On the relation between nucleation work, nucleus size, and nucleation rate

A general thermodynamic relation is proved to exist between the nucleation work and the nucleus size regardless of the model for the excess free energy of the nucleus. When this energy is supersaturation independent, the relation reads as follows: the number of atoms (or molecules) in the nucleus equals the derivative with minus sign of the nucleation work with respect to the supersaturation Δμ. It is shown that, experimentally, a reliable determination of the nucleus size is possible when data for the stationary nucleation rate J are plotted in coordinates kT ln J vs. Δμ (k is the Boltzmann constant and T is the absolute temperature). The slope of such an experimental curve gives information about the nucleus size independently of the kind of nucleation: classical or atomistic, homogeneous or heterogeneous, three dimensional or two dimensional, etc.