Theory and simulation of the cubatic liquid crystalline phase

立方液晶相是物质的一种最特殊的状态。分子没有长程位置有序性，但取向呈现立方对称性。这一阶段已经在截断硬球的模拟中观察到。平均而言，每个粒子沿着x轴、y轴或z轴之一以相等的概率指向。由于这种对称性与其他已知相的对称性完全不同，这种相的材料性质也会有很大的不同。然而，几乎没有人对这一阶段进行研究，所以这项提议旨在纠正这种情况。我们的目的是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相边界。然后，我们将计算立方弹性常数，并在知道这些情况下，继续研究不均匀情况，如缺陷的结构，靠近壁面的材料结构以及与胶体球体的相互作用。我们将使用立方弹性理论来解释这些模拟研究，该理论将与模拟工作一起发展。我们还将首次研究这一阶段的动力学性质。利用分子动力学，我们将研究立方输运系数和各种时间关联函数。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相的影响，寻找剪切诱导的相变。在平衡状态下，立方相有向列相、柱状相和结晶相作为相邻相，因此人们可以预期会有丰富的流动诱导相变。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性质提供基本框架，

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,