Contribution of Disclination Lines to Free Energy of Liquid Crystals in Single-Elastic Constant Approximation

作     者：YANGGuo-Hong WANGYu-Sheng DUANYi-Shi 

作者机构：DepartmentofPhysicsShanghaiUniversityShanghai200436China InstituteofTheoreticalPhysicsLanzhouUniversityLanzhou730000China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2004年第42卷第2X期

页      面：185-188页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 08[工学] 080501[工学-材料物理与化学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0703[理学-化学] 0702[理学-物理学] 

主　　题：向错线 自由能 液晶 单弹性常数近似 拉格朗日多项式 

摘      要：In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange s method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density.