标题： 关于染料液晶现象学模型的综述 显示英文标题

标题： A Review on Phenomenological Models for Chromonic Liquid Crystals

摘要： 液晶（CLCs）是溶致材料，由于其对生命系统的适应性而受到越来越多的关注。 大量工作已经致力于探索它们的特性和应用。 在本文中，我努力回顾一些关于其理论建模的贡献，旨在合理解释实验观察结果。 CLCs的弹性理论尚未完全建立。 它们在三维空间中的基态，如最近的一些实验所揭示的，与普通向列相液晶的基态有很大不同：它是扭曲的而不是均匀的。 在经典的Oseen-Frank弹性理论中，对此状态的常见解释要求违反一个Ericksen不等式。 由于这种违反会使Oseen-Frank存储能密度无界地下降，这些理论处理的合法性受到一系列数学问题的威胁。 为了克服这些困难，已经为CLCs提出并测试了一种新的弹性理论；它通过引入一个四次扭曲项来扩展经典的Oseen-Frank能量。 CLCs的另一个关键特性是它们表现出宽广的双相区域，在这些区域中，向列相和各向同性相共存。 基于实验设置的数学模型已被开发用于二维的CLC液滴。 这里回顾的贡献涉及相变过程中核和拓扑缺陷的形态发生，由向列弹性常数相互作用引起的拓扑形状变换，以及形状双稳态的预测（尚未被观察到），其中 tactoids 和光滑边缘的盘状物可以处于平衡共存。 通用方法也已应用于实验数据，以提取各向同性界面处的各向同性表面张力和chromonics的平面锚定强度的估计值。 显示英文摘要

摘要： 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.