Kinetics and Phases

The process, kinetic, and phase-equilibrium parameters are given in Table 2.5. There is a single feedstream F0 (m3/s) with concentrations of the reactants Cao and Cbo (kmol/m3). A slight excess of reactant B is fed to the reactor, so the conversion is specified in terms of this reactant ... 

Kinetics and Phase Behavior - Table IV represents a simplified picture of the situation however, some polymerizations go through several phase changes in the course of the reaction. For example, in the bulk polymerization of PVC, the reaction medium begins as a low viscosity liquid, progresses to a slurry (the PVC polymer, which is insoluble in the monomer, precipitates), becomes a paste as the monomer disappears and finishes as a solid powder. As might be expected, modelling the kinetics of the reaction in such a situation is not a simple exercise. 

It may be seen that components of the model discussed thus far are generally applicable to any two phase ideal back-mixed reactor. Chemical kinetics and phase equilibrium are the two components which make the model unique. 

The accuracy of the thermodynamic data has a significant effect on RCM computation. In the case of slow reactions both kinetics and phase equilibrium should be modelled accurately. If the reaction is fast enough the chemical reaction prevails. In many cases chemical equilibrium may be taken as the reference. Consequently, accurate knowledge of the chemical equilibrium constant is needed. When reactive azeotropes and/or phase splitting might occur accurate modelling of phase equilibrium is also needed. 

Gribb AA, Banfield JF (1997) Particle size effects on transformation kinetics and phase stability in nanocrystalline Ti02. Am Mineral 82 717-728... 

Complex reaction kinetics and phase behavior In many polymerization processes, the reaction mixture undergoes a significant phase change that affects the polymerization rate, polymer properties, and reactor operations (e.g., viscosity increase, particle formation, precipitation, etc.). 

This study was undertaken to develop techniques for direct monitoring of organic hydrothermal synthesis reactions in DACs combined with direct microscopic and spectroscopic observations. Such direct observation provided additional insight into the mechanism, kinetics and phase behavior (miscibility characteristics) of the fluid-rich system. Described below are some results on the direct monitoring of citric acid-HaO system at high P and T with DAC Raman spectroscopy combined with quench product gas chromatographic analysis. 

He then spent three years as a postdoctoral member of the technical staff at AT T Bell Laboratories, Murray Hill NJ, where he conducted research of the structure, kinetics, and phase transitions of surfaces and interfaces, using X-ray diffraction. He is currently as Senior Research Scientist in the James Franck Institute and Consortium for Advanced Radiation Sources (CARS) at the University of Chicago. He has been involved in synchrotron radiation research since 1986 and during the past seven years has been involved in the design, construction and operation of the GeoSoilEnviroCARS (GSE)CARS laboratory at the Advanced Photon Source. Here he has applied lower dimensional X-ray diffraction, X-ray absorption fine structure, X-ray fluorescence microprobe, microtomography and microcrystallography to study problems in earth and environmental science. 

The first term in equation (9-132) represents the time displacement of the input function and the second is the amplitude attenuation of the input. As can be seen, the amplitude term contains all of the kinetic and phase-distribution parameters. The exit concentration is also given by equation (9-132), but now with... 

Another class of equations subsumes kinetic and phase transformations of all involved reactants. Such equations describe how the reactants molecules are transformed and distributed in the reactor depending on time and other environmental parameters. Depending on the kind of chemical processes under consideration, both classes of equations are of varying importance for modelling. E.g. for catalytic packed-bed reactors the chemicals reaction rates heavily depend on local physical conditions at the (solid) catalyst material. The precise modelling of the local physical conditions and the mixture of chemicals flowing is important and complex in this case. In contrast, for classic stirred-tank reactors kinetic and phase transformations are comparatively easy to model. 

Tanaka T (1985) Critical dynamics, kinetics and phase transitions of polymer gels. Polym Preprt 27(1) 235... 

The details of nucleation and growth theory are given in many standard textbooks on kinetics and phase transformations see the books on interfaces in Chapter 15 and on phase transformations in Chapter 25. 

Deh] Dehlinger, U., Bumm, H., Kinetics and Phase Diagram of Irreversible Transformations in Iron-Nickel System (in German), Z Metallkd., 26(5), 112-116 (1934) (Experimental, Morphology, Phase Diagram, 10)... 

The units lend themselves to slow kinetics and phases exhibiting fairly narrow differences in specific gravity (between 0.10 and 0.20). For difficult dispersions, a single unit can correspond to three or four theoretical transfer stages. In the present application the following orders of magnitude can be considered ... 

Vaden TD, Imre D, Beranek J, Shrivastava M, Zelenyuk A (2011) Evaporation kinetics and phase of laboratory and ambient secondary organic aerosol. Proc Natl Acad Sci USA 108 (6) 2190-2195... 

Wil73] Williams, J.C., Kinetics and Phase TVansformations ACritical Review, in [Jaf73],p. 1433-1494... 

Source J.C. Williams, Critical Review of Kinetics and Phase Transformations, Titanium Science and Tectmology, Vol 3, Plenum Press, 1973... 

The potential of the FRES technique is highlighted in this section, based mainly on papers published in the year 2000 and thereafter. However, as the recent FRES investigations of polymer blends are rather scarce, some examples are also included from earlier studies, many of which were comprehensively reviewed elsewhere [116]. Whilst attention has been focused here on polymer blends, relevant studies of homopolymers, copolymers and polymeric composites will also be presented. The case study examples are divided (to some extent arbitrarily) into four subsections according to the major point of interest, namely diffusion coefficient, interphase behavior, reaction kinetics, and phase separation. 

In-situ studies CAU-1-(0H)2 EDXRD crystallization kinetics and phase formation Influence of heating methods on the kinetics 77... 

The features and detail of the IPN kinetics were also studied in other works [274-276]. The kinetics of thermally initiated cationic epoxy polymerization and free radical acrylate photopolymerization were investigated in [277]. It was found that the preexistence of one polymer has a significant effect on the polymerization of the second monomer. The reaction kinetics and phase separations were studied for sequential IPNs in [278]. The kinetics of IPN formation was studied for IPNs based on PDMS-cellulose acetate butyrate [279]. All these and other works [280-282] confirm the general regularities of the reaction kinetics and its connection with phase separation in forming systems. 

In [308] the filler effect on polymerization kinetics and phase separation in model blends of two linear polymers formed in situ without cross-linking was studied. Blends of PU and PMMA were prepared in the presence of various amounts of fumed silica. It was shown that the filler affects the rates of both reactions. In addition, filler exerts an influence on the phase separation induced by the chemical reaction. Increasing the amount of filler increases the time for the onset of phase separation. The effects observed were explained both by the increase in the viscosity of the reaction system due to introducing filler and by selective adsorption of the reaction components at the interface with filler particles. In all cases, phase separation at the early stages of reaction proceeds in a four-component system (two polymers formed and two initial compounds) and obeys the spinodal mechanism. It was also shown that the final morphology arises far from the end of the reaction and before establishing the equilibrium state. 

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