Supersaturation metastable zone width

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

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. 

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

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. 

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. 

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. 

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... 

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. 

Figure 8-6 A concentration profile for uncontrolled crystallization by evaporation (initial procedure in Example 8-1. The seed was charged to a highly supersaturated solution which may exceed the metastable zone boundary. The metastable zone width was not measured, so this figure is used only for illustration purposes.

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. 

Every solution has a maximum amount that it can be supersaturated before it becomes unstable. The zone between the saturation curve and this unstable boundary is called the metastable zone and is where all crystallization operations occur. The boundary between the unstable and metastable zones has a thermodynamic definition and is called the spinodal curve. The spinodal is the absolute limit of the metastable region where phase separation must occur immediately. In practice, however, the practical limits of the metastable zone are much smaller and vary as a function of conditions for a given substance. This is because the presence of dust and dirt, the cooling rate employed and/or solution history, and the use of agitation can all aid in the formation of nuclei and decrease the metastable zone. Figure 1.17 gives an estimated metastable zone width for KCl in water. 

The choice of the working level of supersaturation should be based on reliable measurements of the metastable limits of the system which may be made in the laboratory under carefully controlled conditions. Metastable zone widths depend on many factors including the temperature, cooling rate, agitation, presence of impurities, etc., but the most important requirement is that they must be determined in the presence of the crystalline phase and, if possible, with the actual liquor to be processed. 

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. 

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]. 

Supersaturation is the difference between the actual concentration and the solubility concentration at a given temperature which is the driving force for all solution crystallization processes. The figure below (Fig. 9) illustrates the concept of supersaturation and introduces the metastable zone width (MSZW), the kinetic boundary at which crystallization occurs (Porter Easterling, 1992). 

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. 

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. 

The metastable zone width is in case independent of the technique with which the supersaturation is generated. Figure 2.26 shows a system in which the width is nearly the same for a cooling and evaporative crystallization. Note the dispersion... 

The supersaturation before the addition of seeds should be adjusted according to the solubility curve and the supersolubility curve (cf. Figure 10.2). Typically, seeding at 4—5 K below saturation temperature is fine. Of course, the metastable zone width has to be considered here and the seeding point should be closer to the solubility curve than to the supersolubility curve. It should be kept in mind that the metastable zone width is not thermodynamically determined, but strongly depends on plant properties and process parameters, such as cooling rate. If the metastable zone width is very narrow, for the sake of process robustness temperature control has to be improved or even an inline measurement of the supersaturation (e.g., by NIR) may have to be used to detect supersaturation close to the solubility curve and to avoid spontaneous nudeation or unwanted dissolving of the seed crystals. In such cases, special care has to be taken that no crystals are present in the crystallizer from the previous batch. 

In this example, it is assumed that desupersaturation is complete when point 0 is again reached. For this case, it is dear that the level of the supersaturation produced at the level of the solution depends on the redrculation flow rate. High recirculation flow rates reduce the supersaturation produced there (dilution), while low redrculation flow rates increase it. The redrculation flow rate, adjusted to the production output, is therefore the most important design parameter in industrial crystallizers. Where the production outputs are the same, this parameter is equal for all crystallizer designs. The required recirculation flow rate depends on the metastable zone width. If this is not known, it has to be determined beforehand by means of measurements. In practice, half of the metastable zone width is used for determining the required redrculation flow rate. Therefore,... 

The smaller the active crystal surface available, the slower the mass deposition rate d7w/df, and the larger the supersaturation remaining after each recirculation cycle. The point 0, in Figures 11.3 and 11.4 moves up, if crystal growth does not desupersaturate to Ac —> 0. As this residual supersaturation is added to the newly created supersaturation, it is certainly possible that the metastable zone width will be... 

Figure 10.3 shows the schematic of solubility curve and metastable hmit. The metastable zone is shown between the solubility curve and metastable limit. Although supersaturation depends on solubility and supersaturation occurs when AC is greater than zero, nuclei may start forming before the supersaturation at any point in the metastable zone. The metastable zone width (MSZW) varies depending on the system being studied. It is usually quite narrow for small ionic crystals, such as NaCl, but can be much wider for organic molecules, such as citric acid. 

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. 

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