  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.
