A Quasi-Chemical Lattice Treatment of Rod-like Molecules. Application to the Nematic-lsotropic Transition

Abstract

A quasi-chemical treatment is applied to a face-centered cubic lattice system containing N₀ holes (or “solute molecules”) and N_x interacting rods of length-to-breadth ratio x. The resulting partition function is then maximized with respect to the numbers of rods in each of the six allowed directions on the lattice. Two stable “phases” are obtained: a completely aligned “phase”, more stable at lower volume fractions of holes ν₀, and an isotropic “phase”, more stable at higher ν₀'s. When alignment is not favored energetically, the relative stabilities of these two “phases” are temperature independent, but when alignment is favored, this is no longer the case and a first-order aligned → isotropic transition is observed. When the dependencies of the transition temperature and enthalpy of transition on the segment interaction energies of the system, on ν₀, and on x are determined, it is found that our simple model is able to predict a number of important aspects of the behavior of nematogenic substances at their nematic-isotropic transitions.