Bethe lattice model with site and bond correlations for continuum percolation by isotropic systems of monodisperse rods

A model for connectedness percolation in isotropic systems of monodisperse cylinders is developed that employs a generalization of the tree-like Bethe lattice. The traditional Bethe lattice is generalized by incorporating (within a heuristic, mean-field framework) a pair of correlation parameters that describe (i) the states of occupancy of neighboring sites and (ii) the states of directly adjacent bonds, which are also allowed to be in either of two possible states. Averaging over the fluctuating states of neighboring bonds provides an operational means to modulate the dependence upon volume fraction of the average number of next-nearest-neighbor rod-rod contacts without altering the number of such nearest-neighbor interparticle contacts. The percolation threshold is shown to be a sensitive function of the average number of such next-nearest-neighbor contacts, and therefore of the quality of dispersion of the particles.