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A fractal model for the impedance of a rough surface
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Ball, R. C. and Blunt, M. J.. (1988) A fractal model for the impedance of a rough surface. Journal of Physics A: Mathematical and General, Vol.21 (No.1). pp. 197-204. ISSN 0305-4470
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Official URL: http://dx.doi.org/10.1088/0305-4470/21/1/024
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Divisions: | Faculty of Science > Physics |
| Library of Congress Subject Headings (LCSH): | Fractals, Interfaces (Physical sciences) -- Mathematical models, Electrodes -- Surfaces, Electrolytes, Surfaces (Physics) |
| Journal or Publication Title: | Journal of Physics A: Mathematical and General |
| Publisher: | Institute of Physics Publishing Ltd. |
| ISSN: | 0305-4470 |
| Date: | 1988 |
| Volume: | Vol.21 |
| Number: | No.1 |
| Page Range: | pp. 197-204 |
| Identification Number: | 10.1088/0305-4470/21/1/024 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/39432 |
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