Crystal nucleation kinetics

Kinetics. Emulsions have long been used to determine crystal nucleation kinetics, i.e., to find values of Acat and of /het or /hom as a function of supersaturation or other conditions. The material is emulsified in a suitable medium, e.g., water in silicone oil or oil in water, with a suitable surfactant, and the droplet size distribution is determined. To obtain useful results, a series of emulsions differing in average droplet size should be made. The emulsions are cooled to various temperatures Tc below Teq, and after a given time the amount of crystalline material is determined, e.g., by a change in density, or from the heat of fusion, or by means of some spectroscopic method. The same method is applied to the bulk material starting at Tc, and from the ratio of the results the value y is calculated,... 

Correlations of nucleation rates with crystallizer variables have been developed for a variety of systems. Although the correlations are empirical, a mechanistic hypothesis regarding nucleation can be helpful in selecting operating variables for inclusion in the model. Two examples are (/) the effect of slurry circulation rate on nucleation has been used to develop a correlation for nucleation rate based on the tip speed of the impeller (16) and (2) the scaleup of nucleation kinetics for sodium chloride crystalliza tion provided an analysis of the role of mixing and mixer characteristics in contact nucleation (17). Pubhshed kinetic correlations have been reviewed through about 1979 (18). In a later section on population balances, simple power-law expressions are used to correlate nucleation rate data and describe the effect of nucleation on crystal size distribution. 

The population balance analysis of the idealized MSMPR crystallizer is a particularly elegant method for analysing crystal size distributions at steady state in order to determine crystal growth and nucleation kinetics. Unfortunately, the latter cannot currently be predicted a priori and must be measured, as considered in Chapter 5. Anomalies can occur in the data and their subsequent analysis, however, if the assumptions of the MSMPR crystallizer are not strictly met. 

Several authors have presented methods for the simultaneous estimation of crystal growth and nucleation kinetics from batch crystallizations. In an early study, Bransom and Dunning (1949) derived a crystal population balance to analyse batch CSD for growth and nucleation kinetics. Misra and White (1971), Ness and White (1976) and McNeil etal. (1978) applied the population balance to obtain both nucleation and crystal growth rates from the measurement of crystal size distributions during a batch experiment. In a refinement, Tavare and... 

Tavare, N.S. and Garside, J., 1986. Simultaneous estimation of crystal nucleation and growth kinetics from batch experiments. Chemical Engineering Research and Design, 64, 109. 

Timm, D.C. and Larson, M.A., 1968. Effect of nucleation kinetics on the dynamic behaviour of a continuous crystallizer. American Institute of Chemical Engineers Journal, 14(3), 452M57. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

As described earlier, Doi s kinetic theory leads to a prediction that the SD is triggered by extension of unoriented crystalline sequences prior to crystal nucleation. In order to confirm this prediction the conformational change... 

Chiang, P-P., M. D. Donohue, and J. L. Katz (1988), "A Kinetic Approach to Crystallization from Ionic Solution. II. Crystal Nucleation", J. Colloid Interf. Sd. 122, 251-265. 

The development and refinement of population balance techniques for the description of the behavior of laboratory and industrial crystallizers led to the belief that with accurate values for the crystal growth and nucleation kinetics, a simple MSMPR type crystallizer could be accurately modelled in terms of its CSD. Unfortunately, accurate measurement of the CSD with laser light scattering particle size analyzers (especially of the small particles) has revealed that this is not true. In mar cases the CSD data obtained from steady state operation of a MSMPR crystallizer is not a straight line as expected but curves upward (1. 32. 33V This indicates more small particles than predicted... 

Crystal Growth and Nucleation Kinetics from Batch Experiments... 

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). 

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. 

Crystal stmcture prediction by computer has made great steps forward in the last 10 years, with progress toward consistent success in blindfold tests. Fundamental uncertainties still remain, due to the unknown role of nucleation kinetics and to the neglect of temperature effects in the calculations. Success or failure still depends to some extent on hardly predictable factors and on the extent to which the experimental polymorph screening has been carried out. Presently, some of the best computational tools are not yet available to the general community of solid state scientists, being implemented in commercial, strictly copyrighted software. 

It is important to weigh Nile Red accurately. Nile Red modifies lipid nucleation kinetics when used at higher concentrations and, thus, modified crystal images may be obtained if the concentration is too high. The concentration recommended in this protocol has been proven not to modify lipid crystallization kinetics. 

The kinetics of transition from the liquid crystal to the fully ordered crystal of flexible, linear macromolecules was studied by Warner and Jaffe 38) on copolyesters of hydroxybenzoic acid, naphthalene dicarboxylic acid, isophthalic acid, and hydro-quinone. The analytical techniques were optical microscopy, calorimetry and wide angle X-ray diffraction. Despite the fact that massive structural rearrangements did not occur on crystallization, nucleation and growth followed the Avrami expression with an exponent of 2. The authors suggested a rod-like crystal growth. 

In order to achieve some understanding of the nucleation of hydrate crystals from supercooled water + gas systems, it is useful to briefly review the key properties of supercooled water (Section 3.1.1.1), hydrocarbon solubility in water (Section 3.1.1.2), and basic nucleation theory of ice, which can be applied to hydrates (since hydrate nucleation kinetics may be considered analogous, to some extent, to that of ice Section 3.1.1.3). The three subsections of 3.1.1 (i.e., supercooled water, solubility of gas in water, and nucleation) are integral parts of conceptual pictures of nucleation detailed in Section 3.1.2. 

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