Randles-Ershler electric equivalent circuit

Electrochemical reactions consist of electron transfer at the electrode surface. These reactions mainly involve electrolyte resistance, adsorption of electroactive species, charge transfer at the electrode surface, and mass transfer from the bulk solution to the electrode surface. Each process can be considered as an electric component or a simple electric circuit. The whole reaction process can be represented by an electric circuit composed of resistance, capacitors, or constant phase elements combined in parallel or in series. The most popular electric circuit for a simple electrochemical reaction is the Randles-Ershler electric equivalent... 

Electrical equivalent circuit representing the model of Ershler-Randles. 

In 1940, Frumkin explored the relationships among the double-layer structure on mercury electrodes, the capacitance measured by use of a Wheatstone bridge, and the surface tension, following the theoretical underpinnings of the Lippmann equation. Grahame ° expanded this treatment of the mercury electrode, providing a fundamental understanding of the structure of the electrical double layer. Dolin and Ershler applied the concept of an equivalent circuit to electrochemical kinetics for which the circuit elements were independent of frequency. Randles developed an equivalent circuit for an ideally polarized mercury electrode that accounted for the kinetics of adsorption reactions. ... 

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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