丝状nematic液晶Fredericksz转变的数值模拟与相关模型剖析  

The Numerical Simulation and the Relative Models for the Fredericksz' Transition of the Threadlike Nematic Liquid Crystal

作　　者：陆章基[1] 孙张风[1] 胡挺[1] 刘文娟[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《复旦学报（自然科学版）》2005年第3期347-354,共8页Journal of Fudan University：Natural Science

基　　金：国家自然科学基金资助项目(10172029;10372023)

摘　　要：液晶Fredericksz转变的研究有实用价值(实验确定若干材料系数)和理论价值(显示机理,弄清不同模型之间联系).用微极电磁液晶模型深入研究丝状nematic液晶的Fredericksz转变,具体给出三类畸变(垂直锚定、水平锚定与扭曲)的临界磁场强度、指向矢角度分布、最大转角的隐式解析解(是含参变量的隐式广义积分),并作精细数值模拟.与此同时,讨论两类重要电磁液晶模型(Leslie Ericksen(LE)模型与微极模型)的内在联系,给出两者材料系数之间的转换关系,以及简化的LE模型近似公式的精度与适用范围.Investigating the Fredericksz'transition of liquid crystal is valuable for both theoretical research and practical application(determining the material coefficients by experiments).The Fredericksz'transitions of the threadlike nematic liquid crystal are investigated using the Micropolar Liquid Crystal model.The analytical expressions of the critical magnetic field intensity,the angle distribution of the director and the maximum rotation angle are obtained for three type distortions (perpendicular anchor,parallel anchor,and twist case and the detailed numerical analysis are performed.At the same time,the relation between the material coefficients obtained from the Leslie-Ericksen model and the micropolar model is discussed,and the discrepancy between the approximation formula and the accurate formula is calculated.

关 键 词：微极液晶模型 LE液晶模型 壁面与磁场效应 Freddcksz转变 广义连续统物理力学 

分 类 号：O331[理学—一般力学与力学基础]