Impedance data graphical representation

This circuit is usually referred to as the Randles circuit and its analysis has been a major feature of AC impedance studies in the last fifty years. In principle, we can measure the impedance of our cell as a function of frequency and then obtain the best values of the parameters Rct,<7,C4i and Rso by a least squares algorithm. The advent of fast micro-computers makes this the normal method nowadays but it is often extremely helpful to represent the AC data graphically since the suitability of a simple model, such as the Randles model, can usually be immediately assessed. The most common graphical representation is the impedance plot in which the real part of the measured impedance (i.e. that in phase with the impressed cell voltage) is plotted against the 90° out-of-phase quadrature or imaginary part of the impedance. 

Gileadi combined adsorption isothenn, 340, 342, 344 Gileadi isotherm, application to electrode kinetics, 344, 347 Gouy-Chapman theory, 190, 193, 200 Graphical representation, (of impedance data), 431... 

Figure 17.1 Equivalent circuits used to demonstrate the graphical representation of reactive impedance data a) Randles circuit and b) blocking circuit.

The graphical representations presented here are intended to enhance analysis and to provide guidance for the development of appropriate physical models. While visual inspection of data alone cannot provide all the nuance and detail that can, in principle, be extracted from impedance data, the graphical methods described in this chapter can provide both qualitative and quantitative evaluation of impedance data. 

M. E. Orazem, N. Pebfere, and B. Tribollet, "A New Look at Graphical Representation of Impedance Data," Journal of The Electrochemical Society, 153 (2006) B129-B136. 

The complex impedance data involves the interplay of three variables, the imaginary component of the impedance, the real component of the impedance, Zreai, and the phase angle, common types of representation for impedance data are, the Nyquist and the Bode representations. Nevertheless, these have become the most widely used graphical representations of impedance data. 

The information provided by EIS can be plotted in different graphical representations. Figure 8.2 shows one common representation of EIS data, called a Bode plot. In a Bode plot, the absolute magnitude of the impedance (Fig. 8.2a) and the phase shift (Fig. 8.2b), both of which are experimentally measured, are plotted against... 

M. E. Orazem, N. Pebere, B. Tribollet, Enhanced graphical representation of electrochemical impedance data, ]. Electrochem. Soc., 2006,153,4, pp. B129-B136. 

Such initial experimental and data-assessment procedures should be supported by a series of measurements at different potentials, temperatures, concentrations, and convections, with the data to be combined with the error analysis. After the data is acquired, it can be initially represented by an equivalent circuit, physical, or continuum level model that is consistent with physical and chemical information and is comparable to previously published EIS and other analytical results on identical or at least similar systems. The preliminary selection of the data representation, such as complex impedance, modulus, and phase- angle notations, is often helpful, as quite often some of these graphic notations are more informative than others. 

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