Electrochemical Methods: Fundamentals and Applications

Description

The long-awaited revision of a classic! This defining textbook on electrochemistry takes the reader from the most basic chemical and physical principles, through fundamentals of thermodynamics, kinetics, and mass transfer, to a thorough treatment of all important experimental methods. It offers comprehensive coverage of all important topics in the field, and is renowned for its accuracy and clear presentation. The 3rd edition of this bestselling textbook has been extensively revised to reflect developments in the field over the past two decades. Updates and new features include: - Three new chapters on Steady-State Voltammetry at Small Electrodes, Inner-Sphere Electrode Reactions and Electrocatalysis, and Single-Particle and Single-Molecule Measurements. - All existing chapters have been fully updated in the light of developments since the 2nd edition. - The introductory chapter has been revised significantly to make it more effective for technical readers coming into electrochemistry from outside the field. - Includes more extensive coverage of simulation methods in the main text and end of chapter exercises. - More how to discussions have been added, covering important practical procedures. Exercises are included at the end of each chapter. Devised as teaching tools, these exercises often extend concepts introduced in the text or show how experimental data are reduced to fundamental results. Cover Title Page Copyright Contents Preface Major Symbols and Abbreviations About the Companion Website Chapter 1 Overview of Electrode Processes 1.1 Basic Ideas 1.1.1 Electrochemical Cells and Reactions 1.1.2 Interfacial Potential Differences and Cell Potential 1.1.3 Reference Electrodes and Control of Potential at a Working Electrode 1.1.4 Potential as an Expression of Electron Energy 1.1.5 Current as an Expression of Reaction Rate 1.1.6 Magnitudes in Electrochemical Systems 1.1.7 Current–Potential Curves 1.1.8 Control of Current vs. Control of Potential 1.1.9 Faradaic and Nonfaradaic Processes 1.2 Faradaic Processes and Factors Affecting Rates of Electrode Reactions 1.2.1 Electrochemical Cells—Types and Definitions 1.2.2 The Electrochemical Experiment and Variables in Electrochemical Cells 1.2.3 Factors Affecting Electrode Reaction Rate and Current 1.3 Mass‐Transfer‐Controlled Reactions 1.3.1 Modes of Mass Transfer 1.3.2 Semiempirical Treatment of Steady‐State Mass Transfer 1.4 Semiempirical Treatment of Nernstian Reactions with Coupled Chemical Reactions 1.4.1 Coupled Reversible Reactions 1.4.2 Coupled Irreversible Chemical Reactions 1.5 Cell Resistance and the Measurement of Potential 1.5.1 Components of the Applied Voltage When Current Flows 1.5.2 Two‐Electrode Cells 1.5.3 Three‐Electrode Cells 1.5.4 Uncompensated Resistance 1.6 The Electrode/Solution Interface and Charging Current 1.6.1 The Ideally Polarizable Electrode 1.6.2 Capacitance and Charge at an Electrode 1.6.3 Brief Description of the Electrical Double Layer 1.6.4 Double‐Layer Capacitance and Charging Current 1.7 Organization of this Book 1.8 The Literature of Electrochemistry 1.8.1 Reference Sources 1.8.2 Sources on Laboratory Techniques 1.8.3 Review Series 1.9 Lab Note: Potentiostats and Cell Behavior 1.9.1 Potentiostats 1.9.2 Background Processes in Actual Cells 1.9.3 Further Work with Simple RC Networks 1.10 References 1.11 Problems Chapter 2 Potentials and Thermodynamics of Cells 2.1 Basic Electrochemical Thermodynamics 2.1.1 Reversibility 2.1.2 Reversibility and Gibbs Free Energy 2.1.3 Free Energy and Cell emf 2.1.4 Half‐Reactions and Standard Electrode Potentials 2.1.5 Standard States and Activity 2.1.6 emf and Concentration 2.1.7 Formal Potentials 2.1.8 Reference Electrodes 2.1.9 Potential–pH Diagrams and Thermodynamic Predictions 2.2 A More Detailed View of Interfacial Potential Differences 2.2.1 The Physics of Phase Potentials 2.2.2 Interactions Between Conducting Phases 2.2.3 Measurement of Potential Differences 2.2.4 Electrochemical Potentials 2.2.5 Fermi Energy and Absolute Potential 2.3 Liquid Junction Potentials 2.3.1 Potential Differences at an Electrolyte–Electrolyte Boundary 2.3.2 Types of Liquid Junctions 2.3.3 Conductance, Transference Numbers, and Mobility 2.3.4 Calculation of Liquid Junction Potentials 2.3.5 Minimizing Liquid Junction Potentials 2.3.6 Junctions of Two Immiscible Liquids 2.4 Ion‐Selective Electrodes 2.4.1 Selective Interfaces 2.4.2 Glass Electrodes 2.4.3 Other Ion‐Selective Electrodes 2.4.4 Gas‐Sensing ISEs 2.5 Lab Note: Practical Use of Reference Electrodes 2.5.1 Leakage at the Reference Tip 2.5.2 Quasireference Electrodes 2.6 References 2.7 Problems Chapter 3 Basic Kinetics of Electrode Reactions 3.1 Review of Homogeneous Kinetics 3.1.1 Dynamic Equilibrium 3.1.2 The Arrhenius Equation and Potential Energy Surfaces 3.1.3 Transition State Theory 3.2 Essentials of Electrode Reactions 3.3 Butler–Volmer Model of Electrode Kinetics 3.3.1 Effects of Potential on Energy Barriers 3.3.2 One‐Step, One‐Electron Process 3.3.3 The Standard Rate Constant 3.3.4 The Transfer Coefficient 3.4 Implications of the Butler–Volmer Model for the One‐Step, One‐Electron Process 3.4.1 Equilibrium Conditions and the Exchange Current 3.4.2 The Current–Overpotential Equation 3.4.3 Approximate Forms of the i–η Equation 3.4.4 Exchange Current Plots 3.4.5 Very Facile Kinetics and Reversible Behavior 3.4.6 Effects of Mass Transfer 3.4.7 Limits of Basic Butler–Volmer Equations 3.5 Microscopic Theories of Charge Transfer 3.5.1 Inner‐Sphere and Outer‐Sphere Electrode Reactions 3.5.2 Extended Charge Transfer and Adiabaticity 3.5.3 The Marcus Microscopic Model 3.5.4 Implications of the Marcus Theory 3.5.5 A Model Based on Distributions of Energy States 3.6 Open‐Circuit Potential and Multiple Half‐Reactions at an Electrode 3.6.1 Open‐Circuit Potential in Multicomponent Systems 3.6.2 Establishment or Loss of Nernstian Behavior at an Electrode 3.6.3 Multiple Half‐Reaction Currents in i–E Curves 3.7 Multistep Mechanisms 3.7.1 The Primacy of One‐Electron Transfers 3.7.2 Rate‐Determining, Outer‐Sphere Electron Transfer 3.7.3 Multistep Processes at Equilibrium 3.7.4 Nernstian Multistep Processes 3.7.5 Quasireversible and Irreversible Multistep Processes 3.8 References 3.9 Problems Chapter 4 Mass Transfer by Migration and Diffusion 4.1 General Mass‐Transfer Equations 4.2 Migration in Bulk Solution 4.3 Mixed Migration and Diffusion Near an Active Electrode 4.3.1 Balance Sheets for Mass Transfer During Electrolysis 4.3.2 Utility of a Supporting Electrolyte 4.4 Diffusion 4.4.1 A Microscopic View 4.4.2 Fick's Laws of Diffusion 4.4.3 Flux of an Electroreactant at an Electrode Surface 4.5 Formulation and Solution of Mass‐Transfer Problems 4.5.1 Initial and Boundary Conditions in Electrochemical Problems 4.5.2 General Formulation of a Linear Diffusion Problem 4.5.3 Systems Involving Migration or Convection 4.5.4 Practical Means for Reaching Solutions 4.6 References 4.7 Problems Chapter 5 Steady‐State Voltammetry at Ultramicroelectrodes 5.1 Steady‐State Voltammetry at a Spherical UME 5.1.1 Steady‐State Diffusion 5.1.2 Steady‐State Current 5.1.3 Convergence on the Steady State 5.1.4 Steady‐State Voltammetry 5.2 Shapes and Properties of Ultramicroelectrodes 5.2.1 Spherical or Hemispherical UME 5.2.2 Disk UME 5.2.3 Cylindrical UME 5.2.4 Band UME 5.2.5 Summary of Steady‐State Behavior at UMEs 5.3 Reversible Electrode Reactions 5.3.1 Shape of the Wave 5.3.2 Applications of Reversible i–E Curves 5.4 Quasireversible and Irreversible Electrode Reactions 5.4.1 Effect of Electrode Kinetics on Steady‐State Responses 5.4.2 Total Irreversibility 5.4.3 Kinetic Regimes 5.4.4 Influence of Electrode Shape 5.4.5 Applications of Irreversible i–E Curves 5.4.6 Evaluation of Kinetic Parameters by Varying Mass‐Transfer Rates 5.5 Multicomponent Systems and Multistep Charge Transfers 5.6 Additional Attributes of Ultramicroelectrodes 5.6.1 Uncompensated Resistance at a UME 5.6.2 Effects of Conductivity on Voltammetry at a UME 5.6.3 Applications Based on Spatial Resolution 5.7 Migration in Steady‐State Voltammetry 5.7.1 Mathematical Approach to Problems Involving Migration 5.7.2 Concentration Profiles in the Diffusion–Migration Layer 5.7.3 Wave Shape at Low Electrolyte Concentration 5.7.4 Effects of Migration on Wave Height in SSV 5.8 Analysis at High Analyte Concentrations 5.9 Lab Note: Preparation of Ultramicroelectrodes 5.9.1 Preparation and Characterization of UMEs 5.9.2 Testing the Integrity of a UME 5.9.3 Estimating the Size of a UME 5.10 References 5.11 Problems Chapter 6 Transient Methods Based on Potential Steps 6.1 Chronoamperometry Under Diffusion Control 6.1.1 Linear Diffusion at a Plane 6.1.2 Response at a Spherical Electrode 6.1.3 Transients at Other Ultramicroelectrodes 6.1.4 Information from Chronoamperometric Results 6.1.5 Microscopic and Geometric Areas 6.2 Sampled‐Transient Voltammetry for Reversible Electrode Reactions 6.2.1 A Step to an Arbitrary Potential 6.2.2 Shape of the Voltammogram 6.2.3 Concentration Profiles When R Is Initially Absent 6.2.4 Simplified Current–Concentration Relationships 6.2.5 Applications of Reversible i–E Curves 6.3 Sampled‐Transient Voltammetry for Quasireversible and Irreversible Electrode Reactions 6.3.1 Effect of Electrode Kinetics on Transient Behavior 6.3.2 Sampled‐Transient Voltammetry for Reduction of O 6.3.3 Sampled Transient Voltammetry for Oxidation of R 6.3.4 Totally Irreversible Reactions 6.3.5 Kinetic Regimes 6.3.6 Applications of Irreversible i–E Curves 6.4 Multicomponent Systems and Multistep Charge Transfers 6.5 Chronoamperometric Reversal Techniques 6.5.1 Approaches to the Problem 6.5.2 Current–Time Responses 6.6 Chronocoulometry 6.6.1 Large‐Amplitude Potential Step 6.6.2 Reversal Experiments Under Diffusion Control 6.6.3 Effects of Heterogeneous Kinetics 6.7 Cell Time Constants at Microelectrodes 6.8 Lab Note: Practical Concerns with Potential Step Methods 6.8.1 Preparation of the Electrode Surface at a Microelectrode 6.8.2 Interference from Charging Current 6.9 References 6.10 Problems Chapter 7 Linear Sweep and Cyclic Voltammetry 7.1 Transient Responses to a Potential Sweep 7.2 Nernstian (Reversible) Systems 7.2.1 Linear Sweep Voltammetry 7.2.2 Cyclic Voltammetry 7.3 Quasireversible Systems 7.3.1 Linear Sweep Voltammetry 7.3.2 Cyclic Voltammetry 7.4 Totally Irreversible Systems 7.4.1 Linear Sweep Voltammetry 7.4.2 Cyclic Voltammetry 7.5 Multicomponent Systems and Multistep Charge Transfers 7.5.1 Multicomponent Systems 7.5.2 Multistep Charge Transfers 7.6 Fast Cyclic Voltammetry 7.7 Convolutive Transformation 7.8 Voltammetry at Liquid–Liquid Interfaces 7.8.1 Experimental Approach to Voltammetry 7.8.2 Effect of Interfacial Potential on Composition 7.8.3 Voltammetric Behavior 7.9 Lab Note: Practical Aspects of Cyclic Voltammetry 7.9.1 Basic Experimental Conditions 7.9.2 Choice of Initial and Final Potentials 7.9.3 Deaeration 7.10 References 7.11 Problems Chapter 8 Polarography, Pulse Voltammetry, and Square‐Wave Voltammetry 8.1 Polarography 8.1.1 The Dropping Mercury Electrode 8.1.2 The Ilkovič Equation 8.1.3 Polarographic Waves 8.1.4 Practical Advantages of the DME 8.1.5 Polarographic Analysis 8.1.6 Residual Current and Detection Limits 8.2 Normal Pulse Voltammetry 8.2.1 Implementation 8.2.2 Renewal at Stationary Electrodes 8.2.3 Normal Pulse Polarography 8.2.4 Practical Application 8.3 Reverse Pulse Voltammetry 8.4 Differential Pulse Voltammetry 8.4.1 Concept of the Method 8.4.2 Theory 8.4.3 Renewal vs. Pre‐Electrolysis 8.4.4 Residual Currents 8.4.5 Differential Pulse Polarography 8.5 Square‐Wave Voltammetry 8.5.1 Experimental Concept and Practice 8.5.2 Theoretical Prediction of Response 8.5.3 Background Currents 8.5.4 Applications 8.6 Analysis by Pulse Voltammetry 8.7 References 8.8 Problems Chapter 9 Controlled‐Current Techniques 9.1 Introduction to Chronopotentiometry 9.2 Theory of Controlled‐Current Methods 9.2.1 General Treatment for Linear Diffusion 9.2.2 Constant‐Current Electrolysis—The Sand Equation 9.2.3 Programmed Current Chronopotentiometry 9.3 Potential–Time Curves in Constant‐Current Electrolysis 9.3.1 Reversible (Nernstian) Waves 9.3.2 Totally Irreversible Waves 9.3.3 Quasireversible Waves 9.3.4 Practical Issues in the Measurement of Transition Time 9.4 Reversal Techniques 9.4.1 Response Function Principle 9.4.2 Current Reversal 9.5 Multicomponent Systems and Multistep Reactions 9.6 The Galvanostatic Double Pulse Method 9.7 Charge Step (Coulostatic) Methods 9.7.1 Small Excursions 9.7.2 Large Excursions 9.7.3 Coulostatic Perturbation by Temperature Jump 9.8 References 9.9 Problems Chapter 10 Methods Involving Forced Convection—Hydrodynamic Methods 10.1 Theory of Convective Systems 10.1.1 The Convective‐Diffusion Equation 10.1.2 Determination of the Velocity Profile 10.2 Rotating Disk Electrode 10.2.1 The Velocity Profile at a Rotating Disk 10.2.2 Solution of the Convective‐Diffusion Equation 10.2.3 Concentration Profile 10.2.4 General i–E Curves at the RDE 10.2.5 The Koutecký–Levich Method 10.2.6 Current Distribution at the RDE 10.2.7 Practical Considerations for Application of the RDE 10.3 Rotating Ring and Ring‐Disk Electrodes 10.3.1 Rotating Ring Electrode 10.3.2 The Rotating Ring‐Disk Electrode 10.4 Transient Currents 10.4.1 Transients at the RDE 10.4.2 Transients at the RRDE 10.5 Modulation of the RDE 10.6 Electrohydrodynamic Phenomena 10.7 References 10.8 Problems Chapter 11 Electrochemical Impedance Spectroscopy and ac Voltammetry 11.1 A Simple Measurement of Cell Impedance 11.2 Brief Review of ac Circuits 11.3 Equivalent Circuits of a Cell 11.3.1 The Randles Equivalent Circuit 11.3.2 Interpretation of the Faradaic Impedance 11.3.3 Behavior and Uses of the Faradaic Impedance 11.4 Electrochemical Impedance Spectroscopy 11.4.1 Conditions of Measurement 11.4.2 A System with Simple Faradaic Kinetics 11.4.3 Measurement of Resistance and Capacitance 11.4.4 A Confined Electroactive Domain 11.4.5 Other Applications 11.5 ac Voltammetry 11.5.1 Reversible Systems 11.5.2 Quasireversible and Irreversible Systems 11.5.3 Cyclic ac Voltammetry 11.6 Nonlinear Responses 11.6.1 Second Harmonic ac Voltammetry 11.6.2 Large Amplitude ac Voltammetry 11.7 Chemical Analysis by ac Voltammetry 11.8 Instrumentation for Electrochemical Impedance Methods 11.8.1 Frequency‐Domain Instruments 11.8.2 Time‐Domain Instruments 11.9 Analysis of Data in the Laplace Plane 11.10 References 11.11 Problems Chapter 12 Bulk Electrolysis 12.1 General Considerations 12.1.1 Completeness of an Electrode Process 12.1.2 Current Efficiency 12.1.3 Experimental Concerns 12.2 Controlled‐Potential Methods 12.2.1 Current–Time Behavior 12.2.2 Practical Aspects 12.2.3 Coulometry 12.2.4 Electrogravimetry 12.2.5 Electroseparations 12.3 Controlled‐Current Methods 12.3.1 Characteristics of Controlled‐Current Electrolysis 12.3.2 Coulometric Titrations 12.3.3 Practical Aspects of Constant‐Current Electrolysis 12.4 Electrometric End‐Point Detection 12.4.1 Current–Potential Curves During Titration 12.4.2 Potentiometric Methods 12.4.3 Amperometric Methods 12.5 Flow Electrolysis 12.5.1 Mathematical Treatment 12.5.2 Dual‐Electrode Flow Cells 12.5.3 Microfluidic Flow Cells 12.6 Thin‐Layer Electrochemistry 12.6.1 Chronoamperometry and Coulometry 12.6.2 Potential Sweep in a Nernstian System 12.6.3 Dual‐Electrode Thin‐Layer Cells 12.6.4 Applications of the Thin‐Layer Concept 12.7 Stripping Analysis 12.7.1 Introduction 12.7.2 Principles and Theory 12.7.3 Applications and Variations 12.8 References 12.9 Problems Chapter 13 Electrode Reactions with Coupled Homogeneous Chemical Reactions 13.1 Classification of Reactions 13.1.1 Reactions with One E‐Step 13.1.2 Reactions with Two or More E‐Steps 13.2 Impact of Coupled Reactions on Cyclic Voltammetry 13.2.1 Diagnostic Criteria 13.2.2 Characteristic Times 13.2.3 An Example 13.2.4 Including Kinetics in Theory 13.2.5 Comparative Simulation 13.3 Survey of Behavior 13.3.1 Following Reaction—Case ErCi 13.3.2 Effect of Electrode Kinetics in ECi Systems 13.3.3 Bidirectional Following Reaction 13.3.4 Catalytic Reaction—Case ErCi′ 13.3.5 Preceding Reaction—Case CrEr 13.3.6 Multistep Electron Transfers 13.3.7 ECE/DISP Reactions 13.3.8 Concerted vs. Stepwise Reaction 13.3.9 Elaboration of Reaction Schemes 13.4 Behavior with Other Electrochemical Methods 13.5 References 13.6 Problems Chapter 14 Double‐Layer Structure and Adsorption 14.1 Thermodynamics of the Double Layer 14.1.1 The Gibbs Adsorption Isotherm 14.1.2 The Electrocapillary Equation 14.1.3 Relative Surface Excesses 14.2 Experimental Evaluations 14.2.1 Electrocapillarity 14.2.2 Excess Charge and Capacitance 14.2.3 Relative Surface Excesses 14.3 Models for Double‐Layer Structure 14.3.1 The Helmholtz Model 14.3.2 The Gouy–Chapman Theory 14.3.3 Stern's Modification 14.3.4 Specific Adsorption 14.4 Studies at Solid Electrodes 14.4.1 Well‐Defined Single‐Crystal Electrode Surfaces 14.4.2 The Double Layer at Solids 14.5 Extent and Rate of Specific Adsorption 14.5.1 Nature and Extent of Specific Adsorption 14.5.2 Electrosorption Valency 14.5.3 Adsorption Isotherms 14.5.4 Rate of Adsorption 14.6 Practical Aspects of Adsorption 14.7 Double‐Layer Effects on Electrode Reaction Rates 14.7.1 Introduction and Principles 14.7.2 Double‐Layer Effects Without Specific Adsorption of Electrolyte 14.7.3 Double‐Layer Effects with Specific Adsorption 14.7.4 Diffuse Double‐Layer Effects on Mass Transport 14.8 References 14.9 Problems Chapter 15 Inner‐Sphere Electrode Reactions and Electrocatalysis 15.1 Inner‐Sphere Heterogenous Electron‐Transfer Reactions 15.1.1 The Role of the Electrode Surface 15.1.2 Energetics of 1e Electron‐Transfer Reactions 15.1.3 Adsorption Energies 15.2 Electrocatalytic Reaction Mechanisms 15.2.1 Hydrogen Evolution Reaction 15.2.2 Tafel Plot Analysis of HER Kinetics 15.3 Additional Examples of Inner‐Sphere Reactions 15.3.1 Oxygen Reduction Reaction 15.3.2 Chlorine Evolution 15.3.3 Methanol Oxidation 15.3.4 CO2 Reduction 15.3.5 Oxidation of NH3 to N2 15.3.6 Organic Halide Reduction 15.3.7 Hydrogen Peroxide Oxidation and Reduction 15.4 Computational Analyses of Inner‐Sphere Electron‐Transfer Reactions 15.4.1 Density Functional Theory Analysis of Electrocatalytic Reactions 15.4.2 Hydrogen Evolution Reaction 15.4.3 Oxygen Reduction Reaction 15.5 Electrocatalytic Correlations 15.6 Electrochemical Phase Transformations 15.6.1 Nucleation and Growth of a New Phase 15.6.2 Classical Nucleation Theory 15.6.3 Electrodeposition 15.6.4 Gas Evolution 15.7 References 15.8 Problems Chapter 16 Electrochemical Instrumentation 16.1 Operational Amplifiers 16.1.1 Ideal Properties 16.1.2 Nonidealities 16.2 Current Feedback 16.2.1 Current Follower 16.2.2 Scaler/Inverter 16.2.3 Adders 16.2.4 Integrators 16.3 Voltage Feedback 16.3.1 Voltage Follower 16.3.2 Control Functions 16.4 Potentiostats 16.4.1 Basic Considerations 16.4.2 The Adder Potentiostat 16.4.3 Refinements to the Adder Potentiostat 16.4.4 Bipotentiostats 16.4.5 Four‐Electrode Potentiostats 16.5 Galvanostats 16.6 Integrated Electrochemical Instrumentation 16.7 Difficulties with Potential Control 16.7.1 Types of Control Problems 16.7.2 Cell Properties and Electrode Placement 16.7.3 Electronic Compensation of Resistance 16.8 Measurement of Low Currents 16.8.1 Fundamental Limits 16.8.2 Practical Considerations 16.8.3 Current Amplifier 16.8.4 Simplified Instruments and Cells 16.9 Instruments for Short Time Scales 16.10 Lab Note: Practical Use of Electrochemical Instruments 16.10.1 Caution Regarding Electrochemical Workstations 16.10.2 Troubleshooting Electrochemical Systems 16.11 References 16.12 Problems Chapter 17 Electroactive Layers and Modified Electrodes 17.1 Monolayers and Submonolayers on Electrodes 17.2 Cyclic Voltammetry of Adsorbed Layers 17.2.1 Fundamentals 17.2.2 Reversible Adsorbate Couples 17.2.3 Irreversible Adsorbate Couples 17.2.4 Nernstian Processes Involving Adsorbates and Solutes 17.2.5 More Complex Systems 17.2.6 Electric‐Field‐Driven Acid–Base Chemistry in Adsorbate Layers 17.3 Other Useful Methods for Adsorbed Monolayers 17.3.1 Chronocoulometry 17.3.2 Coulometry in Thin‐Layer Cells 17.3.3 Impedance Measurements 17.3.4 Chronopotentiometry 17.4 Thick Modification Layers on Electrodes 17.5 Dynamics in Modification Layers 17.5.1 Steady State at a Rotating Disk 17.5.2 Principal Dynamic Processes in Modifying Films 17.5.3 Interplay of Dynamical Elements 17.6 Blocking Layers 17.6.1 Permeation Through Pores and Pinholes 17.6.2 Tunneling Through Blocking Films 17.7 Other Methods for Characterizing Layers on Electrodes 17.8 Electrochemical Methods Based on Electroactive Layers or Electrode Modification 17.8.1 Electrocatalysis 17.8.2 Bioelectrocatalysis Based on Enzyme‐Modified Electrodes 17.8.3 Electrochemical Sensors 17.8.4 Faradaic Electrochemical Measurements in vivo 17.9 References 17.10 Problems Chapter 18 Scanning Electrochemical Microscopy 18.1 Principles 18.2 Approach Curves 18.3 Imaging Surface Topography and Reactivity 18.3.1 Imaging Based on Conductivity of the Substrate 18.3.2 Imaging Based on Heterogeneous Electron‐Transfer Reactivity 18.3.3 Simultaneous Imaging of Topography and Reactivity 18.4 Measurements of Kinetics 18.4.1 Heterogeneous Electron‐Transfer Reactions 18.4.2 Homogeneous Reactions 18.5 Surface Interrogation 18.6 Potentiometric Tips 18.7 Other Applications 18.7.1 Detection of Species Released from Surfaces, Films, or Pores 18.7.2 Biological Systems 18.7.3 Probing the Interior of a Layer on a Substrate 18.8 Scanning Electrochemical Cell Microscopy 18.9 References 18.10 Problems Chapter 19 Single‐Particle Electrochemistry 19.1 General Considerations in Single‐Particle Electrochemistry 19.2 Particle Collision Experiments 19.3 Particle Collision Rate at a Disk‐Shaped UME 19.3.1 Collision Frequency 19.3.2 Variance in the Number of Particle Collisions 19.3.3 Time of First Arrival 19.4 Nanoparticle Collision Behavior 19.4.1 Blocking Collisions 19.4.2 Electrocatalytic Amplification Collisions 19.4.3 Electrolysis Collisions 19.5 Electrochemistry at Single Atoms and Atomic Clusters 19.6 Single‐Molecule Electrochemistry 19.7 References 19.8 Problems Chapter 20 Photoelectrochemistry and Electrogenerated Chemiluminescence 20.1 Solid Materials 20.1.1 The Band Model 20.1.2 Categories of Pure Crystalline Solids 20.1.3 Doped Semiconductors 20.1.4 Fermi Energy 20.1.5 Highly Conducting Oxides 20.2 Semiconductor Electrodes 20.2.1 Interface at a Semiconducting Electrode in the Dark 20.2.2 Current–Potential Curves at Semiconductor Electrodes 20.2.3 Conducting Polymer Electrodes 20.3 Photoelectrochemistry at Semiconductors 20.3.1 Photoeffects at Semiconductor Electrodes 20.3.2 Photoelectrochemical Systems 20.3.3 Dye Sensitization 20.3.4 Surface Photocatalytic Processes at Semiconductor Particles 20.4 Radiolytic Products in Solution 20.4.1 Photoemission of Electrons from an Electrode 20.4.2 Detection and Use of Radiolytic Products in Solution 20.4.3 Photogalvanic Cells 20.5 Electrogenerated Chemiluminescence 20.5.1 Chemical Fundamentals 20.5.2 Fundamental Studies of Radical‐Ion Annihilation 20.5.3 Single‐Potential Generation Based on a Coreactant 20.5.4 ECL Based on Quantum Dots 20.5.5 Analytical Applications of ECL 20.5.6 ECL Beyond the Solution Phase 20.6 References 20.7 Problems Chapter 21 In situ Characterization of Electrochemical Systems 21.1 Microscopy 21.1.1 Scanning Tunneling Microscopy 21.1.2 Atomic Force Microscopy 21.1.3 Optical Microscopy 21.1.4 Transmission Electron Microscopy 21.2 Quartz Crystal Microbalance 21.2.1 Basic Method 21.2.2 QCM with Dissipation Monitoring 21.3 UV–Visible Spectrometry 21.3.1 Absorption Spectroscopy with Thin‐Layer Cells 21.3.2 Ellipsometry 21.3.3 Surface Plasmon Resonance 21.4 Vibrational Spectroscopy 21.4.1 Infrared Spectroscopy 21.4.2 Raman Spectroscopy 21.5 X‐Ray Methods 21.6 Mass Spectrometry 21.7 Magnetic Resonance Spectroscopy 21.7.1 ESR 21.7.2 NMR 21.8 Ex‐situ Techniques 21.8.1 Electron Microscopy 21.8.2 Electron and Ion Spectrometry 21.9 References A Mathematical Methods A.1 Solving Differential Equations by the Laplace Transform Technique A.1.1 Partial Differential Equations A.1.2 Introduction to the Laplace Transformation A.1.3 Fundamental Properties of the Transform A.1.4 Solving Ordinary Differential Equations by Laplace Transformation A.1.5 Simultaneous Linear Ordinary Differential Equations A.1.6 Mass‐Transfer Problems Based on Partial Differential Equations A.1.7 The Zero‐Shift Theorem A.2 Taylor Expansions A.2.1 Expansion of a Function of Several Variables A.2.2 Expansion of a Function of a Single Variable A.2.3 Maclaurin Series A.3 The Error Function and the Gaussian Distribution A.4 Leibnitz Rule A.5 Complex Notation A.6 Fourier Series and Fourier Transformation A.7 References A.8 Problems B Basic Concepts of Simulation B.1 Setting Up the Model B.1.1 A Discrete System B.1.2 Diffusion B.1.3 Dimensionless Parameters B.1.4 Time B.1.5 Distance B.1.6 Current B.1.7 Thickness of the Diffusion Layer B.1.8 Diffusion Coefficients B.2 An Example B.2.1 Organization of the Spreadsheet B.2.2 Concentration Arrays B.2.3 Results and Error Detection B.2.4 Performance B.3 Incorporating Homogeneous Kinetics B.3.1 Unimolecular Reactions B.3.2 Bimolecular Reactions B.4 Boundary Conditions for Various Techniques B.4.1 Potential Steps in Nernstian Systems B.4.2 Heterogeneous Kinetics B.4.3 Potential Sweeps B.4.4 Controlled Current B.5 More Complex Systems B.6 References B.7 Problems C Reference Tables References Index EULA