Metastable zone supersaturation

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. 

As mentioned above, crystallization is possible when the concentration of the solute is larger than the equilibrium saturation, i.e. when the solution is supersaturated with the solute. The state of supersaturation can be easily achieved if the solution is cooled very slowly without agitation. Above a certain supersaturation (this state is also called supersolubility) spontaneous formation of crystals often, but not always, occurs. Spontaneous nucleation is less probable in the state between equilibrium saturation and supersolubility, although the presence of fine solid impurities, rough surfaces, or ultrashort radiation can cause this phenomenon to occur. The three regions (1) unsaturation (stable zone), where crystallization is impossible and only dissolution occurs, (2) metastable zone, extending between equilibrium saturation and supersolubility, and (3) labile zone, are shown in Fig. 5.3-20. 

Supersaturation is the driving force for crystallization and is a prerequisite before a solid phase will appear in a saturated solution. Figure 1. shows the situation for a cooling crystallization. At point 1 the system is under saturated and the concentration of dissolved solute is below the solubility curve defined by Eq 3. As the system cools it becomes saturated at point 2 but remains as a metastable liquid phase until the metastable zone is crossed at point 3, where... 

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

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. 

In considering the state of supersaturation, Ostwald(20) introduced the terms labile and metastable supersaturation to describe conditions under which spontaneous (primary) nucle-ation would or would not occur, and Miers and Isaac(21) have represented the metastable zone by means of a solubility-supersolubility diagram, as shown in Figure 15.8. 

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. 

These principles have been used to detect crystals of a-hydrate, /3-lactose, or both in various products. A supersaturated solution in the metastable zone prepared with respect to the form being tested is unsaturated with respect to the other. When the product in question contains crystals, the solution will become cloudy with newly formed crystals as a result of seeding. If crystals are not present in the material, the solution will remain stable and clear. 

For crystals to form from a liquid state, the molecules of the crystallizing species must come together in sufficient number (form a cluster) to overcome the energy cost of forming a surface. Once this energy barrier is overcome, the latent heat associated with crystallization is released, and further nucleation is strongly promoted. Thus, there often is a metastable zone where a supersaturated or subcooled system may not nucleate for a very long time. 

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. 

Figure 5.13. Effects of US on crystallization parameters. (A) Influence of US on the induction period of roxithromycin. (B) Variation of the induction time as a function of the relative supersolubility. (C) Variation of the induction time as a function of the supersaturation ratio. (D) Effect of US on the metastable zone of roxithromycin. (A.) with US, ( ) without US, (A) solubility curve (Reproduced with permission of Elsevier, Ref [141])... 

Even a few seed crystals, mechanically separated, can be used to produce larger quantities of resolved enantiomerically pure material. A second method of resolution by direct crystallization involves the localized crystallization of each enantiomer from a racemic, supersaturated solution. With the crystallizing solution within the metastable zone, oppositely handed enantiomerically pure seed crystals of the compound are placed in geographically distant locations in the crystallization vessel. These serve as nuclei for the further crystallization of the like enantiomer, and enantiomerically resolved product grows in the seeded locations. 

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. 

Seed crystals can be used to define a metastable zone. If seed crystals dissolve after being added to a solution, saturation conditions have not been achieved. If the addition of seeds leads to the formation of an oil dispersion, supersaturation conditions were reached. 

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.

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