Phase Separationof Homopolymers in Binary Mixed Solvents:the Co-Solvency Effect

As one of the most intriguing phenomena in polymer solutions, the co-solvency effect refers to the improved miscibility of polymers in mixtures of binary poor solvents. The physical mechanism underlying this phenomenon, however, remains obscure. In this work, by using the ternary Flory–Huggins theory, we examine the phase behaviors of polymers in mixtures of binary miscible poor solvents. We derive the general analytical conditions for the co-solvency and the related co-nonsolvency effect in the long chain limit. We find that a repulsion between the two solvents is required to induce the co-solvency effect. When this repulsion is weak, the binodal curve in the surface of polymer concentration and cosolvent composition <i>x</i> is of the hourglass type without a critical point. When this repulsion is modest, the binodal curve splits into two separate branches, with each having a single critical point. For <i>x</i> between these two branches, a solution is homogeneous over all polymer concentrations, and this type of co-solvency occurs for systems with a short chain length, modestly poor quality of both solvents to the polymer, and a relatively large repulsion between the two solvents. The phase behaviors of co-solvency systems differ significantly from those in mixtures of two good solvents and those in mixtures of a good solvent and a poor solvent. These findings, along with our previous results on the phase behaviors of polymers in mixtures of binary good solvents (Zhang, P., <i>Macromolecules</i>, <b>2024</b>, <i>57</i>, 4298), further demonstrate that the co-nonsolvency effect of poly-<i>N</i>-isopropylacrylamide in mixtures of water and small alcohol results from exclusively the preferential attraction of the polymer to the alcohol molecule over to the water molecule. Our findings not only afford the first complete picture of the mean–field phase behaviors of the co-solvency system but also provide a valuable guide in designing solvents to dissolve polymers for various applications such as fiber wet spinning and membrane fabrication.