An Elastic Quartic Twist Theory for Chromonic Liquid Crystals

• Published in: Journal of elasticity Vol. 155; no. 1-5; pp. 469 - 489
• Main Authors: Paparini, Silvia, Virga, Epifanio G.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.07.2024; Springer Nature B.V
• Subjects: Biomechanics; Capillary tubes; Classical and Continuum Physics; Classical Mechanics; Crystal growth; Droplets; Elastic properties; Engineering; Internal energy; Liquid crystals; Materials Science; Mathematical Applications in the Physical Sciences; Paradoxes; Sequences; Theoretical and Applied Mechanics; Chromonic liquid crystals; Curvature elasticity; Nematic liquid crystals; Quartic free energy; 76A15
• ISSN: 0374-3535; 1573-2681
• DOI: 10.1007/s10659-022-09983-4

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 in the theory; this affects the equilibrium of chromonics confined within capillary tubes. Use of published experimental data allows us to estimate .