Classical nucleation theory revisited.

A field-theoretic derivation of the correction to classical nucleation theory due to translational invariance of a nucleating droplet is proposed. The correction is derived from a functional integral representation of the classical partition function, where the two-body interaction potential is decomposed into a short-range repulsive part and a long-range attractive part. The functional integral is evaluated in the mean-field approximation, and the spatially nonuniform density solution of the Euler-Lagrange equation is approximated by a physically motivated hyperbolic tangent profile. Leading-order effects of the nonlocal attractive interaction are highlighted through a density-gradient expansion. The capillarity approximation to the droplet free energy of formation is obtained by performing a density resummation of the uniform state, low-density expansion of the Helmholtz free energy density, and by retaining the leading-order density-gradient term. The resulting translational-invariance correction modifies the droplet free energy by an additive mixing-entropy term. The additional contribution, which contains a logarithmic correction to the surface-energy term, defines a scaling volume that depends on the range of the coarse-grained attractive potential.