Unusual geometric percolation of hard nanorods in the uniaxial nematic liquid crystalline phase

TL;DR

This study explores how uniaxial symmetry breaking in dispersions of hard nanorods influences geometric percolation, revealing non-intuitive behaviors such as loss and re-entrance of percolation with increasing particle density, supported by simulations and theory.

Contribution

It introduces a new closure for the connectedness Ornstein-Zernike equation, improving the understanding of percolation in nematic phases of hard nanorods.

Findings

Percolation can be lost in the nematic phase for aspect ratios over twenty.

Re-entrance behavior of percolation occurs between certain aspect ratios.

Simulation results strongly support the theoretical predictions.

Abstract

We investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rod-like particles. If the particle aspect ratio exceeds about twenty, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition of particles always aids percolation. For aspect ratios between twenty and infinity, but not including infinity, we find re-entrance behavior: percolation in the low-density nematic may be lost upon increasing the amount of nanofillers but can be re-gained by the addition of even more particles to the suspension. Our simulation results for aspect ratios of 5, 10, 20, 50 and 100 strongly support our theoretical predictions, with almost quantitative agreement. We show that a new closure of the connectedness Ornstein-Zernike equation, inspired by Scaled Particle Theory, is more accurate than the Lee-Parsons closure that effectively describes the impact of many-body direct contacts.