Random-walk simulation of the response of irregular or fractal interfaces and membranes

作者：Paul Meakin, B. Sapoval · 发表于：Physical Review A · 年份：1991 · DOI：10.1103/physreva.43.2993 · 被引用次数：45 · 研究领域：Electrochemical Analysis and Applications、Electrostatics and Colloid Interactions、Theoretical and Computational Physics

A method of simulating the response of an irregular interface is investigated. It is based on an exact mapping between the Laplace equation and the steady-state diffusion equation with mixed boundary conditions. Simulations in two dimensions show that diffusion-limited aggregation (DLA) and other self-similar fractal electrodes exhibit the so-called constant-phase-angle (CPA) behavior. In the case of DLA electrodes the CPA exponent is found by this method to be close to the inverse of the fractal dimension. We show that this is directly related to the fact that in d=2 the admittance is proportional to the overall size of the self-similar electrode.