Nucleation metastable zone width

Kim, K.-J. and Mersmann, A., 2001. Estimation of metastable zone width in different nucleation processes. Chemical Engineering Science, 56(7), 2315-2324. 

The metastable zone width can also be reduced by the application of US. The apparent order of nucleation or growth is deoreased by US. Based on available evidence, the metastable zone width can be reduced simply by applying a low US power. Thus, US decreases the apparent order of the primary nucleation rate and increases the rate of appearance of the solid. Seemingly, US modifies the meohanism of nucleation itself as its presence strongly reduces the apparent order of nuoleation. 

Nucleation kinetics are experimentally determined from measurements of the nucleation rates, induction times, and metastability zone widths (the supersaturation or undercooling necessary for spontaneous nucleation) as a function of initial supersaturation. The nucleation rate will increase by increasing the supersaturation, while all other variables are constant. However, at constant supersaturation the nucleation rate will increase with increasing solubility. Solubility affects the preexponential factor and the probability of intermolecular collisions. Furthermore, when changes in solvent or solution composition lead to increases in solubility, the interfacial energy decreases as the affinity between crystallizing medium and crystal increases. Consequently, the supersaturation required for spontaneous nucleation decreases with increasing solubility, ° as shown in Fig. 7. 

Accounts of nucleation inhibition in the pharmaceutical literature are sometimes confusing because the dependence of the nucleation event (nucleation rate, metastability zone width, or induction time) on supersaturation is not considered. In search of additives that inhibit nucleation, induction times are often measured as a function of additive concentration, while the dependence of the nucleation event on supersaturation is neglected. Results from such studies possibly lead to the erroneous conclusion that the additive inhibited nucleation when indeed the additive decreased the supersaturation and frequently led to an undersaturated state. Hence, the system is under thermodynamic control instead of kinetic control. 

In general, for batch crystallization with a narrower metastable zone width, the operating window for generation of supersaturation is smaller. It is more likely to create nucleation with fine crystals, and vice versa. 

As discussed in Chapter 4, the nucleation rate is both species specific and a function of the supersaUiration ratio. The relation between nucleation rate, growth rate, and particle size as a function of the supersaturation ratio is illustrated qualitatively in Fig. 5-1. The acuial rate and supersaturation characteristics, such as metastable zone width, are system specific and can vary over wide ranges. In practice, it has been observed that the nucleation rate may vary from milliseconds to hours, and the metastable zone width may vary from less than 1 mg/ml to tens of mg/ml. 

The strong tendency of this compound to form oils or amorphous solids at increased supersaturation indicates a relatively narrow metastable zone width. Slow simultaneous addition with a large seed area effectively maintains the supersaturation sufficiently low to prevent nucleation of fines and allows some growth. 

The width of the metastable zone is affected by the solvent as well as a number of other factors including the agitation rate, the cooling rate, the presence of soluble additives, and the thermal history of the solution (Birchall and Davey, 1981 Garti etal., 1981 Nakai etal., 1973). The solvent influences the metastable zone width primarily because the nucleation rate of a given compound will vary from solvent to solvent. This is because nucleation rate is directly affected by the supersaturation and solubility a compound may attain in a given solvent, as well as molecular recognition phenomena between solute and solvent, as discussed in the next sections. 

Experimental techniques for determining the metastable zone width, the amount of undercooling that a solution will tolerate before nucleating, are described in section 5.3. The significance of the metastable zone and the interpretation of metastable zone width measurements are somewhat contentious subjects. Experimental values depend very strongly on the method of detection of the onset of nucleation, but it is still possible to extract kinetic information on the nucleation process as well as on the growth behaviour of very small crystals. These topics are discussed in some detail in section 5.3. 

Nyvlt, J. (1983) Induction period of nucleation and metastable zone width. Collections of the Czechoslovak Chemical Communications, 48, 1977-1983. 

Experiments in laboratoiy and industrial ciystallizers have shown that nuclei ate bom at supersaturations Ac Ac gj hom in presence of crystals (either product crystals or added seed ciystals). Such nuclei are called secondary nuclei. This secondary nucleation caused by the removal of preordered species on a crystal sm-face and attrition fragments can take place at very small supersaturations however, < c gj hetsecondary nuclei. In Fig. 8.4-1 the solubility c and the three metastable zone widths ACmet,hom, Ac gj het, a d Ac gj, gg Valid for homogeneous, heterogeneous, and secondary nucleation, respectively, are shown as a function of temperature T. 

Ulrich, J. and Strege, C. 2002. Some aspects of the importance of metastable zone width and nucleation in industrial crystallizers. J. Cryst. Growth 237-239 2130-2135. 

In the nucleation stage, small clusters of solute molecules are formed some of these clusters may grow sufficiently to form stable nuclei and subsequently form crystals. Others fail to reach adequate dimensions before they dissolve again. Within the metastable zone width (MSZW), the induction time to the onset of crystallisation has an inverse relationship with the supersaturation [44-47]. 

An additional selection criterion is a detectable metastable zone width. Every solution has a maximum amount that it can be supersaturated before becoming unstable. The zone between the solubility curve and the unstable boundary is referred to as the metastable zone. In an initial seeded batch the supersaturation is always maintained within the metastable zone to minimise nucleation, the formation of new unwanted tiny crystals known as fines. These either cause filtration problems or reduce batch yields by blocking or passing through screens. 

The metastable control can be achieved if the crystalline compound has a detectable metastable zone width represented by AT et- One of Nyvlt s methods (1985) is used to measure the metastable limit. Saturated solutions of known concentrations containing a few large size seeds are cooled down at a steady cooling rate until the first nuclei appeared. The difference between saturation and nucleation temperatures AT et represents the metastable zone width at a given concentration. Nyvlt s methods are not applicable for slow growth compounds at low temperatures. In this case alternative methods, which increase concentration at a specified temperature instead of reducing temperature at a given concentration, must be employed. Details of these methods will be discussed in another paper due to space limitation. As the metastable limit and the solubility curves respectively serve as upper and lower constraints in a dynamic optimisation problem, they should be estimated beforehand if unavailable in the literature. 

Due to the steep increase of the nucleation rate with supersaturation, primary nucleation in technical system can be differentiated into two categories has-not-yet-occurred and has-occurred. Two types of descriptions are used to quantify the effects of nucleation for a system with a constantly increased supersaturation, the metastable zone width is used for a system with constant supersaturation, the induction time is used. 

Any decrease in nucleation rate leads to an increase in the metastable zone width [9] and the induction time, both of which can be measured using suitable techniques, for example, ultrasonic probe [10]. Figure 6.2 illustrates the impact of Fe on the metastable zone width of ammonium sulfate the width increases from 1 K to more than 4 K. 

Other nucleation thermodynamic parameters such as the interfacial energy between Ndl23 or Y123 and melt, metastable zone width, Gibbs free energy, critical nucleation radii etc. were estimated by Paul et al. (1999, 2000) using classical nucleation theory. 

Systems also vary in the extent of the metastable zone width, the point after which spontaneous nucleation is said to occur. Within the metastable zone, however, seed crystals may grow. Metastable zone width is therefore an important factor in assessing the propensity of a system to crystallize and in deciding the appropriate crystallization technique. Kim and Mersmann (2001) provide a review of methods for estimation for metastable zone widths both unseeded and seeded systems. 

Bensouissi, A., Roge, B., Mathlouthi, M. (2010). Effect of conformation and water interactions of sucrose, maltitol, mannitol and xylitol on their metastable zone width and ease of nucleation. Food Chemistry, 122, 443 46. 

The rate of primary nucleation and width of the associated metastable zone are difficult to measure with precision in the laboratory, because of their dependence on environmental factors. Dust particles contaminating a solution, and imperfections on the surface of the crystallizer and agitator are often... 

Whenever the solubility curve is crossed for the less stable Form II there is a risk that it will nucleate and contaminate the product. This situation is very probable when the solubility curves of the two polymorphs lie close together, as shown in Figure 21 of the Cimetidine case study. The addition of seed crystals of Form I, close to its solubility curve, and minimization of the supersaturation during the growth process is a good method of control in this instance. Solvent selection to extend the width of the Form II metastable zone would also be desired, as discussed in section 2.4.4. 

---