An improved entropic expression for polymer solutions

Elbro et al. [Macromolecules 23 (21) (1990) 4707] proposed a simple but successful entropic expression for polymer and other size-asymmetric solutions. The expression is similar to the Flory–Huggins model, but free-volume (FV) fractions are used instead of segment or volume fractions and much better results are obtained. The FV is simply defined as Vf=V−Vw, where Vw is the van der Waals (vdW) volume, essentially a measure of molecule’s hard-core volume. In this work, we adopt the statement by Bondi that due to the packing of molecules, a higher than Vw inaccessible volume represents more adequately the hard-core volume. Using experimental phase equilibrium data for athermal polymer (and other asymmetric) solutions, we show that the optimum V∗/Vw ratio is equal to 1.2, which is very close to the value expected based on the packing density at 0 K for organic systems. the entropic expression by Elbro et al. [Macromolecules 23 (21) (1990) 4707] and V∗=1.2Vw yields improved results of activities for athermal polymer solutions and alkane–alkane systems over an extensive database. The results are better compared to other existing entropic expressions, e.g. those of Oishi–Prausnitz (Unifac-FV) and of Zhong–Masuoka.