Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids

We report Monte Carlo simulations of systems of polydisperse prolate and oblate ellipsoids using the critical path based tunneling-percolation model. For polydisperse prolate ellipsoids, the critical percolation volume fraction πc is shown to have a quasi-universal dependence on weight-averaged aspect ratio. For polydisperse oblate ellipsoids, πc is shown to have a quasi-universal dependence on the apparent aspect ratio, which is a function of up to fourth moment of the size distribution, as given by the generalized connectedness percolation theory. The functions are observed to approach the theoretical predictions for higher volume fractions and higher aspect ratios. The model predictions are compared with experimental data available on polydisperse multi-walled nanotubes (prolate ellipsoids) and graphene nanoplatelets (oblate ellipsoids) to estimate the tunneling lengthscale which is found to be well within the expected range.