Kinetics and nucleation

Most subsurface fluids are supersaturated with respect to quartz (Figure 11). Thus, secondary porosity formed within detrital quartz in the subsurface is not observed. This is not surprising given the kinetic and nucleation limitations on quartz precipitation (Oelkers et al, 1996 Walderhaug, 1996) and the fact... 

Kim SH, Ahn SH, Hirai T (2003) Crystallization kinetics and nucleation activity of silica nanoparticle-filled poly(ethylene 2,6-naphthalate). Polymer 44(19) 5625-5634... 

Evidence suggests that there is a threshold tensile stress at which void nucleation occurs and spall fracture initiates. Materials subject to transient internal tensions can support tensile stresses significantly in excess of this threshold level, however. Such behavior is a consequence of kinetics and inertia associated with the nucleation and growth of voids during spall. A fairly large body of experimental and theoretical literature on spall phenomena exists and many aspects of the effect are reasonably well understood. Review articles on spall (Curran et al., 1977 Davision and Graham, 1979 Curran, 1982 Meyer and Aimone, 1983 Novikov, 1981) provide access to most of the literature on the subject. 

We can anticipate that the highly defective lattice and heterogeneities within which the transformations are nucleated and grow will play a dominant role. We expect that nucleation will occur at localized defect sites. If the nucleation site density is high (which we expect) the bulk sample will transform rapidly. Furthermore, as Dremin and Breusov have pointed out [68D01], the relative material motion of lattice defects and nucleation sites provides an environment in which material is mechanically forced to the nucleus at high velocity. Such behavior was termed a roller model and is depicted in Fig. 2.14. In these catastrophic shock situations, the transformation kinetics and perhaps structure must be controlled by the defective solid considerations. In this case perhaps the best published succinct statement... 

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. 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

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... 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

An unusual variation in kinetics and mechanisms of decomposition with temperature of the compound dioxygencarbonyl chloro-bis(triphenyl-phosphine) iridium(I) has been reported by Ball [1287]. In the lowest temperature range, 379—397 K, a nucleation and growth process was described by the Avrami—Erofe ev equation [eqn. (6), n = 2]. Between 405 and 425 K, data fitted the contracting area expression [eqn. (7), n = 2], indicative of phase boundary control. At higher temperatures, 426— 443 K, diffusion control was indicated by obedience to eqn. (13). The... 

Sections 2.1—2.3 give accounts of kinetic and mechanistic features of the three rate-limiting processes (i) diffusion at a surface or in a gas (including the nucleation step), (ii) reaction at an interface, and (iii) diffusion across a barrier phase, [(ii) and (iii) are growth processes.] In any particular reaction, the slowest of these processes will, at any particular instant, control the rate of product formation. (A kinetic analysis of rate measurements must also incorporate an allowance for the geometric factors.)... 

While it is possible that surface defects may be preferentially involved in initial product formation, this has not been experimentally verified for most systems of interest. Such zones of preferred reactivity would, however, be of limited significance as they would soon be covered with the coherent product layer developed by reaction proceeding at all reactant surfaces. The higher temperatures usually employed in kinetic studies of diffusion-controlled reactions do not usually permit the measurements of rates of the initial adsorption and nucleation steps. 

The Tafel slopes obtained under concentrations of the chemical components that we suspect act on the initiation reaction (monomer, electrolyte, water contaminant, temperature, etc.) and that correspond to the direct discharge of the monomer on the clean electrode, allow us to obtain knowledge of the empirical kinetics of initiation and nucleation.22-36 These empirical kinetics of initiation were usually interpreted as polymerization kinetics. Monomeric oxidation generates radical cations, which by a polycondensation mechanism give the ideal linear chains ... 

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. 

The kinetics and mechanisms of the C —> G transition in a concentrated solution of PS-fr-PI in the PS-selective solvent di-n-butyl phthalate was studied [137,149]. An epitaxially transformation of the shear-oriented C phase to G, as previously established in melts [13,50,150], was observed. For shallow quenches into G, the transition proceeds directly by a nucleation and growth process. For deeper quenches, a metastable intermediate structure appears, with scattering and rheological features consistent with the hexag-onally perforated layer (PL) state. The C -> G transition follows the same pathways, and at approximately the same rates, even when the initial C phase is not shear-oriented. 

Researchers who have focused more on understanding cause-effect relationships in solution processing have given attention to film drying and pyrolysis behavior, densification processes, and nucleation and growth into the desired crystalline state. Both thermodynamic and kinetic factors associated with the phase transformation from the amorphous state to the crystalline state have been considered.11 119 Control of these factors can lead to improvements in the ability to influence the microstructure. It is noted that in the previous sentence, influence has been carefully chosen, since the ability to manipulate the factors that govern the nature of the phase transformation to the extent that full control of the microstructure is possible remains to be demonstrated. However, trends in characteristics such as film orientation and columnar versus uniaxial grains have certainly already been achieved.120... 

A real surface of a solid metal is inhomogeneous, and nucleation for the growing clusters is favored at certain active sites. To simplify the mathematics we consider an electrode with unit surface area. If there are Mo active sites, the number M(t) of growing nuclei is given by first-order kinetics ... 

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