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Isotropic-nematic transition of D-dimensional hard convex-bodies within the effective-liquid approach

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Cuesta, J. A. and Fernández Tejero, Carlos and Baus, Marc (1992) Isotropic-nematic transition of D-dimensional hard convex-bodies within the effective-liquid approach. Physical Review A, 45 (10). pp. 7395-7412. ISSN 1050-2947

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Official URL: http://dx.doi.org/10.1103/PhysRevA.45.7395


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Abstract

Density-functional theory within the effective-liquid approximation is applied to the problem of the isotropic-nematic transition of D-dimensional hard convex bodies. It is shown that the free-energy functional factorizes into its radial and angular contributions. Due to this factorization two different versions of the self-consistent equations can be implemented, and it is shown that in D = 3 they coincide with previous theories. In the present work all the formulas are worked out with a particular choice for the angular distribution: the one-order-parameter approximation. The problem of determining the excluded volume of two hard convex bodies is discussed. For hard ellipsoids the Gaussian-overlap approximation is used, whereas an exact formula is given for the excluded volume of two hard spherocylinders. For D = 2 the virial coefficients of the isotropic phase as well as the transition are incorrectly predicted, due to the approximation of the direct correlation function involved. For D = 3 the results are in very good agreement with simulations. Expression and data for the isotropic-nematic transition for D > 3 are also provided. Extensive comparisons with the results of other theories are made throughout. The one-order-parameter approximation is proven not to alter the order of the transition. Finally, it is shown that the present approximation becomes exact in the large-D limit.


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© 1992 The American Physical Society. We are grateful to Hong Xu for allowing us to use some of her unpublished material on hard spherocylinders. One of us (J.A.C.) is also indebted to her for some very valuable discussions. We are also grateful to Patricia Lamas. This work has been partially supported by a grant from the Dirección General de Investigación Científica y Técnica (Spain) under Grant No. PB88-0140. One of us (M.B.) acknowledges the financial support of the Fonds National de la Recherche Scientifique and also from the Association Euratom-Etat Belge.

Uncontrolled Keywords:Density-functional theory; Monte-Carlo simulation; Of-revolution fluid; Computer-simulation; Virial-coefficients; Field-theory; Ising-model; Crystals; Ellipsoids; Order
Subjects:Sciences > Physics > Thermodynamics
ID Code:23950
Deposited On:19 Dec 2013 09:19
Last Modified:24 Feb 2015 12:02

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