Fractals and Percolation in the Theory of Porous Electrodes

Abstract

A computer-aided simulation of the structure of a porous electrode is performed using flat lattices of sites (they are capable of conducting electrons and are randomly distributed in the electrode) as an example. To adequately describe properties of a porous electrode, information about the degree of dispersion of the particles that make up the electrode (“fractal dimensionality”) must be complemented by that on their clusterization (presence of “percolation clusters”). These factors impart two properties to a porous electrode, specifically, a developed surface, on which an electrochemical process may proceed, and the possibility of a continuous supply of electrons to this surface. A percolation cluster may be dismembered to a “trunk” (it provides for the electron transport) and a “crown” (aggregate of particles that make a major contribution to the electrochemical process). The dismembering was performed via computer flow diagrams proposed by the authors. A computer-aided analysis of characteristics of a porous electrode points to the existence of an optimum structure in which the electrochemical activity is capable of reaching a maximum.