Thermoreversible Gelation with Two-Component Mixed Cross-Link Junctions of Variable Multiplicity in Ternary Polymer Solutions.

Theoretical scheme is developed to study thermoreversible gelation interfering with liquid-liquid phase separation in mixtures of reactive -functional molecules R{Af} and -functional ones R{Bg} dissolved in a common solvent. Formed polymer networks are assumed to include multiple cross-link junctions containing arbitrary numbers k1 and k2 of functional groups A and B of each species. Sol-gel transition lines and spinodal lines are drawn on the ternary phase plane for some important models of multiple cross-link junctions with specified microscopic structure. It is shown that, if the cross-link structure satisfies a certain simple condition, there appears a special molar ratio of the two functional groups at which gelation takes place with a lowest concentration of the solute molecules, as has been often observed in the experiments. This optimal gelation concentration depends on and (functionality) of the solute molecules and the numbers k1 and k2 (multiplicity) of the functional groups in a cross-link junction. For cross-links which allow variable multiplicity, special attention is paid on the perfectly immiscible cross-links leading to interpenetrating polymer networks, and also on perfectly miscible cross-links leading to reentrant sol-gel-sol transition. Results are compared with recent observations on ion-binding polymer solutions, polymer solutions forming recognizable biomolecular complexes, polymer/surfactant mixtures, hydrogen-bonding polymers, and hydrophobically-modified amphiphilic water-soluble polymers.