Thermoreversible gelation in solutions of associative polymers. 1. Statics

An equilibrium mean-field theory for reversible network formation in solutions of associative polymers is presented. We study polymer solutions with many associating groups per chain and consider pairwise association of these groups. A simple analytical expression for the free energy of these systems is derived and is shown to be consistent with the classical gelation picture developed by Flory and Stockmayer. It is shown that association and formation of a reversible network is always accompanied by a tendency for phase separation which might occur even under marginal solvent conditions. The mean-field theory is also generalized to take into account the effect of local intrachain loops as well as excluded volume interactions (partial swelling of polymer chains). It is shown that phase separation might be suppressed by the excluded volume interactions.