A Monte Carlo simulation model for the random packing of unequal spherical particles is presented in this paper. With this model, the particle radii obeying a given distribution are generated and randomly placed within a cubic packing domain with high packing density and many overlaps. Then a relaxation iteration is applied to reduce or eliminate the overlaps, while the packing space is gradually expanded. The simulation is completed once the mean overlap value falls below a preset value. To simulate the random close packing, a "vibration" process is applied after the relaxation iteration. For log-normal distributed particles, the effect of particle size standard deviation, and for bidisperse particles, the effects of particle size ratio and the volume fraction of large particles on packing density and on coordination number are investigated. Simulation results show good agreement with that obtained by experiments and by other simulations. The randomness, homogeneity, and isotropy, which have not been evaluated before for packing of distributed particles, are also examined using statistical measures.

In this paper, we apply Monte Carlo simulation to investigate the conductive percolation threshold of granular composite of conductive and insulating powders with amorphous structure. We focus on the effect of insulating to conductive particle size ratio λ = di/dc on the conducting percolation threshold pc (the volume fraction of the conductive powder). Simulation results show that, for λ = 1, the percolation threshold pc lies between simple cubic and body centred cubic site percolation thresholds, and that as λ increases the percolation threshold decreases. We also use the structural information obtained by the simulation to study the nonlinear current–voltage characteristics of composite with solid volume fraction of conductive powder below pc in terms of electron tunnelling for nanoscale powders, dielectric breakdown for microscale or larger powders, and pressing induced conduction for non-rigid insulating powders.

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