Randles circuit

A Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance R_S in series with the parallel combination of the double-layer capacitance C_dl and an impedance of a faradaic reaction. It is commonly used in electrochemical impedance spectroscopy (EIS) for interpretation of impedance spectra.

Figure 1 shows the equivalent circuit initially proposed by Randles for modeling of interfacial electrochemical reactions in presence of semi-infinite linear diffusion of electroactive particles to flat electrodes. In this model, the impedance of a faradaic reaction consists of an active charge transfer resistance R_ct and a specific electrochemical element of diffusion W, which is also called Warburg element (Z_W = A_W/(jω)^0.5, where A_W is Warburg coefficient, j – imaginary unit, ω – angular frequency). Figure 2 shows an example of EIS spectrum (presented in the Nyquist plot) simulated using the following parameters: R_S = 20 Ω, C_dl = 25 μF, R_ct = 100 Ω, A_W = 300 Ω•s^-0.5.

In a simple situation, the Warburg element manifests itself in EIS spectra by a line with an angle of 45 degrees in the low frequency region.Values of the charge transfer resistance and Warburg coefficient depend on physico-chemical parameters of a system under investigation. To obtain the Randles circuit parameters, the fitting of the model to the experimental data should be performed using complex nonlinear least-squares procedures [http://www.abc.chemistry.bsu.by/vi/fit.htm available] in numerous EIS data fitting computer programs.The Randles equivalent circuit is one of the simplest possible models describing processes at the electrochemical interface. In real electrochemical systems, impedance spectra are usually more complicated and, thus, the Randles circuit may not give appropriate results.

References

*J.E. Randles. "Kinetics of rapid electrode reactions." Discuss. Faraday Soc. 1 (1947) 11.

*A. Lasia. Electrochemical impedance spectroscopy and its applications. In: Modern Aspects of Electrochemistry. Volume 32. Kluwer Academic/Plenum Pub. 1999, Ch.2, p. 143.