LATTICE MODEL FOR A BINARY MIXTURE OF HARD RODS AND HARD CUBES. APPLICATION TO SOLUTE INDUCED NEMATIC → ISOTROPIC TRANSITIONS

Abstract

A statistical mechanical treatment for a two component mixture of hard rods of dimensions Lx 1x 1 (L = 5.10) and hard cubes of dimensions Dx Dx D (1 ⩽ D ⩽ 2), placed on a simple cubic lattice, is described. The dimensionless pressure-to-temperature ratio Φ = Pν0/kT (where ν0 is the volume of a lattice site) is chosen so that the system is anisotropic when only rods are present. At constant Φ the partially aligned anisotropic mixture can be induced to undergo a first-order transition to the isotropic phase by increasing the concentration x of the cubes. A small two phase region is found. The dependence of this transition on Φ, x, L, and D is described. Recent experimental results for mixtures of nematics with CCl4 are cited and compared with the findings of the lattice calculation. The model successfully predicts the existence, the general position and the extent of the observed two phase region, as well as the correct magnitude of the solute induced nematic — isotropic transition temperature depression. In agreement with experiments, the transition order parameter of the rods is found to be independent of the concentration or size of the cubes. The role of repulsive forces and the limitations of this and other mean field treatments of nematic mixtures are discussed