Dynamic Scaling of Polymer Gels Comprising Nanoparticles

We present dynamic light scattering (DLS) measurements of soft polymethyl-methacrylate (PMMA) and polyacrylamide(PA) polymer gels prepared with trapped bodies (latex spheres or maghemite 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 sub-diffusive regime at long times (increasingly arrested displacement). The characteristic time of transition between these regimes depends on scattering vector as $\sim q^{-2}$ 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.