The effect of surface topology on the edl capacitance: 1_d case

Abstract

An electrical capacitor is an energy storage device that generates an electric field between electrodes and produces potential that can be channeled through associated circuits. The Electrical Double Layer (EDL) capacitor is a unique capacitor with a remarkably higher capacity. The energy densities of these capacitors can range between 0.5 and 10 Wh/kg. This study develops a method to predict the dependence of the double-layer capacitance on the roughness profile of the electrode using the linear Poisson-Boltzmann theory, and the Gouy-Chapman theory for 1-D systems. The roughness dependence of diffuse layer differential capacitance is obtained for a defined roughness profile. The theory developed here helps to understand the Debye-length dependent on the roughness factor and profile. The variation of double-layer capacitance with roughness is analyzed based on a numerical solution obtained for the model roughness profile.