Publication: Isotropic-nematic transition of hard ellipses
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1989-06-15
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American Physical Society
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Abstract
The orientational freezing of a system of hard ellipses, as a first approximation for a nematogen adsorbed on a smooth substrate, is studied with the aid of an approximate density-functional theory used previously for the study of hard ellipsoids. The isotropic-nematic transition, which was first order for the ellipsoids, is shown to proceed via a continuous transition in the case of the ellipses. We also show that when reducing the dimensionality of the angular space of ellipsoids, the width of the transition shrinks continuously and reaches zero only for a strictly two dimensional angular space.
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© 1989 The American Physical Society. One of us (M.B.) acknowledges the support of the Association EURATOM—Etat Belge and also of the Fonds National de la Recherche Scientifique. This work has, moreover, been partially sponsored by the Comisión Asesora de Investigación Científica y Técnica (Spain) Project No. PB85-0024.
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[1] P. G. de Gennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974); G. Vertogen and W. H. de Jeu, Thermotropic Liquid Crystals: Fundamentals (Springer-Verlag, Berlin, 1988).
[2] For a recent review see, e.g., D. Frenkel, J. Phys. Chem. 92, 3280 (1988).
[3] See, for example, B. H. Mulder and D. Frenkel, Mol. Phys. 55, 1193 (1985); U. P. Singh and Y. Singh, Phys. Rev. A 33, 2725 (1986); M. Baus, J. L. Colot, X. G. Wu, and H. Xu, Phys. Rev. Lett. 59, 2184 (1987).
[4] W. Maier and A. Saupe, Z. Naturforsch. , Teil A 13, 564 (1958); W. L. McMillan, Phys. Rev. A 4, 1238 (1971).
[5] J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, London, 1976); D. A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976).
[6] See, for example, K. J. Strandburg, Rev. Mod. Phys. 60, 161 (1988).
[7] Another example of reduced dimensionality is given by the freely suspended liquid-crystal films studied by C. Y. Young., R. Pindak, N. A. Clark, and R. B. Meyer, Phys. Rev. Lett. 40, 773 (1978).
[8] For a recent discussion closely related to the present topic see the introduction of D. H. Van Winkle and N. A. Clark, Phys. Rev. A 38, 1573 (1988). See also J. P. Straley, Phys. Rev. A 4, 675 (1971).
[9] D. Frenkel and R. Eppenga, Phys. Rev. A 31, 1776 (1985).
[10] See D. H. Van Winkle and N. A. Clark, Phys. Rev. A 38, 1573 (1988).
[11] For recent reviews see, e.g., A. D. J. Haymet, Annu. Rev. Phys. Chem. 38, 89 (1987); M. Baus, J. Stat. Phys. 48, 1129 (1987).
[12] J. L. Colot, X. G. Wu, H. Xu, and M. Baus, Phys. Rev. A 38, 2022 (1988) (referred to as I).
[13] J. L. Colot and M. Baus, Phys. Lett. A 119, 135 (1986).
[14] B. J. Berne and P. Pechukas, J. Chem. Phys. 56, 4213 (1972).
[15] M. Baus and J. L. Colot, Phys. Rev. A 36, 3912 (1987).
[16] N. Ja. Vilenkin, Fonctions Spéciales et Théoric de la Représentation des Groupes (Dunod, Paris, 1969).
[17] Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965).
[18] J. Vieillard-Baron, J. Chem. Phys. 56, 4729 (1972).
[19] T. Boublik, Mol. Phys. 29, 421 (1975).
[20] D. A. Ward and F. Lado, Mol. Phys. 63, 623 (1988).
[21] L. Landau and E. Lifchitz, Physique Statistique (Mir, Moscow, 1984).
[22] J. L. Colot and M. Baus, Mol. Phys. 56, 807 (1985).
[23] See also R. F. Kayser and H. J. Raveche, Phys. Rev. A 17, 2067 (1978).
[24] A. Stroobants, H. N. W. Lekkerkerker, and D. Frenkel, Phys. Rev. A 36, 2929 (1987).
[25] Z. Y. Chen, J. Talbot, W. M. Gelbart, and A. Ben-Shaul, Phys. Rev. Lett. 61, 1376 (1988).
[26] D. Henderson, Mol. Phys. 30, 971 (1975).