A GRAIN CONSOLIDATION MODEL FOR THE CRITICAL OR PERCOLATION VOLUME FRACTION IN CONDUCTOR-INSULATOR MIXTURES

The critical volume fraction, at which the conducting component in conductor-insulator mixtures first becomes continuous or percolates, plays a very important role in both percolation theory and the generalized effective-media equation. The growth mechanism, by which very low (less-than-or-equal-to 0.05) critical volume fractions for nearly spherical conducting powders in insulating hosts, such as polymers, are obtained, is not well understood. In this paper a simple model, based on the computer-generated model of Roberts and Schwartz [Phys. Rev. B 31, 5990 (1985)] for grain consolidation in porous media, for the very low critical volume fractions observed in some conductor-insulator mixtures is proposed.