Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects

TL;DR

This study investigates how polydispersity affects percolation thresholds in suspensions of hard rods, revealing quasi-universal behavior dependent mainly on certain distribution cumulants, supported by Monte Carlo simulations and an improved theoretical model.

Contribution

It introduces a connectedness percolation theory that predicts exact universality and demonstrates quasi-universal behavior in polydisperse rod suspensions through simulations.

Findings

Percolation threshold depends mainly on distribution cumulants.

Theory and simulations agree for aspect ratios >20.

Cluster growth mechanisms differ between length and width polydispersity.

Abstract

We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the connectedness criterion, and invoke bimodal, Gaussian and Weibull distributions for these. The main finding from our simulations is that the percolation threshold shows quasi universal behaviour, i.e., to a good approximation it depends only on certain cumulants of the full size and connectivity distribution. Our connectedness percolation theory hinges on a Lee-Parsons type of closure recently put forward that improves upon the often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660]. The theory predicts exact universality. Theory and simulation agree quantitatively for aspect ratios in excess of 20, if we include the connectivity range in our definition of the aspect ratio of the particles. We further discuss the mechanism of cluster growth that, remarkably, differs between systems that are polydisperse in length and in width, and exhibits non-universal aspects.