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A model for homogeneous and inhomogeneous hard molecular fluids: ellipsoidal fluids

The thermodynamic and structural properties of a fluid of hard axially symmetric ellipsoids are studied on the basis of two approximations, namely that (a) the orientations of the molecules can be restricted to a discrete number of directions and (b) the direct correlation function can be written as a superposition of three geometrical functions with weights which depend on the density of the fluid. The variational principle of Anderson and Chandler (1972) is used to determine the weights. The equation of state of the fluid is derived for a range of values of the ratio of axes (elongation) from 0.35 to 5.0. For comparison new simulations have been performed on the same systems. Except at the greatest elongation, the theoretical pressure agrees very well with the simulated pressure of the restricted orientation model as well as with that of a fluid of freely rotating ellipsoids. When the elongation is 5.0, the pressure of the fluid of freely rotating ellipsoids lies somewhat above the pressure of the restricted orientation model, although for this model the theory and simulation are still in accord. Thus far the theory has not revealed a transition to a nematic state although there is some evidence from simulation that when the elongation is 5.0, the isotropic state of the restricted orientation model is not stable. The direct correlation function of the homogeneous phase is used in conjunction with a density functional in order to investigate the density profile of the fluid confined to a slit. Except in the neighbourhood of a wall there is very good agreement between the theory and simulation. The discrepancy near the wall is to be expected from the simple form of functional used. Overall it appears that the approximation developed is adequate for describing the thermodynamic properties of the homogeneous and inhomogeneous isotropic state, but that it needs some improvement for studying the properties of the nematic state.