向列型液晶的硬棒理论与分子取向短程关联

THE HARD ROD THEORY OF NEMATIC LIQUID CRYSTALS AND THE SHORT RANGE CORRELATIONS OF MOLECULAR ORIENTATIONS

在向列型液晶的硬棒理论中引入分子取向短程关联。理论的出发点是Ｓｉｎ－ＤｏｏＬｅｅ的自由能表示，这一表示基于Ｃａｒｎａｈａｎ－Ｓｔａｒｌｉｎｇ状态方程。用包括了分子短程关联的取向熵代替原来平均场形式的取向熵项，得到新的自由能表示。通过自由能对分子取向分布求变分确定平衡态分布。对液晶ＰＡＡ进行了数值计算。给出了相变点序参数、熵变、相变点致密度和相对密度变化的计算值。考虑短程关联后的理论值较通常硬棒理论有显著改进。因此，在某种程度上克服了硬棒理论的困难。

Short range correlations of molecular orientatins are introduced in the hard rod theory of nematic liquid crystals. Our theory′s starting point is the free energy expression of Sin Doo Lee, which is based on the Carnahan Starling equation of state. The orientational entropy term, in the mean field approximation form, is replaced by the one including the molecular short range correlations, so a new free energy expression is obtained. The equilibrium distribution is determined by the minimization of the free energy with respect to the variation of molecular orientational distributions. Numerical calculations are made for liquid crystal PAA. The calculated values of the order parameter at the phase transition, the entropy change, the packing fraction at the phase transion and the relative density change are given. The theoretical values yielded by the present theory in which the short range correlations are considered, are considerably improved in compared with the usual hare rod theory′s. The difficulty in the hard rod theory is thus overcome to some extend.