Critical Shear Rate for Gelation in Aqueous Solutions of Associating Polymers under Shear Flows

The critical shear rate for gelation of hydrophobically-modified water-soluble polymers is calculated as a function of the polymer concentration and temperature in the framework of classical Flory-Stockmayer theory modified to suit for multiple cross-links. The results are compared with the recent experimental data on aqueous solutions of hydrophobically modified poly(dimethylacrylamide)s. Hydrophobes on the polymer chains are activated from intramolecular aggregates to free states by shear, followed by intermolecular cross-linking leading to gelation. The effective chain functionality (number of activated hydrophobes) is a function of the shear rate and temperature. When it reaches the critical value, the solution gels. The temperature activation (heat-setting gels) and shear activation (shear-setting gels) can thus be studied from a unified point of view in the three-dimensional temperature-concentration-shear space.