Large Scale Lattice-Boltzmann Simulation of Liquid Crystals

在简单的流体中，原子或分子是无序的，可以自由流动。在晶体中，它们排列在晶格上，不能相互移动，形成一种坚硬的材料。液晶介于两者之间：它们在某种意义上是有序的，在其他意义上是无序的。一个例子是，当一块肥皂留在一小块水中时，你会看到一团黏糊糊的烂摊子：这是一种近晶液晶，其中的分子堆积成几层。每一层都在晶体堆叠中与下一层对齐，但在层所在的平面中，材料是流体。这就是为什么它有“粘糊糊”的感觉的原因。粘稠度可以通过测量材料的“流变性”来量化。(流变学是研究流动行为的科学。)液晶包括许多用于笔记本电脑显示器、平板电视和其他设备的高科技材料。在许多这样的设备中，材料的流动(例如对电场的响应)是设备工作或不工作的一部分。其中许多器件使用向列型液晶，其中棒状分子沿相同方向排列，但不在晶格上；其他器件使用结构更为复杂的胆甾型或(潜在)蓝相液晶。出于科学和技术原因，正确理解液晶对应力和/或电场或磁场的响应非常重要。这是一项非常困难的任务，原因有两个。首先，需要考虑复杂的偏序结构。其次，这种结构在实际材料中由于所谓的“缺陷”的存在而变得更加复杂。这些缺陷是非常特殊的类型，在每种类型的液晶中是不同的。对于向列相来说，缺陷是奇怪的蠕虫状结构。(事实上，这个名字来自希腊语中蠕虫的意思。)在最简单的情况下，可以用笔和纸来求解描述纯液晶流动的方程，但当存在缺陷时，这几乎总是不可能的。该项目的目的是开发和使用在超大型计算机上求解相关方程的方法。只有最大的计算机才能提供解决缺陷问题所需的高分辨率研究，因为这些是延伸的物体，与分子规模相比更大。这项工作包括将简化方程本身的技能(删除描述中所有不必要的细节)与如何让大型计算机高效地求解此类方程的深入知识相结合。对于每种类型的液晶，我们计划既解决缺陷影响流动行为的方式，也解决流动影响缺陷组织的方式。这一影响圈导致了在实验室中看到的相当复杂的行为，如果了解的话，可能会在下一代液晶技术中被利用。

In simple fluids, the atoms or molecules are disordered and can flow freely. In a crystal, they are arranged on a lattice, and cannot move past one another, creating a rigid material. Liquid crystals are in between: they are ordered in some senses and disordered in others. An example is the slimy mess you get when a bar of soap is left in a patch of water: this is a 'smectic' liquid crystal, in which the molecules pack into layers. Each layer lines up with the next in a crystalline stack, but in the plane of the layers the material is fluid. This is responsible for its 'slimy' feel. The sliminess can be quantified by measuring the material's 'rheology'. (Rheology is the science of flow behaviour.) Liquid crystals include many high tech materials used in laptop displays, flat-screen TVs, and other devices. In many of these devices, the flow of the material (for example in response to an electric field) is part of what makes the device work or not work. Many of these devices use 'nematic' liquid crystals in which rod-shaped molecules are lined up in the same direction but are not on a lattice; others involve 'cholesteric' or (potentially) 'blue phase' liquid crystals whose structure is more complex.For both scientific and technological reasons it is very important to understand properly the flow of liquid crystals in response to stresses and/or electric or magnetic fields. This is a very difficult task for two reasons. Firstly, there is the complicated, partially ordered structure to consider. Secondly, this structure is made even more complex in real materials by the presence of so-called 'defects'. These defects are of quite specific types, different in each type of liquid crystal. For nematics the defects are strange worm-like structures. (In fact, the name 'nematic' comes from the greek word for a worm.) In the simplest cases it is possible to solve using pen and paper the equations that describe the flow of pure liquid crystals, but when defects are present this is almost always impossible. The aim of the project is to develop and use methods for solving the relevant equations on very large computers. Only the biggest computers can provide the high resolution studies needed to address the problem of defects, since these are extended objects, large compared to the molecular scale. The work involves combining skill in simplifying the equations themselves (removing all inessential details from the description) with in-depth knowledge of how to make large computers solve such equations efficiently. For each type of liquid crystal, we plan to address both the way defects influence the flow behaviour, and the way a flow affects the organization of defects. This circle of influence is responsible for quite complex behaviour that is seen in the laboratory and, if understood, might be exploited in the next generation of liquid crystal technologies.