Diffusion growth mechanism

The uniformity of size in the final colloidal system is all the greater as the nucleation stage (zone II) is short compared to the growth stage (zone III). Moreover, a diffusion growth mechanism for the particles explains why the diameters of small particles grow more quickly than those of larger ones. 

For a conserved order parameter, the interface dynamics and late-stage domain growth involve the evapomtion-diffusion-condensation mechanism whereby large droplets (small curvature) grow at tlie expense of small droplets (large curvature). This is also the basis for the Lifshitz-Slyozov analysis which is discussed in section A3.3.4. 

Wagner (1961) examined theoretically the growdr kinetics of a Gaussian particle size distribution, considering two growth mechanisms. When the process is volume diffusion controlled... 

The water solubilities of the functional comonomers are reasonably high since they are usually polar compounds. Therefore, the initiation in the water phase may be too rapid when the initiator or the comonomer concentration is high. In such a case, the particle growth stage cannot be suppressed by the diffusion capture mechanism and the solution or dispersion polymerization of the functional comonomer within water phase may accompany the emulsion copolymerization reaction. This leads to the formation of polymeric products in the form of particle, aggregate, or soluble polymer with different compositions and molecular weights. The yield for the incorporation of functional comonomer into the uniform polymeric particles may be low since some of the functional comonomer may polymerize by an undesired mechanism. 

Massive barite crystals (type C) are also composed of very fine grain-sized (several xm) microcrystals and have rough surfaces. Very fine barite particles are found on outer rims of the Hanaoka Kuroko chimney, while polyhedral well-formed barite is in the inner side of the chimney (type D). Type D barite is rarely observed in black ore. These scanning electron microscopic observations suggest that barite precipitation was controlled by a surface reaction mechanism (probably surface nucleation, but not spiral growth mechanism) rather than by a bulk diffusion mechanism. 

Chain-growth polymerizations are diffusion controlled in bulk polymerizations. This is expected to occur rapidly, even prior to network development in step-growth mechanisms. Traditionally, rate constants are expressed in terms of viscosity. In dilute solutions, viscosity is proportional to molecular weight to a power that lies between 0.6 and 0.8 (22). Melt viscosity is more complex (23) Below a critical value for the number of atoms per chain, viscosity correlates to the 1.75 power. Above this critical value, the power is nearly 3 4 for a number of thermoplastics at low shear rates. In thermosets, as the extent of conversion reaches gellation, the viscosity asymptotically increases. However, if network formation is restricted to tightly crosslinked, localized regions, viscosity may not be appreciably affected. In the current study, an exponential function of degree of polymerization was selected as a first estimate of the rate dependency on viscosity. 

While the growth of thermal oxides is dominated by high-temperature diffusion of oxygen in the oxide matrix, anodic oxide growth is dominated by field-enhanced hydroxyl diffusion at RT. These different growth mechanisms result in pronounced differences in the morphological, chemical and electrical properties of the oxide. 

Despite the vast quantity of data on electropolymerization, relatively little is known about the processes involved in the deposition of oligomers (polymers) on the electrode, that is, the heterogeneous phase transition. Research - voltammetric, potential, and current step experiments - has concentrated largely on the induction stage of film formation of PPy [6, 51], PTh [21, 52], and PANI [53]. In all these studies, it has been overlooked that electropolymerization is not comparable with the electrocrystallization of inorganic metallic phases and oxide films [54]. Thus, two-or three-dimensional growth mechanisms have been postulated on the basis that the initial deposition steps involve one- or two-electron transfers of a soluted species and the subsequent formation of ad-molecules at the electrode surface, which may form clusters and nuclei through surface diffusion. These phenomena are still unresolved. 

A similar chain-growth mechanism was said to occur with the first molybdenum-sulfur-potassium based catalysts of table I (15). For such a chain-growth mechanism, the heavier the average molecular weight of alcohols, the greater the formation of heavy compounds and, more often than not, the lower the alcohols selectivity. Furthermore, in Fischer-Tropsch type catalysts (24,25) diffusion limitations, mostly due to the presence of liquid products condensed in the micro porosity, increase with the size of diffusing molecules. These molecules are capable of... 

Properties of thin layers of lead electrodeposited on vitreous carbon have been found identical with that of metallic lead [304]. Therefore Pb and Pb02 coated reticulated vitreous carbon (RVC) electrodes [185] can be applied as electrodes in lead-acid batteries, as reviewed in [305]. The deposition of lead on carbon is through the diffusion-controlled process with instantaneous or progressive nucleation, for high and low Pb + concentration, respectively, and three-dimensional growth mechanism. The number of nucleation sites increases with deposition overpotential, as shown for vitreous [306] and glassy carbon [307] electrodes. The concentration dependence of the nucleation... 

In the case of supported metal particles, experimental studies of particle growth mechanisms can determine the type of ripening. Generally, studies on supported noble metallic catalysts at elevated temperatures (>500°C) indicate atomic diffusion from smaller metal particles across the surface of the support to... 

The mechanism of particle growth in the course of hydrolysis and condensation of Ti, Zr, and Ta alkoxides has been frequently discussed. Nevertheless, the discussion so far remains open. Ring suggested a diffusion-limited model for growth of particles [484, 1357] other authors, however, assume a growth mechanism limited by reaction on the surface of the growing species [1228, 708, 477]. 

By use of the proper experimental conditions and Ltting the four models described above, it may be possible to arrive at a reasonable mechanistic interpretation of the experimental data. As an example, the crystal growth kinetics of theophylline monohydrate was studied by Rodriguez-Hornedo and Wu (1991). Their conclusion was that the crystal growth of theophylline monohydrate is controlled by a surface reaction mechanism rather than by solute diffusion in the bulk. Further, they found that the data was described by the screw-dislocation model and by the parabolic law, and they concluded that a defect-mediated growth mechanism occurred rather than a surface nucleation mechanism. 

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