Berreman近似下任意形状表面沟槽对双轴向列相方位锚定的影响

郑桂丽; 李根堂; 张志东

doi:10.3788/YJYXS20112602.0137

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Berreman近似下任意形状表面沟槽对双轴向列相方位锚定的影响

材料物理和化学 | 更新时间：2020-08-12

- Berreman近似下任意形状表面沟槽对双轴向列相方位锚定的影响
- Effect of Grooved Surface with Arbitrary Shape on Anchoring Energy of Biaxial Nematic Liquid Crystal
- 液晶与显示 2011年26卷第2期页码：137-141
- 作者机构：
  
  河北工业大学理学院, 天津 300401
- 作者简介：
- 基金信息：
  
  国家自然科学基金(No.60736042)();河北省自然科学基金(No.A2010000004)();河北省重点学科资助项目()
- DOI：10.3788/YJYXS20112602.0137
  中图分类号： O753+.2
- 收稿日期：2010-07-13，
  
  修回日期：2010-08-18，
  
  网络出版日期：2011-04-06，
  
  纸质出版日期：2011-04-06
- 稿件说明：
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郑桂丽, 李根堂, 张志东. Berreman近似下任意形状表面沟槽对双轴向列相方位锚定的影响[J]. 液晶与显示, 2011,26(2): 137-141

ZHENG Gui-li, LI Gen-tang, ZHANG Zhi-dong. Effect of Grooved Surface with Arbitrary Shape on Anchoring Energy of Biaxial Nematic Liquid Crystal[J]. , 2011,26(2): 137-141
郑桂丽, 李根堂, 张志东. Berreman近似下任意形状表面沟槽对双轴向列相方位锚定的影响[J]. 液晶与显示, 2011,26(2): 137-141 DOI： 10.3788/YJYXS20112602.0137.

ZHENG Gui-li, LI Gen-tang, ZHANG Zhi-dong. Effect of Grooved Surface with Arbitrary Shape on Anchoring Energy of Biaxial Nematic Liquid Crystal[J]. , 2011,26(2): 137-141 DOI： 10.3788/YJYXS20112602.0137.

摘要

通过把Berreman近似下任意形状的表面沟槽用傅里叶级数展开

写成正弦函数和的形式

将Fukuda 等人的理论应用于双轴向列相液晶中

考虑表面弹性项的作用后得到了任意形状的沟槽对双轴液晶产生的方位锚定能。在一定的近似条件下得到约化锚定能随着沟槽的方向与液晶主指向矢之间的夹角的变化情况

讨论了双轴弹性常数对液晶易取向方向的影响。

Abstract

Under the approximation of Berreman

any grooved surface with arbitrary shape can be described in terms of Fourier series. Based on the theory of Fukuda et al

the expression of anchoring energy with an additional term was obtained

taking into the surfacelike elastic term in biaxial nematic liquid crystal. The figures of reduced anchoring energies versus the angle between the direction of the grooves and main director were simulated under the different values of surfacelike elastic constant in certain cases and the effect of biaxial elastic constant on easy axes was discussed.

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Keywords

references

Berreman D W. Solid surface shape and alignment of an adjacent nematic liquid crystal [J]. Phys. Rev. Lett., 1972, 28(26):1683-1686.[2] Gwag J S, Oh-e M, Yoneya M, et al. Advanced nanoimprint lithography using a grade functional imprinting material tailored for liquid crystal alignment [J]. J. Appl. Phys., 2007, 102(6):063501(1-5).[3] Kawata Y, Takatoch K, Hasegawa M, et al. The alignment of nematic liquid crystals on photolithographic micro-groove patterns [J]. Liq. Cryst., 1994, 16 (6):1027-1036.[4] Park M J, Park O O. Alignment of liquid crystals on a topographically nano-patterned polymer surface prepared by a soft-imprint technique [J]. Microelectronic Engineering, 2008, 85(11):2261-2265.[5] Fukuda J I, Yoneya M, Yokoyama H. Surface-groove-induced azimuthal anchoring of a nematic liquid crystal:Berremans model reexamined [J]. Phys. Rev. Lett., 2007, 98(18):187803(1-4).[6] Fukuda J I, Yoneya M, Yokoyama H. Erratum:Surface-groove-induced azimuthal anchoring of a nematic liquid crystal:berremans model reexamined [J]. Phys. Rev. Lett., 2007, 99(13):139902(1-2).[7] Fukuda J I, Gwag J S, Yoneya M, et al. Theory of anchoring on a two-dimensionally grooved surface [J]. Phys. Rev. E., 2008, 77(1):011702(1-16).[8] Madsen L A, Dingemans T J, Nakata M, et al. Thermotropic biaxial nematic liquid crystals [J]. Phys. Rev. Lett., 2004, 92(14):145505(1-4).[9] 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).[10] Merkel K, Kocot A, Vij J K, et al. Thermotropic biaxial nematic phase in liquid crystalline organo-siloxane tetrapodes [J]. Phys. Rev. Lett., 2004, 93(23):237801(1-4).[11] Saupe A. Elastic and flow properties of biaxial nematics [J]. J.Chem. Phys., 1981, 75(10):5118-5124.[12] Singh Y, Rajesh K, Menon V J. et al. Molecular theory of elastic constants of liquid crystals. II. Application to the biaxial nematic phase [J]. Phys. Rev. E., 1994, 49(1):501-512.[13] Zhidong Zhang, Wengjiang Ye. The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves [J]. Liq. Cryst., 2009, 36(8):885-888.

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