Equilibrium state of a cylindrical particle with flat ends in nematic liquid crystals

TL;DR

This study uses continuum theory to analyze how the equilibrium orientation and defect structures of cylindrical particles in nematic liquid crystals depend on aspect ratio and size, revealing size-dependent alignment behaviors.

Contribution

It provides a detailed numerical investigation of the size and shape effects on the equilibrium states of cylindrical colloids in nematics, including defect structure analysis.

Findings

Large particles have a specific asymptotic equilibrium angle for each aspect ratio.

Nanoscale particles with aspect ratio >1:1 tend to align parallel to the nematic director.

Nanoscale particles with aspect ratio ≤1:1 tend to align perpendicular to the nematic director.

Abstract

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect ratios of this colloidal geometry from thin discotic to long rod-like shapes and several colloidal length scales ranging from mesoscale to nanoscale are investigated. We show that the equilibrium state of this colloidal geometry is sensitive to the two geometrical parameters: aspect ratio and length scale of the particle. For a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. Upon reducing the particle size to nanoscale, the equilibrium angle follows a descending or ascending trend in such a way that the equilibrium angle of a particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a parallel alignment with respect to the far field nematic, whereas the equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a rod-like particle) tends toward a perpendicular alignment to the uniform nematic direction. The discrepancy between the equilibrium angles of the mesoscopic and nanoscopic particles originates from the significant differences between their defect structures. The possible defect structures related to mesoscopic and nanoscopic colloidal particles of this geometry are also introduced.