Statistical mechanical studies of intermolecular interactions in mesogenic solutions

Abstract

Statistical mechanical models have been used to study the roles of solvent–solvent, solvent–solute, and solute–solute interactions in two types of systems which exhibit mesomorphism. 1. Nematogenic solutions have been studied using a van der Waals approach, in which very short-range intermolecular repulsions are approximated by hard-particle exclusion and somewhat longer-range intermolecular attractions are subject to a self-consistent mean field treatment. The general theory, applicable to mixtures of any number of rodlike or effectively spherical components, has been applied to ( i) binary solutions with rodlike solvent molecules and effectively spherical solute molecules (here, predicted temperature-mole fraction phase diagrams are in rather good-agreement with available experimental data) and ( ii) binary mixtures of nematogens. In the latter case, some very interesting effects are predicted when the two components differ considerably in their molecular dimensions. 2. The formation of lipid bilayers has been studied in amphiphile-water systems which do not form globular/cylindrical micelles ( e.g lecithin-water mixtures), using model system of water molecules and straight, in flexible amphiphilic ‘r- mers’ ( i.e., rodlike molecules with length-to-width ratio r), constrained to lie on a simple cubic lattice. The `r- mers' and water molecules interact via nearest-neighbor segmental interaction energies ϵ AA, ϵ AB, ϵ BB, ϵ AS, ϵ BS and ϵ SS where S, A, and B represent, respectively, a water molecule, a polar head segment, and a lipid tail segment. Using the Bragg-Williams approximation, temperature-mole fraction phase diagrams have been calculated for model systems with various values of the amphiphile length-to-width ratio r and the interaction energies ϵ AA, ϵ AB, etc. in an effort to elucidate more fully the molecular factors which govern the formation and stability of lipid bilayers. This basic model has been modified by allowing the amphiphilic `r- mers' to form bilayer vesicles which can be packed on the lattice together which water molecules and individual amphiphile molecules. It is hoped that this modified model will be useful for studying the phase transition between the bilayer smectic phase and a solution of bilayer vesicles.