Stability Against the Odds: the Case of Chromonic Liquid Crystals

TL;DR

This paper investigates the stability of twisted ground states in chromonic liquid crystals, demonstrating that such states can be locally stable despite violations of classical elastic inequalities, due to boundary conditions and derived stability formulas.

Contribution

It provides a theoretical analysis showing the local stability of twisted states in chromonic liquid crystals, challenging previous assumptions about elastic inequality violations.

Findings

Twisted ground states can be locally stable in chromonic liquid crystals.

Boundary conditions significantly influence the stability of these states.

A new formula for the second variation of Frank's elastic free energy is derived.

Abstract

The ground state of chromonic liquid crystals, as revealed by a number of recent experiments, is quite different from that of ordinary nematic liquid crystals: it is twisted instead of uniform. The common explanation provided for this state within the classical elastic theory of Frank demands that one Ericksen's inequality is violated. Since in general such a violation makes Frank's elastic free-energy functional unbounded below, the question arises as to whether the twisted ground state can be locally stable. We answer this question in the affirmative. In reaching this conclusion, a central role is played by the specific boundary conditions imposed in the experiments on the boundary of rigid containers and by a general formula that we derive here for the second variation of Frank's elastic free energy.