Anomalous diffusion in aqueous solutions of gelatin.

Abstract

Dynamic-light-scattering experiments on semidilute aqueous solutions of gelatin indicate three relaxation processes: an exponential for times less than \ensuremath{\sim}50 \ensuremath{\mu}sec followed by a power law at intermediate time and then a stretched exponential at long time. The characteristic time of the stretched exponential diverges as the system evolves to a gel. The latter two relaxations can be explained in terms of an anomalous diffusion mechanism where the mean-square displacement behaves as 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}lnt at intermediate time and 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\beta}}}$ with \ensuremath{\beta}1 at late time. Length scales derivable from these diffusion mechanisms obey scaling, and it is proposed that \ensuremath{\beta} is related to the fracton density-of-states exponent and the fractal dimension of the gelatin molecules.