Strategies for Evaluating Thermodynamic Properties of Lattice Mixtures of Differently-Sized Particles and Chain Molecules: Application to Partitioning Data Involving Alkanes

Abstract

Simple approximate strategies for treating thermodynamic properties of lattice mixtures of differently sized particles and chain molecules are described. Based on these strategies, expressions for chemical potentials and partition coefficients are derived. These expressions account in a simple way for effects of particle size and chain length. In the limit of long chains and for single-cell solute molecules, the resulting expression for chemical potential reduces to the Flory−Huggins expression. However, for shorter chains such as alkanes and for large globular solutes, the predicted contribution of chain entropy to the chemical potential differs from the Flory−Huggins treatment. The results are used to interpret published partitioning data on xenon in alkanes as a function of chain length and temperature and to interpret published partitioning data on pure alkanes and water. On the basis of these latter results, a contact free energy for the hydrophobic effect of 29 cal A-2 mol-1 is determined. The first strategy for handling disparate molecular sizes gives expressions for the numbers of contacts between differently sized globular particles by introducing weighting factors for particle numbers based on the number of contacts each particle can make with particles of the other type. The second strategy addresses the entropy of mixtures of differently sized globular particles by using a parameter in the partition function that gives the probability that a lattice with a given population of large globular particles can accept another large globular particle inserted at random. The third strategy evaluates chain configuration entropy by calculating the number of configurations available to a mixture of chain and globular particles without regard for intersegment chain connectivity, followed by correction for the fraction of configurations that are consistent with proper chain covalent bonding.