The scaling of nucleation rates

Abstract

The homogeneous nucleation rate,J, forT → T c can be cast into a “corresponding states” form by exploiting scaled expressions for the vapor pressure and for the surface tension, δ. In the vapor-to-liquid case with δ= δ0[T c -T], the classical cluster energy of formation /kT = [16π/3] • Ώ3 [T c -1]3/(lnS)2 = [x0/x]2, where Ώ ≡ δ0/[k n2/3] and n is liquid number density. [1] The Ώ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications ofσ and Ώ.[2]) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data.[3,4] In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with lnJ ≈ const. -[x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), whereT c is the inverse thermal wavelength cubed per second atT =T c . 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 smalln, the discrete integer behavior ofn, and a configurational entropy term, τ ln (n), is presented.