Nucleation exclusion zones modeling particle growth

4 Nucleation exclusion zones modeling particle growth 

The production of single nuclei is somewhat helped by the formation of nucleation exclusion zones around the growing particles (43 5). In the area surrounding a growing particle, there will be a reduction in the concentration of precursor, and this will reduce the probability of nucleating a new particle. Milchev et al. have derived an equation for the stationary nucleation rate around a growing stable cluster (46,47). 

This approach then allows a useful set of conditions under which single particle nucleation and growth are favored (40). The distance from a growing particle within which the nucleation rate decreases by an amount of the value on the unperturbed surface is 

In the limit when 8BV t A (i.e., long time, large Jq, and small cJA), equation (16.3.7) simplifies to 

For most applicable overpotentials, the numerator becomes 1 and the nucleation exclusion zone extends a distance particle radii from the growing particle—that 

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