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

We present a three-dimensional simulation of electrical conductivity in isotropic, polydisperse rod networks from which we determine the percolation threshold (φc). Existing analytical models that account for size dispersity are formulated in the slender-rod limit and are less accurate for predicting φc 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 φc of polydisperse rod networks that is quantitatively accurate across the entire $L/D$ range.