向列相液晶自由能密度的拓扑结构

doi:10.12066/j.issn.1007-2861.2340

上海大学学报(自然科学版) ›› 2022, Vol. 28 ›› Issue (6): 1094-1105.doi: 10.12066/j.issn.1007-2861.2340

向列相液晶自由能密度的拓扑结构

张灿宇¹, 杨国宏¹^,²()

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

收稿日期:2021-06-29 出版日期:2022-12-30 发布日期:2023-01-31
通讯作者: 杨国宏 E-mail:ghyang@shu.edu.cn
作者简介:杨国宏(1968-), 男, 教授, 博士生导师, 博士,研究方向为广义相对论与引力、黑洞物理与宇宙学、凝聚态理论. E-mail:ghyang@shu.edu.cn
基金资助:
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)

Topological structure of free energy density of nematic liquid crystals

ZHANG Canyu¹, YANG Guohong¹^,²()

1. College of Sciences, Shanghai University, Shanghai 200444, China
2. Shanghai Key Lab for Astrophysics, Shanghai 200234, China

Received:2021-06-29 Online:2022-12-30 Published:2023-01-31
Contact: YANG Guohong E-mail:ghyang@shu.edu.cn

摘要/Abstract

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$\phi $映射方法和拓扑流理论研究了集中在缺陷处的自由能密度的表达式. 结果显示, 缺陷自身的自由能密度是以$\frac{1}{2}k\pi $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.

关键词: 液晶, 指向矢, 自由能, 缺陷, 拓扑流

Abstract:

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 of $\phi $-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 $\frac{1}{2}k\pi $, 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.

Key words: liquid crystal, director, free energy, defect, topological current

中图分类号:

O469

张灿宇, 杨国宏. 向列相液晶自由能密度的拓扑结构[J]. 上海大学学报(自然科学版), 2022, 28(6): 1094-1105.

ZHANG Canyu, YANG Guohong. Topological structure of free energy density of nematic liquid crystals[J]. Journal of Shanghai University（Natural Science Edition）, 2022, 28(6): 1094-1105.

图/表 1

参考文献 14

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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

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