Dynamic scaling of polymer gels comprising nanoparticles

Abstract

We present dynamic light scattering (DLS) measurements of soft poly(methyl-methacrylate) (PMMA) and polyacrylamide (PA) polymer gels prepared with trapped bodies (latex spheres or magnetic nanoparticles). We show that the anomalous diffusivity of the trapped particles can be analyzed in terms of a fractal Gaussian network gel model for the entire time range probed by DLS technique. This model is a generalization of the Rouse model for linear chains extended for structures with power law network connectivity scaling, which includes both percolating and uniform bulk gel limits. For a dilute dispersion of strongly scattering particles trapped in a gel, the scattered electric field correlation function at small wavevector ideally probes self-diffusion of gel portions imprisoning the particles. Our results show that the time-dependent diffusion coefficients calculated from the correlation functions change from a free diffusion regime at short times to an anomalous subdiffusive regime at long times (increasingly arrested displacement). The characteristic time of transition between these regimes depends on scattering vector as ∼q-2, while the time decay power exponent tends to the value expected for a bulk network at small q. The diffusion curves for all scattering vectors and all samples were scaled to a single master curve.