Nucleation Zeldovich factor

Equation 19.17 may be interpreted in a simple way. If the equilibrium concentration of critical clusters of size Afc were present, and if every critical cluster that grew beyond size Mc continued to grow without decaying back to a smaller size, the nucleation rate would be equal to J = (3CNexp[-AQc/(kT)]. However, the actual concentration of clusters of size Mc is smaller than the equilibrium concentration, and many supercritical clusters decay back to smaller sizes. The actual nucleation rate is therefore smaller and is given by Eq. 19.17, where the first term (Z) corrects for these effects. This dimensionless term is often called the Zeldovich factor and has a magnitude typically near 10-1. 

The time lapse ro.s can be determined at different amplitudes of the nucleation pulse, so that the/- 7 dependence is easily found. Fig. 5.8 shows a In /vs. 1/171 plot obtained in this way. The relation is linear in this representation, as expected from eq. (5.2). The contributions of the overvoltage dependence of the Zeldovich factor Tand the attachment fi-equency < att,ycrit obviously small enough to produce an appreciable effect on the general In/- 1/171 relation. From the slope, the specific edge... 

The Zeldovich factor generally has a value ranging from 0.1 to 1 and thus has only a slight effect on the rate of nucleation. 

The Zeldovich factor represents a thermodynamic correction parameter and takes into account the fact that a cluster having reached the critical size does not necessarily nucleate, but could fluctuate in size back into the sub-critical region (Schmelzer 2003). The Zeldovich factor for nncleation rate on a polymeric membrane is a function of porosity and contact angle. According to Equation 10.1 ... 

Table 10.3 summarizes the form of the Zeldovich factor for different cases homogeneous nucleation (e = 0, 0 = 180°), heterogeneous nucleation on a nonporous support (e = 0), and heterogeneous nucleation on a microporous membrane. 

Expressions of the Zeldovich Factor (z) for Nucleation on Different Membrane Surfaces... 

FIGURE 10.16 Zeldovich factor for heterogeneous and homogeneous nucleation versus contact angle at different membrane porosity. (Adapted from Journal of Crystal Growth, 310, Curcio, E., Di Profio, G., and Drioli, E., Prohahilistic aspects of polymorph selection by heterogeneous nucleation on microporous hydrophobic membrane surfaces, 5364-5369, Copyright (2008), with permission from Elsevier.)... 

Ter Horst, J.H. and Jansens, P.J. 2005. Nucleus size and Zeldovich factor in two-dimensional nucleation at the Kossel crystal (0 0 1) surface. Surf. Sci. 574 77-88. 

Doring [4] provided an analytical solution considering a system of constant composition in which supercritical clusters are reintroduced into the system as the equivalent amount of discrete units. A steady state expression of the nucleation rate follows, Jg = Zam Cm y where am is the net probability of addition of an atom per unit time from a critical cluster of size m, and Cm, the equilibrium concentration of critical clusters, is related to the monomer concentration through the Bolztmann equation, Cm = Cl exp(—AGm /kT) and the nondimensional Zeldovich factor Z, which accounts for the fact that the steady state concentration at m is only 1 /2 of the concentration at equilibrium, and that critical clusters may still decay [5]. 

In the equation for the nucleation rate J the classical expression was supplemented by the non-equilibrium factor Z, introduced by Zeldovich, and by the so-called non-isothermal factor 0 (cf. [21 ) ... 

---