Nucleation activation energy

This order is indicative of the relative magnitudes of the nucleation activation energies that control the different nucleation mechanisms. 

Calculating Minimum Viable Nucleus Size (r ) and Nucleation Activation Energy ( G ) Since a spherical nucleus minimizes the amount of interfacial area per unit volume, it represents the most likely nucleus shape. The total free-energy change, AG t, involved in forming a spherical nucleus of radius r is therefore... 

Fig. 3. Curve ihustrating the activation energy (barrier) to nucleate a crystalline phase. The critical number of atoms needed to surmount the activation barrier of energy AG is n and takes time equal to the iacubation time. One atom beyond n and the crystahite is ia the growth regime.

Fig. 13. Plot of variations of activation energy ( /kJ mole"1) with water vapour pressure (PHjO/Torr) for dehydration of calcium sulphate. Data from Ball et al. [281,590, 591] who discuss the significance of these kinetic parameters. Dehydrations of CaS04 2 H2O, nucleation ( ), boundary (o) and diffusion (e) control Q-CaSC>4 5 H2O, diffusion control, below (X) and above (+) 415 K j3-CaS04 5 H20, diffusion control ( ).

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

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. 

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