Theory for electrochemical impedance spectroscopy of heterogeneous electrode with distributed capacitance and charge transfer resistance

Abstract

Abstract Randles-Ershler admittance model is extensively used in the modeling of batteries, fuel cells, sensors etc. It is also used in understanding response of the fundamental systems with coupled processes like charge transfer, diffusion, electric double layer charging and uncompensated solution resistance. We generalize phenomenological theory for the Randles-Ershler admittance at the electrode with double layer capacitance and charge transfer heterogeneity, viz., non-uniform double layer capacitance and charge transfer resistance (\(c_d\) and \(R_{CT}\)). Electrode heterogeneity is modeled through distribution functions of \(R_{CT}\) and \(c_d\), viz., log-normal distribution function. High frequency region captures influence of electric double layer while intermediate frequency region captures influence from the charge transfer resistance of heterogeneous electrode. A heterogeneous electrode with mean charge transfer resistance \(\overline{R_{CT}}\) shows faster charge transfer kinetics over a electrode with uniform charge transfer resistance (\(\overline{R_{CT}}\)). It is also observed that a heterogeneous electrode having high mean with large variance in the \(R_{CT}\) and \(c_d\) can behave same as an electrode having low mean with small variance in the \(R_{CT}\) and \(c_d\). The origin of coupling of uncompensated solution resistance (between working and reference electrode) with the charge transfer kinetics is explained. Finally, our model provides a simple route to understand the effect of spatial heterogeneity.Graphical Abstract SYNOPSIS An electrochemical system consisting of heterogeneous working electrode (non-uniform charge transfer (CT) resistance (\(R_{CT}^{(i)}\)) and electric double layer capacitance (\(c_{d}^{(i)}\))) and ohmic losses (\(R_\Omega \)) between working and reference electrode. The analysis suggests that electrode with heterogeneity results in faster CT kinetics as compared to CT kinetics over homogeneous electrode.