Critical exponents and self-similarity for sol-gel transition in aqueous alginate systems induced by in situ release of calcium cations

The sol-gel transition in aqueous alginate systems induced by in situ released calcium cations was monitored with rheology methods. Four alginate samples with different molecular weights and M/G ratios were used over the concentration C(Alg) of 2 approximately 6 wt % with different mole ratios f of Ca2+ to the alginate repeat unit. The scaling for the zero shear viscosity eta(0) before the gel point and the equilibrium modulus Ge after the gel point was described as eta(0) approximately epsilon(-k) and Ge approximately epsilon(z), respectively, where the relative distance to the gel point f(gel) was epsilon = (/f-f(gel)/)/f(gel). The relaxation critical exponent n was determined with Winter's criterion, and the critical exponents k and z estimated respectively from independent measurements of eta(0) and Ge gave n from z/(k + z). Before the gel point, the storage and loss moduli G' and G' obtained at various epsilon can be superposed fairly well to form the master curve. The critical exponents n, k, and z were also evaluated from the shift factors and the structure self-similarity was found in the critical gel. The critical exponents evaluated with different methods agreed well with each other, suggesting two categories of the gelation as growth and cross-link. For the alginate with lower molecular weight, the critical exponents were almost independent of alginate concentration and close to the percolation prediction. For the alginate with higher molecular weight, the critical exponents, however, changed with alginate sample and concentration. The relative alginate concentration C(Alg)/C(Alg)* was found to serve as a criterion to divide these two transitions.