Nucleation transient

The process as a whole is transient nucleation is predominant initially, and nucleus growth is predominant subsequently. Growth of the nuclei usually continues until they have reached a certain mean size. After some time a quasisteady state is attained, when the number of nuclei that cease to grow in unit time has become equal to the number of nuclei newly formed in unit time. 

Transient Nucleation If a liquid is cooled continuously, the liquid structure at a given temperature may not be the equilibrium structure at the temperature. Hence, the cluster distribution may not be the steady-state distribution. Depending on the cooling rate, a liquid cooled rapidly from 2000 to 1000 K may have a liquid structure that corresponds to that at 1200 K and would only slowly relax to the structure at 1000 K. Therefore, Equation 4-9 would not be applicable and the transient effect must be taken into account. Nonetheless, in light of the fact that even the steady-state nucleation theory is still inaccurate by many orders of magnitude, transient nucleation is not discussed further. 

Figure 19.5 Cluster-size distribution during transient nucleation.

H. Merte, H. S. Lee, and J. S. Irvine, Transient Nucleate Pool Boiling in Microgravity—Some Initial Results, Microgravity Sci. Tech. (VII/2) 173-179,1994. 

Equation (11.2) provides the basis for studying transient nucleation. For example, if the monomer concentration is abruptly increased at t = 0, what is the time-dependent development of the cluster distribution Physically, in such a case there is a transient period over which the cluster concentrations adjust to the perturbation in monomer concentration, followed eventually by the establishment of a pseudo-steady-state cluster distribution. Since the characteristic time needed to establish the steady-state cluster distribution is generally short compared to the timescale over which typical monomer concentrations might be changing in the atmosphere, we can assume that the distribution of clusters is always at a steady state corresponding to the instantaneous monomer concentration. There are instances, generally in liquid-to-solid phase transitions, where transient nucleation can be quite important (Shi et al. 1990), although we do not pursue this aspect here. 

Blanke-Bewersdorff, M. Koster, U. (1988). Transient nucleation in zirconium-based metallic glasses. Materials Science and Engineering, 97,313-16. 

Schwarz suggested that the reaction might proceed through a transient nucleation process such as ... 

The transient nucleation behavior of a condensed system is usually approximated by an expression of the form... 

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. 

The predicted transient supersaturation levels (and corresponding nucleation rates) are also shown in Figure 7.3. These considerations predict that the high levels in the early period of natural cooling can be avoided by controlled cooling. 

Achieving steady-state operation in a continuous tank reactor system can be difficult. Particle nucleation phenomena and the decrease in termination rate caused by high viscosity within the particles (gel effect) can contribute to significant reactor instabilities. Variation in the level of inhibitors in the feed streams can also cause reactor control problems. Conversion oscillations have been observed with many different monomers. These oscillations often result from a limit cycle behavior of the particle nucleation mechanism. Such oscillations are difficult to tolerate in commercial systems. They can cause uneven heat loads and significant transients in free emulsifier concentration thus potentially causing flocculation and the formation of wall polymer. This problem may be one of the most difficult to handle in the development of commercial continuous processes. 

By electrodeposition of CuInSe2 thin films on glassy carbon disk substrates in acidic (pH 2) baths of cupric ions and sodium citrate, under potentiostatic conditions [176], it was established that the formation of tetragonal chalcopyrite CIS is entirely prevalent in the deposition potential interval -0.7 to -0.9 V vs. SCE. Through analysis of potentiostatic current transients, it was concluded that electrocrystallization of the compound proceeds according to a 3D progressive nucleation-growth model with diffusion control. 

Chronoamperometric transients for CO stripping on polycrystalline platinum were measured by McCallum and Fletcher [1977], Love and Lipkowski [1988] were the hrst to present chronoamperometric data for CO stripping on single-crystalline platinum. However, they interpreted their data on the basis of a different model than the one discussed above. Love and Lipkowski considered that the oxidation of the CO adlayer starts at holes or defects in the CO adlayer, where OH adsorbs. These holes act as nucleation centers for the oxidation reaction, and the holes grow as the CO at the perimeter of these holes is oxidized away by OHads- This nucleation and growth (N G) mechanism is fundamentally different from the mean held model presented above, because it does not presume any kind of mixing of CO and OH [Koper et ah, 1998]. Basically, it assumes complete surface immobility of the chemisorbed CO. 

McCallum and Fletcher, 1976] and single-crystalline [Love and Lipkowski, 1988 Koper et al., 1998 Lebedeva et al., 2002b] Ft were observed. For extended surfaces, the transient shape was explained by the L-H mechanism [Koper et al., 1998] or the L-H mechanism complicated with nucleation and growth of OHads islands [McCallum and Fletcher, 1976 Love and Lipkowski, 1988]. 

Johans et al. derived a model for diffusion-controlled electrodeposition at liquid-liquid interface taking into account the development of diffusion fields in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173-175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to confirm the absence of preferential nucleation sites at the liquid-liquid interface. Other nucleation work at the liquid-liquid interface has described the formation of two-dimensional metallic films with rather interesting fractal shapes [176]. 

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