Activation energy of nucleation

Nucleation is initiated by local fluctuations of concentration within a metastable region. The activation energy of nucleation depends on the value of the interface energy required to create a nucleus. The droplet grows by diffusion of macromolecules into the nucleate domains. The natural form of the phase separation through NG mechanism is the sea-island type. 

It would be beneficial to have a convenient way of unambiguously determining nucleation induction times when seeking to understand the effects of varying composition and processing conditions on nucleation, and it is essential if the induction times are used in mathematical models such the Fisher-Tumbull equation (5). In the Fisher-Tumbull model, activation energies of nucleation are calculated from nucleation induction times. The usual assumption is that the experimental... 

SAXS measurements are normally performed in situ and therefore require access to synchrotron radiation [21, 23, 27, 46]. SAXS is probably one of the most used in situ techniques for the study of zeolite synthesis. In situ cells, similar to those for WAXS or XRD measurements, can easily cope with elevated synthesis temperatures and pressures. It has been used to determine the activation energy of nucleation, where two independent studies show that it is around 70-85 kj mol [47, 48]. Also, three distinct particle sizes were observed in the reaction mixtures, being primary units of approximately 2.8 nm, their aggregates, and the actual zeolite crystals [47]. Other mechanistic studies include the effect of the precursor molecule, the chemical nature of which appears to be important in... 

The rate of nucleation is dependent on the degree of supersaturation as described in section 2.4.1, and because this will always be larger for Form 1 it may be incorrectly assumed that Form I will always precipitate first. The true situation is somewhat more complicated because the critical size, activation energy and nucleation rate also depend on the solid state that is being formed [6]. It is quite feasible and a regular occurrence, that a less stable polymorph will have a higher rate of nucleation than a more stable form, as illustrated in figure 6. 

Heterogeneous nucleation, however, is in many cases the predominant formation process for crystals in natural waters. In a similar way as catalysts reduces the activation energy of chemical reaction, foreign solids may catalyze the nucleation process by reducing the energy barrier. Qualitatively, if the surface of the solid substrate matches well with the crystal, the interfacial energy between the two solids is smaller than the interfacial energy between the crystal and the solution, and nucleation may take place at a lower saturation ratio on a solid substrate surface than in solution. 

The temperature dependence of the reaction was studied, and the activation energy of the reaction was calculated to be approximately 100 kj mol The exponent n was found to lie in the range 1-2, which is consistent with a 2D diffusion controlled reaction mechanism with deceleratory nucleation. The rate of reaction increases markedly with the amount of water added to the LDH with very small amounts of water added, the deintercalation process does not go to completion. This effect is a result of the LiCl being leached into solution. An equilibrium exists between the LDH and gibbsite/LiCl in solution. The greater [LiCl], the further to the LDH side this lies. 

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 ... 

At a microscopic scale, a single coalescence event proceeds through the nucleation of a thermally activated hole that reaches a critical size, above which it becomes unstable and grows [29]. We shall term E(r) the energy cost for reaching a hole of size r. A maximum of E occurs at a critical size r, E r ) = Ea being the activation energy of the hole nucleation process (Fig. 5.2). 

Measurements were undertaken of the solubility of each phase in acid solutions, of the growth rate of gypsum crystals and the dissolution rate of hemihydrate. The growth rate depends on the square of the supersaturation and on temperature with an activation energy of 64 kJ/mol. The nucleation rate appears to vary linearly with supersaturation. 

The activation energy of decomposition of both irradiated and unirradiated ammonium perchlorate in the orthorhombic form below 240°C is ca. 18.0 kcal/mole according to Freeman. This seems to indicate that irradiation of ammonium perchlorate does not change the decomposition mechanism but provides many more nucleation sites. 

The activation energies of the nucleation and crystal growth can be determined from the crystallization curves at various temperatures with the same batch composition. Assuming that the formation of nuclei of a size stable enough not to redissolve but to grow into a crystal is an energetically activated process, and since the nucleation process is rate-deter-... 

When nucleation of a solid, S, occurs on a preexisting solid surface, Q, the area between the solid, Q, and the liquid, L, is reduced. However, a new surface is created between S and Q. See Figure 10.3. The net effect is a reduction of the activation energy for nucleation,... 

The decomposition follows rapid nucleation and contracting sphere kinetics with an activation energy of 150 kJ, somewhat higher than the enthalpy of decomposition.43"45 Densities are given in Table 2.43, thermal expansion coefficient in Table 2.44, and thermodynamic data in Tables 2.45 to 2.47. From data in Table 2.47, it is apparent that MgC03 is unstable above 700 K, in agreement with quoted experimental studies. 

For both series of metal oxides the apparent activation energies of the catalyzed (spillover) reduction reactions were found to be similar to those of the noncatalyzed reductions. Generally, the effect of the Pt was to increase the available reactive hydrogen and/or to increase the rate of the nucleation (pre-exponential factors). Thus, this catalysis increases the availability of H but does not ("classically ) decrease the activation energy. 

Finally, in classical nucleation theory there are additional terms in the equation for v, notably a second exponential term for the activation energy of transporting a molecule across the phase boundary. It is the inverse dependence of AG on AT2 that is the most strongly varying quantity and determines the nucleation rate, however, so in the interests of simplicity we ignore the other terms (for now). 

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