Percolation of particles on recursive lattices using a nanoscale approach. II. The effect of size and shape disparities.

The preparation of many composites requires the intermixing of several macromolecular fluids along with the addition of rigid filler particles. These fillers are usually polydisperse and there is extensive experimental evidence that their size and shape profoundly affect the properties of the resulting material. In particular, it is generally found that the percolation threshold decreases as the size disparity between the different particles present in a system increases, and that the threshold decreases with increasing aspect ratio of the particles. Here, a recursive approach that we have recently introduced is applied to the study of the percolation of particles of different sizes and shapes, without the presence of a polymer matrix, on a lattice in various phases including metastable states. In our approach, the original lattice is replaced by a recursive structure on which calculations are done exactly and interactions as well as size and shape disparities are easily taken into account. In the previous paper of this series, we introduced the recursive approach and showed how correlations among particles of the same size can affect percolation. Before considering the complete system made of particles of various sizes and shapes embedded in a polymer matrix, in the third paper of the series, we describe here the properties of systems made of particles without any matrix. The approach appears to be extremely successful since it is able to capture most of the important features observed in experiments.