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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Electrochemical Society Series
- Sprache: Englisch
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
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THE ELECTROCHEMICAL SOCIETY SERIES
ECS-The Electrochemical Society65 South Main StreetPennington, NJ 08534-2839http://www.electrochem.org
A complete list of the titles in this series appears at the end of this volume.
Electrochemical Impedance Spectroscopy
Second Edition
Mark E. Orazem
University of Florida
Bernard Tribollet
Université Pierre et Marie Curie
Copyright © 2017 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Names: Orazem, Mark E. | Tribollet, Bernard.
Title: Electrochemical impedance spectroscopy / Mark E. Orazem, University of Florida, Bernard Tribollet, Université Pierre et Marie Curie.
Description: 2nd edition. | Hoboken, New Jersey: John Wiley & Sons, Inc., [2017] | Includes bibliographical references and index.
Identifiers: LCCN 2016039537 (print) | LCCN 2016040277 (ebook) | ISBN 9781118527399 (cloth) | ISBN 9781119341222 (pdf) | ISBN 9781119340928 (epub)
Subjects: LCSH: Impedance spectroscopy.
Classification: LCC QD116.I57 O73 2017 (print) | LCC QD116.I57 (ebook) | DDC 543/.6--dc23
LC record available at https://lccn.loc.gov/2016039537
Dedicated to our families: Jennifer and Athena, Françoise, Julie, and Benjamin
Contents
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
The Blind Men and the Elephant
A Brief Introduction to Impedance Spectroscopy
History of Impedance Spectroscopy
I Background
1 Complex Variables
1.1 Why Imaginary Numbers?
1.2 Terminology
1.2.1 The Imaginary Number
1.2.2 Complex Variables
1.2.3 Conventions for Notation in Impedance Spectroscopy
1.3 Operations Involving Complex Variables
1.3.1 Multiplication and Division of Complex Numbers
1.3.2 Complex Variables in Polar Coordinates
1.3.3 Properties of Complex Variables
1.4 Elementary Functions of Complex Variables
1.4.1 Exponential
1.4.2 Logarithmic
1.4.3 Polynomial
Problems
2 Differential Equations
2.1 Linear First-Order Differential Equations
2.2 Homogeneous Linear Second-Order Differential Equations
2.3 Nonhomogeneous Linear Second-Order Differential Equations
2.4 Chain Rule for Coordinate Transformations
2.5 Partial Differential Equations by Similarity Transformations
2.6 Differential Equations with Complex Variables
Problems
3 Statistics
3.1 Definitions
3.1.1 Expectation and Mean
3.1.2 Variance, Standard Deviation, and Covariance
3.1.3 Normal Distribution
3.1.4 Probability
3.1.5 Central Limit Theorem
3.2 Error Propagation
3.2.1 Linear Systems
3.2.2 Nonlinear Systems
3.3 Hypothesis Tests
3.3.1 Terminology
3.3.2 Student’s
t
-Test for Equality of Mean
3.3.3
F
-Test for Equality of Variance
3.3.4 Chi-Squared Test for Goodness of Fit
Problems
4 Electrical Circuits
4.1 Passive Electrical Circuits
4.1.1 Circuit Elements
Response to a Sinusoidal Signal
Impedance Response of Passive Circuit Elements
4.1.2 Parallel and Series Combinations
4.2 Fundamental Relationships
4.3 Nested Circuits
4.4 Mathematical Equivalence of Circuits
4.5 Graphical Representation of Circuit Response
Problems
5 Electrochemistry
5.1 Resistors and Electrochemical Cells
5.2 Polarization Behavior for Electrochemical Systems
5.2.1 Zero Current
Equilibrium
Nonequilibrium
5.2.2 Kinetic Control
5.2.3 Mixed-Potential Theory
5.2.4 Mass-Transfer Control
5.3 Definitions of Potential
5.4 Rate Expressions
5.5 Transport Processes
5.5.1 Primary Current and Potential Distributions
5.5.2 Secondary Current and Potential Distributions
5.5.3 Tertiary Current and Potential Distributions
5.5.4 Mass-Transfer-Controlled Current Distributions
5.6 Potential Contributions
5.6.1 Ohmic Potential Drop
5.6.2 Surface Overpotential
5.6.3 Concentration Overpotential
5.7 Capacitance Contributions
5.7.1 Double-Layer Capacitance
5.7.2 Dielectric Capacitance
5.8 Further Reading
Problems
6 Electrochemical Instrumentation
6.1 The Ideal Operational Amplifier
6.2 Elements of Electrochemical Instrumentation
6.3 Electrochemical Interface
6.3.1 Potentiostat
6.3.2 Galvanostat
6.3.3 Potentiostat for EIS Measurement
Problems
II Experimental Considerations
7 Experimental Methods
7.1 Steady-State Polarization Curves
7.2 Transient Response to a Potential Step
7.3 Analysis in Frequency Domain
7.3.1 Lissajous Analysis
7.3.2 Phase-Sensitive Detection (Lock-in Amplifier)
7.3.3 Single-Frequency Fourier Analysis
7.3.4 Multiple-Frequency Fourier Analysis
7.4 Comparison of Measurement Techniques
7.4.1 Lissajous Analysis
7.4.2 Phase-Sensitive Detection (Lock-in Amplifier)
7.4.3 Single-Frequency Fourier Analysis
7.4.4 Multiple-Frequency Fourier Analysis
7.5 Specialized Techniques
7.5.1 Transfer-Function Analysis
7.5.2 Local Electrochemical Impedance Spectroscopy
Global Impedance
Local Impedance
Local Interfacial Impedance
Local Ohmic Impedance
Global Interfacial Impedance
Global Ohmic Impedance
Problems
8 Experimental Design
8.1 Cell Design
8.1.1 Reference Electrodes
8.1.2 Flow Configurations
Rotating Disk
Disk under Submerged Impinging Jet
Rotating Cylinders
Rotating Hemispherical Electrode
8.1.3 Current Distribution
8.2 Experimental Considerations
8.2.1 Frequency Range
8.2.2 Linearity
8.2.3 Modulation Technique
8.2.4 Oscilloscope
8.3 Instrumentation Parameters
8.3.1 Improve Signal-to-Noise Ratio
8.3.2 Reduce Bias Errors
Nonstationary Effects
Instrument Bias
8.3.3 Improve Information Content
Problems
III Process Models
9 Equivalent Circuit Analogs
9.1 General Approach
9.2 Current Addition
9.2.1 Impedance at the Corrosion Potential
9.2.2 Partially Blocked Electrode
9.3 Potential Addition
9.3.1 Electrode Coated with an Inert Porous Layer
9.3.2 Electrode Coated with Two Inert Porous Layers
Problems
10 Kinetic Models
10.1 General Mathematical Framework
10.2 Electrochemical Reactions
10.2.1 Potential Dependent
10.2.2 Potential and Concentration Dependent
Charge-Transfer Resistance
Diffusion Impedance
Cell Impedance
10.3 Multiple Independent Electrochemical Reactions
10.4 Coupled Electrochemical Reactions
10.4.1 Potential and Surface Coverage Dependent
10.4.2 Potential, Surface Coverage, and Concentration Dependent
10.5 Electrochemical and Heterogeneous Chemical Reactions
Problems
11 Diffusion Impedance
11.1 Uniformly Accessible Electrode
11.2 Porous Film
11.2.1 Diffusion with Exchange of Electroactive Species
11.2.2 Diffusion without Exchange of Electroactive Species
11.3 Rotating Disk
11.3.1 Fluid Flow
11.3.2 Steady-State Mass Transfer
11.3.3 Convective Diffusion Impedance
11.3.4 Analytic and Numerical Solutions
Nernst Hypothesis
Assumption of an Infinite Schmidt Number
Treatment of a Finite Schmidt Number
11.4 Submerged Impinging Jet
11.4.1 Fluid Flow
11.4.2 Steady-State Mass Transfer
11.4.3 Convective Diffusion Impedance
11.5 Rotating Cylinders
11.6 Electrode Coated by a Porous Film
11.6.1 Steady-State Solutions
11.6.2 Coupled Diffusion Impedance
11.7 Impedance with Homogeneous Chemical Reactions
11.8 Dynamic Surface Films
11.8.1 Mass Transfer in the Salt Layer
11.8.2 Mass Transfer in the Electrolyte
11.8.3 Oscillating Film Thickness
11.8.4 Faradaic Impedance
Problems
12 Impedance of Materials
12.1 Electrical Properties of Materials
12.2 Dielectric Response in Homogeneous Media
12.3 Cole–Cole Relaxation
12.4 Geometric Capacitance
12.5 Dielectric Response of Insulating Nonhomogeneous Media
12.6 Mott-Schottky Analysis
Problems
13 Time-Constant Dispersion
13.1 Transmission Line Models
13.1.1 Telegrapher’s Equations
13.1.2 Porous Electrodes
13.1.3 Pore-in-Pore Model
13.1.4 Thin-Layer Cell
13.2 Geometry-Induced Current and Potential Distributions
13.2.1 Mathematical Development
Blocking Electrode
Blocking Electrode with CPE Behavior
Electrode with Faradaic Reactions
Electrode with Faradaic Reactions Coupled by Adsorbed Intermediates
13.2.2 Numerical Method
13.2.3 Complex Ohmic Impedance at High Frequencies
13.2.4 Complex Ohmic Impedance at High and Low Frequencies
13.3 Electrode Surface Property Distributions
13.3.1 Electrode Roughness
Influence of Roughness on a Disk Electrode
Influence of Surface Roughness on a Recessed Electrode
13.3.2 Capacitance
Capacitance Distribution on Recessed Electrodes
Capacitance Distribution on Disk Electrodes
13.3.3 Reactivity
13.4 Characteristic Dimension for Frequency Dispersion
13.5 Convective Diffusion Impedance at Small Electrodes
13.5.1 Analysis
13.5.2 Local Convective Diffusion Impedance
Low-Frequency Solution
High-Frequency Solution
13.5.3 Global Convective Diffusion Impedance
13.6 Coupled Charging and Faradaic Currents
13.6.1 Theoretical Development
Mass Transport in Dilute Solutions
Coupled Faradaic and Charging Currents
Double-Layer Model
Decoupled Faradaic and Charging Currents
13.6.2 Numerical Method
Steady-State Calculations
Double-Layer Properties
Impedance Calculations
13.6.3 Consequence of Coupled Charging and Faradaic Currents
13.7 Exponential Resistivity Distributions
Problems
14 Constant-Phase Elements
14.1 Mathematical Formulation for a CPE
14.2 When Is a Time-Constant Distribution a CPE?
14.3 Origin of Distributions Resulting in a CPE
14.4 Approaches for Extracting Physical Properties
14.4.1 Simple Substitution
14.4.2 Characteristic Frequency: Normal Distribution
14.4.3 Characteristic Frequency: Surface Distribution
14.4.4 Power-Law Distribution
Bounds for Resistivity
Comparative Analysis
14.5 Limitations to the Use of the CPE
Problems
15 Generalized Transfer Functions
15.1 Multi-input/Multi-output Systems
15.1.1 Current or Potential Are the Output Quantity
15.1.2 Current or Potential Are the Input Quantity
15.1.3 Experimental Quantities
15.2 Transfer Functions Involving Exclusively Electrical Quantities
15.2.1 Ring–Disk Impedance Measurements
15.2.2 Multifrequency Measurements for Double-Layer Studies
15.3 Transfer Functions Involving Nonelectrical Quantities
15.3.1 Thermoelectrochemical (TEC) Transfer Function
15.3.2 Photoelectrochemical Impedance Measurements
15.3.3 Electrogravimetry Impedance Measurements
Problems
16 Electrohydrodynamic Impedance
16.1 Hydrodynamic Transfer Function
16.2 Mass-Transport Transfer Function
16.2.1 Asymptotic Solution for Large Schmidt Numbers
16.2.2 Asymptotic Solution for High Frequencies
16.3 Kinetic Transfer Function for Simple Electrochemical Reactions
16.4 Interface with a 2-D or 3-D Insulating Phase
16.4.1 Partially Blocked Electrode
16.4.2 Rotating Disk Electrode Coated by a Porous Film
Steady-State Solutions
AC and EHD Impedances
Problems
IV Interpretation Strategies
17 Methods for Representing Impedance
17.1 Impedance Format
17.1.1 Complex-Impedance-Plane Representation
17.1.2 Bode Representation
17.1.3 Ohmic-Resistance-Corrected Bode Representation
17.1.4 Impedance Representation
17.2 Admittance Format
17.2.1 Admittance-Plane Representation
17.2.2 Admittance Representation
17.2.3 Ohmic-Resistance-Corrected Representation
17.3 Complex-Capacitance Format
17.4 Effective Capacitance
Problems
18 Graphical Methods
18.1 Based on Nyquist Plots
18.1.1 Characteristic Frequency
18.1.2 Superposition
Mass Transfer
Evolution of Active Area
18.2 Based on Bode Plots
18.2.1 Ohmic-Resistance-Corrected Phase
18.2.2 Ohmic-Resistance-Corrected Magnitude
18.3 Based on Imaginary Part of the Impedance
18.3.1 Evaluation of Slopes
18.3.2 Calculation of Derivatives
18.4 Based on Dimensionless Frequency
18.4.1 Mass Transport
18.4.2 Geometric Contribution
18.5 System-Specific Applications
18.5.1 Effective CPE Coefficient
18.5.2 Asymptotic Behavior for Low-Frequency Mass Transport
18.5.3 Arrhenius Superposition
18.5.4 Mott–Schottky Plots
18.5.5 High-Frequency Cole–Cole Plots
18.6 Overview
Problems
19 Complex Nonlinear Regression
19.1 Concept
19.2 Objective Functions
19.3 Formalism of Regression Strategies
19.3.1 Linear Regression
19.3.2 Nonlinear Regression
19.4 Regression Strategies for Nonlinear Problems
19.4.1 Gauss–Newton Method
19.4.2 Method of Steepest Descent
19.4.3 Levenberg–Marquardt Method
19.4.4 Downhill Simplex Strategies
19.5 Influence of Data Quality on Regression
19.5.1 Presence of Stochastic Errors in Data
19.5.2 Ill-Conditioned Regression Caused by Stochastic Noise
19.5.3 Ill-Conditioned Regression Caused by Insufficient Range
19.6 Initial Estimates for Regression
19.7 Regression Statistics
19.7.1 Confidence Intervals for Parameter Estimates
19.7.2 Statistical Measure of the Regression Quality
Problems
20 Assessing Regression Quality
20.1 Methods to Assess Regression Quality
20.1.1 Quantitative Methods
20.1.2 Qualitative Methods
20.2 Application of Regression Concepts
20.2.1 Finite-Diffusion-Length Model
Quantitative Assessment
Visual Inspection
20.2.2 Measurement Model
Quantitative Assessment
Visual Inspection
20.2.3 Convective-Diffusion-Length Model
Quantitative Assessment
Visual Inspection
Problems
V Statistical Analysis
21 Error Structure of Impedance Measurements
21.1 Error Contributions
21.2 Stochastic Errors in Impedance Measurements
21.2.1 Stochastic Errors in Time-Domain Signals
21.2.2 Transformation from Time Domain to Frequency Domain
21.2.3 Stochastic Errors in Frequency Domain
21.3 Bias Errors
21.3.1 Instrument Artifacts
21.3.2 Ancillary Parts of the System under Study
21.3.3 Nonstationary Behavior
21.3.4 Time Scales in Impedance Spectroscopy Measurements
21.4 Incorporation of Error Structure
21.5 Measurement Models for Error Identification
21.5.1 Stochastic Errors
21.5.2 Bias Errors
Problems
22 The Kramers–Kronig Relations
22.1 Methods for Application
22.1.1 Direct Integration of the Kramers–Kronig Relations
22.1.2 Experimental Assessment of Consistency
22.1.3 Regression of Process Models
22.1.4 Regression of Measurement Models
22.2 Mathematical Origin
22.2.1 Background
22.2.2 Application of Cauchy’s Theorem
22.2.3 Transformation from Real to Imaginary
22.2.4 Transformation from Imaginary to Real
22.2.5 Application of the Kramers–Kronig Relations
22.3 The Kramers–Kronig Relations in an Expectation Sense
22.3.1 Transformation from Real to Imaginary
22.3.2 Transformation from Imaginary to Real
Problems
VI Overview
23 An Integrated Approach to Impedance Spectroscopy
23.1 Flowcharts for Regression Analysis
23.2 Integration of Measurements, Error Analysis, and Model
23.2.1 Impedance Measurements Integrated with Error Analysis
23.2.2 Process Models Developed Using Other Observations
23.2.3 Regression Analysis in Context of Error Structure
23.3 Application
Problems
VII Reference Material
A Complex Integrals
A.1 Definition of Terms
A.2 Cauchy–Riemann Conditions
A.3 Complex Integration
A.3.1 Cauchy’s Theorem
A.3.2 Improper Integrals of Rational Functions
Problems
B Tables of Reference Material
C List of Examples
List of Symbols
References
Author Index
Subject Index
List of Tables
History of Impedance Spectroscopy
Table 1
Chapter 1
Table 1.1
Table 1.2
Table 1.3
Table 1.4
Table 1.5
Table 1.6
Table 1.7
Chapter 3
Table 3.8
Table 3.9
Table 3.13
Chapter 5
Table 5.1
Table 5.2
Table 5.3
Table 5.4
Table 5.5
Table 5.6
Chapter 7
Table 7.1
Table 7.2
Chapter 8
Table 8.1
Chapter 9
Table 9.1
Chapter 10
Table 10.1
Chapter 11
Table 11.1
Table 11.2
Chapter 12
Table 12.1
Table 12.2
Chapter 13
Table 13.1
Table 13.2
Chapter 14
Table 14.1
Table 14.2
Table 14.3
Table 14.4
Chapter 16
Table 16.1
Table 16.2
Chapter 17
Table 17.1
Chapter 18
Table 18.1
Table 18.2
Table 18.3
Table 18.4
Table 18.5
Table 18.6
Chapter 20
Table 20.1
Table 20.2
Table 20.3
Chapter 21
Table 21.1
Chapter 22
Table 22.1
