Kinetic constants from crystallization

A number of methods are available for deriving reaction kinetics constants from DSC thermograms (Wright, 1984). For example, the thermogram obtained during an isothermal DSC experiment at a temperature at which crystallization of a fat occurs can be analyzed in a way similar to that described earlier for the determination of solid fat content, but in this case the evolution of peak area (representing the formation of solid fat crystals) is related to time rather than temperature (Chong, 2001). 

An issue of debate is the relative roles of internal and external sites in the catalytic process. The effects of shape selectivity, clearly present in product distribution, seem to indicate a predominance of intra-porous hydroxylation. However, the different catechol/hydroquinone ratio in methanol (0.5) and acetone (1.3), could indicate a significant contribution of sites located on the outer surface of the crystals, particularly for crystallite sizes <0.3 xm. Tuel and others, studying the time course of the reaction and the solubility of tarry deposits, went further and concluded that catechol and hydroquinone were produced on different sites, external and internal respectively [49]. The effect of acetone and methanol simply reflected their ability to maintain external sites clean from tar deposits, which are soluble in the former and insoluble in the latter. On the other hand, Wilkenhoner and others concluded, with the support of kinetic constants estimated independently for internal and external sites, that catechol was also produced in the pores over the entire reaction profile, albeit at a lower rate [47]. The contribution of the outer surface for crystal sizes close to 0.1 (xm ranged from 46% in methanol to 69% in acetone. 

The precise catalytic roles of Glu 144 and Glu 164 remained uncertain, despite the availability of crystal structures of necessarily nonproductive complexes [31]. These structures pointed to the expected proximity of Glu 164 to carbon-2 and led to the suggestion that it mediates proton transfers to/from carbon. Accordingly, Glu 144 was expected to facilitate attack of water on carbon-3. In addition, the interpretation of the dependence of the kinetic constants for reactions catalyzed by wild type ECH as well as the E144Q and E164Q mutants is uncertain although common sense would require that one be anionic, i.e., a general base, and the other be neutral, i.e., a general acid, no self-consistent, unequivocal support for this expectation could be obtained. 

Probably the simplest laboratory batch crystallizer was described by Misra and White (1971). Kinetics of the crystallization of aluminum trihydroxide from caustic aluminate solutions were studied in a 5 1 round-bottomed Bask equipped with a stirrer, thermometer, and a sampling tube (Figure 10.1). The crystallizer was immersed in a constant-temperature bath. 

Fig, 3. Temperature dependence of the overall kinetic constant (see Eq, (1)) for various PEO/PMMA blends isothermally crystallized from the melt. 

The isothermal crystallization kinetics from the melt of all PEO/PMMA blends follow the Avrami equation until a high degree of conversion. The values of the overall kinetic constant and of the... 

Simple metal single crystals prepared under well-controlled conditions are extensively characterized with respect to their geometric and electronic properties [28, 29]. With techniques such as MBS, one can describe details of reaction mechanisms and obtain reaction probabilities and rate constants for elementary reaction steps, activation barriers for surface processes, and adsorption quantities [30-33], Kinetic data from single crystal experiments may be vastly different from that of technical... 

Fortunately, both 3a and 3b crystallized in a chiral space group, P2i2i2i, and the constituent molecules adopted a chiral and helical conformation in the crystal lattice. The rate of racemization of 3 after dissolving the chiral crystals in a solvent was measured based on the changes in the CD spectra The activation free energy (AG ) was calculated from the temperature dependence of the kinetic constant between 5 and 15°C as 21.2 0.2 kcal moH in THF. These facts indicate that the racemization of 3b is too fast to be resolved in the usual manner. The lifetime can be lengthened by lowering the temperature so that the racemization is sufficiently slow and the reaction can be used to accomplish asymmetric synthesis. 

Similar effects were found by analyzing the overall crystallization kinetics from the melt at the same the crystallization half-time ty of the blend increased exponentially with increasing concentration of the amorphous component. The temperature dependence of the spherulite growth rate (G) and kinetic constant was then examined according to Equation (10.13)... 

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