Nucleation and metastable zone

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 het Ac gt hom IS necessaty to initiate the growth of secondary 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. 

Metastable supersaturation as a function of temperature for different nucleation 

According to the classical theory of nucleation nuclei are bom by the successive addition of units following the formation scheme  

In Fig. 8.4-2 the free enthalpies AG and AGy and also the total enthalpy AG=AGys +AGv are shown as a function of the size of a nucleus. This enthalpy AG can be written with the surface and the volume of a nucleus  

The change of the total free enthalpy as a function of the size L passes through a maximum. A thermodynamically stable nucleus is given when the total free enthalpy is not changed by the addition or removal of few elementary rmits  

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

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. 

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

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. 

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. 

Carefully selected seed crystals are sometimes added to a crystalliser to control the final product crystal size. The rapid cooling of an unseeded solution is shown in Figure 15.20a in which the solution cools at constant concentration until the limit of the metastable zone is reached, where nucleation occurs. The temperature increases slightly due to the release of latent heat of crystallisation, but on cooling more nucleation occurs. The temperature and concentration subsequently fall and, in such a process, nucleation and growth cannot... 

The area of conditions called the metastable zone is situated between the solubility and supersolubility curves on the crystallization phase diagram (Fig. 3.1). The supersolubility curve is defined as the line that separates the conditions where spontaneous nucleation (or phase separation or precipitation) occurs, from those where the crystallization solution remains clear if left undisturbed (Ducruix and Giege, 1992 Ducruix and Giege, 1999). 

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. 

In both cases, the nucleation rate is a very strong function of the driving force. Essentially, the rate of nucleation is very low until some critical value of the driving force is reached. At this critical point, massive nucleation is then observed. This very sharp delineation in nucleation at some critical driving force leads to observation of a metastable zone, and is often related to the energy barrier that must be overcome for nucleation to occur. 

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. 

When the concentration and temperature of crystallization falls outside of the shaded regimes, the polymorphic outcome will be under kinetic control and therefore may depend on the solvent. For instance, a solution of concentration C cooled to a crystallization point Cl will be outside the metastable zones of both polymorphs I and II, such that the either or both may crystallize. The polymorphic outcome will be governed by the relative nucleation rates of the polymorphs, which depend directly on the solvent. Solution D cooled to point D1 will be outside the metastable zone of polymorph I yet still within the metastable zone of polymorph II. The expected outcome would be polymorph I in this case although the solvent may be important. Cooling a solution of concentration E to points El or E2 will result in solutions that are within the metastable zones of both polymorphs I and II. Here the polymorphic outcome will also depend directly on solvent and will be particularly sensitive to accidental seeding. Both polymorphs are likely to crystallize in this regime leading to so-called concomitant polymorphs. ... 

Controlling the crystallization pressure is essential for both purification by crystallization and for efficient operations on scale. By adjusting solution conditions to decrease the solubility of the product within the metastable zone, the desired molecules can be pressured to come out of solution and crystallize (Figure 11.3) [18]. Gradual cooling without seeding leads to one nucleation event and the... 

Figure 4 Phase diagram for a protein solution. In the undersaturation (soluble) zone crystals do not grow but dissolve the first line marks the saturation limit. Above that, the solution is supersaturated and metastable with respect to the crystals existing crystals will grow, but no spontaneous nucleation occurs. In the nucleation zone, new crystals form on their own, and in the precipitation zone nonspecific aggregation dominates.

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