VANDERWAALS THEORY OF NEMATOGENIC SOLUTIONS .1. DERIVATION OF THE GENERAL EQUATIONS

In the Van der Waals theory of liquids, very short-ranged intermolecular repulsions are approximated by hard-particle exclusions and somewhat longer-ranged intermolecular attractions are subject to a self-consistent mean-field treatment. This approach, which has recently been applied to pure nematogens, is here extended to nematogenic solutions. The molecular hard cores are taken to be spherocylindrical or spherical in shape and their contribution to the free energy of the system is evaluated using scaled-particle theory. The general theory, applicable to mixtures of any number of rodlike or effectively spherical molecules is derived and its applications to various types of nematogenic systems are discussed. Finally, the way in which the theory could be modified to treat species whose molecular shapes cannot satisfactorily be approximated by spheres or spherocylinders is indicated. © 1978 The American Physical Society.