Electrochemical Methods

Allen J. Bard is Professor and Hackerman-Welch Regents Chair in Chemistry at the University of Texas at Austin in the United States. His research is focused on the application of electrochemical methods to the study of chemical problems.Larry R. Faulkner is President Emeritus of the University of Texas at Austin in the United States. He has served on the chemistry faculties of Harvard University, the University of Illinois, and the University of Texas. Henry S. White is Distinguished Professor and John A. Widstoe Presidential Chair in the Department of Chemistry at the University of Utah in the United States. His research is focused on experimental and theoretical aspects of electrochemistry.

• Preface xxiMajor Symbols and Abbreviations xxvAbout the Companion Website liii1 Overview of Electrode Processes 11.1 Basic Ideas 21.1.1 Electrochemical Cells and Reactions 21.1.2 Interfacial Potential Differences and Cell Potential 41.1.3 Reference Electrodes and Control of Potential at a Working Electrode 51.1.4 Potential as an Expression of Electron Energy 61.1.5 Current as an Expression of Reaction Rate 61.1.6 Magnitudes in Electrochemical Systems 81.1.7 Current–Potential Curves 91.1.8 Control of Current vs. Control of Potential 161.1.9 Faradaic and Nonfaradaic Processes 171.2 Faradaic Processes and Factors Affecting Rates of Electrode Reactions 171.2.1 Electrochemical Cells—Types and Definitions 171.2.2 The Electrochemical Experiment and Variables in Electrochemical Cells 181.2.3 Factors Affecting Electrode Reaction Rate and Current 211.3 Mass-Transfer-Controlled Reactions 231.3.1 Modes of Mass Transfer 241.3.2 Semiempirical Treatment of Steady-State Mass Transfer 251.4 Semiempirical Treatment of Nernstian Reactions with Coupled Chemical Reactions 311.4.1 Coupled Reversible Reactions 311.4.2 Coupled Irreversible Chemical Reactions 321.5 Cell Resistance and the Measurement of Potential 341.5.1 Components of the Applied Voltage When Current Flows 351.5.2 Two-Electrode Cells 371.5.3 Three-Electrode Cells 371.5.4 Uncompensated Resistance 381.6 The Electrode/Solution Interface and Charging Current 411.6.1 The Ideally Polarizable Electrode 411.6.2 Capacitance and Charge at an Electrode 411.6.3 Brief Description of the Electrical Double Layer 421.6.4 Double-Layer Capacitance and Charging Current 441.7 Organization of this Book 511.8 The Literature of Electrochemistry 521.8.1 Reference Sources 521.8.2 Sources on Laboratory Techniques 531.8.3 Review Series 531.9 Lab Note: Potentiostats and Cell Behavior 541.9.1 Potentiostats 541.9.2 Background Processes in Actual Cells 551.9.3 Further Work with Simple RC Networks 561.10 References 571.11 Problems 572 Potentials and Thermodynamics of Cells 612.1 Basic Electrochemical Thermodynamics 612.1.1 Reversibility 612.1.2 Reversibility and Gibbs Free Energy 642.1.3 Free Energy and Cell emf 642.1.4 Half-Reactions and Standard Electrode Potentials 662.1.5 Standard States and Activity 672.1.6 emf and Concentration 692.1.7 Formal Potentials 712.1.8 Reference Electrodes 722.1.9 Potential–pH Diagrams and Thermodynamic Predictions 762.2 A More Detailed View of Interfacial Potential Differences 802.2.1 The Physics of Phase Potentials 802.2.2 Interactions Between Conducting Phases 822.2.3 Measurement of Potential Differences 842.2.4 Electrochemical Potentials 852.2.5 Fermi Energy and Absolute Potential 882.3 Liquid Junction Potentials 912.3.1 Potential Differences at an Electrolyte–Electrolyte Boundary 912.3.2 Types of Liquid Junctions 912.3.3 Conductance, Transference Numbers, and Mobility 922.3.4 Calculation of Liquid Junction Potentials 962.3.5 Minimizing Liquid Junction Potentials 1002.3.6 Junctions of Two Immiscible Liquids 1012.4 Ion-Selective Electrodes 1012.4.1 Selective Interfaces 1012.4.2 Glass Electrodes 1022.4.3 Other Ion-Selective Electrodes 1062.4.4 Gas-Sensing ISEs 1112.5 Lab Note: Practical Use of Reference Electrodes 1122.5.1 Leakage at the Reference Tip 1122.5.2 Quasireference Electrodes 1122.6 References 1132.7 Problems 1163 Basic Kinetics of Electrode Reactions 1213.1 Review of Homogeneous Kinetics 1213.1.1 Dynamic Equilibrium 1213.1.2 The Arrhenius Equation and Potential Energy Surfaces 1223.1.3 Transition State Theory 1233.2 Essentials of Electrode Reactions 1253.3 Butler–Volmer Model of Electrode Kinetics 1263.3.1 Effects of Potential on Energy Barriers 1273.3.2 One-Step, One-Electron Process 1273.3.3 The Standard Rate Constant 1303.3.4 The Transfer Coefficient 1313.4 Implications of the Butler–Volmer Model for the One-Step, One-Electron Process 1323.4.1 Equilibrium Conditions and the Exchange Current 1333.4.2 The Current–Overpotential Equation 1333.4.3 Approximate Forms of the i–η Equation 1353.4.4 Exchange Current Plots 1393.4.5 Very Facile Kinetics and Reversible Behavior 1393.4.6 Effects of Mass Transfer 1403.4.7 Limits of Basic Butler–Volmer Equations 1413.5 Microscopic Theories of Charge Transfer 1423.5.1 Inner-Sphere and Outer-Sphere Electrode Reactions 1423.5.2 Extended Charge Transfer and Adiabaticity 1433.5.3 The Marcus Microscopic Model 1463.5.4 Implications of the Marcus Theory 1523.5.5 A Model Based on Distributions of Energy States 1623.6 Open-Circuit Potential and Multiple Half-Reactions at an Electrode 1683.6.1 Open-Circuit Potential in Multicomponent Systems 1693.6.2 Establishment or Loss of Nernstian Behavior at an Electrode 1703.6.3 Multiple Half-Reaction Currents in i–E Curves 1713.7 Multistep Mechanisms 1713.7.1 The Primacy of One-Electron Transfers 1723.7.2 Rate-Determining, Outer-Sphere Electron Transfer 1733.7.3 Multistep Processes at Equilibrium 1733.7.4 Nernstian Multistep Processes 1743.7.5 Quasireversible and Irreversible Multistep Processes 1743.8 References 1773.9 Problems 1804 Mass Transfer by Migration and Diffusion 1834.1 General Mass-Transfer Equations 1834.2 Migration in Bulk Solution 1864.3 Mixed Migration and Diffusion Near an Active Electrode 1874.3.1 Balance Sheets for Mass Transfer During Electrolysis 1884.3.2 Utility of a Supporting Electrolyte 1924.4 Diffusion 1934.4.1 A Microscopic View 1934.4.2 Fick’s Laws of Diffusion 1964.4.3 Flux of an Electroreactant at an Electrode Surface 1994.5 Formulation and Solution of Mass-Transfer Problems 1994.5.1 Initial and Boundary Conditions in Electrochemical Problems 2004.5.2 General Formulation of a Linear Diffusion Problem 2014.5.3 Systems Involving Migration or Convection 2024.5.4 Practical Means for Reaching Solutions 2024.6 References 2044.7 Problems 2055 Steady-State Voltammetry at Ultramicroelectrodes 2075.1 Steady-State Voltammetry at a Spherical UME 2075.1.1 Steady-State Diffusion 2085.1.2 Steady-State Current 2115.1.3 Convergence on the Steady State 2115.1.4 Steady-State Voltammetry 2125.2 Shapes and Properties of Ultramicroelectrodes 2145.2.1 Spherical or Hemispherical UME 2155.2.2 Disk UME 2155.2.3 Cylindrical UME 2215.2.4 Band UME 2215.2.5 Summary of Steady-State Behavior at UMEs 2225.3 Reversible Electrode Reactions 2245.3.1 Shape of the Wave 2245.3.2 Applications of Reversible i–E Curves 2265.4 Quasireversible and Irreversible Electrode Reactions 2305.4.1 Effect of Electrode Kinetics on Steady-State Responses 2305.4.2 Total Irreversibility 2325.4.3 Kinetic Regimes 2345.4.4 Influence of Electrode Shape 2345.4.5 Applications of Irreversible i–E Curves 2355.4.6 Evaluation of Kinetic Parameters by Varying Mass-Transfer Rates 2375.5 Multicomponent Systems and Multistep Charge Transfers 2395.6 Additional Attributes of Ultramicroelectrodes 2415.6.1 Uncompensated Resistance at a UME 2415.6.2 Effects of Conductivity on Voltammetry at a UME 2425.6.3 Applications Based on Spatial Resolution 2435.7 Migration in Steady-State Voltammetry 2455.7.1 Mathematical Approach to Problems Involving Migration 2455.7.2 Concentration Profiles in the Diffusion–Migration Layer 2465.7.3 Wave Shape at Low Electrolyte Concentration 2485.7.4 Effects of Migration on Wave Height in SSV 2485.8 Analysis at High Analyte Concentrations 2515.9 Lab Note: Preparation of Ultramicroelectrodes 2535.9.1 Preparation and Characterization of UMEs 2545.9.2 Testing the Integrity of a UME 2545.9.3 Estimating the Size of a UME 2565.10 References 2575.11 Problems 2586 Transient Methods Based on Potential Steps 2616.1 Chronoamperometry Under Diffusion Control 2616.1.1 Linear Diffusion at a Plane 2626.1.2 Response at a Spherical Electrode 2656.1.3 Transients at Other Ultramicroelectrodes 2676.1.4 Information from Chronoamperometric Results 2706.1.5 Microscopic and Geometric Areas 2716.2 Sampled-Transient Voltammetry for Reversible Electrode Reactions 2756.2.1 A Step to an Arbitrary Potential 2766.2.2 Shape of the Voltammogram 2776.2.3 Concentration Profiles When R Is Initially Absent 2786.2.4 Simplified Current–Concentration Relationships 2796.2.5 Applications of Reversible i–E Curves 2796.3 Sampled-Transient Voltammetry for Quasireversible and Irreversible Electrode Reactions 2796.3.1 Effect of Electrode Kinetics on Transient Behavior 2806.3.2 Sampled-Transient Voltammetry for Reduction of O 2826.3.3 Sampled Transient Voltammetry for Oxidation of R 2846.3.4 Totally Irreversible Reactions 2856.3.5 Kinetic Regimes 2876.3.6 Applications of Irreversible i–E Curves 2876.4 Multicomponent Systems and Multistep Charge Transfers 2896.5 Chronoamperometric Reversal Techniques 2906.5.1 Approaches to the Problem 2926.5.2 Current–Time Responses 2936.6 Chronocoulometry 2946.6.1 Large-Amplitude Potential Step 2956.6.2 Reversal Experiments Under Diffusion Control 2966.6.3 Effects of Heterogeneous Kinetics 2996.7 Cell Time Constants at Microelectrodes 3006.8 Lab Note: Practical Concerns with Potential Step Methods 3036.8.1 Preparation of the Electrode Surface at a Microelectrode 3036.8.2 Interference from Charging Current 3056.9 References 3066.10 Problems 3077 Linear Sweep and Cyclic Voltammetry 3117.1 Transient Responses to a Potential Sweep 3117.2 Nernstian (Reversible) Systems 3137.2.1 Linear Sweep Voltammetry 3137.2.2 Cyclic Voltammetry 3217.3 Quasireversible Systems 3257.3.1 Linear Sweep Voltammetry 3267.3.2 Cyclic Voltammetry 3267.4 Totally Irreversible Systems 3297.4.1 Linear Sweep Voltammetry 3297.4.2 Cyclic Voltammetry 3327.5 Multicomponent Systems and Multistep Charge Transfers 3327.5.1 Multicomponent Systems 3327.5.2 Multistep Charge Transfers 3337.6 Fast Cyclic Voltammetry 3347.7 Convolutive Transformation 3367.8 Voltammetry at Liquid–Liquid Interfaces 3397.8.1 Experimental Approach to Voltammetry 3407.8.2 Effect of Interfacial Potential on Composition 3417.8.3 Voltammetric Behavior 3417.9 Lab Note: Practical Aspects of Cyclic Voltammetry 3447.9.1 Basic Experimental Conditions 3447.9.2 Choice of Initial and Final Potentials 3457.9.3 Deaeration 3477.10 References 3477.11 Problems 3498 Polarography, Pulse Voltammetry, and Square-Wave Voltammetry 3558.1 Polarography 3558.1.1 The Dropping Mercury Electrode 3558.1.2 The IlkovičEquation 3568.1.3 Polarographic Waves 3578.1.4 Practical Advantages of the DME 3588.1.5 Polarographic Analysis 3588.1.6 Residual Current and Detection Limits 3598.2 Normal Pulse Voltammetry 3618.2.1 Implementation 3628.2.2 Renewal at Stationary Electrodes 3638.2.3 Normal Pulse Polarography 3648.2.4 Practical Application 3668.3 Reverse Pulse Voltammetry 3678.4 Differential Pulse Voltammetry 3698.4.1 Concept of the Method 3708.4.2 Theory 3718.4.3 Renewal vs. Pre-Electrolysis 3748.4.4 Residual Currents 3758.4.5 Differential Pulse Polarography 3758.5 Square-Wave Voltammetry 3768.5.1 Experimental Concept and Practice 3768.5.2 Theoretical Prediction of Response 3778.5.3 Background Currents 3808.5.4 Applications 3818.6 Analysis by Pulse Voltammetry 3838.7 References 3858.8 Problems 3869 Controlled-Current Techniques 3899.1 Introduction to Chronopotentiometry 3899.2 Theory of Controlled-Current Methods 3919.2.1 General Treatment for Linear Diffusion 3919.2.2 Constant-Current Electrolysis—The Sand Equation 3929.2.3 Programmed Current Chronopotentiometry 3949.3 Potential–Time Curves in Constant-Current Electrolysis 3949.3.1 Reversible (Nernstian) Waves 3949.3.2 Totally Irreversible Waves 3949.3.3 Quasireversible Waves 3959.3.4 Practical Issues in the Measurement of Transition Time 3969.4 Reversal Techniques 3989.4.1 Response Function Principle 3989.4.2 Current Reversal 3989.5 Multicomponent Systems and Multistep Reactions 4009.6 The Galvanostatic Double Pulse Method 4019.7 Charge Step (Coulostatic) Methods 4039.7.1 Small Excursions 4049.7.2 Large Excursions 4059.7.3 Coulostatic Perturbation by Temperature Jump 4059.8 References 4069.9 Problems 40710 Methods Involving Forced Convection—Hydrodynamic Methods 41110.1 Theory of Convective Systems 41110.1.1 The Convective-Diffusion Equation 41210.1.2 Determination of the Velocity Profile 41210.2 Rotating Disk Electrode 41410.2.1 The Velocity Profile at a Rotating Disk 41410.2.2 Solution of the Convective-Diffusion Equation 41610.2.3 Concentration Profile 41810.2.4 General i–E Curves at the RDE 41910.2.5 The Koutecký–Levich Method 42010.2.6 Current Distribution at the RDE 42310.2.7 Practical Considerations for Application of the RDE 42610.3 Rotating Ring and Ring-Disk Electrodes 42610.3.1 Rotating Ring Electrode 42710.3.2 The Rotating Ring-Disk Electrode 42810.4 Transient Currents 43210.4.1 Transients at the RDE 43210.4.2 Transients at the RRDE 43310.5 Modulation of the RDE 43510.6 Electrohydrodynamic Phenomena 43610.7 References 43910.8 Problems 44011 Electrochemical Impedance Spectroscopy and ac Voltammetry 44311.1 A Simple Measurement of Cell Impedance 44411.2 Brief Review of ac Circuits 44611.3 Equivalent Circuits of a Cell 45011.3.1 The Randles Equivalent Circuit 45111.3.2 Interpretation of the Faradaic Impedance 45211.3.3 Behavior and Uses of the Faradaic Impedance 45511.4 Electrochemical Impedance Spectroscopy 45811.4.1 Conditions of Measurement 45811.4.2 A System with Simple Faradaic Kinetics 46011.4.3 Measurement of Resistance and Capacitance 46511.4.4 A Confined Electroactive Domain 46611.4.5 Other Applications 47011.5 ac Voltammetry 47011.5.1 Reversible Systems 47011.5.2 Quasireversible and Irreversible Systems 47311.5.3 Cyclic ac Voltammetry 47711.6 Nonlinear Responses 47711.6.1 Second Harmonic ac Voltammetry 47811.6.2 Large Amplitude ac Voltammetry 47911.7 Chemical Analysis by ac Voltammetry 48111.8 Instrumentation for Electrochemical Impedance Methods 48211.8.1 Frequency-Domain Instruments 48211.8.2 Time-Domain Instruments 48311.9 Analysis of Data in the Laplace Plane 48511.10 References 48511.11 Problems 48712 Bulk Electrolysis 48912.1 General Considerations 49012.1.1 Completeness of an Electrode Process 49012.1.2 Current Efficiency 49112.1.3 Experimental Concerns 49112.2 Controlled-Potential Methods 49512.2.1 Current–Time Behavior 49512.2.2 Practical Aspects 49712.2.3 Coulometry 49812.2.4 Electrogravimetry 50012.2.5 Electroseparations 50112.3 Controlled-Current Methods 50112.3.1 Characteristics of Controlled-Current Electrolysis 50112.3.2 Coulometric Titrations 50312.3.3 Practical Aspects of Constant-Current Electrolysis 50612.4 Electrometric End-Point Detection 50712.4.1 Current–Potential Curves During Titration 50712.4.2 Potentiometric Methods 50812.4.3 Amperometric Methods 50912.5 Flow Electrolysis 51012.5.1 Mathematical Treatment 51012.5.2 Dual-Electrode Flow Cells 51512.5.3 Microfluidic Flow Cells 51612.6 Thin-Layer Electrochemistry 52112.6.1 Chronoamperometry and Coulometry 52112.6.2 Potential Sweep in a Nernstian System 52412.6.3 Dual-Electrode Thin-Layer Cells 52612.6.4 Applications of the Thin-Layer Concept 52612.7 Stripping Analysis 52712.7.1 Introduction 52712.7.2 Principles and Theory 52812.7.3 Applications and Variations 52912.8 References 53112.9 Problems 53413 Electrode Reactions with Coupled Homogeneous Chemical Reactions 53913.1 Classification of Reactions 53913.1.1 Reactions with One E-Step 54113.1.2 Reactions with Two or More E-Steps 54213.2 Impact of Coupled Reactions on Cyclic Voltammetry 54513.2.1 Diagnostic Criteria 54513.2.2 Characteristic Times 54713.2.3 An Example 54713.2.4 Including Kinetics in Theory 54813.2.5 Comparative Simulation 55113.3 Survey of Behavior 55213.3.1 Following Reaction—case E R c I 55213.3.2 Effect of Electrode Kinetics in Ec I Systems 55613.3.3 Bidirectional Following Reaction 55813.3.4catalytic Reaction—case E r c ′ I56113.3.5 Preceding Reaction—Case C r E r 56413.3.6 Multistep Electron Transfers 56913.3.7 ECE/DISP Reactions 57613.3.8 Concerted vs.StepwiseReaction 58413.3.9 Elaboration of Reaction Schemes 59013.4 Behavior with Other Electrochemical Methods 59113.5 References 59313.6 Problems 59514 Double-Layer Structure and Adsorption 59914.1 Thermodynamics of the Double Layer 59914.1.1 The Gibbs Adsorption Isotherm 59914.1.2 The Electrocapillary Equation 60114.1.3 Relative Surface Excesses 60114.2 Experimental Evaluations 60214.2.1 Electrocapillarity 60214.2.2 Excess Charge and Capacitance 60314.2.3 Relative Surface Excesses 60614.3 Models for Double-Layer Structure 60614.3.1 The Helmholtz Model 60714.3.2 The Gouy–Chapman Theory 60914.3.3 Stern’s Modification 61414.3.4 Specific Adsorption 61714.4 Studies at Solid Electrodes 61914.4.1 Well-Defined Single-Crystal Electrode Surfaces 62014.4.2 The Double Layer at Solids 62314.5 Extent and Rate of Specific Adsorption 62714.5.1 Nature and Extent of Specific Adsorption 62814.5.2 Electrosorption Valency 62914.5.3 Adsorption Isotherms 63014.5.4 Rate of Adsorption 63314.6 Practical Aspects of Adsorption 63414.7 Double-Layer Effects on Electrode Reaction Rates 63614.7.1 Introduction and Principles 63614.7.2 Double-Layer Effects Without Specific Adsorption of Electrolyte 63814.7.3 Double-Layer Effects with Specific Adsorption 63914.7.4 Diffuse Double-Layer Effects on Mass Transport 64014.8 References 64514.9 Problems 64815 Inner-Sphere Electrode Reactions and Electrocatalysis 65315.1 Inner-Sphere Heterogenous Electron-Transfer Reactions 65315.1.1 TheRoleoftheElectrodeSurface 65315.1.2 Energetics of 1e Electron-Transfer Reactions 65415.1.3 Adsorption Energies 65715.2 Electrocatalytic Reaction Mechanisms 65715.2.1 Hydrogen Evolution Reaction 65715.2.2 Tafel Plot Analysis of HER Kinetics 66015.3 Additional Examples of Inner-Sphere Reactions 66715.3.1 Oxygen Reduction Reaction 66715.3.2 Chlorine Evolution 67015.3.3 Methanol Oxidation 67015.3.4 CO 2 Reduction 67315.3.5 Oxidation of NH 3 to N 2 67415.3.6 Organic Halide Reduction 67615.3.7 Hydrogen Peroxide Oxidation and Reduction 67715.4 Computational Analyses of Inner-Sphere Electron-Transfer Reactions 67815.4.1 Density Functional Theory Analysis of Electrocatalytic Reactions 67915.4.2 Hydrogen Evolution Reaction 67915.4.3 Oxygen Reduction Reaction 68115.5 Electrocatalytic Correlations 68415.6 Electrochemical Phase Transformations 68815.6.1 Nucleation and Growth of a New Phase 68815.6.2 Classical Nucleation Theory 68915.6.3 Electrodeposition 69915.6.4 Gas Evolution 70715.7 References 71315.8 Problems 71816 Electrochemical Instrumentation 72116.1 Operational Amplifiers 72116.1.1 Ideal Properties 72116.1.2 Nonidealities 72316.2 Current Feedback 72516.2.1 Current Follower 72516.2.2 Scaler/Inverter 72616.2.3 Adders 72616.2.4 Integrators 72716.3 Voltage Feedback 72816.3.1 Voltage Follower 72816.3.2 Control Functions 72916.4 Potentiostats 73016.4.1 Basic Considerations 73016.4.2 The Adder Potentiostat 73116.4.3 Refinements to the Adder Potentiostat 73216.4.4 Bipotentiostats 73316.4.5 Four-Electrode Potentiostats 73416.5 Galvanostats 73416.6 Integrated Electrochemical Instrumentation 73616.7 Difficulties with Potential Control 73716.7.1 Types of Control Problems 73716.7.2 Cell Properties and Electrode Placement 74016.7.3 Electronic Compensation of Resistance 74016.8 Measurement of Low Currents 74416.8.1 Fundamental Limits 74416.8.2 Practical Considerations 74616.8.3 Current Amplifier 74616.8.4 Simplified Instruments and Cells 74616.9 Instruments for Short Time Scales 74816.10 Lab Note: Practical Use of Electrochemical Instruments 74916.10.1 Caution Regarding Electrochemical Workstations 74916.10.2 Troubleshooting Electrochemical Systems 74916.11 References 75116.12 Problems 75217 Electroactive Layers and Modified Electrodes 75517.1 Monolayers and Submonolayers on Electrodes 75617.2 Cyclic Voltammetry of Adsorbed Layers 75717.2.1 Fundamentals 75717.2.2 Reversible Adsorbate Couples 75817.2.3 Irreversible Adsorbate Couples 76317.2.4 Nernstian Processes Involving Adsorbates and Solutes 76617.2.5 More Complex Systems 77017.2.6 Electric-Field-Driven Acid–Base Chemistry in Adsorbate Layers 77117.3 Other Useful Methods for Adsorbed Monolayers 77517.3.1 Chronocoulometry 77517.3.2 Coulometry in Thin-Layer Cells 77717.3.3 Impedance Measurements 77817.3.4 Chronopotentiometry 77917.4 Thick Modification Layers on Electrodes 78017.5 Dynamics in Modification Layers 78217.5.1 Steady State at a Rotating Disk 78317.5.2 Principal Dynamic Processes in Modifying Films 78417.5.3 Interplay of Dynamical Elements 78917.6 Blocking Layers 79117.6.1 Permeation Through Pores and Pinholes 79217.6.2 Tunneling Through Blocking Films 79617.7 Other Methods for Characterizing Layers on Electrodes 79817.8 Electrochemical Methods Based on Electroactive Layers or Electrode Modification 79817.8.1 Electrocatalysis 79917.8.2 Bioelectrocatalysis Based on Enzyme-Modified Electrodes 79917.8.3 Electrochemical Sensors 80317.8.4 Faradaic Electrochemical Measurements in vivo 80917.9 References 81217.10 Problems 81718 Scanning Electrochemical Microscopy 81918.1 Principles 81918.2 Approach Curves 82118.3 Imaging Surface Topography and Reactivity 82518.3.1 Imaging Based on Conductivity of the Substrate 82518.3.2 Imaging Based on Heterogeneous Electron-Transfer Reactivity 82618.3.3 Simultaneous Imaging of Topography and Reactivity 82718.4 Measurements of Kinetics 82818.4.1 Heterogeneous Electron-Transfer Reactions 82818.4.2 Homogeneous Reactions 83118.5 Surface Interrogation 83518.6 Potentiometric Tips 83918.7 Other Applications 83918.7.1 Detection of Species Released from Surfaces, Films, or Pores 83918.7.2 Biological Systems 84018.7.3 Probing the Interior of a Layer on a Substrate 84118.8 Scanning Electrochemical Cell Microscopy 84118.9 References 84618.10 Problems 84919 Single-Particle Electrochemistry 85119.1 General Considerations in Single-Particle Electrochemistry 85119.2 Particle Collision Experiments 85219.3 Particle Collision Rate at a Disk-Shaped UME 85419.3.1 Collision Frequency 85419.3.2 Variance in the Number of Particle Collisions 85519.3.3 Time of First Arrival 85619.4 Nanoparticle Collision Behavior 85719.4.1 Blocking Collisions 85719.4.2 Electrocatalytic Amplification Collisions 86119.4.3 Electrolysis Collisions 86419.5 Electrochemistry at Single Atoms and Atomic Clusters 87019.6 Single-Molecule Electrochemistry 87519.7 References 87919.8 Problems 88120 Photoelectrochemistry and Electrogenerated Chemiluminescence 88520.1 Solid Materials 88520.1.1 The Band Model 88520.1.2 Categories of Pure Crystalline Solids 88620.1.3 Doped Semiconductors 88920.1.4 Fermi Energy 89020.1.5 Highly Conducting Oxides 89120.2 Semiconductor Electrodes 89220.2.1 Interface at a Semiconducting Electrode in the Dark 89220.2.2 Current–Potential Curves at Semiconductor Electrodes 89620.2.3 Conducting Polymer Electrodes 89920.3 Photoelectrochemistry at Semiconductors 90120.3.1 Photoeffects at Semiconductor Electrodes 90120.3.2 Photoelectrochemical Systems 90320.3.3 Dye Sensitization 90520.3.4 Surface Photocatalytic Processes at Semiconductor Particles 90620.4 Radiolytic Products in Solution 90820.4.1 Photoemission of Electrons from an Electrode 90820.4.2 Detection and Use of Radiolytic Products in Solution 90920.4.3 Photogalvanic Cells 90920.5 Electrogenerated Chemiluminescence 91020.5.1 Chemical Fundamentals 91020.5.2 Fundamental Studies of Radical-Ion Annihilation 91220.5.3 Single-Potential Generation Based on a Coreactant 91620.5.4 ECL Based on Quantum Dots 91720.5.5 Analytical Applications of ECL 91820.5.6 ECL Beyond the Solution Phase 92220.6 References 92220.7 Problems 92721 In situ Characterization of Electrochemical Systems 93121.1 Microscopy 93121.1.1 Scanning Tunneling Microscopy 93221.1.2 Atomic Force Microscopy 93421.1.3 Optical Microscopy 93721.1.4 Transmission Electron Microscopy 93821.2 Quartz Crystal Microbalance 94021.2.1 Basic Method 94021.2.2 QCM with Dissipation Monitoring 94221.3 UV–Visible Spectrometry 94221.3.1 Absorption Spectroscopy with Thin-Layer Cells 94221.3.2 Ellipsometry 94521.3.3 Surface Plasmon Resonance 94621.4 Vibrational Spectroscopy 94721.4.1 Infrared Spectroscopy 94721.4.2 Raman Spectroscopy 95021.5 X-Ray Methods 95321.6 Mass Spectrometry 95421.7 Magnetic Resonance Spectroscopy 95521.7.1 Esr 95521.7.2 Nmr 95621.8 Ex-situ Techniques 95721.8.1 Electron Microscopy 95721.8.2 Electron and Ion Spectrometry 95821.9 References 960Appendix A Mathematical Methods 967A.1 Solving Differential Equations by the Laplace Transform Technique 967A.1.1 Partial Differential Equations 967A.1.2 Introduction to the Laplace Transformation 968A.1.3 Fundamental Properties of the Transform 969A.1.4 Solving Ordinary Differential Equations by Laplace Transformation 970A.1.5 Simultaneous Linear Ordinary Differential Equations 972A.1.6 Mass-Transfer Problems Based on Partial Differential Equations 973A.1.7 The Zero-Shift Theorem 975A.2 Taylor Expansions 976A.2.1 Expansion of a Function of Several Variables 976A.2.2 Expansion of a Function of a Single Variable 977A.2.3 Maclaurin Series 977A.3 The Error Function and the Gaussian Distribution 977A.4 Leibnitz Rule 979A.5 Complex Notation 979A.6 Fourier Series and Fourier Transformation 981A.7 References 982A.8 Problems 983Appendix B Basic Concepts of Simulation 985B.1 Setting Up the Model 985B.1.1 A Discrete System 985B.1.2 Diffusion 986B.1.3 Dimensionless Parameters 987B.1.4 Time 990B.1.5 Distance 990B.1.6 Current 991B.1.7 Thickness of the Diffusion Layer 992B.1.8 Diffusion Coefficients 993B.2 An Example 993B.2.1 Organization of the Spreadsheet 993B.2.2 Concentration Arrays 996B.2.3 Results and Error Detection 996B.2.4 Performance 997B.3 Incorporating Homogeneous Kinetics 999B.3.1 Unimolecular Reactions 999B.3.2 Bimolecular Reactions 1000B.4 Boundary Conditions for Various Techniques 1001B.4.1 Potential Steps in Nernstian Systems 1001B.4.2 Heterogeneous Kinetics 1002B.4.3 Potential Sweeps 1003B.4.4 Controlled Current 1003B.5 More Complex Systems 1004B.6 References 1005B.7 Problems 1005Appendix C Reference Tables 1007References 1013Index 1015

"...this third edition of the book that I consider as the Electrochemistry bible is consistent with the evolution and development of electrochemistry in these last twenty years. The new chapters highlight the most recent advances and innovative techniques while the chapters dealing with older electrochemical methods have been lightened.... The authors have made a great job in this third edition to update the book with the electrochemistry currently studied and practiced in laboratories.... Both junior and senior electrochemists, from novices to experts, should have this book available in the laboratory."—Estelle Lebègue, Transition Metal Chemistry (2023) 48:433–436 https://doi.org/10.1007/s11243-023-00555-6