Effect of disorder on a fractal model for the ac response of a rough interface

Abstract

The effect of disorder on the fractal model of Liu for a rough interface between two materials of very different conductivities is examined. It is found that the average admittance has the experimentally observed property of a constant-phase-angle (CPA) element. The exponent \ensuremath{\eta} of the frequency dependence of the CPA element depends on the specific form of the probability distribution of the scaling. Furthermore, the fractal dimension d${\ifmmode\bar\else\textasciimacron\fi{}}_{s}$ of the random surface area of the interface is calculated, and \ensuremath{\eta}=3-d${\ifmmode\bar\else\textasciimacron\fi{}}_{s}$.