Computer Experiment on a 3D Site Percolation Model of Porous Materials-Its Connectivity and Conductivity

Abstract

A site percolation model of 50×50×50 sites is examined by computer to treat the generalized conductivity characteristic of a two-phase material with random structure (porous material). An enumeration of clusters of one phase (pores) in the model provides cluster-size distribution, percolation probability P(p) and an estimate of the critical probability 0.31<p_c<0.32 for the site percolation problem in a simple cubic lattice. A direct calculation of the bulk electrical conductivity of the 3D random resistor network derived from the model reveals a special relation between the conductivity k and the concentration p of the one phase (porosity p of the model): k=Const. (p−p_c)^1.725±0.005 in which p_c=0.318±0.002. The above power law indicates a critical nature of the phenomenon.