A mean-field theory is introduced to describe nematic-isotropic phase trans
itions and phase separations in binary mixtures of a liquid-crystal molecul
e and a semiflexible polymer chain. On the basis of the Onsager model for e
xcluded volume interactions, the Maier-Saupe model for orientational-depend
ent attractive interactions, and the Flory-Huggins theory for isotropic mix
ings, we derive the free energy of the binary mixtures. We examine the co-o
ccurrences of the partial orientational ordering of the polymer chains in t
he liquid-crystal solvents and the phase separations, depending on the stif
fness of the polymer chain and the strength of anisotropic interactions. Th
e new phase behaviors, such as nematic unstable regions, nematic metastable
regions, a critical solution point in a nematic phase, azeotrope points, a
nd triple points, are examined on the temperature-concentration plane. [S10
63-651X(99)06501-0].