Thermoreversible gelation with ion-binding cross-links of variable multiplicity.

Thermoreversible gelation and liquid-liquid phase separation are theoretically studied for the gels of polyfunctional molecules (polymers) whose network junctions are formed by complexation of functional groups on the polymer chains with added metal ions. Phase diagrams on the polymer/ion/solvent concentration plane, including both sol-gel transition lines and liquid-liquid phase separation lines (spinodals), are derived as functions of the polymer functionality, molecular weight, maximum coordination number of ions, and temperature. Binding isotherms of ions are also calculated as functions of the ion concentration. Results of the calculated sol-gel transition lines are compared with our recent experimental data on gelation of star block and telechelic, acrylic copolymers cross-linked by iron ions. It is shown that, owing to reaction stoichiometry, there is an optimal ion concentration at which the solution gels for the lowest polymer concentration and also that a re-entrant sol phase appears in the ion concentrations higher than the optimal one. The effect of stepwise complex formation constants on the re-entrant phase is studied in detail.