Crystallization induction times determination

Induction times determined by pNMR, turbidity, and light-scattering measurements are compared to those determined using PLM in conjunction with image analysis. Isothermal DSC was attempted as a fifth method for comparison. However, because of the inherent lack of sensitivity at the high cooling rates required to obtain isothermal crystallization conditions, it was abandoned. This research was carried out in the context of our milk-fat minor components study (2). 

Fig.1. Determination of crystallization induction times by baseline deviation (A) and linear extrapolation to the time axis (B).

Figure 3 shows thresholded polarized light micrographs of MF-TAG at various crystallization times at 22.5°C. Crystallization curves for AMF, MF-TAG, and MF-DAG by pNMR, turbidity, and PLM-image analysis are shown in Figure 4. MF-TAG crystallized first, followed by AMF and MF-DAG. MF-DAG had the longest induction times determined by pNMR, while by turbidimetry and microscopy, AMF had the longest induction times. Crystallization curves for...

Table 2 shows that the induction times determined by pNMR were the longest, while those determined by the image analysis technique were the shortest. Therefore, with the image analysis approach, we were able to detect some early crystallization events beyond the sensitivity of the other methods. The higher sensitivity demonstrated allowed for the detection of early crystallization events, possibly in the vicinity of the true nucleation events. 

Standard deviations were higher when induction times were measured by microscopy. Significant differences between methods were detected (P < 0.01). Induction times determined by microscopy were not equivalent to those measured by laser turbidimetry. Crystals must reach a minimum size of 0.2 pm to be detected by microscopy, whereas the laser turbidimetric technique is able to detect smaller nuclei [5]. 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

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. 

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. 

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... 

Crystallization curves for pNMR, turbidity, light-scattering, and image analysis were normalized by dividing each value by the maximum crystallization value. The resulting fractional crystallization values were compared. Induction times were determined by extrapolating the linear portion of the crystallization curves to the time axis and by baseline deviation as shown in Figure 1. 

A simple calculation can highlight the reason why the microscopic technique is more sensitive than pNMR and tuibidity measurements. Solids in a 30-mg fat sample (p = 0.90 g/cm ) with an SFC of 0.1% (w/w) occupy a volume of 3.33 10 m. The volume of a spherical nucleus of 0.5 pm diameter is 6.54 10" m. If all of this solid mass corresponded to nuclei, 5.1 10 nuclei would be present in this sample. An SFC of 0.1% is below the detection threshold of a pNMR machine. Two obvious conclusions can be drawn from these calculations. Even at 0.1% SFC, the solids present in the sample cannot solely correspond to nuclei, since their number would be too great. Microscopic observation of a typical 30-mg sample of crystallizing fat (0.1% SFC) should convince any skeptic that 5.1 10 nuclei cannot possibly be present. This suggests that by the time SFC values reach 0.5-1.0%, a typical detectable level in a pNMR machine, significant amounts of crystal growth must have necessarily taken place. Therefore, an induction time of crystallization determined by pNMR does not correspond to the induction time for nucleation. 

Induction time, nucleation rate, and nucleate particle size aU can play key roles in determining the course of a reactive crystallization. These issues are discussed in the crystaUization literature and in Chapters 2,4, and 5 in this book for general crystallization, and their importance in reactive crystallization wUl be summarized here. 

The rate of nucleation can also be determined by observing the time elapsed between the creation of supersaturation and the formation of a new phase. This time interval is defined as the induction time and is a function of the solution temperature and supersaturation. The formation of a new phase can be detected in several different ways—for example, by the appearance of crystals or by changes in properties (turbidity, refractive index) of the solution. 

In this section we have described two methods to determine the kinetics governing the nucleation process. The first method, which utilizes the width of the metastable zone, is easy to use and gives an apparent order of nucleation. The second method uses the induction time to predict the mechanism and order of nucleation processes. A third method, which employs population balance techniques and an MSMPR crystallizer, will be described in Chapter 4 of this volume. 

It was often found that, contrary to the theoretical prediction, the value of n is noninteger (Avrami 1939). The Avrami model is based on several assumptions, such as constancy in shape of the growing crystal, constant rate of radial growth, lack of induction time, uniqueness of the nucleation mode, complete crystallinity of the sample, random distribution of nuclei, constant value of radial density, primary nucleation process (no secondary nucleation), and absence of overlap between the growing crystallization fronts. These assumptions are often not met in polymer (blend) crystallization. Also, erroneous determination of the zero time and an overestimation of the enthalpy of fusion of the polymer at a given time can lead to noninteger values for n (Grenier and Prud homme 1980). 

Whether it is homogeneous or heterogeneous growth, the nucleation rate J is difficult to measure, as the critical clusters formed correspond to a small number of molecules and hence are very small. In practice, the induction time (t) is determined, which is the time between supersaturation and the first appearance of visible crystals. Assuming that the first appearance of the crystals is primarily controlled by the nucleation step, then t is inversely proportional to the rate of nucleation ... 

Differential thermal analysis (DTA) and differential scanning calorimetry (DSC) are similar techniques. They measure change in the heat capacity of a sample. These techniques can be used to determine various transition temperatures (T , Tg, T , Tp, etc.), specific heat, heat of fusion, percent crystallinity, onset of degradation temperature, induction time, reaction rate, crystallization rate, etc. A DSC instrument operates by compensating electrically for a change in sample heat. The power for heating is controlled in such a way that the temperature of the sample and the reference is the same. The vertical axis of a DSC temperature scan shows the heat flow in cal/s. 

Obviously spherulites cannot be assumed to be homogeneous spherical particles, and the fractional n values observed in their crystallization kinetics is a result of their complex structure. With such crystallizations, however, the rate parameter, Zj, must at the moment be of little mechanistic significance as are parameters such as induction times and half-lives derived from it. Determination of surface free energies from their temperature dependence must also be suspect until the exact significance of the Zi rate parameter be known. 

---