Monomer-cluster aggregation

In our studies, we consider several types of aggregated structures such as bispheres, linear chains, plane arrays on a plane rectangular lattice, compact and porous body-centered clusters embedded on the cubic lattice (bcc clusters, the porosity was simulated by random elimination of monomers), and random fractal aggregates (RF clusters). To generate RE clusters, a three-dimensional lattice model with Brownian or linear trajectories of both single particles and intermediate clusters was employed for computer simulations of aggregation process. At the initial time moment, = 50,000 particles are generated at... 

Monomer-cluster or cluster-cluster growth can be limited by diffusion or by reaction. In diffusion-limited monomer-cluster aggregation (DLMCA), simulated by the Witten and Sander model (25) in Fig. 5.11, it is assumed that monomers are released one by one from sites arbitrarily far from a central cluster. The monomers travel by a random walk diffusion mechanism and stick irreversibly at first contact with the growing cluster. Because of this trajectory, the monomers cannot penetrate deeply into a cluster without intercepting a cluster arm and the arms effectively screen the interior of the cluster from incoming monomers. Growth occurs preferentially at exterior sites, resulting in objects in which the density decreases radially from the center of mass (in three dimensions dm = 2.45). 

Hydrolysis and condensation occur by bimolecular nucleophilic displacement reactions involving OH and Si-0 anions. For w > 4, the hydrolysis of all polymeric species is expected to be complete. Dissolution reactions provide a continual source of monomers. Because condensation occurs preferentially between weakly acidic species that tend to be protonated and strongly acidic species that are deprotonated, growth occurs primarily by reaction-limited monomer-cluster aggregation (equivalent to nucleation and growth), leading to compact, nonfractal structures. 

Under the conditions used by Stober et al. [27], primary particles formed by nucleation, growth, and ripening undergo an ordered aggregation process to form monosized spherical particles. This process represents reaction-limited monomer-cluster aggregation occurring concurrently on two length scales. 

Simple two-dimensional lattice model for diffusion-limited monomer-cluster aggregation. Particles are created one at a time from randomly selected points (S, and S ) on... 

These procedures not only indicate the kinetics of aggregation, but also allow study of the size distribution and the fractal geometry of the clusters. Typical results for the fractal dimension of clusters grown in computer simulations are summarized in Table 5. Note that the monomer-cluster aggregation models produce dense nonfractal clusters, except for the diffusion-limited case, whereas cluster-cluster models yield fractal dimensions in good agreement with experiments on real colloids. 

DLMCA Diffusion-limited monomer-cluster aggregation... 

RLMCA Reaction-limited monomer-cluster aggregation or aggregate... 

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