Theory of porous electrodes: The percolation and a calculation of percolation lines

The basis for a theory of porous electrodes is the percolation problem. Its solution would make it possible to answer the question of how effectively the structure of a porous electrode is used for ensuring the occurrence of electrochemical processes on its inner surface, for bringing together all its participants (reagents, ions, electrons, catalyst particles), and for removing the formed products. To solve this problem, it is necessary that both the elements of the structure of a porous electrode and the substances filling it be connected. In the case of hydrophobized electrodes, these are exemplified by a mixture of agglomerated grains of polytetrafluoroethylene and catalyst, the gaseous reagent entering the electrodes, and the electrolyte. In this publication, we describe a general method intended for the calculation of thresholds and lines of percolation and present particular estimates for an important class of lattices modeling porous media-rectangular: plane square lattice, three-dimensional cubic, and their analogues in space of any number of measurements.