Global fluid phase behavior in binary mixtures of rodlike and platelike molecules

Abstract

The phase behavior of a liquid-crystal forming model colloidal system containing hard rodlike and platelike particles is studied using the Parsons–Lee scaling [J. D. Parsons, Phys. Rev. A 19, 1225 (1979); S. D. Lee, J. Chem. Phys. 87, 4972 (1987)] of the Onsager theory. The rod and plate molecules are both modeled as hard cylinders. All of the mixtures considered correspond to cases in which the volume of the plate is orders of magnitude larger that the volume of the rod, so that an equivalence can be made where the plates are colloidal particles while the rods play the role of a depleting agent. A combined analysis of the isotropic–nematic bifurcation transition and spinodal demixing is carried out to determine the geometrical requirements for the stabilization of a demixing transition involving two isotropic phases. Global phase diagrams are presented in which the boundaries of isotropic phase demixing are indicated as functions of the molecular parameters. Using a parameter z which corresponds to the product of the rod and plate aspect ratios, it is shown that the isotropic phase is unstable relative to a demixed state for a wide range of molecular parameters of the constituting particles due to the large excluded volume associated with the mixing of the unlike particles. However, the stability analysis indicates that for certain aspect ratios, the isotropic–nematic phase equilibria always preempts the demixing of the isotropic phase, irrespective of the diameters of the particles. When isotropic–isotropic demixing is found, there is an upper bound at large size ratios (Asakura and Oosawa limit), and a lower bound at small size ratios (Onsager limit) beyond which the system exhibits a miscible isotropic phase. It is very gratifying to find both of these limits within a single theoretical framework. We test the validity of the stability analysis proposed by calculating a number of phase diagrams of the mixture for selected molecular parameters. As the hard rod particles promote an effective attractive interaction between the hard-plate colloidal particles, the isotropic–isotropic demixing usually takes place between two rod-rich fluids. As far as the isotropic–nematic transition is concerned, a stabilization as well as a destabilization of the nematic phase relative to the isotropic phase is seen for varying rod–plate size ratios. Moreover, isotropic–nematic azeotropes and re-entrant phenomena are also observed in most of the mixtures studied. We draw comparisons between the predicted regions of stability for isotropic demixing and recent experimental observations.