Percolation of particles on recursive lattices using a nanoscale approach. III. Percolation of polydisperse particles in the presence of a polymer matrix

Abstract

We use a recently developed lattice model to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long chain to simplify the calculation but we make it more realistic by considering it semi-flexible. We study the effects of the stiffness of the polymer, the size disparity of the filler particles, their aspect ratio and the interactions between fillers and polymer on the percolation properties of the system. The lattice model is solved exactly on a recursive square Husimi lattice, which is an approximation for a square lattice. The solution represent an approximate solution for a square lattice. Our results are able to reproduce most of the experimental findings that have been observed in the literature.In particular, we observe how an increase in the size disparity of the filler particles dispersed in the matrix as well as an increase of their aspect ratio decreases the percolation threshold.

Ising Model for Conductive Percolation in Electrically Conductive Adhesives by Considering Random Arrangement of Conducting Particles

“…It mentions that the interaction energy between particle and matrix element influences the percolation thresholds. The same conclusions have been reported by Miyasaka et al (1982); Sumita et al (1986) and Corsi and Gujrati (2006). The increase in ξ means that the interaction energy between particles and matrix element is more positive that between particles.…”

“…Stromme et al (2003) reported the percolation volume of 0.238 and 0.249 for MMC equilibrated at 45 and 75% RH, respectively. Simulation using lattice models on a recursive square Husimi lattice, Corsi and Gujrati (2006) found a percolation threshold between 0.245-0.25. showed the occurrence of the percolation threshold at 22% in a composite of synthetic graphite particles dispersed in an epoxy-polyurethane resin. (Kota et al, 2007).…”