Theoretical analysis of sorption of a binary solvent in a polymer phase. II. Occurrence of maxima and minima in the curve of total sorption

Abstract

AbstractIt has been shown that sorption equilibrium in the system polymer–mixed solvent and the total sorption as one of its manifestations can be derived from osmotic equilibrium. The equilibrium relation for the dependence of the osmotic pressure II (as the potential for total sorption) on the composition of the ternary polymer‐containing phase also includes the preferential sorption ε. This complication leads to difficulties in the analysis of the dependence of II on composition: for this reason, analysis has been limited to the case of a very dilute polymer phase. If preferential sorption is neglected, the occurrence of an extremum on the curve representing the dependence of the total sorption on the composition of the mixed solvent is affected by the Flory‐Huggins parameters as in the occurrence of an inversion in preferential sorption, with the exception that in the former case the difference in the molar volumes of the solvent components contributes a term smaller by a factor of two. In the general case, however, the contribution of preferential sorption to the osmotic pressure (which has always a negative sign) also plays its role. Consequently, while total sorption, at a low preferential sorption and at a large positive value of the solvent–solvent interaction parameter χ12, can exhibit a maximum, a larger preferential sorption can overcompensate the effect of the parameter χ12, so that a minimum appears. The coexistence of a minimum with a maximum on the same curve is possible in some cases with positive χ12. The latter theoretical predictions have not yet been confirmed experimentally. At a negative χ12 the extremum is always a minimum.