Nucleation competition with crystal growth

The rate of crystal growth is determined by the degree of supersaturation, the rate of molecular diffusion to the crystal surface, and the time required for TAG molecules to fit into the growing crystal lattice (Mulder and Walstra, 1974 Walstra, 1987). Compared to nucleation, the driving force required for crystal growth is relatively low (Sato et al, 1989). However, in a multicomponent fat, the supersaturation for each TAG is small (Walstra, 1998). This fact, combined with competition between similar molecules for the same sites in a crystal lattice, means that milk fat crystallization is especially slow (Skoda and van den Tempel, 1967 Knoester et al, 1968 Grail and Hartel, 1992). 

With respect to the competition between nucleation and crystal growth, evidence has shown that both the nucleation rate and the growth rate increase with increasing temperature. However, it also has been noted that the absolute number of crystals formed actually decreases as the temperature is increased... 

In precipitations, just as in crystallization processes, there is a competition between nucleation and crystal growth. BoUi are controlled by the relative supersaturation, but nucleation is a higher order process. The rate of nucleation increases very sharply with increasing supersaturation. At lower values of the relative supersaturation Ac the nucleation rate appears to be proportional to Ac to a power of about 5 at higher values of Ac the nucleation rate increases exponentially with Ac. 

At higher seed concentrations (about 230 mg HAP 1 ) a more basic calcium phosphate with Ca P = 1.52 + 0.04 crystallizes on the growth sites of the HAP seed material and no evidence is found for the presence of DCPD. The dependence of the growth phase on solid/solution ratio is of particular importance not only for the interpretation of the results of biological precipitation studies but also for the formation of calciiam phosphate in environmental systems. It may be e2q>lained by the competition between heterogeneous nucleation of DCPD and the growth of the active sites already present on the seed si >strate surface. The latter process occurs more extensively in the initial stages of reaction when the seed concentration is... 

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