Statistical Thermodynamics of Short-Chain Molecule Interphases. 1. Theory

Amphiphilic molecules comprised of a polar head and hydrocarbon tail associate in aqueous environment to form micelles, vesicles, bilayers, or other aggregates, consisting of hydrocarbon domains separated from the water regions by the head groups. Statistical theory for the hydrocarbon “interphase” region of such systems is developed, extending previous work to account for chain bending energies and to allow prediction of thermodynamic as well as structural properties. Expressions for the statistical weights of chain configurations and a configurational partition function are obtained subject to the constraint of approximately constant density within the hydrocarbon core, which is a consequence of strongly attractive isotropic van der Waals forces, balanced by hard-core steric repulsive forces. Expressions for positional and orientational probability distributions are derived.