单一弹性常数近似下向错线对液晶自由能的影响  

Effect of Disclination Lines on Free Energy of Two-dimensional Liquid Crystals in Single-elastic Constant Approximation

作　　者：王玉生[1] 杨国宏[1] 

机构地区：[1]上海大学理学院物理系,上海200436

出　　处：《液晶与显示》2004年第2期92-98,共7页Chinese Journal of Liquid Crystals and Displays

基　　金：上海市教育委员会青年教师基金资助项目 (No .2 0 0 0QN64 )

摘　　要：在单一弹性常数近似下 ,利用映射方法和拓扑流理论研究了液晶中向错线对自由能密度的影响。指出自由能密度可以分为两部分 ,一部分是通常的液晶指向矢场在向错线周围的畸变能密度 ;另一部分是向错线自身的自由能密度 ,当指向矢场的Jacobian行列式在指向矢场的奇点处不等于零时 ,它是集中在向错线上并以 12 kπ为单位拓扑量子化的 ,拓扑量子数由指向矢场在向错线处的Hopf指数和Brouwer度 (即向错强度 )决定。当Jacobian行列式等于零时 ,利用拓扑流分歧理论详细研究了在指向矢场的极限点和分岔点处向错线自身的自由能密度的产生、湮灭和分歧过程 ,最后得出 ,具有高的拓扑量子数的向错线是不稳定的 。Using the light of  -mapping method and topological current theory, the effect of disclination lines on the free energy density of liquid crystals was studied in the single-elastic constant approximation. It was pointed out that 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 disclination lines themselves (FEDDLT), which is centralized at the disclination lines and topologically quantized in the unit of12k π when the Jacobian determinant of the director field does not vanish at the singularities of the director field. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees, i.e. the disclination strength, of the director field at the disclination lines. When the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of the FEDDLT are detailed in the neighborhoods of the limit points and bifurcation points by using the bifurcation theory of topological current. It is shown that the disclination lines with higher topological quantum numbers are unstable and they will evolve to the lower topological quantum number states through the bifurcation process.

关 键 词：单一弹性常数 向错线 液晶 自由能密度 指向矢 分歧 Hopf指数 BROUWER度 畸变能密度 

分 类 号：O753.2[理学—晶体学]