  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 semiflexible chain. 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 Husimi lattice. The solution represent an approximate
solution for a regular 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 aincrease of their aspect ratio decreases
the percolation threshold.
