Statistical prefactor and nucleation rate near and out of the critical point

The nucleation rate derived in the classical theory contains at least one undetermined parameter, which may be expressed in terms of the Langer first-principles theory. But the uncertainties in the accounting for fluctuation modes, which are either absorbed into the free energy of a critical cluster or not, result in different evaluations of the statistical prefactor and nucleation rate. We get the scaling approximations of the nucleation rate for the vapour condensation both near and out of the critical range. The results obtained deserve the experimental verification to resolve the theoretical uncertainty. PACS numbers: 64.60.Qb, 05.70.Fh, 64.60.Fr, 64.70.Fx Typeset using REVTEX Alexander von Humboldt Foundation Fellow 1 The homogeneous nucleation occurred in metastable states has been area of much theoretical and experimental activity since time of Maxwell and Van der Waals. The classical nucleation theory was worked out about 60 years ago mainly by Volmer, Becker and Döring, Zeldovich, and Frenkel [1–4]. Under the treatment of relaxation of the initially homogeneous metastable state as a kinetic process, triggered by the creation of spherical clusters of the new, stable, phase as thermal fluctuations in the metastable phase, the classical theory provides us the fundamental nucleation rate I = I0 exp ( −c kBT )