Active surface and adaptability of fractal membranes and electrodes

Ricardo Gutfraind , Bernard Sapoval

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 rs is finite there exists a crossover length Lc : In pores of sizes smaller than Lc. the current is homogeneously distributed. In pores of sizes larger than Lc, the same behavior as in the case rs = 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 rs. We then introduce a coarse-graining procedure which maps the problem of non-null rs into that of rs = 0. This permits us to obtain the dependence of the admittance and of the active surface on rs. 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.


Domaines: Articles anciens

Ricardo Gutfraind, Bernard Sapoval. Active surface and adaptability of fractal membranes and electrodes. Journal de Physique I, 1993, 3 (8), pp.1801-1818. ⟨10.1051/jp1:1993216⟩. ⟨jpa-00246832⟩