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Kinetics and Statistics of Topological Defects in the Phase Ordering of Liquid Crystals

液晶相序拓扑缺陷的动力学和统计

基本信息

批准号：
07640509
负责人：
TOYOKI Hiroyasu
金额：
$ 1.47万
依托单位：
Yamanashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

Equilibrium patterns and those formation process in thin nematic films under hybrid boundary conditions are numerically investigated. The top boundary is homeotropic one where the director is perpendicular to the film and the bittom boundary is homogeneous one where the director is parallel to the film. The surface terms of energy represented by surface integrals in the Frank energy have an important role for forming patterns, thourh those have been neglected in bulk problems. Our present model is an improved cell-dynamical-system model, which does not only includes the surface terms but alsobe able to represent the anisotropy of bulk elastic constants. A main idea is that we do not discretize the Frank energy but does the TDGL equation.The competition between the surface energy and the bulk energy makes periodically modulated patterns. The present simulation shows that periodic pattern is stable above the onset value of the surface constant K_<24>=0.35 and the period is proportional to (K_<24>-K_<13>/2)^<-1> for large K_<24>.The anisotropy due to the lattice affects the direction of the striped pattern. To avoid this unphysical effect, the second nearest interaction must be taken into account.The effect of anisotropic on-site fields at the homogeneous boundary is examined. The unidirectional field makes is found to make string-like Schlieren patterns between a boojum and an antiboojum similar to experimental patterns in films of thickness about 10mum.

数值研究了混合边界条件下向列相薄膜中的平衡模式及其形成过程。顶部边界是同向异性边界，其中导向器垂直于薄膜，而位边界是均匀边界，其中导向器与薄膜平行。在Frank能量中，由表面积分表示的表面能量项对形成图案有重要作用，而这些项在体积问题中被忽略了。我们的模型是一个改进的胞元动力学系统模型，它不仅包括表面项，而且还能够表示体弹性常数的各向异性。其主要思想是，我们不离散Frank能量，而是离散TDGL方程，表面能和体能之间的竞争形成周期性调制图案。模拟结果表明，对于较大的K&lt；24&gt；，周期与(K&lt；24&gt；-13&gt；/2)^&lt；-1&gt；成正比，晶格各向异性影响条纹方向。为了避免这种非物理效应，必须考虑次最近的相互作用。研究了均匀边界上各向异性场强的影响。研究发现，单向磁场可以在Boojum和antibojum之间形成线状纹影图案，类似于厚度约为10微米的薄膜中的实验图案。