THE DOUBLE-LAYER IMPEDANCE AT A ROUGH-SURFACE - THEORETICAL RESULTS

The roughness of an electrode surface can dramatically influence the double layer impedance at that electrode. We review a Green's function approach to this problem. For nearly flat surfaces, this approach can be developed perturbatively. In the more general case, the impedance problem can be mapped onto a problem involving the behavior of random walks near the surface of the electrode. For self-similar surfaces, we develop a scaling theory for this random walk problem. We explore the consequences of this theory for the double layer impedance. We find a stretched-exponential impedance, with the amplitude and exponent of the stretched-exponential decay being related to the multifractal properties of the self-similar surface. At high frequencies, this behavior is similar to the experimentally observed "constant phase angle" (CPA) response. We discuss experimental consequences of these results. © 1992.