Combinatorial and interactional free energies and the critical composition of polymer solutions

Abstract

The classical free-energy expression for a polymer solution with Flory–Huggins (FH) combinatorial together with an interaction free energy reflecting component molecular volumes predicts that as the polymer molecular weight M→∞, the polymer critical composition ϕ_2c→ 0 and the critical temperature T_c→θ, the Flory temperature. Experimental evidence indicates that molecular surfaces should replace molecular volumes in the interaction term. This model leads to limiting ϕ_2c and T_c values which can differ widely from zero and θ, respectively, when the surface/volume ratio of the polymer is less than ⅔ that of the solvent, as found for many systems. The new predictions are contrary to many experimental data. Replacement of the FH combinatorial by the multiple-connected combinatorial of Prausnitz and collaborators restores the usual limiting values of ϕ_2c and T_c for polymer solutions constituting experimental evidence for this combinatorial.