双轴向列相液晶弹性系数的理论推导

张瑞玲; 刘 红

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双轴向列相液晶弹性系数的理论推导

材料物理和化学 | 更新时间：2020-08-12

- 双轴向列相液晶弹性系数的理论推导
- Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal
- 液晶与显示 2009年24卷第1期页码：1-8
- 作者机构：
  
  南京师范大学物理科学与技术学院,江苏南京 210097, E-mail:zhangruiling@126.com
- 作者简介：
- 基金信息：
- DOI：
  中图分类号： O753+.2
- 收稿日期：2008-07-24，
  
  修回日期：1900-01-02，
  
  网络出版日期：2009-02-20，
  
  纸质出版日期：2009-02-20
- 稿件说明：
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张瑞玲;刘红. 双轴向列相液晶弹性系数的理论推导[J]. 液晶与显示, 2009,24(1): 1-8

ZHANG Rui-ling;LIU Hong. Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal[J]. 液晶与显示, 2009,24(1): 1-8
张瑞玲;刘红. 双轴向列相液晶弹性系数的理论推导[J]. 液晶与显示, 2009,24(1): 1-8 DOI：

ZHANG Rui-ling;LIU Hong. Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal[J]. 液晶与显示, 2009,24(1): 1-8 DOI：

摘要

将双轴向列相液晶的分子简化为3根互相垂直的长棒

利用棒与棒之间相互作用能的叠加

得到分子间的总相互作用能。将其展开至指向矢形变的二阶项

得到与指向矢形变有关的12个转动不变量

整理得到与Saupe形式一致的弹性能密度公式

其12个弹性系数与分子结构有明确关系。对12个弹性系数中的9个简单形变弹性系数与分子棒长间的关系进行了讨论。当分子形状为非轴对称时

系统为双轴相。对于3根棒长均不相等的分子

沿指向矢无形变方向(如)的分子长棒对弹性能无贡献

而与

相垂直的两指向矢方向的分子长棒对弹性能有贡献

且弹性系数取决于2棒长差的平方。由于分子形状的非轴对称性与棒长差有关

非轴对称性越强

弹性系数越大。当棒长差为零时

分子形状为轴对称

弹性系数归结为单轴相弹性系数。

Abstract

A general shape of biaxial nematic liquid crystal molecule was abstracted into three perpendicular rods. Using superposition of rod-to-rod interaction energy

the total interaction energy of liquid crystal system was derived. Expanding the total energy into a power series of directors distortion upto second order term

12 rotational invariants related to directors distortion were obtained and the elastic energy density of the system in Saupes form was derived. The corresponding 12 elastic constants were expressed in explicit forms of molecular structure

and the relationship between 9 elastic constants of simple distortions and molecular rod lengths were discussed. When the molecule is non-cylindrical

system becomes biaxial

the molecular rod length along non-distortion director () makes no contribution to elastic energy

while the two rod lengths perpendicular to contribute both to elastic constants. This elastic constant is determined by the square of their difference. Since this difference is related to the non-cylindrical symmetry

the stronger the non-cylindrical symmetry is

the larger the elastic constant is. When this difference is zero

the molecule is cylindrical

the elastic constants are reduced to those of uniaxial nematics.

关键词

Keywords

references

. Freiser M J. Successive transitions in a nematic liquid [J]. Mol. Cryst. Liq. Cryst., 1971, 14:165-182.

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. 张艳君,张志东,崔建坡,等. 基于向列相液晶形变研究空间各向异性两体势 [J]. 液晶与显示, 2006, 21(1):201-205.

. 刘红, 王慧. 双轴性向列相液晶的相变理论 [J]. 物理学报 ,2005, 54 (3):1306-1312.

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