Recapitulation of Classical Theory

The classical theory of homogeneous nucleation dates back to pioneering work by Volmer and Weber (1926), Farkas (1927), Becker and Doring (1935), Frenkel (1955), and Zeldovich (1942). The expression for the constrained equilibrium concentration of clusters (11.57) dates back to Frenkel. The classical theory is based on a blend of statistical and thermodynamic arguments and can be approached from a kinetic viewpoint (Section 11.1) or that of constrained equilibrium cluster distributions (Section 11.2). In either case, the defining crux of the classical thoery is reliance on the capillarity approximation wherein bulk thermodynamic properties are used for clusters of all sizes. 

To maintain the nucleation rate at a constant value J it is necessary that the saturation ratio of vapor be maintained at a constant value.3 Without outside reinforcement of the vapor concentration, the saturation ratio will eventually fall as a result of depletion of vapor molecules to form stable nuclei. The case in which the vapor concentration is augmented by a source of fresh vapor is referred to as nucleation with a continuously reinforced vapor. 

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 

3It is sometimes supposed that to maintain a constant S, im monomers reenter the system at the same rate that W-mers leave. The imax-mcrs are said to be broken up by Maxwell demons. 

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