Connectedness percolation in polydisperse rod systems: A modified Bethe lattice approach

A mean-field theory is presented for the percolation behavior of systems of rodlike particles characterized by length polydispersity. An analogy to the problem of site percolation on a modified Bethe lattice is employed to estimate the percolation threshold, percolation probability, and backbone fraction as functions of the rod volume fraction and polydispersity. Model calculations reveal that the percolation probability and backbone fraction depend sensitively upon the rod length distribution, while the percolation threshold is governed primarily by the weight-averaged rod length.