Fractal model for the ac response of a rough interface

A fractal model is proposed for a rough interface between two materials of very different conductivities, e.g., an electrode and an electrolyte. The equivalent circuit of the model, which takes into consideration the resistance in the two substances and the capacitance of the interface, has the property of the so-called constant-phase-angle element, i.e., a passive circuit element whose complex impedance has a power-law singularity at low frequencies. The exponent of the frequency dependence is related to the fractal dimension. The model also provides insight into the conducting properties of the percolating cluster and the source of the 1/f noise in electronic components