向列相液晶自由能密度的拓扑结构  

Topological structure of free energy density of nematic liquid crystals

作　　者：张灿宇 杨国宏 ZHANG Canyu;YANG Guohong(College of Sciences,Shanghai University,Shanghai 200444,China;Shanghai Key Lab for Astrophysics,Shanghai 200234,China)

机构地区：[1]上海大学理学院,上海200444 [2]上海市星系与宇宙学半解析研究重点实验室,上海200234

出　　处：《上海大学学报（自然科学版）》2022年第6期1094-1105,共12页Journal of Shanghai University:Natural Science Edition

基　　金：上海市星系与宇宙学半解析研究重点实验室开放课题资助项目(SKLA2102)。

摘　　要：通过对经典向列相液晶自由能密度表达式的深入分析,添加了一项代表液晶缺陷自由能的表面项.利用Φ映射方法和拓扑流理论研究了集中在缺陷处的自由能密度的表达式.结果显示,缺陷自身的自由能密度是以1/2kπ为单位拓扑量子化的,且拓扑量子数由Hopf指数和Brouwer度决定.进一步给出了一些不同向错强度下缺陷附近的液晶分子的分布构形.Through the investigation to the classical expressions of free energy density of nematic liquid crystal,a surface term was added to represent the free energy of defects in liquid crystals.By means ofΦ-mapping method and topological current theory,the new expression of free energy density which was concentrated on the defects was studied.It is shown that the free energy density concentrated on the defects is topologically quantized in the unit of 1/2kπ,and the topological quantum numbers are determined by Hopf index and Brouwer degree.The configurations of molecules of liquid crystal around the different disclination strengths of defects are also given in this paper.

关 键 词：液晶 指向矢 自由能 缺陷 拓扑流 

分 类 号：O469[理学—凝聚态物理]