We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.
Algorithms Colloids