The Thermodynamics of High Polymer Solutions. IV. Phase Equilibria in the Ternary System: Polymer—Liquid 1—Liquid 2

Abstract

Two approximate methods of calculating equilibrium phase diagrams in ternary systems of polymer and mixed liquids have been compared with exact phase diagrams based upon the Flory‐Huggins equations. Both a ``single liquid approximation'' and a ``complete immiscibility approximation'' are worthless except for the crudest qualitative considerations. Analytical expressions for the plait points of such ternary systems (a maximum of ten) have been derived. A consideration of the solubility of polymers in mixed solvents leads to the conclusion that a polymer may be completely soluble in certain mixtures of non‐solvents if its internal pressure (cohesive energy density) lies between those of the two liquids and if the two liquids are themselves completely miscible. The position of the phase boundary is nearly independent of the molecular weight of the polymer for molecular weights above 10,000. Osmotic pressures in mixed solvents are discussed, and Gee's suggestion that the osmotic pressure is zero at the critical solubility limit is confirmed.