A fractal model for the impedance of a rough surface

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Abstract
The authors present a fractal model for a rough interface between an electrode and an electrolyte. They calculate that the complex surface impedance is Z=K(Z0)p where Z0 is the impedance of a flat interface. If the fractal dimension, df, of the boundary is written as 2+ delta , where delta is small, then, to first order in delta , p=1-2 delta . For a purely capacitive interface, Z0=1/i omega C, this gives an anomalous power-law frequency dependence as seen experimentally by Bottelberghs and Broers (1976) and by Armstrong and Burnham (1976). The authors explicitly calculate the prefactor K and the range of frequency for which this law is observed in terms of the range of lengths over which the interface is rough.