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

We use a recently developed lattice model of polymers 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 semiflexible. 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 represents 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.