拓扑荷在圆盘状向列相液晶薄膜中的尺寸效应

拓扑现象对于病毒颗粒的空间分布、高分子聚合物纳米囊泡的成型以及玻色-爱因斯坦凝聚物等方面都发挥着重要作用.本文利用Landau-de Gennes理论,构建模型来模拟液晶中拓扑荷分布及其他现象.通过对数值模型序参量场的演化,以及模拟液晶薄膜中所生成的拓扑荷之间的相互作用来分析液晶(Lqc)薄膜的尺寸对拓扑荷的影响.研究结果表明,随着液晶盘半径增大,拓扑荷间最优距离与半径之比渐增并趋于稳定.此研究结论对利用拓扑荷凝聚颗粒物效应设计分离容器有指导意义,有助于进一步理解拓扑胶体和液晶以及液晶共聚物等软物质中的拓扑现象.

Size effect of topological charge in disc-like nematic liquid crystal films

Algebraic topology,algebraic geometry,and category theory are new branches of mathematics that have developed in the last hundred years and have had profound collisions with modern physics in recent decades.A large number of topological phenomena are found in systems such as viruses,bacteria,fingerprints,fish school,typhoons,and the galaxies.Topological phenomena play a significant role in the spatial distribution of viral particles,the formation of nanovesicles of polymer,and Bose-Einstein condensates.In this paper,based on Landau-de Gennes theory,models have been constructed to simulate the topological charge distribution and other topological phenomena in liquid crystals.The research indicates that as the radius of the liquid crystal panel grows,the ratio of the optimal distance between the topological charge to the radius gradually increases and tends to stabilize.The size of the disc affects the equilibrium position of the topological load.The relative equilibrium position of topological load is between 0.542 and 0.558,in which the ratio of the distance between the two+1/2 topological loads in the 0–5 mm disc increases from 0.542 to 0.558,and then in the 5–12 mm section the ratio is almost stable at 0.558.As the size of the disc increases,the influence of the boundary anchoring energy decreases,and the equilibrium position,i.e.the distance between the two topological charges and the diameter of the disc,approaches a constant value.This equilibrium position is the result of the repulsive force of the disc boundary on the+1/2 topological load and the repulsive force between the two topological loads.The angle between two topological charges in a liquid crystal disc is between 140°and 180°.The trajectory of the topological charge is the process of finding the lowest free energy point,and the end of the trajectory is in the region of minimum free energy.The result is instructive significance in the design of classification containers by using topological charge condensate effect.And it is helpful to further understand the topological phenomena in soft materials including topological colloids,liquid crystals,and liquid crystal copolymers.