Stability Against the Odds: The Case of Chromonic Liquid Crystals

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 in Frank's elastic free energy.

Automated summary

Recent experiments have shown that the ground state of chromonic liquid crystals is twisted rather than uniform, leading to a violation of Ericksen's inequality within the classical elastic theory of Frank. Despite this violation potentially making Frank's elastic free-energy functional unbounded below, researchers have determined that the twisted ground state can be locally stable, with specific boundary conditions and a derived formula for the second variation in Frank's elastic free energy playing key roles in this conclusion.