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

Abstract

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.

Controlling 3D Percolation Threshold of Conductor-Insulator Composites by Changing the Granular Size of Conductors

“…The results 4) suggested that in the 3D case, binary distributions in the sizes of the particles may change the percolation threshold. These results demonstrate that the introduction of particle size distribution into a simple percolation system exerts a complex and non-trivial effect 7) that is difficult to be predicted by simple empirical models 8,9) depending on the dimensionality of the space.…”

Carbon Nanotubes as Conductive Filler in Segregated Polymer Composites - Electrical Properties

“…From this point of view ultrahigh molecular weight polyethylene (UHMWPE) is a preferred matrix (Zhang et al, 2005). Since first detailed study of Malliaris & Turner, 1971 many investigations of segregated systems based on metal (and ceramic) particles as conductive filler were fulfilled, for example (Boushet et al, 2000;Bridget et al, 1990;Kusy, 1977;Kusy & Corneliussen, 1975;Lebovka et al, 2006;Mamunya et al, 2002bMamunya et al, , 2002cPrivalko et al, 2000;Yacubowicz et al, 1990b). Extensive study of segregated polymer/metal systems and their possible applications were presented elsewhere (Kusy, 1986) where the prominent achievements in this area have been summarized.…”

“…every polymer particle is covered with a monolayer of conductive particles. Computer simulation on the base of similar model with the linear size of the system   2048 in 2D case and   200 of calculated units in 3D case allowed estimation the value of percolation threshold x c in such a manner (Lebovka et al, 2006):…”

Controlling the Percolation Threshold of Conductor-Insulator Composites by Changing the Granular Size of Insulators

“…Although previous authors have attempted a number of theoretical analyses, 16,17) many of those analyses depend on too many assumptions that deviate from the actual configurations randomly realized in the material. More sophisticated models 18,19) proposed for the percolation behavior of permeable particles are also inappropriate to consider realistic situations because the excluded volume effect between particles are not considered.…”