Probing the viscoelastic properties of polyacrylamide polymer gels in a wide frequency range

Polymer gels have been shown to behave as viscoelastic materials but only a small amount of data is usually provided in the glassy transition. In this paper, the dynamic moduli G' and G'' of polyacrylamide hydrogels are investigated using both an AFM in contact force modulation mode and a classical rheometer. The validity is shown by perfect matching of the two techniques. Measurements are carried out on gels of increasing polymer concentration in a wide frequency range. A model based on fractional derivatives is proposed, covering the whole frequency range. G_0^N, the plateau modulus, as well as nf, the slope of the G'' modulus, are obtained at low frequencies. The model also predicts the slope a of both moduli in the transition regime, as well as a new transition time T. The whole frequency spectrum is recovered, and the model parameters contain interesting information about the physics of such gels.