Irreversible Diffusion-limited Aggregation Research Articles

Cluster aggregation under diffusion

Cluster aggregation limited by cluster diffusion is one of the possible pathways leading to aggregation phenomena as different as phase separation or colloidal gelation. The imprinting of the irreversible diffusion-limited aggregation is observable in the evolution of the scattered intensity I( q, t) and in its dynamical scaling relations. We discuss a recent model for describing the evolution of the scattered intensity both for growing eucledean and fractal clusters.

Cluster-cluster correlation during irreversible diffusion-limited aggregation

In this paper, we discuss the evolution of the scattered intensityI(q) during irreversible diffusion-limited cluster-cluster aggregation. We analyse twodimensional simulations and interpret the results within the framework of a recently proposed theoretical approach. The theory describes the correlation among different clusters which develops during the irreversible aggregation process. The model is based on two coupled differential equations, controlling the growth of the average cluster mass and the time dependence of the probability of finding pairs of clusters as a function of their distance.

Kinetics of Heterocoagulation

The heterocoagulation of colloids A and B was investigated by computer simulation and through experiments. In simulation, the cluster aggregation ability Å n , and cluster size n were correlated using the equation A n = A 1 n gamma; , and the three situations, γ = -0.5, 0, and 0.5 were investigated. The scaling laws of aggregation kinetics were established and the exponents were expressed as a function of the relative concentration x = [A]/([A] + [B]) of the two latices. A unique master curve represented the correlation between the temporal variations of the weight S( t) and number N( t) average sizes. On the contrary, the correlation between the exponents of the dynamic scaling laws and the relative concentration x depended on x. In the experiments, a particle counter technique was used to determine the aggregate concentration c n ( t) as a function of the aggregate size n, thereby allowing the aggregate average sizes S( t) and N ( t), which were directly compared to those obtained from simulation, to be calculated. In the heterocoagulation experiments, mixtures of polystyrene amidine latex (A) and polystyrene sulfate latex (B) of equal size, which exhibited identical electrophoretic mobility at the pH of the experiments, developed different aggregation modes. For x ⪡ 0.5, the process resembled an irreversible diffusion-limited aggregation. For x equal or close to 0.5, S( t) and N( t) increased with the features of a reversible process. Finally, for x ⪢ 0.5, the rate of the process is enhanced. Our experiments also showed that sulfate latex constituted the core of the aggregate and that the amidine latices were located around them.

Growth model of Au films on Ru (001)

In an attempt to find generic features of the fractal growth of Au films deposited on Ru (001), a simple simulation model based on irreversible diffusion-limited aggregation (DLA) is discussed. Highly irregular two-dimensional dendritic islands of Au particles that gradually grow on a larger host lattice of Ru particles and have fractal dimension d f≈1.70 each, are generated via a multiple ad-hoc version of the DLA algorithm for single aggregates. Annealing effects on the island morphology are reproduced assuming different sticking probabilities at nearest-neighbour lattice sites of Au films on Ru(001). Using simulation data, growth of islands is described in analogy to diffusion-limited, precipitate growth with a soft impingement of precipities. This leads one to analyse thin film island growth kinetics in such fractal systems and to predict a main peak in the scattering intensity patterns due to inter-island interference.

Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation

A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.