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.

在杂交边界条件下，在薄列膜中的平衡模式和那些形成过程进行了数值研究。最高边界是同型边界，其中导演垂直于电影，而Bittom边界是同质的，而导演与电影平行。弗兰克能量中表面积分代表的能量的表面术语对于形成模式具有重要作用，thourh在批量问题中被忽略了。我们目前的模型是改进的细胞动力系统模型，它不仅包括表面术语，还包括能够代表大量弹性常数各向异性的ALSOBE。一个主要的想法是，我们不会离散坦克能量，而是要使用TDGL方程。表面能量与批量能量之间的竞争是定期调制的模式。本模拟表明，周期性模式在表面常数k_ <24> = 0.35的发作值上方稳定，并且周期与（k_ <24> -k_ <13>/2）^<-1>对于大k_ <24>。为了避免这种非物理效应，必须考虑第二个最近的相互作用。各向异性现场在同质边界处的影响。发现单向场可以使boojum和抗抗体之间的类似弦状的schlieren模式在大约10mum厚度的膜中类似于实验模式。