Nucleation heterogeneous theory

When the vapor phase is generated at a solid interface rather than in the bulk of the liquid, the process is known as heterogeneous nucleation. Heterogeneous nucleation theories on smooth surfaces yield similar expression to Eq. 8.6-1 for J, with modified groupings A and B that account for the contribution of geometry and energy of the solid surface (22). 

Formation of metal clusters by gas aggregation, in which metal atoms are evaporated or sputtered into a cooled inert gas flow at relatively high pressure, has been well established in last decade. By repeated collisions with the carrier gas, the supersaturated metal vapor nucleates and forms clusters. The mechanism of cluster formation can be explained with homogeneous and heterogeneous nucleation theories. The gas aggregation methods have been applied extensively to produce small clusters of metals such as zinc, copper, silver etc. [23-26]. In some cases this method was used in combination with a mass filter such as a quadruple or a time-of-flight spectrometer [27, 28], The metal vapor for cluster source can be produced by either thermal evaporation [23-28] or sputter discharge [22, 29]. 

This article is organized as follows. We begin with a review of classical homogeneous and heterogeneous nucleation theory in Section II, and then turn in Section III to calculations based on this theory (in particular, to theories for the liquid-solid surface free energy). Section IV contains an account of experimental measurements of nucleation for a variety of systems and relates the results to the theories of the previous section. Finally, Section V presents some steps that have been taken recently to move beyond classical nucleation theory, and examines problems of interest for future theoretical and experimental research. 

Marasll N, Hunt JD (1998) The use of measured values of surface energies to test heterogeneous nucleation theory. J Crystal Growth 191 558-562... 

Nucleation of an ordered phase is often favored when there is an available surface of foreign matter. The free energy of germ formation is then reduced by a favorable interaction of the critical germ with the foreign surface. Classical heterogeneous nucleation theory provides the surface nucleation rate as follows ... 

Finally, heterogeneous nucleation theory can be applied (79), and it affords an independent way of estimating the particle size, particularly difficult if not impossible to measure close to atomic dispersion by conventional methods because of the low metal content of such model catalysts. 

These phenonena can be explained by the plication of heterogeneous nucleation theory (24,25). Silica powder, as an "extraneous solid" can catalyse the nucleaticn process. For the pure polymer, the steady-state nucleaticm rate per unit volume (18), Si is expressed by ... 

A model of a porous lead dioxide electrode has been described and used to investigate lead-sulfate nucleation and growth during discharge by Bemardi [61]. A nucle-ation rate expression that is based on classical, heterogeneous nucleation theory is outlined ... 

The classical theory of nucleation was developed by Volmer and Weber, and Becker and Doring" for the condensation of a pure vapour to form a liquid. The subsequent theory-- for the liquid-solid transformation was based on this earlier work. The theory considered homogeneous nucleation, ia the formation of one phase by the aggregation of components of another phase without change of composition and without being influenced ly impurities or external surfaces. Impurity particles and external surfaces are taken into account in heterogeneous nucleation theory (Section 2.3). Modifications to the classical theory are necessary to allow for the effects of compositional changes. 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

Thermodynamic and mechanical equilibrium on a curved vapor-liquid interface requires a certain degree of superheat in order to maintain a given curvature. Characteristics of homogeneous and heterogeneous nucleation can be estimated in the frame of classical theory of kinetics of nucleation (Volmer and Weber 1926 Earkas 1927 Becker and Doring 1935 Zel dovich 1943). The vapor temperature in the bubble Ts.b can be computed from equations (Bankoff and Flaute 1957 Cole 1974 Blander and Katz 1975 Li and Cheng 2004) for homogeneous nucleation in superheated liquids... 

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. 

Experimental internal nucleation rates are due not to homogeneous nucleation but to heterogeneous nucleation (which would require a different theory) instead. The argument is that it is extremely difficult to... 

Bubble Nucleation in a Liquid Phase The above classical nucleation theory can be easily extended to melt nucleation in another melt. It can also be extended to melt nucleation in a crystal but with one exception. Crystal grains are usually small with surfaces or grain boundaries. Melt nucleation in crystals most likely starts on the surface or grain boundaries, which is similar to heterogeneous nucleation discussed below. Homogeneous nucleation of bubbles in a melt can be treated similarly using the above procedures. Because of special property of gases, the equations are different from those for the nucleation of a condensed phase, and are hence summarized below for convenience. 

Figure 19.13 demonstrates that for a given value of ip, AQc decreases as the dimensionality of the heterogeneous site decreases. However, the number of sites available for nucleation also decreases as the dimensionality decreases. Thus, the kinetic equations for nucleation theory must be used to predict which mechanism will dominate. To accomplish this, some assumptions about the polycrystalline microstructure must be made. Let ... 

To determine the relationship between hydrate nucleation (requiring three phases) and the more usual type (two-phase nucleation) consider the theory of homogeneous and heterogeneous nucleation in crystallization, as reviewed by Mullin (1993, p. 172) and Kashchiev and Firoozabadi (2002b), from which much of the below discussion has been excerpted. 

The kinetics of nucleation of one-component gas hydrates in aqueous solution have been analyzed by Kashchiev and Firoozabadi (2002b). Expressions were derived for the stationary rate of hydrate nucleation,./, for heterogeneous nucleation at the solution-gas interface or on solid substrates, and also for the special case of homogeneous nucleation. Kashchiev and Firoozabadi s work on the kinetics of hydrate nucleation provides a detailed examination of the mechanisms and kinetic expressions for hydrate nucleation, which are based on classical nucleation theory. Kashchiev and Firoozabadi s (2002b) work is only briefly summarized here, and for more details the reader is referred to the original references. 

As mentioned earlier, this paper will stress homogeneous nucleation not only because of its applicability to a broad range of monomers and to systems both aqueous and organic, but also because several features are applicable to systems undergoing heterogeneous nucleation and which were not considered in the original Smith-Ewart theory. To begin with, a brief historical review is in order. 

Below S = 1000, the nucleation rate was essentially constant at 10 cm sec . Mullin and Gaska [8] have also verified this theory experimentally with the nucleation of K2SO4 from aqueous solution. The low S data corresponded to heterogeneous nucleation, which will be discussed later in this chapter. 

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