Frequency dependence of the double-layer impedance at a rough surface

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Abstract
We present a general theoretical framework for understanding the geometrical frequency dependence of the impedance of ionic solutions in contact with rough or irregular metallic electrodes. In two dimensions all relevant information regarding the surface is contained in the conformal transformation that maps the rough surface onto a straight line. The ‘‘constant-phase-angle’’ impedance is related to the scaling of current inhomogeneities within a two-scale model of the structure of the metallic surface. The capacitive effects in this model are controlled by a generalization of the ‘‘Parisi matrix.’’