ACTIVE SURFACE AND ADAPTABILITY OF FRACTAL MEMBRANES AND ELECTRODES

We study the properties of a Laplacian potential around an irregular o bject of finite surface resistance. This can describe the electrical p otential in an irregular electrochemical cell as well as the concentra tion in a problem of diffusion towards an irregular membrane of finite permeability. We show that using a simple fractal generator one can a pproximately predict the localization of the active zones of a determi nistic fractal electrode of zero resistance. When the surface resistan ce r(s) is finite there exists a crossover length L(c) : In pores of s izes smaller than L(c) the current is homogeneously distributed. In po res of sizes larger than L(c) the same behavior as in the case r(s) = 0 is observed, namely the current concentrates at the entrance of the pore. From this consideration one can predict the active surface local ization in the case of finite r(s). We then introduce a coarse-grainin g procedure which maps the problem of non-null r(s) into that of r(s) = 0. This permits us to obtain the dependence of the admittance and of the active surface on r(s). Finally, we show that the fractal geometr y can be the most efficient for a membrane or electrode that has to wo rk under very variable conditions.