Response to ‘ ‘ Comment on ‘ Reversible work of formation of an embryo of a new phase within a uniform macroscopic mother phase ’ ’ ’ † J . Chem . Phys . 111 , 3769

Kusaka correctly points out that his Eqs. ~1! @Eq. ~39! in Ref. 1# and ~2! @Eq. ~43! in Ref. 2# are equivalent. Hence, the statement in Ref. 2 that Nishioka and Kusaka ‘‘arrived at a different expression for the work of embryo formation’’ is incorrect. Our misunderstanding stemmed from a failure to properly translate the notation of Ref. 1 into our own language. At the outset, however, we point out that nowhere in Ref. 2 is it stated that Nishioka and Kusaka’s result was wrong. Nevertheless, Kusaka’s Comment contains several incorrect statements that we wish to clarify in this Reply. Reference 1 applies exclusively to liquid clusters formed in a vapor. Because of the large difference in density between a liquid and a vapor, the authors of Ref. 1 assumed that the molecules in the interfacial region between the liquid cluster and the mother vapor can be regarded as belonging to the cluster. Furthermore, they assumed that the cluster establishes an internal equilibrium in a time scale much shorter than that required for it to exchange molecules with the surrounding vapor, and hence they regard the noncritical liquid cluster to be in partial equilibrium with the surrounding vapor, an equilibrium established under the internal constraint that the vapor and the cluster do not exchange molecules and each subsystem is in internal equilibrium. Clearly, however, time scales and diffusion are not thermodynamic considerations. In a true thermodynamic derivation, time can play no role. This is the central point behind the introduction of external constraints in Ref. 2. The Gibbsian thermodynamics of interfaces applies to equilibrium situations exclusively. This equilibrium can be an unstable one ~e.g., a liquid drop in contact with a vapor such that the vapor phase pressure equals the drop’s vapor pressure!, but it is an equilibrium. Because of this, matter is freely transferable between the droplet and the bulk vapor. An embryo that is not a critical nucleus is not in equilibrium with the surrounding metastable phase ~e.g., a droplet that is surrounded by a vapor in which the pressure of the vapor does not equal the vapor pressure of the droplet!. In this case, matter transfers irreversibly across the interface. Hence, in order to apply thermodynamic reasoning to this situation, we require the imposition of a constraint that prevents the irreversible transfer of matter between the bulk phase and the noncritical embryo. This is what we do in Ref. 2.