Crystal growth crystallization kinetics

On September 25-30, 1988 in Los Angeles, California the first ACS Symposium on zeolite synthesis emphasized the importance that gel chemistiy, zeolite nucleation, crystal growth, crystallization kinetics, and structure-directing phenomena have in understanding zeolite (and molecular sieve) synthesis. The objectives of a similar ACS Symposium held in New York on August 25-30, 1990 where expanded to include papers on pillared clay synthesis and on the synthesis of other microporous materials that could be used in catalyst preparation. About 90% of all the chemical processes in the U.S. are based on catalysis and today catalysts have become indispensable to petroleum refining, an industry that in 1990 had sales of 140 billion (U.S. Dept, of Commerce U.S. Industrial Outlook, 1991). 

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. 

Crystallization kinetics erystal nueleation, growth, aggregation and disruption kineties (Chapters 5 and 6). 

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

By means of our experimental method (twin+single crystal kinetics) steady state growth morphology can be predicted as a function of supersaturation and temperature. 

Etherton studied the growth and nucleation kinetics of gypsum crystallization from simulated stack gas liquor using a one-liter seeded mininucleator with a Mixed Suspension Mixed Product Removal (MSMPR) configuration for the fines created by the retained parent seed. The effect of pH and chemical additives on crystallization kinetics of gypsum was measured. This early fundamental study has been the basis for later CSD studies. 

For effective control of crystallizers, multivariable controllers are required. In order to design such controllers, a model in state space representation is required. Therefore the population balance has to be transformed into a set of ordinary differential equations. Two transformation methods were reported in the literature. However, the first method is limited to MSNPR crystallizers with simple size dependent growth rate kinetics whereas the other method results in very high orders of the state space model which causes problems in the control system design. Therefore system identification, which can also be applied directly on experimental data without the intermediate step of calculating the kinetic parameters, is proposed. 

Three methods to derive a state space model for a crystallizer were discussed. The choice of a method in a specific situation depends on the crystallizer configuration, the growth rate kinetics and the variables to be controlled. 

The first method, the method of moments, is restricted to MSMPR crystallizers with size-independent growth or very simple size-dependent growth rate kinetics. Depending on the control demand, several process outputs can be chosen for the control algorithm. When population densities, or the number or mass of crystals in a size range are to be controlled, the method of moments can not be used because it reveals information on the dynamics of the moments of the crystal size distribution only. 

The lateral surface free energy a is a key parameter in polymer crystallization, and is normally derived from crystallization kinetics. In polydisperse polymers, where the supercooling dependence of growth rate is affected both by changing... 

Crystallization kinetics in polymeric systems. Soc. Plastics Engrs. J. 15, Nr. 1 1959, sowie in "Growth and Perfection of Crystals (45). 

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. 

As fully described below, sPS has been found to be miscible with aPS, PPE, PYME, TMPC and styrene-l,l-diphenylethylene copolymer. Generally the reported investigations deal with the effect of the second component on crystalline features of sPS, such as polymorphic behavior, crystallization kinetics, morphology and growth rate of crystallites. Just one study reports on toughening sPS by adding suitable components. 

In essence, Eq. (16) describes the formation of a two-phase structure in reactive systems, which takes place according to the mechanism of nucleation and growth under the condition that an increase in concentration of the second phase is determined by the chemical reactions. Crystallization may serve as a physical analogue for such a process. Indeed, in Refs. [124,125] a new model of crystallization kinetics was developed, which is reduced to a self-acceleration equation similar to Eq. (16). 

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