Kinetics crystal formation

Here is the equilibrium melting temperature of a flat interface and b is an empirical coefficient. In the limiting case of large b, we have 7 = T. In this special case, crystal formation kinetics are unimportant and the solidification rate is limited solely by heat transport in the liquid. 

Tailoring of the particle size of the crystals from industrial crystallizers is of significant importance for both product quality and downstream processing performance. The scientific design and operation of industrial crystallizers depends on a combination of thermodynamics - which determines whether crystals will form, particle formation kinetics - which determines how fast particle size distributions develop, and residence time distribution, which determines the capacity of the equipment used. Each of these aspects has been presented in Chapters 2, 3, 5 and 6. This chapter will show how they can be combined for application to the design and performance prediction of both batch and continuous crystallization. 

The combination of non-ideal phase behaviour of solutions, the non-linearity of particle formation kinetics, the multi-dimensionality of crystals, their interactions and difficulties of modelling, instrumentation and measurement have conspired to make crystallizer control a formidable engineering challenge. Various aspects of achieving control of crystallizers have been reviewed by Rawlings etal. (1993) and Rohani (2001), respectively. 

Toda demonstrated that significant improvements in the kinetics of co-crystal formation by grinding could be achieved by the addition of minor amounts of appropriate solvent [68]. As a matter of fact, a very common method in the... 

While the emphasis of this section has been on kinetics of liquid crystal formation, the rate of liquid crystal dissolution may also be of interest—e.g., in connection with breaking foams and emulsions by adding materials which destroy the liquid crystalline structure. 

N. Shan, F. Toda, W. Jones, Mechanochemistry and co-crystal formation effect of solvent on reaction kinetics, Chem. Commun. (2002) 2372-2373. 

Crystal formation depends not only on the interaction energy of a particular synthon but on a wide variety of other factors, particular crystal nucleation and growth kinetics and nucleus-solution interfacial energy. Other important factors are lattice enthalpy and lattice entropy, long range interactions... 

There are several cases, however, where the most negative lattice energy does not correspond with the preferred guest in a competition experiment. We attribute this to imprecise force-field parameters and kinetic effects which may be controlling the nucleation step in crystal formation [20]. 

A number of macroscopic observations have been carried out on crystal formation and dissolution in various solvents by the use of optical and electron microscopes. The kinetic and dynamic properties of crystal growth, and dissolution have been investigated in various chemical contexts. The structural analysis of crystals is an indispensable method in chemistry. However, it is still difficult or even impossible to answer the question how a crystal is born. 

Thus, the proposed method for analyzing the kinetics of defect formation, based on the quasi-epitaxy model, clearly demonstrates the role of the surface in the ADC equilibrium and allows one to assess the effects of temperature and Jb of the equilibration of defect concentrations. Computer simulations of defect formation kinetics in II-VI crystal non-equilibrium chalcogen vapor systems indicate that steady state defect concentrations in the surface layer are reached very rapidly and, accordingly, are not... 

Leubner, I. H. Crystal formation (nucleation) under kinetically controlled and diffusion-controlled growth conditions. J. Phys. Chem. 91,6069-6073 (1987). 

The fact that liquids can be supercooled, that is, maintained for extended periods of time at temperatures below their thermodynamic phase transition, indicates that kinetics must play a significant role in crystal formation. The study of nucleation in liquids is aimed at understanding what factors prevent or encourage nucleation, and what rate of nucleation one can expect under a given set of circumstances. As we shall see, nucleation typically involves changes in clusters of molecules in the liquid, with from several tens to several hundreds of molecules taking part in the key steps. These numbers are intermediate between microscopic and macroscopic, so that methods of study based on small clusters and those based on the use of the thermodynamic limit both are useful but both also have limitations. 

There are four types of coprecipitation surface adsorption, mixed-crystal formation, occlusion, and mechanical entrapment." Surface adsorption and mixed-crystal formation are equilibrium processes, whereas occlusion and mechanical entrapment arise from the kinetics of crystal growth. 

Another possible mechanism of trehalose molecules as a kinetic inhibitor is mentioned below. In the growth process of CO2 hydrate, trehalose may work as the kinetic inhibitor that prevents the rate-determining process of the crystal formation at the reaction site which might have small dependence on AT. Trehalose has been observed to prevent ice-crystal growth with the reduction of the free-water providing because trehalose strongly hydrated in the solution. This effect is found apparently when the trehalose concentration increases beyond the intrinsic hydration number of trehalose molecules. It is thus reasonable that the kinetic effect of trehalose on the inhibition of the hydrate formation would be resulted from the smaller supplement of free water from the solution of higher trehalose concentrations. 

If, after the polymer has been formed, a transformation of one structure into another is possible (e.g., formation of an amorphous polymer with its subsequent crystallization), the kinetic characteristics of these transformations will, in their turn, exert the determining effect on the final structure of the polymer. Specifically, the supramolecular structure of a polymer produced in the course of its synthesis will change, depending on the relationship between the rates of three processes (1) chemical reaction of polymer formation, (2) isolation of polymer in a separate phase, (3) structural transformations inside the polymer phase. In the latter two processes, a significant role is played by the ratio between the rates of the formation and growth of the nuclei of one phase inside the other. This is the kinetic aspect of the problem of controlling the polymer structures during synthesis. 

Equation (361) is a sample equation for the rate of formation of droplets in their vapor, and similar equations can be derived for the rate of crystal formation by freezing their liquids, or precipitate formation from supersaturated solutions, although diffusion controlled cluster formation kinetics in liquids, lattice strain and anisotropic growth in crystals must be considered whenever necessary. 

Transformations between the polymorphs of crystalline amino acids often require the reconstruction of the extended hydrogen-bond network in the crystal, are kinet-ically controlled and related to recrystallization. Both the crystal growth and the polymorphic transitions in the crystals are therefore extremely sensitive to the interaction with molecules of gases or liquids that can be involved in the formation of hydrogen bonds with molecules at the surface. 

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