Electrochemical Impedance Spectroscopy

Mark E. Orazem is a Distinguished Professor of Chemical Engineering at the University of Florida, adjunct professor at the Beijing University of Chemical Technology, a Fellow of the Electrochemical Society, past President of the International Society of Electrochemistry, and recipient of the 2012 ECS Linford Award for Outstanding Teaching. He organized the 6th International Symposium on Electrochemical Impedance Spectroscopy and teaches short courses on impedance spectroscopy for industry and for The Electrochemical Society. Bernard Tribollet is Director of Research Emeritus at the Laboratory for Interfaces and Electrochemical Systems (LISE) at the University of Pierre and Marie Curie and adjunct professor at the Beijing University of Chemical Technology. He instructs an annual short course at his university on impedance spectroscopy. He is a Fellow of The Electrochemical Society, Treasurer of the International Society of Electrochemistry, and organized the 2010 Annual Meeting of the International Society of Electrochemistry held in Nice, France.

Preface to the Second Edition xvii Preface to the First Edition xix Acknowledgments xxiii The Blind Men and the Elephant xxv A Brief Introduction to Impedance Spectroscopy xxix History of Impedance Spectroscopy xxxvii I Background 1 1 Complex Variables 3 1.1 Why Imaginary Numbers? 3 1.2 Terminology 4 1.3 Operations Involving Complex Variables 5 1.4 Elementary Functions of Complex Variables 16 Problems 22 2 Differential Equations 25 2.1 Linear First-Order Differential Equations 25 2.2 Homogeneous Linear Second-Order Differential Equations 29 2.3 Nonhomogeneous Linear Second-Order Differential Equations 32 2.4 Chain Rule for Coordinate Transformations 36 2.5 Partial Differential Equations by Similarity Transformations 38 2.6 Differential Equations with Complex Variables 42 Problems 43 3 Statistics 45 3.1 Definitions 45 3.2 Error Propagation 53 3.3 Hypothesis Tests 59 Problems 70 4 Electrical Circuits 73 4.1 Passive Electrical Circuits 73 4.2 Fundamental Relationships 79 4.3 Nested Circuits 80 4.4 Mathematical Equivalence of Circuits 82 4.5 Graphical Representation of Circuit Response 82 Problems 85 5 Electrochemistry 87 5.1 Resistors and Electrochemical Cells 87 5.2 Polarization Behavior for Electrochemical Systems 90 5.3 Definitions of Potential 106 5.4 Rate Expressions 107 5.5 Transport Processes 111 5.6 Potential Contributions 117 5.7 Capacitance Contributions 120 5.8 Further Reading 124 Problems 125 6 Electrochemical Instrumentation 127 6.1 The Ideal Operational Amplifier 127 6.2 Elements of Electrochemical Instrumentation 129 6.3 Electrochemical Interface 131 Problems 135 II Experimental Considerations 137 7 Experimental Methods 139 7.1 Steady-State Polarization Curves 139 7.2 Transient Response to a Potential Step 140 7.3 Analysis in Frequency Domain 141 7.4 Comparison of Measurement Techniques 154 7.5 Specialized Techniques 155 Problems 160 8 Experimental Design 163 8.1 Cell Design 163 8.2 Experimental Considerations 168 8.3 Instrumentation Parameters 181 Problems 186 III Process Models 187 9 Equivalent Circuit Analogs 189 9.1 General Approach 189 9.2 Current Addition 190 9.3 Potential Addition 196 Problems 201 10 Kinetic Models 203 10.1 General Mathematical Framework 203 10.2 Electrochemical Reactions 205 10.3 Multiple Independent Electrochemical Reactions 218 10.4 Coupled Electrochemical Reactions 221 10.5 Electrochemical and Heterogeneous Chemical Reactions 229 Problems 235 11 Diffusion Impedance 237 11.1 Uniformly Accessible Electrode 238 11.2 Porous Film 239 11.3 Rotating Disk 249 11.4 Submerged Impinging Jet 259 11.5 Rotating Cylinders 262 11.6 Electrode Coated by a Porous Film 264 11.7 Impedance with Homogeneous Chemical Reactions 271 11.8 Dynamic Surface Films 280 Problems 290 12 Impedance of Materials 291 12.1 Electrical Properties of Materials 291 12.2 Dielectric Response in Homogeneous Media 292 12.3 Cole-Cole Relaxation 295 12.4 Geometric Capacitance 295 12.5 Dielectric Response of Insulating Non-Homogenous Media 297 12.6 Mott-Schottky Analysis 298 Problems 305 13 Time-Constant Dispersion 307 13.1 Transmission Line Models 307 13.2 GeometryInduced Current and Potential Distributions 325 13.3 Electrode Surface Property Distributions 337 13.4 Characteristic Dimension for Frequency Dispersion 358 13.5 Convective Diffusion Impedance at Small Electrodes 359 13.6 Coupled Charging and Faradaic Currents 365 13.7 Exponential Resistivity Distributions 378 Problems 381 14 ConstantPhase Elements 383 14.1 Mathematical Formulation for a CPE 383 14.2 When is a TimeConstant Distribution a CPE? 384 14.3 Origin of Distributions Resulting in a CPE 388 14.4 Approaches for Extracting Physical Properties 389 14.5 Limitations to the Use of the CPE 404 Problems 406 15 Generalized Transfer Functions 409 15.1 Mult