高分子液晶条带织构的计算机模拟

首先建立了描述液晶畸变的Frank自由能的向量形式与张量形式之间的关系 ,由此得到了Frank弹性常数与描述液晶相变的取向序参量Sij的一阶空间导数的展开系数间的关系 .结合包括Landau deGennes取向自由能、Maier Saupe各向异性相互作用自由能和Frank自由能的液晶自由能泛函 ,用原胞动力学方法对关于Sij的Ginzberg Landau方程进行了数值求解 .在弯曲弹性常数远小于展曲弹性常数的前提下 ,模拟了二维液晶在剪切松弛下条带织构的形成及其小角光散射图样 ,考查了初始剪切速率的影响 .结果发现 ,由于弯曲弹性常数远小于展曲弹性常数 ,使纵向的展曲形变松弛速率远比横向的弯曲形变松弛速率迅速 ,从而导致纵向的条带结构的形成 ;初始剪切速率增大 ,开始出现条带织构的诱导时间减小且条带的特征尺寸变小 ,与实验结果一致 .

Computer Simulation of Band Texture Formation in Liquid Crystalline Polymer

The relationship between the vector version and tensor version of Frank distortion energy for the liquid crystal was established, through which the relationship between the Frank elastic constants and the expansion coefficients of spatial derivatives for the orientational order parameter S ij of liquid crystalline polymer was obtained. Ginzberg-Landau equation for the orientational order parameter S ij was numerically solved by using the cell dynamical system, which involves a free energy functional containing Landau-de Gennes orientational free energy, Maier-Saupe anisotropic interaction free energy and Frank distortion free energy. In case of the splay elastic constant being much lager than the bend elastic constant, the evolution process of band textures in liquid crystalline polymer during the shear relaxation and its small angle light scattering patterns were simulated. The influence of preshear rate on the band forming and band structure was investigated. It was found that the formation of longitudinal band textures is due to the much rapider longitudinal splay relaxation than the latitudinal bend relaxation, and the induced times of band forming and the characteristic length of band structure decrease with the increasing of preshear rate, which is consistent with the experimental results.