双轴向列相液晶混合物系统的弹性系数

发布时间：2018-10-21 08:26

【摘要】：本文考虑由两种非轴对称液晶分子构成的双轴向列相液晶混合物系统。将分子简化为三根互相垂直的长棒,利用棒与棒之间相互作用能的叠加,得到系统总的相互作用能。首先在理想序下,推导出与Saupe形式一致的双轴向列相液晶弹性能密度公式,以及弹性系数与分子结构,相互作用强度,组分比之间的简单解析函数关系,进而对弹性系数与分子棒长间的关系进行讨论。其次,考虑到分子长棒由于热运动将偏离局域双轴相指向矢,需要对分子长棒在指向矢坐标系中的分量取统计平均,由此得到在非理想序下,弹性系数与分子结构,相互作用强度,组分比,分子取向序间的简单解析关系。此种方法可以推广到其它分子结构,以及三种及以上混合物液晶系统的弹性理论。本文考虑由两种V形液晶分子构成的双轴向列相液晶混合物系统,假设分子间的简单相互作用,利用棒与棒间相互作用能的叠加,得到系统弹性系数与分子形状,组分比,分子取向序参数有关的解析表达式。当其中一种V分子夹角为180。时,系统简化为棒状、V形分子混合物系统。考虑到弯曲形变与V形分子形状间存在耦合,V形分子可被诱导产生双轴相,但展曲形变对V形分子短轴取向影响较小,系统可仍处于单轴相。对于弯曲,展曲形变,分别假设系统处于双,单轴向列相。并且为简化起见,作理想序假设,利用前面所得弹性系数的解析表达式,得到系统弯曲,展曲弹性系数比γ与分子形状,组分比之间的关系。结果表明,对于合适的V形分子夹角,随着V分子浓度的增加,此比值显著减小。这含示除了V形分子与弯曲形变存在耦合之外,V形分子的形状对γ的减小有显著贡献。
[Abstract]:A biaxial nematic liquid crystal mixture system consisting of two non-axisymmetric liquid crystal molecules is considered in this paper. The molecule is simplified as three long rods perpendicular to each other. The total interaction energy of the system is obtained by using the superposition of the interaction energy between the rods and the rods. At first, in ideal order, the formula of elastic energy density of biaxial nematic liquid crystal consistent with Saupe's form is derived, as well as the simple analytical function between elastic coefficient and molecular structure, interaction strength and component ratio. The relationship between the elastic coefficient and the length of the molecular rod is discussed. Secondly, considering that the long molecular rod will deviate from the local biaxial phase vector due to the thermal motion, it is necessary to take the statistical average of the component of the long molecular rod in the direction vector coordinate system, and thus obtain the elastic coefficient and the molecular structure in the non-ideal order. The simple analytical relationship between the interaction intensity, the component ratio and the molecular orientation order. This method can be extended to other molecular structures and elastic theory of liquid crystal systems with three or more mixtures. In this paper, a biaxial nematic liquid crystal mixture system consisting of two kinds of V-shaped liquid crystal molecules is considered. Assuming the simple interaction between molecules, the elastic coefficient, molecular shape and component ratio of the system are obtained by the superposition of the interaction energy between rod and rod. Analytical expressions of molecular orientation order parameters. When one of the V molecules has an angle of 180. The system is simplified to a rod-like, V-shaped molecular mixture system. Considering the coupling between the bending deformation and the shape of the V-shaped molecule, the V-shaped molecule can be induced to produce biaxial phase, but the curling deformation has little effect on the short-axis orientation of the V-shaped molecule, and the system can still be in the uniaxial phase. For bending and stretch deformation, the system is assumed to be in biaxial and uniaxial nematic phases, respectively. For the sake of simplification, the ideal order hypothesis is made and the relationship between the elastic coefficient ratio 纬 and the molecular shape and component ratio is obtained by using the analytical expression of the elastic coefficient obtained above. The results show that the ratio decreases significantly with the increase of the concentration of V molecule. This implies that the shape of the V-shaped molecule contributes significantly to the reduction of 纬, except for the coupling between the V-shaped molecule and the bending deformation.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O753.2

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