Characterization crystallization kinetics

Batch crystallization has several desirable features and advantages in laboratory and industrial applications. Industrial batch crystallizers are commonly used to manufacture a wide variety of crystalline materials with desirable product features and quality. Laboratory batch crystallizers are often used to characterize crystallization kinetics and CSDs and to determine the effects of process conditions on these kinetics and CSDs. 

While there are several instances of redundancy among the Avrami exponents arising from different pictures of the crystallization process, there is also enough variety to make the experimental value of this exponent a valuable way of characterizing the crystallization process. In the next section we shall examine the experimental side of crystallization kinetics. 

The crystallization kinetics of bulk triglycerides and oil-in-water emulsions has been characterized by both NMR imaging and localized spectroscopy. The rate of lipid crystallization in an oil-in-water emulsion was affected by the addition of a second homopolymer (addition of trilaurin to trimyristin in this case). The addition of the second homopolymer of higher chain length was observed to slow the rate of crystallization [26]. 

The effect of the minor components was kinetic, rather than thermodynamic. Although the crystallization kinetics were altered, the structure and mechanical properties of milk fat were the same with or without the minor lipids. The samples reached the same SFC value and had a similar microstructure as observed visually and as characterized by the fractal dimension. The rheological properties of the fats were also similar. Neither the storage modulus nor the yield force was affected by removal of the minor components (Wright and Marangoni, 2003). Large changes in the... 

Blaurock and Carothers (1990) and Blaurock and Wan (1990) described a simple way, valid for butteroil, of analyzing isothermal DSC data to characterize the kinetics of early crystallization in a supercooled oil. This approach yielded a single crystallization-temperature dependent combined nucleation/crystal growth constant (which they called NG). The temperature dependence of NG could be modeled with the Arrhenius equation. 

The measured steady-state diffusivity of 3 x 10 m /s is comparable to the effective methanol diffusivity of 1.1 x 10 m /g obtained indirectly from the kinetics data characterizing crystals of various sizes. The consistency between steady-state diffusivity and that determined in reaction experiments is in good agreement with the results of Post et al. 105) and Garcia and Weisz 106). 

Knowledge of the driving force for crystallization is essential, not only to characterize the kinetics, but also... 

Real-life catalysts are thus obviously less accessible for detailed characterization and kinetic model experiments than single-crystal model catalysts. 

Solubility enhancement in the presence of impurities, especially in the mother liquor, is a familiar phenomenon. Impurities in the mother liquor may not be well characterized, although their chemical structures have some similarity to the desired compound. In practical applications, the impact of impurities on solubility generally is unknown a priori and must be determined experimentally. Due to the potential impact of impurities on solubility, care should be taken in conducting crystallization experiments if the starting materials have vaiy-ing levels of impurities from batch to batch. The presence of impurities can further affect crystallization kinetics, which will be addressed in the next chapter. 

The analysis of batch crystallizers normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these nonlinear partial differential equations is relatively difficult. Under certain conditions, these batch conservation equations can be solved numerically by a moment technique. Several simple and useful techniques to study crystallization kinetics and CSDs are discussed. These include the thermal response technique, the desupersaturation curve technique, the cumulative CSD method, and the characterization of CSD maximum. 

The investigation of the compatibilization and crystallization of blends of polyolefins with a semiflexible LCP leads to the following conclusions the compatibilization of polyolefin/LCP blends has been realized successfully by the addition of ad hoc synthesized polyolefin-g-LCP copolymers. The compatibilization results into materials, characterized by a stabilized morphology, improved crystallization kinetics under nonisothermal and isothermal conditions, and enhanced mechanical properties. Moreover, polyolefin processability has been enhanced by the addition of LCP, even in the presence of compatibilizers. New high quality materials with improved processability have been produced by technologies, which are economic, friendly to the environment, and socially acceptable. 

Using N,N,N, N -tetramethyl-l,6-hexandiammine as organic template, SAPO-56 and its metal-containing silicoaluminophosphates (M=Co, Mn and Zr) were synthesized hydro-thermally. The synthesis phase diagram and crystallization kinetics of SAPO-56 were obtained. The synthesis regulation of pure MAPSO-56 molecular sieves was also investigated. The samples were characterized by XRD, SEM, TG-DTA and MAS NMR. SAPO-56 and MAPSO-56 were studied with respect to their catalytic behaviors in the methanol-to-olefms conversion and the oxidation of alkane, respectively. 

A number of laboratory studies have been recorded recently aimed at characterizing the kinetics of both the chemical reaction and crystallization steps in a reaction crystallization process. Examples of liquid phase reactions studied for this purpose are the crystallization of salicylic acid from aqueous solutions of sodium salicylate using dilute sulphuric acid (Franck et al, 1988) and the crystallization of various calcium phosphates by reacting equimolar aqueous solutions of calcium nitrate and potassium phosphate (Tsuge, Yoshizawa and Tsuzuki, 1996). Several aspects of crystal size distribution control in semi-batch reaction crystallization have been considered by Aslund and Rasmuson (1990) who studied the crystallization of benzoic acid by reacting aqueous solutions of sodium benzoate with HCl. An example of crystallization arising from a gas-liquid reaction in an aqueous medium is the precipitation of calcium carbonate from the reaction between calcium hydroxide and CO2 (Wachi and Jones, 1995). 

The details of the polymer crystallization process can be quite complicated. Practically, one may not care about the details of crystal nucleation and the linear crystal growth rates, but just want to characterize the overall crystallization kinetics. The degree of crystallization process can be roughly defined as crystallinity, regardless of their detailed crystal morphologies. The conventional methods to characterize the crystallinity include DSC, X-ray diffraction and dilatometer. Depending on the measured quantity, crystallinity is also separated into the weight crystallinity... 

Hu WB (2005) Molecular segregation in polymer melt crystallization simulation evidence and unified-scheme interpretation. Macromolecules 38 8712-8718 Hu WB, Cai T (2008) Regime transitions of polymer crystal growth rates molecular simulations and interpretation beyond Lauritzen-Hoffman model. Macromolecules 41 2049-2061 Jeziomy A (1971) Parameters characterizing the kinetics of the non-isothermal crystallization of poly(ethylene terephthalate) determined by DSC. Polymer 12 150-158 Johnson WA, Mehl RT (1939) Reaction kinetics in processes of nucleation and growth. Trans Am Inst Min Pet Eng 135 416-441... 

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