Impedance Spectroscopy Theory, Experiment, and Applications

The Essential Reference for the Field, Featuring Protocols, Analysis, Fundamentals, and the Latest Advances

Impedance Spectroscopy: Theory, Experiment, and Applications provides a comprehensive reference for graduate students, researchers, and engineers working in electrochemistry, physical chemistry, and physics. Covering both fundamentals concepts and practical applications, this unique reference provides a level of understanding that allows immediate use of impedance spectroscopy methods.

Step-by-step experiment protocols with analysis guidance lend immediate relevance to general principles, while extensive figures and equations aid in the understanding of complex concepts. Detailed discussion includes the best measurement methods and identifying sources of error, and theoretical considerations for modeling, equivalent circuits, and equations in the complex domain are provided for most subjects under investigation. Written by a team of expert contributors, this book provides a clear understanding of impedance spectroscopy in general as well as the essential skills needed to use it in specific applications.

Extensively updated to reflect the field’s latest advances, this new Third Edition:

• Incorporates the latest research, and provides coverage of new areas in which impedance spectroscopy is gaining importance
• Discusses the application of impedance spectroscopy to viscoelastic rubbery materials and biological systems
• Explores impedance spectroscopy applications in electrochemistry, semiconductors, solid electrolytes, corrosion, solid state devices, and electrochemical power sources
• Examines both the theoretical and practical aspects, and discusses when impedance spectroscopy is and is not the appropriate solution to an analysis problem

Researchers and engineers will find value in the immediate practicality, while students will appreciate the hands-on approach to impedance spectroscopy methods. Retaining the reputation it has gained over years as a primary reference, Impedance Spectroscopy: Theory, Experiment, and Applications once again present a comprehensive reference reflecting the current state of the field.

Evgenij Barsoukov, PhD, is a TI Fellow and the Head of Algorithm Development at the Battery Management unit of Texas Instruments. His research focuses on impedance spectroscopy-based modelling to improve battery monitoring and charging technology.

J. Ross Macdonald, DSc, is the William Rand Kenan, Jr. Professor Emeritus of Physics at the University of North Carolina. His research uses impedance spectroscopy to help analyze the electrical response of high-resistivity ionically conducting solid materials.

Preface to the Third Edition xi

Preface to the Second Edition xiii

Preface to the First Edition xv

Contributors to the Third Edition xvii

Chapter 1 Fundamentals of Impedance Spectroscopy 1
J. Ross Macdonald and William B. Johnson 1

1.1 Background, Basic Definitions, and History 1

1.1.1 The Importance of Interfaces 1

1.1.2 The Basic Impedance Spectroscopy Experiment 2

1.1.3 Response to a Small-Signal Stimulus in the Frequency Domain 3

1.1.4 Impedance-Related Functions 5

1.1.5 Early History 6

1.2 Advantages and Limitations 7

1.2.1 Differences between Solid-State and Aqueous Electrochemistry 9

1.3 Elementary Analysis of Impedance Spectra 10

1.3.1 Physical Models for Equivalent Circuit Elements 10

1.3.2 Simple RC Circuits 11

1.3.3 Analysis of Single Impedance Arcs 12

1.4 Selected Applications of IS 16

Chapter 2 Theory 21
Ian D. Raistrick, J. Ross Macdonald, and Donald R. Franceschetti 21

2.1 The Electrical Analogs of Physical and Chemical Processes 21

2.1.1 Introduction 21

2.1.2 The Electrical Properties of Bulk Homogeneous Phases 23

2.1.2.1 Introduction 23

2.1.2.2 Dielectric Relaxation in Materials with a Single Time Constant 23

2.1.2.3 Distributions of Relaxation Times 27

2.1.2.4 Conductivity and Diffusion in Electrolytes 34

2.1.2.5 Conductivity and Diffusion: A Statistical Description 36

2.1.2.6 Migration in the Absence of Concentration Gradients 38

2.1.2.7 Transport in Disordered Media 40

2.1.3 Mass and Charge Transport in the Presence of Concentration Gradients 45

2.1.3.1 Diffusion 45

2.1.3.2 Mixed Electronic–Ionic Conductors 49

2.1.3.3 Concentration Polarization 50

2.1.4 Interfaces and Boundary Conditions 51

2.1.4.1 Reversible and Irreversible Interfaces 51

2.1.4.2 Polarizable Electrodes 52

2.1.4.3 Adsorption at the Electrode–Electrolyte Interface   54

2.1.4.4 Charge Transfer at the Electrode–Electrolyte Interface 56

2.1.5 Grain Boundary Effects 60

2.1.6 Current Distribution: Porous and Rough Electrodes—The Effect of Geometry 62

2.1.6.1 Current Distribution Problems 62

2.1.6.2 Rough and Porous Electrodes 63

2.2 Physical and Electrochemical Models 67

2.2.1 The Modeling of Electrochemical Systems 67

2.2.2 Equivalent Circuits 67

2.2.2.1 Unification of Immittance Responses 67

2.2.2.2 Distributed Circuit Elements 69

2.2.2.3 Ambiguous Circuits 75

2.2.3 Modeling Results 79

2.2.3.1 Introduction 79

2.2.3.2 Supported Situations 80

2.2.3.3 Unsupported Situations: Theoretical Models 84

2.2.3.4 Equivalent Network Models 96

2.2.3.5 Unsupported Situations: Empirical and Semiempirical Models 97

Chapter 3 Measuring Techniques and Data Analysis 107
Michael C. H. McKubre, Digby D. Macdonald, Brian Sayers, and J. Ross Macdonald 107

3.1 Impedance Measurement Techniques 107

3.1.1 Introduction 107

3.1.2 Frequency Domain Methods 108

3.1.2.1 Audio Frequency Bridges 108

3.1.2.2 Transformer Ratio Arm Bridges 110

3.1.2.3 Berberian–Cole Bridge   112

3.1.2.4 Considerations of Potentiostatic Control 115

3.1.2.5 Oscilloscopic Methods for Direct Measurement 116

3.1.2.6 Phase-Sensitive Detection for Direct Measurement 118

3.1.2.7 Automated Frequency Response Analysis 119

3.1.2.8 Automated Impedance Analyzers 122

3.1.2.9 The Use of Kramers–Kronig Transforms 124

3.1.2.10 Spectrum Analyzers 126

3.1.3 Time-Domain Methods 128

3.1.3.1 Introduction 128

3.1.3.2 Analog-to-Digital Conversion 129

3.1.3.3 Computer Interfacing 133

3.1.3.4 Digital Signal Processing 135

3.1.4 Conclusions 138

3.2 Commercially Available Impedance Measurement Systems 139

3.2.1 General Measurement Techniques 139

3.2.1.1 Current-to-Voltage (I–E) Conversion Techniques 139

3.2.1.2 Measurements Using 2-, 3-, or 4-Terminal Techniques 144

3.2.1.3 Measurement Resolution and Accuracy 146

3.2.1.4 Single Sine and FFT Measurement Techniques 148

3.2.2 Electrochemical Impedance Measurement Systems 152

3.2.2.1 System Configuration 152

3.2.2.2 Why Use a Potentiostat? 152

3.2.2.3 Multi-electrode Techniques 153

3.2.2.4 Effects of Connections and Input Impedance 154

3.2.2.5 Verification of Measurement Performance 155

3.2.2.6 Floating Measurement Techniques 156

3.2.2.7 Multichannel Techniques 157

3.2.3 Materials Impedance Measurement Systems 157

3.2.3.1 System Configuration 157

3.2.3.2 Measurement of Low Impedance Materials 158

3.2.3.3 Measurement of High Impedance Materials 158

3.2.3.4 Reference Techniques 159

3.2.3.5 Normalization Techniques 159

3.2.3.6 High Voltage Measurement Techniques 160

3.2.3.7 Temperature Control 160

3.2.3.8 Sample Holder Considerations 161

3.3 Data Analysis 161

3.3.1 Data Presentation and Adjustment 161

3.3.1.1 Previous Approaches 161

3.3.1.2 Three-Dimensional Perspective Plotting 162

3.3.1.3 Treatment of Anomalies 164

3.3.2 Data Analysis Methods 166

3.3.2.1 Simple Methods 166

3.3.2.2 Complex Nonlinear Least Squares 167

3.3.2.3 Weighting 168

3.3.2.4 Which Impedance-Related Function to Fit? 169

3.3.2.5 The Question of “What to Fit” Revisited 169

3.3.2.6 Deconvolution Approaches 169

3.3.2.7 Examples of CNLS Fitting 170

3.3.2.8 Summary and Simple Characterization Example 172

Chapter 4 Applications of Impedance Spectroscopy 175

4.1 Characterization of Materials 175
N. Bonanos, B. C. H. Steele, and E. P. Butler 175

4.1.1 Microstructural Models for Impedance Spectra of Materials 175

4.1.1.1 Introduction 175

4.1.1.2 Layer Models 176

4.1.1.3 Effective Medium Models 183

4.1.1.4 Modeling of Composite Electrodes 191

4.1.2 Experimental Techniques 194

4.1.2.1 Introduction 194

4.1.2.2 Measurement Systems 195

4.1.2.3 Sample Preparation: Electrodes 199

4.1.2.4 Problems Associated with the Measurement of Electrode Properties 201

4.1.3 Interpretation of the Impedance Spectra of Ionic Conductors and Interfaces 203

4.1.3.1 Introduction 203

4.1.3.2 Characterization of Grain Boundaries by IS 204

4.1.3.3 Characterization of Two-Phase Dispersions by IS 215

4.1.3.4 Impedance Spectra of Unusual Two-Phase Systems 218

4.1.3.5 Impedance Spectra of Composite Electrodes 219

4.1.3.6 Closing Remarks 224

4.2 Characterization of the Electrical Response of Wide-Range-Resistivity Ionic and Dielectric Solid Materials by Immittance Spectroscopy 224
J. Ross Macdonald 224

4.2.1 Introduction 224

4.2.2 Types of Dispersive Response Models: Strengths and Weaknesses 225

4.2.2.1 Overview 225

4.2.2.2 Variable-Slope Models 226

4.2.2.3 Composite Models 227

4.2.3 Illustration of Typical Data Fitting Results for an Ionic Conductor 233

4.2.4 Utility and Importance of Poisson–Nernst–Planck (PNP) Fitting Models 239

4.2.4.1 Introduction 239

4.2.4.2 Selective History of PNP Work 240

4.2.4.3 Exact PNP Responses at All Four Immittance Levels 243

4.3 Solid-State Devices 247
William B. Johnson, Wayne L. Worrell, Gunnar A. Niklasson, Sara Malmgren, Maria Strømme, and S. K. Sundaram 247

4.3.1 Electrolyte–Insulator–Semiconductor (EIS) Sensors 248

4.3.2 Solid Electrolyte Chemical Sensors 254

4.3.3 Photoelectrochemical Solar Cells 258

4.3.4 Impedance Response of Electrochromic Materials and Devices 263

4.3.4.1 Introduction 263

4.3.4.2 Materials 265

4.3.4.3 Theoretical Background 266

4.3.4.4 Experimental Results on Single Materials 270

4.3.4.5 Experimental Results on Electrochromic Devices 280

4.3.4.6 Conclusions and Outlook 280

4.3.5 Fast Processes in Gigahertz–Terahertz Region in Disordered Materials 281

4.3.5.1 Introduction 281

4.3.5.2 Lunkenheimer–Loidl Plot and Scaling of the Processes 282

4.3.5.3 Dynamic Processes 285

4.3.5.4 Final Remarks 292

4.4 Corrosion of Materials 292
Michael C. H. McKubre, Digby D. Macdonald, and George R. Engelhardt 292

4.4.1 Introduction 292

4.4.2 Fundamentals 293

4.4.3 Measurement of Corrosion Rate 293

4.4.4 Harmonic Analysis 297

4.4.5 Kramers–Kronig Transforms 303

4.4.6 Corrosion Mechanisms 306

4.4.6.1 Active Dissolution 306

4.4.6.2 Active–Passive Transition 308

4.4.6.3 The Passive State 312

4.4.7 Reaction Mechanism Analysis of Passive Metals 324

4.4.7.1 The Point Defect Model 324

4.4.7.2 Prediction of Defect Distributions 334

4.4.7.3 Optimization of the PDM on the Impedance Data 335

4.4.7.4 Sensitivity Analysis 339

4.4.7.5 Extraction of PDM Parameters from EIS Data 343

4.4.7.6 Simplified Method for Expressing the Impedance of a Stationary Barrier Layer 349

4.4.7.7 Comparison of Simplified Model with Experiment 355

4.4.7.8 Summary and Conclusions 359

4.4.8 Equivalent Circuit Analysis 360

4.4.8.1 Coatings 365

4.4.9 Other Impedance Techniques 366

4.4.9.1 Electrochemical Hydrodynamic Impedance (EHI) 366

4.4.9.2 Fracture Transfer Function (FTF) 368

4.4.9.3 Electrochemical Mechanical Impedance 370

4.5 Electrochemical Power Sources 373
Evgenij Barsoukov, Brian E. Conway, Wendy G. Pell, and Norbert Wagner 373

4.5.1 Special Aspects of Impedance Modeling of Power Sources 373

4.5.1.1 Intrinsic Relation between Impedance Properties and Power Source Performance 373

4.5.1.2 Linear Time-Domain Modeling Based on Impedance Models: Laplace Transform 374

4.5.1.3 Expressing Electrochemical Model Parameters in Electrical Terms, Limiting Resistances, and Capacitances of Distributed Elements 376

4.5.1.4 Discretization of Distributed Elements, Augmenting Equivalent Circuits 379

4.5.1.5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models 381

4.5.1.6 Special Kinds of Impedance Measurement Possible with Power Sources: Passive Load Excitation and Load Interrupt 384

4.5.2 Batteries 386

4.5.2.1 Generic Approach to Battery Impedance Modeling 386

4.5.2.2 Lead–Acid Batteries 396

4.5.2.3 Nickel–Cadmium Batteries 398

4.5.2.4 Nickel–Metal Hydride Batteries 399

4.5.2.5 Li-ion Batteries 400

4.5.3 Nonideal Behavior Developed in Porous Electrode Supercapacitors 406

4.5.3.1 Introduction 406

4.5.3.2 Equivalent Circuits and Representation of Electrochemical Capacitor Behavior 409

4.5.3.3 Impedance and Voltammetry Behavior of Brush Electrode Models of Porous Electrodes 417

4.5.3.4 Deviations from Ideality 421

4.5.4 Fuel Cells 424

4.5.4.1 Introduction 424

4.5.4.2 Alkaline Fuel Cells (AFCs) 437

4.5.4.3 Polymer Electrolyte Fuel Cells (PEFCs) 443

4.5.4.4 The Solid Oxide Fuel Cells (SOFCs) 454

4.6 Dielectric Relaxation Spectroscopy   459
C. M. Roland 459

4.6.1 Introduction 459

4.6.2 Dielectric Relaxation 460

4.6.2.1 Ion Conductivity 462

4.6.2.2 Dielectric Modulus 467

4.6.2.3 Use of Impedance Function in Dielectric Relaxation Experiments 467

4.6.2.4 Summary 472

4.7 Electrical Structure of Biological Cells and Tissues: Impedance Spectroscopy, Stereology, and Singular Perturbation Theory 472
Robert S. Eisenberg 472

4.7.1 Impedance Spectroscopy of Biological Structures Is a Platform Resting on Four Pillars 474

4.7.1.1 Anatomical Measurements 474

4.7.1.2 Impedance Measurements 475

4.7.1.3 Measurement Difficulties 476

4.7.1.4 Future Measurements 476

4.7.1.5 Interpreting Impedance Spectroscopy 477

4.7.1.6 Fitting Data 477

4.7.1.7 Results 477

4.7.1.8 Future Perspectives 478

Acronym and Model Definitions 479

References 481

Index 517

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