A review on phenomenological models for chromonic liquid crystals

Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. This paper reviews some of the contributions concerning their theoretical modelling, aimed at rationalising experiments. The elastic theory of CLCs is not completely established. Their ground state in $3D$3D space, as revealed by a number of recent experiments, is twisted instead of uniform, differently form ordinary nematics. The common explanation provided for this state within the classical Frank elastic theory demands that one Ericksen's inequality is violated, thus making the Frank stored-energy density unbounded below; the legitimacy of these theoretical treatments is threatened by mathematical issues. To overcome these difficulties, a novel elastic theory has been proposed and tested for CLCs; it extends the Frank energy by incorporating a quartic twist term. CLCs exhibit broad biphasic regions, and mathematical models inspired by experimental settings have been developed for CLC droplets in 2D dimensions; they address the morphogenesis of nuclei and topological defects during phase transitions, topological shape transformations, and the prediction of shape bistability. General methods have been applied to experimental data to extract estimates of isotropic-surface tension and chromonics' anchoring strength.