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 m...

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Bibliographic Details
Published in:Annals of physics 1992-10, Vol.219 (1), p.109-147
Main Authors: Halsey, Thomas C, Leibig, Michael
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1016/0003-4916(92)90314-C