Nucleation from vapor

Dunning, W.I (1955). Theory of crystal nucleation from vapor, liquid, and solid... 

External electric fields affect the freezing of water. For example, the rate of ice nucleation from vapor phase substantially increases from the normal growth rate in electric fields above 10" Vm [18]. 

The data reported in the Porteous-Reid study coupled with those of other investigators strengthened the hypothesis that hydrocarbon-water RPTs could originate from the rapid nucleation of vapor when a liquid was heated well above its expected boiling point. 

This brief commentary on superheated liquids has indicated that they are readily formed if one prevents heterogeneous nucleation of vapor embryos. Also, there is a limit to the degree of superheat for any given liquid, pure or a mixture. This limit may be estimated either from thermodynamic stability theory or from an analysis of the dynamics of the formation of critical-sized vapor embryos. Both approaches yield very similar predictions although the physical interpretation of the results from both differ considerably. 

Absorption resonances resulting from excitation of surface modes are accompanied by scattering resonances at approximately the same frequencies this was pointed out following (12.26). In most experiments transmission is measured to determine extinction, which is nearly equal to absorption for sufficiently small particles. However, surface mode resonances have been observed in spectra of light scattered at 90° by very small particles of silver, copper, and gold produced by nucleation of vapor in an inert gas stream (Eversole and Broida, 1977). The scattering resonance peak was at 3670 A, near the expected position of the Frohlich mode, for the smallest silver particles. Although peak positions were predictable, differences in widths and shapes of the bands were concluded to be the result of nonsphericity. 

With such low concentrations of components available to form critical nuclei, hydrate formation seems unlikely in the bulk phases. However, at an interface where higher concentrations exist through adsorption (particularly at the vapor-liquid interface where both phases appear in abundance) cluster growth to a supercritical size is a more likely event. High mixing rates may cause interfacial gas + liquid + crystal structures to be dispersed within the liquid, giving the appearance of bulk nucleation from a surface effect. 

Nucleation from the vapor phase is not a determining factor in the relative kinetics of formation of either graphite or diamond on a substrate. Which of these two competing stmctures wins out depends on the kinetics of growth. 

For the initial formation of a solid phase on a substrate surface from vapor precursors through heterogeneous nucleation, as is schematically illustrated in Figure 20.2, the critical nucleus size, r, and the corresponding energy barrier, AG, are given by the following equations ... 

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

In thermodynamic theory of heterogeneous nucleation of solid from vapor,P a nucleus on a substrate is considered to be cap-shaped with a contact angle to the substrate. Young s equation dictates the relationship among the surface and interfacial energies as ... 

The factor C is a statistical measure of the rate of formation of embryos that reach the critical size. It is proportional to the concentration of the individual particles and to the rate of collision of these particles with an embryo of the critical size required to form a stable nuclus. Its value for nucleation from solutions is not known. From analogy with nucleation of water drops from su r aturated water vapor, it is of the order of 10 nuclei/cm -s. Its accurate value is not important, because the kinetics of nucleation is dominated by the In a term in the exponent. 

Delale, C. F., and Meier, G. E. A. (1993) A semiphenomenological droplet model of homogeneous nucleation from the vapor phase, J. Chem. Phys. 98, 9850-9858. 

Girshick, S. L., and Chiu, C.-P. (1990) Kinetic nucleation theory A new expression for the rate of homogeneous nucleation from an ideal supersaturated vapor, J. Chem. Phys. 93, 1273-1277. 

Recent developments in the application of molecular dynamics promise a resolution of many questions in nucleation theory. A review of simulation methods in nucleation theory and of their results is given in [2.39]. Consequently, a survey will not be undertaken here. However, some of the results of SCHIEVE and co-workers [2.40-42] will be discussed here as they throw light on several questions of importance in terms of modelling aerosol growth from vapor condensation. 

Fig.2.4. Rate processes in evolution of sulfuric acid aerosol nucleated from sulfuric acid vapor at low humidity. Monomer concentration g/ccx2E-14, 0 total rate g/cc-s 2E-16, + input rate, g/cc-s X 2E-16, nucleation rate g/cc-s X 2E-18, ...

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