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 (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 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.