Phase Separation and Gelation in Solutions and Blends of Hetero-Associative Polymers

An equilibrium statistical mechanical theory for the formation of reversible networks in two-component solutions of associative polymers is presented to account for the phase behavior due to hydrogen bonding, metal–ligand, electrostatic, or other pairwise heterotypic associative interactions. We derive explicit analytical expressions for the binding statistics, gelation condition, and free energy, in which we consider polymers of types A and B with many associating groups per chain and consider only A–B association between the groups. The free energy is approximated at the mean-field level, considering overlapping polymer chains with an ideal gas of "stickers" capable of intermolecular association. It is shown that the number of associations is maximized at stoichiometric conditions between A and B associative groups. Accordingly, homogeneous networks are most easily formed near stoichiometric conditions between A and B associative groups, resulting in a re-entrant sol–gel–sol transition as the overall composition is altered. Association and reversible network formation are found to be accompanied by a tendency for phase separation. These results demonstrate that reversibly associating polymers have a large parameter space in terms of molecular design, binding energy, and mixture compositions. Our predictions are expected to be useful in the rational design of interacting polymer mixtures and the formation of reversible networks.