Clustering and percolation in assemblies of anisotropic particles: Perturbation theory and Monte Carlo simulation

We present a theoretical approach for describing clustering and percolation phenomena in an assembly of nonspherical particles. The theory is based upon calculations of an orientation-dependent pair connectedness function. We show how this function may be approximated using a perturbation expansion in which the reference system is an assembly of spherical particles. The reference system is treated via the connectivity Ornstein-Zernike equation in the Percus-Yevick approximation. Although such an approach might appear to be limited to particles of small anisotropy, we find that as the particle anisotropy increases, the regime of interest (i.e., densities below percolation) moves to lower densities where the theory is increasingly accurate. Results are presented for systems of randomly distributed ellipsoids with aspect ratios varying from unity to 5:1 and are compared with Monte Carlo simulations. The approach successfully describes the pair connectedness function, mean cluster size, and percolation threshold. In principle, the formalism is capable of describing the connectivity of randomly distributed particle systems over a wide range of particle anisotropy, including the limiting cases of randomly distributed spheres and infinitely extended rods.