Supersaturation induction time

Figure 5.8 Induction time-supersaturation plot for cyanazine in 70% wjw aqueous ethanol at 20°C Hurley etal., 1985)...

Induction period measurements can also be used to determine interfacial tensions. To validate the values inferred, however, it is necessary to compare the results with an independent source. Hurley etal. (1995) achieved this for Cyanazine using a dynamic contact angle analyser (Calm DCA312). Solid-liquid interfacial tensions estimated from contact angle measurements were in the range 5-12 mJ/m which showed closest agreement with values (4—20mJ/m ) obtained from the log-log plots of induction time versus supersaturation based on the assumption of — tg. 

We can apply classical germination laws to this supersaturated system thus, the Avrami-Mempel laws confirm the unidimensional growth of the solid-like gel network. Induction times can also be studied in this framework 11). Here, we are interested first by the different kinetic behaviors which are dependent upon the location in the phase diagram of the initial solution defined by its supersaturation degree. 

All these results support our kinetic interpretations of these supersaturated gelling solutions. We assume that the network growth is described by the growth of individual domains, each one ruled by the autocatalytic model (S). This system behaves like an assembly of microdomains. Sach steroid in a supersaturation state is a potential germ of microdo.main. According to distribution curves of induction times for each microdomain, the typical kinetic curves for each part A and B of the phase diagram are obtained. 

In part A, supersaturation is high and equivalent to a high driving force" for the kinetics. The induction times distribution curve is very narrow and the resulting kinetic curve is of type (3) (Figure 12-1). It is a region of a quite in-phase growth of the domains. 

In part B, supersaturation is low and the distribution curve is broad, since induction times are spread over the whole aggregation delay. Thus, the autocatalytic character is lost in the resultant kinetics. According to the width of the induction time distribatior , flat or irregular curves can be obtained (Figure 10).It is a region of random growth of the domains. 

The above studies support the notion that nucleation is a very stochastic phenomenon when the sample is held at constant temperature, compared to when the sample was cooled at a constant cooling rate. As suggested previously, the magnitude of the driving force can affect the degree of stochastic or random behavior of nucleation. For example, on the basis of extensive induction time measurements of gas hydrates, Natarajan (1993) reported that hydrate induction times are far more reproducible at high pressures (>3.5 MPa) than at lower pressures. Natarajan formulated empirical expressions showing that the induction time was a function of the supersaturation ratio. 

Zel dovich theory — The theory determines the time dependence of the nucleation rate 7(f) = d N (f )/df and of the number N(t) of nuclei and derives a theoretical expression for the induction time T needed to establish a stationary state in the supersaturated system. The -> Zel dovich approach [i] (see also [ii]) consists in expressing the time dependence of the number Z(n,t) of the n-atomic clusters in the supersaturated parent phase by means of a partial differential equation ... 

Another parameter often used to characterise nucleation is the induction time or period, t. This is defined as the time taken for the formation of crystals after creating a supersaturated solution. Hence, the measured induction period does depend upon the sensitivity of the recording technique. It is generally assumed that t is inversely proportional to the nucleation rate, i.e. 

Two parameters are necessary to fully describe nucleation kinetics the induction time and the rate of nucleation. The moment a driving force is created, whether a supersaturation in solution systems or a subcooling in melt systems, the molecules begin to organize into crystallite clusters. The time at any given driving force required for the first nuclei to form is called the induction time. Unfortunately, the true induction time is difficult to measure since the exact point when nuclei are first formed is nearly impossible to measure. Nuclei are probably only nanometers in size, too small to be detected with any methods developed to date. Thus, measurement of... 

This parameter (find) is defined as the time elapsed between the creation of supersaturation and the appearance of crystals, and decreases as supersaturation inoreases. Mathematioal equations for the induotion time that hold for all nuclei forming and growing in a saturated solution have been reported [138], The induction time is usually determined from oonduotivity measurements. Thus, the formation of crystals is signaled by a drop in the solution oonductivity. The crystallization time is taken to be the time where the derivative of the oonductivity with respect to time becomes negative. 

The induotion time is dramatically reduced by the presence of US the effect, however, depends on the particular medium and working conditions. Thus, at an absolute supersaturation of 0.0156 g K2S04/g water, the induction time in the absence and presence of US was found to be 9000 and 1000 s, respectively. Also, the conductivity decreased faster with US than without US. Because the conductivity was proportional to the potassium sulphate oonoentration, this difference suggests that more crystalline matter was formed in the presenoe of US [139]. 

The effeot of US on find is especially significant at low absolute supersaturations thus, oontradiotory results have been obtained for highly supersaturated solutions [140]. Figure 5.13 illustrates the effects for the anti-solvent crystallization of roxithromycin in an acetone-water mixture [141]. As can be seen in Fig. 5.13A, the induction time decreased as supersaturation increased, whether or not US was applied. However, US significantly reduces the induction time, particularly at low supersaturations. Therefore, the effect of US on nuoleation is stronger than that of high supersaturation levels [142]. 

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])... 

The macroscopic properties of the supersaturated solution are seemingly unchanged during the induction time. It is reasonable to assume that the initial supersaturation, given by its free energy value, aG, is an essential parameter for the calculation of Tj j. 

The expected correlation between aG and Ti , is confirmed, i.e. the greater the supersaturation is, the shorter is the induction time. Reasonably, Tj j goes to zero in the limit where aG goes to infinity. Conversely, in a saturated solution, aG is equal to zero and Ti j is of course infinitely long. 

Sbhnel and Mullin, Garside and recently Barlow and Haymet have discussed the molecular Interpretation of induction times from the standpoint of classical nucleation theory. Crystal nuclei with a critical size must be formed before the new solid phase is visible. According to the model there exists a free energy barrier, AG to the formation of the crystal nuclei. AG is proportional to (InS), where S is the supersaturation ratio. The Gibb s free energy, AG of the supersaturated solution is equal to -RTlnS (R=gas constant T=temperature). The induction time is a function of AG and thus AG according to the following equation... 

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. 

While nucleation phenomena have their origin at the molecular level, they are often described in terms of macroscopic properties owing to the scarcity of experimental techniques that allow for monitoring events at the molecular level. Nucleation rates can be determined by measuring the induction time, rjnd, for nucleation. The induction time represents the time elapsed between the creation of a supersaturated state to the appearance of a solid phase and is represented by... 

Induction times should decrease with an increase in supersaturation. Under constant supersaturation and all other variables constant, induction times will decrease with an increase in solubility, i.e., nucleation is faster in solvents providing high solubility. The induction time (formation of nuclei) can be detected by the appearance of crystals by optical microscopy or by changes in solution properties such as turbidity and refractive index. 

The induction times of carbamazepine polymorphs [monoclinic, CBZ(M) and trigonal, CBZ(Trg)] were evaluated by optical microscopy. The polymorphs were identified by their crystal morphology where CBZ(M) crystallizes as prismatic crystals and CBZ(Trg) crystallizes as needles, which were confirmed by X-ray powder diffraction. It was determined that under constant supersaturation concomitant crystallization is favored in solvents that accept and donate hydrogen bonds (ethanol, methanol, isopropanol, etc.). However, the metastable CBZ(Trg) polymorph preferentially crystallized in solvents that primarily accept hydrogen bonds (ethyl acetate, methyl acetate, 2-butanone, etc.) with the stable CBZ(M) polymorph crystallizing at least an hour later. The induction times of CBZ polymorphs did not decrease with increases in solubility, suggesting that nucleation is not controlled by solubility differences. It was determined that CBZ polymorph nucleation was governed by the specific solute-solvent interactions that occurred in solution to... 

An adaptation of the Damkochicr number (Da) is a useful concept for evaluation of mixing effects in crystallization. It is the ratio of the characteristic mixing time to its corresponding process time (nucleation induction time, crystal growth/supersaturation release time, or reaction time). Studies of these times and the resulting predicted Damkoehler number in a laboratory setting can provide evidence of possible scale-up problems. 

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). 

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... 

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