Tracking three-phase coexistences in binary mixtures of hard plates and spheres

The stability of demixing phase transition in binary mixtures of hard plates (with thickness L and diameter D) and hard spheres (with diameter $\sigma$) is studied by means of Parsons-Lee theory. The isotropic-isotropic demixing, which is found in mixtures of large spheres and small plates, is very likely to be preempted by crystallization. In contrast, the nematic-nematic demixing, which is obtained in mixtures of large plates and small spheres, can be stabilized at low diameter ratios ($\sigma$/D) and aspect ratios (L/D). At intermediate values of $\sigma$/D, where the sizes of the components are similar, neither the isotropic-isotropic nor the nematic-nematic demixing can be stabilized, but a very strong fractionation takes place between a plate rich nematic and a sphere rich isotropic phases. Our results show that the excluded volume interactions are capable alone to explain the experimental observation of the nematic-nematic demixing, but they fail for the description of isotropic-isotropic one (Chen et. al., Soft Matter, 11, 5775 (2015)).