Fractal model for the ac response of a rough interface

The ac response of an interface between two materials of very different conductivities (e.g., an electrode and an electrolyte) cannot be simply modeled by a resistor and a capacitor. Instead it is found necessary to include a constant-phase-angle (CPA) element whose impedance has the form Z((LC OMEGA)) infinity (j(LC OMEGA))(sup -eta), where (LC OMEGA) is the angular frequency, j = (RADICAL)-1, and 0 eta 1. Furthermore, it is observed that the parameter eta is intimately related to surface roughness, with eta approaching unity when the surface is made increasingly smooth.