Instantaneous nucleation model

In the case of the n-heptyl viologen deposition, nucleation rates of the first molecular layers of this molecule control the deposition rates of subsequent layers. The nucleation reaction follows the instantaneous nucleation model — and is found to be highly sensitive to the chemical and physical nature of the electrode surface prior to deposition. RF-plasma of ion-beam etched surfaces generally show greatly enhanced nucleation and bulk deposition rates. 

A method based on quantitative phase analysis and the instantaneous nucleation model has been developed to quantify form II nuclei in both GSX and MSX samples (50). The method involves measurement of the recrystallization rate of form II from the form I melt in DSC at different scanning speeds, and analysis of the data (expressed as a-time curves) by appropriate kinetic models, as explained next. 

To quantify the amount of preexisting nuclei in GSX and MSX, it would be necessary to find a suitable mathematical relationship that relates the (total) rate constant k, computed by the AE model-fitting procedure to the mole fraction of SX-II. Equation (15) follows from the instantaneous nucleation model (52)... 

With instantaneous nucleation models, it is assumed that the entire surface of every grain of A is covered by B from the initial instant, which is then followed by the growth of a layer of 5. Looking at the state of the powder during the reaction, we will discover that every grain is in the same state, with a nucleus of A covered by a layer of B (see Figure 14.4a). This layer has the same thickness on every grain, whatever its shape and size. 

Fig. 10). With the completion of the structure transition, the current should drop to zero, which is indeed the case except for peak B, where a slight leak current is seen (ascribed to the side reaction Cu++ I c > Cu+). According to the theory by Bewick, Fleischmann and Thirsk (BFT) the transients can be used to distinguish between instantaneous and progressive nucleation [45], A corresponding analysis revealed that the falling part of the transients agrees well with the model for instantaneous nucleation, while the rising part shows a systematic deviation. This was explained by the existence of surface defects on a real electrode in contrast to the ideal case of a defect-free surface assumed in the theoretical model. By including an adsorption term in the BFT theory to account for Cu deposition at defects, the experimentally obtained transients could indeed be reproduced very well [44], We shall return to the important role of surface defects in metal deposition later (sec. 3.2).

The apparent activation energy of decomposition estimated from the Arrhenius plot for gave 120 kJ/mol. Conversely, Stander noticed that if the difference between the experimental dissociation pressures (e.g., 384 kPa) and the equilibrium (plateau) dissociation pressure corresponding to T = const (e.g., 404 kPa at T = 335°C for MgH ) is relatively small, then better fits were obtained with the model of random nucleation followed by one-dimensional growth or instantaneous nucleation followed by two-dimensional growth as given by the equation ... 

Chronoamperometric experiments on zinc electroreduction on GC from acetate solutions showed that the nucleation density increases with increase of temperature [44]. M oreover, the nucleation rate constant is always very large, equal to 1.41 x 10 s . This indicates that the mechanism of zinc electrodeposition on the GC electrode follows a three-dimensional instantaneous nucleation and growth model within the controlled temperature range. 

Formation and stripping of a cobalt adlayer on/from a polycrystalline Au electrode have been studied [469] applying electrochemical methods under underpotential conditions. The kinetics of deposition fitted a model of a simultaneous adsorption and diffusion-controlled two-dimensional instantaneous nucleation of cobalt on the electrode surface. 

Applying the Avrami model to the analysis of the isothermal crystallization of interesterified and noninteresterified 20%SSS/80%000 at 30°C, 40 C and 50 C, many differences can be observed (Table 17.3). At 30°C and 40°C growth would be described as rodlike with instantaneous nucleation for both interesterified and noninteresterified samples. Also, for the noninteresterified system at 50°C spherulitic growth with instantaneous nucleation takes place. The half-time of nucleation... 

Instantaneous nucleation occurs for this model when l< is large, so that all possible nuclei are formed at the onset of reaction // = at virtually zero time and no further nuclei are generated during the subsequent reaction. When is small, the rate of nucleation is approximately constant as reaction proceeds, because the number of sites, N - N), undergoes little change. This is known as the linear law of nucleation-. 

The major assumption made in the present quantitative impurity analysis is the model of instantaneous nucleation, which is characterized by extremely rapid onset and is consistent with a relatively small n value ( 2 for SX) (52). The homogeneous and heterogeneous nucleation processes can proceed simultaneously. However, the former can occur only in the bulk material of molten SX, whereas the latter is initiated by contact with the surface of the form II seeds present. The number of nuclei formed by heterogeneous nucleation is proportional to the surface area of the metastable phase, and will be proportional to x, the weight fraction of SX-II, if the same specific surface area is assumed for both preexisting nuclei and SX-II particles added (as in physical mixtures). Therefore Ax, the total number of nuclei formed at x c 1 can be expressed by... 

The instantaneous nucleation-growth-precipitation model [39] assumes that the film is formed directly on the substrate, without previous dissolution however, it was observed that active dissolution of the metal occurs. Therefore, Equations 8.11 through 8.13 were examined and rewritten considering metal dissolution, that is, terms corresponding to dissolution were added to the mathematical expressions ... 

The number of sites participating in the formation of Sn02 is N0 = 3.0 x 1010 cm-2. This value is similar to those usually found for active sites in the case of metals [67]. As the diagnostic criteria for the instantaneous nucleation-growth-overlap model was fulfilled and physicochemical data obtained for No is physically plausible, we may conclude that instant nucleation with lateral growth of the film occurs. Taking into account that the atomic density of the substrate is of the order of 1015 cm2 [67], we conclude that the density of the active sites on the surface can severely limit the nucleation process. 

The fact that the experimental data fit both models, the dissolution-precipitation and the instantaneous nucleation-growth-overlap models, confirms the assertion made at the beginning of this chapter, that is, some models are complementary to each other. 

Miiller-Calandra, Srinivasan-Gileadi, and instantaneous nucleation-growth overlap models... 

According to the model for instantaneous nucleation followed by three dimensional diffusion limited growth [3,4], tm and im are given by ... 

In the optimal conditions of epitaxy, the analysis of the current transients shows that the best fit is obtained using the Scarifker model, assuming a 3D instantaneous nucleation followed by a rapid diffusion control which is effective less than 0.1 s after the beginning of the pulse. TEM observations of very thin electrodeposits confirm that the coalescence of the first nuclei is achieved. Immeiatly after new epitaxial nuclei appear which coalesce when the the thickness of the deposit reaches 4 nm. The analysis of the moire patterns reveals that these nuclei present small misorientations. 

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