Slow aggregation of colloidal silica

Abstract

We report the results of elastic and quasielastic light scattering measurements on dilute aggregates of colloidal silica. The elastic scattering measurements indicate a fractal dimension of 2.05\ifmmode\pm\else\textpm\fi{}0.06, in agreement with previous results, but the quasielastic measurements demonstrate several novel characteristics. First, it is found that the linewidth \ensuremath{\Gamma} scales as a fractional power, \ensuremath{\Gamma}\ensuremath{\sim}${q}^{2.7}$, of the momentum transfer q. Second, the inverse average relaxation time, defined as the integral of the field autocorrelation function, does not scale with the same power of q as the linewidth, implying that the autocorrelation functions cannot be scaled by a single nondimensioned time. Third, ``stretched'' exponential behavior is found for the long-time behavior of the autocorrelation function. These observations are interpreted in terms of a power-law polydisperse ensemble of aggregate clusters, with a number distribution of the form N(m)\ensuremath{\sim}${m}^{\mathrm{\ensuremath{-}}\ensuremath{\tau}}$, where \ensuremath{\tau}=1.9--2. Finally, the kinetics of growth are studied and the average radius is found to grow exponentially with time. These results are shown to be consistent, in part, with the predictions of the Smoluchowski equation and with simulations of aggregation.