A stochastic simulation method is used to recover the scaling behavior and the complete time evolution of an experimental system of colloidal aggregation of polystyrene particles under both diffusion-limited aggregation and reaction-limited aggregation conditions. Several hypotheses about the underlying kinetics and the scaling properties of the aggregation process are tested by comparing numerical with experimental results. PACS numbers: 82.70.Dd, 02.70. Lq, 82.20.Wt Colloidal aggregation systems of gold [1], polystyrene [2,3], and silica [4 -6] are extensively studied in the literature. In experimental systems two limiting growth processes can be observed: (a) difFusion-limited aggregation (DLA), i.e. , every collision between clusters results in a reaction, and (b) reaction-limited aggregation (RLA), i.e. , many collisions between clusters take place before a reaction occurs. These processes are usually treated within the scaling approach of the Smoluchowski equation [7,8]. Nevertheless, this description is often unsatisfactory since its validity is restricted to the scaling limit of long times and large clusters whereas in experiments small clusters and short times are often of interest. Thus, a description of the complete time evolution of each cluster is desirable.In this Letter we show that a stochastic simulation method [9 -11] based on a master equation is an ideal tool for the investigation of the kinetics and dynamic scaling properties of colloidal aggregation experiments. With the stochastic simulation method a hypothesis about the appropriate kinetics of the aggregation process can easily be tested by comparison of numerical results with experimental data.Our Letter is organized as follows. We begin with a description of the usual deterministic treatment of aggregation processes within the scaling approach of the Smoluchowski equation. Furthermore, we briefiy discuss the corresponding stochastic formulation of the problem. The results and the interpretation of the experimental system in the context of the scaling theory are described in the second part. The stochastic simulation results are discussed in the last part of this Letter. There we compare the simulation results with the predictions of the scaling theory and the experimentally observed data.In general, a colloidal aggregation process can be described by the following reaction scheme: k(i, j) A, +A, ': A+, , where A, denotes a cluster of i unit masses and k(i, j) is the mass dependent rate coefBcient or kernel of the irreversible reaction. The kinetics of the aggregation system is determined by this kernel. In the usual deterministic approach, this process is described by the well-known deterministic Smoluchowski equation,where c~(t) denotes the concentration of clusters of mass m at time t. For convenience, the dynamics of the Smoluchowski equation (2) is often formulated in dimensionless variables defined by the transformations X (T) = c (T)/cp, T = t/t ss, and K(i, j ) 2k(i, j)/k(1, 1), where cp = p~r nc is a constant and tsss --2/cpk...
