Impurities nucleation rates

The size of crystals produced in the gas-liquid system varied from 10 to 100 pm by controlling the level of supersaturation, while the liquid-liquid system produced crystals of 5—30 pm. The wide variation of crystal size is due to the marked sensitivity of the nucleation rate on the level of supersaturation, while the impurity content is another variable that can affect the crystal formation. 

Water soluble impurities and their effect can be easily included in equation (1-4), through which they are going to directly affect the particle nucleation rate, f(t). If one assumes a first order reaction of an active radical with a water soluble impurity (WSI) to give a stable non-reactive intermediate, then one simply has to add another term in the denominator of equation (1-4), of the form kwsr[WSI](t)-kv, and to account for the concentration of WSI with a differential equation as follows ... 

It was suspected that two mechanisms could lead to an increase in the impurity content of crystals as supersaturation increased. The first is through nucleation i.e., an increase in supersaturation leads to greater nucleation rate and, concomitantly, larger numbers of crystals and higher crystal surface areas. As the crystals recovered in the present experiments were washed with acetone, surface impurities are not thought to have been important in the results presented here. 

The work of Yamamoto (43) with growth-active impurities such as Pb+2, Sn+2, and Mn+2 ions reveals that their presence in very small quantities decreases the probability of nucleation, thus extending the metastable region of aqueous solutions of the alkali halides. These ions of the transition elements because of their screening demands withdraw Cl- ions from solution and form complexes such as (PbCl6) 4 and (MnCl6)-4. Without changing the over-all composition of the solution, these ions lower the effective concentration of the Cl ions and thus decrease the nucleation rate of NaCl. 

Secondary nucleation is influenced by numerous parameters, including the driving force for crystallization, temperature, additives, impurities, agitator, agitation rate, the number and size of existing crystals, and roughness of the crystallizer surface. The parameters affecting nucleation and nucleation rate will be reviewed in a subsequent section. 

As with melts, soluble impurities may increase or reduce nucleation rate. Insoluble materials may act as nuclei and promote crystallization. Impurities may also affect crystal form and, in some cases, are deliberately added to secure a product with good appearance, absence of caking, or suitable flow properties. 

Noteworthy, the higher mobility of impurity atoms (molecules) in nanoscale particles can lead to the larger rate of impurity nucleation in them as compared with the bulk substance. 

In addition, for a specific compound, the nucleation rate is also dependent on the sol-vent(s) system, impurities, and mixing. These factors combine to cause the difficulties that arc often encountered in controlling a nucleation-based CrystaUization process, especiaUy on scale-up. 

The critical mixing factors in a stirred tank at e impeller speed and type, as well as their influence on local turbulence and overall circulation. Since all aspects of these factors cannot be maintained constant on scale-up either locally or globally, the extent to which changes in the crystallizing environment will affect nucleation is extremely difficult to predict. To the mixing issue must be added the uncertainties caused by soluble and insoluble impurities that may be present in sufficiently different concentrations from batch to batch to cause variation in induction time, nucleation rate, and particle size. 

There is possible batch-to-batch variation in dissolved and/or undissolved impurities, which can influence the nucleation rate. 

Two factors complicate these simple representations. They are the effect of increasing distiUation temperature caused by the increasing concentration of substrate and impurities. The impurities, in particular, can dramatically increase the solubility of the substrate. They can also decrease the inherent growth rate by blocking or inhibiting surface incorporation on the growing crystals or by reducing the nucleation rate. These effects are represented as curve H-E in Fig. 8-2. As distillation proceeds, the solubility increases. In extreme cases, the crystals once formed could melt as the temperature increases. 

The addition of an antisoivent can be earned out in different ways, as indicated in Fig. 9-1, where the concentration of product is shown on the ordinate and the amount of antisoivent added is shown on the abscissa. A typical equilibrium solubility curve is indicated as A-B-C. (This curve could be concave or linear but is shown as convex for clarity.) The metastable region is indicated as the area between B-C and E-D. From point A to point B, addition of antisoivent will proceed without crystallization because the solution concentration is below the equilibrium solubility. At point B, equilibrium solubility is reached. As the addition of antisoivent continues, supersaturation will develop. The amount of supersaturation that can be developed without nucleation is system specific and will depend on the addition rate, mixing, primaiy and/or secondary nucleation rate, and growth rate, as well as the amount and type of impurities present in solution. 

FIGURE 14.6 Nucleation of emulsified milk fat as a function of cooling temperature, (a) Concentration of catalytic impurities Ncat. (b) Initial heterogeneous nucleation rate J() the broken line gives a rough estimate of the homogeneous nucleation rate. (After results by P. Walstra, E. C. H. van Beresteyn. Neth. Milk Dairy J. 29 (1975) 35.)... 

The presence of impurities can increase nucleation densities. Higher nucleation rates can be obtained with halogen/hydrogen mixtures than with methane/hydrogen mixtures. The presence of a large amount of oxygen in a plasma etches the sp carbon phase which nucleates more easily than diamond, and the Quality and yield of diamond particles may be improved... 

The impurity concentration gradient theory assumes that the solution is more structured in the presence of a crystal. This increases the local supersaturation of the fluid near the crystal, which is the source of crystal nuclie. Changes in the structure of the solution near the crystal surface have been observed experimentally. Dissolved impurities in the solution are known to inhibit nucleation rates. Some of the impurities are incorporated into the crystal surface. Thus, a concentration gradient is formed that enhances the probability of nucleation. Experimental evidence of the theory was presented for the nucleation of potassium chloride in the presence of lead impurities. As expected, stirring the solution causes the impurity concentration gradient to disappear and hence, lower the nucleation rates (Denk 1970). 

It is well known that a small amount of impurity can profoundly affect the nucleation rate, however, it is impossible to predict the effect prior. The presence of additives can either enhance or inhibit the solubility of a substance. Enhanced solubilities would lead to lower supersaturations and lower growth rates. If it is postulated that the impurity adsorbs on the crystal surface, then two opposing effects come into play—the presence of an additive would lower the surface tension and lead to higher growth rates, however, the impurity adsorption blocks potential growth sites and lowers nucleation rates. Thus, the effect of impurities is complex and unpredictable. 

---