Supersaturation vapor phase

Homogeneous nucleation occurs in a supersaturated vapor phase. The degree of supersaturation of a solute A in air at temperature T is defined by the saturation ratio... 

A cloud chamber operates on the principle that a supersaturated vapor phase is caused to condense into visible droplets by the passage of high energy particles. In a hypothetical experiment, an unknown particle induces the formation of 200 water droplets 2000 nm in diameter in a cloud chamber at 1 atm pressure and 25°C. The density and surface tension of water under the conditions of the experiment are 0.9971 g cm and 72.49 mN m respectively. Calculate the free energy increase caused by the passage of the particle. The surface tensions of a series of solutions of an unknown surfactant where found to be the following Concentration Concentration (mM) [Pg.175]

Figure 2.20 Nudeation of a droplet with size rfrom a supersaturated vapor phase. The free enthalpy for the formation of such a droplet is given by the two rhs terms of Equation 2.5 and are sketched together with the resulting free enthalpy of formation of such a droplet.

Because Fig. 7 could equally be used to describe a cap-shaped liquid drop nucleus on a solid surface, the same type of analysis will apply to the case of heterogeneous nucleation of a liquid from a supersaturated vapor phase. The only difference is that now the contact angle (as always, measured through the liquid) is equal to the complement (= 180 — 0) of that for a bubble, and thus the expression for the fraction of the whole sphere has its signs reversed ... 

A detailed theory of the spiral growth of crystals has been developed by Burton, Cabrera, Frank, Mott and Levine [4.33-4.41] who have considered the case of spiral growth from a supersaturated vapor phase. Later the theory was adapted to electrocrystahization by Vermilyea [4.44] and Fleischmann and Thirsk [4.48] and developed further and verified experimentally by Budevski, Bostanov, Staikov, Nanev et al. [4.28, 4.69-4.75] (see also the pioneering work of Kaischew, Budevski and MaUnovski [4.76]). 

Frequently, vapor-phase supersaturation is studied not by varying the vapor pressure P directly but rather by cooling the vapor and thus changing If To is the temperature at which the saturation pressure is equal to the actual pressure P, then at any temperature T, Pjf = x is given by... 

Condensation is the result of collisions between a gaseous molecule and an existing aerosol droplet when supersaturation exists. Condensation occurs at much lower values of supersaturation than nucleation. Thus, when particles already exist in sufficient quantities, condensation will be the dominant process occurring to relieve the supersaturated condition of the vapor-phase material. 

Here, /x, /xjs>, and are, respectively, the chemical potentials of the supersaturated vapor (or the ambient phase such as the solution phase), the saturated phase, and the solid phase. From this, a generalized driving force maybe expressed as... 

Crystals grow from their supersaturated vapor by the addition of vapor atoms at their free surfaces. In this process, the surface is subjected to an effective pressure due to the difference in free energy between the solid and vapor. The interface moves outward toward the vapor as it acts as a sink for the incoming flux of atoms. The mechanism by which atoms leave the vapor phase and eventually become permanently incorporated in the crystal is often relatively complex, and the kinetics of the process depends upon the type of surface involved (i.e., singular, vicinal,... 

It has been established experimentally that all thermodynamic properties of supersaturated phases (a supersaturated vapor, a liquid heated beyond the boiling point, or a liquid cooled down below the melting point) are in no way remarkable and fail to show any substantial deviations that would point to strong heterophase fluctuations. All the more, d, fortiori, it may hence be concluded that before the transition point and at the point itself the quantity J is negligibly small. 

There is no reason to expect that as the dimensions of a phase are reduced to the point where it contains a small number of molecules, its surface tension remains constant. This question has obvious relevance to important problems, such as condensation of droplets from supersaturated vapors. Although a number of authors have considered this problem, in these days of supercomputers, it is probably best handled by considering individual intermolecular interactions rather than a bulk property, such as surface tension. 

In the crystallization of melts, where relatively large degrees of supersaturation are attainable, nucleation and growth phenomena are more easily separated and studied experimentally than in crystallization from solution, which is characterized by rather narrow metastable regions. However, the basic concepts of nucleation are the same in both types of processes. In fact, much of the experimental verification of nucleation theory has come from studies of condensation and precipitation from the vapor phase. The highly publicized rainmaking experiments of several years ago made significant contributions (S6). 

Frenkel (F2) derived an important equation for the work of nucleogenesis in terms of p/p , the degree of supersaturation in the vapor phase... 

Several grams of the semi>fluorinated compound were placed in a windowed Jergeson Cell. The cell was placed in a horizontal position and the FnHm distributed on the window so that visual observations could easily be made. CO2 was then compressed into the windowed cell until the F Hm dissolved completely. In order to obtain a supersaturated liquid phase the vapor phase above the solution was vented. The progression from liquid to gel occurred in both of the compounds tested as shown in Figure 7. Unfortunately not enough of the FnHm was available to conduct PVT... 

The transitions from the supersaturated vapor to the drop and from the drop to the slab configurations represent barriers in the configuration space which are not removed by the multicanonical reweighting scheme. Hence, these shape transitions limit the applicability of reweighting methods in the study of phase equilibria. 

K. Binder and M. H. Kalos (1980) Critical clusters in a supersaturated vapor -theory and Monte-Carlo simulation. J. Stat. Phys. 22, pp. 363-396 H. Furukawa and K. Binder (1982) 2-phase equilibria and nucleation barriers near a critical-point. Phys. Rev. A 26, pp. 556-566... 

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