Homogeneous nucleation embryos

From nucleation theory (see Section IX), one can estimate the expected rate of formation of critical-sized vapor embryos in a liquid as a function of temperature. This rate is a very strong function of temperature emd changes from a vanishingly low value a few degrees below the homogeneous nucleation temperature to a very large value at this temperature. 

Increasing the temperature or lowering the pressure on a superheated liquid will increase the probability of nucleation. Also, the presence of solid surfaces enhances the probability because it is often easier to form a critical-sized embryo at a solid-liquid interface than in the bulk of the liquid. Nucleation in the bulk is referred to as homogeneous nucleation whereas if the critical-sized embryo forms at a solid-liquid (or liquid-liquid) interface, it is termed heterogeneous nucleation. Normal boiling processes wherein heat transfer occurs through the container wall to the liquid always occur by heterogeneous nucleation. 

When a phase transition occurs from a pure single state and in the absence of wettable surfaces the embryogenesis of the new phase is referred to as homogeneous nucleation. What is commonly referred to as classical nucleation theory is based on the following physical picture. Density fluctuations in the pre-transitional state result in local domains with characteristics of the new phases. If these fluctuations produce an embryo which exceeds a critical size then this embryo will not be dissipated but will grow to macroscopic size in an open system. The concept is applied to very diverse phenomena ... 

A central assertion of homogeneous nucleation theory is that interfacial free energy costs induce a spherical symmetry in the phase embryo. However, these simulation studies indicate that inter molecular interactions may not permit the development of spherical symmetry when these interactions are strong and highly asymmetric. 

Homogeneous nucleation is very difficult because of the large interface energy involved. If there are already interfaces in the system, an embryo may grow from... 

Homogeneous nucleation is thought to take place in three steps. First, the vapor must be supersaturated to an extent that condensation will take place second, small clusters of molecules or embryos must form third, the vapor must condense on these embryos so that the embryo grows into a full-fledged nucleus which subsequently becomes a droplet. For heterogeneous nucleation only two steps take place, the first and third. 

Currently there is no one definitive theory that deals with nucleation processes in the presence of foreign substrate. The classical approach, as formulated by Fletcher (1960), is basically similar to the case of homogeneous nucleation, except for the introduction of a new parameter, y, which is a measure of the disparity between the solid embryo and the foreign nucleating substance. 

To understand how catalytic impurities may work, it will be useful to consult Section 10.6.1 first. In Figure 14.5a an embryo is shown that may lead to homogeneous nucleation, if it is small enough. If now a surface of a material k is present, an embryo may be formed on that surface, as depicted in Figure 14.5b, provided that cos 6 is finite. Its value depends on the three interfacial tensions (specific interfacial free energies) according to the Young equation (10.10), which can be written as... 

FIGURE 14.5 Homogeneous and heterogeneous nucleation. Embryos (radius r) of phase p formed from phase a (a) in the absence of foreign particles, and (b) at the surface of foreign particles of material k1 or k2 in frames 2-5, the contact angle 0 = 45 degrees. 

Nucleation of gas bubbles is notoriously difficult, and the following calculation may explain it. Assume that a gas embryo of 2 nm radius is formed in a liquid at atmospheric pressure. The interfacial tension will generally be about 0.07N-m 1. The Laplace pressure in the embryo will then be about 2x0.07/2-10 9 = 7-107 Pa, which equals 700 bar. The supersaturation ratio of the gas should then be about 700 for such a small bubble to survive, and that is very unlikely to be the case. In a beer bottle the pressure is a few bar, in an aerosol can with N20 about 7 bar. Moreover, the number of gas molecules inside the embryo would be about 560 (try to make the calculation), more than could possibly associate by chance. Homogeneous nucleation can therefore not occur. By similar reasoning, it can be derived that heterogeneous nucleation on a surface, as depicted in Figure 14.5b, frames 1 and 2, is not possible either, even if 6 is quite small. 

The Kinetic Limit. To initiate homogeneous nucleation, a vapor embryo is required that has the critical radius r. In principle, the formation of just one such embryo would be sufficient to initiate the nucleation process, but in practice it is found that conditions must be such that J, the number of vapor embryos formed in a unit volume per unit time, has a high value (typically J > 1012). Carey [4] derives the following expression for J ... 

Very slowly precipitating material may be due to homogeneous nucleation. For this case is expected to be in the order of 100 hrs. Heterogeneous nucleation will be similar to homogeneous nucleation, except that the energy levels in fig. 10 are lower. This leads either to more embryos of critical size, to smaller critical sizes, or to both. 

The main concern of the classical homogeneous nucleation theory has been a thermodynamic description of the initial stage of nucleation from embryo to nucleus with a little larger size over the critical one (Seinfeld 1986, Pruppacher and Klett 1997, Seinfeld and Pandis 1998, Kulmala et al. 2000). The change of the free enthalpy of the cluster is at first positive because the decrease of entropy is initially larger (regular structure formation) than the decrease in enthalpy ... 

Similar to the homogeneous nucleation, there is a threshold temperature, at which the number of embryos increases rapidly. This is referred to as the heterogeneous nucleation temperature. Equatimi 10.18 represents the number of embryos formed close to an interface. It indicates that the threshold temperature depends on the contact angle of the liquid and sohd wall ... 

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