On the thermodynamic expansion of the nucleation free-energy barrier

Abstract

Mean field density functional theory is used to calculate the nucleation free-energy barrier height, W( *), in vapor-liquid nucleation as a function of the excess chemical potential Deltamu. Calculations are performed for a range of temperatures and for both Lennard-Jones and Yukawa interactions, scaled to give the same bulk properties. The leading terms in the expansion of W( *) in powers of Deltamu depend on the planar surface tension and the planar limit of the Tolman length, which are obtained from density functional calculations for planar interfaces. The first correction term to the large cluster (classical) limit is proportional to (Deltamu)(-1) and is shown to be significant. For the Lennard-Jones interaction, W( *) also includes a term proportional to ln(Deltamu). Once the leading terms are subtracted from W( *), the residual is almost independent of Deltamu. For the Yukawa fluid, values for this residual are compared to values found using a new formula for the rigidity constants and satisfactory agreement is found.