The latest edition of a classic textbook in electrochemistry
The third edition of Electrochemical Methods has been extensively revised to reflect the evolution of electrochemistry over the past two decades, highlighting significant developments in the understanding of electrochemical phenomena and emerging experimental tools, while extending the book's value as a general introduction to electrochemical methods.
This authoritative resource for new students and practitioners provides must-have information crucial to a successful career in research. The authors focus on methods that are extensively practiced and on phenomenological questions of current concern.
This latest edition of Electrochemical Methods contains numerous problems and chemical examples, with illustrations that serve to illuminate the concepts contained within in a way that will assist both student and mid-career practitioner.
Significant updates and new content in this third edition include:
- An extensively revised introductory chapter on electrode processes, designed for new readers coming into electrochemistry from diverse backgrounds
- New chapters on steady-state voltammetry at ultramicroelectrodes, inner-sphere electrode reactions and electrocatalysis, and single-particle electrochemistry
- Extensive treatment of Marcus kinetics as applied to electrode reactions, a more detailed introduction to migration, and expanded coverage of electrochemical impedance spectroscopy
- The inclusion of Lab Notes in many chapters to help newcomers with the transition from concept to practice in the laboratory
The new edition has been revised to address a broader audience of scientists and engineers, designed to be accessible to readers with a basic foundation in university chemistry, physics and mathematics. It is a self-contained volume, developing all key ideas from the fundamental principles of chemistry and physics.
Perfect for senior undergraduate and graduate students taking courses in electrochemistry, physical and analytical chemistry, this is also an indispensable resource for researchers and practitioners working in fields including electrochemistry and electrochemical engineering, energy storage and conversion, analytical chemistry and sensors.
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
