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 cP and mutual cohesive energy density c12 so that they can be extended to polymers. We recognize the inherent limitations of c12 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 cP. We point out that the other severe restriction on c12 is the use of pure components in its definition because of which c12 is not merely controlled by mutual interactions. Another quantity image as a measure of mutual cohesive energy density that does not suffer from the above limitations of c12 is introduced. It reduces to c12 in the RMA limit. We are able to express image in terms of c12 and pure component cP’s. We also revisit the concept of the internal pressure and its relationship with the conventional and the newly defined cohesive energy densities. In order to investigate volume of mixing effects, we introduce two different mixing processes in which volume of mixing remains zero. We then carry out a comprehensive reanalysis of various quantities using a recently developed recursive lattice theory that has been tested earlier and has been found to be more accurate than the conventional regular solution theory such as the Flory–Huggins theory for polymers. In the RMA limit, our recursive theory reduces to the Flory–Huggins theory or its extension for a compressible blend. Thus, it supersedes the Flory–Huggins theory. Consequently, the conclusions based on our theory are more reliable and should prove useful.