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 phi 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(f)=d(f)(0)+a phi(beta), with d(f)(0)=1.80+/-0.01, a=0.91+/-0.03, and beta=0.51+/-0.02. for RLCA the same type of behavior was found, this time with d(f)(0)=2.10+/-0.01, a=0.47+/-0.03, and beta=0.66+/-0.08. In the case of DLCA, the exponent z that defines the power law increase of the weight-average cluster size (S-w) with time also increases as a square root type with concentration: z=z(0)+b phi(alpha), with z(0)=1.07+/-0.06, b=3.09+/-0.22, and alpha=0.55+/-0.03, while the exponent z' that describes the power law increase of the number-average cluster size (S-n) with time follows the same law: z'=z'(0)+b'phi(alpha'), now with z'(0)=1.05+/-0.04, b'=3.41+/-0.24, and alpha'=0.46+/-0.02. We have also found that the cluster size distribution function scales as N-s(t)approximate to N(0)S(w)(-2)f(s/S-w), where N-0 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 times: S-w similar to e(p phi t) and S-n similar to e(q phi t), with p approximate to 2q. For longer times the behavior departs from the exponential increase and, in the case of S-w 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 tau, f(x)similar to x(-tau)g(x), with g(x) decaying exponentially fast for x>1. A slight dependence of the exponent tau on concentration was computed around to the value tau=1.5.