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.

对混合边界条件下向列薄膜中的平衡模式及其形成过程进行了数值研究。顶部边界是垂直边界，其中指向矢垂直于胶片，而下边界是均匀边界，其中指向矢平行于胶片。由弗兰克能量中的表面积分表示的能量的表面项对于形成图案具有重要作用，尽管这些在体问题中被忽略了。我们目前的模型是一种改进的细胞动力系统模型，它不仅包含表面项，而且能够表示体弹性常数的各向异性。主要思想是我们不离散 Frank 能量，而是离散 TDGL 方程。表面能量和体能量之间的竞争形成周期性调制模式。当前的模拟表明，周期性图案在表面常数 K_<24>=0.35 的起始值以上是稳定的，并且对于较大的 K_，周期与 (K_<24>-K_<13>/2)^<-1> 成正比。 <24>.晶格引起的各向异性影响条纹图案的方向。为了避免这种非物理效应，必须考虑第二最近的相互作用。检查均匀边界处各向异性现场场的影响。发现单向场在 boojum 和 antiboojum 之间形成弦状纹影图案，类似于厚度约为 10μm 的薄膜中的实验图案。