Percolative properties of hard oblate ellipsoids of revolution with a soft shell

TL;DR

This paper investigates the percolation behavior of random assemblies of oblate ellipsoids with a soft shell, revealing how aspect ratio and interaction distance influence critical volume fractions and providing a volume-based estimation method.

Contribution

It introduces a simple relation based on excluded volume to estimate percolation thresholds across various aspect ratios and interaction distances.

Findings

Critical volume fraction decreases with increasing aspect ratio.

A volume-based relation estimates percolation thresholds effectively.

Excluded volume calculations support the proposed relation.

Abstract

We present an in-depth analysis of the geometrical percolation behavior in the continuum of random assemblies of hard oblate ellipsoids of revolution. Simulations where carried out by considering a broad range of aspect-ratios, from spheres up to aspect-ratio 100 plate-like objects, and with various limiting two particle interaction distances, from 0.05 times the major axis up to 4.0 times the major axis. We confirm the widely reported trend of a consistent lowering of the hard particle critical volume fraction with the increase of the aspect-ratio. Moreover, assimilating the limiting interaction distance to a shell of constant thickness surrounding the ellipsoids, we propose a simple relation based on the total excluded volume of these objects which allows to estimate the critical concentration from a quantity which is quasi-invariant over a large spectrum of limiting interaction distances. Excluded volume and volume quantities are derived explicitly.