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Computer simulation of liquid crystals

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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

  1. de Gennes, P.G., Physics of Liquid Crystals, Oxford University Press, Oxford, 1974.

    Google Scholar 

  2. Luckhurst, G.R. and Gray, G.W., The Molecular Physics of Liquid Crystals, Academic Press, New York, London, 1979.

    Google Scholar 

  3. Hansen, J.P. and McDonald, I.R., Theory of Simple Liquids, 2nd ed., Academic Press, New York, London, 1986.

    Google Scholar 

  4. Onsager, L., Ann. N.Y. Acad. Sci., 51 (1949) 627.

    Google Scholar 

  5. Frenkel, D., Mol. Phys., 60 (1987) 1.

    Google Scholar 

  6. Vieillard-Baron, J., J. Chem. Phys., 56 (1972) 4729; Vieillard-Baron, J., Mol. Phys., 28 (1974) 809.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. Boublik, T. and Nezbeda, I., Coll. Czech. Chem. Commun., 51 (1986) 2301.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. Allen, M.P., Frenkel, D. and Talbot, J., Comput. Phys. Rep., 9 (1989) 301.

    Google Scholar 

  12. Allen, M.P., Mol. Simul., 2 (1989) 301.

    Google Scholar 

  13. Frenkel, D. and Eppenga, R., Phys. Rev. Lett., 49 (1982) 1089; Eppenga, R. and Frenkel, D., Mol. Phys., 52 (1984) 1303.

    Google Scholar 

  14. Allen, M.P. and Frenkel, D., Phys. Rev. Lett., 58 (1987) 1748.

    PubMed  Google Scholar 

  15. 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.

  16. Stroobants, A., Lekkerkerker, H.N.W. and Frenkel, D., Phys. Rev. Lett., 57 (1986) 1452;ibid., Phys. Rev. A, 36 (1987) 2929.

    PubMed  Google Scholar 

  17. Frenkel, D., Lekkerkerker, H.N.W. and Stroobants, A., Nature, 332 (1988) 822.

    Google Scholar 

  18. Frenkel, D., Liq. Cryst., 5 (1989) 929.

    Google Scholar 

  19. Frenkel, D., unpublished results.

  20. Berne, B.J. and Pechukas, P., J. Chem. Phys., 56 (1972) 4213.

    Google Scholar 

  21. Kushick, J. and Berne, B.J., J. Chem. Phys., 64 (1976) 1362.

    Google Scholar 

  22. Tsykalo, A.L. and Bagmet, A.D., Mol. Cryst. Liq. Cryst., 46 (1978) 111.

    Google Scholar 

  23. Decoster, D., Constant, E. and Constant, M., Mol. Cryst. Liq. Cryst., 97 (1983) 263.

    Google Scholar 

  24. Adams, D.J., Luckhurst, G.R. and Phippen, R.W., Mol. Phys., 61 (1987) 1575.

    Google Scholar 

  25. Gay, J.G. and Berne, B.J., J. Chem. Phys., 74 (1981) 3316.

    Google Scholar 

  26. Luckhurst, G.R., Phippen, R.W. and Stephens, R.A., to be submitted for publication.

  27. Kihara, T., J. Phys. Soc. Japan, 6 (1951) 289.

    Google Scholar 

  28. Vega, C. and Frenkel, D., Mol. Phys., 67 (1989) 633.

    Google Scholar 

  29. Leadbetter, A.J., In Gray, G.W. (Ed.) Thermotropic Liquid Crystals, John Wiley and Sons, Chichester, 1987, pp. 1–27.

    Google Scholar 

  30. Toyne, K.J., In Gray, G.W. (Ed.) Thermotropic Liquid Crystals, John Wiley and Sons, Chichester, 1987, pp. 28–63.

    Google Scholar 

  31. Eidenschink, R., Erdmann, D., Krause, J. and Pohl, L., Angew. Chem., Int. Ed. Engl., 16 (1977) 100.

    Google Scholar 

  32. Villiger, A., Boller, A. and Schadt, M., Z. Naturforsch., 34B (1979) 1535.

    Google Scholar 

  33. Wilson, M.R. and Dunmur, D.A., Liq. Cryst., 5 (1989) 987; Dunmur, D.A. and Wilson, M.R., Mol. Simul., 4 (1989) 37.

    Google Scholar 

  34. 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.

  35. Toriyama, K. and Dunmur, D.A., Mol. Cryst. Liq. Cryst., 139 (1986) 123.

    Google Scholar 

  36. 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.

    Google Scholar 

  37. 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.

    Google Scholar 

  38. Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S. and Karplus, M., J. Comput. Chem., 4 (1983) 187.

    Google Scholar 

  39. Wilson, M.R., Ph. D. Thesis, University of Sheffield, 1988, Ch. 2.

  40. Allen, M.P. and Tildesley, D.J., Computer Simulation of Liquids, Oxford University Press, Oxford, 1989.

    Google Scholar 

  41. Ryckaert, J.P., Ciccotti, G. and Berendsen, H.J.C., J. Comput. Phys., 23 (1977) 327.

    Google Scholar 

  42. Andersen, H.C., J. Comput. Phys., 52 (1983) 24.

    Google Scholar 

  43. Picken, S.J., van Gunsteren, W.F., van Duijnen, P.Th. and de Jeu, W.H., Liq. Cryst., 6 (1989) 357.

    Google Scholar 

  44. Maier, W. and Saupe, A., Z. Naturforsch. (a), 13 (1958) 564;ibid., 14 (1958) 882;ibid., 15 (1960) 287.

    Google Scholar 

  45. Lebwohl, P.A. and Lasher, G., Phys. Rev. A, 6 (1972) 426;ibid., 7 (1973) 2222.

    Google Scholar 

  46. Luckhurst, G.R. and Simpson, P., Mol. Phys., 47 (1982) 251.

    Google Scholar 

  47. Fabbri, U. and Zannoni, C., Mol. Phys., 58 (1986) 763.

    Google Scholar 

  48. Mann, M.E., Marshall, C.H. and Haymet, A.D.J., Mol. Phys., 66 (1989) 493.

    Google Scholar 

  49. Allen, M.P., Mol. Phys., 68 (1989) 181.

    Google Scholar 

  50. Luckhurst, G.R., Sluckin, T.J. and Zewdie, H.B., Mol. Phys., 59 (1986) 657.

    Google Scholar 

  51. Allen, M.P., Mol. Simul., 4 (1989) 61.

    Google Scholar 

  52. see Sluckin, T.J. and Poniewierski, A., In Croxton, C.R. (Ed.) Fluid Interfacial Phenomena, John Wiley and Sons, Chichester, 1985, and references therein.

    Google Scholar 

  53. 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.

    Google Scholar 

  54. 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.

    Google Scholar 

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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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