Phase separations in mixtures of a liquid crystal and a nanocolloidal particle.

We present a mean field theory to describe phase separations in mixtures of a liquid crystal and a nanocolloidal particle. By taking into account a nematic, a smectic A ordering of the liquid crystal, and a crystalline ordering of the nanoparticle, we calculate the phase diagrams on the temperature-concentration plane. We predict various phase separations, such as a smectic A-crystal phase separation and a smectic A-isotropic-crystal triple point, etc., depending on the interactions between the liquid crystal and the colloidal surface. Inside binodal curves, we find new unstable and metastable regions, which are important in the phase ordering dynamics. We also find a crystalline ordering of the nanoparticles dispersed in a smectic A phase and a nematic phase. The cooperative phenomena between liquid-crystalline ordering and crystalline ordering induce a variety of phase diagrams.