First-order correction to classical nucleation theory: A density functional approach

It is shown that the classical expression for the change in grand potential of a system on formation of a cluster of radius R is modified by a factor [1−(2w+6δT)/R], to first order in 1/R, where w is a correction due to the nonzero compressibilities of liquid and vapor (near the triple point, w is approximately equal to the product of liquid compressibility and surface tension), and δT is the coefficient in the expression relating the surface tension of the droplet, γ(R), to the planar surface tension, γ∞, i.e., γ(R)=γ∞(1−2δT/R). An expression for δT is derived involving the pair and triplet correlation functions and the density profile of the planar surface. This complements the expression for δT involving the pair distribution function derived by Blokhuis and Bedeaux; the equivalence of the two expressions in the low density limit is demonstrated. Calculations of δT and w are performed using mean-field density functional theory for the Yukawa potential and an r−6 potential, as well as using the square-g...