Solubility in compressible polymers: Beyond the regular solution theory

Abstract

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 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 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 SRS as a measure of mutual cohesive energy density that does not suffer from the above limitations of c 12 is introduced. It reduces to c 12 in the RMA limit. We are able to express c 12 SRS in terms of c 12 and pure component c P’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.