Ershler-Randles model

Electrical equivalent circuit representing the model of Ershler-Randles. 

Features of the impedance spectra of Fig. 3.15a may be modeled by a simple modified Randles-Ershler equivalent circuit shown in Fig. 3.15c. In this model, is the solution resistance, and is the charge-transfer resistance at the electrode/eIectrol e interface. A constant phase element (CPE) was used instead of a doublelayer capacitance to take into account the surface roughness of the particle. Qn is the insertion capacitance, and Zw is the Warbui impedance that corresponds to the solid-state diffusion of the Li-ion into the bulk anode. The Warburg element was used only for impedance data obtained at the tenth charge. The electrical components of the surface film which is likely formed on the electrode were disregarded, because no time constant related to this process could be seen in the electrochemical impedance spectroscopy (EIS) spectra. It was also checked that their inclusion in the model of Fig. 3.15c does not improve the fit. 

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