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 reference compressibility factor and Helmholtz free energy have been correlated for various molecular structures from single to infinite chain lengths. The mixtures included small n-alkanes, branched alkanes, aromatics, and alcohols, with polymeric molecules of: n-alkanes, ethyl-styrenes, ethyl-propylenes, and isoprenes. We find that the athermal entropy of mixing at constant packing fraction deviates significantly from ideality as the volume ratio increases, but the nonideality is fairly insensitive to structural details like branching and rings. Volume ratio alone does not provide a complete characterization, however. For example, a mixture of C40 and C80 would yield a small deviation whereas a mixture of C2 and C4 would provide a relatively large deviation. This observation leads to the introduction of a characteristic parameter in terms of entropy density, designated as an entropic solubility parameter. In both ideal and nonideal solutions, the trends still follow van der Waals (vdW) mixing. This leads to an accurate characterization of the entropic contribution to the χ parameter (χ^S) 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 and entropic solubility parameter of the constituent molecules. The simulations are compared to Flory-Huggins (FH), group contribution lattice fluid theory (GCLF), statistical associating fluid theory (SAFT), Sanchez-Lacombe (SL), and Guggenheim-Staverman (GS) theories of polymer chains.