Stretched-exponential relaxation at a self-similiar surface

The double-layer impedance at a rough electrode can be related to properties of random walks near the surface of that electrode. We apply this method to the calculation of the double-layer impedance at a self-similar electrode in two dimensions. We find that the impedance at a self-similar surface shows stretched-exponential behavior. At high frequencies, this behavior is similar to the experimentally observed constant phase-angle behavior, with an exponent determined by the multifractal properties of the surface.