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We use a recently developed lattice model to study the percolation ofparticles of different sizes and shapes in the presence of a polymer matrix.The polymer is modeled as an infinitely long semiflexible chain. We study theeffects of the stiffness of the polymer, the size disparity of the fillerparticles, their aspect ratio and the interactions between fillers and polymeron the percolation properties of the system. The lattice model is solvedexactly on a recursive Husimi lattice. The solution represent an approximatesolution for a regular lattice. Our results are able to reproduce most of theexperimental findings that have been observed in the literature. In particular,we observe how an increase in the size disparity of the filler particlesdispersed in the matrix as well as an aincrease of their aspect ratio decreasesthe percolation threshold.Comment: Submitted to Physical Review

physical review. e, statistical, nonlinear and soft matter physics

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