Quasiuniversal Connectedness Percolation of Polydisperse Rod Systems

Abstract

The connectedness percolation threshold (ηc) and critical coordination number (Zc) of systems of penetrable spherocylinders characterized by a length polydispersity are studied by way of Monte Carlo simulations for several aspect ratio distributions. We find that (i) ηc is a nearly universal function of the weight-averaged aspect ratio, with an approximate inverse dependence that extends to aspect ratios that are well below the slender rod limit and (ii) that percolation of impenetrable spherocylinders displays a similar quasiuniversal behavior. For systems with a sufficiently high degree of polydispersity, we find that Zc can become smaller than unity, in analogy with observations reported for generalized and complex networks.