Effects of Voltage-Dependence of the Constant Phase Element and Ohmic Parameters in the Modeling and Simulation of Cyclic Voltammograms

Abstract

Although the constant phase element (CPE) parameters have been found to vary with DC bias voltage in electrochemical impedance spectroscopy measurement, to date, the CPE parameters are assumed to be constant within the voltage window in cyclic voltammetry (CV) simulation. This leads to failure in predicting the voltammetric response of a double layer in some cases. In this study, the voltage-dependent CPE and ohmic parameters are used to simulate the capacitive current. The results show good agreement with the experimental measurements of commercial electrical double layer capacitors. The model is extended to predict the response of a system involving both Faradaic and capacitive currents by combining the conventional physicochemical transport model with circuit analysis to include effects of the resistances and CPE. To accurately predict the entire CV responses, a modified Randles circuit with an additional resistance connected in series with the CPE is proposed to be an equivalent circuit of the system. Furthermore, the closed-form analytical solution of the time-domain response of CPE under CV conditions is also derived and presented to gain better understanding of the CPE response. Using the derived equation, CV can serve as an alternative approach for determining the CPE parameters.