Concentration dependence of structural and dynamical quantities in colloidal aggregation: Computer simulations.

We have performed extensive numerical simulations of diffusion-limited ~DLCA! and reaction-limited ~RLCA! colloid aggregation to obtain the dependence on concentration of several structural and dynamical quantities, among them the fractal dimension of the clusters before gelation, the average cluster sizes, and the scaling of the cluster size distribution function. A range in volume fraction f spanning two and a half decades was used for this study. For DLCA, a square root type of increase of the fractal dimension with concentration from its zero-concentration value was found: d f5d f 1af, with d f 51.8060.01, a50.9160.03, and b50.51 60.02. For RLCA the same type of behavior was found, this time with d f 52.1060.01, a50.4760.03, and b50.6660.08. In the case of DLCA, the exponent z that defines the power law increase of the weight-average cluster size (Sw) with time also increases as a square root type with concentration: z5z 1bf, with z51.0760.06, b53.0960.22, and a50.5560.03, while the exponent z8 that describes the power law increase of the number-average cluster size (Sn) with time follows the same law: z85z8 1b8f8, now with z851.0560.04, b853.4160.24, and a850.4660.02. We have also found that the cluster size distribution function scales as Ns(t)'N0S w 22 f (s/Sw), where N0 is the number of initial colloidal particles and f is a concentration-dependent function displaying an asymmetric bell shape in the limit of zero concentration. For RLCA, we found an exponential increase of the average cluster sizes for a substantial range of the aggregation time: Sw;e pft and Sn;e , with p'2q . For longer times the behavior departs from the exponential increase and, in the case of Sw for low concentration, it crosses over to a power law increase. In the RLCA case the scaling is as in DLCA where now a power law decay of the function f defines the exponent t, f (x);xg(x), with g(x) decaying exponentially fast for x.1. A slight dependence of the exponent t on concentration was computed around to the value t51.5. @S1063-651X~96!10311-1#