Solvation of polymers as mutual association. I. General theory

A Flory-Huggins (FH) type lattice theory of self-assembly is generalized to describe the equilibrium solvation of long polymer chains B by small solvent molecules A. Solvation is modeled as a thermally reversible mutual association between the polymer and a relatively low molar mass solvent. The FH Helmholtz free energy F is derived for a mixture composed of the A and B species and the various possible mutual association complexes AiB, and F is then used to generate expressions for basic thermodynamic properties of solvated polymer solutions, including the size distribution of the solvated clusters, the fraction of solvent molecules contained in solvated states (an order parameter for solvation), the specific heat (which exhibits a maximum at the solvation transition), the second and the third osmotic virial coefficients, and the boundaries for phase stability of the mixture. Special attention is devoted to the analysis of the "entropic" contribution χ(s) to the FH interaction parameter χ of polymer solutions, both with and without associative interactions. The entropic χ(s) parameter arises from correlations associated with polymer chain connectivity and disparities in molecular structure between the components of the mixture. Our analysis provides the first explanation of the longstanding enigma of why χ(s) for polymer solutions significantly exceeds χ(s) for binary polymer blends. Our calculations also reveal that χ(s) becomes temperature dependent when interactions are strong, in sharp contrast to models currently being used for fitting thermodynamic data of associating polymer-solvent mixtures, where χ(s) is simply assumed to be an adjustable constant based on experience with solutions of homopolymers in nonassociating solvents.