Two-dimensional continuum percolation and conduction. II

Abstract

By computer simulation we have been studying the relation between the effective conductivity and the geometrical configuration of two-dimensional composite or inhomogeneous materials consisting of a metal and an insulator, considering the problem as a continuum percolation problem. Following our previous paper [J. Appl. Phys. 56, 806 (1984)], we further simulate two new types of continuum percolation models, and compute the effective conductivities by the finite element method. We compare the calculated conductivities with previous results, theoretical formulas, and experimental data. We clearly show that the critical volume fractions for the metal-insulator transition and the conductivities of the continuum percolation problem greatly depend on the geometrical configuration of the metal areas of the formed patterns. The extended Watson–Leath equation is a good approximation to the conductivity of the two-dimensional continuum percolation problem.