Local structure in nematic and isotropic liquid crystals
2003, The Journal of Chemical Physics
https://doi.org/10.1063/1.1577322Abstract
By computer simulations of systems of ellipsoids, we study the influence of the isotropic/nematic phase transition on the direct correlation functions (DCF) in anisotropic fluids. The DCF is determined from the pair distribution function by solving the full Ornstein-Zernike equation, without any approximations. Using a suitable molecular-fixed reference frame, we can distinguish between two qualitatively different contributions to the DCF: One which preserves rotational invariance, and one which breaks it and vanishes in the isotropic phase. We find that the symmetry preserving contribution is barely affected by the phase transition. However, symmetry breaking contributions emerge in the nematic phase and may become quite substantial. Thus the DCF in a nematic fluid is not rotationally invariant. In the isotropic fluid, the DCF is in good agreement with the prediction of the Percus-Yevick theory.
References (66)
- J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic Press, London, 1986).
- R. Evans, in Fundamentals of Inhomogeneous Fluids, p. 86, D. Henderson ed. (Marcel Dekker, New York, 1992).
- C. G. Gray and K. E. Gubbins, Theory of Molecular Fluids, Vol. 1 (Oxford, New York, 1984).
- J. E. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958).
- R. Pynn, Solid State Comm. 14, 29 (1974).
- Y. Chen and W. A. Steele, J. Chem. Phys. 54, 703 (1971).
- A. Wulf, J. Chem. Phys. 55, 4512 (1971).
- P. H. Fries and G. N. Patey, J. Chem. Phys. 82, 429 (1985);
- J. Chem. Phys. 85, 7007 (1986).
- R. C. Singh, J. Ram, Y. Singh, Phys. Rev. E 54, 977 (1996).
- A. Perera, P. G. Kusalik, and G. N. Patey, Mol. Phys. 60, 77 (1987);
- J. Chem. Phys. 87, 1295 (1987); ibid 89, 5969 (1988);
- A. Perera and G. N. Patey, J. Chem. Phys. 89, 5861 (1988);
- J. Talot, A. Perera, and G. N. Patey, Mol. Phys. 70, 285 (1990).
- R. Pospisil, A. Malijevsky, W. R. Smith, Mol. Phys. 79, 1011 (1993).
- J. Ram, Y. Singh, Phys. Rev. A 44, 3718 (1991);
- J. Ram, R. C. Singh, Y. Singh, Phys. Rev. E 49, 5117 (1994);
- S. Gupta, J. Ram, R. C. Singh, Physica A 278, 447 (2000).
- M. Letz and A. Latz, Phys. Rev. E 60, 5865 (1999).
- A. Wulf, J. Chem. Phys. 71, 104 (1979).
- G. Rickayzen, Mol. Phys. 75, 333 (1992);
- M. Calleja and G. Rickayzen, Mol. Phys. 76, 693 (1992);
- P. Kalpaxis and G. Rickayzen, Mol. Phys. 80, 391 (1993).
- M. Calleja and G. Rickayzen, Phys. Rev. Lett. 74, 4452 (1995);
- J. Phys.: Cond. Matt. 7, 8839 (1995).
- G. Rickayzen and M. Calleja, Mol. Phys. 90, 869 (1997);
- G. Rickayzen, Mol. Phys. 95, 393 (1998).
- A. Chamoux and A. Perera, J. Chem. Phys. 104, 1493 (1995);
- Phys. Rev. E 58, 1933 (1998).
- Y. Rosenfeld, Phys. Rev. Lett. 63, 980 (1989).
- A. Wulf, J. Chem. Phys. 67, 2254 (1977).
- J. D. Parsons, Phys. Rev. A 19, 1125 (1979).
- S.-D. Lee, J. Chem. Phys. 87, 4972 (1987).
- M. Baus, J.-L. Colot, X.-G. Wu, H. Xu, Phys. Rev. Lett. 59, 2184 (1987).
- J. F. Marko, Phys. Rev. A 39, 2050 (1989).
- M. P. Allen, C. P. Mason, E. de Miguel, J. Stelzer, Phys. Rev. E 52, R25 (1995).
- J. G. Gay and B. J. Berne, J. Chem. Phys. 74, 3316 (1981).
- M. P. Allen, J. T. Brown, and M. A. Warren, J. Phys.: Cond. Matter 8, 9433 (1996).
- M. P. Allen and M. A. Warren, Phys. Rev. Lett. 78, 1291 (1997).
- P.-G. de Gennes and J. Prost, The Physics of Liquid Crys- tals (Oxford University Press, Oxford, 1995).
- S. Chandrasekhar, Liquid Crystals (Cambridge University Press, Cambridge, 1992).
- K. E. Gubbins, Chem. Phys. Lett. 76, 329 (1980).
- H. Zhong, R. G. Petschek, Phys. Rev. E 51, 2263 (1994).
- H. Workman and M. Fixman, J. Chem. Phys. 58, 5024 (1973).
- J. M. Caillol, J. J. Weis, and G. N. Patey, Phys. Rev. A 38, 4772 (1988);
- J. M. Caillol and J. J. Weis, J. Chem. Phys. 90, 7403 (1989).
- H. Zhong, R. G. Petschek, Phys. Rev. E 53, 4944 (1995).
- M. F. Holovko, T. G. Sokolovska, J. Mol. Liqu. 82, 161 (1999).
- J. Stelzer, L. Longa, and H. R. Trebin J. Chem. Phys. 103, 3098 (1995); ibid 107, 1295 (1997);
- Mol. Cryst. Liqu. Cryst. 262, 455 (1995);
- J. Stelzer, M. A. Bates, L. Longa, and G. R. Luckhurst, J. Chem. Phys. 107, 7483 (1997).
- A. V. Zakharov and A. Maliniak, Eur. Phys. J. E 4, 85 (2001).
- L. Longa, G. Cholewiak, R. Trebin, G. R. Luckhurst, Eur. Phys. J. E 4, 51 (2001).
- A. Poniewierski, J. Stecki, Mol. Phys. 38, 1931 (1979).
- M. P. Allen, M. A. Warren, M. R. Wilson, A. Sauron, and W. Smith, J. Chem. Phys. 105, 2850 (1996).
- N. H. Phuong, G. Germano, and F. Schmid, J. Chem. Phys. 115, 7227 (2001).
- B. J. Berne and P. Pechukas, J. Chem. Phys. 56, 4213 (1975).
- H. Lange and F. Schmid, J. Chem. Phys. 117, 362 (2002);
- Comp. Phys. Comm. 147, 276 (2002).
- In the isotropic phase, a "director" obviously does not ex- ist. The choice of the coordinate system is then arbitrary. For reasons of consistency, we still use the Eigenvector cor- responding to the (small) largest Eigenvalue of the order tensor Q.
- W. B. Streett and D. J. Tildesley, Proc. Roy. Soc. Lond. A 348, 485-510 (1975).
- L. R. Pratt and S. W. Haan, J. Chem. Phys. 74, 1873 (1980).
- Some restrictions still remain in uniaxial nematic fluids: All molecular frame coefficients are real and vanish unless m = 0 and l1 +l2 is even. In our case, l1 and l2 must also be even individually because of the symmetry of the particles.
- G. Cinacchi and F. Schmid, J. Phys.: Cond. Matter 14, 12223 (2002);
- G. Cinacchi and F. Schmid, in preparation.
- Nguyen H. Phuong, Dissertation Universität Bielefeld (2002).