An Elastic Quartic Twist Theory for Chromonic Liquid Crystals

TL;DR

This paper introduces a new elastic theory for chromonic liquid crystals by adding a quartic twist term to the classical model, ensuring bounded energy and resolving paradoxes in free-boundary problems.

Contribution

It proposes a novel quartic twist extension to the Oseen-Frank theory, addressing stability issues and boundedness of energy in chromonic liquid crystals.

Findings

The quartic twist term bounds the total energy of droplets.

The phenomenological length scale $a$ influences equilibrium configurations.

Experimental data allows estimation of the length scale $a$.

Abstract

Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adapatbility to living systems. To describe their elastic properties, the classical Oseen-Frank theory requires anomalously small twist constants and (comparatively) large saddle-splay constants, so large as to violate one of Ericksen's inequalities, which guarantee that the Oseen-Frank stored-energy density is bounded below. While such a violation does not prevent the existence and stability of equilibrium distortions in problems with fixed geometric confinement, the study of free-boundary problems for droplets has revealed a number of paradoxical consequences. Minimizing sequences driving the total energy to negative infinity have been constructed by employing ever growing needle-shaped tactoids incorporating a diverging twist [Phy. Rev. E 106, 044703 (2022)]. To overcome these difficulties, we propose here a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term. We show that the total energy of droplets is bounded below in the quartic twist theory, so that the known paradoxes are ruled out. The quartic term introduces a phenomenological length $a$ in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate $a$.