Conductive percolation threshold of conductive-insulating granular composites

The percolationphenomenon of conductive-insulating composites has been extensively studied because of their wide applications in the electronic industry [1–7]. Such materials possess special physical properties different from metals, for example the thermal conductivityof conductivepolymers is lower, the wear resistance of conductiveceramics is higher. Conductive-insulating composites can be made by dispersing conductiveparticles into the melt of an insulating matrix, such as a polymer [1–3], by thermal pressing of a mixture of conductiveinsulating powders, such as metal and ceramic powders [4–6], and by growing a thin film on a substrate [7]. In such a material, when the volume fraction of the conductivepowders is lower than a critical valve, it behaves as an insulator; as the volume fraction of the conductivepowders reaches the critical valve, its electrical conductivitysharply increases by several orders of magnitude. This critical valve is referred to as the percolation thresholdat which a conductivenetwork is formed to span the entire cross section of the body of the material. For materials with crystal structures, such as simple cubic, body centered cubic (BCC) and face centred cubic (FCC) lattices, the exact or very accurate values of the percolation thresholdshave been obtained by theoretical analysis or by computer simulation. For example, the site percolation thresholdis about 0.3116 for the simple cubic lattice and is about 0.246 for the BCC lattice [8]. However, for composites with amorphous structures, such as a compact of a mixture of conductive-insulating powders, only experimental data and simplified analytical models are available. Using a Monte Carlo simulation model, we studied the percolationbehavior of such granular composites with amorphous structure. In this letter we briefly review the simulation model first; then we report our simulation result on conductiveand insulating powders with equal particle size. The assumptions made in this study are that the particles have spherical shape and are rigid so that overlap is not allowed. For convenience, the particle diameter is set to one unit.