Theoretical analysis of sorption of a binary solvent in a polymer phase. I. Occurrence and character of inversion in preferential sorption

Osmotic and sorption equilibria in the system polymer–binary solvent can be represented with advantage in coordinates (u₁, v₃), where v₃ is the volume fraction of the polymer and u₁ gives the composition (volume fraction) of the binary solvent in the polymer phase. The coexistence lines and osmotic isobars are plotted; the former are used to read the preferential sorption ε of one of the solvent components in the polymer. The newly formulated equilibrium condition for the preferential sorption is applied to the Flory–Huggins theory extended by the ternary interaction parameter χ_T. This is used as a starting point for analyzing the conditions under which inversion of preferential sorption takes place, i.e., the sign of ε changes. The existence of inversion and the course of the inversion line in the v₃ versus u₁ plot are affected in a decisive manner by the extent to which the effect of the mutual interaction of solvent components prevails over the effect of the relative difference between their molar volumes and of the difference in strength of their interaction with the polymer. The effect of the ratio of molar volumes upon the preferential sorption increases with the concentration of the polymer, so that for v₃ not too far from unity the component having the smaller molecule is necessarily sorbed preferentially. If, therefore, both types of small molecules are not of the same size, the inversion vanishes for large v₃ even in systems where it actually occurs if v₃ is small. On the contrary, the same effect can in other cases have as its consequence an inversion at moderate values of v₃, even if it does not appear as v₃ approaches zero; a similar effect can also be produced by a nonzero value of the interaction parameter χ_T. The neighborhood of the inversion line can have a “divergent” or a “convergent” character, depending on whether the component being preferentially sorbed is that present in excess. The former case is observed with negative and the latter for the positive values of the binary solvent–solvent interaction parameter χ₁₂. The inversion with the divergent neighborhood has not yet been confirmed experimentally, owing to the small number of systems investigated.