Rheology of Guar and HPG Cross-Linked by Borate

Measurements have been conducted on the linear viscoelastic properties of guar and (hydroxypropyl)guar (HPG) polymer solutions cross-linked with borate ions to form gels. Chemical equilibria involving boric acid, borate ions, and borate ions associated with cis-diol sites on the polysaccharide chains determine the number of cross-links. These equilibria are functions of temperature and pH, and thus the rheology of the borate gels depends on temperature and pH. Measurements on 0.48 wt % polymer solutions were performed over the temperature range from 15 to 65 °C and the pH range from 6.35 to 9.5. The storage and loss moduli obey time–temperature superposition so that master curves can be constructed over 6 decades in frequency. The shift factors along the time axis follow a single-exponential Arrhenius form at pH values above 8 with activation energies that vary from 90 to 115 kJ/mol. The activation energies for guar and HPG are identical, which is consistent with the cis-diols on each polymer being the active site for cross-linking. Also, the data at different pH values can be superimposed by “time–pH” shifting to produce master curves from which the temperature and pH sensitivity of the gel rheology can be determined. Leibler et al. have recently proposed a theory for the rheology of associating polymer systems. Following this theory, we have subtracted the solution moduli from the gel moduli, and the resulting reduced moduli data follow a single time constant Maxwell model, where the time constant reflects the relaxation time ofborate/cis-diol interactions in the network.