Metastability zone widths

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

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. 

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

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

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

Both types of US effects (namely physical, which facilitate mixing-homogenization, and chemical, resulting from radical formation through cavitation) influence crystallization by altering the principal variables involved in this physical process (namely induction period, supersaturation concentration and metastable zone width). These effects vary in strength with the nature of the US source and its location also, their influence is a function of the particular medium to which this form of energy is applied. 

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. 

Consider the solubility curves and metastable zone widths for a hypothetical enantiotopic system of polymorphs I (high melting) and II (low melting) with transition temperature Tt shown in Fig. 15. The lines initiated at points A, B, C, D, E, F, and G represent the cooling of undersaturated solutions of various concentrations to a temperature of crystallization... 

Threlfall s analysis has direct applications in the isolation of the desired polymorphs on scale. For this, it is essential to know the solubility as a function of temperature and metastable zone widths of the polymorphic system to reach those regimes in which the desired polymorph is exclusively crystallized. 

Barrett, P. Glennon, B. Characterizing the metastable zone width and solubihty curve using Lasentec FBRM and PVM. Chem. Eng. Res. Des. 2002, 80 (A7), 799-805. 

Basic crystal properties include solubility, supersaturation, metastable zone width, oil, amorphous solid, polymorphism, occlusion, morphology, and particle size distribution. Clearly. 

The solution is supersaturated when the solute concentration exceeds its solubility limit. A solution may maintain its supersatiuation over a concentration range for a certain period without the formation of a secondary phase. This region is called the metastable zone. From the creation of supersaturation to the first appearance of the secondary (solid) phase, the time elapsed is called induction time. As supersaturation increases, the induction time is reduced. When the supersaturation reaches a certain level, the formation of the secondary phase becomes spontaneous as soon as supersamration is generated. This point is defined as the metastable zone width. Figure 2-7 is a typical diagram of the equilibrium solubility curve and the metastable zone curve (Mullin 2001). 

Figure 2-8 Qualitative illustration of the relationship of the free energy profile and the metastable zone width. Beyond the metastable zone width, any disturbance to the system will result in a mixture which has a lower free energy than in the initial condition. Within the metastable zone width, the system could be metastable and remain supersaturated, or it can form a second phase with certain disturbances.

Clearly, depending upon the nature of the system, a supersaturated solution could have a wide range of metastable zone width. Also, the supersaturated solution may remain metastable for a long time, i.e., a long induction time, before it forms the secondary solid phase. 

Similar to solubility, the metastable zone width and induction time of a supersaturated solution are affected by various factors, including temperature, solvent composition, chemical structure, salt form, impurities in the solution, etc. Therefore, although the spinodal point is a thermodynamic property, it is very difficult to measure the absolute value of the metastable zone width experimentally. Regardless, understanding the qualitative behavior of the metastable zone width and the induction time can be helpful for the design of crystallization processes. 

Other factors, such as the presence of seed of the desired compound, undissolved extraneous solid particles, and even agitation intensity can affect the metastable zone width and induction time. Clearly, these factors can perturb and alter the free energy-composition phase curve. In general, these factors will lower both the metastable zone width and the induction time. 

Reliable determination of metastable zone width and induction time-generally is more time-consuming and difficult than the determination of supersaturation. This is because metastable zone width and induction time are affected by various factors. Therefore, the... 

The discussion of solubility above shows that it is theoretically possible to deduce the metastable zone width through the free energy-composition curve if such a curve is available (Kim and Mersmann 2001). Due to the complexity of the problem, experimental verification is preferred for practical applications. 

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. 

Figure 2-10 outlines the relationship of oil, amorphous material, and crystalline material with respect to supersaturation. We should emphasize that this diagram is primarily based upon empirical observation over years of development of crystallization with various compounds. The authors do not intend to use it to build a theoretical framework. In comparison to metastable zone width, there is relatively little discussion on the oiling phenomenon in the literature (Bonnet et al. 2002 Lafferrere et al. 2002). Therefore, it is beneficial to present such a diagram even without much theoretical derivation. 

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. 

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