Microscopic theory of binary mixtures of uniaxial nematic liquid crystals

Based on the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy equations a microscopic theory of binary mixtures of nematic liquid crystals has been derived. The resulting integral equations for the equilibrium single-particle distribution functions are of the Hammerstein type. The functional form of the free energy has been constructed on the basis of the state equations. A realistic soft intermolecular potential is applied to the theory. A potential for two different molecules is proposed as a function of characteristic parameters for molecules of the type A and B. A general discussion of the stability conditions is presented for both homogeneous and heterogeneous mixtures.