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+6 delta(T))/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 delta(T) is the coefficient in the expression relating the surface tension of the droplet, gamma(R), to the planar surface tension, gamma(infinity), i.e., gamma(R)=gamma(infinity)(1-2 delta(T)/R). An expression for delta(T) is derived involving the pair and triplet correlation functions and the density profile of the planar surface. This complements the expression for delta(T) 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 delta(T) 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-gradient approximation. delta(T) is found to be negative for all conditions investigated; its magnitude depends on the potential used, and tends to increase with increasing temperature. However, the ratio delta(T)/w is found to be relatively insensitive to potential and to temperature, being between about -1.2 and -1.5 for the conditions investigated. The effect of using a weighted density approximation in place of the local density approximation for the hard-sphere part of the potential is estimated in a square-gradient approximation and found to be small. (C) 1999 American Institute of Physics. [S0021- 9606(99)51437-2].