Preface. Preface to the First Edition. Contributors. Contributors to the First Edition. Chapter 1. Fundamentals of Impedance Spectroscopy (J.Ross Macdonald and William B. Johnson). 1.1. Background, Basic Definitions, and History. 1.1.1 The Importance of Interfaces. 1.1.2 The Basic Impedance Spectroscopy Experiment. 1.1.3 Response to a Small-Signal Stimulus in the Frequency Domain. 1.1.4 Impedance-Related Functions. 1.1.5 Early History. 1.2. Advantages and Limitations. 1.2.1 Differences Between Solid State and Aqueous Electrochemistry. 1.3. Elementary Analysis of Impedance Spectra. 1.3.1 Physical Models for Equivalent Circuit Elements. 1.3.2 Simple RC Circuits. 1.3.3 Analysis of Single Impedance Arcs. 1.4. Selected Applications of IS. Chapter 2. Theory (Ian D. Raistrick, Donald R. Franceschetti, and J. Ross Macdonald). 2.1. The Electrical Analogs of Physical and Chemical Processes. 2.1.1 Introduction. 2.1.2 The Electrical Properties of Bulk Homogeneous Phases. 2.1.2.1 Introduction. 2.1.2.2 Dielectric Relaxation in Materials with a Single Time Constant. 2.1.2.3 Distributions of Relaxation Times. 2.1.2.4 Conductivity and Diffusion in Electrolytes. 2.1.2.5 Conductivity and Diffusion-a Statistical Description. 2.1.2.6 Migration in the Absence of Concentration Gradients. 2.1.2.7 Transport in Disordered Media. 2.1.3 Mass and Charge Transport in the Presence of Concentration Gradients. 2.1.3.1 Diffusion. 2.1.3.2 Mixed Electronic-Ionic Conductors. 2.1.3.3 Concentration Polarization. 2.1.4 Interfaces and Boundary Conditions. 2.1.4.1 Reversible and Irreversible Interfaces. 2.1.4.2 Polarizable Electrodes. 2.1.4.3 Adsorption at the Electrode-Electrolyte Interface. 2.1.4.4 Charge Transfer at the Electrode-Electrolyte Interface. 2.1.5 Grain Boundary Effects. 2.1.6 Current Distribution, Porous and Rough Electrodes- the Effect of Geometry. 2.1.6.1 Current Distribution Problems. 2.1.6.2 Rough and Porous Electrodes. 2.2. Physical and Electrochemical Models. 2.2.1 The Modeling of Electrochemical Systems. 2.2.2 Equivalent Circuits. 2.2.2.1 Unification of Immitance Responses. 2.2.2.2 Distributed Circuit Elements. 2.2.2.3 Ambiguous Circuits. 2.2.3 Modeling Results. 2.2.3.1 Introduction. 2.2.3.2 Supported Situations. 2.2.3.3 Unsupported Situations: Theoretical Models. 2.2.3.4 Unsupported Situations: Equivalent Network Models. 2.2.3.5 Unsupported Situations: Empirical and Semiempirical Models. Chapter 3. Measuring Techniques and Data Analysis. 3.1. Impedance Measurement Techniques (Michael C. H. McKubre and Digby D. Macdonald). 3.1.1 Introduction. 3.1.2 Frequency Domain Methods. 3.1.2.1 Audio Frequency Bridges. 3.1.2.2 Transformer Ratio Arm Bridges. 3.1.2.3 Berberian-Cole Bridge. 3.1.2.4 Considerations of Potentiostatic Control. 3.1.2.5 Oscilloscopic Methods for Direct Measurement. 3.1.2.6 Phase-Sensitive Detection for Direct Measurement. 3.1.2.7 Automated Frequency Response Analysis. 3.1.2.8 Automated Impedance Analyzers. 3.1.2.9 The Use of Kramers-Kronig Transforms. 3.1.2.10 Spectrum Analyzers. 3.1.3 Time Domain Methods. 3.1.3.1 Introduction. 3.1.3.2 Analog-to-Digital (A/D) Conversion. 3.1.3.3 Computer Interfacing. 3.1.3.4 Digital Signal Processing. 3.1.4 Conclusions. 3.2. Commercially Available Impedance Measurement Systems (Brian Sayers). 3.2.1 Electrochemical Impedance Measurement Systems. 3.2.1.1 System Configuration. 3.2.1.2 Why Use a Potentiostat? 3.2.1.3 Measurements Using 2, 3 or 4-Terminal Techniques. 3.2.1.4 Measurement Resolution and Accuracy. 3.2.1.5 Single Sine and FFT Measurement Techniques. 3.2.1.6 Multielectrode Techniques. 3.2.1.7 Effects of Connections and Input Impedance. 3.2.1.8 Verification of Measurement Performance. 3.2.1.9 Floating Measurement Techniques. 3.2.1.10 Multichannel Techniques. 3.2.2 Materials Impedance Measurement Systems. 3.2.2.1 System Configuration. 3.2.2.2 Measurement of Low Impedance Materials. 3.2.2.3 Measurement of High Impedance Materials. 3.2.2.4 Reference Techniques. 3.2.2.5 Normalization Techniques. 3.2.2.6 High Voltage Measurement Techniques. 3.2.2.7 Temperature Control. 3.2.2.8 Sample Holder Considerations. 3.3. Data Analysis (J. Ross Macdonald). 3.3.1 Data Presentation and Adjustment. 3.3.1.1 Previous Approaches. 3.3.1.2 Three-Dimensional Perspective Plotting. 3.3.1.3 Treatment of Anomalies. 3.3.2 Data Analysis Methods. 3.3.2.1 Simple Methods. 3.3.2.2 Complex Nonlinear Least Squares. 3.3.2.3 Weighting. 3.3.2.4 Which Impedance-Related Function to Fit? 3.3.2.5 The Question of "What to Fit" Revisited. 3.3.2.6 Deconvolution Approaches. 3.3.2.7 Examples of CNLS Fitting. 3.3.2.8 Summary and Simple Characterization Example. Chapter 4. Applications of Impedance Spectroscopy. 4.1. Characterization of Materials (N. Bonanos, B. C. H. Steele, and E. P. Butler). 4.1.1 Microstructural Models for Impedance Spectra of Materials. 4.1.1.1 Introduction. 4.1.1.2 Layer Models. 4.1.1.3 Effective Medium Models. 4.1.1.4 Modeling of Composite Electrodes. 4.1.2 Experimental Techniques. 4.1.2.1 Introduction. 4.1.2.2 Measurement Systems. 4.1.2.3 Sample Preparation-Electrodes. 4.1.2.4 Problems Associated With the Measurement of Electrode Properties. 4.1.3 Interpretation of the Impedance Spectra of Ionic Conductors and Interfaces. 4.1.3.1 Introduction. 4.1.3.2 Characterization of Grain Boundaries by IS. 4.1.3.3 Characterization of Two-Phase Dispersions by IS. 4.1.3.4 Impedance Spectra of Unusual Two-phase Systems. 4.1.3.5 Impedance Spectra of Composite Electrodes. 4.1.3.6 Closing Remarks. 4.2. Characterization of the Electrical Response of High Resistivity Ionic and Dielectric Solid Materials by Immittance Spectroscopy (J. Ross Macdonald). 4.2.1 Introduction. 4.2.2 Types of Dispersive Response Models: Strengths and Weaknesses. 4.2.2.1 Overview. 4.2.2.2 Variable-slope Models. 4.2.2.3 Composite Models. 4.2.3 Illustration of Typical Data Fitting Results for an Ionic Conductor. 4.3. Solid State Devices (William B. Johnson and Wayne L. Worrell). 4.3.1 Electrolyte-Insulator-Semiconductor (EIS) Sensors. 4.3.2 Solid Electrolyte Chemical Sensors. 4.3.3 Photoelectrochemical Solar Cells. 4.3.4 Impedance Response of Electrochromic Materials and Devices (Gunnar A. Niklasson, Anna Karin Johsson, and Maria Stromme). 4.3.4.1 Introduction. 4.3.4.2 Materials. 4.3.4.3 Experimental Techniques. 4.3.4.4 Experimental Results on Single Materials. 4.3.4.5 Experimental Results on Electrochromic Devices. 4.3.4.6 Conclusions and Outlook. 4.3.5 Time-Resolved Photocurrent Generation (Albert Goossens). 4.3.5.1 Introduction-Semiconductors. 4.3.5.2 Steady-State Photocurrents. 4.3.5.3 Time-of-Flight. 4.3.5.4 Intensity-Modulated Photocurrent Spectroscopy. 4.3.5.5 Final Remarks. 4.4. Corrosion of Materials (Digby D. Macdonald and Michael C. H. McKubre). 4.4.1 Introduction. 4.4.2 Fundamentals. 4.4.3 Measurement of Corrosion Rate. 4.4.4 Harmonic Analysis. 4.4.5 Kramer-Kronig Transforms. 4.4.6 Corrosion Mechanisms. 4.4.6.1 Active Dissolution. 4.4.6.2 Active-Passive Transition. 4.4.6.3 The Passive State. 4.4.7 Point Defect Model of the Passive State (Digby D. Macdonald). 4.4.7.1 Introduction. 4.4.7.2 Point Defect Model. 4.4.7.3 Electrochemical Impedance Spectroscopy. 4.4.7.4 Bilayer Passive Films. 4.4.8 Equivalent Circuit Analysis (Digby D. Macdonald and Michael C. H. McKubre). 4.4.8.1 Coatings. 4.4.9 Other Impedance Techniques. 4.4.9.1 Electrochemical Hydrodynamic Impedance (EHI). 4.4.9.2 Fracture Transfer Function (FTF). 4.4.9.3 Electrochemical Mechanical Impedance. 4.5. Electrochemical Power Sources. 4.5.1 Special Aspects of Impedance Modeling of Power Sources (Evgenij Barsoukov). 4.5.1.1 Intrinsic Relation Between Impedance Properties and Power Sources Performance. 4.5.1.2 Linear Time-Domain Modeling Based on Impedance Models, Laplace Transform. 4.5.1.3 Expressing Model Parameters in Electrical Terms, Limiting Resistances and Capacitances of Distributed Elements. 4.5.1.4 Discretization of Distributed Elements, Augmenting Equivalent Circuits. 4.5.1.5 Nonlinear Time-Domain Modeling of Power Sources Based on Impedance Models. 4.5.1.6 Special Kinds of Impedance Measurement Possible with Power Sources-Passive Load Excitation and Load Interrupt. 4.5.2 Batteries (Evgenij Barsoukov). 4.5.2.1 Generic Approach to Battery Impedance Modeling. 4.5.2.2 Lead Acid Batteries. 4.5.2.3 Nickel Cadmium Batteries. 4.5.2.4 Nickel Metal-hydride Batteries. 4.5.2.5 Li-ion Batteries. 4.5.3 Impedance Behavior of Electrochemical Supercapacitors and Porous Electrodes (Brian E. Conway). 4.5.3.1 Introduction. 4.5.3.2 The Time Factor in Capacitance Charge or Discharge. 4.5.3.3 Nyquist (or Argand) Complex-Plane Plots for Representation of Impedance Behavior. 4.5.3.4 Bode Plots of Impedance Parameters for Capacitors. 4.5.3.5 Hierarchy of Equivalent Circuits and Representation of Electrochemical Capacitor Behavior. 4.5.3.6 Impedance and Voltammetry Behavior of Brush Electrode Models of Porous Electrodes. 4.5.3.7 Impedance Behavior of Supercapacitors Based on Pseudocapacitance. 4.5.3.8 Deviations of Double-layer Capacitance from Ideal Behavior: Representation by a Constant-phase Element (CPE). 4.5.4 Fuel Cells (Norbert Wagner). 4.5.4.1 Introduction. 4.5.4.2 Alkaline Fuel Cells (AFC). 4.5.4.3 Polymer Electrolyte Fuel Cells (PEFC). 4.5.4.4 Solid Oxide Fuel Cells (SOFC). Appendix. Abbreviations and Definitions of Models. References. Index.

Impedance spectroscopy : theory, experiment, and applications

Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites

http://mocha-java.uccs.edu/dossier/RESEARCH/2004jps2-.pdf

Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 2. Modeling and identification

When asked to explain the importance of the discovery of conducting polymers, I offer two basic answers: first they did not (could not?) exist, and second, that they offer a unique combination of properties not available from any other known materials. The first expresses an intellectual challenge; the second expresses a promise for utility in a wide variety of applications.

Semiconducting and Metallic Polymers: The Fourth Generation of Polymeric Materials (Nobel Lecture).

This is an overview of some of the important, challenging, and problematic issues in contemporary electron transfer research. After a qualitative discussion of electron transfer, its time and distance scales, energy curves, and basic parabolic energy models are introduced to define the electron transfer process. Application of transition state theory leads to the standard Marcus formulation of electron transfer rate constants. Electron transfer in solution is coupled to solvent polarization effects, and relaxation processes can contribute to and even control electron transfer. The inverted region, in which electron transfer rate constants decrease with increasing exoergicity, is one of the most striking phenomena in electron transfer chemistry. It is predicted by both semiclassical and quantum mechanical models, with the latter appropriate if there are coupled high- or medium-frequency vibrations. The intramolecular reorganizational energy has different contributions from different vibrational modes, whic...

Contemporary Issues in Electron Transfer Research

Critical behavior of the electrical conductivity near the disorder-induced metal-insulator (MI) transition has been observed in polyaniline (PANI) doped with camphor sulfonic acid (CSA). The temperature dependence of the resistivity (\ensuremath{\rho}) depends on the degree of disorder present in the PANI-CSA films. In the most metallic samples the resistivity is nearly temperature independent; whereas in the critical region of MI transition, \ensuremath{\rho}(T) is characterized by a power-law temperature dependence, \ensuremath{\rho}(T)\ensuremath{\propto}${\mathit{T}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$. Resistivity ratios \ensuremath{\rho}(1.4 K)/\ensuremath{\rho}(300 K) as low as 1.6 have been observed in the most metallic samples of PANI-CSA. In the metallic regime, the conductivity is characterized by \ensuremath{\sigma}(T)=\ensuremath{\sigma}(0)+${\mathit{mT}}^{1/2}$ at low temperatures; the dependence of m(H) on magnetic field provides information on the role of electron-electron interactions in the transport near the MI transition. The ${\mathit{T}}^{\mathrm{\ensuremath{-}}1}$ dependence found for inelastic-scattering time (${\mathrm{\ensuremath{\tau}}}_{\mathrm{in}}$) is in agreement with that predicted for metallic systems near the MI transition. For the samples initially in the critical regime, a magnetic field of 8--10 T induces the transition to variable-range hopping. The typical localization length in PANI-CSA just on the insulating side of the MI transition is about 80--130 \AA{}. The magnitude of the positive magnetoresistance increases considerably as the system moves from the metallic to the insulating regime. The magnitude and quasilinear temperature dependence of the thermopower near the critical regime of the MI transition is typical of that expected for a metal.

Transport in polyaniline near the critical regime of the metal-insulator transition.

Hopping transport in doped conducting polymers in the insulating regime near the metal-insulator boundary: polypyrrole, polyaniline and polyalkylthiophenes

The self-assembled network of conducting polyaniline (PANI), protonated by camphor sulfonic acid (CSA), in a matrix of insulating polymethylmethacrylate (PMMA) has a remarkably low percolation threshold. The critical volume fraction (f) of the PANI-CSA phase segregated in PMMA is inferred from the concentration dependence of the conductivity, ${\mathit{f}}_{\mathit{c}}$\ensuremath{\approxeq}0.003 (0.3%). The conductivity at room temperature near the percolation threshold is quite high, 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ S/cm. Transmission-electron microscopy (TEM) results are in agreement with the percolation threshold inferred from the transport data; the TEM micrographs show that the connectivity of the PANI-CSA network decreases rapidly for f0.005. Near room temperature, the positive temperature coefficient of resistivity (\ensuremath{\rho}), a feature typical of the intrinsic metallic nature of PANI-CSA, is retained in the networks. At lower temperatures, \ensuremath{\rho}(T) exhibits a temperature-dependence characteristic of variable range-hopping transport, \ensuremath{\rho}(T)\ensuremath{\propto}exp[(${\mathit{T}}_{0}$/T${)}^{\ensuremath{\gamma}}$], with the exponent increasing from \ensuremath{\gamma}=0.25 to 1 upon decreasing the volume fraction of PANI-CSA from f=1 to ${\mathit{f}}_{\mathit{c}}$. This systematic increase in \ensuremath{\gamma} results from transport on the fractal structure and to the related superlocalization of the electronic wave functions. Below the percolation threshold, the temperature dependence of the resistivity is like that of granular metals with \ensuremath{\gamma}\ensuremath{\approxeq}0.5, consistent with the morphology and microstructure seen in the TEM micrographs. The positive magnetoresistance shows a maximum upon decreasing the volume fraction of PANI-CSA in agreement with effective-medium theory. Analysis of the magnetoresistance indicates that the localization length near the percolation threshold is approximately 25 \AA{} at 4.2 K.

Transport in polyaniline networks near the percolation threshold.

Heavily doped polypyrrole-hexafluorophosphate, PPy(${\mathrm{PF}}_{6}$), undergoes a metal-insulator (M-I) transition at resistivity ratio ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$=\ensuremath{\rho}(1.4 K)/${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$(300 K)\ensuremath{\approxeq}10: for ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$10, the system is metallic with \ensuremath{\rho}(T) remaining finite as T\ensuremath{\rightarrow}0, whereas for ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$g10, the system is an insulator with \ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\infty} as T\ensuremath{\rightarrow}0. In the critical regime, \ensuremath{\rho}(T) shows a power-law temperature dependence, \ensuremath{\rho}(T)=${\mathit{T}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$, with 0.31. The effect of the partially screened Coulomb interaction is substantial at low temperatures for samples on both sides of the M-I transition. In the insulating regime, the crossover from Mott variable-range hopping (VRH) to Efros-Shklovskii hopping is observed. In the metallic regime, the sign of the temperature coefficient of the resistivity changes at ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$\ensuremath{\approxeq}2. At T=1.4 K, the interaction length ${\mathit{L}}_{\mathit{T}}$=(\ensuremath{\Elzxh}D/${\mathit{k}}_{\mathit{B}}$T${)}^{1/2}$\ensuremath{\approxeq}30 \AA{}.Since this is smaller than the inelastic-scattering length, ${\mathit{L}}_{\mathrm{in}\mathrm{\ensuremath{\approxeq}}}$300 \AA{}, the contribution to \ensuremath{\rho}(T) from the electron-electron interaction is dominant. Application of high pressure decreases ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$, induces the transition into the metallic regime, and enables fine tuning of the M-I transition. For samples close to the M-I transition, the thermoelectric power is proportional to the temperature in both the metallic and insulating regimes. The correlation length (${\mathit{L}}_{\mathit{c}}$) increases as the disorder, characterized by ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$, approaches the M-I transition from either side. The expected divergence in ${\mathit{L}}_{\mathit{c}}$ at the M-I transition is qualitatively consistent with the values for ${\mathit{L}}_{\mathit{c}}$ inferred from the extrapolated \ensuremath{\sigma}(0) in the metallic regime and from analysis of the VRH magnetoresistance in the insulating regime. Thus, by using ${\mathrm{\ensuremath{\rho}}}_{\mathit{r}}$ to characterize the magnitude of the disorder, a complete and fully consistent picture of the M-I transition in PPy(${\mathrm{PF}}_{6}$) is developed.

Erratum: Transport near the metal-insulator transition: Polypyrrole doped with PF6

By controlling the extent of disorder through electrochemical synthesis at reduced temperatures, conducting polypyrrole (PPy) can be obtained in the metallic regime, in the insulating regime, and in the critical regime of the disorder-induced metal-insulator (M-I) transition. We present the results of reflectance measurements (0.002--6 eV) of PPy carried out at room temperature on the metallic side and on the insulating side of the M-I transition. While the reflectance spectra obtained from samples on both sides of the M-I transition exhibit spectral features expected for a partially filled conduction band, the electronic states near the Fermi energy (${\mathit{E}}_{\mathit{F}}$) are different in the two regimes. The data obtained from metallic samples indicate delocalized electronic wave functions in the conduction band, whereas the spectral features which characterize the insulating regime indicate that the states near ${\mathit{E}}_{\mathit{F}}$ are localized. Consistent with theoretical predictions for the metallic and insulating regimes, the optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) and the real part of the dielectric function ${\mathrm{\ensuremath{\varepsilon}}}_{1}$(\ensuremath{\omega}) each show different frequency dependences in the far infrared. In the metallic regime \ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{1/2}$ for \ensuremath{\Elzxh}\ensuremath{\omega}600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and ${\mathrm{\ensuremath{\varepsilon}}}_{1}$(\ensuremath{\omega}) (g0) increases rapidly as \ensuremath{\omega}\ensuremath{\rightarrow}0, as described by the ``localization-modified Drude model,'' leading to the conclusion that metallic polypyrrole is a disordered metal near the M-I transition. In contrast, the insulating regime is characterized as a Fermi glass as confirmed by \ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\propto}${\mathrm{\ensuremath{\omega}}}^{2}$ for \ensuremath{\Elzxh}\ensuremath{\omega}600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.

C.O. Yoon

Papers

Transport in polyaniline near the critical regime of the metal-insulator transition.

Hopping transport in doped conducting polymers in the insulating regime near the metal-insulator boundary: polypyrrole, polyaniline and polyalkylthiophenes

Transport in polyaniline networks near the percolation threshold.

Erratum: Transport near the metal-insulator transition: Polypyrrole doped with PF6

Reflectance of conducting polypyrrole: Observation of the metal-insulator transition driven by disorder.