Theory and simulation of the cubatic liquid crystalline phase

立方体液晶相是物质的一种最不寻常的状态。分子没有长程位置顺序，但取向呈立方对称。这一相已在截断硬球的模拟中观察到。平均而言，每个粒子以相同的概率沿着x、y或z轴中的一个点。因为这种对称性与其他已知相完全不同，所以这种相的材料性质也会非常不同。然而，在这一阶段几乎没有进行任何研究，因此本建议旨在纠正这种情况。其目的是利用模拟和理论为描述这种奇异物质状态的行为提供科学基础。更详细地说，我们将首先进行蒙特卡罗模拟来绘制截断球体的立方体相位边界。然后，我们将计算立方弹性常数，并知道这些，继续研究非均匀情况，如缺陷的结构，壁附近材料的结构和与胶体球的相互作用。我们将使用立方体弹性理论来解释这些模拟研究，这将与模拟工作一起发展。我们还将首次研究，这个相的动力学性质。利用分子动力学，我们将研究立方输运系数和各种时间相关函数。这些将与Enksog动力学理论计算进行比较。在此之后，我们将研究剪切立方体相的影响，寻找剪切诱导的相变。在平衡状态下，立方体相有向列相、柱状相和结晶相作为近邻，所以人们会期望有大量的流动引起的转变。这项工作的总体目标是产生一系列基础工作，为理解这种未被探索的物质状态的基本特性提供基本框架，

The cubatic liquid crystalline phase is a most extraordinary state of matter. The molecules have no long-range positional order but the orientations exhibit a cubic symmetry. This phase has been observed in the simulation of truncated hard spheres. Each particle points, on average, along one of the x-, y- or z-axes with equal probability. Because this symmetry is completely different from that of other known phases, the material properties of this phase will also be very different. Virtually no research, however, has been carried out on this phase, so this proposal aims to rectify this situation. The aim is to use simulation and theory to provide the scientific foundations for describing the behaviour of this exotic state of matter.In more detail, we will firstly carry out Monte Carlo simulations to map out the boundaries of the cubatic phase for truncated spheres. We will then calculate the cubatic elastic constants and, knowing these, go on to study inhomogeneous situations, such as the structure of defects, the structure of the material near a wall and the interactions with colloidal spheres. We will interpret these simulation studies using cubatic elastic theory, which will be developed in tandem with the simulation work.We will study also, for the first time, the dynamical properties of this phase. Using molecular dynamics, we will look at the cubatic transport coefficients and a variety of time correlation functions. These will be compared with Enksog kinetic theory calculations. After this we will investigate the effects of shearing a cubatic phase, looking for shear induced phase transitions. At equilibrium the cubatic phase has nematic, columnar and crystalline phases as close neightbours, so one would expect a rich crop of flow-induced transitions.The overall aim of this work is to produce a body of fundamental work, giving the basic framework for understanding the fundamental properties of this unexplored state of matter,