Homogeneous nucleation critical size

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 ... 

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... 

Figure 4.6 shows the dependence on r for both contributions with small values of r its square is predominant and AG increases with increasing r the nucleus will stop growing and (with homogeneous nucleation) it disappears. From a certain value of r, the critical nucleus size, rk, AG decreases upon growth the nucleus is then stable and continues growing. The value of rk can be easily calculated at rk ... 

Let us consider the thermodynamics of processes of the homogeneous nucleation of a new phase with the formation of fluid drops from the over saturated vapor as an example. While the chemical potential of the equihb rium substance vapor over spherical particles of its condensed phase is given by the Kelvin Thomson equation (5.2), only those drops that have the critical size r.. 

For the onset of homogeneous in addition to heterogeneous nucleation, the supersaturation ratio must be high. Walton compiled estimates of the critical size of cluster for several substances as shown in Table 8-1. Serious difficulties in making estimates of this type arise from the dearth of knowledge about the surface tension of soUds with extremely small particles and the assumption that the particles are spheres with equivalent surface sites. 

Nucleation is the science investigating the kinetics and thermodynamics of the formation of a new phase of a material at a size just sufficient to be stable. In addition to their role in new particle formation, nucleation processes are also critical to an accurate understanding of a number of other atmospheric events, including cloud droplet activation on CCN, ice formation, and the deliquescence/efflorescence of particles. In this section we focus on the nucleation of new particles through homogeneous nucleation, i.e., from gaseous precursors. The theoretical treatment of new particle nucleation, as well as field and laboratory measurements of nanoparticle formation, are addressed. 

There are several other points of view regarding the definition of the nucleus of zeolite. For example, it was suggested that some primary structural units of the framework, such as rings and basic cages, could be defined as the nucleus of zeolites and other microporous crystals. It was also proposed that the nucleus of zeolite could be defined as particles with critical size. These particles should be stable under crystallization conditions. Compared with the classical theory of nucleation from homogeneous solution, the theory developed by Pope could well explain the significant decrease of the free-energy barrier of nucleation for zeolites and other microporous compounds.[43] This... 

The particle size corresponding to the maximum in p/p, does not in general corre.spond to a critical size at which nucleation takes place. Development of a more complete theory of nucleation by ions will require the use of fluctuation theory, introduced at the end of this chapter for equilibrium systems and in Chapter 10 for homogeneous nucleation in supersaturated vapors. 

On physical grounds, loa = 0 because there is no toss of particles by growth from the upper end of the distribution. The term /,/ is the particle current (lowing into the lower end of the spectrum. When homogeneous niicleation takes place, this term is important. For vj = v, the critical particle size, /,j, is the particle current of homogeneous nucleation theory. Hence the dynamic equation for the number concentration is... 

The term (3 /g v dv)/dt represents the accumulation of material in the cluster size range below the critical particle size range u. In homogeneous nucleation theoiy (Chapter 10), this term vanishes there is a steady state for this portion of the distribution in which material is removed as fast as it is supplied. (This is actually true only as a quasi-steady approximation.) The second term on the right-hand side of (11.18) can be written as follows ... 

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