Decay of density fluctuations in gels.

Abstract

Near the sol-gel transition, gelling systems exhibit an extremely slow relaxation of thermally driven density fluctuations. We have made a detailed quasielastic light scattering study of the decay of density fluctuations in reacting silica sol-gels in the pre- and post-gel regimes, and at the gel point. In the pre-gel regime the dynamic structure factor {ital S}({ital q},{ital t}) for the branched polymer melt has a stretched exponential tail whose characteristic time diverges at the gel point. This {ital critical} {ital slowing} {ital down} is due to the divergence of the average cluster size and is distinct from the usual critical slowing down observed in second-order thermodynamic phase transitions, since the initial decay rate of {ital S}({ital q},{ital t}) is nondivergent at the gel point. In fact, at the gel point, {ital S}({ital q},{ital t}) becomes a power law, indicating a fractal time set in the scattered field. These observations are accounted for by considering the dynamics of percolation clusters, and in this connection the analogy to viscoelasticity is described. Beyond the gel point {ital S}({ital q},{ital t}) remains a power law, but the amplitude of the relaxing part of the intensity autocorrelation function diminishes. Finally, the dynamics of clusters dilutedmore » from the reaction bath is studied, and a crossover from power law to stretched exponential decay of {ital S}({ital q},{ital t}) is observed. It is shown that at infinite dilution the long-time tail of the correlation function describes the internal modes of a single percolation cluster.« less