Water homogeneous nucleation rate

Figure 9. Temperature ranges of states of stable, superheated and supercooled water at atmospheric pressure. Stationary homogeneous nucleation rate during crystallization (1) and boiling-up (2). Inverse isothermal compressibility for stable and metastable states of water (3) in the absence of the spinodal in a supercooled liquid (3 ) and in the case of its presence according to (3 % T - the temperature of the spinodal of a superheated liquid.

Indicated in Fig. 9 are temperature ranges of supercooled, stable and superheated water at atmospherie pressure. Ibidem one can see curves representing the temperature dependenee of the logarithm of the homogeneous nucleation rate for crystallization (curve 1) and boiling-up (curve 2). The maximum rate of formation of vapor nuclei is attained at the approach of the spinodal determined by condition (3). Fig. 9 also shows how the inverse isothermal eompressibility =-v(5p/5v) changes with temperature (curve 3). An arrow shows the temperature of the spinodal of superheated water. 

Wolk, J., Strey, R. Wyslouzil, B. E. (2004) Homogeneous Nucleation Rates of Water State of the Art. In Nucleation and Atmospheric Aerosols 2004 if International Conference, Conference Proceedings (Eds. M. Kasahara, M. Kulmala) 101-114... 

Let us evaluate the homogeneous nucleation rate for water as a function of the saturation ratio S. To do so, we use (11.47). Table 11.4 gives the nucleation rate at 293 K for saturation ratios ranging from 2 to 10. By comparing Tables 11.1 and 11.4, the effect of temperature on i can be seen also. We see that the nucleation rate of water varies over 70... 

TABLE 11.4 Homogeneous Nucleation Rate and Critical Cluster Size for Water at T = 293 K ... 

Wagner, P. E., and Strey, R. (1981) Homogeneous nucleation rates of water vapor measured in a two-piston expansion chamber, J. Phys. Chem. 85, 2694-2698. 

The classical homogeneous nucleation rate depends on two dimensionless parameters, / and 5. In the presence of a preexisting aerosol the flux depends, in addition, on a dimensionless aerosol surface area, A = Ap/N a ). Figure 10.14 shows A,/Ai as a function of / for 5 = 4 and i = 87 (water at 273 K). The expected decrease in /-mer concentration with increasing aerosol surface area is demonstrated. 

After repeating this procedure at various temperatures, we arrive at a curve that gives the homogeneous nucleation rate of water as a function of temperature in an interval between 236 and 238 K (see Fig. 7). Note that the nucleation rate changes in this small interval by almost three orders of magnitude. 

A simulated homogeneous nucleation rate of 6.6 x 10 cm s was determined from our calculations. The values of the free energy barrier and the rate of nucleation are in reasonable agreement with experimental and simulation values obtained for the homogeneous nucleation of water and urea. Current woik in our group is focused on the study of nucleation of ILs near surfaces and inside pores. 

Fig. 6. Homogeneous nucleation rate J of water vapor at 0°C as a function of the supersaturation S, as predicted by classical nucleation theory, Eq. (42). Note the very large dependence of the nucleation rate on the supersaturation.

Not surprisingly, the attempts to improve on Eq. (52) took the same direction as those to improve on the drop model itself. First Russell " discussed statistical-mechanical corrections to Eq. (52). His corrections were very similar to the corrections of Lothe and Pound to the drop model. Then various workers, " following the success of Burton s microscopic approach to calculating homogeneous nucleation rates (Section 3.8), started trying to calculate properties of water clusters containing ions from a purely microscopic point of view. We will not review all of this work here but will only summarize that of Briant and Burton, which appears to be the most extensive study to date. None of the workers on this problem have reached a point where they expect to be able reliably to calculate nucleation rates of on ions in the near future. Our principal purpose will be to see how bad Eq. (52) is and what are the prospects for improving on it. 

Miller, R.C., Anderson, R.J., Kassner, J.L., and Hagen, D.E. (1983) Homogeneous nucleation rate measurements for water over a wide range of temperature and nucleation rate, J. Chem. Phys. 78, 3204. 

Viisanen, Y., Strey, R., and Reiss, H. (1993) Homogeneous nucleation rates for water, J. Chem. Phys. 99, 4680-4692. 

Homogeneous nucleation may be described by assuming that critical-size nuclei will be formed from ideal vapor (water or air) at a rate, I, given by classical nucleation theory [4]. The equation is... 

Claverie et al. [325] have polymerized norbornene via ROMP using a conventional emulsion polymerization route. In this case the catalyst was water-soluble. Particle nucleation was found to be primarily via homogenous nuclea-tion, and each particle in the final latex was made up of an agglomeration of smaller particles. This is probably due to the fact that, unlike in free radical polymerization with water-soluble initiators, the catalyst never entered the polymer particle. Homogeneous nucleation can lead to a less controllable process than droplet nucleation (miniemulsion polymerization). This system would not work for less strained monomers, and so, in order to use a more active (and strongly hydrophobic) catalyst, Claverie employed a modified miniemulsion process. The hydrophobic catalyst was dissolved in toluene, and subsequently, a miniemulsion was created. Monomer was added to swell the toluene droplets. Reaction rates and monomer conversion were low, presumably because of the proximity of the catalyst to the aqueous phase due to the small droplet size. 

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