Rate of Nucleation and Crystal Growth

Rates of nucleation and crystal growth may be given, respectively, as... 

As discussed in section 2.4.4 the coordinating ability of a solvent will often affect the rate of nucleation and crystal growth differently between two polymorphs. This can be used as an effective means of process control and information on solvent effects can often be obtained from polymorph screening experiments. There are no theoretical methods available at the present time which accurately predict the effect of solvents on nucleation rates in the industrial environment. 

Figure 1-20 Schematic Representation of the Rate of Nucleation and Crystal Growth...

Impurities can affect the rates of nucleation and crystal growth, often (or usually) with an effect disproportionate to the amount involved. Part per million levels of impurity have been shown to profoundly influence the size, shape, and rate of growth of some industrially important compounds. Entities as common as table salt are often modified intentionally by producers seeking desirable properties. 

Impurities, added or unintentional, can have a major effect on rates of nucleation and crystal growth. Table 4-1 shows the effect of an impurity, structurally similar to the crystallizing solute, added to an all-growth crystallization (separation of stereoisomers. Examples 7-6 and 11-6). The data for a continuous stirred tank (CSTR) operation show a sevenfold decrease in the first order growth rate constant as a result of addition of this impurity to prevent nucleation of the undesired isomer. 

In general, kinetic resolution requites the presence of a racemic mixture (conglomerate) and the absence of a (generally lower-solubility) racemic compound (both enantiomers in the crystal lattice). This is not always the case, however, and depending on the relative rates of nucleation and crystal growth of the respective forms, a kinetic (nonthermodynamic) isomer separation can sometimes be effected even when a racemic compound is possible. In the case of solid solution of the enantiomers (no lattice fit requirement), an equilibrium process will essentially always be requited. 

Three additional considerations are required to successfully control a crystallization process. Local conditions rather than bulk, and instantaneous rates of change rather than mean values control the relative rates of nucleation and crystal growth. Further, the response of the system to control changes is history dependent. Spontaneous nucleation that accompanies an excursion beyond the supersaturation metastable limit dramatically affects the surface area available for crystal growth and influences the product CSD of a continuous process for several residence times or the final CSD of a batch process. 

In systems displaying polymorphism, embryonic nuclei with structures resembling each of the mature phases may be present. The appearance of polymorphs is then kinetically controlled by the relative rates of nucleation and crystal growth of the different polymorphs [64]. The presence of impurities may lead to the formation of a particular polymorph by either... 

Figure 2.1 Effect of temperature on the rates of nucleation and crystal growth for a glass forming melt...

For fiber reinforced composites based on semicrystalline matrix, the ultimate properties are determined in part by the crystalline morphology of the polymer matrix, which in turn depends on the rates of nucleation and crystal growth. Therefore, the knowledge and understanding of crystallization mechanisms are crucial for designing the tailored materials or products with the desirable properties. In this section, we would like to introduce the crystallization kinetics of PET/PP MRCs first, and then the crystaUine structures and aggregated morphology will be also presented. 

It was shown above that the total crystal number, surface area and the mass mean size are affected by the mean residence time and the rates of nucleation and crystal growth respectively. Since both these kinetic processes depend upon the working level of supersaturation which will itself depend on the amount of surface area available and crystal mass deposited, the question arises what will be the effect of a change in residence time on crystallizer performance Consider the idealized MSMPR crystallizer depicted in Figure 7.8. 

Rates of nucleation, and crystal growth, G, are respectively evaluated as the functions of supersaturation. The level of supersaturation, AC, is determined... 

Fig. 2.4. Effect of the degree of supercooling below the melting temperature on the viscosity and rates of nucleation and crystal growth...

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