Scaling of Nucleation Rates
The homogeneous nucleation rate, J, for T ≪ Tc can be cast into a "corresponding states" form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ0[Tc-T], the classical cluster energy of formation /kT = [16π/3]·Ω3[Tc/T-1]3/(ln S)2 ≡ [x0/x]2, where Ω ≡ σ0[k ñ2/3] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), where Γc is the inverse thermal wavelength cubed per second at T = Tc. The ln (Γc) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n, the discrete integer behavior of n, and a configurational entropy term, τ ln (n), is presented.
B. N. Hale, "Scaling of Nucleation Rates," Metallurgical Transactions. A: Physical Metallurgy and Materials Science, vol. 23 A, no. 7, pp. 1863-1868, Springer Verlag, Jul 1992.
The definitive version is available at https://doi.org/10.1007/BF02647536
Keywords and Phrases
Mathematical Models; Phase Transitions; Surface Tension; Thermal Effects; Vapor Pressure; Cluster Energy; Homogeneous Nucleation Rates; Scaled Nucleation Model; Crystal Growth
International Standard Serial Number (ISSN)
Article - Journal
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