Reversible work of formation of an embryo of a new phase within a uniform macroscopic mother phase

A thermodynamically consistent formalism is derived for calculating the reversible work needed to form a small amount of a new phase (embryo) within a uniform macroscopic mother phase. The treatment goes beyond the classic work of Gibbs, who solved the problem for the particular case in which the embryo is in equilibrium with the mother phase, constituting a so-called critical nucleus. The formalism results in a new expression for the reversible work of embryo formation, the extrema conditions for which yield the correct conditions of equilibrium between the critical nucleus and the mother phase, as well as Gibbs' result for the reversible work needed to form the critical nucleus. The new expression for the work of embryo formation differs from the one commonly used in the nucleation literature. In order to extend the Gibbsian formalism to noncritical nuclei, it is necessary to introduce a constraint that prevents the free transfer of matter between the embryo and the mother phase. The present approach is valid in the limit in which curvature contributions to the interfacial energy can be neglected.