Analysis of the Charging Current in Cyclic Voltammetry and Supercapacitor's Galvanostatic Charging Profile Based on a Constant-Phase Element.

We investigated the charging current in cyclic voltammetry and the galvanostatic charging/discharging behavior of a controversial constant-phase element (CPE) to describe an electrical double layer used only in electrochemical impedance spectroscopy. The linear potential sweep in the time domain was transformed into the frequency domain using a Fourier transform. The current phasor was estimated by Ohm's law with the voltage phasor and a frequency-dependent CPE, followed by an inverse Fourier transform to determine the current in the time domain. For galvanostatic charging/discharging, the same procedure, apart from swapping the voltage signal with the current signal, was applied. The obtained cyclic voltammetry (CV) shows (1) a gradual increase in the charging current, (2) a higher charging current at a low scan rate, and (3) a deviation from the linear relationship between the charging current and the scan rate. For galvanostatic charging/discharging, the results demonstrate (1) curved charging/discharging behavior, (2) a higher voltage in the early stage, and (3) a lower voltage during longer charging periods. In contrast to a previous approach based on solving a differential equation with a simple RC circuit, our Fourier transform-based approach enables an analysis of electrochemical data with an arbitrary and complex circuit model such as a Randles equivalent circuit. The CPE model is more consistent with previous experimental results than a simple ideal capacitor, indicating a ubiquitous CPE in electrochemistry and a fair figure of merit for supercapacitors.