Percolation in suspensions of hard nanoparticles: From spheres to needles

TL;DR

This paper develops a new connectedness percolation theory for nanorods with various aspect ratios, accurately predicting percolation thresholds and revealing deviations from traditional inverse aspect ratio scaling, especially for finite slenderness.

Contribution

A novel version of connectedness percolation theory is introduced and validated against Monte Carlo simulations, improving understanding of percolation in nanorod suspensions across a wide aspect ratio range.

Findings

Percolation thresholds are accurately predicted for aspect ratios as low as 10.

Deviations from inverse aspect ratio scaling occur for aspect ratios below 1000.

Differences between hard rod and ideal rod thresholds depend on connectivity distance.

Abstract

We investigate geometric percolation and scaling relations in suspensions of nanorods, covering the entire range of aspect ratios from spheres to extremely slender needles. A new version of connectedness percolation theory is introduced and tested against specialized Monte Carlo simulations. The theory accurately predicts percolation thresholds for aspect ratios as low as 10. The percolation threshold for rod-like particles of aspect ratios below 1000 deviates significantly from the inverse aspect ratio scaling prediction, thought to be valid in the limit of infinitely slender rods and often used as a rule of thumb for nano-fibers in composite materials. Hence, most fibers that are currently used as fillers in composite materials cannot be regarded as practically infinitely slender for the purposes of percolation theory. Comparing percolation thresholds of hard rods and new benchmark results for ideal rods, we find that (i) for large aspect ratios, they differ by a factor that is inversely proportional to the connectivity distance between the hard cores, and (ii) they approach the slender rod limit differently.