Fractal electrodes and constant phase angle response: Exact examples and counter examples

Abstract

The ac response of a fractal electrode has been proposed recently to be of the constant phase angle type (CPA) in the approximate model of a hierarchical lumped circuit. In that model the phase angle exponent η is related to the fractal dimension D of the surface by the relation η = (3- D). We present special fractal electrodes for which the calculation can be made without model approximations. This permits to distinguish two categories of electrodes. In the first category with a fractal dimension larger than 5 2 , the response of the system is indeed of the CPA type but the above relation is not verified. In the second category ( D< 5 2 ) the above relation is shown to be verified exactly for a finite size electrode while an infinite electrode is shown to be a counter example to the same relation.