Effect of Nanowire Size Dispersity and Orientation on Electrical Conductivity in Polymer Nanocomposites

We model the percolation threshold ($\phi _{c})$ and electrical conductivity of isotropic and oriented three-dimensional networks containing finite, conductive cylinders with experimentally typical (Gaussian) and engineered (bidisperse) distributions in their length and/or diameter. Our results show that narrow Gaussian distributions do not affect the threshold concentration or electrical conductivity significantly in either isotropic or oriented networks. In contrast, the addition of a small fraction of longer rods in a bidisperse system can improve the electrical properties considerably. We have also successfully extended the excluded volume percolation theory to predict $\phi _{c}$ of polydisperse networks of soft-core rods with finite-L/D by generalizing the monodisperse case and applying an empirical calibration factor from our simulations. Our analytical expression finds the critical concentration in nanocomposites with arbitrary distributions in L and/or D.