AC response of fractal interfaces

Abstract

The small signal ac impedance of the interface between a blocking electrode and a aqueous or solid electrolyte often contains a constant-phase-angle (CPA) element whose impedance has the frequency dependence according to Z ∝ (jω) −ν. Recently it has been demostrated experimentally that the exponent ν is intimately related to the roughness of the interface, with ν approaching 1 when the surface is made increasingly smooth. We propose to model the interface by a fractal called Cantor bar. The equivalent circuit of the model has the property of the CPA element with the exponent ν = 3 − d s, where 2 < d s < 3 is the fractal dimension of the interface. The model has been made more realistic by assuming random branching number and scaling ratio, and the relation between ν and d s remains the same. For real fractal surfaces the relation between ν and d s may hold approximately.