Lattice model for a binary mixture of hard rods of different lengths. Application to solute induced nematic→isotropic transitions

A statistical mechanical treatment for two-component mixtures of hard rods placed on a simple cubic lattice is presented. Each mixture is composed of two types of rods of different length-to-breadth ratios; and the pressure-to-temperature ratios are chosen so that the system is anisotropic when only longer rods are present but isotropic when composed of only shorter rods. Such solutions can be induced to undergo a first-order anisotropic-isotropic phase transition, with a small two phase region, by increasing the concentration of the shorter rods. The dependence of this transition on the parameters of the model is described and deviations from ideal solution behavior are discussed. Recent experimental data are cited and compared with the results of the lattice calculation.