Percolation thresholds for rod-like particles: polydispersity effects

A model based upon excluded volume considerations is presented for the connectedness percolation thresholds in polydisperse systems of cylindrical rod-like nanoparticles. The dependence of the percolation threshold upon polydispersity index and number-averaged aspect ratio is examined for two different distribution functions for the rod radii and lengths. The importance of accounting for polydispersity is explored in the context of measurements of the elastic moduli and electrical conductance in fibre-filled nanocomposites