Universal reaction-limited colloid aggregation

Abstract

We study slow, or reaction-limited, colloid aggregation (RLCA) with both static and dynamic light scattering and develop a self-consistent interpretation of the results. Static light scattering is used to determine the fractal dimension of the clusters and the cutoff mass of the power-law cluster-mass distribution. Using this same cutoff cluster mass, we can predict the shape of the temporal autocorrelation function measured by dynamic light scattering. Good agreement with experiments is obtained provided the effects of rotational diffusion are included. In addition, we determine the ratio of the hydrodynamic radius to the radius of gyration of individual RLCA clusters and find \ensuremath{\beta}=1.0. A scaling method is used for the q-dependent first cumulants of the temporal autocorrelation functions to obtain a single master curve for data obtained at different times in the aggregation process. The shape of this master curve is very sensitive to several key features of the process of reaction-limited colloid aggregation. It allows us to unambiguously determine the exponent for the power-law cluster-mass distribution, \ensuremath{\tau}=1.5\ifmmode\pm\else\textpm\fi{}0.05. Furthermore, we show that the master curves for three completely different colloids, gold, silica, and polystyrene, are indistinguishable. In addition, the fractal dimensions of their RLCA clusters, as measured by static light scattering, are all ${d}_{f}$=2.1\ifmmode\pm\else\textpm\fi{}0.05, while the aggregation kinetics for each colloid are exponential. This demonstrates that reaction-limited colloid aggregation is universal, independent of the detailed chemical nature of the colloid system.