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Abstract

Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. A considerable body of works has been devoted to exploring their properties and applications. In this paper, I endeavour to review some of the contributions concerning their theoretical modelling, aimed at rationalizing experimental observations. The elastic theory of CLCs is not completely established. Their ground state in the 3D space, 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 Oseen-Frank elastic theory demands that one Ericksen's inequality is violated. Since such a violation would make the Oseen-Frank stored energy density unbounded below, the legitimacy of these theoretical treatments is threatened by a number of mathematical issues. To overcome these difficulties, a novel elastic theory has been proposed and tested for CLCs; it extends the classical Oseen-Frank energy by incorporating a quartic twist term. Another key characteristic of CLCs is that they exhibit broad biphasic regions, in which the nematic and isotropic phases coexist. Mathematical models inspired by experimental settings have been developed for CLC droplets in 2D. The contributions reviewed here address the morphogenesis of nuclei and topological defects during phase transitions, the topological shape transformations arising from the interplay of nematic elastic constants, and the prediction of shape bistability (yet to be observed) where tactoids and smooth-edged discoids can coexist in equilibrium. General methods have also been applied to experimental data to extract estimates of the isotropic surface tension at the nematic isotropic interface and the chromonics' planar anchoring strength.