Kinetic of crystallization

The kinetics of crystal growth has been much studied Refs. 98-102 are representative. Often there is a time lag before crystallization starts, whose parametric dependence may be indicative of the nucleation mechanism. The crystal growth that follows may be controlled by diffusion or by surface or solution chemistry (see also Section XVI-2C). 

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 ... 

In order to carry out an experimental study of the kinetics of crystallization, it is first necessary to be able to measure the fraction d of polymer crystallized. While this is necessary, it is not sufficient we must also be able to follow changes in the fraction of crystallinity with time. So far in this chapter we have said nothing about the experimental aspects of determining 6. We shall now briefly rectify this situation by citing some of the methods for determining 6. It must be remembered that not all of these techniques will be suitable for kinetic studies. 

Nancollas, G.H. and Gardner, G.L., 1974. Kinetics of crystal growth of calcium oxalate monohydrate. Journal of Crystal Growth, 21, 267-276. 

Kinetics of Crystallization of Polypropylene Fractions and Polybutene-1-Part I", ONR Tech Rept 43, Contract Nonr 3357(00), Univ of Mass, Amherst (1962) 4) A. Opschoor,... 

KNUDSEN J c, ANTANUSE H s, RisBO j and SKIBSTED L H (2002) Induction time and kinetics of crystallization of amorphous lactose, infant formula and whole milk powder as studied by isothermal differential scanning calorimetry, Milchwissenschaft, 57, 543-546. 

Nielsen, A.E. (1958) The kinetics of crystal growth in barium sulphate precipitation. Acta Chem. Scand., 12, 951-958. 

Before discussing the effect of short-chain branching on the kinetics of crystallization process, it is necessary to revisit the theory of secondary nucleation and the concept of regimes as given by Lauritzen and Hoffmann... 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

G. Shan, K. Igarashi, H. Ooshima. Dissolution kinetics of crystal in suspension and its application to L-aspartic acid crystals. Chem. Eng. 

The overall kinetics of crystal precipitation has to consider that the process consists of a series of consecutive processes in simple cases, the slowest is the rate determining step. Assuming the volume diffusion is not the rate determining step, we still have at least the following reaction sequences ... 

Buchner, S., Wiswe, D. and Zachman, H. G., Kinetics of crystallization and melting behaviour of poly(ethylene naphthalene-2,6-dicarboxylate),... 

In this study, D-SCMC seed crystals were put in a racemic SCMC supersaturated solution in a batchwise agitated vessel and growth rates in longitudinal and lateral directions and the optical purity of D-SCMC crystals were measured. The growth rates and optical purity were discussed considering surface states of grown crystal observed by a microscope. The kinetics of crystal growth were measured and a model of inclusion of impurity was proposed. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

Even when the principles of interface reaction and diffusion are thought to be understood, the integrated results may still require major new work. For example, the growth rate of an individual crystal in an infinite melt can be predicted if parameters are known, but the growth rates of many crystals (and different minerals), i.e., the kinetics of crystallization of a magma, is not quantitatively understood. 

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