Nucleation Reactions

In Table 4-2, we show both phase-boundaiy controlled and diffusion-controlled nucleation reactions as a function of both constant and zero rate of nucleation. 

At some distance close to the mineral surface, the saturation index (SI, IAP/Xsp) of pyromorphite must be greater than zero to allow local super saturation and precipitation. The question is whether this is a heterogeneous nucleation/ surface precipitation reaction or a dissolution homogeneous nucleation reaction. 

J.W. Cahn. The kinetics of grain boundary nucleated reactions. Acta Metall., 4(5) 449-459, 1956. 

Figure 7 The fraction polymerized material fas a function of the dimensionless time Ty according the kinetic Landau model discussed in the main text, with h the nucleation rate. Shown are results valid in the limit where the nucleation reaction is rate limiting, for a quench to X/Xp = 2 where in equilibrium f— 0.5. Depolymerization is much faster than polymerization.

Polymerization is influenced by the physical structure and phase of the monomer and polymer. It proceeds in the monomer, and the chemical configuration of the macromolecules formed depends on whether the monomer is a liquid, vapor, or solid at the moment of polymerization. The influence of structural phenomena is evident in the polymerization of acrylic monomer either as liquids or liquid crystals. Supermolecular structures are formed in solid- and liquid-state reactions during and simultaneously with polymerization. Structural effects can be studied by investigating the nucleation effect of the solid phase of the newly formed polymer as a nucleation reaction by itself and as nuclei for a specific supermolecular structure of a polymer. Structural effects are demonstrated also using macromo-lecular initiators which influence the polymerization kinetics and mechanism. 

Evidendy AG(nucl, r) can be considered as the affinity nud(r) of this nucleation reaction ... 

Quantum chemistry has also been applied to investigating whether other sulfur-containing molecules than sulfuric acid itself might participate in nucleation reactions. Some recent experimental evidence [71,72] indicates that the mixture of sulfuric acid and some intermediate products of the SO2 oxidation chain may promote nucleation even more effectively than sulfuric acid on its own. Similar... 

Barium sulfate precipitation has been reported to be controlled initially by nucleation reaction and, finally, by growth reaction. The growth kinetics was represented by the equation ... 

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. 

All of these equations allow us to calculate numbers and rate of creation of nuclei in mechanisms of crystal growth. We can also show the differences in both phase-boundary controlled and diffusion-controlled nucleation reactions as a function of both constant and zero rate of nucleation. This is given in Table 3-2, given on the next page. 

The nucleation reaction can be regarded as the phase transition of the monomer from solution to crystal. Then, the reaction rate of nucleation can be written in the Arrhenius form ... 

In the homogeneous solution, nucleation is accompanied by the formation of an interface between solution and crystal at the cost of an increase in the free energy. On the other hand, the monomer in crystal has a smaller free energy than that in solution if the solution is supersaturated (S > 1). Therefore, there are two opposite tendencies in the nucleation reaction. The first is the increase in the free energy caused by the formation of the interface, which is reflected in the first term on the right-hand side of Equation (6.2). This term is always positive. The other tendency is the decrease in the free energy caused by the formation of the crystal, which is shown in the second term, which is negative when 5 > 1. 

The induction of the high supersaturation and the initiation of burst nucleation are explained by the theory of homogeneous nucleation. As discussed in Section 6.3.1, the interfacial free energy acts as an energy barrier for the nucleation reaction. Because the... 

At the analysis of the experimental data it was discovered that the rate of the nanoparticles nucleation (W linearly depends on the concentrations of sodium hydroxide and on the concentration of the silver ions (Fig. 2 a, b). Such dependencies confirm the first reaction order for the silver nanoparticles nucleation reaction per hydroxide ions and per silver ions. 

Table 1. The kinetic parameters of nucleation reaction chain (RH +02) in pwlyethylene, 7 polypropylene and liquid hydrocarbons...

Homogeneous chemical nucleation is similar both to stepwise polymerization reactions in fluid media and to spinodal decomposition in mixtures. The characteristic differences with a binodal-type nucleation reaction are a strong sensitivity to the presence of impurities, the absence of an activation barrier and a concentration threshold, and no incubation time. 

The association of solvation molecules to an ion is called nucleation reactions. It is normally conducted under low vacuum conditions to facilitate ion-molecule interactions. 

This equation indicates that the dependence of the logarithm of the maximum undercooling, ATmax on the logarithm of the cooling rate, b, should be linear and the slope is equal to the nucleation reaction order, m. 

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