Physical properties of polyacrylamide gels probed by AFM and rheology

Polymer gels have been shown to behave as viscoelastic materials but only a small amount of data is usually provided in the glass 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 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 successfully used, covering the whole frequency range. GN, the plateau modulus, as well as several other parameters are obtained at low frequencies. The model also predicts the slope a of both moduli in the glass transition, and a transition frequency fT is introduced to separate the gel–like behavior with the glassy state. Its variation with polymer content c gives a dependence fT ∼ c , in good agreement with previous theories. Therefore the AFM data provides new information on the physics of polymer gels. Introduction. – Polymers exhibit interesting rheological behavior for they can successively behave as liquids, elastic materials showing a rubbery plateau, then undergo a glass transition before reaching the solid domain [1]. These processes are temperature-dependent. Because of this broad range of properties, polymers are widely used in industrial applications, as well as biological processes. However, it is often difficult to characterize their material properties, as the range of relevant frequencies covers several decades [2,3]. Techniques such as classical rheometry, diffusing-wave spectroscopy (DWS) [4], dynamic light scattering [5] or ultrasonic experiments have been used to describe the complex behavior of polymers each in its own range of frequencies [6,7]. In particular, an important way to extend the linear viscoelastic behavior (LVE) is to use the time–temperature superposition principle, wherein re(a)E-Mail: [email protected] (b)E-Mail: [email protected] sults obtained at various temperatures are shifted onto a reference temperature master curve [3]. These observations have motivated quite a lot of theoretical studies. Different models providing relaxation spectra have been proposed, ranging from multiple Maxwell models to continuous relaxation spectra [2], involving both liquid and glassy modes. The concept of soft glassy rheology [8, 9] appeared recently and provides another alternative suited for many systems. Indeed it is based on the idea that sub–elements in the microstructure are linked via weak interactions, in a disordered metastable state. Based on this concept, many complex fluids can be described thanks to this model, in particular packed colloidal suspensions, the cell cytoskeleton [10] as well as foams or slurries. Due to their cross-linked network, polymer gels share similar properties [8] with polymers. They can be characterized using microrheology techniques [11,12], as applied in particular for actin networks [13, 14]. The behavior of