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<p>Preface to the Second Edition xvii</p> <p>Preface to the First Edition xix</p> <p>Acknowledgments xxiii</p> <p>The Blind Men and the Elephant xxv</p> <p>A Brief Introduction to Impedance Spectroscopy xxix</p> <p>History of Impedance Spectroscopy xxxvii</p> <p><b>I Background 1</b></p> <p><b>1 Complex Variables 3</b></p> <p>1.1 Why Imaginary Numbers? 3</p> <p>1.2 Terminology 4</p> <p>1.3 Operations Involving Complex Variables 5</p> <p>1.4 Elementary Functions of Complex Variables 16</p> <p>Problems 22</p> <p><b>2 Differential Equations 25</b></p> <p>2.1 Linear First-Order Differential Equations 25</p> <p>2.2 Homogeneous Linear Second-Order Differential Equations 29</p> <p>2.3 Nonhomogeneous Linear Second-Order Differential Equations 32</p> <p>2.4 Chain Rule for Coordinate Transformations 36</p> <p>2.5 Partial Differential Equations by Similarity Transformations 38</p> <p>2.6 Differential Equations with Complex Variables 42</p> <p>Problems 43</p> <p><b>3 Statistics 45</b></p> <p>3.1 Definitions 45</p> <p>3.2 Error Propagation 53</p> <p>3.3 Hypothesis Tests 59</p> <p>Problems 70</p> <p><b>4 Electrical Circuits 73</b></p> <p>4.1 Passive Electrical Circuits 73</p> <p>4.2 Fundamental Relationships 79</p> <p>4.3 Nested Circuits 80</p> <p>4.4 Mathematical Equivalence of Circuits 82</p> <p>4.5 Graphical Representation of Circuit Response 82</p> <p>Problems 85</p> <p><b>5 Electrochemistry 87</b></p> <p>5.1 Resistors and Electrochemical Cells 87</p> <p>5.2 Polarization Behavior for Electrochemical Systems 90</p> <p>5.3 Definitions of Potential 106</p> <p>5.4 Rate Expressions 107</p> <p>5.5 Transport Processes 111</p> <p>5.6 Potential Contributions 117</p> <p>5.7 Capacitance Contributions 120</p> <p>5.8 Further Reading 124</p> <p>Problems 125</p> <p><b>6 Electrochemical Instrumentation 127</b></p> <p>6.1 The Ideal Operational Amplifier 127</p> <p>6.2 Elements of Electrochemical Instrumentation 129</p> <p>6.3 Electrochemical Interface 131</p> <p>Problems 135</p> <p><b>II Experimental Considerations 137</b></p> <p><b>7 Experimental Methods 139</b></p> <p>7.1 Steady-State Polarization Curves 139</p> <p>7.2 Transient Response to a Potential Step 140</p> <p>7.3 Analysis in Frequency Domain 141</p> <p>7.4 Comparison of Measurement Techniques 154</p> <p>7.5 Specialized Techniques 155</p> <p>Problems 160</p> <p><b>8 Experimental Design 163</b></p> <p>8.1 Cell Design 163</p> <p>8.2 Experimental Considerations 168</p> <p>8.3 Instrumentation Parameters 181</p> <p>Problems 186</p> <p><b>III Process Models 187</b></p> <p><b>9 Equivalent Circuit Analogs 189</b></p> <p>9.1 General Approach 189</p> <p>9.2 Current Addition 190</p> <p>9.3 Potential Addition 196</p> <p>Problems 201</p> <p><b>10 Kinetic Models 203</b></p> <p>10.1 General Mathematical Framework 203</p> <p>10.2 Electrochemical Reactions 205</p> <p>10.3 Multiple Independent Electrochemical Reactions 218</p> <p>10.4 Coupled Electrochemical Reactions 221</p> <p>10.5 Electrochemical and Heterogeneous Chemical Reactions 229</p> <p>Problems 235</p> <p><b>11 Diffusion Impedance 237</b></p> <p>11.1 Uniformly Accessible Electrode 238</p> <p>11.2 Porous Film 239</p> <p>11.3 Rotating Disk 249</p> <p>11.4 Submerged Impinging Jet 259</p> <p>11.5 Rotating Cylinders 262</p> <p>11.6 Electrode Coated by a Porous Film 264</p> <p>11.7 Impedance with Homogeneous Chemical Reactions 271</p> <p>11.8 Dynamic Surface Films 280</p> <p>Problems 290</p> <p><b>12 Impedance of Materials 291</b></p> <p>12.1 Electrical Properties of Materials 291</p> <p>12.2 Dielectric Response in Homogeneous Media 292</p> <p>12.3 Cole-Cole Relaxation 295</p> <p>12.4 Geometric Capacitance 295</p> <p>12.5 Dielectric Response of Insulating Non-Homogenous Media 297</p> <p>12.6 Mott-Schottky Analysis 298</p> <p>Problems 305</p> <p><b>13 Time-Constant Dispersion 307</b></p> <p>13.1 Transmission Line Models 307</p> <p>13.2 Geometry–Induced Current and Potential Distributions 325</p> <p>13.3 Electrode Surface Property Distributions 337</p> <p>13.4 Characteristic Dimension for Frequency Dispersion 358</p> <p>13.5 Convective Diffusion Impedance at Small Electrodes 359</p> <p>13.6 Coupled Charging and Faradaic Currents 365</p> <p>13.7 Exponential Resistivity Distributions 378</p> <p>Problems 381</p> <p><b>14 Constant–Phase Elements 383</b></p> <p>14.1 Mathematical Formulation for a CPE 383</p> <p>14.2 When is a Time–Constant Distribution a CPE? 384</p> <p>14.3 Origin of Distributions Resulting in a CPE 388</p> <p>14.4 Approaches for Extracting Physical Properties 389</p> <p>14.5 Limitations to the Use of the CPE 404</p> <p>Problems 406</p> <p><b>15 Generalized Transfer Functions 409</b></p> <p>15.1 Multi-Input/Multi-Output Systems 409</p> <p>15.2 Transfer Functions Involving Exclusively Electrical Quantities 417</p> <p>15.3 Transfer Functions Involving Nonelectrical Quantities 422</p> <p>Problems 429</p> <p><b>16 Electrohydrodynamic Impedance 431</b></p> <p>16.1 Hydrodynamic Transfer Function 433</p> <p>16.2 Mass-Transport Transfer Function 436</p> <p>16.3 Kinetic Transfer Function for Simple Electrochemical Reactions 441</p> <p>16.4 Interface with a 2-D or 3-D Insulating Phase 442</p> <p>Problems 454</p> <p><b>IV Interpretation Strategies 455</b></p> <p><b>17 Methods for Representing Impedance 457</b></p> <p>17.1 Impedance Format 459</p> <p>17.2 Admittance Format 468</p> <p>17.3 Complex-Capacitance Format 474</p> <p>17.4 Effective Capacitance 478</p> <p>Problems 482</p> <p><b>18 Graphical Methods 483</b></p> <p>18.1 Based on Nyquist Plots 484</p> <p>18.2 Based on Bode Plots 491</p> <p>18.3 Based on Imaginary Part of the Impedance 495</p> <p>18.4 Based on Dimensionless Frequency 496</p> <p>18.5 System–Specific Applications 502</p> <p>18.6 Overview 512</p> <p>Problems 515</p> <p><b>19 Complex Nonlinear Regression 517</b></p> <p>19.1 Concept 517</p> <p>19.2 Objective Functions 519</p> <p>19.3 Formalism of Regression Strategies 521</p> <p>19.4 Regression Strategies for Nonlinear Problems 524</p> <p>19.5 Influence of Data Quality on Regression 527</p> <p>19.6 Initial Estimates for Regression 533</p> <p>19.7 Regression Statistics 533</p> <p>Problems 536</p> <p><b>20 Assessing Regression Quality 539</b></p> <p>20.1 Methods to Assess Regression Quality 539</p> <p>20.2 Application of Regression Concepts 540</p> <p>Problems 555</p> <p><b>V Statistical Analysis 557</b></p> <p><b>21 Error Structure of Impedance Measurements 559</b></p> <p>21.1 Error Contributions 559</p> <p>21.2 Stochastic Errors in Impedance Measurements 560</p> <p>21.3 Bias Errors 566</p> <p>21.4 Incorporation of Error Structure 570</p> <p>21.5 Measurement Models for Error Identification 572</p> <p>Problems 583</p> <p><b>22 The Kramers-Kronig Relations 585</b></p> <p>22.1 Methods for Application 585</p> <p>22.2 Mathematical Origin 590</p> <p>22.3 The Kramers-Kronig in an Expectation Sense 601</p> <p>Problems 605</p> <p><b>VI Overview 607</b></p> <p><b>23 An Integrated Approach to Impedance Spectroscopy 609</b></p> <p>23.1 Flowcharts for Regression Analysis 609</p> <p>23.2 Integration of Measurements, Error Analysis, and Model 610</p> <p>23.3 Application 613</p> <p>Problems 619</p> <p><b>VII Reference Material 621</b></p> <p><b>A Complex Integrals 623</b></p> <p>A.1 Definition of Terms 623</p> <p>A.2 Cauchy-Riemann Conditions 625</p> <p>A.3 Complex Integration 627</p> <p>Problems 633</p> <p><b>B Tables of Reference Material 635</b></p> <p>C List of Examples 637</p> <p>List of Symbols 643</p> <p>References 655</p> <p>Index 684</p>

<p><b> Mark E. Orazem</b> 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. <p><b> Bernard Tribollet</b> 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.

<p><b> Using electrochemical impedance spectroscopy in a broad range of applications </b> <p><i> Electrochemical Impedance Spectroscopy, Second Edition</i> provides fundamentals needed to apply impedance spectroscopy to a broad range of applications, such as corrosion, biomedical devices, semiconductors, batteries, fuel cells, coatings, analytical chemistry, electrocatalysis, materials, and sensors. The emphasis is on obtaining physically meaningful insights from measurements. <p> This updated edition provides many new examples and homework problems. It has more in-depth treatment of background material needed to understand impedance spectroscopy, including electrochemistry, complex variables, and differential equations. It also includes expanded treatment of the influence of mass transport and kinetics, and reflects recent advances in the understanding of frequency dispersion and interpretation of constant-phase elements. <p><i> Electrochemical Impedance Spectroscopy, Second Edition</i> is ideal either for course study or for independent self-study as it features: <ul> <li>Illustrative examples throughout the text that show how the principles are applied to common impedance problems</li> <li>Background information needed to understand impedance spectroscopy</li> <li>Guidelines on the design of experiments and selection of appropriate experimental parameters</li> <li>Explanation of the manner in which electrical circuits provide a framework for model development</li> <li>Systematic method to convert proposed reaction mechanisms to impedance models</li> <li>Fundamental understanding of frequency dispersion, including transmission lines and constant-phase elements</li> <li>Explanation of error structure for impedance spectroscopy, including applications of the Kramers-Kronig relations</li> </ul> <br> <p> This is an excellent textbook for graduate students in electrochemistry, materials science, and chemical engineering. It continues to provide as a great self-study guide and reference for scientists and engineers who work with electrochemistry, corrosion, and electrochemical technology, including those in the biomedical field, and for users and vendors of impedance-measuring instrumentation.

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