Monomer-cluster growth model

Nucleation of protein crystals typically requires extremely high supersaturation levels. Studies of protein nucleation are limited, with most efforts focused on light scattering as a tool to detect nucleation. Feher and Kam s work set the tone for much of the work that followed (Feher and Kam 1985). They model nucleation in a classical fashion, as a cooperative step-by-step addition of monomers to a cluster. Light scattering is utilized to follow the cluster size distribution as a function of time and solution variables, which yield estimates for the relative forward (cluster growth) and reverse (cluster dissolution) rates of monomer addition. Certainly, the protein crystal nucleation is an area that deserves additional study. 

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). 

An alternative description of gelation is given by kinetic growth models. These also explain the different microstructures upon changing the reaction conditions. Depending on the conditions, growth in silicate systems may occur predominantly by condensation of clusters with monomers or with other clusters. The rate of the condensation reactions may be diffusion or reaction limited. 

Catalyst particle nucleation in the initial stages and their subsequent growth play an important role in catalytic mechanisms. In a model Pt/alumina catalyst, the general view is that the formation of particles is a stepwise process incorporating the following steps (Wynblatt and Gjostein 1975, Cottrell 1971) individual metal atoms (called monomers) transform to two-dimensional islands, which subsequently transform to three-dimensional clusters. These clusters eventually transform into finite-sized particles. 

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