Free Energy of a Nonuniform System. III. Nucleation in a Two-Component Incompressible Fluid

Abstract

By finding the saddle point in the expression derived in Paper I (see reference 8) for the free energy of a nonuniform system, we have derived the properties of a critical nucleus in a two-component metastable fluid. At very low supersaturations, we find that the properties of the nucleus approach those predicted by the classical theory that assumes the nucleus to be homogeneous with an interfacial energy that does not vary with curvature. However, with increasing supersaturation, the following changes occur in the properties of the critical nucleus. (a) The work required for its formation becomes progressively less than that given by the classical theory, and approaches continuously to zero at the spinodal. (b) The interface with the exterior phase becomes more diffuse until eventually no part of the nucleus is even approximately homogeneous. (c) The composition at the center of the nucleus approaches that of the exterior phase. (d) The radius and excess concentration in the nucleus at first decrease, then pass through a minimum and become infinite again at the spinodal. These properties are deduced without resort to any specific solution model. In addition, they are evaluated for a regular solution to permit a quantitative comparison with the predictions of previous treatments.