Quasiuniversal connectedness percolation of polydisperse rod systems

TL;DR

This study investigates how the percolation threshold and critical coordination number in polydisperse rod systems depend on aspect ratio distributions, revealing near-universal behaviors and novel network-like properties.

Contribution

It introduces a comprehensive Monte Carlo simulation analysis of polydisperse spherocylinder systems, highlighting quasiuniversal relationships and the emergence of Z_c below unity in highly polydisperse systems.

Findings

ta_c depends inversely on the weight-averaged aspect ratio.

Percolation exhibits quasiuniversal behavior across distributions.

Z_c can be less than one in highly polydisperse systems.

Abstract

The connectedness percolation threshold (eta_c) and critical coordination number (Z_c) 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) \eta_c 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 Z_c can become smaller than unity, in analogy with observations reported for generalized and complex networks.