Phase transitions of hard ellipses and hard ellipses with circular square-wells based upon density functional theory

Two versions of the decoupling approximation (DA) are used to study the isotropic-nematic phase transition of hard ellipse systems. The results of the scaling procedure with respect to hard discs and the scaling with respect to the isotropic phase of hard ellipses are compared with the corresponding Monte Carlo simulation data. In spite of the fact that, in comparison with other theories, the DA yields the best critical densities for the isotropic-nematic phase transition of hard convex bodies with respect to other theories, it is unable to predict correctly the order of orientational phase transitions in the narrow range of aspect ratio k = 4. Via the hard ellipse with circular square-wells model system the effect of the attractive forces on the isotropic-nematic phase transition is studied also. The role of these attractive forces is studied on the basis of a simple perturbation theoretical method. It is shown that at low temperatures attraction causes first-order isotropic-nematic phase separation for the values of aspect ratio studied and moreover both stable and metastable vapour-liquid coexistence can be found.