Kinetics primary nucleation

If all possible combinations were equally probably, we would observe stochastic behavior like primary nucleation, so that crystal growth kinetics would be virtually unpredictable. However, a few molecular paths for crystal growth are highly preferred over others, these paths combine in an ensemble to provide the macroscopic observations of crystal growth described in the next section. 

The classical nucleation theory embodied in Eq. (16) has a number of assumptions and physical properties that cannot be estimated accurately. Accordingly, empirical power-law relationships involving the concept of a metastable limit have been used to model primary nucleation kinetics ... 

The process of formation of the crystalline state is controlled by the kinetics of nucleation and this may arise in a number of ways. Primary nucleation in a quiescent state must be associated with foreign bodies such as deliberately added nucleating agents, such as fine talc particles, or residual impurities such as heterogeneous catalyst particles followed by spherulite growth. The plot of extent of crystallinity, (p, as a function of time is sigmoidal in nature and follows an Avrami equation of the form... 

An ideal emulsion or suspension is difficult to physically, chemically or kinetically realize. Mixed mechanisms exist. Nonetheless categorizations can still be made such as the two styrene and two acrylamide examples discussed in the previous paragraph. These are distinguishable by the primary nucleation mechanism and the primary phase of initiator and monomer solubility. However, the possibility of having mixed emulsion and suspension mechanisms, which are largely indistinguishable, also exists. Consider two scenarios ... 

Dealing with industrial ciystallization it is necessary to limit the supersaturation and the kinetic parameter nucleation and growth to produce crystals with sizes and purities wanted by the customer. The metastable zone valid for primary homogeneous nucleation has already been discussed, see Fig. 8.4-5. Industrial crystallizers are operated at supersaturations which are one order of magnitude lower than ACmet, hom (Ac 0.1 Ac j om ) This means that substances with a high solubility... 

Rysehenkow, G., Eaivre, G. Bulk erystallization of liquid selenium Primary nucleation, growth kinetics and modes of crystallization. J. Cryst Growth 87, 221 (1988)... 

The second kinetic pathway considered (run 36) was started in domain 2b. It followed a vertical direction until equilibrium was reached. Only CBZ crystals have nucleated and grow. No significant deviation from the vertical line, which could indicate the temporary presence of co-crystals could be detected. Under similar conditions, the nucleation of CBZ/NCT co-crystals was reported but the kinetic pathway was not monitored. The occurrence of a metastable CBZ/NCT crystal population by primary nucleation would have... 

Experiments were performed with the CBZ/NCT/ethanol system in domains of the phase diagram that were always undersaturated with respect to NCT (see Figure 9.9). Crystallizations were started in domains 2a or 3. Once the equilibrium was reached at 25 °C, a known amount of NCT in dry form was added in order to shift the overall composition of the slurry in domain 4a in the phase diagram. The previously stable CBZ solid phase became metastable. Henceforth the stable phase was the CBZ/NCT co-crystal. A SMPT started with the primary nucleation of the co-crystals if they were absent in the slurry and continued with the dissolution of the CBZ crystals and with co-crystal growth, until the new equilibrium was reached. Three kinetic pathways are displayed in Figure 9.9. 

Compared with run 52, the passage from domain 2 to domain 4 in run 54 was much slower. This slowness was due to the induction time of the co-crystal primary nucleation and to the great quantity of co-crystals produced. Run 61 differed from run 54 by the amount of CBZ crystals in the initial slurry (0.63 wt% for run 61) and also by the amount of NCT used to trigger the SMPT from domains 2 to 4. The differences in the pathways could be translated in terms of kinetics. First, the induction time of co-crystal primary nucleation at point G was reduced to 15 minutes due to a higher CBZ/NCT supersaturation ratio. Second, no plateau of CBZ dissolution o-crystal growth was detected and the pathway was parallel to the bisecting line up until the final equilibrium (point H ). An important desupersaturation rate was also observed. 

These and other kinetic data in which only i and not Ac is measured in general give i values between 1 and 2. Since the maximum value ofgRtl, then the maximum value of ft 3—4, with most values closer to 1. These data therefore imply that the dependence of nucleation in these studies is much lower than the corresponding exponential dependence predicted for primary nucleation, illustrated in Figure 5.15. 

In order to bypass such limitations, the overall crystallization kinetics may be determined by DSC. However, in this case, both primary nucleation and crystal growth will make a contribution to the overall isothermal crystallization rate [6,7,12]. Ideally, it would be better to determine both spherulitic growth rate and overall isothermal crystallization kinetics in separate experiments, if possible. In the literature, the most commonly reported [30] type of isothermal crystallization kinetic data is that measured by DSC, because it is the easier to obtain. The DSC experimental approach can be very useful and in some cases, the DSC data thus obtained can provide not only the overall crystallization rate but also the separation of the individual contributions of the primary nucleation and growth rate (more details to follow). 

If the crystallization kinetics is determined by DSC, both primary nucleation and crystal growth will make a contribution, resulting in a mathematical superposition of both bell-shaped curves shown in Figure 11.6. It is useful to be able to extract from DSC data not only the conomonly obtained overall crystallization rate but also the separation of the individual contributions of the primary nucleation and the growth rate. 

When the isothermal crystallization is determined by spherulitic growth experiments, the energy barrier determined by applying the LH model refers exclusively to secondary nucleation or crystal growth. Instead, when the inverse of half-crystallization time (1/t5q%) values obtained from DSC isothermal overall crystallization kinetic data is considered, both primary nucleation and crystal growth are considered. Therefore, the energetic parameters that we obtained after applying any classical kinetic crystallization theory to DSC data will include contributions from both processes. 

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