Scaling-law analysis to describe the impedance behavior of fractal electrodes

Abstract

In order to explain the frequency dispersion of the impedance spectra of irregular surfaces and the frequent occurrence of the constant-phase element (CPE), several authors have proposed a fractal description for the capacitive (blocking) interface. These models, however, lead to different conclusions. In this paper it is shown how analysis of the scaling laws of electrochemical cells can be applied to predict the dependence of the CPE exponent on the Hausdorff dimension. Our general treatment reproduces the results of about a dozen published models. Furthermore, four other, new fractal models are presented, and it is shown that analysis of the scaling laws yields the same result as independent numerical or analytical methods.