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

Abstract

Theoretical scheme is developed to study thermoreversible gelation interfering with liquid–liquid phase separation in mixtures of reactive f-functional molecules R{Af} and g-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 f and g (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.

Thermoreversible Gelation Interfering with Phase Separation in Multicomponent Mixtures of Associating Polymers

“…A reentrant sol− gel−sol transition with an optimal gel point often occurs. 43 To avoid a complex description of the spinodal condition in terms of κ i,j , we here present the explicit result only for a fixed multiplicity model. We have…”

“…We next consider binary association , where f -functional molecules R­{A} ( i = 1) and g -functional molecules R­{B} ( i = 2) form mixed networks in an inert solvent S ( i = 3). In the special case of no solvent, gel-point conditions and average molecular weights of cross-linked polymers were studied for chemical reaction by covalent bonds , and for multiple reactions. − …”

“…From the temperature dependence of χ-parameters and equilibrium constants, we can also explore temperature–concentration cross sections of the ternary phase diagrams. A reentrant sol–gel–sol transition with an optimal gel point often occurs …”

“…All these studies were confined to chemical gels. On the basis of these preceding studies, thermoreversible gelation with binary pairwise cross-links was studied by Tanaka et al − and later extended to gels with multiple cross-link junctions. − Their results were recently applied to ion-responsive hydrogels and gelation in hydrogen-bonding mixed solvents …”

Thermoreversible Gelation of Associating Polymers in Hydrogen-Bonding Mixed Solvents

“…Gordon matrix D̂ appearing in the weight-average molecular weight of three-dimensional polymers for ternary systems is given by in general form where is the partial derivative of the conservation functions. These κ functions will also be necessary for the calculation of the liquid–liquid phase-separation lines, , but we will confine them to thermoreversible gelation in the present study.…”