Modern electrochemistry, vol 2a fundamentals of electrodics, 2nd edition john OM bockris, amulya k n reddy, maria gamboa aldeco

VOLUME 2A

MODERN
ELECTROCHEMISTRY
SECOND EDITION

Fundamentals of
Electrodics


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To J. A. V. Butler and Max Volmer


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VOLUME 2A

MODERN
ELECTROCHEMISTRY
SECOND EDITION

Fundamentals of
Electrodics
John O’M Bockris
Molecular Green Technology
College Station, Texas

Amulya K. N. Reddy
President
International Energy Initiative
Bangalore, India

and
Maria Gamboa-Aldeco
Texas A&M University
College Station, Texas

KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW


eBook ISBN:
Print ISBN:

0-306-47605-3
0-306-46166-8

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PREFACE TO THE FIRST EDITION
This book had its nucleus in some lectures given by one of us (J.O’M.B.) in a course
on electrochemistry to students of energy conversion at the University of Pennsylvania. It was there that he met a number of people trained in chemistry, physics, biology,
metallurgy, and materials science, all of whom wanted to know something about
electrochemistry. The concept of writing a book about electrochemistry which could
be understood by people with very varied backgrounds was thereby engendered. The
lectures were recorded and written up by Dr. Klaus Muller as a 293-page manuscript.
At a later stage, A.K.N.R. joined the effort; it was decided to make a fresh start and
to write a much more comprehensive text.
Of methods for direct energy conversion, the electrochemical one is the most
advanced and seems the most likely to become of considerable practical importance.
Thus, conversion to electrochemically powered transportation systems appears to be
an important step by means of which the difficulties of air pollution and the effects of
an increasing concentration in the atmosphere of carbon dioxide may be met. Corrosion is recognized as having an electrochemical basis. The synthesis of nylon now
contains an important electrochemical stage. Some central biological mechanisms
have been shown to take place by means of electrochemical reactions. A number of
American organizations have recently recommended greatly increased activity in
training and research in electrochemistry at universities in the United States. Three
new international journals of fundamental electrochemical research were established
between 1955 and 1965.
In contrast to this, physical chemists in U.S. universities seem—perhaps partly
because of the absence of a modern textbook in English—out of touch with the
revolution in fundamental interfacial electrochemistry which has occurred since 1950.
The fragments of electrochemistry which are taught in many U.S. universities belong

not to the space age of electrochemically powered vehicles, but to the age of
vii


viii

PREFACE TO THE FIRST EDITION

thermodynamics and the horseless carriage; they often consist of Nernst’s theory of
galvanic cells (1891) together with the theory of Debye and Hückel (1923).
Electrochemistry at present needs several kinds of books. For example, it needs
a textbook in which the whole field is discussed at a strong theoretical level. The most
pressing need, however, is for a book which outlines the field at a level which can be
understood by people entering it from different disciplines who have no previous
background in the field but who wish to use modern electrochemical concepts and
ideas as a basis for their own work. It is this need which the authors have tried to meet.
The book’s aims determine its priorities. In order, these are:
1. Lucidity. The authors have found students who understand advanced courses
in quantum mechanics but find difficulty in comprehending a field at whose center
lies the quantum mechanics of electron transitions across interfaces. The difficulty is
associated, perhaps, with the interdisciplinary character of the material: a background
knowledge of physical chemistry is not enough. Material has therefore sometimes
been presented in several ways and occasionally the same explanations are repeated
in different parts of the book. The language has been made informal and highly
explanatory. It retains, sometimes, the lecture style. In this respect, the authors have
been influenced by The Feynman Lectures on Physics.
2. Honesty. The authors have suffered much themselves from books in which
proofs and presentations are not complete. An attempt has been made to include most
of the necessary material. Appendices have been often used for the presentation of
mathematical derivations which would obtrude too much in the text.

3. Modernity. There developed during the 1950’s a great change in emphasis in
electrochemistry away from a subject which dealt largely with solutions to one in
which the treatment at a molecular level of charge transfer across interfaces dominates.
This is the “new electrochemistry,” the essentials of which, at an elementary level, the
authors have tried to present.
4. Sharp variation is standard. The objective of the authors has been to begin each
chapter at a very simple level and to increase the level to one which allows a connecting
up to the standard of the specialized monograph. The standard at which subjects are
presented has been intentionally variable, depending particularly on the degree to
which knowledge of the material appears to be widespread.
5. One theory per phenomenon. The authors intend a teaching book, which acts
as an introduction to graduate studies. They have tried to present, with due admission
of the existing imperfections, a simple version of that model which seemed to them
at the time of writing to reproduce the facts most consistently. They have for the most
part refrained from presenting the detailed pros and cons of competing models in areas
in which the theory is still quite mobile.
In respect to references and further reading: no detailed references to the literature
have been presented, in view of the elementary character of the book’s contents, and
the corresponding fact that it is an introductory book, largely for beginners. In the


PREFACE TO THE FIRST EDITION

ix

“further reading” lists, the policy is to cite papers which are classics in the development
of the subject, together with papers of particular interest concerning recent developments, and in particular, reviews of the last few years.
It is hoped that this book will not only be useful to those who wish to work with
modern electrochemical ideas in chemistry, physics, biology, materials science, etc.,
but also to those who wish to begin research on electron transfer at interfaces and

associated topics.
The book was written mainly at the Electrochemistry Laboratory in the University
of Pennsylvania, and partly at the Indian Institute of Science in Bangalore. Students
in the Electrochemistry Laboratory at the University of Pennsylvania were kind
enough to give guidance frequently on how they reacted to the clarity of sections
written in various experimental styles and approaches. For the last four years, the
evolving versions of sections of the book have been used as a partial basis for
undergraduate, and some graduate, lectures in electrochemistry in the Chemistry
Department of the University.
The authors’ acknowledgment and thanks must go first to Mr. Ernst Cohn of the
National Aeronautics and Space Administration. Without his frequent stimulation,
including very frank expressions of criticism, the book might well never have emerged
from the Electrochemistry Laboratory.
Thereafter, thanks must go to Professor B. E. Conway, University of Ottawa, who
gave several weeks of his time to making a detailed review of the material. Plentiful
help in editing chapters and effecting revisions designed by the authors was given by
the following: Chapters IV and V, Dr. H. Wroblowa (Pennsylvania); Chapter VI, Dr.
C. Solomons (Pennsylvania) and Dr. T. Emi (Hokkaido); Chapter VII, Dr. E. Gileadi
(Tel-Aviv); Chapters VIII and IX, Prof. A. Despic (Belgrade), Dr. H. Wroblowa, and
Mr. J. Diggle (Pennsylvania); Chapter X, Mr. J. Diggle; Chapter XI, Dr. D. Cipris
(Pennsylvania). Dr. H. Wroblowa has to be particularly thanked for essential contributions
to the composition of the Appendix on the measurement of Volta potential differences.
Constructive reactions to the text were given by Messers. G. Razumney, B. Rubin,
and G. Stoner of the Electrochemistry Laboratory. Advice was often sought and
accepted from Dr. B. Chandrasekaran (Pennsylvania), Dr. S. Srinivasan (New York),
and Mr. R. Rangarajan (Bangalore).
Comments on late drafts of chapters were made by a number of the authors’
colleagues, particularly Dr. W. McCoy (Office of Saline Water), Chapter II; Prof. R.
M. Fuoss (Yale), Chapter III; Prof. R. Stokes (Armidale), Chapter IV; Dr. R. Parsons
(Bristol), Chapter VII; Prof. A. N. Frumkin (Moscow), Chapter VIII; Dr. H. Wroblowa, Chapter X; Prof. R. Staehle (Ohio State), Chapter XI. One of the authors

(A.K.N.R.) wishes to acknowledge his gratitude to the authorities of the Council of
Scientific and Industrial Research, India, and the Indian Institute of Science, Bangalore, India, for various facilities, not the least of which were extended leaves of
absence. He wishes also to thank his wife and children for sacrificing many precious
hours which rightfully belonged to them.


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PREFACE TO VOLUME 2A
Bockris and Reddy is a well-known text in the electrochemical field. Originally
published in 1970, it has had a very long life as an introduction to a vast interdisciplinary area. The updating of the book should have been carried out long ago, but this
task had to compete with other needs, for example, preparation of an advanced
graduate text (Bockris and Khan, Surface Electrochemistry, Plenum, 1993), and while
the sales of the first edition continued to be significant, the inevitable second edition
remained a future project. Its time has come.
It may first be restated for whom this book is intended. Its obvious home is in the
chemistry and chemical engineering departments of universities. Electrochemistry is
also often the basis of fields treated in departments of engineering, materials, science,
and biology. However, the total sales of the first edition far exceeded the number of
electrochemists in the Electrochemical Society—evidence that the book is used by
scientists who may have backgrounds in quite other subjects, but find that their
disciplines involve the properties of interfaces and thus, in practice, the interfacial part
of electrochemistry (for the ionics part, see Vol. 1).
This broad audience, professionals all, affects the standard of the presentation,
and it is important to stress that this book assumes an audience that has an undergraduate knowledge of chemistry. The text starts from the beginning and climbs quite high,
from place to place reaching the frontier of a changing field in the late 1990s. However,
it does not try, as graduate student texts must, to cover all the advancing fronts.
Lucidity is the main characteristic where the book carries over from the first edition
and lucidity needs increasingly more space as complexity increases. For those who

want to see how the material developed here approaches a graduate standard, Surface
Electrochemistry (1993) is available, as well as the monograph series, Modern Aspects
of Electrochemistry (Kluwer-Plenum), which is published, roughly, at one volume per
year.
xi


xii

PREFACE TO VOLUME 2A

Modern Electrochemistry was a two-volume work in 1970, but advances in the
field since then have made it necessary to considerably enlarge the scope of this text.
Whereas in Vol. 1 on ionics (Chapters 1 through 5), about a third of the first edition
could be retained, the material in these two volumes, 2A and 2B, had to be nearly
completely rewritten and six new chapters added.
The advances made since 1970 start with the fact that the solid/solution interface
can now be studied at an atomic level. Single-crystal surfaces turn out to manifest
radically different properties, depending on the orientation exposed to the solution.
Potentiodynamic techniques that were raw and quasi-empirical in 1970 are now
sophisticated experimental methods. The theory of interfacial electron transfer has
attracted the attention of physicists, who have taken the beginnings of quantum
electrochemistry due to Gurney in 1932 and brought that early initiative to a 1990
level. Much else has happened, but one thing must be said here. Since 1972, the use
of semiconductors as electrodes has come into much closer focus, and this has
enormously extended the realm of systems that can be treated in electrochemical
terms.
Volume 2A consists of Chapters 6 through 9 and covers the fundamentals of
electrodics. Chapters 10 through 15, which make up Vol. 2B, discuss electrodics in
chemistry, engineering, biology, and environmental science. It would be a misapprehension to think of these chapters as being applied electrochemistry, for the considerations are not at all technological. The material presented serves to illustrate the

breadth of fields that depend upon the properties of wet surfaces.
Each chapter has been reviewed by a scientist whose principal or even sole
activity is in the area covered. The advice given has usually been accepted. The
remaining inevitable flaws and choice of material are the responsibility of the authors
alone.
A teaching book should have problems for students to solve and as explained in
the preface to Vol. 1, acknowledgment must be made here to the classification of these
problems according to a scheme used in Atkins, Physical Chemistry (Freeman).
TEXT REFERENCES AND READING LISTS
Because electrochemistry, as in other disciplines, has been built on the foundations established by individual scientists and their collaborators, it is important that
the student know who these contributors are. These researchers are mentioned in the
text, with the date of their most important work (e.g., Gurney, 1932). This will allow
the student to place these leaders in electrochemistry in the development of the field.
Then, at the end of sections is a suggested reading list. The first part of the list
consists of some seminal papers, publications which, in the light of history, can be
seen to have made important contributions to the buildup of modern electrochemical
knowledge. The student will find these earlier papers instructive in comprehending
the subject’s development. However, there is another reason to encourage the reading


PREFACE TO VOLUME 2A

xiii

of papers written in earlier decades; they are generally easier to understand than the
later, necessarily more sophisticated, papers.
Next in the reading list, are recent reviews. Such documents summarize the
relevant field and the student will find them invaluable; only it must be remembered
that these documents were written for the scientists of their time. Thus, they may prove
to be less easy to understand than the text of this book, which is aimed at students in

the field.
Finally, the reading lists offer a sampling of some papers of the past decade. These
should be understandable by students who have worked through the book and
particularly those who have done at least some of the exercises and problems.
There is no one-to-one relation between the names (with dates) that appear in the
text and those in the reading list. There will, of course, be some overlap, but the seminal
papers are limited to those in the English language, whereas physical electrochemistry
has been developed not only in the United Kingdom and the United States, but also
strongly in Germany and Russia. Names in the text, on the other hand, are given
independently of the working language of the author.
ACKNOWLEDGEMENTS. Much help was obtained from colleagues in a general way.
Their advice has been, by and large, respected. Dr. Ron Fawcett of the University of
California, Davis, read and criticized part of Chapter 6. Chapters 8 and 9 were reported
upon by Prof. Brian B.E. Conway, University of Ottawa. Chapter 9 was monitored by
Dr. Rey Sidik at Texas A&M University. Chapter 10 was discussed with Prof. Nathan
Lewis, Stanford University. Chapter 11 was commented upon by Dr. Norman Weinberg. Chapter 12 was studied and corrected by Dr. Robert Kelly, University of
Virginia. Chapter 13 was read and criticized by Prof. A.J. Appleby, Texas A&M
University and Dr. Supramaniam Srinivasan, Princeton University. Chapter 14 was
commented upon by Dr. Martin Blank, State University of New York, and Chapter
15 by Dr. Robert Gale of Louisiana State University.
John O’M. Bockris, College Station, Texas
Amalya K. Reddy, Bangalore, India
Maria Gamboa-Aldeco, Superior, Colorado


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CONTENTS
CHAPTER 6

THE ELECTRIFIED INTERFACE
6.1.

Electrification of an Interface

771

6.1.1.
6.1.2.
6.1.3.
6.1.4.
6.1.5.

771
771
774
774

6.1.10.

The Electrode/Electrolyte Interface: The Basis of Electrodics
New Forces at the Boundary of an Electrolyte
The Interphase Region Has New Properties and New Structures
An Electrode Is Like a Giant Central Ion
The Consequences of Compromise Arrangements: The Electrolyte
Side of the Boundary Acquires a Charge
Both Sides of the Interface Become Electrified: The Electrical Double
Layer
Double Layers Are Characteristic of All Phase Boundaries
What Knowledge Is Required before an Electrified Interface Can Be

Regarded as Understood?
Predicting the Interphase Properties from the Bulk Properties of the
Phases
Why Bother about Electrified Interfaces?

6.2.

Experimental Techniques Used in Studying Interfaces

782

6.2.1.

What Type of Information Is Necessary to Gain an Understanding of
Interfaces?
The Importance of Working with Clean Surfaces (and Systems)
Why Use Single Crystals?
In Situ vs. Ex Situ Techniques
Ex Situ Techniques
Low-Energy Electron Diffraction (LEED)
6.2.5.1.
X-Ray Photoelectron Spectroscopy (XPS)
6.2.5.2.

782
782
784
785
788
788

794

6.1.6.
6.1.7.
6.1.8.
6.1.9.

6.2.2.
6.2.3.
6.2.4.
6.2.5.

xv

775

775
778
778
780
780


xvi CONTENTS

6.2.6.

In Situ Techniques
Infrared-Reflection Spectroscopy
6.2.6.1.

6.2.6.2.
Radiochemical Methods

797
797
804

6.3.

The Potential Difference Across Electrified Interfaces

806

6.3.1.

What Happens When One Tries to Measure the Potential Difference
Across a Single Electrode/Electrolyte Interface?
Can One Measure Changes in the Metal–Solution Potential Difference?
The Extreme Cases of Ideally Nonpolarizable and Polarizable Interfaces
The Development of a Scale of Relative Potential Differences
Can One Meaningfully Analyze an Electrode–Electrolyte Potential
Difference?
The Outer Potential of a Material Phase in a Vacuum
The Outer Potential Difference,
between the Metal and the Solution
The Surface Potential, of a Material Phase in a Vacuum
The Dipole Potential Difference
across an Electrode–Electrolyte
Interface
The Sum of the Potential Differences Due to Charges and

Dipoles: The Inner Potential Difference,
The Outer, Surface, and Inner Potential Differences
Is the Inner Potential Difference an Absolute Potential
Difference?
The Electrochemical Potential, the Total Work from Infinity to
Bulk
6.3.13.1. Definition of Electrochemical Potential
6.3.13.2. Can the Chemical and Electrical Work Be Determined
Separately?
6..3.13.3. A Criterion of Thermodynamic Equilibrium between Two
Phases: Equality of Electrochemical Potentials
6.3.13.4. Nonpolarizable Interfaces and Thermodynamic Equilibrium.
The Electron Work Function, Another Interfacial Potential
The Absolute Electrode Potential
6.3.15.1. Definition of Absolute Electrode Potential.
6.3.15.2. Is It Possible to Measure the Absolute Potential?
Further Reading

6.3.2.
6.3.3.
6.3.4.
6.3.5.
6.3.6.
6.3.7.
6.3.8.
6.3.9.
6.3.10.
6.3.11.
6.3.12.
6.3.13.

6.3.14.
6.3.15.

806
811
813
815
817
821
822
823
824
826
828
829
830
830
832
833
834
834
837
837
839
841

6.4.

The Accumulation and Depletion of Substances at an Interface

6.4.1.

6.4.5.

What Would Represent Complete Structural Information on an Electrified
Interface?
The Concept of Surface Excess
Is the Surface Excess Equivalent to the Amount Adsorbed?
Does Knowledge of the Surface Excess Contribute to Knowledge of the
Distribution of Species in the Interphase Region?
Is the Surface Excess Measurable?

846
847

6.5.

The Thermodynamics of Electrified Interfaces

848

6.4.2.
6.4.3.
6.4.4.

842
842
843
845

CONTENTS

6.5.1.

6.5.2.
6.5.3.
6.5.4.
6.5.5.
6.5.6.
6.5.7.
6.5.8.
6.5.9.

The Measurement of Interfacial Tension as a Function of the Potential
Difference across the Interface
6.5.1.1.
Surface Tension between a Liquid Metal and Solution.
6.5.1.2.
Is It Possible to Measure Surface Tension of Solid Metal
and Solution Interfaces?
Some Basic Facts about Electrocapillary Curves
Some Thermodynamic Thoughts on Electrified Interfaces
Interfacial Tension Varies with Applied Potential: Determination of the
Charge Density on the Electrode
Electrode Charge Varies with Applied Potential: Determination
of the Electrical Capacitance of the Interface
The Potential at which an Electrode Has a Zero Charge
Surface Tension Varies with Solution Composition: Determination

of the Surface Excess
Summary of Electrocapillary Thermodynamics
Retrospect and Prospect for the Study of Electrified Interfaces
Further Reading

xvii

848
848
849
852
854

858
859
861
862
866
869
870

6.6.

The Structure of Electrified Interfaces

871

6.6.1
6.6.2.
6.6.3.

A Look into an Electrified Interface
The Parallel-Plate Condenser Model: The Helmholtz–Perrin Theory
The Double Layer in Trouble: Neither Perfect Parabolas nor
Constant Capacities
The Ionic Cloud: The Gouy–Chapman Diffuse-Charge Model of the
Double Layer
The Gouy–Chapman Model Provides a Potential Dependence of the
Capacitance, but at What Cost?
Some Ions Stuck to the Electrode, Others Scattered in Thermal Disarray:
The Stern Model
The Contribution of the Metal to the Double-Layer Structure
The Jellium Model of the Metal
How Important Is the Surface Potential for the Potential of the Double
Layer?
Further Reading

871
873

880

6.7.

Structure at the Interface of the Most Common Solvent: Water

895

6.7.1.
6.7.2.

6.7.3.

An Electrode Is Largely Covered with Adsorbed Water Molecules
Metal–Water Interactions
One Effect of the Oriented Water Molecules in the Electrode Field:
Variation of the Interfacial Dielectric Constant
Orientation of Water Molecules on Electrodes: The Three-State Water
Model
How Does the Population of Water Species Vary with the Potential of the
Electrode?
The Surface Potential,
Due to Water Dipoles
The Contribution of Adsorbed Water Dipoles to the Capacity of the
Interface

895
896

6.6.4.
6.6.5.
6.6.6.
6.6.7.
6.6.8.
6.6.9.

6.7.4.
6.7.5.
6.7.6.
6.7.7.

876
876

882
887
890
893
894

897
898
900
904
910


xviii

CONTENTS

Solvent Excess Entropy of the Interface: A Key to Obtaining Structural
Information on Interfacial Water Molecules
If Not Solvent Molecules, What Factors Are Responsible for
Variation in the Differential Capacity of the Electrified Interface with
Potential?
Further Reading

915
918

6.8.

Ionic Adsorption

919

6.8.1.
6.8.2.

How Close Can Hydrated Ions Come to a Hydrated Electrode?
What Parameters Determine if an Ion Is Able to Contact Adsorb
on an Electrode?
6.8.2.1.
Ion–Electrode Interactions.
Solvent Interactions.
6.8.2.2.
Lateral Interactions.
6.8.2.3.
The Enthalpy and Entropy of Adsorption
Effect of the Electrical Field at the Interface on the Shape of the Adsorbed
Ion
Equation of States in Two Dimensions
Isotherms of Adsorption in Electrochemical Systems
A Word about Standard States in Adsorption Isotherms
The Langmuir Isotherm: A Fundamental Isotherm
The Frumkin Isotherm: A Lateral Interaction Isotherm
The Temkin Isotherm: A Heterogeneous Surface Isotherm
The Flory–Huggins–Type Isotherm: A Substitutional Isotherm
Applicability of the Isotherms
An Ionic Isotherm for Heterogeneous Surfaces

Thermodynamic Analysis of the Adsorption Isotherm
Contact Adsorption: Its Influence on the Capacity of the Interface
6.8.15.1. The Constant-Capacity Region.
6.8.15.2. The Capacitance Hump and the Capacity Minimum.
Looking Back
Further Reading

919

929
931
933
936
937
938
938
941
941
944
955
959
961
962
963
967

6.9.

The Adsorption Process of Organic Molecules

968

6.9.1.
6.9.2.
6.9.3.

The Relevance of Organic Adsorption
Is Adsorption the Only Process that the Organic Molecules Can Undergo?
Identifying Organic Adsorption
Test 1: The Almost-Null Current.
6.9.3.1.
Test 2: The Parabolic Coverage-Potential Curve.
6.9.3.2.
Test 3: The Maximum of the Coverage-Potential Curve
6.9.3.3.
Lies Close to the pzc.
Forces Involved in Organic Adsorption
The Parabolic Coverage-Potential Curve
Other Factors Influencing the Adsorption of Organic Molecules
on Electrodes
6.9.6.1.
Structure, Size, and Orientation of the Adsorbed
Organic Molecules

968
969
970
970
970

6.7.8.
6.7.9.

6.8.3.
6.8.4.
6.8.5.
6.8.6.
6.8.7.
6.8.8.
6.8.9.
6.8.10.
6.8.11.
6.8.12.
6.8.13.
6.8.14.
6.8.15.

6.8.16.

6.9.4.
6.9.5.
6.9.6.

912

920
920
923
924
926

971
971
972
978
978


CONTENTS

6.9.6.2.
6.9.6.3.

Electrode Properties.
Electrolyte Properties.

xix

979
981

6.10.

The Structure of Other Interfaces

984

6.10.1.

The Structure of the Semiconductor–Electrolyte Interface

6.10.1.1. How Is the Charge Distributed inside a Solid Electrode?
6.10.1.2. The Band Theory of Crystalline Solids.
6.10.1.3. Conductors, Insulators, and Semiconductors.
6.10.1.4. Some Analogies between Semiconductors and Electrolytic
Solutions
6.10.1.5. The Diffuse-Charge Region Inside an Intrinsic Semiconductor:
The Garett–Brattain Space Charge
6.10.1.6. The Differential Capacity Due to the Space Charge.
6.10.1.7. Impurity Semiconductors, n-Type and p-Type.
6.10.1.8. Surface States: The Semiconductor Analogue of
Contact Adsorption
Colloid Chemistry
6.10.2.1. Colloids: The Thickness of the Double Layer and the Bulk
Dimenstions Are of the Same Order
6.10.2.2. The Interaction of Double Layers and the Stability of Colloids
6.10.2.3. Sols and Gels.

984
984
985
988

1001
1002
1005

6.11.

Double Layers Between Phases Moving Relative to Each Other

1006

6.11.1.

The Phenomenology of Mobile Electrified Interfaces:
Electrokinetic Properties
The Relative Motion of One of the Phases Constituting an
Electrified Interface Produces a Streaming Current
A Potential Difference Applied Parallel to an Electrified
Interface Produces an Electro-osmotic Motion of One of the
Phases Relative to the Other
Electrophoresis: Moving Solid Particles in a Stationary Electrolyte
Further Reading

6.10.2.

6.11.2.
6.11.3.

6.11.4.

990
992
995
997

1000
1001

1006

1008

1011
1012
1015

Exercises

1015

Problems

1020

Micro Research Problems

1029

Appendix 6.1

1031

CHAPTER 7
ELECTRODICS
7.1.

Introduction

1035

xx

CONTENTS

7.1.4.

Some Things One Has to Know About Interfacial Electron Transfer:
It’s Both Electrical and Chemical
Uni-electrodes, Pairs of Electrodes in Cells and Devices
The Three Possible Electrochemical Devices
7.1.3.1.
The Driven Cell (or Substance Producer).
The Fuel Cell (or Electricity Producer).
7.1.3.2.
The Electrochemical Undevice: An Electrode that
7.1.3.3.
Consumes Itself while Wasting Energy
Some Special Characteristics of Electrochemical Reactions

7.2.

Electron Transfer Under an Interfacial Electric Field

7.2.1.

A Two-Way Traffic Across the Interface: Equilibrium and the Exchange
Current Density
The Interface Out of Equilibrium
A Quantitative Version of the Dependence of the Electrochemical

Reaction Rate on Overpotential: The Butler–Volmer Equation
7.2.3.1.
The Low Overpotential Case.
7.2.3.2.
The High Overpotential Case.
Polarizable and Nonpolarizable Interfaces
The Equilibrium State for Charge Transfer at the Metal/Solution Interface
Treated Thermodynamically
The Equilibrium Condition: Kinetic Treatment
The Equilibrium Condition: Nernst’s Thermodynamic Treatment
The Final Nernst Equation and the Question of Signs
Why Is Nernst’s Equation of 1904 Still Useful?
Looking Back to Look Forward
Further Reading

7.1.1.
7.1.2.
7.1.3.

7.2.2.
7.2.3.

7.2.4.
7.2.5.
7.2.6.
7.2.7.
7.2.8.
7.2.9.
7.2.10.

7.3.

A More Detailed Look at Some Quantities in the Butler–Volmer
Equation

1035
1036
1036
1036
1039
1040
1041

1042
1047
1049
1052
1054
1054
1055
1057
1058
1058
1062
1064
1065
1067

1067

Does the Structure of the Interphasial Region Influence the
Electrochemical Kinetics There?
What About the Theory of the Symmetry Factor, ?
The Interfacial Concentrations May Depend on Ionic Transport
in the Electrolyte
Further Reading

1072
1073

7.4.

Electrode Kinetics Involving the Semiconductor/solution Interface

1074

7.4.1.

Introduction
7.4.1.1.
General.
The n-p Junction.
7.4.1.2.
The Current-Potential Relation at a Semiconductor/Electrolyte Interface
(Negligible Surface States)
Effect of Surface States on Semiconductor Electrode Kinetics
The Use of n- and p-Semiconductors for Thermal Reactions
The Limiting Current in Semiconductor Electrodes
Photoactivity of Semiconductor Electrodes

1074
1074
1075

7.3.1.
7.3.2.
7.3.3.

7.4.2.
7.4.3.
7.4.4.
7.4.5.
7.4.6.

1068
1071

1082
1086
1086
1088
1089


CONTENTS

xxi

Further Reading

1090

7.5.

Techniques of Electrode Kinetics

1091

7.5.1.
7.5.2.
7.5.3.
7.5.4.

Preparing the Solution
Preparing the Electrode Surface
Real Area
Microelectrodes
The Situation.
7.5.4.1.
Lessening Diffusion Control by the Use of a Microelectrode
7.5.4.2.
Reducing Ohmic Errors by the Use of Microelectrodes.
7.5.4.3.
7.5.4.4.
The Downside of Using Microelectrodes.
7.5.4.5.
Arrays.
7.5.4.6.
The Far-Ranging Applications of Microelectrodes.
Thin-Layer Cells

Which Electrode System Is Best?
The Measurement Cell
7.5.7.1.
General Arrangement.
More on Luggin Capillaries and Tips.
7.5.7.2.
7.5.7.3.
Reference Electrodes.
Keeping the Current Uniform on an Electrode
Apparatus Design Arising from the Needs of the Electronic
Instrumentation
Further Reading
Measuring the Electrochemical Reaction Rate as a Function of
Potential (at Constant Concentration and Temperature)
7.5.10.1. Temperature Control in Electrochemical Kinetics.
The Dependence of Electrochemical Reaction Rates on
Temperature
Electrochemical Reaction Rates as a Function of the System
Pressure
7.5.12.1. The Equations.
7.5.12.2. What Is the Point of Measuring System Pressure Effects?
Impedance Spectroscopy
7.5.13.1. What Is Impedance Spectroscopy?
7.5.13.2. Real and Imaginary Impedance.
7.5.13.3. The Impedance of a Capacitor in Series with a Resistor.
7.5.13.4. Applying ac Impedance Methods to Obtain Information on
Electrode Processes
7.5.13.5. The Warburg Impedance.
7.5.13.6. The Simplest “Real” Electrochemical Interface.
7.5.13.7. The Impedance (or Cole–Cole) Plot.

7.5.13.8. Calculating Exchange Current Densities and Rate
Constants from Impedance Plots .
7.5.13.9. Impedance Spectroscopy for More Complex Interfacial
Situations
7.5.13.10. Cases in which Impedance Spectroscopy Becomes Limited
Rotating Disk Electrode

1091
1094
1095
1097
1097
1098
1099
1100
1100
1102
1103
1103
1104
1104
1107
1108
1111

7.5.5.
7.5.6.
7.5.7.

7.5.8.

7.5.9.

7.5.10.

7.5.11.
7.5.12.

7.5.13.

7.5.14.

1112
1113
1115
1121
1122
1123
1123
1125
1127
1127
1128
1129
1131
1133
1133
1135
1136
1136
1138

1139


xxii

CONTENTS

General.
Are Rotating Disk with Ring Electrodes Still Useful
in the Twenty-first Century
7.5.14.3. Other Unusual Electrode Shapes.
Spectroscopic Approaches to Electrode Kinetics
7.5.15.1. General.
7.5.15.2. FTIR Spectroscopy and Mechanisms on Electrode.
Ellipsometry
7.5.16.1. What Is Ellipsometry?
7.5.16.2. Is Ellipsometry Any Use in Electrochemistry?
7.5.16.3. Some Understanding as to How Ellipsometry Works.
7.5.16.4. Ellipsometric Spectroscopy.
7.5.16.5. How Can Ellipsometry Be So Sensitive?
7.5.16.6. Does Ellipsometry Have a Downside?
Isotopic Effects
7.5.17.1. Use of Isotopic Effects in the Determination of
Electro-Organic Reaction Mechanisms
Atomic-Scale In Situ Microscopy
Use of Computers in Electrochemistry
7.5.19.1. Computational.
7.5.19.2. Computer Simulation.
7.5.19.3. Use of Computer Simulation to Solve Differential Equations
Pertaining to Diffusion Problems

7.5.19.4. Use of Computers to Control Experiments: Robotization
of Suitable Experiments
7.5.19.5. Pattern Recognition Analysis
Further Reading

1139

7.6.

Multistep Reactions

1166

7.6.1.
7.6.2.
7.6.3.
7.6.4.
7.6.5.
7.6.6.
7.6.7.
7.6.8.

The Difference between Single-Step and Multistep Electrode Reactions
Terminology in Multistep Reactions
The Catalytic Pathway
The Electrochemical Desorption Pathway
Rate-Determining Steps in the Cathodic Hydrogen Evolution Reaction
Some Ideas on Queues, or Waiting Lines
The Overpotential Is Related to the Electron Queue at an Interface
A Near-Equilibrium Relation between the Current Density and

Overpotential for a Multistep Reaction
The Concept of a Rate-Determining Step
Rate-Determining Steps and Energy Barriers for Multistep
Reactions
How Many Times Must the Rate-Determining Step Take Place
for the Overall Reaction to Occur Once? The Stoichiometric
Number
The Order of an Electrodic Reaction
Blockage of the Electrode Surface during Charge Transfer:
The Surface-Coverage Factor

1166
1167
1167
1168
1168
1169
1171

7.5.14.1.
7.5.14.2.

7.5.15.

7.5.16.

7.5.17.

7.5.18.
7.5.19.

7.6.9.
7.6.10.
7.6.11.

7.6.12.
7.6.13.

1143
1144
1145
1145
1147
1147
1147
1148
1149
1152
1153
1154
1154
1156
1157
1159
1159
1160
1161
1162
1162
1164

1172
1175
1180

1182
1187
1190


CONTENTS

Further Reading

xxiii

1192

7.7.

The Intermediate Radical Concentration,
on Electrode Kinetics

7.7.1.
7.7.2.
7.7.3.
7.7.4.
7.7.5.

Heat of Adsorption Independent of Coverage

Heat of Adsorption Dependent on Coverage
Frumkin and Temkin
Consequences from the Frumkin–Temkin Isotherm
When Should One Use the Frumkin–Temkin Isotherms in Kinetics Rather
than the Simple Langmuir Approach?
Are the Electrode Kinetics Affected in Circumstances under which
Varies with
Further Reading

1197
1201

7.8.

The Reactivity of Crystal Planes of Differing Orientation

1201

7.8.1.
7.8.2.
7.8.3.

Introduction
Single Crystals and Planes of Specific Orientation
Another Preliminary: The Voltammogram as the Arbiter of a
Clean Surface
Examples of the Different Degrees of Reactivity Caused by
Exposing Different Planes of Metal Single Crystals to the Solution
General Assessment of Single-Crystal Work in Electrochemistry
Roots of the Work on Kinetics at Single-Crystal Planes

Further Reading

1201
1201

1205
1209
1210
1210

7.9.

Transport in the Electrolyte Effects Charge Transfer at the Interface

1211

7.9.1.
7.9.2.

Ionics Looks after the Material Needs of the Interface
How the Transport Flux Is Linked to the Charge-Transfer Flux: The
Flux-Equality Condition
Appropriations from the Theory of Heat Transfer
A Qualitative Study of How Diffusion Affects the Response of an
Interface to a Constant Current
A Quantitative Treatment of How Diffusion to an Electrode Affects the
Response with Time of an Interface to a Constant Current
The Concept of Transition Time
Convection Can Maintain Steady Interfacial Concentrations
The Origin of Concentration Overpotential

The Diffusion Layer
The Limiting Current Density and Its Practical Importance
7.9.10.1. Polarography: The Dropping-Mercury Electrode.
The Steady-State Current–Potential Relation under
Conditions of Transport Control
The Diffusion-Activation Equation
The Concentration of Charge Carriers at the Electrode
Current as a Function of Overpotential: Interfacial and
Diffusion Control
The Reciprocal Relation

1211

7.7.6.

7.8.4.
7.8.5.
7.8.6.

7.9.3.
7.9.4.
7.9.5.
7.9.6.
7.9.7.
7.9.8.
7.9.9.
7.9.10.
7.9.11.
7.9.12.
7.9.13.

7.9.14.
7.9.15.

and Its Effect
1193
1193
1194
1195
1195
1197

1203

1213
1215
1216
1218
1221
1225
1230
1232
1235
1237
1246
1247
1247
1248
1250

xxiv

CONTENTS

7.9.16.
7.9.17.
7.9.18.
7.9.19.

Reversible and Irreversible Reactions
Transport-Controlled Deelectronation Reactions
What Is the Effect of Electrical Migration on the Limiting
Diffusion Current Density?
Some Summarizing Remarks on the Transport Aspects of Electrodics
Further Reading

1251
1252
1253
1254
1256

7.10.

How to Determine the Stepwise Mechanisms of Electrodic
Reactions

7.10.1.
7.10.2.

7.10.5.

Why Bother about Determining a Mechanism?
What Does It Mean: “To Determine the Mechanism of an
Electrode Reaction”?
7.10.2.1. The Overall Reaction.
7.10.2.2. The Pathway
7.10.2.3. The Rate-Determining Step
The Mechanism of Reduction of
on Iron at Intermediate pH’s
Mechanism of the Oxidation of Methanol
Further Reading
The Importance of the Steady State in Electrode Kinetics

1258
1258
1259
1260
1263
1269
1273
1274

7.11.

Electrocatalysis

1275

7.11.1.

7.11.2.

Introduction
At What Potential Should the Relative Power of Electrocatalysts Be
Compared?
How Electrocatalysis Works
Volcanoes
Is Platinum the Best Catalyst?
Bioelectrocatalysis
7.11.6.1. Enzymes.
7.11.6.2. Immobilization.
7.11.6.3. Is the Heme Group in Most Enzymes Too Far Away
from the Metal for Enzymes to Be Active in Electrodes?
7.11.6.4. Practical Applications of Enzymes on Electrodes.
Further Reading

1275

7.12.

The Electrogrowth of Metals on Electrodes

1293

7.12.1.
7.12.2.
7.12.3.

The Two Aspects of Electrogrowth
The Reaction Pathway for Electrodeposition

Stepwise Dehydration of an Ion; the Surface Diffusion of
Adions
The Half-Crystal Position
Deposition on an Ideal Surface: The Resulting Nucleation
Values of the Minimum Nucleus Size Necessary for Continued
Growth
Rate of an Electrochemical Reaction Dependent on 2D
Nucleation
Surface Diffusion to Growth Sites

1293
1294

7.10.3.
7.10.4.

7.11.3.
7.11.4.
7.11.5.
7.11.6.

7.12.4.
7.12.5.
7.12.6.
7.12.7.
7.12.8.

1257
1257

1277
1280
1284
1286
1287
1287
1289
1289
1291
1292

1296
1301
1302
1305
1306
1307