| 单一弹性常数近似下向错线对二维液晶自由能的贡献 |
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| 引用本文： | 王玉生,张慧,杨国宏.单一弹性常数近似下向错线对二维液晶自由能的贡献[J].上海大学学报(英文版),2004,8(2):155-158. |
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| 作者姓名： | 王玉生 张慧 杨国宏 |
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| 作者单位： | [1]DepartmentofPhysics,CollegeofSciences,ShanghaiUniversity,Shanghai200436,P.R.China [2]DepartmentofChemistry,CollegeofSciences,ShanghaiUniversity,Shanghai200436,P.R.China |
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| 摘 要： | In light of the Ф-mapping method,the contribution of disclination linges to the free energy density of 2-dimensional liquid crystals is studied in the single-elastic constant approximation.It is pointed out that ,compared with the previous theory ,the 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 endrgy density of the disclination lines themselves which is centralized at the disclination lines and topoligically quantized in a unit of 1/2kπ .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 strength.From the method of Lagrangian multipliers,the equilibrium equation and the molecular field of 2-dimensional liquid crystals are also obtained.It is shown that the physical meaning of the Lagrangian multiplier is just the distorted energy density.
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| 关 键 词： | 单一弹性常数近似 向错线 二维液晶 自由能 Ф-映象 拓扑量子数 拉格朗日乘数 |
| 收稿时间： | 30 April 2003 |
Contribution of disclination lines to free energy of 2-dimensional liquid crystals in single-elastic constant approximation |
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| Wang?Yu-sheng,Zhang?Hui,Yang?Guo-hong.Contribution of disclination lines to free energy of 2-dimensional liquid crystals in single-elastic constant approximation[J].Journal of Shanghai University(English Edition),2004,8(2):155-158. |
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| Authors: | Wang Yu-sheng Zhang Hui Yang Guo-hong |
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| Institution: | 1. Department of Physics, College of Sciences, Shanghai University, Shanghai 200436, P. R. China
2. Department of Chemistry, College of Sciences, Shanghai University, Shanghai 200436, P. R. China |
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| Abstract: | In light of the φ-mapping method, the contribution of disclination lines to the free energy density of 2-dimensional liquid
crystals is studied in the single-elastic constant approximation. It is pointed out that, compared with the previous theory,
the 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 the disclination lines themselves which is centralized at
the disclination lines and topoligically quantized in a unit of 1/2kπ. 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 strength. From the method of Lagrangian multipliers, the equilibrium equation and the molecular field of
2-dimensional liquid crystals are also obtained. It is shown that the physical meaning of the Lagrangian multiplier is just
the distorted energy density. |
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| Keywords: | director field disclination line free energy Lagrangian multiplier |
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