fundamentals of electrochemistry 2ed 2006 - bagotsky

FUNDAMENTALS OF
ELECTROCHEMISTRY
Second Edition
V. S. BAGOTSKY
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry
Russian Academy of Sciences
Moscow, Russia
A JOHN WILEY & SONS, INC., PUBLICATIO
N
THE ELECTROCHEMICAL SOCIETY, INC. Pennington, New Jersey
Sponsored by
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Library of Congress Cataloging-in-Publication Data:
Bagotsky, V. S. (Vladimir Sergeevich)
Fundamentals of electrochemistry / V. S. Bagotsky—2nd ed.
p. cm.
Includes bibliographical references and index.
ISBN-13 978-0-471-70058-6 (cloth : alk. paper)
ISBN-10 0-471-70058-4 (cloth : alk. paper)
1. Electrochemistry I. Title.
QD553.B23 2005
541Ј.37—dc22 2005003083
Printed in the United States of America
10987654321
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CONTENTS
Contributors xv
Preface to the Second Edition xvii
Preface to the First Edition xix
List of Photographs xxii
Abbreviations xxiii
Symbols xxv
PART I BASIC CONCEPTS 1
1. Electric Currents in Ionic Conductors 3
1.1 Various Types of Conductors, 3
1.2 Ions in Electrolyte Solutions, 4

1.3 Conductivity of Electrolyte Solutions, 5
1.4 Circuits Involving Ionic Conductors. Electrodes, 9
1.5 Passage of Current Through Electrodes. Electrode Reactions, 10
1.6 Classification of Electrodes and Electrode Reactions, 12
1.7 Faraday’s Laws, 15
1.8 Equations for Mass Balance, 16
1.9 Sign Convention for Currents and Fluxes, 18
2. Electrode Potentials 19
2.1 Interfacial Potential Differences (Galvani Potentials), 20
2.2 Exchange Currents, 23
2.3 Open-Circuit Voltages, 24
2.4 Electrode Potentials, 26
2.5 Cell Voltage at Nonzero Current, 29
3. Thermodynamics of Electrochemical Systems 33
3.1 Conventional and Undefined Parameters, 33
3.2 Thermodynamic Functions in Electrochemistry, 34
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3.3 Thermodynamic Activity, 36
3.4 Equations for the EMF of Galvanic Cells, 39
3.5 Concentration Dependence of Electrode Potentials, 41
3.6 Special Thermodynamic Features of Electrode Potentials, 46
4. Mass Transfer in Electrolytes 51
4.1 Basic Laws of Ionic Diffusion in Solutions, 51
4.2 Limiting Diffusion Currents in Electrolytes, 53
4.3 Ionic Transport by Migration and Diffusion, 55
4.4 Convective Transport, 60
5. Phase Boundaries (Interfaces) Between Miscible Electrolytes 69
5.1 Types of Interfaces Between Electrolytes, 69
5.2 Potentials Between Similar Electrolytes

(Diffusion Potentials), 71
5.3 Distribution of the Ions Between Dissimilar but
Miscible Electrolytes, 73
5.4 Distribution of Ions in Cells with Membrane, 75
5.5 Galvanic Cells with Transference, 76
6. Polarization of Electrodes 79
6.1 Basic Concepts, 79
6.2 Laws of Activation Polarization, 82
6.3 Diffusional Concentration Polarization, 89
6.4 Superposition of Concentration and Activation Polarization, 93
7. Aqueous Electrolyte Solutions 99
7.1 Electrolytic Dissociation, 99
7.2 Ionic Solvation (Hydration) in Solutions, 106
7.3 Activity of Real Electrolyte Solutions, 112
7.4 Physical Theories of Ion–Ion Interactions, 116
8. Nonaqueous Electrolytes 127
8.1 Different Types of Electrolytes and Their Practical
Utilization, 127
8.2 Nonaqueous Electrolyte Solutions, 128
8.3 Ionically Conducting Melts, 131
8.4 Inorganic Solid Electrolytes, 134
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9. Electron Work Functions and Volta Potentials 139
9.1 Surface Potential of a Phase, 139
9.2 Work Functions, 140
9.3 Volta Potentials, 143
9.4 Two Problems in Electrochemistry, 144
10. Structure and Properties of Surface Layers 147
10.1 Electrical Structure of Interphases, 148

10.2 Adsorption Phenomena, 156
10.3 Thermodynamics of Surface Phenomena, 162
10.4 Mercury Electrode Surface, 169
10.5 Platinum Electrode Surface, 172
10.6 Surfaces of Other Electrodes, 178
11. Transient Processes 181
11.1 Evidence for Transient Conditions, 181
11.2 Transient Diffusion to Electrodes of Large Size, 182
11.3 Transient Diffusion to Electrodes of Finite Size, 188
12. Electrochemical Research Techniques 191
12.1 Reference Electrodes, 192
12.2 Voltage and Electrode Potential Measurements
(Potentiometry), 195
12.3 Steady-State Polarization Measurements, 195
12.4 Transient (Pulse) Measurements, 199
12.5 Impedance Measurements, 207
PART II KINETICS OF ELECTROCHEMICAL REACTIONS 217
13. Multistep Electrode Reactions 219
13.1 Intermediate Reaction Steps, 219
13.2 Rate-Determining Step, 220
13.3 Two-Step Electrochemical Reactions, 222
13.4 Complex Electrochemical Reactions, 227
13.5 Reactions with Homogeneous Chemical Steps, 229
13.6 Reactions with Mediators, 233
13.7 Parallel Electrode Reactions, 235
CONTENTS vii
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14. Some Aspects of Electrochemical Kinetics 239
14.1 Energy of Activation, 239
14.2 Kinetic Influence of the Electric Double Layer, 245

14.3 Kinetic Influence of Adsorption, 248
14.4 Special Features of Reactions at Semiconductor Electrodes, 250
14.5 Reactions Producing a New Phase, 252
15. Reactions at Nonconsumable Electrodes 261
15.1 Simple Electrochemical Reactions, 261
15.2 Hydrogen Evolution and Ionization, 263
15.3 Reactions Involving Oxygen, 272
15.4 Reactions Involving Chlorine and Other Halogens, 277
15.5 Reactions Involving Organic Substances, 280
15.6 Reactions at High Anodic Potentials, 288
15.7 Reaction of Carbon Dioxide Reduction, 291
15.8 Reaction of Nitrogen Reduction, 294
16. Reactions Involving Metals 297
16.1 Reacting Metal Electrodes, 297
16.2 Anodic Metal Dissolution, 299
16.3 Surface-Layer Formation, 301
16.4 Passivation of Electrodes, 305
16.5 Cathodic Metal Deposition, 310
16.6 Electrochemical Metal Treatments, 315
PART III APPLIED ASPECTS OF ELECTROCHEMISTRY 319
17. Industrial Electrolytic Processes 321
17.1 Chlor-Alkali Electrolysis, 321
17.2 Water Electrolysis, 323
17.3 Electrometallurgy, 323
17.4 Electroplating, 324
18. Electrochemical Reactors 327
18.1 Design Principles, 327
18.2 Separators, 330
18.3 Macrokinetics of Electrochemical Processes
(Systems with Distributed Parameters), 334

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18.4 Porous Electrodes, 337
18.5 Three-Dimensional Electrodes, 342
19. Batteries (Electrochemical Power Sources) 343
19.1 Chemical Current-Producing Reactions in Batteries, 344
19.2 Performance of Batteries, 345
19.3 Electrochemical Systems, 349
19.4 Primary Batteries, 350
19.5 Storage Batteries, 353
19.6 Lithium Batteries, 367
20. Fuel Cells 361
20.1 Introduction, 361
20.2 Design Principles of Fuel Cells, 363
20.3 Proton-Exchange Membrane Fuel Cells, 364
20.4 Direct Methanol Fuel Cells, 366
21. Some Electrochemical Devices 369
21.1 Electrochemical Capacitors and Supercapacitors, 369
21.2 Electrochemical Transducers, 375
22. Corrosion of Metals 379
22.1 Various Types of Corrosion, 380
22.2 Mechanisms of Corrosion Processes, 381
22.3 Corrosion Protection, 384
23. Electrochemical Methods of Analysis 387
23.1 Conductometry, 388
23.2 Coulometry, 388
23.3 Amperometry, 389
23.4 Polarography, 390
23.5 Transient Voltammetric Techniques, 394
23.6 Potentiometry, 398

24. Electrochemistry and the Environment 405
Alexander Skundin (Sections 24.1 to 24.4) and Alvin J. Salkind
(Section 24.5)
24.1 Chemical and Electrochemical Processes, 405
24.2 Monitoring the Environment, 406
24.3 Purification Procedures (Elimination of Pollutants), 408
CONTENTS ix
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24.4 Medical Applications of Electrochemistry, 411
24.5 Electrochemical Aspects of Bone Remodeling and
Fracture Repair, 413
PART IV SELECTED TOPICS IN ELECTROCHEMISTRY 417
25. Solid-State Electrochemistry 419
Ulrich Stimming and Hengyong Tu (Part A)
Part A. Solid Electrolytes, 419
25.1 Defects in Solids, 419
25.2 Solid Ion Conductors, 425
25.3 Solid Mixed Ionic–Electronic Conductors, 436
25.4 Electrochemical Reactions at Interfaces with Solid
Electrolytes, 438
Part B. Solid-State Reactions, 441
25.5 Heterogeneous Solid-State Reactions, 441
25.6 Electrochemical Intercalation, 443
26. Conductive Polymers 449
Klaus Müller
26.1 Active Polymers, 449
26.2 Polymers with Ionic Functions, 450
26.3 Polymers with Electronic Functions, 457
27. Physical Methods for Investigation of Electrode Surfaces 467
James McBreen

27.1 Topics of Investigation, 468
27.2 X-Ray Methods, 470
27.3 Scanning Probe Methods, 484
27.4 Electrochemical Quartz Crystal Microbalance, 487
27.5 Optical Spectroscopy, 491
27.6 Infrared Spectroscopy, 503
27.7 Electrochemical NMR, 506
27.8 Ex Situ Methods, 507
27.9 The Future of Physical Methods in Electrochemistry, 516
28. Electrocatalysis 521
28.1 Introduction, 521
28.2 Electrocatalysis and Adsorption Effects, 523
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28.3 Metal Electrodes: Influence of the Nature of the Metal, 524
28.4 Metal Electrodes: Influence of Surface State and Structure, 530
28.5 Highly Disperse Metal Catalysts, 535
28.6 Binary and Multicomponent Metal Catalysts, 539
28.7 Nonmetallic Catalysts, 542
28.8 Stability of Electrocatalysts, 550
28.9 Other Aspects of Electrocatalysis, 551
28.10 Discussion, 552
29. Photoelectrochemistry 557
29.1 Energy Levels of Electrons, 558
29.2 Electron Photoemission into Solutions, 562
29.3 Photoexcitation of Semiconductor Electrodes, 564
29.4 Photoexcitation of Reacting Species, 570
30. Bioelectrochemistry 573
30.1 Transmission of the Nervous Impulse, 575
30.2 Bioenergetics, 584

30.3 Electrochemical Methods in Biology and Medicine, 589
31. Electrokinetic Processes 595
31.1 Electrokinetic Potential, 597
31.2 Basic Equations of Electrokinetic Processes, 600
31.3 Practical Use of Electrokinetic Processes, 605
32. Interfaces Between Two Immiscible Electrolyte Solutions 607
Zdeněk Samec
32.1 Equilibrium Galvani Potential Difference, 608
32.2 Ideally Polarizable ITIES, 612
32.3 Polarization Measurements, 612
32.4 Structure of ITIES, 614
32.5 Charge-Transfer Rate, 616
32.6 Applications, 618
33. Various Electrochemical Phenomena 621
Yurij Tolmachev (Section 33.1) and Leonid Kanevsky
(Section 33.2)
33.1 Electrochromism, 621
33.2 Electrochemical Noise, 626
CONTENTS xi
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33.3 Electrochemical Properties of High-Temperature
Superconductors, 630
33.4 Electrochemical “Cold Fusion”, 632
34. Main Concepts of Elementary Reaction Act Theory 637
Alexander Kuznetsov
34.1 Outer-Sphere Electron Transfer Reactions in the Bulk Solution, 638
34.2 Adiabatic and Nonadiabatic Reactions, 643
34.3 Electrochemical Electron Transfer, 645
34.4 Electrochemical Adiabaticity Parameter. Medium Dynamics
vs. Static Distribution, 650

34.5 Adiabatic Electrochemical Electron Transfer Reactions, 652
34.6 Electric Double-Layer Effects on the Elementary Act
of Electron Transfer, 653
34.7 Bond-Breaking Electron Transfer, 655
34.8 Reorganization Energy of the Medium and the
Frequency Factor, 657
34.9 Electrochemical Proton Transfer, 658
35. Computer Simulation in Electrochemistry 661
Ezequiel Leiva
35.1 Introduction, 661
35.2 Molecular(Atom) Dynamics, 662
35.3 Monte Carlo Methods, 668
36. Nanoelectrochemistry 679
Ezequiel Leiva
36.1 Introduction, 679
36.2 Probe-Induced Electrochemical Nanostructuring
of Metallic Surfaces, 680
36.3 Defect Nanostructuring, 681
36.4 Tip-Induced Local Metal Deposition, 684
36.5 Localized Electrochemical Nucleation and Growth, 686
36.6 Electronic Contact Nanostructuring, 688
36.7 Nanostructuring by Scanning Electrochemical Microscopy, 689
37. Development of Electrochemistry 693
37.1 First Electrochemical Power Sources, 693
37.2 Development of a Large-Scale Electrochemical Industry, 696
37.3 Fuel Cells and Lithium Batteries, 699
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Appendix A: Derivation of the Main Equation of
Debye–Hückel Theory 701

Appendix B: Derivation of the Main Equation of
Gouy–Chapman Theory 705
General Bibliography 709
Author Index 711
Subject Index 715
CONTENTS xiii
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xv
CONTRIBUTORS
PROF. VLADIMIR S. BAGOTSKY (retired from the A. N. Frumkin Institute
of Physical Chemistry and Electrochemistry, Russian Academy of Sciences,
Leninskij Prospekt 31, 119071 Moscow, Russia), Mountain View, CA 94043,
E-mail: —main author
DR. LEONID S. KANEVSKY, A. N. Frumkin Institute of Physical Chemistry and
Electrochemistry, Russian Academy of Sciences, Leninskij Prospekt 31, 119071
Moscow, Russia, E-mail: c/o —Section 33.2
PROF. ALEXANDER M. KUZNETSOV, A. N. Frumkin Institute of Physical Chemistry
and Electrochemistry, Russian Academy of Sciences, Leninskij Prospekt 31,
119071 Moscow, Russia, E-mail: —Chapter 34
PROF. EZEQUIEL P. M. LEIVA, INFIQC-Facultad de Ciencias Químicas, Universidad
Nacional de Córdoba, 5000 Córdoba, Argentina, E-mail:
edu.ar—Chapters 35 and 36
D
R. JAMES MCBREEN, Brookhaven National Laboratory, Material Sciences
Department, P.O. Box 5000, Upton, NY 11973-5000, E-mail: jmcbreen@
bnl.gov—Chapter 27
DR. KLAUS MÜLLER (retired from Battelle, Geneva, Switzerland), D-85560
Ebersberg, Germany, E-mail: —Chapter 25
PROF. ALVIN J. SALKIND, Bioengineering Division, University of Medicine and
Dentistry of New Jersey, Piscataway, NJ 08854-3635, E-mail: Alvin.

—Section 24.5
PROF. ZDENE

K SAMEC, J. Heyrovský Institute of Physical Chemistry, Academy of
Sciences of the Czech Republik, CZ-182 23 Prague, Czech Republic, E-mail:
—Chapter 32
D
R. ALEXANDER M. SKUNDIN, A. N. Frumkin Institute of Physical Chemistry and
Electrochemistry, Russian Academy of Sciences, Leninskij Prospekt 31, 119071
Moscow, Russia, E-mail: —Sections 24.1 to 24.4
P
ROF. ULRICH STIMMING, Physik-Department E-19, Technische Universität
München, D-85748 Garching, Germany, E-mail: —Chapter
26, Part A
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PROF. YURIJ TOLMACHEV, Kent State University, Kent, OH 44242-0001,
E-mail: —Section 33.1
DR. HENGYONG TU, Physik-Department E-19, Technische Universität München, D-
85748 Garching, Germany—Chapter 26, Part A
xvi CONTRIBUTORS
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PREFACE TO THE
SECOND EDITION
Substantial changes from the first English edition of this book (1993, Plenum Press,
New York) have been introduced in this second edition. The content was rearranged
such that all basic knowledge is contained in the first part of the book. This part
was rewritten and to some extent simplified and can be used as a textbook for
undergraduate students in electrochemistry and related branches. More advanced
topics that will be of interest for people at a postgraduate level can be found in the
subsequent parts. Eight new chapters have been added to these parts, most of which

describe recent developments in theoretical and applied electrochemistry. Some of
the new chapters were written by the author; other chapters and sections of the book
were written by well-known experts in the corresponding fields. The author is very
grateful to all coauthors for their cooperation in preparing this book and to Dr. Nina
Osetrova and Dr. Alexander Skundin from Moscow for compiling the references for
many chapters. The author is also greatly indebted to Dr. Klaus Müller from Geneva
for translating from Russian the chapters or sections written by the main author and
some coauthors, and for many helpful comments and remarks during preparation of
the manuscript.
VLADIMIR SERGEEVICH BAGOTSKY
Moscow and Mountain View, CA
December 2004
xvii
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PREFACE TO THE FIRST EDITION
Of all electrical phenomena electrolysis appears the most likely to furnish us
with a real insight into the true nature of the electric current. because we find
currents of ordinary matter and currents of electricity forming essential parts of
the same phenomenon.
—James Clerk Maxwell
A Treatise on Electricity and Magnetism,
Vol. 1, Oxford, 1873
Two very important fields of natural science—chemistry and the science of electricity—
matured and grew vigorously during the first half of the nineteenth century. Electro-
chemistry developed simultaneously. From the very beginning, electrochemistry was
not merely a peripheral field but evolved with an important degree of independence, and
it also left very significant marks on the development of chemistry and of the theory of
electricity.
The first electrochemical device was the voltaic pile, built in 1800. For the first time,
scientists had a sufficiently stable and reliable source of electric current. Research into

the properties of this current provided the basis for progress in electrodynamics and
electromagnetism. The laws of interaction between electric currents (André-Marie
Ampère, 1820), of proportionality between current and voltage (Georg Simon Ohm,
1827), of electromagnetic induction (Michael Faraday, 1831), of heat evolution during
current flow (James Prescott Joule, 1843), and others were discovered.
Work involving the electrolysis of aqueous solutions of salts and salt melts that was
performed at the same time led to the discovery and preparation of a number of new
chemical elements, such as potassium and sodium (Sir Humphry Davy, 1807). Studies
of current flow in solutions (Theodor von Grotthuss, 1805) formed the starting point
for the concept that the molecular structure of water and other substances is polar, and
led to the electrochemical theory of the structure of matter formulated by Jons Jakob
Berzelius (1820). The laws of electrolysis discovered in 1833 by Faraday had an even
greater significance for knowledge concerning the structure of matter. During the
second half of the nineteenth century, the development of chemical thermodynamics
was greatly facilitated by the analysis of phenomena occurring in electrochemical cells
at equilibrium.
Today, electrochemistry is a rigorous science concerned with the quantitative
relations among the chemical, surface, and electrical properties of systems.
Electrochemistry has strong links to many other fields of science. Electrochemical
concepts proved particularly fruitful for studying and interpreting a number of very
important biological processes.
xix
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Modern electrochemistry has vast applications. Electrochemical processes form
the basis of large-scale chemical and metallurgical production of a number of materials.
Electrochemical phenomena are responsible for metallic corrosion, which causes
untold losses in the economy. Modern electrochemical power sources (primary and
secondary batteries) are used in many fields of engineering, and their production
figures are measured in billions of units. Other electrochemical processes and devices
are also used widely.

A variety of definitions exist for electrochemistry as a subject. Thus, electro-
chemistry can be defined as the science concerned with the mutual transformation of
chemical and electrical energy. According to another definition, electrochemistry
deals with the structure of electrolyte solutions as well as with the phenomena
occurring at the interfaces between metallic electrodes and electrolyte solutions.
These and similar definitions are incomplete and do not cover all subject areas
treated in electrochemistry. By the very general definition adopted today by most
research workers, electrochemistry is the science concerned with the physical and
chemical properties of ionic conductors as well as with phenomena occurring at the
interfaces between ionic conductors, on the one hand, and electronic conductors or
semiconductors, other ionic conductors, and even insulators (including gases and
vacuum), on the other hand. All these properties and phenomena are studied both under
equilibrium conditions, when there is no current flow, and under nonequilibrium
conditions, when there is electric current flow in the system. In a certain sense,
electrochemistry can be contrasted to electronics and solid-state theory, where the
properties of electronic conductors and electronic or hole-type semiconductors as
well as the phenomena occurring at the interfaces between these materials or
between the materials and vacuum are examined.
This definition of electrochemistry disregards systems in which nonequilibrium
charged species are produced by external action in insulators: for example, by electric
discharge in the gas phase (electrochemistry of gases) or upon irradiation of liquid and
solid dielectrics (radiation chemistry). At the same time, electrochemistry deals with
certain problems often associated with other fields of science, such as the structure and
properties of solid electrolytes and the kinetics of ionic reactions in solutions.
This book seeks essentially to provide a rigorous, yet lucid and comprehensible
outline of the basic concepts (phenomena, processes, and laws) that form the subject
matter of modern theoretical and applied electrochemistry. Particular attention is
given to electrochemical problems of fundamental significance, yet those often
treated in an obscure or even incorrect way in monographs and texts. Among these
problems are some, that appear elementary at first glance, such as the mechanism of

current flow in electrolyte solutions, the nature of electrode potentials, and the values
of the transport numbers in diffusion layers.
By considering the theoretical and applied aspects of electrochemistry jointly,
one can more readily comprehend their intimate correlation and gain a fuller insight
into this science as a whole. The applied part of the book outlines the principles of
some processes and illustrates their practical significance but does not describe
technical or engineering details or the design of specific equipment, as these can be
found in specialized treatises on applied electrochemistry.
xx PREFACE TO THE FIRST EDITION
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As a rule, the mathematical tools used in electrochemistry are simple. However,
in books on electrochemistry, one often finds equations and relations that are quite
unwieldy and not transparent enough. The author’s prime aim is that of elucidating
the physical ideas behind the laws and relations and of presenting all equations in the
simplest possible, though still rigorous and general, form.
There is a great deal of diversity in the terminology and names used for electro-
chemical concepts in the literature. It is the author’s aim to introduce uniform termi-
nology in accordance with valid standards and recommendations. For a profitable
reading of the book and understanding of the material presented, the reader should
know certain parts of physics (e.g., electrostatics), the basics of higher mathematics
(differentiation and integration), and the basics of physical chemistry, particularly
chemical thermodynamics.
VLADIMIR SERGEEVICH BAGOTSKY
PREFACE TO THE FIRST EDITION xxi
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LIST OF PHOTOGRAPHS
Some outstanding scientists who have advanced the science of electrochemistry
Svante August Arrhenius (1859–1927; Nobel prize, 1903), 102
David L. Chapman (1867–1958), 151
Peter Debye (1884–1966; Nobel prize, 1936), 116

Boris V. Ershler (1908–1978), 199
Michael Faraday (1791–1867), 16
Alexander N. Frumkin (1895–1976), 246, 698
Luigi Galvani (1737–1798), 574
Josiah Willard Gibbs (1839–1903), 163
Georges Gouy (1854–1926), 151
David C. Grahame (1912–1958), 153
Jaroslav Heyrovský (1890–1967; Nobel prize, 1959), 393
Erich Hückel (1896–1980), 116
Boris N. Kabanov (1904–1988), 445
Irving Langmuir (1881–1957; Nobel prize, 1932), 159
Veniamin G. Levich (1917–1987), 65
Walther Nernst (1864–1941; Nobel prize, 1920), 42
Friedrich Wilhelm Ostwald (1853–1932; Nobel prize, 1909), 695
Otto Stern (1888–1969; Nobel prize, 1943), 153
Julius Tafel (1862–1918), 82
Michail I. Temkin (1908–1991), 159
Jacobus Hendricus van’t Hoff (1852–1911; Nobel prize, 1901), 101
Max Volmer (1885–1965), 268
Alessandro Volta (1745–1827), 574
Hermann von Helmholtz (1821–1894), 148
xxii
Italic numbers at the end are pages where the photographs appear.
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ABBREVIATIONS
ac alternating current
AFC alkaline fuel cell
AE auxiliary electrode
BL γ-butyrolactone
CD current density

dc direct current
DME dropping mercury electrode
DMF dimethylformamide
DMFC direct methanol fuel cell
DSA
®
dimensionally stable anode
ECC electrocapillary curves
EDL electric double layer
EMF electromotive force
EPS electrochemical power source
ESE excess surface energy
ETR electron transfer reaction
eV electron-volt
hap high anodic potentials
ITIES interface between two immiscible electrolyte solutions
LPD linear potential scan
MCFC molten carbonate fuel cell
MEA membrane-electrode assembly
MIEC mixed ionic-electronic conductor
OCP open-circuit potential
OCV open-circuit voltage
Ox, ox oxidized form
PAFC phosphoric acid fuel cell
PEMFC proton exchange membrane fuel cell
PC propylene carbonate
PD potential difference
PTFE polytetrafluoroethylene
PVC poly(vinyl chloride)
PZC point (or potential) of zero charge

RDE rotating disk electrode
These abbreviations are used in most chapters. In some chapters other (specific) abbreviations are used.
Abbreviations employed in physical experimental methods used in electrochemistry are listed in Chapter 27.
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RDS rate determining step
RE reference electrode
Red, red reduced form
RHE reversible hydrogen electrode
RRDE rotating ring disk electrode
SCE saturated calomel electrode
SECM scanning electrochemical microscope
THF tetrahydrofuran
SCE saturated calomel electrode
SOFC solid oxide fuel cell
SHE standard hydrogen electrode
UDP underpotential deposition
UME ultramicroelectrode
WE working electrode
YSZ yttria stabilized zirconia
xxiv ABBREVIATIONS
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SYMBOLS
Usual
Dimensions Section
Symbol Meaning (values) References
*
Roman Symbols
a
j

thermodynamic activity molиdm
Ϫ3
3.3.1
a
Ϯ
mean ion thermodynamic activity molиdm
Ϫ3
3.3.2
(2) activation energy kJиmol
Ϫ1
8.3
(3) adsorption molиcm
Ϫ2
10.2
B adsorption coefficient dm
3
иmol
Ϫ1
10.2.4
c
j
concentration molиdm
Ϫ3
1.2
C differential double layer capacity µFиcm
Ϫ2
10.1.2
D
j
diffusion coefficient cm

2
иs
Ϫ1
4.1
E electrode potential V 2.4
E electrostatic field strength Vиcm
Ϫ1
1.3
E
1/2
half-wave potential V 6.3.1
ε voltage of a galvanic cell V 2.3
f (1) number of revolutions per
second s
Ϫ1
4.4.2
(2) ac frequency s
Ϫ1
12.5
f
j
activity coefficient none 3.3.1
F Faraday constant 96485 Cиmol
Ϫ1
1.2
G Gibbs energy kJиmol
Ϫ1
3.3.2
h Planck constant (h
–

ϵh/2π) 6.626и10
Ϫ34
Jиs 14.1.1
h
j
generalized rate constant cmиs
Ϫ1
6.4
H enthalpy kJиmol
Ϫ1
3.2.1
i current density (CD) mAиcm
Ϫ2
1.3
i
O
exchange current density mAиcm
Ϫ2
2.2
i
→
partial anodic CD mAиcm
Ϫ2
2.2
i
←
partial cathodic CD mAиcm
Ϫ2
2.2
I

c
ionic strength molиdm
Ϫ3
7.3.2
These symbols are used in most chapters, but in some chapters other symbols are also used. Symbols sim-
ilar to those listed may have different meanings in a local context.
*
Sections where this symbol is used for the first time and/or where its definition is given.
xxv
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J
j
flux density molиs
Ϫ1
иcm
Ϫ2
1.3
k (1) rate constant cmиs
Ϫ1
6.2.2
(2) Boltzman constant 1.381и10
Ϫ23
JиK
Ϫ1
14.1.1
m molal concentration molиkg
Ϫ1
M molar concentration molиdm
Ϫ3
n number of electrons in the

reaction’s elementary act none 1.6
N
A
Avogadro constant 6.022и10
23
mol
Ϫ1
1.2
p (1) gas pressure MPa 3.2.1
(2) reaction order none 6.2
(3) specific power kWиkg
Ϫ1
19.2.1
P power W, kW 19.2.1
Q heat of reaction J 7.2
Q electric charge C, µC 1.2
Q
0
elementary electric charge 1.602и10
Ϫ19
C 1.2
R (1) molar gas constant 8.314 Jиmol
Ϫ1
иK
Ϫ1
3.2.1
(2) resistance Ω
S (1) surface area cm
2
(2) entropy kJиK

Ϫ1
3.2.1
t
j
transport number of ions j none 1.3
T absolute temperature K
u
j
mobility of ion j cm
2
иV
Ϫ1
иs
Ϫ1
1.2
U (1) internal energy kJиmol
Ϫ1
3.2.1
(2) level of electron energy eV 29.1

(1) linear velocity cmиs
Ϫ1
1.3
(2) rate of reaction (specific) molиcm
Ϫ2
иs
Ϫ1
1.7
(3) linear scan rate Vиs
Ϫ1

23.5.3
w (1) work kJ
(2) specific energy kWhиkg
Ϫ1
19.2.1
X
j
reactant in an electrode reaction none
Y
ෆ
admittance (ac conductance) complex 12.5
z
j
charge number of ions j none
Z
ෆ
impedance of ac circuits complex 12.5
Greek Symbols
α (1) transfer coefficient none 6.2.1
(2) enhancement factor none 3.3.4
β transfer coefficient none 6.2.3
γ formal roughness factor none 18.4
γ
j
(1) stoichiometric activity
coefficient none 3.3.2
(2) nonequilibrium factor none 6.3.3
Γ Gibbs surface excess molиcm
Ϫ2
10.3

δ diffusion layer thickness cm 4.2
xxvi SYMBOLS
flast.qxd 10/29/2005 12:13 PM Page xxvi
ε (1) relative permittivity of a
dielectric none 2.0
(2) coefficient of resistance rise none 18.2.2
ε
0
permittivity of vacuum (8.85и10
Ϫ14
Fиcm
Ϫ1
) 2.0
ζ electrokinetic potential V 3.1.1
η (1) cell overvoltage V 2.5.2
(2) viscosity coefficient Nиs/cm
2
4.4.1
θ (1) drag coefficient J/s 1.3
(2) degree of surface coverage none 10.2
κ diffusion flux constant cmиs
Ϫ1
4.2
λ degree of partial charge transfer none 10.1.2
λ
j
molar conductivity of ions j Sиcm
Ϫ2
иmol
Ϫ1

1.3
Λ molar conductivity of an
electrolyte solution Sиcm
Ϫ2
иmol
Ϫ1
1.3
µ
j
chemical potential kJиmol
Ϫ1
3.2.1
µ
ෆ
j
electrochemical potential kJиmol
Ϫ1
3.2.2
ν
j
stoichiometric coefficient none 1.5
ν
kin
kinematic viscosity m
2
иs
Ϫ1
4.4.1
Π (1) osmotic pressure MPa 7.1
(2) pore perimeter cm 19.3

ρ resistivity Ωиcm 1.3
σ conductivity Sиcm
Ϫ2
1.3
τ
j
number of ions j none 1.2
ϕ
G
Galvani potential V 2.1
ϕ
V
Volta potential V 9.3
χ surface potential V 9.1
Ψ electrostatic potential V 2.0
ω (1) angular velocity radianиs
Ϫ1
4.4.2
(2) angular ac frequency radianиs
Ϫ1
12.5
Subscripts
ads adsorbed
A acid
B base
e electrical
ext external
d discharge
E electrolyte
ch (1) chemical

(2) charge
fin final
in initial
j any ion
ϩ cation
Ϫ anion
SYMBOLS xxvii
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ddiffusion
k kinetic
l limiting
m (1) migration
(2) maximal
(3) any electrode reaction
M metal
ohm ohmic
R reference electrode
r reactant
p product
red reducer
S per unit area
V per unit volume
ox oxidizer
k solute
kv convection
0 (1) standard
(2) without current
σ all particles in electrolyte
Superscripts
E electrolyte

M metal
or orientational
σ surface excess
xxviii SYMBOLS
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