Role of free volume changes in polymer solution thermodynamics

The thermodynamic effect of free volume changes in mixing is treated with the use of the corresponding states theory of Prigogine and collaborators. The interaction parameters χ 1 , κ 1 , ψ 1 and their concentration dependences are derived. Each parameter contains two terms. The first is due to differences in cohesive energy and sizes between segments of polymer and solvent: the second or “structural” contribution is due principally to the difference in chain lengths between polymer and solvent. The structural effect gives a large value of χ 1 ∼ 0.4 for a polymer with a chemically identical short oligomer as solvent. A minimum but nonzero value of χ 1 occurs for a solvent with higher cohesive energy than between polymer segments. At high temperatures a lower critical solution temperature must occur due to the increase of the solvent configurational heat capacity to infinity as the solvent vapor‐liquid critical point is approached, the heat and entropy of dilution becoming negative. At ordinary temperatures χ and κ increase with polymer concentration. The solubility parameter approach is compared; particular polymer liquid models used by Prigogine and by Flory are briefly discussed. χ 1 as calculated for natural rubber and a variety of solvents and fair agreement is obtained with published values.