Heterogeneous nucleation processes

Distinguish between homogeneous and heterogeneous nucleation processes. 

FIGURE 20.2 Schematic illustrating heterogeneous nucleation process with all related surface energy in equilibrium. 

Heterogeneous nucleation processes are of fundamental and practical importance in pharmaceutical systems as unintentionally or intentionally added surfaces or interfaces may promote nucleation. The reactivity of crystal surfaces as heterogeneous nucleants has significant consequences in the isolation of the desired... 

The major assumption made in the present quantitative impurity analysis is the model of instantaneous nucleation, which is characterized by extremely rapid onset and is consistent with a relatively small n value ( 2 for SX) (52). The homogeneous and heterogeneous nucleation processes can proceed simultaneously. However, the former can occur only in the bulk material of molten SX, whereas the latter is initiated by contact with the surface of the form II seeds present. The number of nuclei formed by heterogeneous nucleation is proportional to the surface area of the metastable phase, and will be proportional to x, the weight fraction of SX-II, if the same specific surface area is assumed for both preexisting nuclei and SX-II particles added (as in physical mixtures). Therefore Ax, the total number of nuclei formed at x c 1 can be expressed by... 

Heterogeneous nucleation on active sites Real surfaces, for instance obtained with melt-grown gold, silver, or platinum single-crystal electrodes, exhibit various sites and structural imperfections of different dimensionahty, such as kinks, vacancies, monatomic steps, reconstructed surface domains, 2D islands, and holes [2, 129, 130]. Defining the number of active sites S under particular experimental conditions as No, one may consider the heterogeneous nucleation process as the successive incorporation of monomers Ml into site-confined clusters S — Mi... 

In both homogeneous and heterogeneous nucleation processes, the monomer attachment usually occurs by diffusion of the monomers in the volume of the solution toward the nucleus or by transfer of solute across the nucleation/solution interface. 

The crystallization of a polymer in the presence of solidified domains of the second phase takes place through a heterogeneous nucleation process. Since the rate of heterogeneous nucleation is higher than that of homogeneous nucleation, and since primary nucleation is the rate-controlling step for polymer crystallization, the crystallization rate is expected to be higher in such blends when compared to homopolymers (Nadkami and Jog 1991). 

So far, we have only determined the number of viable nuclei for homogeneous and heterogeneous nucleation processes (n, as a function of the temperature T. What we would really like to determine is the rate of nucleation, N, that is, the concentration of viable nuclei that are created per unit time during a transformation process. 

Under certain circumstances stable embryos of long chain molecules can be retained in cavities above their melting temperature.(137) This conclusion is in accord with results for monomeric substances. A general analysis that encompasses all possible heterogeneous nucleation processes cannot be formulated. The detailed nature of the substrate and the manner in which chain units fill cavities must be specified before the problem can be solved. 

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