defects can be inferred if a
resistive component detected at the lowest measured frequencies is detected immediately, or shortly after exposure to an aggressive electrolyte.
EIS can also detect defects arising from lack of adhesion at adhesively
bonded surfaces (111). The presence of such defects produces pronounced
changes in the character of the data presented either in complex plane plots or
in Bode plots. Figure 38 illustrates the measurement configuration and provides
examples of EIS data for defective and defect-free samples. Studies have shown
that the presence of defects is readily revealed and that the geometry of the defects
and their spatial extent can be inferred from a detailed analysis of EIS spectra.
322
Chapter 8
Figure 37 Scanning electron micrograph of metal flake paint for trucks showing entrained dirt and intentionally added metal flakes. The particulate material in this micrograph averages several micrometers in diameter.
2. Ingress of Electrolyte
Electrolytes will penetrate through defects to the coating–metal interface. They
will also penetrate through pore space in many types of coatings. Water residing
in the pore space changes the effective dielectric constant of the film in a way that
can be detected by measurement of film capacitance (112,113). The capacitance
method for determining water uptakes has considerable advantage over traditional
gravimetric methods. It is also possible to determine water diffusivity, equilibrium constant, and dielectric constant. Capacitance measurements are particularly
sensitive to water uptake because the dielectric constant for water (ε ⫽ 80) is at
least four times greater than that of a typical organic coating. For low volume
fractions of water in polymer, the water volume fraction is given by the Brasher–
Kingsbury equation (114).
φ⫽
log (C t /C o)
log 80
(15)
In this expression, ϕ is the volume fraction of water, C t is the capacitance after
some exposure time t, C o is the capacitance of a “dry” film, which is usually
measured at the outset of an exposure experiment. The relative permittivity of
water at 25°C is reflected in the denominator of the expression. This expression
applies only when water is homgeneously dispersed in the polymer, no water–
Study of Surface Treatments
323
(a)
(b)
Figure 38 (a) Schematic illustration of moisture ingress into an edge-exposed defect.
(b) Theoretical impedance response of a defect-containing laminate specimen. (From G.
R. T. Schueller, S. R. Taylor. ASTM STP1188. p. 328, ASTM, Philadelphia, PA (1993).)
polymer chemical interactions occur, the absolute water content in the polymer is
low, and there is negligible swelling of the polymer due to water uptake. Strictly
speaking, this expression is only valid for binary water–polymer systems. However, it has been applied to the characterization of water uptake in multicomponent paints with apparent success (115,116).
Figure 39 is an example of water uptake for polyester coated steel immersed
in a NaCl solution. In this example one coating was subject to 100 h of UV
exposure prior to immersion (112). Both coatings absorb water at fast rates during
the first 200 minutes of immersion, but the UV-exposed sample accomodates
324
Chapter 8
Figure 39 Water uptake trend for a polyester coated galvanized steel immersed in sodium chloride solution, before and after about 100 h of UV irradiation. (From P. L. Bonora,
F. Deflorian, L. Fedrizzi. Electrochim. Acta 41, 1073 (1996).)
more than twice as much water at steady state owing to the UV-induced damage
to the polymer. The ability to detect water uptake is significant because this is
often a prelude to corrosion (112).
3. Loss of Adhesion and Corrosion of the Substrate
With increased exposure time to an aggressive environment, ionic conduction
pathways through the coating short the coating capacitance, and a resistive impedance develops. Once electrolyte contacts bare metal, faradaic reactions occur and
corrosion is underway. Several equivalent circuit models are commonly used to
analyze EIS data from degraded organic coatings. Examples of common equivalent circuits are shown in Fig. 40 (110,117). In these models, the impedance
response of intact areas of the coating is represented by a capacitor, C c . There
is a coating resistance, but it is usually too large to measure. The impedance
response at defects varies from sample to sample but falls into three general
categories, which distinguish the models in Fig. 40. In all models, R po represents
the pore resistance, which is the ionic resistance to current flow between the bulk
electrolyte and the metal–film interface. This pathway exists through microscopic
pores at defects, and through the pore space containing water and ions in the
polymer film. The further distinction between models I and II depends on the
impedance behavior at low frequencies. In the case where the spectrum achieves
a DC limit (equivalent to R Ω ⫹ R po ⫹ R t), localized corrosion occurs under charge
transfer control, and model I applies. In cases where the Bode plots indicate a
ω ⫺1/2 or ω ⫺1/4 dependence, localized corrosion is under diffusion control and
model II applies.
Study of Surface Treatments
325
Figure 40 Equivalent circuit models for analyzing impedance data from degraded polymer coated metals. (a) General model. (b) Model I: for coatings with defects corroding
under activation control. (c) Model II: for coatings with defects corroding under diffusion
control. (From F. Mansfeld, M. W. Kendig, S. Tsai. Corrosion 38, 478 (1982) and M.
Kendig, J. Scully. Corrosion 46, 22 (1990).)
Figure 41 shows an equivalent circuit model and resulting simulated EIS
data in Bode plot format for a failed organic coating (110). At high frequencies,
the response is due to the capacitance associated with the coating, C c , and a
solution resistance is usually not observed. At intermediate frequencies, a resistive plateau is observed in the Bode magnitude plot, which is equal to the sum
of the solution resistance and the pore resistance, R po ⫹ R Ω . At lower frequencies,
a second capacitive region is found corresponding to the capacitance associated
with corrosion at defects, C d . At the lowest frequencies, a DC limit is observed,
and the magnitude of the resistance is equal to R t ⫹ R po ⫹ R Ω . The phase angle
information indicates two distinct time constants in this example, although separation as clear as this is not normally the case in experimental situations.
As organic coatings degrade, regular changes in the EIS data occur that
signal the initiation and propagation of coating breakdown and substrate corrosion. Figure 42 shows Bode magnitude and phase angle plots for an epoxy resin–
based coating on phosphated steel substrates exposed to 0.5 M NaCl solution
(118). Initially, the coating exhibits quasi-ideal capacitive behavior associated
with an intact coating. However, with increasing exposure time, a two-time constant response emerges indicating coating breakdown as shown in Fig. 41. With
326
Chapter 8
Figure 41 Example of simulated EIS data from the equivalent circuit model shown
with circuit element values indicated in the plot. (From M. Kendig, J. Scully. Corrosion
46, 22 (1990).)
increasing exposure time, the DC limit falls as the extent of corrosion progresses.
These types of regular changes in the EIS data with increasing exposure time
suggest the possibility of using EIS quantitatively to track the progress of corroded surface area.
a. The Breakpoint Frequency Method. Experimental observations of
polymer coated metals exposed to aggressive solutions for increasing lengths of
time typically show decreases in R po and R p and increases in C dl . These regular
Study of Surface Treatments
327
Figure 42 Bode plots of an epoxy-resin-based coating on phosphated steel exposed to
0.5 M NaCl solution. (a) Quasi-ideal coating. (b) Sample exposed for 1 hour. (c) Sample
exposed for 48 h. (From J. Titz, G. H. Wagner, H. Spahn, M. Ebert, K. Juttner, W. J.
Lorenz. Corrosion 46, 221 (1990).)
changes are consistent with an increase in the delaminated area associated with
underfilm corrosion. Although the charge transfer resistance and double layer
capacitance values scale with defect area, the values for these elements must be
extracted from the low-frequency part of the EIS spectrum. In many experimental
situations, measurements at low frequency are complicated by signal instability,
mixed reaction control, or changes in the specific interfacial resistance and capacitance associated with the accumulation of corrosion products (119). To circumvent these difficulties, the breakpoint frequency method was developed to make
estimates of the delaminated area from high-frequency EIS data, which are not
affected by these factors (119–122). This method was based on analysis of the
value of the frequency (the breakpoint) separating coating capacitance–dominated response (higher frequencies) from resistive response due to the sum of
the pore resistance and solution resistance (lower frequencies). The location of
328
Chapter 8
Figure 43 Equivalent circuit model for a degraded polymer coating on a metal substrate
and the corresponding EIS data presented in Bode plot format. The breakpoint frequency
is indicated as f b in the plot. (From C. H. Tsai, F. Mansfeld. Corrosion 49, 726 (1993).)
the breakpoint frequency in Bode plots is shown in Fig. 43. An equivalent circuit
model with labeled circuit parameters and the corresponding simulated EIS data
are also indicated.
The breakpoint frequency analysis assumes that the pore resistance R po , the
polarization resistance of the defect, R p , and the double layer capacitance in the
defects, C dl , scale with the area of substrate–coating delamination, A d by
R po ⫽
R 0po
Ad
(16)
Study of Surface Treatments
Rp ⫽
329
R 0p
Ad
(17)
C dl ⫽ C 0dl A d
(18)
In these expressions, R ⫽ ρt (ohm-cm ), and R (ohm-cm ) and C (µF/cm 2)
are characteristic (area-specific) values that do not change with time; t is coating
thickness, and ρ is coating resistivity, which must also be time-independent. Furthermore, the coating capacitance, C c , is given by
o
po
C c ⫽ C 0c A
2
o
p
2
o
dl
(19)
where A is the area of the intact coating. At the breakpoint frequency the magnitude of the impedance from the resistive plateau is equal to the magnitude of the
impedance from the coating capacitance,
R po ⫹ R s ⫽
1
ωC c
(20)
Assuming that R po ⬎⬎ R s , which is usually the case in chloride solutions like
seawater,
R po ⫽
1
2πf b C C
(21)
and upon rearranging,
fb ⫽
1
2πR po C C
(22)
If it is assumed that
R po ⫽
ρt
Ad
(23)
CC ⫽
εε o (A ⫺ A d )
t
(24)
and
and that total electrode area, A, is much greater than the delaminated area, A d
(e.g., A d ⬍ 1%), the breakpoint frequency is
fb ⫽
A
1
⋅ d
2πεε o ρ A
(25)
The practical consequence of this analysis is that the breakpoint frequency is
directly proportional to the delaminated area, and can be monitored with a fast
330
Chapter 8
high-frequency EIS measurement. It must be stressed that this analysis assumes
that ρ and ε are independent of thickness and do not change with exposure time.
It must also be recognized that this analysis is subject to the assumption that the
delaminated area is a small fraction of the total area under analysis.
Figure 44 shows the variation in f b for different defect area fractions. The
value of f b ranges from 10 3 to 10 5 Hz for defect area percentages of 0.001 to
0.05%, respectively (119). The ability to measure small defect area fractions is
compromised by incomplete resolution of the resistive plateau, which occurs
when R po is large and C dl is small; f b measurements are also limited at high frequencies by the use of potentiostatic control. This normally imposes an upper
limit of 10 5 Hz. A further limitation occurs for thick coatings whose capacitive
response shifts the breakpoint to low frequencies where it is difficult to identify
confidently and may fall in a range where the EIS data are affected by electrode
Figure 44 Effect of defect area percentage on impedance magnitude behavior of a
coated steel. Total cell area assumed is 10 cm 2. (From H. P. Hack, J. R. Scully. J. Electrochem. Soc. 138, 33 (1991).)
Study of Surface Treatments
331
instability. To avoid these complications, other parameters such as the low-frequency breakpoint (119) and the phase angle minimum (122) have been investigated for determining the delaminated area.
The theoretical underpinning of the breakpoint frequency method has also
been challenged (123,124). This stems from the definition of R po and the resistance of free-standing polymer films to ionic conduction. The somewhat unsatisfying definition of R po is that it represents the ionic resitance of the polymer film,
but only in areas where delamination has occurred. In other locations on the
surface, R po is essentially infinite. The ionic resistance of free-standing films can
be measured directly and is found to be large, about 10 7 ohm ⋅ cm 2, and independent of exposure time in aggressive solutions. If R po does not vary with exposure
time, and the coating capacitance is assumed not to vary with time, then no variation in f b should be possible according to Eq. (22). Therefore it has been argued
that R po really represents the resistance to ionic current flow within growing defects. Since this resistance is a function of several variables including local chemistry variation, defect geometry, and accumulation of corrosion product, the direct
relationship between f b and A d indicated by Eq. (25) is in doubt.
Despite inherent assumptions and objections to the breakpoint frequency
method, experiments show that there is general agreement between f b and delaminated area (119). Figure 45 shows the relationship between f b and the estimated
delamination area for opaque and transparent epoxy coatings on steel. The figure
supports the positive relationship between f b and delaminated area indicated by
Eq. (25), but the scatter in the relationship is relatively large, suggesting that
sample-to-sample variation and frequency dispersion in the EIS data may affect
the determination of f b for any specific amount of delamination.
b. Life Prediction. From a practical perspective, EIS characterization of
polymer coated metal degradation may be most useful for rapidly assessing the
protectiveness of a coating and making a service life prediction. EIS is sensitive
to damage accumulation in its earliest stages in controlled laboratory testing.
These tests can be carried out easily and rapidly, and it is easy to imagine EISbased methods being used to make many individual measurements in a short
period of time. However, it is not well established if the result of such tests can
be used to predict service life. For this reason, there has been great interest in
determining if short-term EIS data are related to long-term exposure performance.
An example of the use of EIS measurements to make long-term corrosion
predictions for polymer coated metals is shown in Fig. 46 (110). In this plot, the
ASTM D610 and D714 visual rankings of corrosion damage after 550 days of
exposure in simulated seawater are plotted against a protection index, Φ( f ), determined after only 10 days of exposure. The damage protection index is determined from the breakpoint frequency, f b , as
φ( f ) ⫽ 10 ⫺2 log f b
(26)
332
Chapter 8
Figure 45 Relationship between the breakpoint frequency and the estimated active area
for opaque and transparent epoxy coatings on steel. (From H. P. Hack, J. R. Scully. J.
Electrochem. Soc. 138, 33 (1991).)
On the vertical axis, high ASTM rating numbers correspond to lower amounts
of visual corrosion damage, with 10 indicating no visible damage. Φ( f ) does not
discriminate well among coatings with the best performance, but it does separate
coatings with inferior performance (ASTM rating ⬍7) after 550 days of exposure.
This example illustrates the possibility of making gross distinctions among coating performance for long-term exposures.
It is also desirable to have predictive tests that are rapid and are grounded
by benchmarking with older exposure-based tests. Rapid validated tests are necessary for quality control and lot release inspection. Often the results of such tests
are needed within hours. Cabinet exposure testing that requires days or weeks is
obviously impractical.
To determine if short-term electrochemical test results were related to
longer term salt spray exposure results, a two-part test was conducted, and results
were correlated to results from salt spray testing. The first part of the test involved
measurement of impedance immediately upon exposure and after 24 hours of
Study of Surface Treatments
333
Figure 46 Correlation between the protection index, Φ( f ), determined after 10 days
exposure to 0.5 M NaCl and the ASTM D 610 visual rating determined after 550 days
exposure. (From M. Kendig, J. Scully. Corrosion 46, 22 (1990).)
exposure to aerated 0.5 M NaCl solution. Coating capacitance was extracted from
the data for estimation of water uptake using the Brasher–Kingsbury equation
[Eq. (15)]. The corrosion resistance of the coated metal at 24 hours was also
determined. Cathodic disbondment comprised the second evaluation. In this test,
intersecting scribes were made through the coating to expose bare metal. The
sample was then exposed to 0.5 M NaCl solution and then cathodically polarized
at ⫺1.05V sce for 24 hours. After exposure, the sample was removed from solution,
and loose coating was removed from the surface. The area exposed was measured
and used in the subsequent correlation. Other identically coated samples were
subject to salt spray exposure until failure. Several different failure criteria were
invoked. The failure time was taken as either
1. The time required for paint pullback from a scribe to exceed 3 mm
2. The time required for the ASTM D610 visual rating to drop below 9
3. The average time for criteria 1 and 2
Analysis showed that time to failure (TTF) did not correlate well with the
results of the EIS or the cathodic disbondment individually. However, when the
334
Chapter 8
Figure 47 Relation between observed salt spray TTF and TTF predicted from the regression model in Eq. (15). (From M. Kendig, S. Jeanjaquet, R. Brown, F. Thomas. J.
Coat. Tech. 68, 39 (1996).)
results of both tests were included in the analysis, a good correlation was obtained. The empirical relationship between TTF (according to criterion 3) and
the electrochemical results was found to be
TTF ⫽ ⫺804.5 ⫽ 109.4 log R cor ⫺ 118.7 log
冢冣
dx
dt
(27)
In this expression, TTF is measured in hours, the corrosion resistance of the
painted metal is taken as the charge transfer resistance of the actively corroding
metal surface in ohm ⋅ cm 2, and dx/dt is the delaminated area from cathodic
disbondment measured in mm 2. Figure 47 shows the relationship between the
observed and the predicted TTF based on Eq. (27). While the data are somewhat
scattered, a strong positive correlation between prediction and observation is indicated, supporting the idea that short-term electrochemical characterization is relatable to longer term performance in cabinet exposure testing. This kind of
benchmarking information is crucial for the introduction and regular use of electrochemical methods for routine industrial testing.
VII. NEW TECHNIQUES
A.
Scanning Reference Electrode Technique (SRET)
On a freely corroding electrode surface, ionic currents flow in solution between
local anodic and cathodic sites. A spatially varying potential field is associated
with ionic current flow so that the potential field lines and lines of current flux
Study of Surface Treatments
335
Figure 48 The potential distribution associated with a Pt cathode on a Zn anode in 0.05
M HCl, showing the measured normal variation in the potential field. (From H. S. Isaacs.
In: Localized Corrosion. p. 158, NACE, Houston, TX (1974).)
always intersect normally, as is depicted in the simple cross sectional schematic
of small anode surrounded by a larger cathode (Fig. 48) (125). The relationship
between the current density flowing through solution and potential field is given
by
(28)
1 ∂V
i⫽ ⋅
ρ ∂l
where i is the current density in solution (A/cm 2), ρ is the solution resistivity (Ω
⋅ cm), and ∂V/∂l is the gradient of the voltage field in the direction of current
flow (V/cm). The largest gradients of the voltage field exist near the electrode
surface. By scanning a reference electrode near the corroding surface and measuring its potential with respect to a reference electrode positioned far away (centimeters), it is possible to measure the near surface potential variation in either a
one-dimensional line scan mode or a two-dimensional mapping mode.
The experimental apparatus normally consists of a drawn glass capillary
microreference electrode that minimizes screening between anodic and cathodic
sites, an apparatus for rastering the microreference electrode across the corroding
electrode surface in a systematic manner, high-impedance voltmeters, and the
necessary data recording devices. A representative schematic of the apparatus is
shown in Fig. 49 (125). The sensitivity and resolution of the measurement depend
on the diameter of the tip of the microreference electrode, the standoff distance
336
Chapter 8
Figure 49 Schematic illustration of the scanning reference electrode probe apparatus
used by Isaacs. (From H. S. Isaacs. In: Localized Corrosion. p. 158, NACE, Houston, TX,
1974.)
between the microreference and the surface, the scan rate, and the solution resistivity. In measurements of weldments in carbon steels in line scan mode using
a 75 µm reference electrode tip scanned at 50 mm/min in a synthetic seawater,
millivolt potential resolution and millimeter spatial resolution can be achieved
(126). Potential field maps collected on pitting 304 stainless steel using a 250
µm diameter microreference tip and a scan rate of 75 mm/min in 0.4 M FeCl 3
solution adjusted to a pH of 0.9 yielded 0.3 mV resolution and millimeter spatial
resolution (127)
It is also possible to scan a pair of reference or pseudoreference electrodes
separated by a small, fixed distance of a few micrometers to measure the local
potential field gradient, ∂v/∂l, and estimate the local current density from Eq.
(48) (128). This is a slightly more sophisticated measurement because the anodic
or cathodic character of local sites can be determined from the polarity of the
current, and the intensity of the attack can be estimated from the current density
flowing in solution. The difficulty with this arrangement is that the potential difference between two closely spaced reference electrodes in a conductive solution
is usually less than 1 microvolt. The stability of reference electrodes is on the
order of microvolts, and thus it often exceeds the magnitude of the potential
difference signal. This imposes a fundamental limitation on the usefulness of this
technique.
Study of Surface Treatments
337
B. Scanning Vibrating Electrode Techniques (SVET)
To overcome the limitations associated with the poor signal-to-noise ratio in the
paired reference electrode measurement scheme, the scanning vibrating electrode
technique was developed. In this technique, a single pseudoreference electrode
is subject to a small periodic mechanical perturbation that induces an electrical
oscillation of known amplitude. The peak-to-peak AC voltage measured by the
tip is equal in magnitude to the potential gradient in solution over the distance
of travel of the oscillation amplitude. The current density in the direction of the
electrode oscillation can be calculated from Eq. (28). To eliminate noise interference, the signal from the oscillating tip is extracted using a lock-in amplifier,
which is tuned to measure the signal only at the oscillation frequency of the
vibrating tip. It is also possible to superimpose two orthogonal mechanical oscillations on the pseudoreference electrode. If the imposed oscillations are of different frequencies, each signal can be separately measured using lock-in detection,
and the directional components of current flow can be resolved. The vibrating
tip can be scanned across the corroding surface to identify anode and cathode
locations, the current density, and the current density vectors in solution. This
enables direct measurement of the progress and intensity of local corrosion processes on a site-by-site basis.
An example of the use of SVET in studies of Ce corrosion inhibitors is
found in the work of Aldykewicz et al. (129). Figure 50 shows a representative
schematic illustration of the apparatus used in these experiments. The vibrating
probe consisted of a 5 µm diameter Pt–Ir wire tipped with platinum black at the
sensing end of the wire. The diameter of the tip at the sensing end of the wire
was about 20 µm. The wire was attached to two piezo crystals that were capable
of inducing mutually orthogonal oscillations in the wire at different frequencies.
Lock-in detection of the AC voltage signal from the tip was capable of resolving
current densities normal and horizontal to the sample surface, although this was
not exploited in this particular study. The vibrating tip was rastered over the
surface at a standoff distance of about 150 µm using a programmed stepper motor
with a 2.5 µm step size. Areas with dimensions of about 1000 ⫻ 1500 µm were
scanned in several minutes. In a 12 mM NaCl solution with a solution resistivity
of 830 Ω ⋅ cm, a current density resolution of 2 µA/cm 2 was possible. Spatial
resolution in these experiments is difficult to specify, as it depends on the intensity
and spacing of active areas, which are not easily controlled in real materials.
However, areas on corroding Al alloy surfaces that were sufficiently active and
separated appeared to be detectable with approximately 10 µm spatial resolution.
Assuming that the current density in solution due to pit dissolution is uniform
across an imaginary hemispherical surface around the pit, the pit current can be
determined from the peak current density in solution, which is measured over
338
Chapter 8
Figure 50 Schematic illustration of the 2D scanning vibrating probe system used by
Aldykewicz, et al. (From A. J. Aldykewicz, H. S. Isaacs, A. J. Davenport. J. Electrochem.
Soc. 142, 3342 (1995).)
Study of Surface Treatments
339
the center of the pit at a standoff distance equal to the radius of the hemisphere,
i pit ⫽ (2πh 2)j measured
(29)
In this expression, i pit is the pit current density, j measured is the measured current
density in solution due to the vibrating probe, and h is the standoff distance, which
is equal to the radius of the hemisphere of uniform current density surrounding the
pit. A pit current of 3 nA is possible given a current density measurement sensitivity of 2 µA/cm 2.
In addition to the constraints mentioned above, active areas must be sufficiently long-lived and nearly fixed in position for detection by SVET. This is
not normally a problem in the study of coatings where the location of active areas
are often fixed by existing or emergent coating defects. However, some pitting
phenomena, especially metastable pitting, may not be detected well by this technique.
Aldykewicz et al. used SVET to study the inhibiting effects of CeCl 3 on
localized corrosion of 2024-T3 (Al-4.4Cu-1.5Mg-0.6Mn). Current density maps
were made for samples exposed to 12 mM NaCl and 4 mM CeCl 3 solutions over
several hours. Figure 51 shows current density maps from this study. Discrete
and intense sites of anodic activity were detected, but intense cathodes were not.
This suggests that anodic activity is very focussed, while the cathodic reaction
is supported at a lower rate over a much larger surface area. At short times, the
anodic activity is more intense in the presence of CeCl 3 and NaCl, but after 2
hours of exposure, the number and intensity of sites is vastly diminished in the
Ce-bearing solution, which was taken as an indication of its ability to inhibit
corrosion.
Locally intense anodes and cathodes can be observed in current density
maps made in the vicinity of scribes in galvanized steel surfaces in chloride solutions (130). Figure 52 shows a time series of current density maps in the scribe
regions of a hot dip galvanized surface during exposure to aerated 0.01 M NaCl
solution. Cathodic regions corresponding to exposed steel in the scribe and anodic
regions are due to local Zn dissolution. Galvanic coupling, which is the origin
of sacrificial protection in this system, is highly localized, and interacting anodes
and cathodes are separated by only tens of micrometers.
C. Local Electrochemical Impedance Spectroscopy (LEIS)
LEIS techniques spatially resolve changes in impedance (or admittance) at a single frequency, or collect impedance spectra over a range of frequencies at a single
location (131,132) Traditional EIS measurements contain contributions from corroding and noncorroding regions of the surface, but LEIS permits interrogation
of locally corroding sites directly (133). In these measurements, a two-element
340
Chapter 8
Figure 51 Measured current density flowing normal to the electrode surface at a height
of 150 µm above 2024-T3 in 12 mM NaCl after immersion for (a) 0 and (b) 2 h. (From
A. J. Aldykewicz, H. S. Isaacs, A. J. Davenport. J. Electrochem. Soc. 142, 3342 (1995).)
Figure 52 Normal current density distribution over a scribed electrogalvanized steel
sample in 0.01 M NaCl as a function of time: (a) 15 min, (b) 1 h, (c) 2 h. (From H. S.
Isaacs, A. J. Aldykewicz, D. Thierry, T. C. Simpson. Corrosion 52, 163 (1996).)
Study of Surface Treatments
341
342
Chapter 8
Figure 53 Schematic illustration of the pseudoreference electrode pair used to make
LEIS measurements. In this diagram, d refers to the electrode separation and h refers to
the height of the probe from the working electrode surface. (From F. Zou, D. Thierry,
H. S. Isaacs. J. Electrochem. Soc. 144, 1957 (1997).)
pseudoreference electrode is used to measure the normal component of the AC
current density in solution as a function of signal frequency and/or position over
a coated metal surface. An example of the two-element electrode used to make
this type of measurement is shown in Fig. 53 (134).
In LEIS measurements, the working electrode is under potential control in
a three-electrode cell. The pseudoreference electrode pair is then brought close
to the sample surface to measure the local AC current density. A key assumption
behind LEIS is that in the potential field near a working electrode surface, the
AC solution current density is proportional to the local electrode impedance, and
at any given measurement frequency, ω, the current density in solution is
i(ω) ⫽
∆V(ω) ⋅ σ
l
(30)
where i(ω) is the current density in solution, ∆V(ω) is the AC voltage drop that
is measured between the two pseudoreference electrodes, ρ is the solution conductivity, and l is the separation distance between the pseudoreference electrodes.
The magnitude of the local impedance is then
| Z(ω)| local ⫽
V(ω) V(ω) applied l
⫽
⋅
i(ω)
V(ω) probe ρ
(31)
Study of Surface Treatments
343
Here, | Z(ω)| local is the magnitude of the local impedance, V(ω) applied is the magnitude of the voltage between the working electrode and a distant reference electrode, and V(ω) probe is the AC voltage drop measured by the pseudoreference
electrode pair. Again, it is implicitly assumed that the current density measured
in solution is equal to the current density at the electrode surface.
The pseudoreference probe electrode sizes that have been used to study
coatings have ranged from 100 to about 250 µm in diameter, with vertical offsets
between the probe elements of about 1 mm. The probe pair is usually brought
to within a few hundred micrometers of the surface for measurement. The impedance of the probe pair is usually quite large, and the voltage signal small. Therefore it is necessary to amplify the probe signal before it is applied to the frequency
response analyzer. For mapping, the probe pair is rastered using a high-precision
x–y stepper motor system. Vibration isolation of the entire apparatus is important
for proper measurement.
Spatial resolution of 30 to 40 µm has been demonstrated, but submillimeter
spatial resolution of the impedance variation is typical in studies on coated metals.
The probe is able to resolve variations at distances equal to the size of the probe
or larger. The probe size may be decreased to increase spatial resolution, but this
strategy is limited by a corresponding increase in the probe impedance, which
reduces AC signal sensitivity. Current flow in an electrolyte will spread radially
from a localized site in a manner determined primarily by the solution conductivity. Therefore the probe–working electrode separation distance will also affect
spatial resolution. The apparent size of impedance variation is also frequencydependent. At high excitation frequencies, the current distribution is altered because the interfacial impedance is shorted by capacitive charge transfer. It is also
possible that the directional components of current flow are frequency dependent.
LEIS is usually conducted to detect the component of current flow normal to the
working electrode surface. Should the magnitude of the component flowing parallel to the surface change with frequency, impedance variations may shrink or
grow in their spatial extent as a function of measurement frequency. Additional
details on the effects of probe configuration, separation, solution conductivity,
and excitation frequency on spatial resolution of the impedance variation can be
found in result presented by Thierry (134).
Taylor et al. conducted LEIS in a mapping mode to characterize the spatial
variation in the admittance associated with various types of intentionally formed
defects on organically coated metal surfaces (135). The LEIS probe used in these
experiments consisted of chloridized silver wires to form Ag | AgCl reference
electrodes. Excitation frequencies between 100 and 1000 Hz were used for mapping admittance. The precise frequency used was selected to maximize the admittances differences observed. Admittance mapping resolved differences due to
millimeter-sized defects associated with adsorbed machine oil, underfilm NaCl
344
Chapter 8
deposits, and arrays of pinhole defects. These findings are significant because
subtle defects that lead to corrosion are detectable before corrosion is observed
visually. Admittance mapping was also found to be sensitive to underfilm corrosion. Figure 54 shows the admittance map taken over two parallel scribes made
in a 10 µm thick polymer coating on an aluminum substrate. The figure shows
that the extent of the admittance variation is considerably wider than the width
of the scribe. This region was found to correspond to a region where corrosion
had propagated laterally away from the scribe defect.
Admittance mapping by LEIS has also been used on naturally formed defects on polymer coated metals (136,137). Al alloy 2024-T3 coated with polyvinyl chloride/polyvinyl acetate and polyurethane-based polymer films will form
blisters when immersed in dilute chloride or sulfate solutions for several days.
Two different types of blisters were found to evolve that were distinguishable
in LEIS mapping. Black blisters, named for their color, were round defects 1 to
2 mm in diameter. Red defects were irregularly shaped and ranged from 1 to 7
mm in diameter. The admittance response from each of these defects was substantially different, as shown in Figure 55. Black defects exhibited a comparatively
low admittance indicating a low rate of corrosion, while red defects exhibited a
high admittance and a greater rate of corrosion. These findings correlated well
with local measurements, which showed symptoms of aggressive local attack
including high metal cation concentrations, high chloride ion concentrations, low
pH, hydrogen evolution, and active open circuit potentials. These symptoms were
not found to the same extent in black defects. These findings show that LEIS
is a sensitive indicator of localized corrosion intensity in film defects, and can
distinguish the severity of defects occurring on the same sample.
In another study, LEIS was used to show that subtle differences in Al alloy
surfaces due to mechanical surface treatment produced different admittance responses (136). Regions of high admittance were found to exist in bands that
were associated with surface deformation. The admittance response was found
to correlate well with local determinations of the pitting potential. On average,
high admittance regions exhibited a pitting potential that was 150 mV more negative than the pitting potential on other regions of the surface.
Another method of spatially resolving variations in impedance involves
constructing regular arrays of small cells on a sample surface and performing
conventional EIS measurements in them on a serial basis (138). This method
does not require any special measurement equipment beyond that needed for
conventional EIS measurement. However, as the cell size and working electrode
area is reduced, the measured current will be reduced to the point where noise
and instrument current resolution become factors. These factors limit how small
a cell can be and determine the spatial resolution of the technique. This technique
has been used to examine the changes in the EIS response on coil coated galva-
Study of Surface Treatments
345
Figure 54 LEIS admittance map of two scribe marks on 10 µm thick polyvinyl chloride/
polyvinyl acetate coating on Al alloy 5182 (Al-2.5 Mg) after exposure to 3.5 wt% NaCl
for 24 h. The map was collected using a 15 mV amplitude voltage perturbation at 500
Hz. Underfilm corrosion is occurring in association with the rightmost scribe, as indicated
by the extended high admittance region located approximately at x ⫽ 2, y ⫽ 1. (From
M. W. Wittmann, R. B. Leggat, S. R. Taylor. J. Electrochem. Soc. 146, 4071 (1999).)
346
Chapter 8
Figure 55 Comparison of LEIS admittance maps for red (right) and black (left) defects
under a vinyl coating on 2024-T3 after 35 h exposure to 0.6 M NaCl. The large admittance
peak for the red defect indicates aggressive local corrosion. (From A. M. Miersch, J. Yuan,
R. G. Kelly, S. R. Taylor. J. Electrochem. Soc. 146, 4449 (1999).)
Study of Surface Treatments
347
nized steel after corrosion testing. Rows of cylindrical cells 8 mm in diameter
were glued to painted surfaces 2 mm apart from one another. Cell centers were
located 6, 20, and 34 mm away from the cut edge of the coil. Prior to the local
EIS characterization, the coil coated samples were exposed to cyclic exposure
in simulated acidified rain solution. Local EIS was conducted in each cell, and
the results were fitted to an equivalent circuit model. Results suggested that corrosion at the cut edge undercutting the paint was detectable by local EIS.
A single vibrating platinum wire pseudoreference electrode has been used
in another variant of the local impedance technique (139). In a demonstration
experiment, a 250 µm diameter Fe wire was inserted into a 316 stainless steel
sample to form a galvanic couple. The composite electrode was immersed in a
0.1 M Na 2 SO 4 solution, and a 0.2 µA DC current with a 3 µA current perturbation, whose frequency was swept between 0.1 and 1000 Hz, was applied between
the stainless steel and the Fe wire. A Pt/Ir needle with a 15 µm diameter Pt black
tip was vibrated mechanically at 266 Hz normal to the sample surface with a 15
µm amplitude. The probe signal was influenced by both the mechanical and the
current oscillations and contained both local potential and local current information. To extract and separate the useful information, the probe signal was amplified and filtered using phase-sensitive detection. From this information, the local
impedance was computed yielding a depressed semicircular arc in the complex
plane at frequencies between 0.1 and about 100 Hz. An interfacial capacitance
of about 80 µF/cm 2 was estimated from the data, which was generally consistent
with the capacitance of actively corroding iron. This technique is a distinct variant
of the local impedance technique because the local impedance is defined by the
ratio of the local current density to the local potentials rather than by the local
current density to the global potential as was the case in LEIS.
D. Electrochemical Noise (ECN)
Electrochemical noise consists of low-frequency, low-amplitude fluctuations of
current and potential due to electrochemical activity associated with corrosion
processes. ECN occurs primarily at frequencies less than 10 Hz. Current noise
is associated with discrete dissolution events that occur on a metal surface, while
potential noise is produced by the action of current noise on an interfacial impedance (140). To evaluate corrosion processes, potential noise, current noise, or
both may be monitored. No external electrical signal need be applied to the electrode under study. As a result, ECN measurements are essentially passive, and
the experimenter need only ‘‘listen’’ to the noise to gather information.
Potential noise is measured by collecting the potential versus time record
between a noisy corroding electrode and a noiseless reference electrode using a
high-impedance digital voltmeter (DVM). This is essentially a measurement of
348
Chapter 8
Figure 56 Schematic illustration of an ECN measurement system.
the open circuit potential. Measurement of current noise is made using a zero
resistance ammeter (ZRA) connecting two identical working electrodes immersed
in the same electrolyte. Potential and current noise can also be measured simultaneously by connecting working electrodes through a ZRA and measuring the
potential of one electrode against a reference electrode using a DVM. In these
types of measurements, the current and potential noise can be made simultaneously, and are said to be correlated (141). Usually, the measurement of correlated data is orchestrated by computer. A schematic illustration of the apparatus
for making correlated noise measurements is shown in Fig. 56. General purpose
DVMs and ZRAs are usually unsuitable for electrochemical noise measurements
because the magnitude of the signals is quite small. However, commercial systems, including both hardware and software, are available for making correlated
noise measurements.
Electrochemical noise can be characterized by some common statistical
parameters including the mean, the variance, and the standard deviation. In particular, the standard deviation, σ, is used as a measure of the amplitude of the
variation in the noise signal. Skew and kurtosis sometimes give indications of
the form of corrosion occurring (140). For unfiltered digitized noise data in a
time record, the noise resistance, R n , is
Rn ⫽
σV
σI
(32)
where R n is the noise resistance in ohms, and σ V and σ I are the standard deviation
Study of Surface Treatments
349
in the potential and current noise signals, respectively (142). This definition assumes that potential noise arises due to the action of current noise across the
interfacial impedance. R n , as it is used in corrosion studies, is based on simple
statistical evaluation of noise signals, and an equally simple Ohm’s law formalism. However, a widely accepted fundamental, first-principles derivation of the
noise resistance has not yet emerged (143,144).
Determination of R n does not require that the current and potential signal
be correlated. However, if measurements are made at different times, they should
be made with similar working electrodes and similar exposure conditions. R n
values have been used to assess the degradation of organically coated metals. In
these studies, R n data appeared to correlate with the film resistance (impedance
magnitude at low frequency) values determined from EIS (145), or with visual
inspection of painted samples subject to various cabinet exposures (146).
In the case of general corrosion, R n can be used in the Stern–Geary equation
to estimate corrosion rate:
i corr ⫽
1
ba bc
⋅
R n 2.3(b a ⫹ b c)
(33)
In this expression, b a and b c refer to the appropriate anodic and cathodic Tafel
constants. Comparison of weight loss data collected as a function of exposure
time determined from R n , R p from EIS, and gravimetric measurements of mild
steel exposure to 0.5 M H 2 SO 4 are often within a factor of two. This suggests
that use of R n in the Stern–Geary equation may be appropriate for the estimation
of corrosion rate (147–150). However, R n measurements may underestimate corrosion rates. R p is often measured at effective frequencies of 10 ⫺2 Hz or less in
linear polarization or EIS measurements, while R n is measured at 1 Hz or greater.
An example of this is provided in Fig. 57, which shows the corrosion rate of
carbon steel in 3% NaCl solution as a function of exposure time determined by
EIS, linear polarization, noise resistance, and direct current measurement with a
ZRA. Among these data, the corrosion rates determined by noise resistance are
consistently the lowest.
Correlated noise data can be transformed to the frequency domain using a
fast Fourier transform (FFT) or the maximum entropy method (MEM) (151) A
spectral noise impedance, R sn ( f ), can then be calculated (152):
R sn ( f ) ⫽
En ( f )
In( f )
(34)
and
R sn ( f ) ⫽ | R( f )| ⫽ √(R 2Re ⫹ R 2Im)
(35)
350
Chapter 8
Figure 57 Corrosion rate of carbon steel in 3% sodium chloride solution as a function
of exposure time. (From J. L. Dawson. p. 3, Electrochemical Noise Measurements for
Corrosion Applications, ASTM STP 1277. ASTM, Philadelphia, PA (1996).)
In this expression, E n and I n are the magnitude of the potential and current noise
at any given frequency, f. R Re and R Im are the real and imaginary components of
R sn . Plots of spectral noise impedance versus frequency resemble Bode magnitude
plots of EIS data as shown in Fig. 58. Meaningful phase angle information is
not usually obtained, as this is not preserved by the MEM transform, and data
are usually of insufficient quality for accurate phase information to be obtained
from the FFT.
The spectral noise resistance, determined from the DC limit in a spectral
noise impedance plot, is defined as
R 0sn ⫽ lim 冦R sn ( f )冧
(36)
f→0
which is equal to the magnitude of the impedance at the DC limit, provided that
instrumentation is sufficiently sensitive to very small currents.
Noise resistance monitoring has been used to track the long-term degradation of marine coatings under laboratory exposures (153), and remotely under
natural exposure conditions (154). In studies of epoxy and alkyd coatings on steel
Study of Surface Treatments
351
Figure 58 Frequency dependence of the spectral noise resistance, R sn , for iron in aerated, and aerated and inhibited 0.5 M NaCl after exposure for (a) 1 h and (b) 24 h. (From
F. Mansfeld, H. Xiao. p. 59, Electrochemical Noise Measurements for Corrosion Applications, ASTM STP 1277. ASTM, Philadelphia, PA (1996).)
352
Chapter 8
substrates exposed to chloride solutions or natural seawater, there appeared to
be good qualitative correlation between the noise resistance, R n , and the spectral
noise resistance, R osn (141,155). Additionally, these two parameters were observed
to exhibit the same time-dependent trends as the pore resistance, R po , and the
polarization resistance, R p , determined from EIS experiments carried out over
the same exposure time interval.
Power spectra estimation can be carried out with correlated ECN data. Data
are plotted in power spectral density (PSD) plots, which show the power of a
noise signal over frequencies that range from 1/T, where T is the sampling period,
to the maximum sampling rate. Normally data are plotted as the logarithm of the
power using units of V 2 /Hz or A 2 /Hz versus the logarithm of frequency. PSD
plots have three characteristics: the roll-off slope, which is observed at the highfrequency regime, the DC limit at the lowest frequency, and the roll-off frequency, which separates the two regimes (156). The overall shape of the PSD
may give an indication of the shape and duration of individual current or potential
transients, and their distribution in time (157). The roll-off slope itself may indicate the nature of the corrosion process. A slope of ⫺2 may indicate a Gaussian
process characteristic of general corrosion, a slope of ⫺1 is consistent with a
diffusion-controlled process, and a slope of 0 indicates a stochastic or Poisson
process, which is characteristic of localized corrosion (158). As a result, PSD
analysis can discriminate among different types of corrosion.
Under the proper conditions there are important relations among the PSDs,
the noise resistance, and the spectral noise resistance that make PSD measurement
useful in corrosion studies (159–161). The variance of a random signal, x, is the
integral of its PSD in the frequency domain:
⫹∞
σ ⫽
2
x
冮 Ψ ( f ) df
(37)
x
0
where Ψ x (f ) is the PSD of the signal. Therefore the noise resistance, R n , can be
determined from the integration of the potential and current PSDs as
冢
冣
f
∫ f max ΨV ( f )df
σ
R n ⫽ V ⫽ fmin
σI
∫ f max
ΨI ( f )df
min
1/2
(38)
where f min is the inverse of measurement time length and f max is one-half of the
maximum sampling rate. The voltage and current PSDs are also related to the
spectral noise resistance:
R sn ( f ) ⫽
冢
冣
ΨV ( f )
ΨI ( f )
1/2
(39)
Study of Surface Treatments
353
When the current and voltage PSDs decrease faster than 1/f, R n and R sn ( f ) are
related via the voltage and current PSDs as
Rn ⫽
冢
f
max
∫ f min
Ψ I ( f )R 2sn ( f ) df
f
max
∫ f min
Ψ I ( f ) df
冣
1/2
(40)
If R sn ( f ) is frequency-independent in the range of f max to f min , then R n will equal
R sn . If the spectral noise resistance is equal to the magnitude of the impedance,
which is reasonable at low frequencies, then
R n ⫽ R sn (0) ⫽ | Z(0) |
(41)
Area normalization of ECN data is not as straightforward as with other
type of electrochemical data (140). Current and potential noise may scale differently with electrode area. For example, if it is considered that the mean current
is the sum of contributions from discrete events across the electrode surface, then
the variance associated with the mean value will be proportional to the electrode
area. The standard deviation of the current noise, σ I, a measure of current amplitude, will then scale as the square root of the area. If is assumed that potential
noise originates from current noise acting on the interfacial impedance, then σ E
will scale with the inverse root of the area. Therefore it is inappropriate to normalize current and potential noise by electrode area linearly. On the contrary, area
normalization of noise resistance does appear to be appropriate. This is so because
the potential and current noise have a constant relationship with one another. As
a result, it is appropriate to report noise resistance in units of Ω ⋅ cm 2, remembering that the total area for normalization is given by the sum of the areas on both
working electrodes.
A fundamental assumption in the interpretation of current noise from correlated noise data is that the two working electrodes in a working electrode pair
are sufficiently identical that they have the same polarization resistance and the
same mean current (162). In corrosion studies, this is sometimes not the case.
Often one electrode is slightly more passive than the other in the pair. The more
passive electrode develops into a net cathode, while the other electrode activates
and becomes a net anode. The working electrode pair now behaves like a galvanic
couple, and this asymmetry invalidates noise data. Another type of electrode
asymmetry develops with coated metals. In this case, corrosion occurs at widely
separated defects in the coating. In high-quality coatings, the areal density of
defects is very small and the spacing between them is very large. Any given
working electrode may only have one or two defects, and if a sample containing
a defect is paired with one that does not have a defect, the working electrode
pair will be asymmetric, thereby invalidating the noise data.
354
Chapter 8
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9
Experimental Procedures
LABORATORY I
PART A: GALVANIC SERIES AND REFERENCE
ELECTRODES
A. Objective
In this laboratory, you will construct a number line for reference electrode conversions, measure the corrosion potentials of several alloys in a salt water solution,
construct a galvanic series with two different reference electrodes, and convert
the two galvanic series to the NHE scale to determine if they agree (as they
should). This lab will demonstrate some of the concepts discussed in Chapter 2.
B. Experimental Procedure
1. When you enter the laboratory, first check that you have the following:
A container of 3.5 wt% NaCl in water with five electrodes already immersed
A saturated calomel reference electrode (SCE)
A mercury/mercurous sulfate (Hg/Hg 2SO 4) reference electrode
A voltmeter
The five electrodes in solution will be AISI 1020 carbon steel, tin graphite,
an aluminum alloy, and 303 stainless steel. The SCE has a potential of ⫹0.241
V NHE, whereas the Hg/Hg 2SO 4 has a potential of ⫹0.400 V SCE.
2. Construct a number line with units of volts vs. NHE and indicate the
position of the SCE on it. Next, measure the potential of the Hg/Hg 2SO 4 electrode
relative to the SCE in the salt solution with the voltmeter. Remember that, in
this case, the SCE is the reference electrode, so it should be connected to the
negative lead (or common) of the voltmeter. Convert the Hg/Hg 2SO 4 potential
vs. SCE to the proper potential vs. NHE. Now, using the number line to help
361
362
Chapter 9
you, indicate the position of the Hg/Hg 2SO 4 reference electrode on the number
line.
3. Measure the open circuit potential of each of the five electrodes relative
to the SCE and record these values in the table provided under Results. Convert
each of these to the NHE scale with the help of the number line. Now, measure
the corrosion potential of each of the five electrodes relative to the Hg/Hg 2SO 4
and record these values in the table. Convert each of these to the NHE scale with
the help of the number line. Compare the values of each of the electrodes vs.
NHE as determined by the two different reference electrodes. It should not make
any difference which reference electrode was used, as a reference electrode is
simply a reference point or benchmark.
4. A standard electrode potential series consists of equilibrium potentials,
not corrosion potentials as you have been measuring in this laboratory. These
potentials are usually referenced to NHE but could be referenced to any reference
electrode system. How would you convert a standard electrode potential series
from V NHE to V SCE?
5. Note the potentials of the graphite and the aluminum alloy that you
determined. If these two are connected with an electrical contact, their potentials
should move toward each other. Further, since the solution is relatively conductive, and assuming that the electrical lead connecting them was highly conductive,
they would come to the same potential. Therefore connect the leads of the two
electrodes together and connect them both to the positive (or V) lead of the voltmeter. Measure the potential of this galvanic couple relative to one of the reference electrodes and confirm that the couple potential does indeed rest somewhere
in between the corrosion potentials of the two materials.
C.
Results
Potential of Hg/Hg 2SO 4 relative to SCE:
Material
E corr
(V SCE)
E corr
(V NHE)
E corr
(V Hg/Hg2SO4)
E corr
(V NHE)
Experimental Procedures
363
Potential of 7075-T76 aluminum coupled to
graphite:
Number lines:
(vs. NHE)
(vs. SCE)
D. Sample Results
Potential of Hg/Hg 2SO 4 relative to SCE: 0.400 V
Material
E corr
(V SCE)
E corr
(V NHE)
E corr
(V Hg/Hg2S04)
E corr
(V NHE)
Graphite
303 SS
Tin
1020 steel
AA 7075
0.227
⫺0.375
⫺0.650
⫺0.702
⫺0.778
0.468
⫺0.134
⫺0.409
⫺0.461
⫺0.537
⫺0.189
⫺0.771
⫺1.049
⫺1.103
⫺1.180
0.468
⫺0.134
⫺0.409
⫺0.461
⫺0.537
LABORATORY I
PART B:
POLARIZATION CURVES
In this experiment, polarization curves for carbon steel and copper in 3.5 wt%
NaCl will be determined. From these data, the corrosion rates will be estimated
for the individual metals freely corroding in solution and for the metals electrically coupled in solution as would be the case for an immersed, riveted connection, for example.
364
A.
Chapter 9
Background
Potentiostatic polarization is widely used to determine the steady-state corrosion
behavior of metals and alloys as a function of potential in environments of interest. This technique involves holding a specimen’s surface at a series of constant
potentials versus a reference electrode, and then measuring the current necessary
to maintain each of the applied potentials. From this dependence of the current
on the applied potential of the sample, a number of parameters important for
understanding the corrosion behavior of the material in the environment (such
as i corr , b a, and b c) can be determined as pointed out in Chapter 2.
It is important to remember that the measured current is the applied current,
defined as
i app ⫽ i a ⫺ i c
(1)
where
i app ⫽ applied current
i a ⫽ total anodic current
i c ⫽ total cathodic current
Thus at potentials close to the corrosion potential, i app is very small, since
i a and i c are very close in magnitude. Note that this is true even if i a and i c are
themselves large in magnitude. However, at large anodic overpotentials, i a is
much larger than i c , and therefore i app approaches i a. Conversely, at large cathodic
overpotentials, i c is much larger than i a, and i app approaches i c. By determining
the Tafel slopes of the reaction in these regions, an estimate of the corrosion rate
can be performed by Tafel extrapolation as demonstrated in Chapter 2. In addition, the “hidden” portions of the anodic and cathodic lines can also be estimated
by continuing the Tafel lines back to the reversible potentials of the reactions.
In this way, an estimate of the oxidation rate of the material can be made at any
given cathodic protection potential. This estimate can be of great importance
where information on the level of cathodic protection necessary to reduce the
corrosion rate of a material must be made in a short time. As was pointed out
in Chapter 2 and will be seen in this experiment, care must be taken in interpreting
the results of extrapolating the behavior to service times longer than the duration
of the experiment.
The importance of area ratios in discussing galvanic corrosion cannot be
overemphasized. Because charge (and therefore current) is conserved, our analysis of the galvanic couple of copper and steel will focus on studying E vs. log
I (current) plots rather than the more traditional E vs. log i (current density) plots.
Because the specimens will have different geometric areas, it will be important
to keep this in mind during the analysis section of the laboratory session. By
plotting the data initially in the E vs. log I format, the “natural” coordinate system
Experimental Procedures
365
of galvanic corrosion, an understanding of the system behavior can be obtained.
When the materials are coupled, they will come to the same potential and will
pass a current of the same magnitude through their exposed surfaces. The current
densities will, of course, be different if the specimens have different exposed
areas. However, because current is conserved, it is from this vantage point that the
analysis must begin. After determining the corrosion current for each specimen at
their respective open circuit potentials and at the couple potential, a corrosion
current density and then a penetration rate can be calculated knowing the exposed
areas and material properties (density, molecular weight, number of electrons
transferred, etc.) through the use of Faraday’s law, as discussed in Chapter 1.
USEFUL INFORMATION
Areas of Working Electrodes
Carbon steel: 3.8 cm2
Copper: 2.8 cm2
Atomic Mass of Materials
Carbon steel: 55.85 g/mol
Copper: 63.55 g/mol
Density
Carbon steel: 7.8 g/cm3
Copper: 8.96 g/cm3
Dissolution Reactions
Cu → Cu2⫹ ⫹ 2e⫺
Fe → Fe2⫹ ⫹ 2e⫺
B. Experimental Procedure
There are two types of potentiostat setups in the laboratory, and each requires a
different procedure to perform a potentiostatic polarization. Determine which
type of potentiostat (PAR 273 or VersaStat) is at your station and use the appro-
366
Chapter 9
Figure 1 The wiring diagram for connecting the experimental cell electrodes to the
potentiostat.
priate procedure described below. If you have trouble identifying the type of
potentiostat ask a lab assistant to figure it out.
1.
To apply a potential using the VersaStat or PAR 273 potentiostat:
a. Connect the working electrode (green lead) to the sample to be
polarized (either the carbon steel or copper). Connect the counter
electrode (red lead) to the graphite rod. Use the calomel electrode
as the reference and connect it to the white Reference jack on the
electrometer.
b. Turn the VersaStat or PAR 273 power ON. For the VersaStat make
sure the potentiostat/galvanostat toggle switch is in the potentiostat position.
c. Turn the VersaStat cell on by pressing the button labeled “Cell
Switch” until the red light comes on. For the PAR 273, press the
“Cell Enable” button. This button should now display the word
ON.
NOTE: THE CELL IS NOW “HOT.” DO NOT TOUCH ANY
LEAD WITHOUT TURNING THE CELL OFF. IT IS TURNED
OFF BY PUSHING THE CELL SWITCH SO THAT THE WORD
OFF IS DISPLAYED.
Experimental Procedures
367
Figure 2 The opening window for PARC 352 SoftCorr III. Begin a new experimental
setup by choosing New Setup.
d. Both the VersaStat and the PAR 273 are controlled by the accompanying computer and PAR 352 software. Select NEW SETUP (or
type “e”) from the FILE menu to begin a new experimental setup.
e. Select the POTENTIOSTATIC option under the TECHNIQUE
menu.
f. Enter the potential to be applied by clicking on the INITIAL POT.
Dialog box. At the prompt enter a potential from Table 1 from the
following “Results and Data Analysis Section.”
g. To run the experiment select the RUN option by clicking on the
button or by pressing “R”. If the prompt Save Data, Results &/or
Labels? Pstat #1 appears, choose NO. Once the potential is applied,
the current, potential, and time will appear in the upper left-hand
corner of the computer screen. Wait for a stable current and record
on the worksheet. This process will take about 5 minutes at each
potential. If, at the end of 5 minutes, the current has not stabilized,
take a reading and move to the next potential.
h. Stop the experiment after the current has been recorded by selecting
STOP (press “S”) under the EXPERIMENT menu.
368
Chapter 9
Figure 3 The experimental setup window showing the potentiostatic technique option.
i. A graph of current vs. time will appear on the screen. Current values
may be obtained by selecting CURVE CURSOR under the CURVE
option of the VIEW menu and recording the final value shown at
the bottom of the screen. Values may also be obtained from the data
table at the far right side of the window. The table can be accessed
by selecting DATA TABLE under the VIEW menu.
j. Return to the setup menu by closing the data file; choose CLOSE
under the FILE menu. To apply the next potential repeat steps e
through h.
k. After all potentials for a given specimen have been applied, turn the
potentiostat cell off by pressing the “cell switch” so that the word
OFF is displayed.
2.
Measure the short-circuit current between the steel and copper. This
current measured represents the current that would flow between the
two materials if they were in electrical contact with one another in the
saltwater environment.
a. Connect one specimen to the CE and RE leads and the other to
the working electrode lead.
Experimental Procedures
369
Figure 4 A potentiostatic scan on steel. Data can be viewed from the graph and curve
cursor or from the data table.
b. Apply zero volts between the working and reference electrodes.
c. The applied current is the short circuit current. Record the result.
3. Measure the potential of the couple versus the SCE reference electrode.
a. MAKE SURE THE POTENTIOSTAT IS NOT “HOT.” For
the 273 press the “CELL ON” and “CELL ENABLE” buttons so
that they are unlit. For the VersaStat push the “CELL SWITCH”
so that the word OFF is displayed.
b. Use a wire with alligator clips to electrically connect the steel to
the copper.
c. Use the digital voltmeter (DVM) to measure the potential of the
couple vs. the SCE reference electrode and record the result.
C. Results and Data Analysis
Areas of working electrodes:
Copper:
Carbon steel:
E corr ⫽
cm2
cm
2
E corr ⫽
V SCE
V SCE
370
Chapter 9
Table 1 Potential-Current Data from Polarization Experiment
Carbon steel
Potential
(V vs SCE)
Copper
Potential
(V vs SCE)
Current
⫺0.900
⫺0.850
⫺0.800
⫺0.750
⫺0.700
⫺0.675
⫺0.650
⫺0.625
⫺0.600
Ecouple ⫽
D.
Current
⫺0.500
⫺0.450
⫺0.400
⫺0.350
⫺0.300
⫺0.250
⫺0.225
⫺0.200
⫺0.175
⫺0.150
VSCE
Icouple ⫽
µA
Analysis
From the plots of E vs. log I for steel and zinc that you have generated:
I corr(Carbon steel) ⫽
µA
i corr(Carbon steel) ⫽
µA/cm
I corr(Copper) ⫽
2
i corr(Copper) ⫽
µA
µA/cm2
Corr. rate (Carbon steel) in mpy:
Corr. rate (Copper) in mpy:
From the Nernst equation calculate the reversible potential for copper in a neutral
solution containing 10⫺6 mol/L Cu2⫹. Plot this value on your E vs. log I curve.
E r(Cu/Cu2⫹):
mV (vs. SCE)
From the direct coupling of the steel and copper:
i couple(Carbon steel) ⫽
µA/cm2
i couple(Copper) ⫽
Corr. rate (Carbon steel) in mpy:
From extrapolation of the cathodic portion of the copper to E couple :
I Fe/Fe⫹⫹(E ⫽ E couple) ⫽
µA
i Fe/Fe⫹⫹(E ⫽ E couple) ⫽
µA/cm2
Corr. rate of steel at E couple (in mpy):
µA/cm2
Experimental Procedures
RECALL: MPY ⫽
371
0.129 * Ai
nD
A ⫽ atomic weight
i ⫽ corrosion rate (µA/cm2)
D ⫽ density (g/cm3)
E.
Questions
1. What are the anodic and cathodic reactions observed for each electrode
material?
2. Calculate the corrosion rate for the carbon steel when it is coupled to
the copper. Express the results in both µA/cm2 and mpy.
Assume that
a. The self-corrosion of the anode is negligible.
b. The galvanic current measured is due solely to the oxidation of
the anode.
c. Your measurements reflects the steady-state condition.
d. All corrosion is electrochemical (e.g., there is no appreciable grain
fall-out).
3. Which of the assumptions in question 2 do you think is the best? Which
is the worst?
4. Prove that when coupled to steel the corrosion rate of copper is zero.
Assume that the concentration of copper ions in solution is 10⫺6.
5. Estimate the corrosion rate of the copper under freely corroding conditions and when it is coupled to the steel by extrapolating the anodic
portion of the copper polarization curve to E couple. Compare these oxidation rates. Why can’t either rate be measured directly?
6. Compare values of E couple and I couple for a 1: 1 cathode-to-anode area
ratio to the values calculated with a 1000: 1 copper-to-steel area ratio.
What is the dissolution rate of copper at this area ratio?
7. An interesting exercise is to try to generate Evans diagrams for the
copper and steel (mostly Fe) from theoretical data (i.e., reversible
potentials, exchange current densities, Tafel slopes, expected limiting
currents, etc.) and compare to the experimental data obtained.
F.
Significant Observations
Figure 5 and Table 3 show typical data for the specimens studied. These data
can be compared with those experimentally generated to get an idea of the degree
of variability. It should be noted that very few experimental variables, such as
degree of aeration, surface finish, or temperature, were controlled to any great
372
Chapter 9
Figure 5 Sample polarization curves for copper and steel samples.
extent in these experiments. In general, such variables (and others) should be
considered in the experimental design in order to make the testing as relevant as
possible to the service conditions of interest.
There are a number of significant observations which should have been
made during this experiment. First, the relative corrosion potentials of the steel
and the copper should be noted. These would be the potentials that would be
included in a galvanic series of materials in 3.5% NaCl, if that were our intention.
Simply on this basis, it can be seen that while steel has the possibility of acting
as a sacrificial anode for copper, copper cannot do so for steel. In addition, the
potentials are well separated in this environment (approximately 0.4 V), giving
further evidence that, for most kinetic schemes found experimentally, there is a
significant driving force available to reduce the corrosion rate of copper by coupling to steel. With respect to the E corr measurements made in this experiment,
the short period of time used to allow for attainment of steady state must be kept
in mind when trying to extrapolate the behavior found to service conditions. It is
usually feasible to allow longer exposure times before conducting the polarization
experiments in order to develop a situation at the interface that is more relevant.
Experimental Procedures
373
Table 2 Sample Potential-Current Data from Polarization
Experiment
Carbon Steel
Potential
(V vs SCE)
Current
⫺0.900
⫺0.850
⫺0.800
⫺0.750
⫺0.700
⫺0.675
⫺0.650
⫺0.625
⫺0.600
Ecouple ⫽
Copper
Potential
(V vs SCE)
Current
⫺0.500
⫺0.450
⫺0.400
⫺0.350
⫺0.300
⫺0.250
⫺0.225
⫺0.200
⫺0.175
⫺0.150
⫺87.6e-6
⫺60.0e-6
⫺41.2e-6
⫺23.8e-6
⫺25.4e-6
7.44e-6
1.29e-5
3.78e-5
1.23e-4
3.78e-4
⫺7.46e-5
⫺5.42e-5
⫺2.3e-5
7.71e-6
2.47e-5
7.88e-5
2.19e-4
4.58e-4
8.04e-4
Icouple ⫽
VSCE
µA
In analyzing the polarization data, it can be seen that the cathodic reaction
on the copper (oxygen reduction) quickly becomes diffusion controlled. However, at potentials below ⫺0.4 V, hydrogen evolution begins to become the dominant reaction, as seen by the Tafel behavior at those potentials. At the higher
anodic potentials applied to the steel specimen, the effect of uncompensated
ohmic resistance (IR ohmic) can be seen as a “curving up” of the anodic portion of
the curve.
Finally, the increase in the corrosion rate of the steel and the reduction of
the corrosion rate of the copper upon coupling can be easily seen in the results;
they demonstrate the usefulness of cathodic protection and the detrimental effect
of improper control of galvanic couple corrosion.
G.
Results and Data Analysis
Areas of working electrodes:
Copper: 2.8 cm2
E corr ⫽ ⫺264 V SCE
Carbon steel: 3.8 cm2
E corr ⫽ ⫺684 V SCE
H. Analysis
From the plots of E vs. log I for steel and zinc that you have generated:
I corr(Carbon steel) ⫽ 32 µA
I corr(Copper) ⫽ 24 µA
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Chapter 9
i corr(Carbon steel) ⫽ 8.42 µA/cm2
i corr(Copper) ⫽ 8.6 µA/cm2
Corr. rate (Carbon steel) in mpy: 3.88
Corr. rate (Copper) in mpy: 3.93
From the direct coupling of the steel and copper:
i couple(Carbon steel) ⫽ 2.62 µA/cm2
i couple(Copper) ⫽ 3.56 µA/cm2
Corr. rate (Steel) in mpy: 1.20
From extrapolation of the cathodic portion of the copper to E couple :
I Fe/Fe⫹⫹(E ⫽ E couple) ⫽ 2.8e2 µA
i Fe/Fe⫹⫹(E ⫽ E couple) ⫽ 73.7 µA/cm2
Corr. rate of steel at E couple (in mpy): 34.3
0.129 * Awi
nD
Aw ⫽ atomic weight
i ⫽ corrosion rate (µA/cm2)
D ⫽ density (g/cm3)
RECALL: MPY ⫽
LABORATORY II
LOCALIZED CORROSION
A.
Objective
The goals of this laboratory session are to introduce you to potentiodynamic
polarization measurements for the determination of localized susceptibility, demonstrate the effect of the presence of non-Cl⫺ ions on pitting, and present examples of metastable pitting (one type of “electrochemical noise”).
B.
Experimental Procedure
Cell connections for all tests are as follows (see Fig. 6):
1.
2.
3.
4.
Green lead: connect to the working electrode (302SS wire loop).
Red lead: connect to the counter electrode (graphite).
Black lead: not connected.
RE pin connector: connect to the reference electrode (SCE).
Experimental Procedures
375
Figure 6 Cell connections for Lab II.
You have been provided with five 302 stainless steel wire loops and strips of
600 grit sand paper. Prior to each test, lightly polish the loops to remove any
dirt and oil that may be present due to handling. Do not touch the loop with your
hands; use disposable gloves. This is very important!
Test 1: Cyclic Polarization of 302SS in 1000 ppm
(0.017 M) NaCl
In this first experiment you will run a standard cyclic polarization curve on stainless steel.
1. Partially immerse one loop into 1.5 L of 1000 ppm NaCl solution. This
loop will serve as the working electrode. Do not immerse the entire loop. Make
sure that the windings do not enter the solution.
2. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE and select ECORR VS. TIME. Set TIME STEP 1 to “300”
seconds and TIME/PT. to “1” second. Your setup window should look like the
376
Chapter 9
Figure 7 Example of screen setup to measure open circuit.
one shown in Fig. 7. Select the RUN button. Record the final value for the potential in the table provided. You will know the scan is completed when the words
DATA GRAPH appear in the lower left corner of the window.
3. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE and select CYCLIC POLARIZATION. You will now have
on display the setup menu for the experiment.
a. Select INITIAL POT. and enter “ⴚ.300” (this will begin the scan at
⫺0.300V vs SCE).
b. Select VERTEX 1 POT. and enter “0.1.”
c. Select FINAL POT. and enter “0.050.” Click on the box next to OC
so that a check mark appears. This means that the current is measured
versus the open circuit.
Experimental Procedures
377
d. Select I THRESHOLD and enter “2e-3” A/cm2.
e. Select SCAN RATE and enter “1” mV/s.
f. Add the appropriate information for the Density (“7.94” g/cc), Equiv.
Wt. (“25”), Elec. Area (“0.4” cm2) and Ref. Elec (“SCE”). The setup
window should look like the one in Fig. 8 below.
g. Switch the Cell Enable Key “ON” on the potentiostat. Select RUN and
the experiment will start. “SETTING UP EXPERIMENT” and then
“RUNNING EXPERIMENT” will appear on the lower left corner of
the window. (This scan will take approximately half an hour.)
h. The end of the experiment is indicated by the signal “DATA GRAPH”
on the lower left corner. Press the Cell Enable Switch to “OFF.” Select
FILE, SAVE to save the data as a “.dat” file.
4. From the resulting curve, determine E bd, E repass, and i pass. (See Fig. 14
at the end of this write-up.)
Figure 8 Example of screen setup to run cyclic polarization as in Test 1.
378
Chapter 9
Test 2: Determination of E repass Using Electrochemical Scratch
From an engineering perspective, the repassivation potential is a more important
parameter than the potential for pit nucleation. We want to know the potential
below which pits will not grow. This is analogous in theory to measuring K IC or
K ISCC in mechanical and SCC testing. One way to test this is to produce a completely bare surface that is dissolving rapidly, and determine at what potential it
can repassivate. An easy way to do this is what may be termed an “electrochemical scratch.”
1. Partially immerse a new polished loop (working electrode) in 1000
ppm NaCl. Do not use the loop from the previous experiment.
2. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE and select ECORR VS. TIME. Set TIME STEP 1 to “300”
seconds and TIME/PT. to “1” second. Select the RUN button. Record the final
value for the potential in the table provided.
Figure 9 Example of screen setup to run potentiostatic holds as in tests 2 and 3.
Experimental Procedures
379
3. Using the POTENTIOSTATIC technique, you will sequence through
a series of increasing applied potentials while monitoring the current.
4. Perform the following:
a. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE.
b. Select POTENTIOSTATIC from the menu.
c. You will now see the setup sheet for the potentiostatic experiment.
Select INITIAL POT. and enter “0.035” to apply ⫹35 mV vs SCE to
the sample.
d. Select TIME STEP 1 and enter “240” seconds.
e. Select TIME/PT. and enter “1” second.
f. Select COND. POT. and enter “1.2” V.
g. Select COND. TIME and enter “3” seconds.
h. Add appropriate information for Density, Equiv. Wt., and Ref. Elec.
(See 3f in Test 1) The setup window should look like the one in Fig. 9.
i. Press the Cell Enable Switch to “ON.”
j. Select RUN. Click on DISPLAY to view the progress of the experiment.
k. Save the data using FILE, SAVE.
l. Go to the MAIN Menu to GRAPH the data.
m. If the current is observed to be rising after 240 seconds, you can stop
the experiment. If not, go to the FILE Menu and select SETUP.
Change INITIAL POT. by ⫹0.05 V and repeat steps 4j through 4m.
Observe the current in each case. Record the last potential for which
the current was not rising after 240 seconds.
n. Press the Cell Enable Switch to “OFF.”
Test 3: Potentiostatic Holds on 302SS—Metastable Pitting
In class, we discussed metastable pitting, and you may have seen some indications
of it in some of the previous tests. The easiest way to see metastable pits is to
perform potentiostatic holds at potentials just below the pitting potential. In order
to reduce our background current, as well as provide a baseline, we will first
grow the passive film at a low potential before moving it to a potential where
metastable pitting can be observed. Finally, we will polarize just above the pitting
potential to see the induction time and the similarity between metastable and
stable pits.
1. Partially immerse a fresh wire loop electrode in 1000 ppm NaCl solution.
2. Perform the following:
a. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE.
Figure 10 Data obtained in test 2 showing potentiostatic holds at four different potentials after electrochemical scratch.
Figure 11 Data obtained from potentiostatic holds in test 3. This shows the final run
where active pitting occurs.
380
Figure 12 Data from the first two potentiostatic holds in test 3 showing metastable
pitting.
Figure 13 Data from test 1 taken in 1000 ppm NaCl ⫹ 9650 ppm Na2SO4. Sample
is 302SS and scan rate is 2.5 mV/sec. Arrows indicate scan direction.
381
382
Chapter 9
Figure 14 Data from test 1 taken in 1000 ppm NaCl. Sample is 302SS and scan rate
is 1.0 mV/sec.
b. Select POTENTIOSTATIC.
c. Select TIME STEP 1 and enter “1200” seconds. Select TIME/PT. and
enter “1” second. Select INITIAL POT. and enter “0.00” volts. Make
sure that there is no condition potential or condition time entered.
d. Add the appropriate information for Density, Equiv. Wt, Elec. Area,
and the Ref. Elec. as given in 3f of Test 1. Save the setup by selecting
FILE, SAVE and entering a file name (.set).
e. Press the Cell Enable Switch to ON to activate the Cell. After the run
is complete, save the data (SAVE option under FILES Menu, “.dat”
form).
f. Click on FILE, OPEN, and the file name for your setup. Change Initial
Pot. to “0.250” V and TIME STEP 1 to “600” seconds. Run the experiment as in 2e.
g. Repeat the experiment (see 2f ) for Initial Pot. ⫽ “0.350” V.
h. Repeat the test (see 2f ) for Initial Pot. ⫽ “0.450” V. Stop the experiment when the current reaches 200 µA/cm2. Press the Cell Enable
Switch to OFF to deactivate the cell.
Experimental Procedures
383
Test 4: Cyclic Polarization of 302SS in 1000 ppm (0.017 M)
NaCl ⫹ 9650 ppm (0.068 M) Na 2SO 4
The fourth experiment shows the effect of supporting electrolyte. The aggressive
local chemistry cannot develop because sulfate dominates the transport into any
incipient pits.
1. Partially immerse a new wire loop in the 1000 ppm NaCl ⫹ 9650 ppm
Na 2SO 4 solution. Use the counterelectrode to completely mix the solution.
2. Select FILE, NEW SETUP from the top of the window. Press the arrow
next to TECHNIQUE and select ECORR VS. TIME. Set TIME STEP 1 to “300”
seconds and TIME/PT. to “1” second. Select the RUN button. Record the final
value for the potential in the table provided.
3. Follow the instructions in Test 1, steps 3a through 3g, with the exception of changing the SCAN RATE from 1 mV/s to “2.5” mV/s.
4. From the resulting curve, determine E bd, E rp, and i pass.
C. Significant Observations
These tests focused on the determination of a materials resistance to localized
(pitting) corrosion. To accomplish this goal, three types of electrochemical experiments were conducted (cyclic polarization, electrochemical scratch, and potentiostatic holds) to measure several key parameters associated with pitting corrosion. These parameters were the breakdown potential, E bd, the repassivation
potential, E rp, and the passive current density, i pass.
The initially cathodic current in test 2 is due to the reduction of the oxygen
evolved during the pulse portion of the test. When the voltage is pulsed to 1.2
volts, oxygen is evolved. When the potential is held at the lower voltages, the
solution closest to the interface is now saturated. The total current is cathodic
while this oxygen is reduced.
Two main points should be remembered from this lab. First, the breakdown
potential is not necessarily the best measurement of pitting resistance. This is
because pitting can occur at potentials below E bd, as was demonstrated by metastable pitting in test 4. E bd corresponds to the potential for stable pit growth and
propagation only. Pits can nucleate, however, at any potential above the repassivation potential. Secondly, the effects that additional anions have on the pitting
behavior is concentration dependent and not mass dependent.
D. Results
For examples of data scans generated during each test, see Figs. 14, 10, 12, 11,
and 13.
384
Chapter 9
Test no.
E corr
(mV SCE)
E bd
(mV SCE)
E rp
(mV SCE)
i pass
µA/cm2
⫺50
⫺50
⫺50
⫺50
400
550
N/A
None
10
N/A
N/A
None
0.9
N/A
N/A
0.5
1
2
3
4
Conversion: 1 µA/cm2 ⫽ 10⫺6 A/cm2.
For Test 3, you have to decide which peaks to count as pitting events.
Potential
Number of metastable
pits in 10 min
Nucleation frequency
(events/s/cm2)
4
12
0.017
0.050
0V
0.25V
LABORATORY III
ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY AND
POLARIZATION RESISTANCE MEASUREMENTS
A.
Objective
In this experiment, corrosion rates will be estimated via the Stern–Geary relationship by measuring the polarization resistance, R p. This parameter will be measured in two ways: via conventional polarization resistance (PR) measurements
and via electrochemical impedance spectroscopy (EIS). In addition, the errors in
corrosion rate estimation introduced by the use of a finite scan rate and the presence of uncompensated ohmic resistance will be demonstrated.
B.
Background
There are many situations where a nondestructive estimation of corrosion rate is
necessary. However, electrochemical processes are inherently nonlinear, making
this task more difficult. Recall that many electrochemical processes have current–
voltage relationships that follow Butler–Volmer kinetics, which for a corroding
electrode would be expressed as
冢
i ⫽ i corr exp
η
η
⫺ exp
ba
bc
冣
(2)
Experimental Procedures
385
where η is the overpotential, b a is the anodic Tafel slope, and b c is the cathodic
Tafel slope. This equation indicates that unless the overpotentials are small compared to the Tafel slopes, large, potentially damaging currents will be generated
upon polarization of the material. However, for small overpotentials (usually on
the order of 10 to 15 mV), the Butler–Volmer equation can be linearized. This
was done by Stern and Geary [ JECS, 104, 56 (1959)] to arrive at the following
relationship:
i corr ⫽
b ab c
(b a ⫹ b c)R p
(3)
where R p is the polarization resistance. The polarization resistance is found to
be inversely proportional to the corrosion rate (the equation was developed upon
the assumption that both anodic and cathodic processes are under activation control). Therefore, by determining the polarization resistance of a material in an
environment, the corrosion rate can be estimated, assuming a knowledge of the
Tafel slopes (a more complete discussion of this can be found in the Significant
Observations section). Two of the most widely used methods for determining R p
are polarization resistance and electrochemical impedance spectroscopy. The two
techniques are explained in detail in Chapter 4. Briefly, both impose small amplitude perturbations of the potential and measure the current necessary to attain
such perturbations. While the PR measurements utilize a slow voltage ramp, EIS
measurements utilize a sinusoidal voltage waveform over a wide range of frequencies. The goal of both techniques is to evaluate the opposition of the electrochemical interface to the passage of current, which in many cases is inversely
related to the rate of the oxidation of the material. However, before using the R p
determined experimentally to estimate corrosion rate, complications due to scan
rate and uncompensated solution or ohmic resistance must be taken into account.
In order to explain the importance of these errors, the Randles equivalent circuit
is helpful (see Appendix 1).
The effect of too high a scan rate is due to the existence of the interfacial
capacitance, whereas the effect of uncompensated ohmic resistance is the result
of the solution resistance between the working electrode surface and the point
in solution at which the reference electrode senses this potential. These effects
are explained in more detail below.
C. Scan Rate
The impedance of a capacitor is inversely proportional to the frequency of the
oscillation of the voltage field across it. An equivalent way to state the same
property is that the current through a capacitor is directly proportional to the time
derivative of the potential field across it.
386
Chapter 9
i capacitor ⫽ C
dV
dt
(4)
Thus the importance of using a slow scan rate in the PR measurements (or equivalently, measuring down to a low frequency in the EIS measurements) can be seen.
At very slow sweep rates, dV/dt is small, so the current through the capacitor is
small. Therefore the impedance of the RC combination is only R p. As the scan
rate is increased, the fraction of current that flows through the capacitor increases,
and the measured impedance falls, since the parallel combination of the resistor
and capacitor will have a smaller impedance than the resistor alone. This effect
will cause an underestimation of R p and hence an overestimation of the corrosion
rate.
D.
Uncompensated Ohmic Resistance
The effect of uncompensated ohmic resistance is to overestimate R p, and hence
to underestimate the corrosion rate. Reference to the Randles circuit in Appendix 1 shows that if a slow enough scan rate is used, so that the capacitor effectively acts as an open circuit (i.e., its impedance is very high, hence the current
allowed through it is very low), the impedance value actually measured is R p ⫹
R Ω. This is true in all cases, even in conductive electrolytes. Because this effect
increases the impedance measured over that which is of interest, its magnitude,
relative to R p, is of interest. In conductive solutions, R Ω may be very small, but
it is never zero. In more resistive media, such as soil, R Ω may be a significant
fraction of, or even greater than, R p, and will then introduce large errors in the
corrosion rate calculations if the low-frequency limit of the impedance is used
as R p without correction for the effects of R Ω. Hence it is always important to
correct one’s data for the effect. At this point, one advantage of EIS over PR
measurements is obvious. EIS measurements, when conducted over a wide frequency range, can be used to determine the values of R Ω, the sum of R Ω and R p,
and C dl. The disadvantage is that the EIS measurements usually take more time
and require more sophisticated equipment.
The goals of this lab are to acquaint the student with the following effects:
the effect of reference electrode placement on R Ω, the effect of scan rate on R p
measurements, and the effect of R Ω on R p measurements.
E.
Experimental Procedures
Part A: Polarization Resistance
1. The Type 303SS samples are already in the solutions (0.01 M
H 2SO 4 ⫹ 0.02 M HCl) and have equilibrated for approximately 12 hours. The
instrumentation has been turned on and warmed up.
Experimental Procedures
387
Figure 15 PAR 352 SoftCorr III Linear Polarization experimental setup window.
2. Make sure the cell enable switch is turned off. Connect the cell cables
to the cell: green lead to the working electrode, red lead to the counter electrode,
and the reference to the white pin jack. If a dummy cell is being connected, attach
the leads as indicated in step 3 below.
a. To set up a new experiment select FILE, NEW SETUP from the opening window.
b. Select LINEAR POLARIZATION from the Technique combo box.
c. Use the default settings, except for the scan rate (see below), to run
the experiment.
d. Add the appropriate information for the working electrode density and
area. (D ⫽ 7.9 g/cm3, area ⫽ 3.14 cm2)
e. Enter the appropriate Reference Electrode (SCE).
388
Chapter 9
f. Enter the appropriate scan rate from #3 below.
g. Press the Cell Enable Switch on the potentiostat to enable the cell or
if a VersaStat is being used press the Cell On button.
h. Select RUN to start the experiment.
i. When finished with the scan, press the Cell Enable Switch to disconnect
the cell.
j. After each experiment is complete, save the data by selecting FILE
then SAVE AS. Enter a name for the data file and press RETURN.
3. There are four polarization resistance experiments that need to be run.
Two are experiments on dummy cells, and two are experiments on real cells. For
the dummy cell experiments, use the dummy cell labeled Polarization Resistance.
For the actual cell experiments, use the 303SS immersed in the acidified chloride
solution. Repeat steps 2a through 2f for each experiment.
a. Attach the working (green) lead at WE and the counter lead (red) at
CE.
1. Expt #1—Attach the reference cable to B; scan rate is to be 0.2
mV/s.
2. Expt #2—Attach the reference cable to B; scan rate is to be 10
mV/s.
b. For the 303SS in acidified chloride experiments, attach the green lead
to the working electrode, the red lead to the counterelectrode (graphite
rod), and the reference to the white pin jack.
1. Expt #3—Move the reference electrode close to but not touching
the working electrode; use a scan rate of 0.2 mV/s.
Figure 16 Wiring diagram for dummy cell with reference electrode (RE) at point B.
Experimental Procedures
389
Figure 17 Experimental wiring diagram for the 303SS in acidified chloride environment.
Expt #4—Move the reference electrode far from the working electrode; use a scan rate of 0.2 mV/s.
4. Data Analysis
For each experiment,
a. Select FILE, OPEN from the initial window. Recall the appropriate
data file.
b. Select ANALYZE to perform a polarization resistance calculation.
c. Press “R” from the pull-down menu or select Rp CALC with the
mouse. The calculation is done automatically. Record the value for R p.
(See Fig. 18).
d. Select FILE, SAVE to resave the data with the calculated results.
e. Repeat steps 4a through 4g for each experiment just performed.
2.
Part B: Electrochemical Impedance Spectroscopy
1. Use PAR 398 Electrochemical Impedance Spectroscopy software. If
you are unsure how to access this software ask a lab assistant for help.
2. The following four experiments will be run in this laboratory:
a. Dummy Cell (labeled EIS) with working electrode (green) at WE and
counterelectrode (red) at CE (see Fig. 20 for wiring diagram).
1. With RE attached to B, run 100 kHz to 0.1 Hz.
390
Chapter 9
Figure 18 PAR 352 SoftCorr III window displaying selections for a Rp calculation.
2. With RE attached to A, run 10 kHz to 10 Hz. This scan is run to
see the change in the ohmic resistance only, so you will not see
a full semicircle.
b. 303 Stainless steel in 0.01 M H 2SO 4 ⫹ 0.02 M HCl (see Fig. 17 for
wiring diagram).
1. With RE far from WE, run 100 kHz to 0.1 Hz.
2. With RE close to but not touching WE, run 10 kHz to 10 Hz. This
scan is run to see the change in the ohmic resistance only, so you
will not see a full semicircle.
3. To run experiments from 100 kHz to 0.1 Hz use the following procedure:
a. From the Main Menu select SETUP.
b. Select NEW TECHNIQUE and then select SINGLE SINE EIS Z( f ).
c. Set INITIAL FREQUENCY to 100 KHz. Set FINAL FREQUENCY
to 0.1 Hz. Change the AC AMPLITUDE to 20 mV rms. For the remaining options use the default settings.
d. Now press the Cell Enable switch to enable the cell and select RUN.
e. The data can be viewed during the experiment in several forms. To
Experimental Procedures
Figure 19
formed.
391
Typical PAR 352 SoftCorr III window after a Rp calculation has been per-
Figure 20 Wiring diagram for EIS dummy cell with the reference electrode (RE) at
points A or B.
392
Chapter 9
Figure 21 PAR M398 Single Sine experiment setup.
f.
g.
h.
4.
a.
b.
select the format for viewing, select the TO...option from the top
banner.
Once the experiments are complete, the message “After Run” will appear in the top right corner of the screen. To view both sets of data,
select MAIN from the banner. Next select FILES, and choose the GET
DATA option. Enter the name of the data file for the Single Sine Experiment (O1) and press RETURN.
Next, press the ESC key and select GRAPH from the banner. Select
STYLE from the banner to choose the format in which the data is
presented. In this case, you will want the data in the Nyquist format.
To select this, type “5.”
To obtain a printout of the data, select MAIN from the banner. Next
select FILE from the banner and choose the PRINT/PLOT DATA
option.
To run experiments from 10 kHz to 10 Hz use the following procedure:
From the Main Menu select SETUP.
Select NEW TECHNIQUE and then select SINGLE SINE EIS Z(f ).
Experimental Procedures
393
Figure 22 An example of the semicircle fit function of the PAR M398 EIS software.
c. Set INITIAL FREQUENCY to 10 KHz. Set FINAL FREQUENCY
to 10 Hz. Change the AC AMPLITUDE to 20 mV rms. For the remaining options use the default settings.
d. Now press the Cell Enable switch to enable the cell and select RUN.
5. Data analysis to determine R p, R Ω, and C dl.
a. From the Main Menu select GRAPH, CURVE, SEMICIRCLE FIT.
b. Use the mouse buttons or “B” and “E” (begin and end) to select point
limits on the semicircle. (One point should be a high value of the real
impedance while the other point should be a low value of the real impedance.)
c. Press F-10 to display the real impedance intercepts. Intercept 1 is
equivalent to R Ω. Intercept 2 is equivalent to R Ω ⫹ R P.
d. From this same screen the frequency at the maximum value of the
imaginary impedance can be determined. Move the cursor until you
have reached the maximum value of the imaginary impedance (top of
semicircle). Record the frequency value. Use Appendix 1 to calculate
C dl.
394
F.
Chapter 9
Results and Data Analysis
1. Polarization Resistance
Dummy cell
R p (measured) (Ω)
RE at “B,” scan rate ⫽ 0.2 mV/s
RE at “B,” scan rate ⫽ 10 mV/s
Experimental cell
R p (measured) (Ω)
RE close to WE, scan rate ⫽ 0.2 mV/s
RE far from WE, scan rate ⫽ 0.2 mV/s
2. Electrochemical Impedance Spectroscopy
Dummy cell
R Ω with RE at B ⫽
R Ω with RE at A ⫽
Rp ⫽
C dl ⫽
Experimental cell
R Ω with RE close ⫽
R Ω with RE far ⫽
Rp ⫽
G.
C dl ⫽
Questions
1. For the dummy cell polarization resistance experiments, calculate the
percentage error in R p at 0.2 mV/s and 10 mV/s.
Experimental Procedures
395
2. Compare the R p values from EIS to those obtained from PR measurements. Give reasons for any differences.
3. Based upon the EIS measurements, what would be the maximum scan
rate that could be used without having appreciable capacitive current?
4. Explain why errors resulting from the presence of appreciable ohmic
resistance are usually more severe than those that result from the use of too fast
a scan rate.
H. Significant Observations
This set of experiments has focused on the use of two nondestructive electrochemical techniques to measure polarization resistance and thereby estimate the
corrosion rate. In addition, the effects of scan rate and uncompensated ohmic
resistance were studied. Three main points should have been made by this lab:
(1) Uncompensated ohmic resistance is always present and must be measured
and taken into account before R p values can be converted into corrosion rates,
otherwise an overestimation of R p will result. This overestimate of R p leads to
an underestimate of corrosion rate, with the severity of this effect dependent upon
the ratio R p /R Ω. (2) Finite scan rates result in current shunted through the interfacial capacitance, thereby decreasing the observed impedance and overestimating
the corrosion rate. (3) Both of these errors can be taken into account by measuring
R Ω via EIS or current interruption and by using a low enough scan rate as indicated by an EIS measurement in order to force the interfacial capacitance to take
on very large impedance values in comparison to R p.
It should be pointed out that an exact knowledge of the Tafel slopes is
often unnecessary, because in the normal range of values experienced in electrochemical systems, the effect on the corrosion rate of wide changes in Tafel constants is small as compared to equivalent changes in R p. To prove this to yourself,
range the Tafel slopes from 40 to 200 mV/decade to find out what combinations
give more than a factor of 2 from the value of 100 mV/decade.
Finally, the basic equivalence of the two measuring techniques should be
appreciated. Although there are many ways to approach such a comparison, the
following simplified explanation will, we hope, give a more intuitive feeling for
the relationship between EIS and PR measurements. As stated above, both techniques rely on the frequency dependence of the impedance of the double-layer
capacitance in order to determine the polarization resistance. EIS uses low frequencies to force the capacitor to act like an open circuit. PR measurements use
a slow scan rate to do the same thing. To make comparisons, the idea of “equivalent scan rate” is useful. Suppose that a particular electrochemical system requires
EIS measurements to be made down to 1 mHz in order to force 99% of the
current through R p. What would the equivalent scan rate be for PR measurements?
A frequency of 1 mHz corresponds to a period of 1000 s. If the sine wave is
396
Chapter 9
approximated by a sawtooth wave of the same period and 10 mV peak-to-peak
amplitude such as would be typical in PR measurements, this frequency corresponds to 0.02 mV/s:
20 mV 1 cycle
⫻
⫽ 0.02 mV/s
cycle
1000 s
The ASTM standard for PR measurements stipulates that a scan rate of 6 V/h
(0.167 mV/s) be used. For a 10 mV p–p scan, this corresponds to an “equivalent
frequency” of 8 mHz. While there are many corrosion systems in which this is
a low enough frequency to resolve R p (⫹R Ω), there are also many cases where
it is not. In these cases, the estimates of the corrosion rate will be overestimates,
as pointed out in the section on scan rate effects.
I.
Results and Data Analysis
Part A: Polarization Resistance
Dummy cell
R p (measured) (Ω)
RE at “B”, scan rate ⫽ 0.2 mV/s
7052
RE at “B”, scan rate ⫽ 10 mV/s
5245
Experimental cell
R p (measured) (Ω)
RE close to WE, scan rate ⫽ 0.2
mV/s
57.48
RE far from WE, scan rate ⫽ 0.2
mV/s
80.63
Part B: Electrochemical Impedance Spectroscopy
Experimental cell
R Ω with RE close ⫽ 8.852 ohms
R Ω with RE far ⫽ 23.42 ohms
R p ⫽ 88.46 ⫺ 23.42 ⫽ 65.04 ohms
C dl ⫽
1
0.1 ⫻ 2π ⫻ 65.04
C dl ⫽ 2.44 ⫻ 10⫺2 F
Figure 23 Linear polarization curves from the dummy cell showing the influence of
scan rate.
Figure 24 Linear polarization of 303SS in an acidified chloride environment showing
the influence of solution resistance.
397
Figure 25 EIS results of dummy cell simulating two different solution resistances. At
point A no solution resistance is simulated. At point B a solution resistance of 4700 Ω
is simulated.
Figure 26 EIS results of 303SS in an acidified chloride environment showing the influence of solution resistance.
398
Experimental Procedures
399
Figure 27 EIS data shown in Fig. 26 scanned to very low frequencies.
Dummy cell
R Ω with RE at B ⫽ 1.248 ohms
R Ω with RE at A ⫽ 4645 ohms
R p ⫽ 6861 ⫺ 4645 ⫽ 2216 ohms
C dl ⫽
1
15.85 ⫻ 2π ⫻ 2216
C dl ⫽ 4.5 ⫻ 10⫺6 F ⫽ 4.5 µF
J. Data Analysis
A. Polarization resistance
Dummy cell
R p (measured) (Ω)
RE at “B”, scan rate ⫽ 0.2 mV/s
7052
400
Chapter 9
RE at “B”, scan rate ⫽ 10 mV/s
5245
Experimental cell
R p (measured) (Ω)
RE close to WE, scan rate ⫽ 0.2 mV/s
57.48
RE far from WE, scan rate ⫽ 0.2 mV/s
80.63
B. Electrochemical impedance spectroscopy
Dummy cell
R Ω with RE at B ⫽ 1.248 ohms
R Ω with RE at A ⫽ 4645 ohms
R p ⫽ 6861 ⫺ 4645 ⫽ 2216 ohms
1
15.85 ⫻ 2π ⫻ 2216
C dl ⫽ 4.5 ⫻ 10⫺6 F ⫽ 4.5 µF
C dl ⫽
Experimental cell
R Ω with RE close ⫽ 8.852 ohms
R Ω with RE far ⫽ 23.42 ohms
R p ⫽ 88.46 ⫺ 23.42 ⫽ 65.04 ohms
1
0.1 ⫻ 2π ⫻ 65.04
C dl ⫽ 2.44 ⫻ 10⫺2 F
C dl ⫽
APPENDIX 1: CALCULATION OF THE DOUBLE
LAYER CAPACITANCE
For the Randles circuit:
The total impedance of this circuit is
Z total
冢
⫺1
冣
1
⫽ Rs ⫹
⫹ jωC dl
Rp
⫽ RS ⫹
Rp
1 ⫹ j ωR p C dl
where
Rs
Rp
ω
C dl
j
denotes
denotes
denotes
denotes
denotes
the solution resistance
the polarization resistance
frequency
the double layer capacitance
imaginary number
Experimental Procedures
401
Figure 28 Randles’ circuit that serves as an electrical analog of the corroding interface.
Multiplying by the complex conjugate and rearranging into the real and imaginary
components, we obtain
Z total ⫽ Z real ⫹ Z imaginary
Z total ⫽
R s(1 ⫹ ω2R 2pC 2dl) ⫹ R p
jωR pC dl
⫺
1 ⫹ ω2R 2pC 2dl
1 ⫹ ω2R 2pC 2dl
Using the Nyquist Plot to Find C dl
Define ω max,Nyq as the frequency at which the imaginary component of the
impedance has its largest value.
Find ω max,Nyq by taking the derivative of the imaginary impedance component with respect to ω and setting equal to zero.
冢
∂Z j
⫺jωR p C dl
∂
⫽
∂ω
∂ω 1 ⫹ ω 2 R 2pC 2dl
冣
⫽
⫺ j R p C dl(1 ⫹ ω 2R 2pC 2dl) ⫺ j ωR p C dl(2ωR 2pC 2dl)
(1 ⫹ ω 2R 2pC 2dl)2
⫽
⫺ j RpCdl(1 ⫺ ω2 R 2pC 2dl)
(1 ⫹ ω 2R 2p C 2dl)
402
Chapter 9
Setting the derivative equal to zero, we obtain
0 ⫽ (1 ⫺ ω 2max ,Nyq R 2p C 2dl)
Cdl ⫽
1
ω max, Nyq Rp
Using the Bode Plot to Find Cdl
Define ωmax,Bode as the frequency at which the phase angle has the highest
magnitude. (This is the frequency at which the ratio of the imaginary
impedance component to the real impedance component is maximum.)
Note: The frequency selected for ωmax,Bode is not the same as the frequency
selected using the Nyquist plot.
Find ωmax,Bode by taking the derivative of this ratio with respect to ω and
setting equal to zero.
冢
冣
∂(Z j /Z r )
⫺jωR 2p C dl
∂
⫽
∂ω
∂ω Rs ⫹ R p ⫹ ω2Rs R 2p C 2dl
⫽
⫺ j R 2p Cdl (R s ⫹ R p ⫹ ω2 RsR 2p C 2dl ) ⫺ jωR 2p C dl (2ωRs R 2pC 2dl)
(Rs ⫹ Rp ⫹ ω 2 RsR 2p C 2dl)2
⫽
⫺ j R 2p Cdl(Rs ⫹ Rp ⫺ ω 2Rs R 2p C 2dl)
(Rs ⫹ R p ⫹ ω 2R s R 2pC 2dl) 2
Setting the derivative equal to zero, we obtain
0 ⫽ (R s ⫹ R p ⫺ ω 2max,Bode R s R 2p C 2dl)
Cdl ⫽
C dl ⫽
1
ωmax,Bode R p
1
ω max,Bode Rp
冢
冣
Rs ⫹ Rp
Rs
冢
1⫹
Rp
Rs
冣
1/2
1/2
APPENDIX 2: IMPEDANCE MEASUREMENTS IN DETAIL
Impedance measurements performed with PAR M398 software in conjunction
with a potentiostat and a lock-in amplifier or frequency response analyzer are
obtained using one or both of two techniques, depending on the frequency range
Experimental Procedures
403
of interest. The lower frequency range (5 Hz and lower) is collected using a
multisine technique, while the upper frequency range (5 Hz to 100 kHz) is collected using a single sine technique. For the experiments performed in this laboratory from 100 kHz to 0.1 Hz it is necessary to use both techniques, whereas the
experiments from 10 kHz to 10 Hz can be performed using only the single sine
technique. The auto execute mode is most convenient for collecting data over
both frequency ranges, as the data can be automatically merged into one data
file and collected in a single, automated experiment.
Single Sine Technique
The single sine technique is used to acquire data over the frequency range 5 Hz
to 100 kHz when a LIA is used and 50 µHz to 100 kHz when a FRA is used.
To access the single sine technique from the main menu select SETUP, then
select NEW TECHNIQUE from the banner. Select the Single Sine option. The
options from the single sine technique that were specified in this lab are discussed
in the following paragraphs.
Initial Frequency
This option allows the user to specify the frequency at which the impedance
measurements will begin. The value entered must be between 5 Hz and 100 kHz
(LIA) or between 50 µHz and 100 kHz (FRA). In this lab 100 kHz and 10 kHz
were used for initial frequencies.
Final Frequency
This option allows the user to specify the frequency at which the impedance
measurements will terminate. The value must fall in the same range stated for
Initial Frequency. For the LIA stations, the limit was set to 5 Hz for the scans
ranging from 100 kHz to 0.1 Hz, and the frequencies below 5 Hz were collected
using the multisine technique. For the FRA stations, 0.1 Hz was entered. For
experiments ranging from 10 kHz to 10 Hz, the multisine technique was not
required for either FRA or LIA stations, and this parameter was set to 10 Hz.
Points/Decade
This parameter specifies how many data points will be collected over each decade
of frequencies, a decade being defined as an order of magnitude base 10 (i.e., 1
to 10 Hz, 1000 to 100,000 Hz, etc). The program allows values from 0 to 20 to
be entered. In laboratory work it is customary to collect between 5 and 15 data
points per decade. In this laboratory 10 data points per decade were collected.
404
Chapter 9
AC Amplitude
This option allows the user to define the amplitude of the AC perturbation applied
to the system for determination of impedance response. The AC signal is usually
a small voltage signal in the range of 5 to 20 mV for typical applications. Small
values perturb the system to a lesser degree and do not disturb the steady state
as much as large values. Thus smaller AC signals are “less destructive” than
larger values. However, larger values may be able to increase the signal-to-noise
ratio observed in the system response. These basic ideas demonstrate the tradeoffs
in selecting an AC amplitude.
DC Potential
This parameter specifies the potential upon which the AC signal is imposed.
Oftentimes, to maintain the steady state of the system, the DC potential is selected
as 0 mV vs. open circuit. However, the response of a system can be evaluated
over a potential range by running successive experiments with different DC potentials. Thus the impedance response of a system could be mapped to a potentiodynamic polarization curve by specifying various DC potentials defined by the
polarization curve. In all experiments performed in this laboratory, the DC potential was set to 0 mV versus open circuit.
Condition Time
This parameter defines the length of time that the system will be held at a potential
defined by Condition Potential. A condition time may be useful to study systems
at potentials away from open circuit. By applying the desired potential for a
length of time before the experiment is run, the system is allowed to stabilize
before the data is collected. In the lab #3 experiments, this value is set to zero vs.
open circuit, since the samples are already at a steady-state open circuit potential.
Condition Potential
This option allows the user to specify a potential at which the sample will be
held for a period of time defined by Condition Time. Normally this potential
would be set to the same value as DC potential. Using Condition Time and
Condition Potential allows the system to stabilize at an applied potential before
data collection is initiated. Remember that a system does not immediately attain
a stable response to an applied potential (lab #1 part B).
Open Circuit Delay
This option allows the user to specify a length of time prior to the impedance
experiment during which the system will remain under free corrosion conditions.
Experimental Procedures
405
Note that this option precludes using a condition potential and vice versa. This
option is useful if it is known that the system requires a significant time to stabilize under open circuit conditions. Thus the software can be told to wait a specified amount of time before initiating the impedance scan.
Multisine Technique (5 ⴛ 10ⴚ5 ⴚ5 Hz)
The multisine technique is used to acquire data over the frequency range 5 ⫻
10⫺5 Hz to 5 Hz. To access the multisine technique from the main menu select
SETUP, and then select NEW TECHNIQUE. Select the Multisine option. The
options from the multisine technique that were specified in this lab are discussed
in the following paragraphs. Although the multisine technique commonly only
provides one or two decades of information out of a total of six or seven, the
data from this frequency range is significant, as they often give insight into the
polarization resistance and thus the corrosion rate of the material.
Initial Frequency
This option allows the user to specify the frequency at which the impedance
measurements will begin. The value entered must be between 50 µHz and 100
mHz.
Final Frequency
The final frequency is automatically determined by setting the initial frequency.
The value of the final frequency is Initial Frequency multiplied by 113.
Points/Decade
This parameter specifies how many data points will be collected over each decade
of frequencies, a decade being defined as an order of magnitude base 10 (i.e., 1
to 10 Hz, 1000 to 100,000 Hz, etc). The program allows values from 0 to 20 to
be entered. In laboratory work it is customary to collect between 5 and 15 data
points per decade. In this laboratory 10 data points per decade were collected.
AC Amplitude
This option allows the user to define the amplitude of the AC perturbation applied
to the system for determination of impedance response. The AC signal is usually
a small voltage signal in the range of 5 to 20 mV for typical applications. Small
values perturb the system to a lesser degree and do not disturb the steady state
as much as large values. Thus smaller AC signals are “less destructive” than
larger values. However, larger values may be able to increase the signal-to-noise
ratio observed in the system response. These basic ideas demonstrate the tradeoffs
in selecting an AC amplitude.
406
Chapter 9
DC Potential
This parameter specifies the potential upon which the AC signal is imposed.
Oftentimes, to maintain the steady state of the system, the DC potential is selected
as 0 mV vs. open circuit. However, the response of a system can be evaluated
over a potential range by running successive experiments with different DC potentials. Thus the impedance response of a system could be mapped to a potentiodynamic polarization curve by specifying various DC potentials defined by the
polarization curve. In all experiments performed in this laboratory, the DC potential was set to 0 mV versus open circuit.
Condition Time
This parameter defines the length of time that the system will be held at a potential
defined by Condition Potential. A condition time may be useful to study systems
at potentials away from open circuit. By applying the desired potential for a
length of time before the experiment is run, the system is allowed to stabilize
before the data is collected. In the lab #3 experiments, this value is set to zero vs.
open circuit since the samples are already at a steady-state open circuit potential.
Condition Potential
This option allows the user to specify a potential at which the sample will be
held for a period of time defined by Condition Time. Normally this potential
would be set to the same value as DC potential. Using Condition Time and
Condition Potential allows the system to stabilize at an applied potential before
data collection is initiated. Remember that a system does not immediately attain
a stable response to an applied potential (lab #1 part B).
Open Circuit Delay
This option allows the user to specify a length of time prior to the impedance
experiment during which the system will remain under free corrosion conditions.
Note that this option precludes using a condition potential and vice versa. This
option is useful if it is known that the system requires a significant time to stabilize under open circuit conditions. Thus the software can be told to wait a specified amount of time before initiating the impedance scan.
LABORATORY IV
PART A: CURRENT DISTRIBUTION
A.
Objective
The objective of the current distribution lab is to explore the influence of electrode
geometry, solution conductivity, and electrode polarization characteristics on ca-
Experimental Procedures
407
thodic current–potential distributions. The influence of these three parameters
will be assessed experimentally by potential mapping techniques. The geometry
chosen represents a 2D simulation of a 3D tube–tubesheet heat exchanger. Students will potentiostatically polarize the entrance to the tube–tubesheet arrangement to ⫺1.0 V vs. SCE and determine the potential distribution as a function
of position down the tube. Solution conductivity will be varied to show its effect
on the resulting potential distribution. The component of current density parallel
to the center line of the tube will be calculated.
B. Approach
The student will apply an impressed cathodic current to the entrance of the tube–
tubesheet arrangement using a potentiostat in the conventional three-electrode
arrangement with a counterelectrode (CE) and controlling reference electrode
(RE). These electrodes will be placed at a distance from the tube–tubesheet arrangement as illustrated in Fig. 29. The working electrode (WE) consists of 304
stainless steel, the RE is a saturated calomel electrode (SCE), and the two test
Figure 29 Tube–tubesheet simulation schematic.
408
Chapter 9
solutions are 0.06 M NaCl and 0.6 M NaCl. For this experiment the PAR 352
SoftCorr III software will be utilized to apply the potentiostatic polarization required.
Two basins are provided, the first containing 6 liters of 0.06 M NaCl and
the second containing 6 liters of 0.6 M NaCl. The WE samples should not be
completely immersed. Ensure that the stainless steel sheets are in the grooves of
the Plexiglas provided.
Prior to applying a potential of ⫺1.0 V, the open circuit potential will be
monitored. Verify with the second “measuring RE” (connected to the WE through
a digital voltmeter) that the open circuit potential is approximately the same no
matter where the measuring RE is placed with respect to the WE surface. Cell
connections, shown in Fig. 30 are as follows:
PAR 273 electrometer:
1.
2.
3.
4.
5.
Green lead: connect to stainless steel working electrode.
Red lead: connect to graphite counter electrode.
Black lead: not connected.
RE pin connector: connect to controlling RE.
Toggle switch: toggle to ext. cell.
Figure 30 Wiring diagram for tube-tubesheet.
Experimental Procedures
409
Digital voltmeter (DVM):
1. Ground lead (black): connect to measuring RE.
2. Positive lead (red): connect to steel WE.
NOTE: Before touching anything other than the “measuring reference”turn
the cell OFF and press the cell enable switch to disconnect the cell from the
potentiostat.
Experimental Procedure
Setup the experiment using PAR 352 SoftCorr III software:
a.
b.
c.
d.
e.
f.
g.
h.
i.
From the main menu of the software select FILE.
Select NEW SETUP.
Select POTENTIOSTATIC from the Technique combo box.
Set the INITIAL POT to “⫺1.0” volts. The potentiostat will apply
⫺1 V vs. the RE.
Select the TIME STEP and set to “3600” seconds.
Set the TIME/POINT to “5” seconds.
Set the REFERENCE ELECTRODE TO “SCE”. Figure 31 shows the
POTENTIOSTATIC Technique combo box after setup.
Press the Cell Enable Switch on the potentiostat to activate the cell.
Press RUN to start the experiment.
Section 1
After activating the cell to apply the cathodic potential, the system should be
allowed to stabilize for 5 minutes. This stabilization can be observed by noting
the stability of the current displayed on the monitor or the potential monitored
by the measuring RE (read from the DVM).
After the system stabilizes, measure the potential at the various marked
positions down the length of the tube using the second measuring RE. Leave the
PSTAT on while making measurements with the measuring RE. Allow 2 minutes
before recording the value on the data sheet provided. Take care to keep the basin
stable; solution flow can affect the measurements.
Record the cell current (Icell) from the PAR 273 front panel or the Versastat
monitor. Also record the cell voltage (Vcell) by using the DVM to measure the
potential between the WE and CE (to do this you must temporarily connect the
black DVM lead to the CE).
When you have completed all of the measurements outlined above, stop the
potentiostatic hold by selecting EXPERIMENT from the menu bar and selecting
410
Chapter 9
Figure 31 PARC 352 SoftCorr III Potentiostatic technique combo box.
STOP. Deactivate the cell by pressing the Cell Enable switch. Do not save the
data file.
Section 2
Move the Plexiglas support, CE, and WEs to the second basin and repeat the
above experiment. IF YOU ARE PART OF THE SECOND GROUP, IT IS IMPORTANT TO RINSE THE ELECTRODES WITH DISTILLED WATER
WHEN MOVING THE SETUP FROM THE 0.6 M TO THE 0.06 M SOLUTION
TO AVOID CONTAMINATION FROM THE MORE CONCENTRATED SOLUTION. As before, apply a potential of ⫺1.0 vs. controlling RE using the controlling RE/CE arrangement described previously and allow it to stabilize for 5
minutes. Measure the potential at the various marked positions down the length
of the tube using the measuring RE, allowing 2 minutes before recording the
measurement on the data sheet provided. Record the cell current from the PAR
Experimental Procedures
411
Figure 32 Measured potential versus position.
273 front panel or the Versastat monitor. Also record the cell voltage (Vcell) by
using the DVM to measure the potential between the WE and CE (to do this you
must temporarily connect the black DVM lead to the CE).
When you have completed all of the measurements outlined above, stop the
potentiostatic hold by selecting EXPERIMENT from the menu bar and selecting
412
Chapter 9
Figure 33 Measured potentials for simulated tube–tubesheet experiment.
STOP. Deactivate the cell by pressing the Cell Enable switch. Do not save the
data file.
Analysis
Plot the measured potential versus position for each test solution on the graphs
provided. For each solution, determine the component of applied current density
parallel to the center line of the tube as a function of position by calculating the
Table 3
Position
(cm)
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Potential and Current Distribution Data for 0.06 M NaCl
Potential
(mV)
Potential grad.
(mV/cm)
Current
density
(mA/cm2)
Current
density
(µA/cm2)
⫺889
⫺821
⫺769
⫺743
⫺726
⫺719
⫺714
⫺713
29.60
27.20
20.80
10.40
6.80
2.80
2.00
0.40
0.1717
0.1578
0.1206
0.0603
0.0394
0.0162
0.0116
0.0023
171.68
157.76
120.64
60.32
39.44
16.24
11.60
2.32
Experimental Procedures
Table 4
Position
(cm)
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
413
Potential and Current Distribution Data for 0.6 M NaCl
Potential
(mV)
Potential grad.
(mV/cm)
Current
density
(mA/cm2)
Current
density
(µA/cm2)
⫺968
⫺956
⫺950
⫺946
⫺945
⫺942
⫺940
⫺938
8.53
4.80
2.40
1.60
0.40
1.20
0.80
0.80
0.4250
0.2390
0.1195
0.0797
0.0199
0.0598
0.0398
0.0398
424.96
239.04
119.52
79.68
19.92
59.76
39.84
39.84
potential gradient (difference between two successive potentials divided by 2.5
cm) at each position and multiplying the result by the solution conductivity (provided). Plot current density as a function of position. Sample data are provided
in Tables 3 and 4 for the two solutions of different concentration. Figures 33
and 34 show the measured potentials and calculated current densities, respectively. Calculate the cell power in each case by multiplying Vcell ⫻ Icell. Describe
qualitatively the effect of solution conductivity on the results.
Figure 34 Calculated current density for simulated tube–tubesheet experiment.
414
Chapter 9
Current Distribution Experiment
Sample Data Sheet
Solution concentration: 0.06 M NaCl
Conductivity: 0.0058 (ohm-cm)⫺1
Applied potential: ⫺1.0 V
Tube diameter: 1.5 cm
Cell voltage (Vcell) (WE-CE):
Cell current (Icell) from 273 display or Versastat monitor:
Cell power (VcellIcell):
Reference
position
(cm)
Potential gradient
(mV/cm)
⫺1000
0
1
Potential
(mV)
0
mV/3.75 cm
⫽
2
2.5
mV/2.5 cm
⫽
3
5
mV/cm
mV/2.5 cm
⫽
4
mV/cm
7.5
mV/cm
mV/2.5 cm
mV/cm
5
10
mV/2.5 cm
⫽
6
12.5
mV/cm
mV/2.5 cm
⫽
mV/cm
Current
density
(mA/cm2)*
Current
density
(µA/cm2)
Experimental Procedures
7
415
15
mV/2.5 cm
⫽
8
mV/cm
17.5
mV/2.5 cm
⫽
mV/cm
* mV/cm ⫻ 1/ohm-cm ⫽ mA/cm2
1 µA ⫽ 10⫺3 mA
Current Distribution Experiment
Sample Data Sheet
Solution concentration: 0.6 M NaCl.
Conductivity: 0.0498 (ohm-cm)⫺1
Applied potential: ⫺1.0 V
Tube diameter: 1.5 cm
Cell voltage (Vcell) (WE-CE):
Cell current (Icell) from 273 display or Versastat monitor:
Cell power (VcellIcell):
Reference
position
(cm)
Potential gradient
(mV/cm)
⫺1000
0
1
Potential
(mV)
0
mV/3.75 cm
⫽
2
2.5
mV/2.5 cm
⫽
3
mV/cm
5
mV/cm
mV/2.5 cm
⫽
mV/cm
Current
density
(mA/cm2)*
Current
density
(µA/cm2)
416
Chapter 9
Reference
position
(cm)
4
Potential
(mV)
Potential gradient
(mV/cm)
7.5
10
12.5
15
mV/cm
mV/2.5 cm
⫽
8
mV/cm
mV/2.5 cm
⫽
7
mV/cm
mV/2.5 cm
⫽
6
Current
density
(µA/cm2)
mV/2.5 cm
⫽
5
Current
density
(mA/cm2)*
17.5
mV/cm
mV/2.5 cm
⫽
mV/cm
* mV/cm ⫻ 1/ohm-cm ⫽ mA/cm2
1 µA ⫽ 10⫺3
LABORATORY IV
PART B: MASS TRANSPORT EFFECTS
A.
Objective
The objective of the mass transport lab is to explore the effect of controlled
hydrodynamics on the rate at which a mass transport controlled electrochemical
reaction occurs on a steel electrode in aqueous sodium chloride solution. The
experimental results will be compared to those predicted from the Levich equation. The system chosen for this experiment is the cathodic reduction of oxygen
at a steel electrode in neutral 0.6 M NaCl solution. The diffusion-limited cathodic
current density will be calculated at various rotating disk electrode rotation rates
and compared to the cathodic polarization curve generated at the same rotation
rate.
Experimental Procedures
417
B. Approach
A cathodic potentiodynamic scan will be conducted on an AISI 1020 steel rotating disk electrode (RDE) that has been polished to a 600 grit finish. The electrolyte consists of 2 liters of 0.6 M NaCl, the counterelectrode is a graphite rod,
and an SCE will be used for the reference electrode. Make the connections shown
below with the cell off, taking care to keep all leads away from the moving parts.
Ensure that electrical contact is made between the RDE and the rotator using the
DVM.
Cell connections, shown in Fig. 35, are as follows:
1.
2.
3.
4.
5.
Green lead: connect to steel working electrode.
Red lead: connect to graphite counter electrode.
Black lead: connect the cell ground to rotator.
RE pin connector: connect to controlling RE.
Toggle switch: toggle to ext. cell.
Figure 35 Wiring diagram for rotating disk electrode.
418
Chapter 9
Your results will depend upon the length of time the sample is exposed to the
electrolyte prior to the scan, so it is best to set up the software before immersing
the sample. After setting up the software to step g shown below, lower the electrode the rest of the way; continue with step h and start the experiment. Do not
lower the electrode more than 1.5″ below the water line; the seam between the
mantle and the sample shank should not be immersed.
C.
Experimental Procedure
Set up the experiment using PAR 352 SoftCorr III software:
a. From the main menu, select FILE, then select NEW SETUP.
b. Select POTENTIODYNAMIC from the Technique combo box.
c. For INITIAL DELAY enter “300” to monitor the open circuit potential
for 300 seconds.
d. Select INITIAL POTENTIAL, enter “0”, and click on the box beside
OC so that an “X” appears in the box. This setting will start the cathodic scan at 0 volts vs. open circuit.
e. Select FINAL POTENTIAL and enter “⫺1.0” to get ⫺1 volts vs. the
RE. (Make sure that there is no “X” in the box beside OC on the FINAL
POTENTIAL line or else the experiment will terminate at ⫺1 V vs.
OCP!)
f. Select SCAN RATE and enter “5” mV/s.
g. Add the appropriate information for the REFERENCE ELECTRODE,
DENSITY, EQUIVALENT WEIGHT, and the AREA (see the experimental data sheet below). The completed setup for the potentiodynamic
test technique is shown in Fig. 36.
h. For the first test set the rotation speed to 500 rpm. Turn the rotator on
and press the cell enable switch to activate the cell. Lower RDE into
solution. Select RUN to begin the experiment. Because the open circuit
potential is near ⫺500 mV vs. SCE, the 500 mV cathodic scan should
take approximately 100 seconds.
i. When the experiment is finished, save the data to a file by selecting
FILE and SAVE. Note the open circuit potential and the limiting cathodic current density. Figure 37 shows a typical cathodic scan under
diffusion limited conditions.
j. Close the current window which shows the last cathodic scan performed.
k. Press the Cell Enable switch to disconnect the cell.
Following each cathodic scan, but before repeating the experiment at a different
rotation rate, the WE should be polished on the 600 grit paper provided. A small
Experimental Procedures
419
Figure 36 PARC 352 SoftCorr III Potentiodynamic technique combo box window.
spring is inserted into the threaded back of the RDE to establish electrical contact
between the RDE and the rotator; when removing the RDE from the mandrel to
polish the electrode surface be careful not to dislodge and lose it. Before running
the experiment, again ensure that electrical contact is made between the rotator
and the RDE with the DVM. Repeat steps h through k above at rotation rates
of 2500 and 5000 rpm, respectively. Press RUN from the POTENTIOSTATIC
experiment to start the test using the setup from the previous scan.
Figure 38 shows typical data for this experiment. To overlay the three cathodic scans, open each data file using the FILE, OPEN DATA command. From
VIEW select OVERLAID FILES and select the files.
D. Analysis
Calculate the diffusion-limited current density that is expected for each rotation
rate assuming a dissolved oxygen concentration of 6–8 ppm (see experimental
data sheet for calculation procedure).
Figure 37 Cathodic polarization of carbon steel RDE in 0.6 M NaCl at 500 rpm.
Figure 38 Cathodic polarization scans for rotating disk electrode experiment.
420
Experimental Procedures
421
1. Why is the open circuit potential more positive when the rotation rate
is increased? (Hint: use mixed potential theory to prove that it should be!)
2. How does the calculated limiting C.D. compare to the actual? What
additional factors may account for any differences?
3. What is the effect of increasing surface roughness and corrosion product layer thickness on results?
4. What is wrong with the assumption of purely one-dimensional diffusion? It turns out that a small-diameter rotating disk may be more appropriately
described by hemispherical diffusion. The limiting current density in the hemispherical case is greater than that in the linear case by a factor that remains
constant with time and rotation rate. This situation is in fact observed in Fig.
39, which compares the experimental data to the predicted results assuming 1D
diffusion. (See Bard and Faulkner. Electrochemical Methods—
Fundamentals
and Applications, pp. 136–146.)
Experimental Data Sheet
Density:
Equivalent weight:
Electrode area:
Rotation
rate(rpm)
7.8 g/cm3
28 g/mole-equiv
PAR rotators ⫽ 1 cm2
Pine rotators ⫽ 0.317 cm2
OCP
(mV vs. SCE)
Exp. limiting C.D.
(µA/cm2)
Calc. limiting C.D.
(µA/cm2)
500 rpm
2500 rpm
5000 rpm
The Levich equation:
il ⫽ 0.62 nFD2/3 Cb ν⫺1/6 ω1/2
For oxygen reduction:
D⫽
n ⫽
Cb ⫽
⫽
F⫽
ν ⫽
1.9 ⫻ 10⫺5 cm2 /s
4 equiv/mole
6–8 ppm ⫽ [(6–8 mg/liter)*(1 liter/103 cm3)]/(32 ⫻ 103 mg/mole)
0.22 ⫻ 10⫺6 moles/cm3
96487 coulombs/equiv
1.0 ⫻ 10⫺2 cm2 /sec
422
Chapter 9
Figure 39 Experimental and calculated diffusion-limited current densities for RDE experiment.
Rewriting the Levich equation in a more abbreviated and convenient form:
il ⫽ K ω1/2
where K ⫽ 80.7 ⫻ 10⫺6 coulombs/cm2-s1/2 and ω is in units of radians/s.
When rpm are expressed in units of radians/s the resulting units for il are
coulombs/cm2-s. Recognizing that 10⫺6 coulombs/s is equivalent to microamperes, it is easy to determine the theoretical limiting current density in µA/cm2
from the abbreviated form of the Levich equation.
Hence at 50 rpm:
ω ⫽ (50 rev/min)*(1 min/60 s)*(2 rad/rev ⫽ 5.24 rad/s
and
il ⫽ 185 µA/cm2
You should be able to calculate a theoretical “predicted” limiting current density
for each rpm selected; the results are shown in Fig. 39.
Index
Active region, hidden, 60, 62
Admittance, 304
Anodic protection, 69
to mitigate SCC, 72
vs. cathodic protection, 70
Anodization, 61, 302
sealing, 308
Applied current, 42
Artificial crevice electrode, 271
ASTM standards
A 262, 93, 114
D 2776, 130
D 610, 331
D 714, 331
E 112, 102
G 106, 132
G 48, 90
G 59, 130
G 67, 93
Avesta cell, 98
Bleedthrough rusting, 25
Bode plot, 134, 226
Breakpoint frequency, 326
Butler–Volmer kinetics, 126, 215
Capacitance
double layer, 130
measurement lead, 319
pseudo, 134
Cathode :anode ratio
galvanic corrosion, 51
localized corrosion, 76
Cathodic loops, 63, 67
Cell voltage, 37
Chromate
anodic inhibition, 263
cathodic inhibition, 274
effect on metastable pits, 264
effect on stable pits, 267
Complexation, 218
Conservation of charge, 6, 48, 76,
81
Conversion coatings, 282
cerium, 287, 337
chromate, 282
testing by anodic polarization,
283
Counter electrode, 63, 73
reactions at, 36
Crevice corrosion, 30
alloy effects, 252
monitoring, 244
stages, 74
Critical crevice solution, 73, 81, 239
Critical current density, 62
Current distribution (see Wagner
number)
Current noise (see Electrochemical
noise)
Descaling, 257
423
424
Diffusion limited current density, 40,
155
Diffusivity, 158
effective, 225
Driven cell (see Electrochemical cells)
Driving cell (see Electrochemical cells)
Electrochemical cells, 39, 65, 154, 279,
416
driven, 27
driving, 27
polarity, 28
Electrochemical impedance, 130, 298
correlation to salt spray, 300
evaluation of anodization, 306
local, 340
Electrochemical noise, 115
analysis issues, 118
spectral analysis, 119, 350
statistical analysis, 118, 347
Electromotive (emf) series, 10
E-pH diagrams (see Pourbaix diagrams)
EPR testing
double loop, 102
single loop, 101
Equilibrium vs. steady state, 46
Equivalent circuit model
active surface, 135
degraded polymer coating, 325
pitting, 312
porous oxides, 131, 291, 309, 312
Erosion, 173
Evans diagram, 32, 41, 217
Exchange current density, 32, 41, 61,
82
Faraday
constant, 4, 85
laws, 4, 213, 245, 267
on passivity, 59
Ferric chloride, 90
Flag electrode, 99
Foil penetration, 268
Index
Galvanic
corrosion, 47, 66, 361
prediction, 47
series, 49
Gaseous oxidation, 7
Gibbs free energy, 9
Huey test, 93
Hydrogen cracking, 237
Hydrogen evolution, 34, 242
Hydrolysis, 74, 274
Interfacial potential difference, 11, 50
Intergranular corrosion testing, 91
Isopotential lines, 180
Knife-edge washers, 95
Koutecky–Levich equation, 215, 279
Linear polarization (see Polarization resistance)
Localized corrosion, 73
accelerated coupon testing, 88
electrochemical phenomenology, 80
galvanostatic testing, 113
limitations on rates, 78, 241
peak rates in pitting, 85
potentiostatic tests, 111
stability, 77
test techniques, 87
Mass loss, calculation, 5
Mass transport, 151
circular tube, 166
correlations, 158
impinging jet, 169
Metastable pits, 104, 260, 379
Mils per year (mpy), definition, 5
NAMLT test, 93
Index
Nernst
diffusion layer, 157, 225
equation, 16, 33, 39, 216
Nyquist plot, 134
Ohmic drop
annular cells, 185
circular pipe, 199
crevice, 197
microelectrode disk, 195
near inclusions, 203
parallel plates, 183
rotating cylinder, 190
rotating disk, 191
Operational amplifier, 29
Organic coatings, 317
adhesion loss, 324
DC methods to evaluate defects, 318,
321
EIS to evaluate, 319
water uptake, 323
Overpotentials, 178
Oxidation, definition, 28
Oxygen concentration, 152
Oxygen reduction reaction, 18, 21, 75,
144, 152, 216, 242, 279
Passivation (see Descaling)
Passivation potential, 60
Passivity, 57
cathodic kinetics, 65
film growth, 234
fluid velocity effects, 69, 156
galvanic couples, 66
thick film, 57
thin film, 58
Pitting potential
critical temperatures, 112
distributions, 110, 284
effect of charge density, 106
effect of surface finish, 259
nomenclature, 83, 105, 259, 264
repassivation, 103, 111, 239, 378
vertex current density effect, 108
425
Polarization curves
complications, 137
cyclic, 80, 104, 375
hysteresis, 40, 81
Polarization resistance
definition, 127
deviations from linearity, 138
effect of Tafel slopes, 127
potential distribution effects, 147
Potential distribution, 175
Potential noise (see Electrochemical
noise)
Potentiostat, 29, 88, 319, 365
Pourbaix diagrams, 17, 151
alloys, 22
effect of temperature, 22
metastable species, 22
types of lines, 18
Reaction rates, range, 34
Redox reactions, 44, 88, 138, 207
Reduction, definition, 28
Reference electrode, 11, 361, 407
conversion between scales, 16
Cu/CuSO 4 , 16
Hg/Hg 2 SO 4, 14
leak rate, 15
NHE, 12
pseudoreference, 346
SCE, 14
Repassivation potential (see Pitting potential)
Reynolds number, 159
Rotating cylinder electrode, 164
current distribution to, 190
Rotating disk electrode, 161, 277,
416
current distribution to, 190
Salt spray, correlations, 300
Scanning methods
LEIS, 340
SRET, 334
SVET, 336
426
Schmidt number, 160
Scratched electrode testing, electrochemical scratch, 111
Self-healing, 285, 317
Sensitization of stainless steel
detecting, 93
quantifying, 99
Sherwood number, 159
Simulated scratch cell, 287
Solution conductivity, 147
Solution resistance, 130, 182
Solution velocity, 152
Specimen mounting, 95
Stern–Geary equation, 127, 348, 385
Stern–Makrides washer, 96
Streicher test, 93
Stress-corrosion cracking, 57, 72
Surface shear stress, 171
Tafel
analysis issues, 44, 218
extrapolation, 44
slope, 34, 58, 127, 154, 215, 364
Index
Thermodynamics, 9
Three-electrode cell, 30
effect of ohmic resistance, 176
Throwing power, 175
Ti corrosion, Pourbaix diagram, 24
Time constants, 142, 308
Transpassivity, 58
UO 2 corrosion, 210
Voltmeter, need for high impedance, 33,
39
Wagner number, 147, 189, 197
Water reduction (see Hydrogen evolution)
Wire loop electrode, 99
Working electrode, 12
1/--pages
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