Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal

ZHANG Rui-ling; LIU Hong

doi:null

您当前的位置：

首页 >

文章列表页 >

Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal

Material Physics & Chemistry | 更新时间：2020-08-12

- Theoretical Derivation of Elastic Constants of Biaxial Nematic Liquid Crystal
- Chinese Journal of Liquid Crystals and Displays Vol. 24, Issue 1, Pages: 1-8(2009)
- 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：
  CLC： O753+.2
- Received：24 July 2008，
  
  Revised：02 January 1900，
  
  Published Online：20 February 2009，
  
  Published：20 February 2009
- 稿件说明：
移动端阅览
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.

. Yu L J, Saupe A. Observation of a biaxial nematic phase in potassium laurate-1-decanol-water mixtures [J]. Phys. Rev. Lett., 1980, 45(12):1000-1003.

. Acharya B R,Primak A,Kumar S. Biaxial nematic phase in bent-core thermotropic mesogens [J]. Phys. Rev. Lett., 2004, 92(14):145506(1-4).

. Bates M A, Luckhurst G R. Biaxial nematic phases and V-shaped molecules:A Monte Carlo simulation study [J]. Phys. Rev. E, 2005, 72(5):051702(1-15).

. Saupe A. Elastic and flow properties of biaxial nematics [J]. J. Chem. Phys., 1981, 75(10):5118-5124.

. Govers E, Vertogen G. Elastic continuum theory of biaxial nematics [J]. Phys. Rev. A, 1984, 30(4):1998-2001.

. 刘红.弹性形变对丝状相液晶相变的影响 [J]. 物理学报 , 2000, 49(5):0931-0935.

. Liu H. Theory of nine elastic constants of biaxial nematics [J]. Chin. Phys. B,2008,17(3):1060-1069.

. Vertogen G,Flapper S D P, Dullemond O. Elastic constants of nematic and cholesteric liquid crystals and tensor fields [J]. J. Chem. Phys., 1982, 76(1):616-618.

. Priest R G. Theory of Frank elastic constants of nematic liquid crystals [J]. Phys. Rev. A, 1973,7(2):720-729.

. 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.

Views

125

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Effect of Grooved Surface with Arbitrary Shape on Anchoring Energy of Biaxial Nematic Liquid Crystal

Elastic Distortion of Biaxial Nematic Liquid Crystal Induced by Surface Grooves

Related Author

ZHENG Gui-li

LI Gen-tang

ZHANG Zhi-dong

YE Wen-jiang

ZHANG Lu

Related Institution

School of Sciences, Hebei University of Technology, Tianjin 300401, China

School of Sciences, Hebei University of Technology, Tianjin 300401, China,E-mail: zhidong_zhang@yahoo.

AI问答

Address：No.3888 Dong Nanhu Road, Changchun, Jilin, China 130033 Postal code：130033
Tel：0431-86176059 Email：yjxs@ciomp.ac.cn
Technical support is provided by Beijing Founder electronics co., LTD 吉ICP备11002662号-17 京公网安备11010802024621
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰