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The preparation of many composites requires the intermixing of severalmacromolecular fluids along with the addition of solid filler particles. Thesefillers are usuallly polydisperse and there is an extensive experimentalevidence that their size and shape profoundly affects the properties of theresulting material. In particular, it is generally found that the percolationthreshold decreases as the size disparity between the different particlespresent in a system increases and that the threshold decreases with the aspectratio of the particles. Here a recursive approach that we have recentlyintroduced is applied to the study of the percolation of particles of differentsizes and shapes, without the presence of a polymer matrix, on a lattice invarious phases including metastable states. In our approach the originallattice is replaced by a recursive structure on which calculations are doneexactly and interactions as well as size and shape disparities can be easilytaken into account In the previous paper we have introduced the recursiveapproach and shown how correlations among particles of the same size can affectpercolation. Before considering the complete system made of particles ofvarious sizes and shapes embedded in a polymer matrix here we describe theproperties of systems made of particles without any matrix. The approachappears to be extremely successful since it is able to capture most of theimportant features observed in experiments.Comment: Submitted to Physical Review

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