Scaling in percolation behaviour in conductive–insulating composites with particles of different size

The percolation behaviour of conductive composites containing particles of different sizes was analysed. A composite was simulated as the media containing small conductive particles distributed in the channels between large insulative particles, where each large particle is covered by n monolayers of the filler particles. The simulations were done for the cases of two-dimensional (2D) and three-dimensional (3D) lattices. It was shown that the percolation filler concentration x* versus the particle size ratio λ = R/r and the number of monolayers n may be approximated as , where d is the space dimensionality; is the site random percolation threshold; neff is the effective number of monolayers, which decreases with increase in n and neff → n in the limit of n → ∞. The scaling behaviour of the percolation threshold inside the layers confined by the large particles was analysed. The data obtained at different values of λ and n gave the same correlation length exponent values as for the classical random percolation both for 2D and 3D cases. Analysis of the electrical conductivity behaviour near the percolation threshold in 2D systems showed the existence of the obvious differences at different values of λ and n, though the conductivity exponents s and t retained their universal values typical for the random percolation. The accuracy of the developed theoretical approach was experimentally tested for the polyvinyl chloride–copper (PVC–Cu) and polycarbonate–copper (PC–Cu) composites.