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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 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 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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