Mathematical Modelling of Exotic Liquid Crystalline Phases

液晶是一种有趣的物质状态，具有长程取向有序性但没有位置有序性。因此，这些材料可以像液体一样流动，但同时保持对其取向顺序变形的滞弹性、类似固体的响应。预计到2023年，液晶产业的价值将超过1900亿美元，但其背后的技术仍然在很大程度上依赖于向列相，向列相是由Leslie，Ericksen和DeGennes等人最先研究的。在20世纪60年代，液晶中常见的向列相是由棒状分子形成的。在高温下，分子的取向是完全随机的[这被称为各向同性相，见图1(A)左侧]。另一方面，在低温下，分子倾向于沿着一些自发断裂的方向排列[这被称为向列相，见图1(A)右侧]。下面的YouTube视频，由我的学生制作：https://www.youtube.com/watch?v=dzS7-ddZAzQ演示了一个简单的各向同性-向列型相变，只使用了一个气体打火机和一个笔记本电脑屏幕

Liquid crystals are an interesting state of matter with long-range orientational order but withoutpositional order. Consequently these materials can flow like liquids but at the same time, retain anelastic, solid-like response to deformations in their orientational order. The liquid crystal industryis expected to be worth more than 190 billions US dollars by 2023, and yet the technology behindit still relies largely on the nematic phase which was first studied by Leslie, Ericksen and deGennes et al. in the 1960's.The usual nematic phase in liquid crystals is formed by rod-shaped molecules. At hightemperature, the molecules' orientations are completely random [this is called the isotropic phase,see Fig. 1(a) left]. On the other hand at low temperature, the molecules tend to align along somespontaneously broken direction [this is called the nematic phase, see Fig. 1(a) right]. The followingyoutube video, by my student: https://www.youtube.com/watch?v=dzS7-ddZAzQ demonstrates asimple isotropic-nematic phase transition using just a gas lighter and a laptop screen