Violation of Ericksen Inequalities in Lyotropic Chromonic Liquid Crystals

Cheng, Ling; Selinger, Jonathan V.

doi:10.1007/s10659-022-09899-z

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…Very recently, such a violation has also been investigated in Long and Selinger (2022), which proposed that the pure (double) twist mode that would characterize the ground state of chromonics, 18 being non-uniform and so unable to fill space (Virga 2019) prompts the excitation of other elastic modes whose positive cost counterbalances the divergence to negative infinity of the total free energy. Here, concerned as we were by tackling a variational problem with indefinite energy, we gave a different, but complementary explanation.…”

Section: Discussionmentioning

confidence: 99%

Stability Against the Odds: The Case of Chromonic Liquid Crystals

Paparini

Virga

2022

J Nonlinear Sci

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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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Section: Discussionmentioning

confidence: 99%

Stability Against the Odds: The Case of Chromonic Liquid Crystals

Paparini

Virga

2022

J Nonlinear Sci

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“…10,12 Some recent studies have shown that the inequality ( K 22 − K 24 ) > 0 can be violated in lyotropic chromonic liquid crystals. 13–15 However, to our knowledge, there are no reports of liquid crystals violating the Ericksen inequality K 24 > 0. Indeed, any violation of that inequality would lead to a peculiar liquid crystal with a spontaneous Δ deformation.…”

Section: Optimum Local Deformationmentioning

confidence: 94%

“…In this limit, the Ericksen inequality K 22 − K 24 > 0 is violated, and the liquid crystal is at a critical point for the formation of spontaneous double twist, as discussed in ref. 15. At the critical point, it has a divergent susceptibility to q 0 , which might be regarded as a applied chiral field.…”

Section: Chiral Liquid Crystal In a Cylindermentioning

confidence: 99%

Explicit demonstration of geometric frustration in chiral liquid crystals

Cheng

Selinger

2023

Soft Matter

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An Elastic Quartic Twist Theory for Chromonic Liquid Crystals

Paparini

Virga

2023

J Elast

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Chromonic liquid crystals are lyotropic materials which are attracting growing interest for their adaptability 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 (Paparini and Virga in Phys. 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 "Equation missing" in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate "Equation missing".

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Violation of Ericksen Inequalities in Lyotropic Chromonic Liquid Crystals

Cited by 8 publications

References 26 publications

Stability Against the Odds: The Case of Chromonic Liquid Crystals

Stability Against the Odds: The Case of Chromonic Liquid Crystals

Explicit demonstration of geometric frustration in chiral liquid crystals

An Elastic Quartic Twist Theory for Chromonic Liquid Crystals

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