Kinetic factors crystallization

More recently, studies of the hysteresis of these phase transitions have illuminated the importance of kinetic factors in solid-solid phase transitions [224]. The change between crystal stmctures does not occur at the same point when pressure is increasing, as when it is decreasing the difference between this up-stroke and down-stroke pressure... 

We shall take up the kinetics of crystallization in detail in Secs. 4.5 and 4.6. For the present, our only interest is in examining what role kinetic factors play in complicating the crystal-liquid transition. In brief, the story goes like this. Polymers have a great propensity to supercool. If and when they do crystallize, it is an experimental fact that smaller crystal dimensions are obtained the lower the temperature at which the crystallization is carried out. The following considerations supply some additional details ... 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

Since interactions at the molecular level between polymer components in the blends occur only in the amorphous phase, it is reasonable to assume that these effects are due to kinetic factors and, in particular, to the influence of a polymer component on the nucleation or crystallization kinetics of the other one. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

It is important to have an understanding of the competing thermodynamic and kinetic factors that govern crystallization. Situations exist where one polymorph formation is kinetically controlled, while another is thermodynamically controlled. 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

Both thermodynamic and kinetic factors need to be considered. Take, for instance, acetic acid. The liquid contains mostly dimer but the crystal contains the catemer and no (polymorphic) dimer crystal has ever been obtained. Various computations (R. S. Payne, R. J. Roberts, R. C. Rowe, R. Docherty, Generation of crystal structures of acetic acid and its halogenated analogs , J. Comput. Chem, 1998, 19,1-20 W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, J. Kroon, Crystal structure predictions for acetic acid , J. Comput. Chem., 1998, 19, 459-474) show the relative stability of the dimer. Perhaps the dimer is not formed in the crystal because it is 0-dimensional and as such, not able to propagate so easily to the bulk crystal as say, the 1-dimensional catemer. 

Let us now And out how the system works. Assume that it starts at a large reduced flow-rate (point A) and reduce the input slowly. Up to the point C, any deviation from the equilibrium curve will die out rapidly. At C, concentration fluctuations become unstable and the system evolves quite rapidly towards D (p is fixed) where it finds a stable steady-state. The system has become unstable because reducing the flow-rate enhances crystallization which through the kinetic factor enhances the rate of precipitation and thereby depletes the residual liquid. The system quenches. Upon reducing the flow-rate further, the stable evolution continues towards point E. 

Whether a task can be performed concurrently with other tasks depends on two factors. One is whether the input information for the activity under consideration depends on the output from other activities. The other is the availability of manpower and equipment. Consider a team that has only one chemical engineer to design both the reactor and the crystallizer. Even though reaction kinetics, solid-liquid equilibrium data and crystallization kinetics can be measured in parallel, the total time for these activities is determined by what the single individual can achieve. 

Crystallization of magnesium hydroxide by a continuous mixed suspension mixed product removal crystallizer was conducted to make clear the characteristics of reactive crystallization kinetics of magnesium hydroxide, which was produced by the precipitation from magnesium chloride with calcium hydroxide. The following operating factors were investigated affecting the crystallization kinetics the initial concentration of feeds, residence time of reactants, feed ratio of reactants, and concentrations of hydroxide and chloride ions. 

The interpretation the experimental data obtained in the SCISR and STR, respectively, with the Arrhenius relationship yield the measured values for the active energies in the two reactors being EiS = 57.5 kJ-moF1 and EST = 60.1 kJ-moF1. The difference between the two values is small, and is actually within the scope of experimental error so that they can be considered to be identical. These results lead to the conclusion similar to that obtained in the investigation on the crystallization kinetics of Na2HP04, i.e., with the values for the frequency factor of the reaction represented by Eq. (12-10) measured in the two reactors, there must be k0jis > V.st-... 

In this case, the kinetic factor is dependent on the solubility of the materials and the frequency at which critical nuclei become supersaturated and transform into crystals. Hence,... 

Although the basic principle and procedure of diastereomeric resolution are not difficult to understand, the chiral discrimination mechanism involved in the selective crystallization of one diastereomer from the mixture is very complicated. The chiral discrimination mechanism for diastereomeric resolution changes in accord with the resolving system, since not only the properties of diastereomeric crystals but also the conditions for crystallization strongly influence the chiral discrimination mechanism. In particular, the polymorphism of crystal, the severe solvent effect on solubility, and the kinetic factor for crystal growth are still not perfectly understood regarding this chiral discrimination phenomenon. The study is therefore limited in its investigation of the chiral discrimination mechanism for the diastereomeric resolution, as the mechanism involves both the crystal and solution properties of diastereomers.7... 

Another problem is explaining the mechanism of solvation of an organic molecule at a molecular level. It is well known that even for the same compound, different polymorphic crystals have different solubility characteristics. In addition the rate of solvation varies according to the face of the crystals this is also observed in crystal growth. These phenomena could be influenced by kinetic factors, which have a significant effect on the efficiency of resolution. Thus treatment of the kinetic factors of solvation is another problem that must be explored. 

Table 3.13 shows that the kinetic factor A increases with temperature. This fact cannot be explained without knowing the concrete mechanism of formation of the holes in the foam bilayer. A possible explanation is the occurrence of hole nucleation on preferred sites, for example along line defects (such as domain boundaries) in the bilayer. A similar preferential nucleation of voids on structural defects is known to occurs in crystals [422], If the density N0 of these preferred sites in the bilayer decreases with increasing temperature, according to Eq. (3.125). A will increase with Tprovided oKT) dependence is not significant. 

Although crystallization is controlled by kinetic factors, it is a phenomenon that is thermodynamic in origin (a first-order phase transition). On the other hand, the glass transition may be purely kinetic. We ll say more about that shortly, but one manifestation of this is the dependence of the T on the rate of cooling. It is observed at a somewhat lower temperature if a sample is cooled slowly than if it is cooled quickly (Figure 10-16). 

Gibbs notes that for macroscopic crystals, the free energy associated with the volume of the crystal will be larger than changes in free energy, due to departures from its equilibrium shape. For these crystals, their shape will depend on kinetic factors, which are affected by crystal defects, surface roughing, and impurities in the solvent. 

All of these changes in ciystal habit caused by kinetic factors are drastically effected by the presence of impurities that adsorb specifically to one or another face of a growing ciystal. The first example of crystal habit modification was described in 1783 by Rome de Lisle [77], in which urine was added to a saturated solution d NaCl changing the crystal habit from cubes to octahedra. A similar discovery was made by Leblanc [78] in 1788 when alum cubes were changed to octahedra by the addition of urine. Buckley [65] studied the effect of organic impurities on the growth of inoiganic crystals from aqueous solution, and in Mullin s book [66] he discusses the industrial importance of this practice. 

Main factors which affect a hydrothermal reaction are the initial eomposition, reaction temperature and time. In mild hydrothermal synthesis, reaction temperatures lower than 240 °C are respected for both safety of high pressure in normal autoclaves and protection of softness of Teflon line. In our specific synthesis system, high temperature favorites the reaction and the most important factor was the base concentration in the initial reaction mixtures. The reaction time associated with reaction temperature affected the reaction. Crystallization kinetic experiment for a typical reaction showed that a reaction time more than lOh gave well-crystallized product and the further crystal growth needed additional time. Table 1 lists the starting reaction compositions and phase identification of products obtained at 240 °C for lOh. 

However, for this process to be realized in nature a combination of several conditions is necessary. Kinetic factors—high rate of crystallization of the oxide compared to silicates or carbonates—would favor the deposition of iron in the form of magnetite. For Fe(OH)3 to convert to Fe304, the presence of a sufficient amount of a reducing agent, for instance organic matter, in the lower water layer or directly in the sediment is necessary, but in that case the final product more likely will be siderite or greenalite ... 

From these data it follows that when iron is precipitated in acid and neutral environments the first products should be X-ray-amorphous highly dispersed iron hydroxides, which in the course of time acquire the crystal structure of goethite or hematite. The mechanism of this process depends on kinetic factors (rate of oxidation of Fe " ), form of migration of the iron (ionic or colloidal), and acidity of the parent solution. In neutral environments ferrihydrite possibly is formed as an intermediate metastable phase, especially if the iron migrates in colloidal form or in the form of the Fe ion. The products of diagenesis of such a sediment may be both goethite (in the case of low Eh values typical of the Precambrian iron-ore process) and dispersed hematite (in the case of deposition of the oxide facies of BIF). 

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