Simulations and generalized model of the effect of filler size dispersity on electrical percolation in rod networks

Abstract

We present a three-dimensional simulation of electrical conductivity in isotropic, polydisperse rod networks from which we determine the percolation threshold (ϕ[subscript c]). Existing analytical models that account for size dispersity are formulated in the slender-rod limit and are less accurate for predicting ϕ[subscript c] in composites with rods of modest L/D. Using empirical approximations from our simulation data, we generalized the excluded volume percolation model to account for both finite L/D and size dispersity, providing a solution for ϕ[subscript c] of polydisperse rod networks that is quantitatively accurate across the entire L/D range.