Connectedness percolation of hard convex polygonal rods and platelets

TL;DR

This paper analyzes how the shape of convex particles, like polygonal rods and platelets, influences the percolation threshold in polymer composites, revealing that fewer sides lower the threshold due to surface area effects.

Contribution

It introduces an analytical method to compute the percolation threshold based on particle shape, extending understanding beyond idealized models.

Findings

Fewer sides in polygonal particles lower the percolation threshold.

Surface area to volume ratio increases as the number of sides decreases.

Universal scaling of the percolation threshold is affected by particle shape.

Abstract

The properties of polymer composites with nanofiller particles change drastically above a critical filler density known as the percolation threshold. Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not idealized disks and rods but are often modeled as such. Here we investigate the effect of the shape of the particle cross section on the geometric percolation threshold. Using connectedness percolation theory and the second-virial approximation, we analytically calculate the percolation threshold of hard convex particles in terms of three single-particle measures. We apply this method to polygonal rods and platelets and find that the universal scaling of the percolation threshold is lowered by decreasing the number of sides of the particle cross section. This is caused by the increase of the surface area to volume ratio with decreasing number of sides.