受限液晶系统的理论新进展

梁琴; 陈征宇

doi:10.7498/aps.65.174201

摘要

受限液晶体系是软物质领域里一类基本的问题，理论方法是研究该问题的一种重要的手段. 本综述简要回顾了液晶体系理论的发展历程，介绍了Onsager模型、 Maier-Saupe模型、Landau-de Gennes展开、 Frank弹性模型和高分子液晶的自洽场模. 近几十年，使用这些理论模型，辅以适合的边界条件，已有大量的针对受限液晶体系的理论研究，本文重点介绍了受限体系最近20-30年的主要进展，包括狭缝中液晶体系的实验与理论进展、限制在二维平面中封闭曲线内液晶体系的指向行为、限制在三维球面上刚性分子的缺陷结构的研究进展，在此基础上指出了学科中尚未解决的前沿问题及与实际应用有关的重大问题.

关键词:

液晶 /
受限体系 /
Onsager模型 /
自洽场

Abstract

Liquid-crystal polymers in confined system is a fundamental issue in soft matter. Theoretical method plays animportant role in studying these systems. The intention of this work is to give a thorough reviewof the theoretical methodologies used in tackling confined liquid crystals. At first, some basic concept of liquid crystal, such as a vital order parameter for orientation, phases of liquid crystal, the uniaxial and biaxial of liquid crystal, are presented. After that, a brief review of the development of liquid-crystal theories, which include the Onsager model, the Maier-Saupe model, the McMillanmodel, the Landau-de Gennes expansion, the Frank elastic model and the self-consistent field model for liquid-crystal polymers, are given. All these theories havetheir own advantages and disadvantages. For example, the phenomenological Frank elastic model is the most widely used model due to its simplicity. In contrast, parameters in the self-consistent field model are physically meaningful, however, it is rather complicated. During recent decades, with these theories and suitable boundary treatment, plenty confined liquid crystal systems are investigated. In this review, we focus on three kinds of confined systems: 1) the surface wetting behavior in slits; 2) the two-dimensional liquid crystals confined by a boundary line and 3) defects in the orientational field of rigid rods on spherical surface. Results arrived from different At the end of this review, we give a list of frontier issues and an outlook for thecoming ten years.

Keywords:

作者及机构信息

梁琴¹,
陈征宇²

1.
湘潭大学数学与计算科学学院, 湘潭 411105;

2.
滑铁卢大学天体物理学院, 滑铁卢 N2L 3G1, 加拿大

通信作者: 梁琴, liangqin1997@xtu.edu.cn

基金项目: 国家自然科学基金青年科学基金（批准号：11301444）、高等学校博士学科点专项科研基金（批准号：20134301120001）和加拿大自然科学与工程委员会资助的课题.

Authors and contacts

Liang Qin¹,
Jeff Z. Y. Chen²

1.
Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;

2.
Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Corresponding author: Liang Qin, liangqin1997@xtu.edu.cn

Funds: Project supported by theYoung Scientists Fund of the National Natural Science Foundation of China (Grant No. 11301444), theSpecialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134301120001). and theNatural Science and Engineering Council of Canada.

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[115]	Wu L, Muller E A, Jackson G 2014 Macromolecules 47 1482
[116]	Varga S, Mart'tnez-Rat'tn Y, Velasco E 2010 Eur. Phys. J. E 32 89
[117]	Varga S, Mart'tnez-Rat'tn Y, Velasco E 2014 J. Phys.: Condens. Matter 26 075104

施引文献

[1]	Nguyen T S, Geng J, Selinger R L B, Selinger J V 2013 Soft Matter 9 8314
[2]	Cheng L, Sun J, Zhang K, Mou Z, Huang X, Ji G, Sun F, Zhang J, Zhu P 2011 National Acad Sciences 108 1373
[3]	Yang C, Ji G, Liu H, Zhang K, Liu G, Sun F, Zhu P, Cheng L 2012 National Acad Sciences 109 6118
[4]	Sun F, Wang X, Xu F, Liu J, Gao B, Liu Y, Zhai Y, Ma J, Zhang K, Baker T 2013 Biophys J 104 414a
[5]	Li F, Yoo W C, Beernink M B, Stein A 2009 J. Amer. Chem. Soc. 131 18548
[6]	Lopez-Leon T, Koning V, Devaiah K B S, Vitelli V, Fernandez-Nieves A 2011 Nat.Phys. 7 391
[7]	Liang H L, Noh J, Zentel R, Rudquist P, Lagerwall J P 2013 Philos. Trans. R. Soc. London, Ser. A 371
[8]	Reisner W, Pedersen J N, Austin R H 2012 Rep. Prog. Phys. 75 106601
[9]	Scalia G, von Bhler C, Hgele C, Roth S, Giesselmann F, Lagerwall J P 2008 Soft Matter 4 570
[10]	Zakri C, Poulin P 2006 J. Mater. Chem. 16 4095
[11]	Gu L, Elkin T, Jiang X, Li H, Lin Y, Qu L, Tzeng T R J, Joseph R, Sun Y P 2005 Chem. Commun. 8 74
[12]	JOHN L 1994 Technological Applications of Dispersions 52 349(CRC Press)
[13]	Crawford G P, Zumer S 1996 Liquid crystals in complex geometries: formed by polymer and porous networks (CRC Press)
[14]	Dubois-Violette E, Parodi O 1969 Le Journal de Physique Colloques 30 C4
[15]	Meyer R B 1969 Phys Rev Lett. 22 918
[16]	de Gennes P G, Prost J 1995 The Physics of Liquid Crystals (New York: Oxford University Press)
[17]	Berreman D W 1972 Phys. Rev. Lett. 28 1683
[18]	Fukuda J i, Yoneya M, Yokoyama H 2007 Phys. Rev.Lett. 98 187803
[19]	Cladis P, Kleman M 1972 J. Phys. 33 591
[20]	Meyer R B 1973 Philos Mag 27 405
[21]	Saupe A 1973 Mol. Cryst. Liq. Cryst. 21 211
[22]	Williams C, Piera'nski P, Cladis P 1972 Phys. Rev. Lett. 29 90
[23]	Candau S, Le Roy P, Debeauvais F 1973 Mol. Cryst. Liq. Cryst. 23 283
[24]	Press M, Arrott A 1974 Phys. Rev. Lett. 33 403
[25]	Cladis P 1974 Philos. Mag. 29 641
[26]	Cladis P, White A, Brinkman W 1979 J Phys 40 325
[27]	Melzer D, Nabarro F 1977 Philos. Mag. 35 901
[28]	Volovik G, Lavrentovich O 1983 Zh Eksp Teor Fiz 85 1997
[29]	Kralj S, Zumer S, Allender D W 1991 Phys. Rev. A 43 2943
[30]	Crawford G, Stannarius R, Doane J 1991 Phys. Rev. A 44 2558
[31]	Kralj S, Zumer S 1993 Liq. Cryst 15 521
[32]	Allender D W, Crawford G, Doane J 1991 Phys. Rev. Lett. 67 1442
[33]	Crawford G, Ondris-Crawford R, Zumer S, Doane J 1993 Phys. Rev. Lett. 70 1838
[34]	McMillan W L 1971 Phys. Rev. A 4 1238
[35]	Onsager L 1949 Ann. N. Y. Acad. Sci. 51 627
[36]	Maier W, Saupe A 2014 Zeitschrift Fur Naturforschung A 13 564
[37]	Edwards S F 1965 Proc. Phys. Soc 85 613
[38]	Matsen M W, Schick M 1994 Phys. Rev. Lett. 72 2660
[39]	Ceniceros H D, Fredrickson G H 2004 Mult. Mod. Simul. 2 452
[40]	Jiang K, Huang Y, Zhang P 2010 J Comp Phys 229 7796
[41]	Khokhlov A, Semenov A 1982 Phys. A 112 605
[42]	Odijk T 1986 Macromolecules 19 2313
[43]	Lasher G 1970 J. Chem Phys 53 4141
[44]	Kayser R, Ravech'e H 1978 Phys. Rev. A 17 2067
[45]	Lekkerkerker H N W, Coulon P, Van Der Haegen R, Deblieck R 1984 J. Chem. Phys. 80 3427
[46]	Chen Z Y 1993 Macromolecules 26 3419
[47]	Chen Z Y 1993 Phys. Rev. Lett. 71 93
[48]	Leferink op Reinink A, van den Pol E, Petukhov A, Vroege G, Lekkerkerker H 2013 The Eur Phys J Special Topics 222 3053
[49]	Sheng P 1976 Phys. Rev. Lett. 37 1059
[50]	Sheng P 1982 Phys. Rev. A 26 1610
[51]	Sluckin T J, Poniewierski A 1985 Phys. Rev. Lett. 55 2907
[52]	Sen A K, Sullivan D E 1987 Phys. Rev. A 35 1391
[53]	Chen Z Y, Cui S M 1995 Phys. Rev. E 52 3876
[54]	Shundyak K, van Roij R 2006 Europhys. Lett. 74 1039
[55]	Emelyanenko A V, Aya S, Sasaki Y, Araoka F, Ema K, Ishikawa K, Takezoe H 2011 Phys. Rev. E 84 041701
[56]	Dijkstra M, Roij R v, Evans R 2001 Phys. Rev. E 63 051703
[57]	Chen J Z Y, Sullivan D E, Yuan X 2005 Europhys. Lett. 72 89
[58]	Chen J Z Y, Sullivan D E, Yuan X 2007 Macromolecules 40 1187
[59]	Ivanov V A, Rodionova A S, An E A, Martemyanova J A, Stukan M R, Mller M, Paul W, Binder K 2011 Phys. Rev. E 84 041810
[60]	Ivanov V A, Rodionova A S, Martemyanova J A, Stukan M R, Mller M, Paul W, Binder K 2013 J. Chem. Phys. 138 234903
[61]	Ivanov V A, Rodionova A S, Martemyanova J A, Stukan M R, Mller M, Paul W, Binder K 2014 Macromolecules 47 1206
[62]	van Roij, R, Dijkstra, M, Evans, R 2000 Europhys. Lett. 49 350
[63]	van Roij R A, Dijkstra M, Evans R 2000 J. Chem. Phys. 113 7689
[64]	Zwanzig R 1963 J. Chem. Phys. 39 1714
[65]	Chrzanowska A, Teixeira P I C, Ehrentraut H, Cleaver D J 2001 J. Phys.: Condens. Matter 13 4715
[66]	Chrzanowska A 2003 J. Comp. Phys. 191 265
[67]	de las Heras D, Velasco E, Mederos L 2004 J. Chem. Phys. 120 4949
[68]	Galanis J, Harries D, Sackett D L, LosertW, Nossal R 2006 Phys. Rev. Lett. 96 028002
[69]	Galanis J, Nossal R, Losert W, Harries D 2010 Phys. Rev. Lett. 105 168001
[70]	Soares e Silva M, Alvarado J, Nguyen J, Georgoulia N, Mulder B M, Koenderink G H 2011 Soft Matter 7 10631
[71]	Tsakonas C, Davidson A, Brown C, Mottram N 2007 Appl. Phys.s Lett. 90 111913
[72]	Dzubiella J, Schmidt M, Lwen H 2000 Phys. Rev. E 62 5081
[73]	de las Heras D, Velasco E, Mederos L 2009 Phys. Rev. E 79 061703
[74]	Frank F C 1958 Discuss. Faraday Soc. 25 19
[75]	Luo C, Majumdar A, Erban R 2012 Phys. Rev. E 85 061702
[76]	Chen J Z Y 2013 Soft Matter 9 10921
[77]	Frenkel D, Eppenga R 1985 Phys. Rev. A 31 1776
[78]	Lagomarsino M C, Dogterom M, Dijkstra M 2003 J. Chem. Phys. 119 3535
[79]	Poniewierski A, Holyst R 1988 Phys. Rev. A 38 3721
[80]	Bates M A, Frenkel D 2000 J. Chem. Phys. 112 10034
[81]	Wang X J 1996 Liq. Cry. Dis. 11 1 (in Chinese) [王新久 1996 液晶与显示 11 1]
[82]	Lubensky T C, Prost J 1992J. Phys. II (France) 2 371
[83]	Nelson D R 2002 Defects and Geometry in Condensed Matter Physics (Cambridge University Press) p392
[84]	Arsenault A, Fournier-Bidoz S, Hatton B, Miguez H, Tetreault N, Vekris E, Wong S, Ming Yang S, Kitaev V, Ozin G A 2004 J. Mater. Chem. 14 781
[85]	Bowick M J, Giomi L 2009 Adv. Phys. 58 449
[86]	Fern'andez-Nieves A, Vitelli V, Utada A S, Link D R, M'arquez M, Nelson D R, Weitz D A 2007 Phys. Rev. Lett. 99 157801
[87]	Huber M, Stark H 2005 Europhys. Lett. 69 135
[88]	Nelson D R 2002 Nano Lett. 2 1125
[89]	Skaej G, Zannoni C 2008 Phys. Rev. Lett. 100 197802
[90]	Shin H, Bowick M, Xing X 2008 Phys. Rev. Lett. 101 037802
[91]	Bates M A 2008 J. Chem. Phys. 128 104707
[92]	Dhakal S, Solis F J, Olvera de la Cruz M 2012 Phys. Rev. E 86 011709
[93]	Zhang W Y, Jiang Y, Chen J Z Y 2012 Phys. Rev. Lett. 108 057801
[94]	Zhang W Y, Jiang Y, Chen J Z Y 2012 Phys. Rev. E 85 061710
[95]	Liang Q, Ye S, Zhang P, Chen J Z Y 2014 J. Chem. Phys. 141 244901
[96]	Sec D, Lopez-Leon T, Nobili M, Blanc C, Fernandez-Nieves A, Ravnik M, Žumer S 2012 Phys. Rev. E 86 020705
[97]	Vitelli V, Nelson D R 2006 Phys. Rev. E 74 021711
[98]	Straley J P 1973 Phys. Rev. A 8 2181
[99]	Sato T, Teramoto A 1996 Macromolecules 29 4107
[100]	Akinchina A, Linse P 2002 Macromolecules 35 5183
[101]	Stoll S, Chodanowski P 2002 Macromolecules 35 9556
[102]	Spakowitz A J, Wang Z G 2003 Phys. Rev. Lett. 91 166102
[103]	Bruinsma, R F 2006 Physics of rna and viral assembly Eur. Phys. J. E 19 303
[104]	Kusner I, Srebnik S 2007 Macromolecules 40 6432
[105]	Morrison G, Thirumalai D 2009 Phys. Rev. E 79 011924
[106]	Zhang W Y, Chen J Z Y 2011 EPL 94 43001
[107]	Liang H L, Schymura S, Rudquist P, Lagerwall J 2011 Phys. Rev. Lett. 106 247801
[108]	Koning V, Lopez-Leon T, Fernandez-Nieves A, Vitelli V 2013 Soft Matter 9 4993
[109]	Lin C H, Tsai Y C, Hu C K 2007 Phys. Rev. E 75 031903
[110]	Evans R M 1995 J. Phys. II 5 507
[111]	Selinger R L B, Konya A, Travesset A, Selinger J V 2011 J. Phys. Chem. B 115 13989
[112]	Li Y, Miao H, Ma H, Chen J Z Y 2014 RSC Adv. 4 27471
[113]	Liang Q, Li J, Zhang P, Chen J Z Y 2013 J. Chem. Phys. 138 244910
[114]	Khokhlov A, Semenov A 1985 J. Stat Phys. 38 161
[115]	Wu L, Muller E A, Jackson G 2014 Macromolecules 47 1482
[116]	Varga S, Mart'tnez-Rat'tn Y, Velasco E 2010 Eur. Phys. J. E 32 89
[117]	Varga S, Mart'tnez-Rat'tn Y, Velasco E 2014 J. Phys.: Condens. Matter 26 075104

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