Reconciling Gibbs and van der Waals: A new approach to nucleation theory

A new approach for the determination of the work of critical cluster formation in the description of nucleation processes is developed. For an illustration, the method is applied here to phase formation processes in solid and liquid solutions. However, it is applicable quite generally and not restricted to this particular important case. The present approach represents a generalization of the classical Gibbs' method. It is-like the classical method-conceptionally simple and directly applicable to real systems, but avoids its shortcomings. Central to our method is the formulation and application of a new well-founded principle we denote as generalized Ostwald's rule in nucleation. The method allows the determination of the work of critical cluster formation provided the bulk properties and the macroscopic values of the surface tension (at planar interfaces) for the possible different states of the system under consideration are known. Similarly to the van der Waals-Cahn-Hilliard and density functional calculations in the determination of the work of critical cluster formation, the newly developed method reproduces the results of the classical Gibbs' nucleation theory (involving the capillarity approximation) for small values of the supersaturation. However, in contrast to the classical and in agreement with van der Waals-type methods, for initial states approaching the spinodal curve, the work of critical cluster formation, determined via the newly developed approach, is shown to tend to zero. As an immediate additional consequence, the method gives a more accurate description of the experimental results on nucleation rates also in the intermediate ranges of the initial supersaturation. Some further implications for the theoretical interpretation of nucleation-growth experiments are discussed as well. (C) 2000 American Institute of Physics. [S0021-9606(00)50307-9].