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Nematic ordering in a Vycor-like restrictive geometry: A two-dimensional model

Zhengping Zhang and Amitabha Chakrabarti

  • Department of Physics, Kansas State University, Manhattan, Kansas 66506

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Phys. Rev. E 52, 4991 – Published 1 November, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.4991

Abstract

We report results from Monte Carlo simulations of the orientational ordering of the two-dimensional Lebwohl-Lasher model for nematic liquid crystals confined inside a model porous medium of Vycor-like tortuous geometry. We find that the magnitude of the order parameter and the susceptibility are strongly suppressed in the presence of the porous medium. The system breaks into many nematic domains with a random distribution of nematic directors. This feature is similar to the ‘‘nematic-glass’’ behavior that is seen in experiments. We find that the relaxation of the order parameter autocorrelation function satisfies an activated dynamical scaling, which is in agreement with recent simulations of random-field models and some recent experiments.

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References (45)

  1. J. D. Gunton, M. San Miguel, and P. S. Sahni, in Phase Transitions and Critical Phenomena, edited by C. Domb, and J. L. Lebowitz (Academic, New York, 1983), Vol. 8.
  2. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993).
  3. See, for example, W. I. Goldburg, in Dynamics of Ordering Processes in Condensed Matter, edited by S. Komura and H. Furukawa (Plenum, New York, 1988).
  4. W. I. Goldburg, F. Aliev and X. L. Wu, Physica A 213, 61 (1995), and references therein.
  5. F. Brochard and P. G. de Gennes, J. Phys. (Paris) Lett. 44, 785 (1983); P. G. de Gennes, J. Phys. Chem. 88, 6469 (1984); D. Andelman and J. F. Joanny, in Scaling Phenomena in Disordered Systems, edited by R. Pynn and A. Skjeltorp (Plenum, New York, 1985).
  6. A. J. Liu, D. J. Durian, E. Herbolzheimer and S. A. Safran, Phys. Rev. Lett. 65, 1897 (1990).
  7. A. J. Liu and G. S. Grest, Phys. Rev. A 44, R7894 (1991); L. Monette, A. J. Liu and G. S. Grest, ibid. 46, 7664 (1992).
  8. A. Bhattacharya, M. Rao and A. Chakrabarti, Phys. Rev. E 49, 524 (1994).
  9. Z. Zhang and A. Chakrabarti, Phys. Rev. E 50, R4290 (1994).
  10. For a review see, for example, B. Jerome, Rep. Prog. Phys. 54, 391 (1991).
  11. H. Yokoyama, J. Chem. Soc. Farady Trans. 2 84, 1023 (1988); G. P. Crawford, R. Stannarius and J. W. Doane, Phys. Rev. A 44, 2558 (1991); G. P. Crawford et al., Phys. Rev. Lett. 66, 723 (1991); , ibid. 70, 1838 (1993); S. Kralj, S. Zumer and D. W. Allender, Phys. Rev. A 43, 1943 (1991); I. Vilfan, M. Vilfan and S. Zumer, ibid. 40, 4724 (1989).
  12. P. Sheng, Phys. Rev. Lett. 37, 1059 (1976); Phys. Rev. A 26, 1610 (1982).
  13. A. Golemme et al., Phys. Rev. Lett. 61, 2937 (1988).
  14. X-l. Wu, W. I. Goldburg, M. X. Liu and J. Z. Xue, Phys. Rev. Lett. 69, 470 (1992).
  15. G. S. Iannacchione et al., Phys. Rev. Lett. 71, 2595 (1993); (unpublished).
  16. T. Bellini et al., Phys. Rev. Lett. 69, 788 (1992).
  17. S. Tripathi, C. Rosenblatt and F. M. Aliev, Phys. Rev. Lett. 72, 2725 (1995).
  18. T. Bellini, N. A. Clark and D. W. Schaefer, Phys. Rev. Lett. 74, 2740 (1995).
  19. G. Schwalb and F. W. Deeg, Phys. Rev. Lett. 74, 1383 (1995).
  20. M. Gingras (unpublished).
  21. A. Maritan, M. Cieplak, T. Bellini and J. R. Banavar, Phys. Rev. Lett. 72, 4113 (1993).
  22. Y. Y. Goldschmidt and A. Aharony, Phys. Rev. B 32, 264 (1985); R. Harris, M. Plischke and M. J. Zuckermann, Phys. Rev. Lett. 31, 160 (1973).
  23. A. T. Ogielski and D. A. Huse, Phys. Rev. Lett. 56, 1298 (1986).
  24. Z. Zhang and A. Chakrabarti (unpublished).
  25. A. Chakrabarti, Phys. Rev. Lett. 69, 1548 (1992).
  26. D. W. Grunau, T. Lookman, S. Y. Chen and A. S. Lapedes, Phys. Rev. Lett. 71, 4198 (1993).
  27. A. Falicov and A. N. Berker, Phys. Rev. Lett. 74, 426 (1995).
  28. P. A. Lebwohl and G. Lasher, Phys. Rev. A 6, 426 (1972).
  29. W. Maier and A. Saupe, Z. Naturforsch. Teil A 14, 882 (1959); ibid. 15, 287 (1960).
  30. Z. Zhang, O. G. Mouritsen and M. J. Zukermann, Phys. Rev. Lett. 69, 2803 (1992).
  31. U. Fabbri and C. Zannoni, Mol. Phys. 58, 763 (1986).
  32. J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973); J. M. Kosterlitz, ibid. 7, 1046 (1974).
  33. J. F. Fernandez, M. F. Ferreira and J. Stankiewicz, Phys. Rev. B 34, 292 (1986).
  34. J. Y. Denham, G. R. Luckhurst, C. Zannoni and J. W. Lewis, Mol. Cryst. Liq. Cryst. 60, 185 (1980).
  35. Y. Oono and S. Puri, Phys. Rev. Lett. 58, 863 (1987).
  36. L. Monette, G. S. Grest and M. P. Anderson, Phys. Rev. E 50, 3361 (1994).
  37. N. Metropolis et al., J. Chem. Phys. 21, 1087 (1953).
  38. J. Tobochnik and G. V. Chester, Phys. Rev. B 20, 3761 (1979).
  39. M. Mondello and N. Goldenfeld, Phys. Rev. A 42, 5865 (1990); M. Zapotocky, P. M. Goldbart and N. Goldenfeld, Phys. Rev. E 51, 1216 (1995).
  40. P. Olsson and P. Minnhagen, Phys. Sci. 43, 203 (1991).
  41. R. Gupta et al., Phys. Rev. Lett. 61, 1996 (1988).
  42. R. Gupta and C. F. Bailli, Phys. Rev. B 45, 2883 (1992).
  43. N. Schultka and E. Manousakis, Phys. Rev. B 49, 12071 (1994).
  44. It is interesting to note that a vortex-free pinned phase has been predicted in the random-field XY model. See M. Gingras and D. A. Huse (unpublished).
  45. F. Aliev (private communication).

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Phys. Rev. E 52, 4991– Published 1 November, 1995
  • Received 21 April 1995

© 1995 American Physical Society

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