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以修正后的Rapini-Papoular锚定能公式为基础, 用理论分析和数值计算相结合的方法, 详细研究表面极化对液晶盒饱和特性的影响. 得出了求解指向矢分布的数学方程, 推导出了计算正常二级转变饱和电压的解析式, 同时结合最新报道, 给出了异常一级转变饱和电压的数值计算方法. 此外, 本文引入了反映指向矢分布特征的参量, 讨论了表面极化对此参量的影响. 结果表明, 指向矢最大倾角的位置随表面极化的增大将远离中央平面向基板移动. 一级转变饱和电压随弱锚定基板表面极化的增大而减小, 随强锚定基板表面极化的增大而增大. 而对二级转变, 饱和电压随表面极化的变化与一级转变恰恰相反. 本文所得结论对液晶表面物理的理解及液晶实际应用都具有重要的指导意义.Based on the modified Rapini-Papoular formula for surface anchoring energy, the saturation behaviour of a weak anchoring nematic liquid crystal cell is studied. The mathematical equations of solving director distribution are obtained. A parameter reflecting the characteristic of director distribution is introduced. Expressions for saturation voltage and the parameter reflecting the characteristic of director distribution are obtained for the second order transition. The methods of calculating the two quantities for the first order transition are also given. The influences of surface polarization on the two quantities are discussed in detail. The results show that whether the second or the first order transition, the position of the maximal tilt angle of director will shift towards the substrates with the increase of surface polarization. The influences of surface polarization on saturation voltage for the second and the first order are reverse. The saturation voltage will increase for the second order but decrease for the first order with the increase of surface polarization.
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Keywords:
- liquid crystal /
- surface polarization /
- saturation behaviour
[1] Xie Y Z 1998 physics of liquid crystal (Beijing: Science Press) (in Chinese) [谢毓章 1998 液晶物理学 (北京: 科学出版社)]
[2] Prost J, Marcerou J P 1977 J. Phys. Paris 38 315
[3] Petrov A G, Derzhanski A 1977 Mol. Crysaals. 41 41
[4] Barbero G, Dozov I, Palierne J F, Durand G 1986 Phys. Rev. Lett. 56 2056
[5] Blinov M L, Barnik M I, Ozaki M, Shtykov N M, Yoshino K 2000 Phys. Rev. E 62 8091
[6] Zakharov A V, Dong Y 2001 Phys. Rev. E 64 042701
[7] Nazarenko V G, Lavrentovich O D 1994 Phys. Rev. E 49 990
[8] Liu J W, Zhang S H, Yang Y Y, An H L, Zhang Z D, Yang G C 2007 Liq. Cryst. 34 1425
[9] Guan R H 2011 Acta Phys. Sin. 60 016105 (in Chinese) [关荣华 2011 物理学报 60 016105]
[10] Rapini A, Papoular M 1969 J. Phys. (Paris) Colloq 30 C4-54
[11] Barbero G, Madhusudana N V, Palierne J F 1983 Phys. Lett. 103A 385
[12] Barbero G, Madhusudana N V, Durand G Z 1983 Naturf. 39A 1066
[13] Yokoyama H, Van Sprang H A 1985 J. Appl. Phys. 57 4520
[14] Warenghem M 1984 Mol. Phys. 53 1381
[15] Stallinga S, Van Haaren J A M M, Van Den Erenbeemd J M A 1996 Phys. Rev. E 53 1701
[16] Yang G C, Shi J R, Liang Y 2000 Liq. Cryst. 27 875
[17] Zhang S H, Han H L, Guan R H, Yang G C 2006 Liq. Cryst. 33 227
[18] Meyer R B 1969 Phys. Rev. Lett. 22 918
[19] Frisken B J, Palffy-Muhoray P 1989 Phys. Rev. A 40 6099
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[1] Xie Y Z 1998 physics of liquid crystal (Beijing: Science Press) (in Chinese) [谢毓章 1998 液晶物理学 (北京: 科学出版社)]
[2] Prost J, Marcerou J P 1977 J. Phys. Paris 38 315
[3] Petrov A G, Derzhanski A 1977 Mol. Crysaals. 41 41
[4] Barbero G, Dozov I, Palierne J F, Durand G 1986 Phys. Rev. Lett. 56 2056
[5] Blinov M L, Barnik M I, Ozaki M, Shtykov N M, Yoshino K 2000 Phys. Rev. E 62 8091
[6] Zakharov A V, Dong Y 2001 Phys. Rev. E 64 042701
[7] Nazarenko V G, Lavrentovich O D 1994 Phys. Rev. E 49 990
[8] Liu J W, Zhang S H, Yang Y Y, An H L, Zhang Z D, Yang G C 2007 Liq. Cryst. 34 1425
[9] Guan R H 2011 Acta Phys. Sin. 60 016105 (in Chinese) [关荣华 2011 物理学报 60 016105]
[10] Rapini A, Papoular M 1969 J. Phys. (Paris) Colloq 30 C4-54
[11] Barbero G, Madhusudana N V, Palierne J F 1983 Phys. Lett. 103A 385
[12] Barbero G, Madhusudana N V, Durand G Z 1983 Naturf. 39A 1066
[13] Yokoyama H, Van Sprang H A 1985 J. Appl. Phys. 57 4520
[14] Warenghem M 1984 Mol. Phys. 53 1381
[15] Stallinga S, Van Haaren J A M M, Van Den Erenbeemd J M A 1996 Phys. Rev. E 53 1701
[16] Yang G C, Shi J R, Liang Y 2000 Liq. Cryst. 27 875
[17] Zhang S H, Han H L, Guan R H, Yang G C 2006 Liq. Cryst. 33 227
[18] Meyer R B 1969 Phys. Rev. Lett. 22 918
[19] Frisken B J, Palffy-Muhoray P 1989 Phys. Rev. A 40 6099
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