Modern Electrochemistry 2A. Second Edition. Fundamentals of Electrodics

Modern Electrochemistry 2A. Second Edition. Fundamentals of Electrodics

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English

Description

This long-awaited and thoroughly updated version of the classic text (Plenum Press, 1970) explains the subject of electrochemistry in clear, straightforward language for undergraduates and mature scientists who want to understand solutions. Like its predecessor, the new text presents the electrochemistry of solutions at the molecular level. The Second Edition takes full advantage of the advances in microscopy, computing power, and industrial applications in the quarter century since the publication of the First Edition. Such new techniques include scanning-tunneling microscopy, which enables us to see atoms on electrodes; and new computers capable of molecular dynamics calculations that are used in arriving at experimental values.
A description of the electrochemical stage - the high field region near the interface - is the topic of Chapter 6 and involves a complete rewrite of the corresponding chapter in the First Edition, particularly the various happenings which occur with organic molecules which approach surfaces in solution. The chapter on electrode kinetics retains material describing the Butler-Volmer equation from the First Edition, but then turns to many new areas, including electrochemical theories of potential-dependent gas catalysis. Chapter 8 is a new one devoted to explaining how electrochemists deal with the fast-changing nature of the electrode surface. Quantum Mechanics as the basis to electrode kinetics is given an entirely new look - up to and including considerations of bond-breaking reactions.

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Published 01 January 2001
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EAN13 0306476053
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CONTENTS
CHAPTER 6
THE ELECTRIFIED INTERFACE
6.1. 6.1.1. 6.1.2. 6.1.3. 6.1.4. 6.1.5.
6.1.6.
6.1.7. 6.1.8.
6.1.9.
6.1.10. 6.2. 6.2.1.
6.2.2. 6.2.3. 6.2.4. 6.2.5.
Electrification of an Interface 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? Experimental Techniques Used in Studying Interfaces 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 Situvs.Ex SituTechniques Ex SituTechniques 6.2.5.1.LowEnergy Electron Diffraction (LEED) 6.2.5.2.XRay Photoelectron Spectroscopy (XPS)
xv
771 771 771 774 774
775
775 778
778
780 780 782
782 782 784 785 788 788 794
xviCONTENTS
6.2.6.
6.3. 6.3.1.
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.
6.4. 6.4.1.
6.4.2. 6.4.3. 6.4.4.
6.4.5. 6.5.
In SituTechniques 6.2.6.1.InfraredReflection Spectroscopy 6.2.6.2.Radiochemical Methods
The Potential Difference Across Electrified Interfaces 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 The Accumulation and Depletion of Substances at an Interface 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? The Thermodynamics of Electrified Interfaces
797 797 804 806
806 811 813 815
817 821 822 823
824
826 828
829
830 830
832
833 834 834 837 837 839 841
842
842 843 845
846 847 848
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.
6.6. 6.6.1 6.6.2. 6.6.3.
6.6.4.
6.6.5.
6.6.6.
6.6.7. 6.6.8. 6.6.9.
6.7. 6.7.1. 6.7.2. 6.7.3.
6.7.4.
6.7.5.
6.7.6. 6.7.7.
CONTENTSxvii
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 The Structure of Electrified Interfaces 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 Structure at the Interface of the Most Common Solvent: Water 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
848 848
849 852 854
858
859 861
862 866 869 870 871 871 873
876
876
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882 887 890
893 894 895 895 896
897
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900 904
910
xviiiCONTENTS
6.7.8.
6.7.9.
6.8. 6.8.1. 6.8.2.
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. 6.9.1. 6.9.2. 6.9.3.
6.9.4. 6.9.5. 6.9.6.
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
Ionic Adsorption 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. 6.8.2.2.Solvent Interactions. 6.8.2.3. Lateral Interactions. 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
The Adsorption Process of Organic Molecules The Relevance of Organic Adsorption Is Adsorption the Only Process that the Organic Molecules Can Undergo? Identifying Organic Adsorption 6.9.3.1.Test 1: The AlmostNull Current. 6.9.3.2.Test 2: The Parabolic CoveragePotential Curve. 6.9.3.3.the CoveragePotential CurveTest 3: The Maximum of 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
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915 918 919 919
920 920 923 924 926
929 931 933 936 937 938 938 941 941 944 955 959 961 962 963 967 968 968 969 970 970 970
971 971 972
978
978
6.9.6.2. 6.9.6.3.
Electrode Properties. Electrolyte Properties.
CONTENTSxix
6.10.The Structure of Other Interfaces 6.10.1.the Semiconductor–Electrolyte InterfaceThe Structure of 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 andpType. 6.10.1.8.Surface States: The Semiconductor Analogue of Contact Adsorption 6.10.2. Colloid Chemistry 6.10.2.1.the Double Layer and the BulkColloids: The Thickness of 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. 6.11.Double Layers Between Phases Moving Relative to Each Other 6.11.1.The Phenomenology of Mobile Electrified Interfaces: Electrokinetic Properties 6.11.2.The Relative Motion of One of the Phases Constituting an Electrified Interface Produces a Streaming Current 6.11.3.A Potential Difference Applied Parallel to an Electrified Interface Produces an Electroosmotic Motion of One of the Phases Relative to the Other 6.11.4. Electrophoresis: Moving Solid Particles in a Stationary Electrolyte Further Reading Exercises Problems Micro Research Problems
Appendix 6.1
CHAPTER 7
ELECTRODICS
7.1.
Introduction
979 981 984 984 984 985 988
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992 995 997
1000 1001
1001 1002 1005 1006
1006
1008
1011 1012 1015 1015 1020 1029 1031
1035
xxCONTENTS
7.1.1.
7.1.2. 7.1.3.
7.1.4. 7.2. 7.2.1.
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.
7.3.1.
7.3.2. 7.3.3.
7.4. 7.4.1.
7.4.2.
7.4.3. 7.4.4. 7.4.5. 7.4.6.
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). 7.1.3.2.The Fuel Cell (or Electricity Producer). 7.1.3.3.The Electrochemical Undevice: An Electrode that Consumes Itself while Wasting Energy Some Special Characteristics of Electrochemical Reactions Electron Transfer Under an Interfacial Electric Field 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 A More Detailed Look at Some Quantities in the Butler–Volmer Equation 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 Electrode Kinetics Involving the Semiconductor/solution Interface Introduction 7.4.1.1.General. 7.4.1.2. ThenpJunction. The CurrentPotential Relation at a Semiconductor/Electrolyte Interface (Negligible Surface States) Effect of Surface States on Semiconductor Electrode Kinetics The Use ofnandpSemiconductors for Thermal Reactions The Limiting Current in Semiconductor Electrodes Photoactivity of Semiconductor Electrodes
1035 1036 1036 1036 1039
1040 1041 1042
1047 1049
1052 1054 1054 1055
1057 1058 1058 1062 1064 1065 1067
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1068 1071
1072 1073 1074 1074 1074 1075
1082 1086 1086 1088 1089
7.5. 7.5.1. 7.5.2. 7.5.3. 7.5.4.
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.
CONTENTSxxi
Further Reading Techniques of Electrode Kinetics Preparing the Solution Preparing the Electrode Surface Real Area Microelectrodes 7.5.4.1. The Situation. 7.5.4.2. Lessening Diffusion Control by the Use of a Microelectrode 7.5.4.3.Microelectrodes.Reducing Ohmic Errors by the Use of 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. 7.5.7.2. More on Luggin Capillaries and Tips. 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
1090 1091 1091 1094 1095 1097 1097 1098 1099 1100 1100 1102 1103 1103 1104 1104 1107 1108 1111
1112 1113
1115 1121
1122
1123 1123 1125 1127 1127 1128 1129
1131 1133 1133 1135
1136
1136 1138 1139
xxiiCONTENTS
7.5.15.
7.5.16.
7.5.17.
7.5.18. 7.5.19.
7.6. 7.6.1. 7.6.2. 7.6.3. 7.6.4. 7.6.5. 7.6.6. 7.6.7. 7.6.8.
7.6.9. 7.6.10.
7.6.11.
7.6.12. 7.6.13.
7.5.14.1.General. 7.5.14.2. 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ScaleIn SituMicroscopy 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
Multistep Reactions 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
1139
1143 1144 1145 1145 1147 1147 1147 1148 1149 1152 1153 1154 1154
1156 1157 1159 1159 1160
1161
1162 1162 1164 1166 1166 1167 1167 1168 1168 1169 1171
1172 1175
1180
1182 1187
1190
7.7.
7.7.1. 7.7.2. 7.7.3. 7.7.4. 7.7.5.
7.7.6.
7.8. 7.8.1. 7.8.2. 7.8.3.
7.8.4.
7.8.5. 7.8.6.
7.9. 7.9.1. 7.9.2.
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.
CONTENTS
Further Reading The Intermediate Radical Concentration, and Its Effect on Electrode Kinetics 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 The Reactivity of Crystal Planes of Differing Orientation 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 Transport in the Electrolyte Effects Charge Transfer at the Interface 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
xxiii
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1197 1201 1201 1201 1201
1203
1205 1209 1210 1210 1211 1211
1213 1215
1216
1218 1221 1225 1230 1232 1235 1237
1246 1247 1247
1248 1250
xxivCONTENTS
7.9.16. 7.9.17. 7.9.18.
7.9.19.
7.10.
7.10.1. 7.10.2.
7.10.3. 7.10.4.
7.10.5. 7.11. 7.11.1. 7.11.2.
7.11.3. 7.11.4. 7.11.5. 7.11.6.
7.12. 7.12.1. 7.12.2. 7.12.3.
7.12.4. 7.12.5. 7.12.6.
7.12.7.
7.12.8.
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 How to Determine the Stepwise Mechanisms of Electrodic Reactions 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 Electrocatalysis 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.Enzymes on Electrodes.Practical Applications of Further Reading The Electrogrowth of Metals on Electrodes 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
1251 1252
1253 1254 1256
1257 1257
1258 1258 1259 1260 1263 1269 1273 1274 1275 1275
1277 1280 1284 1286 1287 1287 1289
1289 1291 1292 1293 1293 1294
1296 1301 1302
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1306 1307