Metastable widths

Metastable zone width should be less than 25°C for efficient crystallisation. 

Within the metastable regioa, primary aucleatioa will aot occur, and the width of the metastable zone, as reflected by — c or T —, varies... 

Systems also vary in the extent of the metastable zone width, the point after whieh spontaneous nueleation is said to oeeur. Within the metastable zone, however, seed erystals may grow. Metastable zone width is therefore an important faetor in assessing the propensity of a system to erystallize and in deeiding the appropriate erystallization teehnique. Kim and Mersmann (2001) provide a review of methods for estimation for metastable zone widths both unseeded and seeded systems. 

Solution characteristics eomposition, equilibrium relationships (solubility), metastable zone width, purity, partition eoeffieient, liquid density, viseosity, and their temperature dependenee (Chapter 3). 

The most frequent site for erystal enerustation is on a eompatible solid surfaee within a zone of high supersaturation and low agitation. Seleetion of a less eompatible material having a smooth surfaee ean avoid the major exeesses of enerustation. Dunean and Phillips (1979) and Shoek (1983), respeetively, reveal a eonneetion between the metastable zone width of erystallizing solutions and their propensity to enerust. It is well known that judieious erystal seeding ean also help minimize enerustation. Simple laboratory tests are reeommended to determine all these issues before the plant is built. 

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

Sohnel, O. and Mullin, J.W., 1988. The role of time in metastable zone width determinations. Chemical Engineering Research and Design, 66, 537-540. 

The ultimate limit of metastability is reached in reality when AF /kaTc is of order unity. Thus the width over which the spinodal singularities are rounded can be estimated from AF /kaTc oc 1 as... 

The extrapolated value of aTi// ) on this plot corresponds to the width of the metastable zone as expressed in terms of temperature, The width of the metastable zone expressed in... 

Quite complex kinetic behavior has been identified on some surfaces. For instance, on Ir(100), the TPD data from NO-saturated surfaces display two N2 desorption peaks, one at 346 K from the decomposition of bridge-bonded NO, and a second at 475 K from the decomposition of atop-bonded NO molecules [13], Interestingly, the first feature is quite narrow, indicating an autocatalytic process for which the parallel formation of N20 appears to be the crucial step. An additional complication arises from the fact that this Ir(100) surface undergoes a (1x5) reconstruction, and that NO adsorbed on the metastable unreconstructed (lxl) phase leads to N2 desorption at lower temperatures. In another example, on the reconstructed hexagonal Pt(100) surface, when a mixed NO + CO adsorbed layer is heated, a so-called surface explosion is observed where the reaction products (N2, C02 and N20) desorb simultaneously in the form of sharp peaks with half-widths of only 7 to 20 K. The shape of the TPD spectra suggests again an autocatalytic mechanism [14],... 

Here, I designates the ion core (NHJ in the case of ammonia) and L the clustering ligand (e.g. NH3). The intensity and width of the metastable ion peaks carry information on the internal energy of the parent cluster ions. 

Shortly after, we recognized that ScCu4Ga2 (Im3) [70] might also be tuned to a QC, but the correct stoichiometry and reaction conditions were not achieved in our limited experiments. Recently, Honma and Ishimasa [71] have reported that i-QC phase forms almost exclusively from a rapidly quenched ScisCu48Ga34 composition, emphasizing a very narrow phase width and its thermodynamic metastability at room temperature. However, the failure turned us to other Ga intermetallics, which led to the pseudogap tuning concepts that follow. 

The width of the metastable zone is system dependent and generally increases as the solute molecules become more complex and flexible. For inorganic salts the metastable zone may be 1 to 2 °C, however in pharmaceutical systems it is typically 20 to 40 °C, and in some instances it can be much larger. 

Figure 1 Supersaturation and Metastable Zone Width in a Cooling Crystallization...

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... 

At point 1, the only form that is supersaturated is Form I, and because supersaturation is a pre-requisite to crystallization it is the only form that could precipitate as a solid phase. If the metastable zone is crossed for Form I before the solubility curve is reached for Form II then Form I will crystallize first and continue to grow unhindered. Unfortunately the width of the metastable zone cannot be predicted theoretically at the present time and is sensitive to physical and chemical impurities and the surface quality of the crystallization vessel. This leads to uncertainty in process scale up. 

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. 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Figure 15.10. Simple apparatus for measuring metastable zone widths 36 ...

Figure 15.11. Metastable zone width of aqueous ammonium1-3)...

Finally, it should be pointed out that Tjh represents the half width of the energy distribution. From eq. (2-7) we see that V is also the reciprocal of the lifetime of the initial nonstationary state. Of course, the width and the lifetime of the metastable level are related by the uncertainty principle. 

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