Frank elasticity of composite colloidal nematics with anti-nematic order

TL;DR

This paper derives scaling laws for the elastic moduli of composite nematic liquid crystals with anti-nematic order, revealing how particle shape and concentration influence their elastic properties.

Contribution

It introduces explicit scaling expressions for elastic moduli in composite nematics with anti-nematic order, considering particle shape and surface anchoring effects.

Findings

Elastic moduli scale logarithmically with anti-nematic order degree.

Bend-splay ratio is significantly higher in anti-nematic discotic nematics.

Elastic properties depend strongly on particle shape and surface anchoring.

Abstract

Mixing colloid shapes with distinctly different anisotropy generates composite nematics in which the order of the individual components can be fundamentally different. In colloidal rod-disk mixtures or hybrid nematics composed of anisotropic colloids immersed in a thermotropic liquid crystal, one of the components may adopt so-called anti-nematic order while the other exhibits conventional nematic alignment. Focussing on simple models for hard rods and disks, we employ Onsager-Straley's second-virial theory to derive scaling expressions for the elastic moduli of rods and disks in both nematic and anti-nematic configurations and identify their explicit dependence on particle concentration and shape. We demonstrate that the splay, bend and twist elasticity of anti-nematically ordered particles scale logarithmically with the degree of anti-nematic order, with the bend-splay ratio for anti-nematic discotic nematics being far greater than for conventional nematic systems. The impact of surface anchoring on the elastic properties of hybrid nematics will also be discussed in detail. We further demonstrate that the elasticity of mixed uniaxial rod-disk nematics depends exquisitely on the shape of the components and we provide simple scaling expressions that could help engineer the elastic properties of composite nematic liquid crystals.