Kinetics of nucleation

The kinetics of nucleation can obviously be considered only in one concrete case starting from a precise mechanism however, a certain number of eommon natures are met in all the reactions of nucleation and then generic models can be discussed. This can be the object of our study of kinetics of nucleatioa 

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Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

Using the properties of water Li and Cheng (2004) computed from the classical kinetics of nucleation the homogeneous nucleation temperature and the critical nu-cleation radius ra. The values are 7s,b = 303.7 °C and r nt = 3.5 nm. However, the nucleation temperatures of water in heat transfer experiments in micro-channels carried out by Qu and Mudawar (2002), and Hetsroni et al. (2002b, 2003, 2005) were considerably less that the homogeneous nucleation temperature of 7s,b = 303.7 °C. The nucleation temperature of a liquid may be considerably decreased because of the following effects dissolved gas in liquid, existence of corners in a micro-channel, surface roughness. 

Bishop MF, Ferrone FA. Kinetics of nucleation-controlled polymerization. A perturbation treatment for use with a secondary pathway. Biophys J 1984 46 631-644. 

Mahrapatra, P. P., Sarangi, D. S. Mishra, B. 1995. Kinetics of nucleation of lead hydroxylapatite and preparation of solid solutions of calcium-cadmium-lead hydroxyapatite an x-ray and IR study. Journal of Solid State Chemistry, 116, 8-14. 

Order arising through nucleation occurs both in equilibrium and nonequilibrium systems. In such a process the order that appears is not always the most stable one there are often competing processes that will lead to different structures, and the structure that appears is the one that nucleates first. For instance, in the analysis of the different possible structures in diffusion-reaction systems17-20 one can show, by analyzing the bifurcation equations, that there are several possible structures and some of them require a finite amplitude to become stable if this finite amplitude is realized through fluctuation, this structure will appear. In the formation of crystals (hydrates) the situation is similar the structure that is formed depends, according to the Ostwald rule, on the kinetics of nucleation and not on the relative stability. 

The kinetics of nucleation of one-component gas hydrates in aqueous solution have been analyzed by Kashchiev and Firoozabadi (2002b). Expressions were derived for the stationary rate of hydrate nucleation,./, for heterogeneous nucleation at the solution-gas interface or on solid substrates, and also for the special case of homogeneous nucleation. Kashchiev and Firoozabadi s work on the kinetics of hydrate nucleation provides a detailed examination of the mechanisms and kinetic expressions for hydrate nucleation, which are based on classical nucleation theory. Kashchiev and Firoozabadi s (2002b) work is only briefly summarized here, and for more details the reader is referred to the original references. 

Powers, E.T., and Powers, D.L. "The kinetics of nucleated polymerisations at high concentrations amyloid bril formation near and above the supercritical concentration". Biophys. J. 91,122-131 (2006). 

The dimensions of the space available are in the nanometer range. At this length scale, water is supposed to behave as a constrained liquid, which follows rules of diffusion, flow and structuring more akin to those of gels than to those observed in free liquids [108]. Furthermore, if the silk is present as a gel phase, the structured nature of the water molecules is even more enhanced. This in turn affects the activities of the ions within this medium, especially where polyelectrolytes are also involved. This speculative scenario envisages that the chemical environment of nucleation is very different from a simple saturated solution, and that the thermodynamics and kinetics of nucleation are more akin to crystallization from hydrogels. The same situation exists also in collagen-mediated mineralization, where the tiny apatite crystals form inside the... 

Kiebach et al. (2005) SEM Organogermanates Multiple kinetics of nucleation and growth + + n.a. Solvothermal synthesis... 

To truly control crystallization to give the desired crystalline microstructure requires an advanced knowledge of both the equilibrium phase behavior and the kinetics of nucleation and growth. The phase behavior of the particular mixture of TAG in a lipid system controls both the driving force for crystallization and the ultimate phase volume (solid fat content) of the solidified fat. The crystallization kinetics determines the number, size, polymorph, and shape of crystals that are formed as well as the network interactions among the various crystalline elements. There are numerous factors that influence both the phase behavior and the crystallization kinetics, and the effects of these parameters must be understood to control lipid crystallization. 

Strictly speaking, the surface tension of water is the tension of water with respect to vacuum but one usually refers to the interfacial tension between water and air. As will be discussed in Chapter 13, the interfacial tension between water and solid minerals is of importance in the kinetics of nucleation and precipitation. 

Thus, the kinetics of nucleation of the new metallic phase and its form and growth rate can play a dominant role in determining the overall deposition kinetics, as well as the appearance, structure, and properties of metallic coatings, as discussed in detail by Fischer as early as 1954 [4.1]. 

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