Geometric percolation of hard nanorods: the interplay of spontaneous and externally induced uniaxial particle alignment

TL;DR

This study uses numerical methods to explore how external fields and spontaneous alignment influence nanoparticle network formation in liquid dispersions, revealing complex re-entrance phenomena and the importance of connectivity length.

Contribution

It introduces a combined continuum percolation and Onsager theory approach to analyze the effects of external alignment on percolation in nanorod dispersions, highlighting the role of connectivity length.

Findings

Percolation islands depend on connectivity length.

External fields can cause multiple network formation and breakdown.

Re-entrance effects occur with increasing particle density.

Abstract

We present a numerical study on geometric percolation in liquid dispersions of hard slender colloidal particles subjected to an external orienting field. In the formulation and liquid-state processing of nanocomposite materials, the alignment of particles by external fields such as electric, magnetic or flow fields is practically inevitable, and often works against the emergence of large nanoparticle networks. Using continuum percolation theory in conjunction with Onsager theory, we investigate how the interplay between externally induced alignment and the spontaneous symmetry breaking of the uniaxial nematic phase affects cluster formation within nanoparticle dispersions. It is known that the enhancement of particle alignment by means of a density increase or an external field may result in the breakdown of an already percolating network. As a result, percolation can be limited to a small region of the phase diagram only. Here, we demonstrate that the existence and shape of such a "percolation island" in the phase diagram crucially depends on the connectivity length -- a critical distance defining direct connections between neighbouring particles. Deformations of this percolation island can lead to peculiar re-entrance effects, in which a system-spanning network forms and breaks down multiple times with increasing particle density.