Nematic Tactoid Population

TL;DR

This paper investigates the equilibrium shapes of nematic tactoids, revealing how their prevalence depends on volume and saddle-splay constant, using a novel class of bipolar droplet solutions.

Contribution

It introduces a new class of admissible shapes for nematic droplets, providing insights into shape prevalence influenced by volume and material constants.

Findings

Tactoids are more prevalent at small volumes and low saddle-splay constants.

The novel shape class uncovers a different role of the saddle-splay constant compared to previous models.

Shape prevalence depends on volume and material parameters, with specific conditions favoring tactoids.

Abstract

Tactoids are pointed, spindle-like droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a novel class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primarily among them). We show how the prevalence of a shape is affected by the drop's volume $V_0$ and the saddle-splay constant $K_{24}$ of the material. Tactoids, in particular, prevail for small $V_0$ and small $K_{24}$ (appropriately scaled). Our class of shapes (and director fields) is sufficiently different from those employed so far to unveil a rather different role of $K_{24}$.