Supersaturation nucleation kinetics

The concentration threshold above which crystallization is observed at times shorter than the processing time or desired product shelf-life or GI transit time, is determined by the kinetic stability of supersaturated states and is regulated by the nucleation mechanisms and kinetics. Nucleation phenomena are equally important in the control of micrometric properties and in the selective crystallization of a particular polymorph. 

Girshick, S. L., and Chiu, C.-P. (1990) Kinetic nucleation theory A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor, J. Chem. Phys. 93, 1273-1277. 

When a homogeneous aqueous phase becomes supersaturated with respect to a solid phase, the rate of appearance of the new solid phase is controlled by nucleation kinetics. Nucleation occurs whenever enough of the solute species come together to create a particle that can grow spontaneously. Classical models of nucleation kinetics are based on a combination... 

Evidence for secondary nucleation has came from the early continuous MSMPR studies. MSMPR crystallization kinetics are usually correlated with supersaturation using empirical expressions of the form... 

The nucleation rate is plotted versus the supersaturation for different stirrer speeds in a log-log diagram (Figure 6.21). The kinetic order n in the correlating equation... 

The reactor has been successfully used in the case of forced precipitation of copper and calcium oxalates (Jongen etal., 1996 Vacassy etal., 1998 Donnet etal., 1999), calcium carbonate (Vacassy etal., 1998) and mixed yttrium-barium oxalates (Jongen etal., 1999). This process is also well adapted for studying the effects of the mixing conditions on the chemical selectivity in precipitation (Donnet etal., 2000). When using forced precipitation, the mixing step is of key importance (Schenk etal., 2001), since it affects the initial supersaturation level and hence the nucleation kinetics. A typical micromixer is shown in Figure 8.35. 

In c-Hxn solutions the nucleation behavior is similar to that in EtOH solutions. It is presumed that the concentrations of conformer regarding to the A and B form are competitive and the nucleation process of the polymorph is determined by the supersaturation and the kinetic process. On the other hand in MeCN solutiorrs orrly the stable form nucleates. In MeCN solution it is considered that the thermodynamic stability of the meta-stable form is extremely low due to the large solvent-solute... 

NUCLEATION. Nucleation creates a new phase that is organizationally more related to the crystal lattice than to the monomeric species that undergoes crystallization. This process permits solutions that are of high relative supersaturation to crystallize and thereby reach equilibrium between liquid and sohd phases . Nucleation occurs when the local concentration of components that will comprise the solid phase exceeds a threshold level as a result of short-range concentration fluctuations in the bulk solution. In this respect, the kinetics of nucle-... 

Tavare and Garside ( ) developed a method to employ the time evolution of the CSD in a seeded isothermal batch crystallizer to estimate both growth and nucleation kinetics. In this method, a distinction is made between the seed (S) crystals and those which have nucleated (N crystals). The moment transformation of the population balance model is used to represent the N crystals. A supersaturation balance is written in terms of both the N and S crystals. Experimental size distribution data is used along with a parameter estimation technique to obtain the kinetic constants. The parameter estimation involves a Laplace transform of the experimentally determined size distribution data followed a linear least square analysis. Depending on the form of the nucleation equation employed four, six or eight parameters will be estimated. A nonlinear method of parameter estimation employing desupersaturation curve data has been developed by Witkowki et al (S5). 

In this section, a brief description of the necessary experiments to identify the kinetic parameters of a seeded naphthalene-toluene batch crystallization system is presented. Details about the experimental apparatus and procedure are given by Witkowski (12). Operating conditions are selected so that the supersaturation level is kept within the metastable region to prevent homogeneous nucleation. To enhance the probability of secondary nucleation, sieved naphthalene seed particles are introduced into the system at time zero. 

The kinetic behaviour of fructose crystallization from aqueous ethanolIc solutions, typical in composition to those operated on an industrial scale, is strongly dependent on supersaturation, solvent composition and temperature. Provided the supersaturation is kept below 35 C of subcooling, nucleation does not occur. 

Literature has revealed limited kinetic data on secondary nucleation of alumina trihydrate in the precipitator of the Bayer Process for alumina production. A batch agitated, isothermal, three litre crystallizer was used in the study. A Coulter-Counter was utilized as the particle sizing equipment. The effects of seed density, supersaturation and temperature on secondary nucleation were investigated. Maximum nucleation rates were found to occur at about 70 C and for any crystallization temperature, the nucleation rate passed through a maximum. The correlated equation for the effective secondary nucleation rate of alumina trihydrate is... 

Crystallization is a polymerization process that has comparable kinetics to the reactions making conventional polymers but whose products are quite different In crystallization one allows supersaturated monomer to nucleate and grow into crystals. We usually do not regard crystallization as a chemical reaction at aU because the process is... 

From a kinetic point of view, the homogeneous nucleation rate (Nr) [57] and the growth rate (Gr) [58] can be expressed as a function of the supersaturation ratio ... 

Both these succinct theoretical models, derived from both a thermodynamic and kinetic perspective, underline the role of the supersaturation ratio during nucleation and growth steps. They strongly indicate that control of this supersaturation parameter will improve the processes by which chemical vapour deposition occurs. 

Katz described the homogeneous nucleation of a supersaturated vapour using J(i), the net rate at which clusters of size i grow to size i + 1 [63]. In this kinetic equation, J(i) is the difference between the rate at which clusters of size i add an additional monomer, and the rate at which clusters of size i + 1... 

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