Skip to main content

Computer Simulations of Phase Transitions in Liquid Crystals

  • Chapter
Phase Transitions in Liquid Crystals

Part of the book series: NATO ASI Series ((NSSB,volume 290))

Abstract

The aim of these lectures is twofold. First, I wish to give a simple introduction to the computer simulations of classical many-body systems, with special emphasis on those technical aspects that are of particular relevance for simulation of liquid crystals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.P. Allen and D.J. Tildesley, “Computer Simulation of Liquids”, Clarendon, Oxford, 1987.

    MATH  Google Scholar 

  2. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, J.Chem.Phys. 21: 1087 (1953).

    Article  ADS  Google Scholar 

  3. M. Parrinello and A. Rahman, Phys. Rev. Lett. 45: 1196 (1980).

    Article  ADS  Google Scholar 

  4. M. Parrinello and A. Rahman, J. Appl. Phys. 52: 7182 (1981).

    Article  ADS  Google Scholar 

  5. R. Najafabadi and S. Yip, Scripta Metall. 17: 1199 (1983).

    Article  Google Scholar 

  6. M.J. Mandell, J. Stat. Phys. 15: 299 (1976).

    Article  ADS  Google Scholar 

  7. P.J. Steinhardt, D.R. Nelson and M. Ronchetti, Phys. Rev. B 28: 784 (1983).

    Article  ADS  Google Scholar 

  8. R.W. Impey, P.A. Madden and D.J. Tildesley, Mol. Phys. 44: 1319 (1981).

    Article  ADS  Google Scholar 

  9. M. Fixman, Proc. Nat Acad. Sci. 71: 3050 (1974).

    Article  ADS  Google Scholar 

  10. L. Verlet, Phys. Rev. 159: 98 (1967).

    Article  ADS  Google Scholar 

  11. H.J.C. Berendsen and W.F. van Gunsteren, in: “Molecular Dynamics Simulations of Statistical Mechanical Systems”, Proceedings of the 97th International School of Physics ‘Enrico Fermi’, G. Ciccotti and W. G. Hoover, editors. NorthHolland, Amsterdam, 1985, p.43.

    Google Scholar 

  12. M.P. Allen, D. Frenkel and J. Talbot, Computer Physics Reports 9: 301 (1989).

    Article  ADS  Google Scholar 

  13. J.J. Erpenbeck and W.W. Wood in: “Statistical Mecahnics”, Part B, ed. B.J. Berne, Plenum Press, New York, 1977.

    Google Scholar 

  14. J.L. Lebowitz, J.K. Percus and L. Verlet, Phys. Rev. 153: 250 (1967).

    Article  ADS  Google Scholar 

  15. H.C. Andersen, J. Chem. Phys. 72: 2384 (1980).

    Article  ADS  Google Scholar 

  16. S. Nose, J. Chem. Phys. 81: 511 (1984).

    Article  ADS  Google Scholar 

  17. W.W. Wood, J. Chem. Phys. 48: 415 (1968).

    Article  ADS  Google Scholar 

  18. I.R. McDonald, Mol. Phys. 23: 41 (1972).

    Article  ADS  Google Scholar 

  19. G.E. Norman and V.S. Filinov, High Temp. Res. USSR 7: 216 (1969).

    Google Scholar 

  20. D.J. Adams, Mol. Phys. 28: 1241 (1974).

    Article  ADS  Google Scholar 

  21. M. Creutz, Phys. Rev. Lett. 50: 1411 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  22. A. Panagiotopoulos, Mol. Phys. 61: 813 (1987).

    Article  ADS  Google Scholar 

  23. G. Ciccotti, D. Frenkel and I.R. McDonald, “Simulation of Liquids and Solids”, NorthHolland, Amsterdam, 1987. This reprint collection contains, among others, Ref.s 2, 4, 14, 15, 16, 18, 10, 24, 28.

    Google Scholar 

  24. R. Zwanzig and NX Ailawadi, Phys. Rev. 182: 280 (1969).

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Frenkel in: “Intermolecular Spectroscopy and Dynamical Properties of Dense Systems”, Proceedings of the 75th International School of Physics ‘Enrico Fermi’, J. van Kranendonk, ed., Soc. Italiana di Fisica, Bologna, 1980, p.156.

    Google Scholar 

  26. G. Jacucci and A. Rahman, Nuovo Cimento D 4: 341 (1984).

    Article  ADS  Google Scholar 

  27. D. Frenkel in: “Molecular Dynamics Simulations of Statistical Mechanical Systems”, Proceedings of the 97th International School of Physics ‘Enrico Fermi’, G. Ciccotti and W. G. Hoover, editors. NorthHolland, Amsterdam, 1985, p.151.

    Google Scholar 

  28. W.G. Hoover and F.H. Ree, J. Chem. Phys. 47: 4873 (1967).

    Article  ADS  Google Scholar 

  29. L.P. Hansen and L.R. McDonald, “Theory of Simple Liquids”, 2nd edition, Academic Press, London, 1986.

    Google Scholar 

  30. E.J. Meijer, D. Frenkel, R.A. LeSar and A.J.C. Ladd, J. Chem. Phys. 92: 7570 (1990).

    Article  ADS  Google Scholar 

  31. D. Frenkel and B.M. Mulder, Mol. Phys. 55: 1171 (1985).

    Article  ADS  Google Scholar 

  32. W.G.T. Kranendonk and D. Frenkel, Mol. Phys. 72: 699 (1991).

    Article  ADS  Google Scholar 

  33. P.G. de Germes, “Physics of Liquid Crystals”, Oxford University Press, Oxford, England (1974).

    Google Scholar 

  34. L. Onsager, Proc. NY. Acad. Sci. 51: 627 (1949).

    Article  ADS  Google Scholar 

  35. W. Maier and A. Saupe, Z. Naturforsch. A 13: 564 (1958).

    ADS  Google Scholar 

  36. F. Dowell and D.E. Martire, J. Chem. Phys. 68: 1088(1978),

    Article  ADS  Google Scholar 

  37. ibid.: 68: 1094 (1978),

    Article  ADS  Google Scholar 

  38. ibid.: 69: 2322 (1978).

    ADS  Google Scholar 

  39. F. Dowell, Phys. Rev. A 28: 3526 (1983).

    Article  ADS  Google Scholar 

  40. W.M. Gelbart and A. Gelbart, Mol. Phys. 33: 1387 (1977).

    Article  ADS  Google Scholar 

  41. B.J. Alder and T.E. Wainwright, J. Chem. Phys. 27: 1208 (1957).

    Article  ADS  Google Scholar 

  42. J.D. Weeks, D. Chandler and H.C. Andersen, J. Chem. Phys. 54: 5237 (1971).

    Article  ADS  Google Scholar 

  43. See, for instance: C. Zannoni in “The molecular physics of liquid crystals”, G.R. Luckhurst and G.W. Gray editors, Academic Press, London, 1979, p. 191.

    Google Scholar 

  44. P.A. Lebwohl and G. Lasher, Phys. Rev. A 6: 426 (1972).

    Article  ADS  Google Scholar 

  45. J. Vieillard-Baron, J. Chem. Phys. 56: 4729 (1972).

    Article  ADS  Google Scholar 

  46. J. Vieillard-Baron, Mol. Phys. 28: 809 (1974).

    Article  ADS  Google Scholar 

  47. W.G. Hoover and F.H. Ree, J. Chem. Phys. 49: 3609 (1968).

    Article  ADS  Google Scholar 

  48. R. Eppenga and D. Frenkel, Mol. Phys. 52: 1303 (1984).

    Article  ADS  Google Scholar 

  49. M.P. Allen and M.R. Wilson, J. Computer-Aided Molec. Design 3: 335 (1989).

    Article  ADS  Google Scholar 

  50. D. Frenkel, Mol. Phys. 54: 145 (1985).

    Article  ADS  Google Scholar 

  51. M.P. Allen, Liquid Crystals, 8: 499 (1990).

    Article  Google Scholar 

  52. B.M. Mulder, Phys. Rev. A 39: 360 (1989),

    Article  ADS  Google Scholar 

  53. B.M. Mulder Liquid Crystals 8: 527 (1990).

    Article  MathSciNet  Google Scholar 

  54. M.A. Cotter and D.E. Martire, J. Chem. Phys. 52: 1902 (1970),

    Article  ADS  Google Scholar 

  55. M.A. Cotter and D.E. Martire, J. Chem. Phys. 53: 4500 (1970).

    Article  ADS  Google Scholar 

  56. M.A. Cotter, Phys. Rev. A 10: 625 (1974),

    Article  ADS  Google Scholar 

  57. M.A. Cotter, J. Chem. Phys. 66: 1098 (1977).

    Article  ADS  Google Scholar 

  58. B. Barboy and W.M. Gelbart, J. Chem. Phys. 71: 3053 (1979).

    Article  ADS  Google Scholar 

  59. B. Barboy and W.M. Gelbart, J. Stat. Phys. 22: 685 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  60. B.M. Mulder and D. Frenkel, Mol. Phys. 55 1193 (1985).

    Article  ADS  Google Scholar 

  61. U.P. Singh and Y. Singh, Phys. Rev. A 33: 2725 (1986).

    Article  ADS  Google Scholar 

  62. M. Baus, J.L. Colot, X.G. Wu and H. Xu, Phys. Rev. Lett. 59: 2148 (1987).

    Article  Google Scholar 

  63. J.F. Marko, Phys. Rev. Lett. 60: 325 (1989).

    Article  ADS  Google Scholar 

  64. J.F. Marko, Phys. Rev. A 39: 2050 (1989).

    Article  ADS  Google Scholar 

  65. J.L. Colot, X.G. Wu, H. Xu and M. Baus, Phys. Rev. A 38: 2022 (1988).

    Article  ADS  Google Scholar 

  66. A. Perera, P.G. Kusalik and G.N. Patey, J. Chem. Phys. 87: 1295 (1987),

    Article  ADS  Google Scholar 

  67. A. Perera, P.G. Kusalik and G.N. Patey, J. Chem. Phys. 89: 5969 (1988).

    Article  ADS  Google Scholar 

  68. A. Perera, G.N. Patey and J.J. Weis, J. Chem. Phys. 89: 6941 (1989).

    Article  ADS  Google Scholar 

  69. A. Perera and G. N. Patey, J. Chem. Phys. 89: 5861 (1989).

    Article  ADS  Google Scholar 

  70. J.M. Kosterlitz and D. Thouless, J. Phys. C6: 1181 (1973).

    ADS  Google Scholar 

  71. M. Romeiro, J. Math. Phys. 19: 802 (1978).

    Article  ADS  Google Scholar 

  72. D. Frenkel and R. Eppenga, Phys. Rev. A 31: 1776 (1985).

    Article  ADS  Google Scholar 

  73. R.F. Kayser and H.J. Raveche, Phys. Rev. A 17: 2067 (1978).

    Article  ADS  Google Scholar 

  74. J.A. Cuesta, CF. Tejero and M. Baus, Phys. Rev. A 39: 6498 (1989).

    Article  ADS  Google Scholar 

  75. J.A. Cuesta and D. Frenkel, Phys. Rev. A 42: 2126 (1990).

    Article  ADS  Google Scholar 

  76. M.J.P. Gingras, P.C.W. Holdsworth and B. Bergersen, in “Proceedings of the 13th International Liquid Crystal Conference” (in press), and

    Google Scholar 

  77. M.J.P. Gingras, P.C.W. Holdsworth and B. Bergersen, Phys. Rev. A 41: 6786 (1990).

    Article  ADS  Google Scholar 

  78. M. Hosino, H. Nakano and H. Kimura, J.Phys. Soc. Japan 46: 1709 (1979).

    Article  ADS  Google Scholar 

  79. Recently, it has been shown that this argument does not extend to models that include attractive forces. In particular, it has been shown that the Gay-Berne model, i.e. the ‘ellipsoidal’ generalization of the Lennard-Jones model for atomic fluids, does indeed exhibit one or more stable smectic phases68.

    Google Scholar 

  80. E. de Miguel, L.F. Rull, M.K. Chalam, K.E. Gubbins and F. van Swol, Mol. Phys. 72: 593 (1991).

    Article  ADS  Google Scholar 

  81. A. Stroobants, H.N.W. Lekkerkerker and D. Frenkel, Phys. Rev. Lett. 57: 1452 (1986).

    Article  ADS  Google Scholar 

  82. A. Stroobants, H.N.W. Lekkerkerker and D. Frenkel, Phys. Rev. A 36: 2929 (1987).

    Article  ADS  Google Scholar 

  83. J.A.C. Veerman, thesis, University of Utrecht, 1991. J.A.C. Veerman and D.Frenkel, Phys. Rev. A (in press).

    Google Scholar 

  84. B.M. Mulder, Phys. Rev. A 35: 3095 (1987).

    Article  ADS  Google Scholar 

  85. X. Wen and R.B. Meyer, Phys. Rev. Lett. 59: 1325 (1987).

    Article  ADS  Google Scholar 

  86. A.M. Somoza and P. Tarazona, Phys. Rev. Lett. 61: 2566 (1988).

    Article  ADS  Google Scholar 

  87. R. Holyst and A. Poniewierski, Phys. Rev. 39: 2742 (1988).

    Google Scholar 

  88. A. Poniewierski and R. Holyst, Phys. Rev. Lett. 61: 2461 (1988).

    Article  ADS  Google Scholar 

  89. R. Holyst and A. Poniewierski, preprint.

    Google Scholar 

  90. M.P. Taylor, R. Hentschke and J. Herzfeld, Phys. Rev. Lett. 62: 800 (1989),

    Article  ADS  Google Scholar 

  91. ibid: 62: 1577 (1989).

    Article  ADS  Google Scholar 

  92. M.P. Taylor, R. Hentschke and J. Herzfeld, Phys. Rev. A 40: 1678 (1989).

    Article  ADS  Google Scholar 

  93. J.M. Caillol and J.J. Weis, J. Chem. Phys. 90: 7403 (1989).

    Article  ADS  Google Scholar 

  94. T.J. Sluckin, Liquid Crystals 6: 111 (1989).

    Article  Google Scholar 

  95. T.E. Strzelecka, M.W. Davidson and R.L. Rill, Nature, 331: 457 (1988).

    Article  ADS  Google Scholar 

  96. F. Livolant, A.M. Levelut, J. Doucet and J.P. Benoit, Nature 339: 724 (1989).

    Article  ADS  Google Scholar 

  97. D. Frenkel, J. Phys. Chem. 92: 3280 (1988).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  99. J.A.C. Veerman and D. Frenkel, Phys. Rev. A 41: 3237 (1990).

    Article  ADS  Google Scholar 

  100. A.M. Somoza and P. Tarazona, Phys. Rev. A 41: 965 (1990).

    Article  ADS  Google Scholar 

  101. A.M. Somoza and P. Tarazona, J. Chem. Phys. 91: 517 (1989).

    Article  ADS  Google Scholar 

  102. D. Frenkel, Liquid Crystals, 5: 929 (1989).

    Article  Google Scholar 

  103. T. Boublik and I. Nezbeda, Coll. Czechoslovak. Chem. Commun. 51: 2301 (1986).

    Article  Google Scholar 

  104. J.A.C. Veerman, thesis, University of Utrecht, 1991. J.A.C. Veerman and D. Frenkel, to be published.

    Google Scholar 

  105. J. Billart, C.R. Acad. Sci. Paris, 305: 843 (1987).

    Google Scholar 

  106. J.I. Siepmann, Mol. Phys. 70: 1145 (1990).

    Article  ADS  Google Scholar 

  107. D. Frenkel, J. Phys. Condensed Matter 2(SA): 265 (1990).

    Article  ADS  Google Scholar 

  108. D. Frenkel, Physica A, submitted for publication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer Science+Business Media New York

About this chapter

Cite this chapter

Frenkel, D. (1992). Computer Simulations of Phase Transitions in Liquid Crystals. In: Martellucci, S., Chester, A.N. (eds) Phase Transitions in Liquid Crystals. NATO ASI Series, vol 290. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-9151-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-9151-7_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-9153-1

  • Online ISBN: 978-1-4684-9151-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics