Equivalent-circuit, scaling, random-walk simulation, and an experimental study of self-similar fractal electrodes and interfaces

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Abstract
A comprehensive study of the macroscopic transport parameters of self-similar interfaces is presented. The iteration of a simplified equivalent leads to the prediction of a simple mathematical expression for the impedance of fractal electrodes in d=2 and 3 dimensions. The same value is predicted by scaling arguments and verified by extended numerical simulations in d=2. Experiments on model electrodes confirm the theoretical prediction. We introduce the approximate concept of an information fractal. It gives a very simple access to the theory and a description of the regions of the fractal surface which are really active for the transport. The same result should apply to transport across fractal membranes and to certain Eley-Rideal heterogeneous catalysis processes.