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 quanti ties, among them the fractal dimension of the clusters before gelation , the average cluster sizes, and the scaling of the cluster size distr ibution function. A range in volume fraction phi spanning two and a ha lf decades was used for this study. For DLCA, a square root type of in crease of the fractal dimension with concentration from its zero-conce ntration 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 defin es the power law increase of the weight-average cluster size (S-w) wit h 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 t he 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 distribu tion function scales as N-s(t)approximate to N(0)S(w)(-2)f(s/S-w), whe re N-0 is the number of initial colloidal particles and f is a concent ration-dependent function displaying an asymmetric bell shape in the l imit of zero concentration. For RLCA, we found an exponential increase of the average cluster sizes for a substantial range of the aggregati on times: S-w similar to e(p phi t) and S-n similar to e(q phi t), wit h 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 exponenti ally fast for x>1. A slight dependence of the exponent tau on concentr ation was computed around to the value tau=1.5.