Stability Against the Odds: The Case of Chromonic Liquid Crystals

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作者
Silvia Paparini
Epifanio G. Virga
机构
[1] Università di Pavia,Dipartimento di Matematica
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Chromonic liquid crystals; Local stability; Frank’s free-energy functional; Ericksen’s inequalities; Elastic frustration;
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摘要
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.
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