Electrochemical Impedance Spectroscopy

Provides fundamentals needed to apply impedance spectroscopy to a broad range of applications with emphasis on obtaining physically meaningful insights from measurements.  Emphasizes fundamentals applicable to a broad range of applications including corrosion, biomedical devices, semiconductors, batteries, fuel cells, coatings, analytical chemistry, electrocatalysis, materials, and sensors  Provides illustrative examples throughout the text that show how the principles are applied to common impedance problems New Edition has improved pedagogy, with more than twice the number of examples New Edition has more in-depth treatment of background material needed to understand impedance spectroscopy, including electrochemistry, complex variables, and differential equations  New Edition includes expanded treatment of the influence of mass transport and kinetics and reflects recent advances in understanding frequency dispersion and constant-phase elements

Table of Contents:
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 Geometry–Induced 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 Constant–Phase Elements 383 14.1 Mathematical Formulation for a CPE 383 14.2 When is a Time–Constant 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 Multi-Input/Multi-Output Systems 409 15.2 Transfer Functions Involving Exclusively Electrical Quantities 417 15.3 Transfer Functions Involving Nonelectrical Quantities 422 Problems 429 16 Electrohydrodynamic Impedance 431 16.1 Hydrodynamic Transfer Function 433 16.2 Mass-Transport Transfer Function 436 16.3 Kinetic Transfer Function for Simple Electrochemical Reactions 441 16.4 Interface with a 2-D or 3-D Insulating Phase 442 Problems 454 IV Interpretation Strategies 455 17 Methods for Representing Impedance 457 17.1 Impedance Format 459 17.2 Admittance Format 468 17.3 Complex-Capacitance Format 474 17.4 Effective Capacitance 478 Problems 482 18 Graphical Methods 483 18.1 Based on Nyquist Plots 484 18.2 Based on Bode Plots 491 18.3 Based on Imaginary Part of the Impedance 495 18.4 Based on Dimensionless Frequency 496 18.5 System–Specific Applications 502 18.6 Overview 512 Problems 515 19 Complex Nonlinear Regression 517 19.1 Concept 517 19.2 Objective Functions 519 19.3 Formalism of Regression Strategies 521 19.4 Regression Strategies for Nonlinear Problems 524 19.5 Influence of Data Quality on Regression 527 19.6 Initial Estimates for Regression 533 19.7 Regression Statistics 533 Problems 536 20 Assessing Regression Quality 539 20.1 Methods to Assess Regression Quality 539 20.2 Application of Regression Concepts 540 Problems 555 V Statistical Analysis 557 21 Error Structure of Impedance Measurements 559 21.1 Error Contributions 559 21.2 Stochastic Errors in Impedance Measurements 560 21.3 Bias Errors 566 21.4 Incorporation of Error Structure 570 21.5 Measurement Models for Error Identification 572 Problems 583 22 The Kramers-Kronig Relations 585 22.1 Methods for Application 585 22.2 Mathematical Origin 590 22.3 The Kramers-Kronig in an Expectation Sense 601 Problems 605 VI Overview 607 23 An Integrated Approach to Impedance Spectroscopy 609 23.1 Flowcharts for Regression Analysis 609 23.2 Integration of Measurements, Error Analysis, and Model 610 23.3 Application 613 Problems 619 VII Reference Material 621 A Complex Integrals 623 A.1 Definition of Terms 623 A.2 Cauchy-Riemann Conditions 625 A.3 Complex Integration 627 Problems 633 B Tables of Reference Material 635 C List of Examples 637 List of Symbols 643 References 655 Index 684