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

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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 > 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:	Date Event 1988 Published
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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