An Introduction to electrochemical impedance spectroscopy

✍ Scribed by Ramanathan Srinivasan, Fathima Fasmin

• Publisher: CRC Press
• Year: 2021
• Tongue: English
• Leaves: 263
• Category: Library

✦ Synopsis

This book covers fundamental aspects and application of electrochemical impedance spectroscopy (EIS), with emphasis on step-by-step procedure for mechanistic analysis of data. It enables the reader to learn the EIS technique, correctly acquire data from a system of interest, and effectively interpret the same. Detailed illustrations of how to validate the impedance spectra, use equivalent circuit analysis, and identify the reaction mechanism from the impedance spectra are given, supported by derivations and examples. MATLAB® programs for generating EIS data under various conditions are provided along with free online video lectures to enable easier learning. Features: Covers experimental details and nuances, data validation method, and two types of analysis - using circuit analogy and mechanistic analysis Details observations such as inductive loops and negative resistances Includes dedicated chapter on an emerging technique (Nonlinear EIS), including code in supplementary material illustrating simulations Discusses diffusion, constant phase element, porous electrodes and films Contains exercise problems, MATLAB codes, PPT slide and illustrative examples This book is aimed at Senior Undergraduates and advanced graduates in chemical engineering, analytical chemistry, electrochemistry, spectroscopy.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Authors
Chapter 1 Introduction
1.1 Electrode–Electrolyte Interface
1.2 Electrochemical Reaction
1.2.1 Electrode–Electrolyte Interface – The Double-Layer
1.2.2 Electrical Circuit Model of the Interface
1.2.3 Effect of Potential on the Rate Constant
1.2.4 DC Current vs. Potential in an Electrochemical Reaction
1.3 Three-Electrode Cell
1.4 Use of Reference Electrodes
1.5 What Is EIS?
1.5.1 Phase and Magnitude
1.5.2 DC vs. AC Potential
1.5.3 Differential Impedance
1.6 Series and Parallel Connections
1.6.1 Example Circuit – 1
1.6.2 Example Circuit – 2
1.7 Data Visualization
1.8 Circuit Parameter Value Extraction from Data
1.9 Reaction Mechanism Analysis
1.10 Other Electrochemical Techniques
1.10.1 Open-Circuit Potential vs. Time
1.10.2 Potentiodynamic Polarization
1.10.3 Voltammetry
1.10.4 Potential Step
1.10.5 Electrochemical Quartz Crystal Microbalance (EQCM)
1.10.6 Scanning Electrochemical Microscopy (SECM)
1.11 Exercise – Electrochemistry Basics and Circuit-Based Impedance
Chapter 2 Experimental Aspects
2.1 Instrumentation
2.2 Potentiostatic vs. Galvanostatic Modes
2.3 Supporting Electrolyte
2.4 Location of the Reference Electrode
2.5 Shielded Cables and Faraday Cage
2.6 Single Sine vs. Multi-Sine
2.6.1 Single Sine Input
2.6.2 Multi-Sine
2.7 Repeatability, Linearity, and Stability
2.7.1 Repeatability
2.7.2 Linearity
2.7.3 Stability
2.7.4 Data Validation
2.8 Lab Experiments
2.8.1 Experimental Variables and Data Acquisition Software
2.8.1.1 Single-Channel vs. Multi-Channel Potentiostats
2.8.1.2 Equipment to Cell Connections
2.8.1.3 Type of EIS Experiment
2.8.1.4 DC Bias
2.8.1.5 Frequencies
2.8.1.6 Amplitude
2.8.1.7 Current/Potential Range
2.8.1.8 Current/Potential Overload
2.8.1.9 Other Options
2.8.2 Circuit Impedance Measurements
2.8.3 Simple Electron Transfer Reaction
2.8.4 Metal Deposition in Acidic Media
2.8.5 Metal Dissolution in Acidic Media
2.8.6 Passivation
2.9 General Issues with EIS Data Acquisition
2.9.1 Reproducibility
2.9.2 Signal-to-Noise Ratio, Linearity Requirements, and Experiment Duration
2.10 Exercise – Experimental Aspects
Chapter 3 Data Validation
3.1 Kramers–Kronig Transforms
3.1.1 KKT Validation – Example of a Good Quality Spectrum
3.1.2 KKT Validation – Example of an Incomplete Spectrum
3.1.3 KKT Validation – Examples of Spectra of Unstable Systems
3.1.4 KKT Validation – Example of Spectra with Nonlinear Effects
3.2 Transformation of Data in Impedance vs. Admittance Form
3.2.1 KKT Validation – Example of a Spectrum Showing Negative Resistance
3.3 Challenges in KKT Validation
3.4 Application of KKT
3.4.1 Data Validation
3.4.2 Extrapolation
3.5 Alternatives to Direct Integration of KKT – Measurement Models
3.5.1 Introduction to the Measurement Model Approach
3.5.2 Advantages of the Measurement Model Approach
3.5.3 Linear KKT
3.5.4 Summary
3.6 Experimental Validation Methods
3.7 Software
3.8 Exercise – Impedance Data Validation Using KKT
Chapter 4 Data Analysis – Equivalent Electrical Circuits
4.1 Equivalent Electrical Circuits: What Circuit to Choose?
4.1.1 What Circuit to Choose?
4.1.2 How Many Elements Should One Use in the Electrical Circuit?
4.2 Distinguishability
4.2.1 Equivalent Circuits
4.3 Zeros and Poles Representation
4.4 Model Fitting
4.4.1 Software Choices
4.4.2 Parameter Values – Initial Guess
4.4.3 Circuit Choices
4.4.4 High and Low-Frequency Limits of Impedance
4.5 Limitations
4.5.1 Inductance and Negative (Differential) Resistance
4.5.2 Challenges in EEC Analysis
4.6 Exercise – Equivalent Circuits
Chapter 5 Mechanistic Analysis
5.1 Reaction Mechanism Analysis – Linearization of Equations
5.1.1 Simple Electron Transfer Reaction
5.1.1.1 Linearization
5.1.2 Reaction with an Adsorbed Intermediate
5.1.2.1 Linearization of Charge Balance Equations
5.1.2.2 Linearization of the Mass Balance Equation
5.1.2.3 Types of Complex Plane Plots We Can Expect for This Mechanism
5.1.3 Reaction with an Adsorbed Intermediate – Two Electrochemical Steps
5.1.4 Electron Transfer – Electroadsorption Reaction (E-EAR) – Negative Impedance
5.1.5 More Reactions with One Adsorbed Intermediate
5.1.6 Reaction with Two Adsorbed Intermediates
5.1.6.1 Linearization of Mass Balance Equations
5.1.6.2 Linearization of Charge Balance Equations
5.1.7 More Reactions with Two Adsorbed Intermediate
5.1.8 Catalytic Mechanism – One Adsorbed Intermediate – Negative Impedance
5.1.8.1 Physical Picture
5.1.8.2 An Issue with the Steady-State Solution
5.1.8.3 A Variation That Admits Steady Dissolution
5.1.9 Two-Step Reaction, With the Frumkin Adsorption Isotherm Model
5.1.10 Identification of a Reaction Mechanism – EIS Data as Complex Plane Plots
5.1.10.1 Challenges in Identifying a Reaction Mechanism
5.2 Parameter Estimation
5.2.1 Error Calculation
5.2.1.1 Data Form
5.2.1.2 Constraint
5.2.1.3 Software
5.2.1.4 Direct Optimization
5.2.1.5 Utilizing EEC Results
5.2.1.6 Grid Search
5.3 Relevance of RMA
5.3.1 The Number of Parameters. EEC vs. RMA
5.3.2 Physical Interpretation
5.4 Minimum Number of Potentials (E[sub(dc)]) Where Spectra Must Be Acquired
5.4.1 Example – Multiple Solutions
5.4.2 Example – Calculation of Min Number of (E[sub(dc)]) Where EIS Data Must Be Acquired
5.4.3 Why Is not the Kinetic Parameter Set Unique?
5.4.4 Frequency Intervals, Frequency Range, and dc Potential
5.5 Limitations of the RMA Methodology
5.5.1 Software Availability
5.5.2 Unambiguous Mechanism Identification
5.6 Summary
5.7 Exercise – Mechanistic Analysis
Chapter 6 EIS – Other Physical Phenomena
6.1 Constant Phase Elements (CPE)
6.1.1 Experimental Results
6.1.2 Models to Explain the Origin of CPE
6.1.3 Equations to Relate CPE to the Effective Capacitance
6.2 Diffusion Effects
6.2.1 Finite Boundary Conditions
6.2.1.1 Unsteady-State Conditions
6.2.1.2 Zero dc Bias
6.2.2 Semi-infinite Boundary Conditions
6.2.3 Blocking Boundary Conditions
6.2.4 Reactions with Adsorbed Intermediates, Coupled with Diffusion
6.3 Porous Electrodes
6.4 Film Formation and Passivation
6.4.1 Models Employed
6.4.2 Point Defect Model
6.4.2.1 Pitting Corrosion
6.4.3 Surface Charge Approach
6.4.4 Anion Incorporation Model
6.5 Exercise – Impedance of CPE, Diffusion, and Film
Chapter 7 Applications – A Few Examples
7.1 Corrosion
7.1.1 Corrosion of Valve Metals in Acidic Fluoride Media
7.1.2 Mechanistic Analysis of a Metal Dissolution Reaction
7.2 Biosensors
7.2.1 Detection of Chikungunya Protein Using EIS
7.2.2 DNA Sensing
7.3 Batteries
7.3.1 Battery Status Evaluation
7.3.2 Application of EIS in Battery Research
7.4 Exercise: Applications – A Few Examples
Chapter 8 Nonlinear EIS
8.1 Introduction
8.1.1 What Exactly Is NLEIS?
8.2 Mathematical Background
8.2.1 Taylor Series and Fourier Series
8.2.2 NLEIS Analysis Methods
8.3 Estimation of Nonlinear Charge-Transfer and Polarization Resistances
8.4 Calculation of the NLEIS Response of Electrochemical Reactions
8.4.1 Simple Electron Transfer Reaction
8.4.2 Reaction with an Adsorbed Intermediate
8.5 Simulation NLEIS under Galvanostatic Conditions
8.6 Simulation of Instability in Electrochemical Systems
8.7 Incorporation of Solution Resistance Effects in NLEIS Simulations
8.8 Frumkin Isotherm – Simulation of the Impedance Response
8.9 Exercise – Nonlinear EIS
Appendix 1: Complex Numbers Refresher
Appendix 2: Differential Equations Refresher
Appendix 3: Multi-sine Waves
Appendix 4: Experiments and Analysis – Few Hints
Appendix 5: Manufacturers and Suppliers of EIS Equipment
References
Index