Self-affine fractal model for a metal-electrolyte interface

Fractal models of rough interfaces have provided a possible explanation for the observed ac response of an interface between a metal and an electrolyte with blocking contacts which displays the constant-phase-angle (CPA) behavior. For this system, two different relations between the exponent η of the frequency dependence of the CPA element and the fractal dimension $d_s$ of the interface have been proposed. By solving for the properties of a self-affine fractal model of an interface and using Mandelbrot’s box dimension for the fractal dimension it is demonstrated that there is no universal relation in which η is simply a function of $d_s$.