Analysis of Impedance Spectra

Electrochemical impedance spectroscopy (EIS) is widely used for characterizing electrochemical systems. By measuring the impedance as a function of frequency, EIS provides a powerful tool for analyzing the performance losses in batteries and fuel cells. For example, Adler et al. have used EIS to identify the causes of fuel cell inefficiencies over a range of experimental operating conditions. KMC simulations can be used to better interpret experimental EIS observations and trace their atomic origins. Diffusion coefficients, electrode resistance, and reaction rates of elementary reactions can be identified with KMC simulations under various applied frequencies, and this information can be used to clarify the connections between EIS peaks or frequencies and the underlying reaction mechanisms. 

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Establishing the surface area is the next concern. Electrode surfaces are seldom flat. Instead, they tend to display a set of different crystal faces. Sliver Iodide electrodes, prepared by amalgamation of silver with mercury, followed by vapour deposition of iodine, look smooth and shiny to the naked eye but reveeil crystallites under the electron microscope. Surface Irregularities not only complicate the assessment of the real area, they may also Interfere in the analysis of impedance spectra In terms of equivalent circuits. After drying, the surface may be studied by the usual optical methods (sec. 1.2) with the famlllrir caveat that drying may change these properties. Anyway, for a number of oxides and silver iodide It Is now established that electrodes can be made which have... 

J. R. Dygas and M. W. Breiter, "Variance of Errors and Elimination of Outliers in the Least Squares Analysis of Impedance Spectra," Electrochimica Acta, 44 (1999) 4163 174. 

P. Agarwal, O. C. Moghissi, M. E. Orazem, and L. H. Garda-Rubio, "Application of Measurement Models for Analysis of Impedance Spectra," Corrosion, 49(1993) 278-289. 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

Gheorghiu, M., Gersing, E., Gheorghiu, E., 1999. Quantitative analysis of impedance spectra of organs during ischemia. Ann. N.Y. Acad. Sci. 873, 65—71. 

Based on these ideas, the following theoretical models were derived and applied to the analysis of impedance spectra obtained for Au PPD electrodes [66],... 

The dEldc dependence on state of charge of battery materials is also significantly different from Nemstian but is often weU described by the Frumkin isotherm which takes into account attractive or repulsive interactions of adsorbed species, as reviewed by Levi and Aurbach [1999]. The actual dE/dc in the case of any particular material can be obtained by discharge/relaxation experiments, and knowledge of its value can significantly assist quantitative analysis of impedance spectra, as will be shown in the section on battery-spedfic improvanent in impedance spectra fitting. 

Impedance of the Series and Parallel RC Circuits. In the simplest analysis, the circuits I and II represent the electrical configurations encountered in measurement and interpretation of experimental impedance spectroscopic behavior of the double-layer at electrode interfaces. They provide the basis for analysis of impedance spectra of more complex RC networks that arise in representation of supercapacitor behavior. 

Furthermore, by varying other experimental conditions such as current load, temperature, gas composition, and as recently shown by Andreaus et al. [2002] hydrogen humidification and membrane thickness, measured cell impedance can be split into anode impedance, cathode impedance and electrolyte resistance, without using reference electrodes. These results were used to derive appropriate equivalent circuits for the analysis of impedance spectra measured on fuel cells operating with H2/O2, H2/air and H2 + lOOppm CO/O2. The variation of the experimental conditions is also a useful method to confirm the accuracy of the equivalent circuit. 

A. D. Franklin and H. J. de Bruin [1983] The Fourier Analysis of Impedance Spectra of Electroded Solid Electrolytes, Phys. Stat. Sol. (a) 75, 647-656. 

Figure 16.13 Proposed equivalent circuit model for the CNLS fit analysis of impedance spectra.

Analysis of impedance spectra with a fitted equivalent circuit allows the assessment of the variability of individual circuit elements with the change of potential and current intensity flowing in the corrosion system. 

Consecutive charge transfer steps are typical of Cu(Il) reduction. To study processes of this kind, different transient techniques can be applied, including the EIS. Proper analysis of impedance spectra often involves use of adequate equivalent circuits (ECs). However, sometimes they lack substantiation and, as a consequence, the physical meaning of EC elements is treated at random. Preferable... 

More definite conclusions may be drawn on the basis of exhaustive analysis of impedance spectra that carry information not only on the kinetics of faradaic processes but also on the characteristics of a double electric layer. As for gluconate systems, such investigations are scarce. A great variety of Nyquist plots (relationships between real, and imaginary, components of impedance) are demonstrated in Ref [99] that deal with the deposition of tin from neutral gluconate baths, but no quantitative analysis is presented. As we established earlier [100, 101], Nyquist plots obtained at open-circuit potentials for surfactant-free solutions are nothing else than lines that were observed over an entire range of applied frequencies. This means that Sn(II) reduction is mainly controlled by diffusive mass transport. 

Further details on representation and analysis of impedance spectra, especially in more complicated situations, may be found in references (1,2). 

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