Solubility in Compressible Polymers: Beyond the Regular Solution Theory

The age-old idea of "like dissolves like" requires a notion of "likeness" that is hard to quantify for polymers. We revisit the concepts of pure component cohesive energy density $c^{\text{P}}$ and mutual cohesive energy density $c_{12}$ so that they can be extended to polymers. We recognize the inherent limitations of $c_{12}$ due to its very definition, which is based on the assumption of no volume of mixing (true for incompressible systems), one of the assumptions in the random mixing approximation (RMA); no such limitations are present in the identification of $c^{\text{P}}.$ We point out that the other severe restriction on $c_{12}$ is the use of pure components in its definition because of which $c_{12}$ is not merely controlled by mutual interactions. Another quantity $c_{12}^{\text{SRS}}$ as a measure of mutual cohesive energy density that does not suffer from the above limitations of $c_{12}$ is introduced. We also revisit the concept of the internal pressure and its relationship with the conventional and the newly defined cohesive energy densities. We pay close attention to volume of mixing effects, and carry out a comprehensive reanalysis of various quantities using a recently developed recursive lattice theory in our group, which goes beyond the regular solution theory such as the Flory-Huggins theory for polymers.