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A fractal model for the impedance of a rough surface

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Ball, Robin 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. doi:10.1088/0305-4470/21/1/024 ISSN 0305-4470.

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Official URL: http://dx.doi.org/10.1088/0305-4470/21/1/024

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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, Engineering and Medicine > 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
Official Date: 1988
Dates:
DateEvent
1988Published
Volume: Vol.21
Number: No.1
Page Range: pp. 197-204
DOI: 10.1088/0305-4470/21/1/024
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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