摘要
基于格点模型空间各向异性两体势研究扭曲向列(TN)液晶盒的Fredericksz转变。该作用势不仅是空间各向异性的并且依赖于液晶的弹性常数。理论处理中假定具有理想向列序,这意味着分子长轴取向方向与液晶指向矢是重合的,而总自由能等于总相互作用能。分别对指向矢的倾角和方位角进行傅里叶展开,通过二阶导矩阵方法确定TN盒的阈值磁场。该磁场依赖于总扭曲角和液晶的弹性常数,并与连续体理论结果进行了比较。通过平衡态下系统自由能取最小,得到指向矢满足的平衡态方程。基于平衡态方程,对TN液晶盒中指向矢在磁场作用下的分布进行了数值计算。数值结果验证了液晶指向矢所满足的平衡态方程的正确性。进一步证实了文献中最近提出的两种从弹性能到两体作用势的映射方案之一(即模型Ⅰ)可以给出与连续体理论相一致的结果。
Freedericksz transitions of twist nematic liquid tropic pair potential of lattice model which is not crystal cells are studied by using spatially aniso only spatially anisotropic, but also dependent on elastic constants of liquid crystals. The perfect nematic order is assumed in the theoretical treatment, which means the orientation of the molecular long axis coincides with the director of liquid crystal and the total free energy equals to the total interaction energy. Tilt and azimuth angels of the director are expanded respectively through Fourier series and then threshold magnetic field of TN cells can be ascertained by way of the second derivative matrix. The magnetic field depends on the total twist angle and elastic constants of liquid crystals,which is compared with that of continuum theory. The equilibrium equation, which is satisfied by the director of liquid crystal, can be obtained by the way that the systematic free energy should be minimized with the state of equilibrium. Based upon the equilibrium equation, numerical calculations are made for the director profiles in a TN liquid crystal cell with the action of magnetic field. Numerical results verified the equilibrium equation satisfied by the director of liquid crystal. It is further proved that one of two mapping schemes from the elastic energy to the pair potential proposed recently in the literature, i.e. model 1, can give the result consistent with the continuum theory.
出处
《液晶与显示》
CAS
CSCD
北大核心
2007年第5期591-597,共7页
Chinese Journal of Liquid Crystals and Displays
基金
河北省高校重点学科建设项目资助
