Percolation of particles on recursive lattices: (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 solid filler particles. These fillers are usuallly polydisperse and there is an extensive experimental evidence that their size and shape profoundly affects 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 the 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 can be easily taken into account In the previous paper we have introduced the recursive approach and shown 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 here we describe 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. 
Andrea Corsi and P. D. Gujrati (The Department of Physics and The   Department of Polymer Science, The University of Akron)