Numéro
J. Phys. I France
Volume 3, Numéro 8, August 1993
Page(s) 1801 - 1818
DOI https://doi.org/10.1051/jp1:1993216
DOI: 10.1051/jp1:1993216
J. Phys. I France 3 (1993) 1801-1818

Active surface and adaptability of fractal membranes and electrodes

Ricardo Gutfraind and Bernard Sapoval

Laboratoire de Physique de la Matière Condensée , C.N.R.S., Ecole Polytechnique, 91128 Palaiseau, France


(Received 4 March 1993, accepted in final form 5 April 1993)

Abstract
We study the properties of a Laplacian potential around an irregular object of finite surface resistance. This can describe the electrical potential in an irregular electrochemical cell as well as the concentration in a problem of diffusion towards an irregular membrane of finite permeability. We show that using a simple fractal generator one can approximately predict the localization of the active zones of a deterministic fractal electrode of zero resistance. When the surface resistance $r_{\rm s}$ is finite there exists a crossover length $L_{\rm c}$ : In pores of sizes smaller than $L_{\rm c}$. the current is homogeneously distributed. In pores of sizes larger than $L_{\rm c}$, the same behavior as in the case $r_{\rm s}$ = 0 is observed, namely the current concentrates at the entrance of the pore. From this consideration one can predict the active surface localization in the case of finite $r_{\rm s}$. We then introduce a coarse-graining procedure which maps the problem of non-null $r_{\rm s}$ into that of $r_{\rm s}$ = 0. This permits us to obtain the dependence of the admittance and of the active surface on $r_{\rm s}$. Finally, we show that the fractal geometry can be the most efficient for a membrane or electrode that has to work under very variable conditions.



© Les Editions de Physique 1993

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.