A probabilistic aggregation kernel for the computer-simulated transition from DLCA to RLCA

– A simple sticking probability model is used for deducing a kernel capable to describe the kinetics of computer-simulated irreversible aggregation processes. Not only the diffusionand reaction-limited aggregation regimes were fitted but also the whole transition region. The deduced kernel establishes λ = 0 for the entire range of sticking probabilities and helps to understand how irreversible cluster-cluster aggregation works. Aggregation phenomena occur in a wide variety of physical, chemical and biological processes [1]. The stage of aggregation for a given system may be characterized by the cluster size distribution, N = (N1, N2, ..., Ni, ...), where Ni denotes the number of i-size clusters. For irreversible aggregation processes in diluted systems, the time evolution of the probability, P ( N, t), for finding the system in a given state, N , is given by the non-deterministic master equation [2, 3] dP ( N, t) dt = 1 2V ∑ i,j kij [(Ni + 1)(Nj + 1 + δij)P ( N ∗ ij , t)−Ni(Nj − δij)P ( N, t)] , (1) where V is the volume of the system and N ∗ ij is defined as N ∗ ij = { (..., Ni + 1, ..., Nj + 1, ..., Ni+j − 1, ...) for i = j , (..., Ni + 2, ..., N2i − 1, ...) for i = j . All physical information about the aggregation mechanism is contained in the kernel, kij , which quantifies the mean aggregation rate for a pair of iand j-size cluster. Initial studies were concerned principally with the diffusion-limited cluster aggregation regime (DLCA) where the clusters diffuse freely and form a new bond as soon as they collide. (∗) Permanent address: Departamento de Qúımica F́ısica y Matemática, Facultad de Qúımica, Universidad de la República 11800 Montevideo, Uruguay. (∗∗) E-mail: [email protected]