Summary
We review recent progress in the computer simulation of liquid crystals, with special emphasis on hard particle models. Surprisingly, the simplest molecular models, taking account only of molecular size and shape, are sufficient to generate a wide variety of liquid crystalline phases, closely analogous to those observed in real life. Thermodynamic stability of different phases is very sensitive to shape, and presumably will also be sensitive to further details of intermolecular interactions as they are incorporated into the model. Realistic atom-atom potential models of liquid crystals are available, but the associated simulations are quite expensive. Thus, while idealized models may be used to study quite general, fundamental properties of mesophases, the modelling of specific liquid crystal systems in a realistic way remains a great challenge. Progress continues to be made on both these fronts.
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References
de Gennes, P.G., Physics of Liquid Crystals, Oxford University Press, Oxford, 1974.
Luckhurst, G.R. and Gray, G.W., The Molecular Physics of Liquid Crystals, Academic Press, New York, London, 1979.
Hansen, J.P. and McDonald, I.R., Theory of Simple Liquids, 2nd ed., Academic Press, New York, London, 1986.
Onsager, L., Ann. N.Y. Acad. Sci., 51 (1949) 627.
Frenkel, D., Mol. Phys., 60 (1987) 1.
Vieillard-Baron, J., J. Chem. Phys., 56 (1972) 4729; Vieillard-Baron, J., Mol. Phys., 28 (1974) 809.
Levesque, D., Weis, J.J. and Hansen, J.P., In Binder, K. (Ed.) Applications of the Monte Carlo Method in Statistical Physics, 2nd ed., Springer-Verlag, Berlin, 1987, Chapter 2.
Boublik, T. and Nezbeda, I., Coll. Czech. Chem. Commun., 51 (1986) 2301.
Perram, J.W. and Wertheim, M.S., J. Comput. Phys., 58 (1985) 409; Perram, J.W., Wertheim, M.S., Lebowitz, J.L. and Williams, G.O., Chem. Phys. Lett., 105 (1984) 277.
Frenkel, D., Mulder, B.M. and McTague, J.P., Phys. Rev. Lett., 52 (1984) 287; Frenkel, D. and Mulder, B.M., Mol. Phys., 55 (1985) 1171.
Allen, M.P., Frenkel, D. and Talbot, J., Comput. Phys. Rep., 9 (1989) 301.
Allen, M.P., Mol. Simul., 2 (1989) 301.
Frenkel, D. and Eppenga, R., Phys. Rev. Lett., 49 (1982) 1089; Eppenga, R. and Frenkel, D., Mol. Phys., 52 (1984) 1303.
Allen, M.P. and Frenkel, D., Phys. Rev. Lett., 58 (1987) 1748.
Allen, M.P. and Frenkel, D., Phys. Rev. A, 37 (1988) 1813; we have recently discovered that the numerical results presented in this paper are in error, and should be multiplied by a factor 2.25: a correction is in preparation.
Stroobants, A., Lekkerkerker, H.N.W. and Frenkel, D., Phys. Rev. Lett., 57 (1986) 1452;ibid., Phys. Rev. A, 36 (1987) 2929.
Frenkel, D., Lekkerkerker, H.N.W. and Stroobants, A., Nature, 332 (1988) 822.
Frenkel, D., Liq. Cryst., 5 (1989) 929.
Frenkel, D., unpublished results.
Berne, B.J. and Pechukas, P., J. Chem. Phys., 56 (1972) 4213.
Kushick, J. and Berne, B.J., J. Chem. Phys., 64 (1976) 1362.
Tsykalo, A.L. and Bagmet, A.D., Mol. Cryst. Liq. Cryst., 46 (1978) 111.
Decoster, D., Constant, E. and Constant, M., Mol. Cryst. Liq. Cryst., 97 (1983) 263.
Adams, D.J., Luckhurst, G.R. and Phippen, R.W., Mol. Phys., 61 (1987) 1575.
Gay, J.G. and Berne, B.J., J. Chem. Phys., 74 (1981) 3316.
Luckhurst, G.R., Phippen, R.W. and Stephens, R.A., to be submitted for publication.
Kihara, T., J. Phys. Soc. Japan, 6 (1951) 289.
Vega, C. and Frenkel, D., Mol. Phys., 67 (1989) 633.
Leadbetter, A.J., In Gray, G.W. (Ed.) Thermotropic Liquid Crystals, John Wiley and Sons, Chichester, 1987, pp. 1–27.
Toyne, K.J., In Gray, G.W. (Ed.) Thermotropic Liquid Crystals, John Wiley and Sons, Chichester, 1987, pp. 28–63.
Eidenschink, R., Erdmann, D., Krause, J. and Pohl, L., Angew. Chem., Int. Ed. Engl., 16 (1977) 100.
Villiger, A., Boller, A. and Schadt, M., Z. Naturforsch., 34B (1979) 1535.
Wilson, M.R. and Dunmur, D.A., Liq. Cryst., 5 (1989) 987; Dunmur, D.A. and Wilson, M.R., Mol. Simul., 4 (1989) 37.
Pitzer, K.S., In Prigogine, I., (Ed.) Advances in Chemical Physics, Vol. II, Interscience, New York, pp. 59–83; Dunfield, L.G., Burgess, A.W. and Scheraga, H.A., J. Phys. Chem., 82 (1978) 2609; Momany, F.A., Carruthers, L.M. and Scheraga, H.A., J. Phys. Chem., 78 (1974) 1595; Hagler, A.T., Huler, E. and Lifson, S., J. Am. Chem. Soc., 96 (1974) 5319; Hagler, A.T. and Lifson, S., J. Am. Chem. Soc., 96 (1974) 5327.
Toriyama, K. and Dunmur, D.A., Mol. Cryst. Liq. Cryst., 139 (1986) 123.
Allinger, N.L., Tribble, M.T., Miller, M.A. and Wertz, D.H., J. Am. Chem. Soc., 93 (1971) 1637; Wertz, D.H. and Allinger, N.L., Tetrahedron, 30 (1974) 1579; Allinger, N.L. and Sprague, J.T., J. Am. Chem. Soc., 95 (1973) 3893; Allinger, N.L., Sprague, J.T. and Liljefors, T., J. Am. Chem. Soc., 96 (1974) 5100; Allinger, N.L., J. Am. Chem. Soc., 99 (1977) 8127.
Weiner, P.K. and Kollman, P.A., J. Comput. Chem., 2 (1981) 287–303; Weiner, S.J., Kollman, P.A., Nguyen, D.T. and Case, D.A., J. Comput. Chem., 7 (1986) 230; Weiner, S.J., Kollman, P.A., Case, D.A., Singh, U.C., Ghio, C., Alagona, G., Profeta, Jr., S. and Weiner, P.J., J. Am. Chem. Soc., 106 (1984) 765; Singh, U.C., Weiner, P.K., Caldwell, J. and Kollman, P.A., AMBER 3.0, University of California, San Francisco, 1987.
Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S. and Karplus, M., J. Comput. Chem., 4 (1983) 187.
Wilson, M.R., Ph. D. Thesis, University of Sheffield, 1988, Ch. 2.
Allen, M.P. and Tildesley, D.J., Computer Simulation of Liquids, Oxford University Press, Oxford, 1989.
Ryckaert, J.P., Ciccotti, G. and Berendsen, H.J.C., J. Comput. Phys., 23 (1977) 327.
Andersen, H.C., J. Comput. Phys., 52 (1983) 24.
Picken, S.J., van Gunsteren, W.F., van Duijnen, P.Th. and de Jeu, W.H., Liq. Cryst., 6 (1989) 357.
Maier, W. and Saupe, A., Z. Naturforsch. (a), 13 (1958) 564;ibid., 14 (1958) 882;ibid., 15 (1960) 287.
Lebwohl, P.A. and Lasher, G., Phys. Rev. A, 6 (1972) 426;ibid., 7 (1973) 2222.
Luckhurst, G.R. and Simpson, P., Mol. Phys., 47 (1982) 251.
Fabbri, U. and Zannoni, C., Mol. Phys., 58 (1986) 763.
Mann, M.E., Marshall, C.H. and Haymet, A.D.J., Mol. Phys., 66 (1989) 493.
Allen, M.P., Mol. Phys., 68 (1989) 181.
Luckhurst, G.R., Sluckin, T.J. and Zewdie, H.B., Mol. Phys., 59 (1986) 657.
Allen, M.P., Mol. Simul., 4 (1989) 61.
see Sluckin, T.J. and Poniewierski, A., In Croxton, C.R. (Ed.) Fluid Interfacial Phenomena, John Wiley and Sons, Chichester, 1985, and references therein.
Pusey, P.N. and van Megen, W., Nature, 320 (1986) 340–342; van Megen, W., Ottewill, R.H., Owens, S.M. and Pusey, P.N., J. Chem. Phys., 82 (1985) 508.
Nagy, M. and Keller, A., Polymer Commun., 30 (1989) 130; Odell, J.A., Keller, A., Atkins, E.D.T., Nagy, M., Feijoo, J.L. and Ungar, G., in Adams, W. (Ed.) Rigid Rod Polymer Molecules, Mat. Res. Soc. Symp. Proc. 134, Materials Research Society, Pittsburgh, 1989, pp. 223–234.
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Allen, M.P., Wilson, M.R. Computer simulation of liquid crystals. J Computer-Aided Mol Des 3, 335–353 (1989). https://doi.org/10.1007/BF01532020
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DOI: https://doi.org/10.1007/BF01532020