A scaling function of nucleation barrier based on the diffuse interface theory

Abstract

We present a phenomenological approach to determine the scaling function for the free energy barrier of fluid phase nucleation. The essential ingredients of our approach are (1) thermodynamic consistency imposed at the phase coexistence and at the mean-field spinodal, (2) the assumed quadratic functional form of the scaling function, and (3) the diffuse interface theory applied at the low supersaturation limit. The accuracy of the scaling function was tested for simple fluids, i.e., square-well fluids and truncated and shifted Lennard-Jones fluids. Despite the simplicity of the approach, the resulting scaling function is moderately successful in reproducing free energy barrier calculated by density functional theory for both vapor phase condensation and bubble nucleation, though the agreement is worse for the latter case.