Abstract

Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. To describe their elastic properties, the classical Oseen-Frank theory, which posits a stored energy quadratic in the gradient of the director filed n, 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 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. A CLC droplet tactoidal in shape is predicted by the classical theory to be unstable against shape changes: it would split indefinitely in smaller tactoids while the total energy plummets to negative infinity. To overcome these difficulties, a novel elastic theory that extends for chromonics the classical Oseen-Frank stored energy by adding a quartic twist term has been proposed. The total energy of droplets is bounded below in the quartic twist theory, and paradoxes evaporate. The aim of this talk is to identify a means to differentiate these theories both qualitatively and quantitatively on the basis of the different structures they predict when CLCs are confined to fixed spherical cavities with homeotropic anchoring.Co-Author: Epifanio G. Virga.