A unified statistical mechanical description of a rigid-rod fluid

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Abstract
The van Kampen analysis of condensation in a fluid of hard spheres with long-range attractions is extended to investigate the statistical mechanics of a fluid of rigid rod-like molecules which interact through both short-range repulsive and long-range attractive forces and which assume only a restricted set of three mutually orthogonal orientations. The thermodynamic properties are derived for the fluid near the liquid-gas critical point and at the nematic-isotropic transition. The model predicts that both isotropic and anisotropic attractive and repulsive interactions contribute to the stabilization of the nematically ordered fluid when a density change accompanies the transition. However, when the transition occurs at constant density, only the anisotropic contributions of the long-range dispersion energy and short-range repulsions are found to stabilize the transition in partial accord with the Maier-Saupe theory. Numerical results for a rigid-rod fluid with length-to-breadth ratio 3 at various packing fractions are presented for the order parameter, entropy and the density change at the nematic-isotropic transition. The results obtained give reasonable agreement with the experimental results for 4,4′-dimethoxyazoxybenzene and compare favourably with the calculations of Cotter and Ypma. The Landau-de Gennes treatment of the nematic-isotropic transition is also discussed in the framework of the present model. Order-parameter fluctuations, the properties of the nematic-isotropic interface and thermodynamic stability of co-existing nematic and isotropic phases at the transition are also considered.