A lattice model for connectedness percolation in mixtures of rods and disks

Geometric percolation in mixtures of isotropically oriented rods and disks is examined from the perspective of a tree-like lattice model with a distribution over the co-ordination numbers (or vertex degrees). Correlations between the particle locations are described within a mean-field approximation that employs operationally-defined parameters to characterize pairwise interactions. The percolation threshold is studied as a function of the particle size disparity and the strength of inter-particle correlations. For certain combinations of the particle size ratio and inter-particle interaction strength, the volume fraction at the percolation threshold is found to vary non-monotonically as a function of the composition of the mixture.