Analytical expressions for electrochemical supercapacitor with potential dependent capacitance

Abstract

Distinctly from ordinary capacitors which have a fixed capacitance, the capacitance of electrochemical supercapacitors is dependent on the applied potential. This feature introduces an additional complication to the analytical solution representing the supercapacitor circuit. Here a simplified equivalent circuit of electric double layer capacitors or electrochemical supercapacitors is proposed so that expressions evaluating the potential-dependent capacitance are derived considering short periods of charging and discharging process as in cyclic voltammetry carried out in a few minutes. Comparisons between such theoretical development and experimental cyclic voltammetry data – presenting a very good agreement – are presented and discussed.