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Excluded-volume potential for rigid molecules endowed with C2v symmetry

Published online by Cambridge University Press:  14 January 2011

F. BISI  and
R. ROSSO
F. BISI
Affiliation:
Dipartimento di Matematica and CNISM, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy email: fulvio.bisi@unipv.it Laboratory of Applied Mathematics, Fondazione Università di Mantova, Via Scarsellini 2, 46100 Mantova, Italy
R. ROSSO
Affiliation:
Dipartimento di Matematica and CNISM, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy email: fulvio.bisi@unipv.it
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Abstract

The excluded volume of a pair of molecules is proportional to the second virial coefficient in hard-core models that represent, for instance, the reference model in perturbation approaches to statistical theories of fluids [see, e.g. Chap. 5 of Kalikmanov, V. (2001), Statistical Physics of Fluids. Texts and Monograph in Physics, Springer, Berlin]. In three space dimensions, there exist exact results for convex molecules and in fact lack of convexity has been a major obstacle in applying the mathematical techniques employed in the convex case. In this paper, we illustrate how a mixed—analytical and numerical—method can be used to obtain exact expressions of the excluded volume for a pair of non-convex molecules conceived as aggregates of hard spheres; these can model van der Waals regions associated to the atoms forming each molecule. To compute the excluded volume for molecules endowed with C2v symmetry, modelled as chains of tangent hard spheres, we adapt a numerical code available to the scientific community. Because the result is a rather cumbersome expression in term of the relative orientation of the interacting molecules, we expand it over a suitable set of symmetry adapted Wigner functions to build up approximate, but faithful expressions, and we also prove analytical results announced elsewhere [Bisi, F., Durand, G., Rosso, R. & Virga, E. (2008), Polar steric interactions for v-shaped molecules. Phys. Rev. E, 78, 011705].

Keywords

Liquid crystalsMixed volumes and related topicsGroup actions and symmetry propertiesComputational methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 1: Liquid Crystals , February 2012 , pp. 29 - 60
Copyright
Copyright © Cambridge University Press 2011

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