Phase separations and orientational ordering of polymers in liquid crystal solvents

A mean-field theory is introduced to describe nematic-isotropic phase transitions and phase separations in binary mixtures of a liquid-crystal molecule and a semiflexible polymer chain. On the basis of the Onsager model for excluded volume interactions, the Maier-Saupe model for orientational-dependent attractive interactions, and the Flory-Huggins theory for isotropic mixings, we derive the free energy of the binary mixtures. We examine the co-occurrences of the partial orientational ordering of the polymer chains in the liquid-crystal solvents and the phase separations, depending on the stiffness of the polymer chain and the strength of anisotropic interactions. The new phase behaviors, such as nematic unstable regions, nematic metastable regions, a critical solution point in a nematic phase, azeotrope points, and triple points, are examined on the temperature-concentration plane.