Electrochemical Methods
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Table of Contents

Preface xxi

Major Symbols and Abbreviations xxv

About the Companion Website liii

1 Overview of Electrode Processes 1

1.1 Basic Ideas 2

1.1.1 Electrochemical Cells and Reactions 2

1.1.2 Interfacial Potential Differences and Cell Potential 4

1.1.3 Reference Electrodes and Control of Potential at a Working Electrode 5

1.1.4 Potential as an Expression of Electron Energy 6

1.1.5 Current as an Expression of Reaction Rate 6

1.1.6 Magnitudes in Electrochemical Systems 8

1.1.7 Current–Potential Curves 9

1.1.8 Control of Current vs. Control of Potential 16

1.1.9 Faradaic and Nonfaradaic Processes 17

1.2 Faradaic Processes and Factors Affecting Rates of Electrode Reactions 17

1.2.1 Electrochemical Cells—Types and Definitions 17

1.2.2 The Electrochemical Experiment and Variables in Electrochemical Cells 18

1.2.3 Factors Affecting Electrode Reaction Rate and Current 21

1.3 Mass-Transfer-Controlled Reactions 23

1.3.1 Modes of Mass Transfer 24

1.3.2 Semiempirical Treatment of Steady-State Mass Transfer 25

1.4 Semiempirical Treatment of Nernstian Reactions with Coupled Chemical Reactions 31

1.4.1 Coupled Reversible Reactions 31

1.4.2 Coupled Irreversible Chemical Reactions 32

1.5 Cell Resistance and the Measurement of Potential 34

1.5.1 Components of the Applied Voltage When Current Flows 35

1.5.2 Two-Electrode Cells 37

1.5.3 Three-Electrode Cells 37

1.5.4 Uncompensated Resistance 38

1.6 The Electrode/Solution Interface and Charging Current 41

1.6.1 The Ideally Polarizable Electrode 41

1.6.2 Capacitance and Charge at an Electrode 41

1.6.3 Brief Description of the Electrical Double Layer 42

1.6.4 Double-Layer Capacitance and Charging Current 44

1.7 Organization of this Book 51

1.8 The Literature of Electrochemistry 52

1.8.1 Reference Sources 52

1.8.2 Sources on Laboratory Techniques 53

1.8.3 Review Series 53

1.9 Lab Note: Potentiostats and Cell Behavior 54

1.9.1 Potentiostats 54

1.9.2 Background Processes in Actual Cells 55

1.9.3 Further Work with Simple RC Networks 56

1.10 References 57

1.11 Problems 57

2 Potentials and Thermodynamics of Cells 61

2.1 Basic Electrochemical Thermodynamics 61

2.1.1 Reversibility 61

2.1.2 Reversibility and Gibbs Free Energy 64

2.1.3 Free Energy and Cell emf 64

2.1.4 Half-Reactions and Standard Electrode Potentials 66

2.1.5 Standard States and Activity 67

2.1.6 emf and Concentration 69

2.1.7 Formal Potentials 71

2.1.8 Reference Electrodes 72

2.1.9 Potential–pH Diagrams and Thermodynamic Predictions 76

2.2 A More Detailed View of Interfacial Potential Differences 80

2.2.1 The Physics of Phase Potentials 80

2.2.2 Interactions Between Conducting Phases 82

2.2.3 Measurement of Potential Differences 84

2.2.4 Electrochemical Potentials 85

2.2.5 Fermi Energy and Absolute Potential 88

2.3 Liquid Junction Potentials 91

2.3.1 Potential Differences at an Electrolyte–Electrolyte Boundary 91

2.3.2 Types of Liquid Junctions 91

2.3.3 Conductance, Transference Numbers, and Mobility 92

2.3.4 Calculation of Liquid Junction Potentials 96

2.3.5 Minimizing Liquid Junction Potentials 100

2.3.6 Junctions of Two Immiscible Liquids 101

2.4 Ion-Selective Electrodes 101

2.4.1 Selective Interfaces 101

2.4.2 Glass Electrodes 102

2.4.3 Other Ion-Selective Electrodes 106

2.4.4 Gas-Sensing ISEs 111

2.5 Lab Note: Practical Use of Reference Electrodes 112

2.5.1 Leakage at the Reference Tip 112

2.5.2 Quasireference Electrodes 112

2.6 References 113

2.7 Problems 116

3 Basic Kinetics of Electrode Reactions 121

3.1 Review of Homogeneous Kinetics 121

3.1.1 Dynamic Equilibrium 121

3.1.2 The Arrhenius Equation and Potential Energy Surfaces 122

3.1.3 Transition State Theory 123

3.2 Essentials of Electrode Reactions 125

3.3 Butler–Volmer Model of Electrode Kinetics 126

3.3.1 Effects of Potential on Energy Barriers 127

3.3.2 One-Step, One-Electron Process 127

3.3.3 The Standard Rate Constant 130

3.3.4 The Transfer Coefficient 131

3.4 Implications of the Butler–Volmer Model for the One-Step, One-Electron Process 132

3.4.1 Equilibrium Conditions and the Exchange Current 133

3.4.2 The Current–Overpotential Equation 133

3.4.3 Approximate Forms of the i–η Equation 135

3.4.4 Exchange Current Plots 139

3.4.5 Very Facile Kinetics and Reversible Behavior 139

3.4.6 Effects of Mass Transfer 140

3.4.7 Limits of Basic Butler–Volmer Equations 141

3.5 Microscopic Theories of Charge Transfer 142

3.5.1 Inner-Sphere and Outer-Sphere Electrode Reactions 142

3.5.2 Extended Charge Transfer and Adiabaticity 143

3.5.3 The Marcus Microscopic Model 146

3.5.4 Implications of the Marcus Theory 152

3.5.5 A Model Based on Distributions of Energy States 162

3.6 Open-Circuit Potential and Multiple Half-Reactions at an Electrode 168

3.6.1 Open-Circuit Potential in Multicomponent Systems 169

3.6.2 Establishment or Loss of Nernstian Behavior at an Electrode 170

3.6.3 Multiple Half-Reaction Currents in i–E Curves 171

3.7 Multistep Mechanisms 171

3.7.1 The Primacy of One-Electron Transfers 172

3.7.2 Rate-Determining, Outer-Sphere Electron Transfer 173

3.7.3 Multistep Processes at Equilibrium 173

3.7.4 Nernstian Multistep Processes 174

3.7.5 Quasireversible and Irreversible Multistep Processes 174

3.8 References 177

3.9 Problems 180

4 Mass Transfer by Migration and Diffusion 183

4.1 General Mass-Transfer Equations 183

4.2 Migration in Bulk Solution 186

4.3 Mixed Migration and Diffusion Near an Active Electrode 187

4.3.1 Balance Sheets for Mass Transfer During Electrolysis 188

4.3.2 Utility of a Supporting Electrolyte 192

4.4 Diffusion 193

4.4.1 A Microscopic View 193

4.4.2 Fick’s Laws of Diffusion 196

4.4.3 Flux of an Electroreactant at an Electrode Surface 199

4.5 Formulation and Solution of Mass-Transfer Problems 199

4.5.1 Initial and Boundary Conditions in Electrochemical Problems 200

4.5.2 General Formulation of a Linear Diffusion Problem 201

4.5.3 Systems Involving Migration or Convection 202

4.5.4 Practical Means for Reaching Solutions 202

4.6 References 204

4.7 Problems 205

5 Steady-State Voltammetry at Ultramicroelectrodes 207

5.1 Steady-State Voltammetry at a Spherical UME 207

5.1.1 Steady-State Diffusion 208

5.1.2 Steady-State Current 211

5.1.3 Convergence on the Steady State 211

5.1.4 Steady-State Voltammetry 212

5.2 Shapes and Properties of Ultramicroelectrodes 214

5.2.1 Spherical or Hemispherical UME 215

5.2.2 Disk UME 215

5.2.3 Cylindrical UME 221

5.2.4 Band UME 221

5.2.5 Summary of Steady-State Behavior at UMEs 222

5.3 Reversible Electrode Reactions 224

5.3.1 Shape of the Wave 224

5.3.2 Applications of Reversible i–E Curves 226

5.4 Quasireversible and Irreversible Electrode Reactions 230

5.4.1 Effect of Electrode Kinetics on Steady-State Responses 230

5.4.2 Total Irreversibility 232

5.4.3 Kinetic Regimes 234

5.4.4 Influence of Electrode Shape 234

5.4.5 Applications of Irreversible i–E Curves 235

5.4.6 Evaluation of Kinetic Parameters by Varying Mass-Transfer Rates 237

5.5 Multicomponent Systems and Multistep Charge Transfers 239

5.6 Additional Attributes of Ultramicroelectrodes 241

5.6.1 Uncompensated Resistance at a UME 241

5.6.2 Effects of Conductivity on Voltammetry at a UME 242

5.6.3 Applications Based on Spatial Resolution 243

5.7 Migration in Steady-State Voltammetry 245

5.7.1 Mathematical Approach to Problems Involving Migration 245

5.7.2 Concentration Profiles in the Diffusion–Migration Layer 246

5.7.3 Wave Shape at Low Electrolyte Concentration 248

5.7.4 Effects of Migration on Wave Height in SSV 248

5.8 Analysis at High Analyte Concentrations 251

5.9 Lab Note: Preparation of Ultramicroelectrodes 253

5.9.1 Preparation and Characterization of UMEs 254

5.9.2 Testing the Integrity of a UME 254

5.9.3 Estimating the Size of a UME 256

5.10 References 257

5.11 Problems 258

6 Transient Methods Based on Potential Steps 261

6.1 Chronoamperometry Under Diffusion Control 261

6.1.1 Linear Diffusion at a Plane 262

6.1.2 Response at a Spherical Electrode 265

6.1.3 Transients at Other Ultramicroelectrodes 267

6.1.4 Information from Chronoamperometric Results 270

6.1.5 Microscopic and Geometric Areas 271

6.2 Sampled-Transient Voltammetry for Reversible Electrode Reactions 275

6.2.1 A Step to an Arbitrary Potential 276

6.2.2 Shape of the Voltammogram 277

6.2.3 Concentration Profiles When R Is Initially Absent 278

6.2.4 Simplified Current–Concentration Relationships 279

6.2.5 Applications of Reversible i–E Curves 279

6.3 Sampled-Transient Voltammetry for Quasireversible and Irreversible Electrode Reactions 279

6.3.1 Effect of Electrode Kinetics on Transient Behavior 280

6.3.2 Sampled-Transient Voltammetry for Reduction of O 282

6.3.3 Sampled Transient Voltammetry for Oxidation of R 284

6.3.4 Totally Irreversible Reactions 285

6.3.5 Kinetic Regimes 287

6.3.6 Applications of Irreversible i–E Curves 287

6.4 Multicomponent Systems and Multistep Charge Transfers 289

6.5 Chronoamperometric Reversal Techniques 290

6.5.1 Approaches to the Problem 292

6.5.2 Current–Time Responses 293

6.6 Chronocoulometry 294

6.6.1 Large-Amplitude Potential Step 295

6.6.2 Reversal Experiments Under Diffusion Control 296

6.6.3 Effects of Heterogeneous Kinetics 299

6.7 Cell Time Constants at Microelectrodes 300

6.8 Lab Note: Practical Concerns with Potential Step Methods 303

6.8.1 Preparation of the Electrode Surface at a Microelectrode 303

6.8.2 Interference from Charging Current 305

6.9 References 306

6.10 Problems 307

7 Linear Sweep and Cyclic Voltammetry 311

7.1 Transient Responses to a Potential Sweep 311

7.2 Nernstian (Reversible) Systems 313

7.2.1 Linear Sweep Voltammetry 313

7.2.2 Cyclic Voltammetry 321

7.3 Quasireversible Systems 325

7.3.1 Linear Sweep Voltammetry 326

7.3.2 Cyclic Voltammetry 326

7.4 Totally Irreversible Systems 329

7.4.1 Linear Sweep Voltammetry 329

7.4.2 Cyclic Voltammetry 332

7.5 Multicomponent Systems and Multistep Charge Transfers 332

7.5.1 Multicomponent Systems 332

7.5.2 Multistep Charge Transfers 333

7.6 Fast Cyclic Voltammetry 334

7.7 Convolutive Transformation 336

7.8 Voltammetry at Liquid–Liquid Interfaces 339

7.8.1 Experimental Approach to Voltammetry 340

7.8.2 Effect of Interfacial Potential on Composition 341

7.8.3 Voltammetric Behavior 341

7.9 Lab Note: Practical Aspects of Cyclic Voltammetry 344

7.9.1 Basic Experimental Conditions 344

7.9.2 Choice of Initial and Final Potentials 345

7.9.3 Deaeration 347

7.10 References 347

7.11 Problems 349

8 Polarography, Pulse Voltammetry, and Square-Wave Voltammetry 355

8.1 Polarography 355

8.1.1 The Dropping Mercury Electrode 355

8.1.2 The IlkovičEquation 356

8.1.3 Polarographic Waves 357

8.1.4 Practical Advantages of the DME 358

8.1.5 Polarographic Analysis 358

8.1.6 Residual Current and Detection Limits 359

8.2 Normal Pulse Voltammetry 361

8.2.1 Implementation 362

8.2.2 Renewal at Stationary Electrodes 363

8.2.3 Normal Pulse Polarography 364

8.2.4 Practical Application 366

8.3 Reverse Pulse Voltammetry 367

8.4 Differential Pulse Voltammetry 369

8.4.1 Concept of the Method 370

8.4.2 Theory 371

8.4.3 Renewal vs. Pre-Electrolysis 374

8.4.4 Residual Currents 375

8.4.5 Differential Pulse Polarography 375

8.5 Square-Wave Voltammetry 376

8.5.1 Experimental Concept and Practice 376

8.5.2 Theoretical Prediction of Response 377

8.5.3 Background Currents 380

8.5.4 Applications 381

8.6 Analysis by Pulse Voltammetry 383

8.7 References 385

8.8 Problems 386

9 Controlled-Current Techniques 389

9.1 Introduction to Chronopotentiometry 389

9.2 Theory of Controlled-Current Methods 391

9.2.1 General Treatment for Linear Diffusion 391

9.2.2 Constant-Current Electrolysis—The Sand Equation 392

9.2.3 Programmed Current Chronopotentiometry 394

9.3 Potential–Time Curves in Constant-Current Electrolysis 394

9.3.1 Reversible (Nernstian) Waves 394

9.3.2 Totally Irreversible Waves 394

9.3.3 Quasireversible Waves 395

9.3.4 Practical Issues in the Measurement of Transition Time 396

9.4 Reversal Techniques 398

9.4.1 Response Function Principle 398

9.4.2 Current Reversal 398

9.5 Multicomponent Systems and Multistep Reactions 400

9.6 The Galvanostatic Double Pulse Method 401

9.7 Charge Step (Coulostatic) Methods 403

9.7.1 Small Excursions 404

9.7.2 Large Excursions 405

9.7.3 Coulostatic Perturbation by Temperature Jump 405

9.8 References 406

9.9 Problems 407

10 Methods Involving Forced Convection—Hydrodynamic Methods 411

10.1 Theory of Convective Systems 411

10.1.1 The Convective-Diffusion Equation 412

10.1.2 Determination of the Velocity Profile 412

10.2 Rotating Disk Electrode 414

10.2.1 The Velocity Profile at a Rotating Disk 414

10.2.2 Solution of the Convective-Diffusion Equation 416

10.2.3 Concentration Profile 418

10.2.4 General i–E Curves at the RDE 419

10.2.5 The Koutecký–Levich Method 420

10.2.6 Current Distribution at the RDE 423

10.2.7 Practical Considerations for Application of the RDE 426

10.3 Rotating Ring and Ring-Disk Electrodes 426

10.3.1 Rotating Ring Electrode 427

10.3.2 The Rotating Ring-Disk Electrode 428

10.4 Transient Currents 432

10.4.1 Transients at the RDE 432

10.4.2 Transients at the RRDE 433

10.5 Modulation of the RDE 435

10.6 Electrohydrodynamic Phenomena 436

10.7 References 439

10.8 Problems 440

11 Electrochemical Impedance Spectroscopy and ac Voltammetry 443

11.1 A Simple Measurement of Cell Impedance 444

11.2 Brief Review of ac Circuits 446

11.3 Equivalent Circuits of a Cell 450

11.3.1 The Randles Equivalent Circuit 451

11.3.2 Interpretation of the Faradaic Impedance 452

11.3.3 Behavior and Uses of the Faradaic Impedance 455

11.4 Electrochemical Impedance Spectroscopy 458

11.4.1 Conditions of Measurement 458

11.4.2 A System with Simple Faradaic Kinetics 460

11.4.3 Measurement of Resistance and Capacitance 465

11.4.4 A Confined Electroactive Domain 466

11.4.5 Other Applications 470

11.5 ac Voltammetry 470

11.5.1 Reversible Systems 470

11.5.2 Quasireversible and Irreversible Systems 473

11.5.3 Cyclic ac Voltammetry 477

11.6 Nonlinear Responses 477

11.6.1 Second Harmonic ac Voltammetry 478

11.6.2 Large Amplitude ac Voltammetry 479

11.7 Chemical Analysis by ac Voltammetry 481

11.8 Instrumentation for Electrochemical Impedance Methods 482

11.8.1 Frequency-Domain Instruments 482

11.8.2 Time-Domain Instruments 483

11.9 Analysis of Data in the Laplace Plane 485

11.10 References 485

11.11 Problems 487

12 Bulk Electrolysis 489

12.1 General Considerations 490

12.1.1 Completeness of an Electrode Process 490

12.1.2 Current Efficiency 491

12.1.3 Experimental Concerns 491

12.2 Controlled-Potential Methods 495

12.2.1 Current–Time Behavior 495

12.2.2 Practical Aspects 497

12.2.3 Coulometry 498

12.2.4 Electrogravimetry 500

12.2.5 Electroseparations 501

12.3 Controlled-Current Methods 501

12.3.1 Characteristics of Controlled-Current Electrolysis 501

12.3.2 Coulometric Titrations 503

12.3.3 Practical Aspects of Constant-Current Electrolysis 506

12.4 Electrometric End-Point Detection 507

12.4.1 Current–Potential Curves During Titration 507

12.4.2 Potentiometric Methods 508

12.4.3 Amperometric Methods 509

12.5 Flow Electrolysis 510

12.5.1 Mathematical Treatment 510

12.5.2 Dual-Electrode Flow Cells 515

12.5.3 Microfluidic Flow Cells 516

12.6 Thin-Layer Electrochemistry 521

12.6.1 Chronoamperometry and Coulometry 521

12.6.2 Potential Sweep in a Nernstian System 524

12.6.3 Dual-Electrode Thin-Layer Cells 526

12.6.4 Applications of the Thin-Layer Concept 526

12.7 Stripping Analysis 527

12.7.1 Introduction 527

12.7.2 Principles and Theory 528

12.7.3 Applications and Variations 529

12.8 References 531

12.9 Problems 534

13 Electrode Reactions with Coupled Homogeneous Chemical Reactions 539

13.1 Classification of Reactions 539

13.1.1 Reactions with One E-Step 541

13.1.2 Reactions with Two or More E-Steps 542

13.2 Impact of Coupled Reactions on Cyclic Voltammetry 545

13.2.1 Diagnostic Criteria 545

13.2.2 Characteristic Times 547

13.2.3 An Example 547

13.2.4 Including Kinetics in Theory 548

13.2.5 Comparative Simulation 551

13.3 Survey of Behavior 552

13.3.1 Following Reaction—case E R c I 552

13.3.2 Effect of Electrode Kinetics in Ec I Systems 556

13.3.3 Bidirectional Following Reaction 558

13.3.4

catalytic Reaction—case E r c ′ I

561

13.3.5 Preceding Reaction—Case C r E r 564

13.3.6 Multistep Electron Transfers 569

13.3.7 ECE/DISP Reactions 576

13.3.8 Concerted vs.StepwiseReaction 584

13.3.9 Elaboration of Reaction Schemes 590

13.4 Behavior with Other Electrochemical Methods 591

13.5 References 593

13.6 Problems 595

14 Double-Layer Structure and Adsorption 599

14.1 Thermodynamics of the Double Layer 599

14.1.1 The Gibbs Adsorption Isotherm 599

14.1.2 The Electrocapillary Equation 601

14.1.3 Relative Surface Excesses 601

14.2 Experimental Evaluations 602

14.2.1 Electrocapillarity 602

14.2.2 Excess Charge and Capacitance 603

14.2.3 Relative Surface Excesses 606

14.3 Models for Double-Layer Structure 606

14.3.1 The Helmholtz Model 607

14.3.2 The Gouy–Chapman Theory 609

14.3.3 Stern’s Modification 614

14.3.4 Specific Adsorption 617

14.4 Studies at Solid Electrodes 619

14.4.1 Well-Defined Single-Crystal Electrode Surfaces 620

14.4.2 The Double Layer at Solids 623

14.5 Extent and Rate of Specific Adsorption 627

14.5.1 Nature and Extent of Specific Adsorption 628

14.5.2 Electrosorption Valency 629

14.5.3 Adsorption Isotherms 630

14.5.4 Rate of Adsorption 633

14.6 Practical Aspects of Adsorption 634

14.7 Double-Layer Effects on Electrode Reaction Rates 636

14.7.1 Introduction and Principles 636

14.7.2 Double-Layer Effects Without Specific Adsorption of Electrolyte 638

14.7.3 Double-Layer Effects with Specific Adsorption 639

14.7.4 Diffuse Double-Layer Effects on Mass Transport 640

14.8 References 645

14.9 Problems 648

15 Inner-Sphere Electrode Reactions and Electrocatalysis 653

15.1 Inner-Sphere Heterogenous Electron-Transfer Reactions 653

15.1.1 TheRoleoftheElectrodeSurface 653

15.1.2 Energetics of 1e Electron-Transfer Reactions 654

15.1.3 Adsorption Energies 657

15.2 Electrocatalytic Reaction Mechanisms 657

15.2.1 Hydrogen Evolution Reaction 657

15.2.2 Tafel Plot Analysis of HER Kinetics 660

15.3 Additional Examples of Inner-Sphere Reactions 667

15.3.1 Oxygen Reduction Reaction 667

15.3.2 Chlorine Evolution 670

15.3.3 Methanol Oxidation 670

15.3.4 CO 2 Reduction 673

15.3.5 Oxidation of NH 3 to N 2 674

15.3.6 Organic Halide Reduction 676

15.3.7 Hydrogen Peroxide Oxidation and Reduction 677

15.4 Computational Analyses of Inner-Sphere Electron-Transfer Reactions 678

15.4.1 Density Functional Theory Analysis of Electrocatalytic Reactions 679

15.4.2 Hydrogen Evolution Reaction 679

15.4.3 Oxygen Reduction Reaction 681

15.5 Electrocatalytic Correlations 684

15.6 Electrochemical Phase Transformations 688

15.6.1 Nucleation and Growth of a New Phase 688

15.6.2 Classical Nucleation Theory 689

15.6.3 Electrodeposition 699

15.6.4 Gas Evolution 707

15.7 References 713

15.8 Problems 718

16 Electrochemical Instrumentation 721

16.1 Operational Amplifiers 721

16.1.1 Ideal Properties 721

16.1.2 Nonidealities 723

16.2 Current Feedback 725

16.2.1 Current Follower 725

16.2.2 Scaler/Inverter 726

16.2.3 Adders 726

16.2.4 Integrators 727

16.3 Voltage Feedback 728

16.3.1 Voltage Follower 728

16.3.2 Control Functions 729

16.4 Potentiostats 730

16.4.1 Basic Considerations 730

16.4.2 The Adder Potentiostat 731

16.4.3 Refinements to the Adder Potentiostat 732

16.4.4 Bipotentiostats 733

16.4.5 Four-Electrode Potentiostats 734

16.5 Galvanostats 734

16.6 Integrated Electrochemical Instrumentation 736

16.7 Difficulties with Potential Control 737

16.7.1 Types of Control Problems 737

16.7.2 Cell Properties and Electrode Placement 740

16.7.3 Electronic Compensation of Resistance 740

16.8 Measurement of Low Currents 744

16.8.1 Fundamental Limits 744

16.8.2 Practical Considerations 746

16.8.3 Current Amplifier 746

16.8.4 Simplified Instruments and Cells 746

16.9 Instruments for Short Time Scales 748

16.10 Lab Note: Practical Use of Electrochemical Instruments 749

16.10.1 Caution Regarding Electrochemical Workstations 749

16.10.2 Troubleshooting Electrochemical Systems 749

16.11 References 751

16.12 Problems 752

17 Electroactive Layers and Modified Electrodes 755

17.1 Monolayers and Submonolayers on Electrodes 756

17.2 Cyclic Voltammetry of Adsorbed Layers 757

17.2.1 Fundamentals 757

17.2.2 Reversible Adsorbate Couples 758

17.2.3 Irreversible Adsorbate Couples 763

17.2.4 Nernstian Processes Involving Adsorbates and Solutes 766

17.2.5 More Complex Systems 770

17.2.6 Electric-Field-Driven Acid–Base Chemistry in Adsorbate Layers 771

17.3 Other Useful Methods for Adsorbed Monolayers 775

17.3.1 Chronocoulometry 775

17.3.2 Coulometry in Thin-Layer Cells 777

17.3.3 Impedance Measurements 778

17.3.4 Chronopotentiometry 779

17.4 Thick Modification Layers on Electrodes 780

17.5 Dynamics in Modification Layers 782

17.5.1 Steady State at a Rotating Disk 783

17.5.2 Principal Dynamic Processes in Modifying Films 784

17.5.3 Interplay of Dynamical Elements 789

17.6 Blocking Layers 791

17.6.1 Permeation Through Pores and Pinholes 792

17.6.2 Tunneling Through Blocking Films 796

17.7 Other Methods for Characterizing Layers on Electrodes 798

17.8 Electrochemical Methods Based on Electroactive Layers or Electrode Modification 798

17.8.1 Electrocatalysis 799

17.8.2 Bioelectrocatalysis Based on Enzyme-Modified Electrodes 799

17.8.3 Electrochemical Sensors 803

17.8.4 Faradaic Electrochemical Measurements in vivo 809

17.9 References 812

17.10 Problems 817

18 Scanning Electrochemical Microscopy 819

18.1 Principles 819

18.2 Approach Curves 821

18.3 Imaging Surface Topography and Reactivity 825

18.3.1 Imaging Based on Conductivity of the Substrate 825

18.3.2 Imaging Based on Heterogeneous Electron-Transfer Reactivity 826

18.3.3 Simultaneous Imaging of Topography and Reactivity 827

18.4 Measurements of Kinetics 828

18.4.1 Heterogeneous Electron-Transfer Reactions 828

18.4.2 Homogeneous Reactions 831

18.5 Surface Interrogation 835

18.6 Potentiometric Tips 839

18.7 Other Applications 839

18.7.1 Detection of Species Released from Surfaces, Films, or Pores 839

18.7.2 Biological Systems 840

18.7.3 Probing the Interior of a Layer on a Substrate 841

18.8 Scanning Electrochemical Cell Microscopy 841

18.9 References 846

18.10 Problems 849

19 Single-Particle Electrochemistry 851

19.1 General Considerations in Single-Particle Electrochemistry 851

19.2 Particle Collision Experiments 852

19.3 Particle Collision Rate at a Disk-Shaped UME 854

19.3.1 Collision Frequency 854

19.3.2 Variance in the Number of Particle Collisions 855

19.3.3 Time of First Arrival 856

19.4 Nanoparticle Collision Behavior 857

19.4.1 Blocking Collisions 857

19.4.2 Electrocatalytic Amplification Collisions 861

19.4.3 Electrolysis Collisions 864

19.5 Electrochemistry at Single Atoms and Atomic Clusters 870

19.6 Single-Molecule Electrochemistry 875

19.7 References 879

19.8 Problems 881

20 Photoelectrochemistry and Electrogenerated Chemiluminescence 885

20.1 Solid Materials 885

20.1.1 The Band Model 885

20.1.2 Categories of Pure Crystalline Solids 886

20.1.3 Doped Semiconductors 889

20.1.4 Fermi Energy 890

20.1.5 Highly Conducting Oxides 891

20.2 Semiconductor Electrodes 892

20.2.1 Interface at a Semiconducting Electrode in the Dark 892

20.2.2 Current–Potential Curves at Semiconductor Electrodes 896

20.2.3 Conducting Polymer Electrodes 899

20.3 Photoelectrochemistry at Semiconductors 901

20.3.1 Photoeffects at Semiconductor Electrodes 901

20.3.2 Photoelectrochemical Systems 903

20.3.3 Dye Sensitization 905

20.3.4 Surface Photocatalytic Processes at Semiconductor Particles 906

20.4 Radiolytic Products in Solution 908

20.4.1 Photoemission of Electrons from an Electrode 908

20.4.2 Detection and Use of Radiolytic Products in Solution 909

20.4.3 Photogalvanic Cells 909

20.5 Electrogenerated Chemiluminescence 910

20.5.1 Chemical Fundamentals 910

20.5.2 Fundamental Studies of Radical-Ion Annihilation 912

20.5.3 Single-Potential Generation Based on a Coreactant 916

20.5.4 ECL Based on Quantum Dots 917

20.5.5 Analytical Applications of ECL 918

20.5.6 ECL Beyond the Solution Phase 922

20.6 References 922

20.7 Problems 927

21 In situ Characterization of Electrochemical Systems 931

21.1 Microscopy 931

21.1.1 Scanning Tunneling Microscopy 932

21.1.2 Atomic Force Microscopy 934

21.1.3 Optical Microscopy 937

21.1.4 Transmission Electron Microscopy 938

21.2 Quartz Crystal Microbalance 940

21.2.1 Basic Method 940

21.2.2 QCM with Dissipation Monitoring 942

21.3 UV–Visible Spectrometry 942

21.3.1 Absorption Spectroscopy with Thin-Layer Cells 942

21.3.2 Ellipsometry 945

21.3.3 Surface Plasmon Resonance 946

21.4 Vibrational Spectroscopy 947

21.4.1 Infrared Spectroscopy 947

21.4.2 Raman Spectroscopy 950

21.5 X-Ray Methods 953

21.6 Mass Spectrometry 954

21.7 Magnetic Resonance Spectroscopy 955

21.7.1 Esr 955

21.7.2 Nmr 956

21.8 Ex-situ Techniques 957

21.8.1 Electron Microscopy 957

21.8.2 Electron and Ion Spectrometry 958

21.9 References 960

Appendix A Mathematical Methods 967

A.1 Solving Differential Equations by the Laplace Transform Technique 967

A.1.1 Partial Differential Equations 967

A.1.2 Introduction to the Laplace Transformation 968

A.1.3 Fundamental Properties of the Transform 969

A.1.4 Solving Ordinary Differential Equations by Laplace Transformation 970

A.1.5 Simultaneous Linear Ordinary Differential Equations 972

A.1.6 Mass-Transfer Problems Based on Partial Differential Equations 973

A.1.7 The Zero-Shift Theorem 975

A.2 Taylor Expansions 976

A.2.1 Expansion of a Function of Several Variables 976

A.2.2 Expansion of a Function of a Single Variable 977

A.2.3 Maclaurin Series 977

A.3 The Error Function and the Gaussian Distribution 977

A.4 Leibnitz Rule 979

A.5 Complex Notation 979

A.6 Fourier Series and Fourier Transformation 981

A.7 References 982

A.8 Problems 983

Appendix B Basic Concepts of Simulation 985

B.1 Setting Up the Model 985

B.1.1 A Discrete System 985

B.1.2 Diffusion 986

B.1.3 Dimensionless Parameters 987

B.1.4 Time 990

B.1.5 Distance 990

B.1.6 Current 991

B.1.7 Thickness of the Diffusion Layer 992

B.1.8 Diffusion Coefficients 993

B.2 An Example 993

B.2.1 Organization of the Spreadsheet 993

B.2.2 Concentration Arrays 996

B.2.3 Results and Error Detection 996

B.2.4 Performance 997

B.3 Incorporating Homogeneous Kinetics 999

B.3.1 Unimolecular Reactions 999

B.3.2 Bimolecular Reactions 1000

B.4 Boundary Conditions for Various Techniques 1001

B.4.1 Potential Steps in Nernstian Systems 1001

B.4.2 Heterogeneous Kinetics 1002

B.4.3 Potential Sweeps 1003

B.4.4 Controlled Current 1003

B.5 More Complex Systems 1004

B.6 References 1005

B.7 Problems 1005

Appendix C Reference Tables 1007

References 1013

Index 1015

About the Author

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.

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