双轴向列相液晶的表面能

Surface energy of the biaxial nematic liquid crystal

利用双轴向列相液晶表面能对指向矢和序参量矩阵的旋转不变性 ,构造了与指向矢 ^a ,^b ,^c对易取向轴 ^a0 ,^b0 ,^c0 的偏离有关的表面能Fs(a ,b ,c) ,以及与序参量矩阵有关的表面能Fs(Q) ,并得到两种表达式的等价形式 .在Fs(a ,b ,c)和Fs(Q)中分别有四个和两个独立参量 .为讨论上述独立参量的物理意义 ,假设一液晶分子对表面相互作用的简单模型 ,将液晶分子沿易取向轴 ^b0 ,^c0 的双轴性取向看成是受到沿 ^b0 ,^c0 两相互垂直的平均场作用的结果 .为测量表面锚泊系数 ,考虑了三种简单形变位型 ,即在外磁场中 ^b和 ^c绕 ^a0 ,^c和 ^a绕 ^b0 ,^a和^b绕 ^c0 的Freedericksz相变 .通过测量其Freedericksz相变的磁场阈值 ,可求出表面能中与这三个形变有关的锚泊系数Wa,Wb,Wc.

In this paper, two forms of surface energy of the biaxial nematic liquid crystal are derived. One is related to the deviation of surface directors (a) over cap, (b) over cap and (c) over cap with respect to the easy axes (a) over cap (0), (b) over cap (0) and (c) over cap (0) in the surface. The other is related to the surface order parameter matrix Q. The relations between the two forms are derived. In the former one, four independent coefficients are involved while in the latter one, only two independent coefficients are involved. In order to inspect the physical meaning of these coefficients, a simple model of molecular interaction between liquid crystal and boundary plate is proposed. In the model, the biaxial orientation of molecules along (b) over cap (0) and (c) over cap (0) is assumed to arise from two perpendicular mean fields along Lo, eo competing with each other. In three geometric features of Freedericksz transition where (a) over cap and (b) over cap rotate around (c) over cap (0), (b) over cap and (c) over cap around (a) over cap (0), (c) over cap and (a) over cap around io respectively, possible experimental measurements of surface anchoring coefficients W-a, W-b and W-c involved in the distortions are explored.