Trends in the Athermal Entropy of Mixing of Polymer Solutions

Polymeric mixtures of hydrocarbons and alcohols have been simulated with discontinuous potential models to characterize the Helmholtz energy of the repulsive reference fluids. This quantity is equivalent to the athermal mixture entropy. The mixtures included small hydrocarbons with alcohols and n-alkanes, branched hydrocarbons, and aromatics with polymeric molecules of: n-alkanes, ethyl-styrenes, ethyl-propylenes, and isoprenes. We find that the athermal entropy of mixing deviates significantly from ideality, but still follows the van der Waals mixing formula and approach to an asymptote in the long chain limit. This leads to an accurate characterization of the entropic contribution to the χ parameter (χS) of Flory-Huggins theory for mixtures of all sizes, shapes, and compositions of molecular structures. A general rule is developed for predicting the athermal entropy of mixing based on knowledge of the volume ratios of the constituent molecules. Combined with the usual approach to characterizing the energetic contribution to the χ parameter, a complete formulation is provided for characterizing the mixture thermodynamics. The simulations are compared to SAFT, and Guggenheim-Staverman (GS) theories of polymer chains.