THE SCALING OF NUCLEATION RATES

The homogeneous nucleation rate, J, for T much less than T(c) can be cast into a "corresponding states" form by exploiting scaled expressions for the vapor pressure and for the surface tension, sigma. In the vapor-to-liquid case with sigma = sigma-0[T(c) - T], the classical cluster energy of formation /kT = [16-pi/3].OMEGA-3[T(c)/T - 1]3/(ln S)2 = [x0/x]2, where OMEGA = sigma-0/[k n2/3] and n is liquid number density. [1] The OMEGA almost-equal-to 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 sigma and OMEGA. [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 ln J almost-equal-to const. - [X0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by In (GAMMA(c)), where GAMMA(c) is the inverse thermal wavelength cubed per second at T = T(c). The ln (GAMMA(c)) is almost-equal-to 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, tau-ln (n), is presented.