Concentration effects on two- and three-dimensional colloidal aggregation

By means of extensive numerical simulations of diffusion-limited colloidal aggregation in two and three dimensions, we have found the concentration dependence of the structural and dynamical quantities. Both on- and off-lattice simulations were used in 2D to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned two-and-a-half orders of magnitude, in both dimensionalities. In two dimensions, it was found that the cluster fractal dimension difference from the zero-concentration value shows a linear increase with the concentration, while this increase is of a square root type for the three-dimensional case. For the exponent z, defining the increase of the weight-average cluster size as a function of time, the difference from the zero-concentration value in three dimensions is again of a square root type increase with concentration, while in two dimensions this increase goes as the 0.6 power of the concentration. We give arguments for the drastic change in the power laws for the case of the fractal dimension, when going from two to three dimensions, and for the small change for the case of the kinetic exponent z. We also present the master curves for the scaling of the cluster size distribution and their dependence on concentration, in both dimensionalities.