Eden model

Y. Saito, H. Muller-Krumbhaar. Eden model with elastic interactions. J Phys Soc Jpn (57 3661, 1998. 

Figure 3. Two-dimensional clusters grown with the poisoned Eden model. The average functionality of the monomers in each cluster is three. The distribution of functional groups among the monomers causes the different structures.

In their version of the Eden model, one starts with a seed, that is, one site on a two-dimensional lattice, and randomly chooses and occupies one of the four neighboring sites. The next growth site is picked from the resulting six neighboring sites, etc. This method results in spherical particles with uniform interiors and smooth surfaces relative to their radii. 

Surface scaling parameters for a number of nonequilibrium atomistic models have also been established [6, 10]. Continuum equations for the surface motion have to be used to find a solution for discrete models. Thus, for ballistic deposition [14] and the Eden model [15] the inter ce saturates, resulting in a = 1/2 and P = 1/3 for Z>pop = 2, and a 0.35 and 0.21 for Z>top = 3. Conversely, from the random deposition model P - 1/2 and, since the correlation length is always zero, fire interface does not saturate and, therefore, a is not defined. Depending on the rules used in the simulations, for the atomistic model including surfece difrusion a = 3/2 and p = 3/7 [6], a = 3/2 and p =... 

Small Angle X-ray Scattering was used to determine the fractal property of silica aggregates prepared by base-catalyzed hydrolysis and condensation of alkoxides in alcohol. As-produced samples were found to be mass fractals. The fractal dimensions spanned the regime 2.1 2.6 corresponding to more branched and compact structures. Both RLCA and Eden models dominated the kinetic growth under base-catalyzed condition... 

For w 4, unhydrolyzed sites are incorporated into the growing cluster. The probability of condensation at these sites is less than at hydrolyzed sites. Under these conditions, growth is described by a poisoned Eden model. Depending on the number and distribution of the poisoned sites, mass fractals, surface fractals or uniformly porous objects can result. The addition of more water in a second hydrolysis step is expected to completely hydrolyze the clusters and further growth should be described by the Eden model. 

Lebovka NI, Ivanenko YV, Vygomitskii NV (1998) Deterministic eden model of charged-particles aggregatirai. Europhys Lett 41(1) 19... 

The poisoned Eden mode) is relevant to silicate condensation under neutral conditions where the hydrolysis rate is minimized. Ether-forming (ROR) condensation is forbidden, and the rate of the alcohol-forming condensation reaction is lower than that of the water-forming condensation reaction [6,95]. Therefore, unhydrolyzed alkoxide sites, which are most abundant at neutral pH, act as poisons by inhibiting condensation (at least temporarily). Keefer argues that once unhydrolyzed sites are incorporated in the cluster, their hydrolysis may be impeded due to steric factors [136], If so, the poisoned Eden model would be physically and chemically relevant. 

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