Computational studies of 3D self-assembly of nematic colloids

向列型胶体是由分散在向列型液晶基质中的胶体颗粒组成的混合软物质体系。胶体包裹体局部扰动向列相有序化，在向列相介质中引起能量上不利的扭曲和拓扑缺陷。该系统通过共享代价高昂的扭曲来最小化自由能的驱动，赋予胶体颗粒高度各向异性、弹性中介的相互作用，这种相互作用可以用多极膨胀来描述。近年来，向列型胶体已经成为一类极具吸引力的胶体自组装材料，具有丰富的拓扑设计平台，有望扩展已有的“胶体原子”模式。尽管如此，向列型胶体自组装的研究主要集中在实现二维晶体结构上，对其在三维中的相行为知之甚少。为了解决这一知识缺口，我们开发了一个计算框架，用于预测球形向列相胶体的晶体结构并研究其在3D中的相行为，使用有效的对势，该对势从多极近似下屏蔽的静电斥力和弹性介导的相互作用中获得贡献。本文将描述这一计算框架的发展，并提供案例研究，以报告当有效对势被调谐时的新的相行为。在某些情况下，将介绍对晶体结构如何自组装的见解。

Nematic colloids are a hybrid soft-matter system consisting of colloidal particles dispersed in a nematic liquid-crystalline host. Colloidal inclusions, which locally perturb nematic ordering, induce energetically unfavourable distortions and topological defects in the nematic medium. The system's drive to minimise free energy via the sharing of costly distortions endow the colloidal particles with highly anisotropic, elasticity-mediated interactions, which can be described in terms of a multipole expansion. In recent years, nematic colloids have emerged as an attractive class of building blocks for colloidal self-assembly with a rich playground for topological design, promising to extend the well-established `colloidal atom' paradigm.Despite this promise, studies of self-assembly of nematic colloids have largely focused on realising crystal structures in 2D, and a little is known about their phase behaviour in 3D. To address this knowledge gap, we have developed a computational framework for predicting crystal structures for spherical nematic colloids and studying their phase behaviour in 3D, using an effective pair potential that draws contributions from screened electrostatic repulsion and elasticity-mediated interactions under the multipolar approximation. The thesis will describe the development of this computational framework and present case studies to report novel phase behaviour as the effective pair potential is tuned. In certain cases, insight into how the crystal structures are self-assembled will be presented.