Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex-bodies

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Recent attempts to generalize the classical Onsager theory of nematic ordering to finite-density systems of finite-length hard convex bodies are related and compared. It is pointed out that, although good results can be obtained in three-dimensions (3D), in two dimensions (2D) the underlying factorization approximation of the radial and angular variables always implies a second-order isotropic-nematic transition instead of the crossover from a weakly first-order transition to a continuous (Kosterlitz-Thouless) transition as seen in the simulations. The quantitative agreement with the simulations is also much poorer in 2D than in 3D. On the contrary, for large spatial dimensions these theories become exact.
© 1991 The American Physical Society. 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. Hong Xu acknowledges the financial support of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) of the Netherlands.
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