Classical and generalized Gibbs' approaches and the work of critical cluster formation in nucleation theory

In the theoretical interpretation of the kinetics of first-order phase transitions, thermodynamic concepts developed long ago by Gibbs are widely employed giving some basic qualitative insights into these processes. However, from a quantitative point of view, the results of such analysis, based on the classical Gibbs approach and involving in addition the capillarity approximation, are often not satisfactory. Some progress can be reached here by the van der Waals and more advanced density functional methods of description of thermodynamically heterogeneous systems having, however, its limitations in application to the interpretation of experimental data as well. Moreover, both mentioned theories--Gibbs' and density functional approaches--lead to partly contradicting each other's results. As shown in preceding papers, by generalizing Gibbs' approach, existing deficiencies and internal contradictions of these two well-established theories can be removed and a new generally applicable tool for the interpretation of phase formation processes can be developed. In the present analysis, a comparative analysis of the basic assumptions and predictions of the classical and the generalized Gibbs approaches is given. It is shown, in particular, that--interpreted in terms of the generalized Gibbs approach--the critical cluster as determined via the classical Gibbs approach corresponds not to a saddle but to a ridge point of the appropriate thermodynamic potential hypersurface. By this reason, the classical Gibbs approach (involving the classical capillarity approximation) overestimates as a rule the work of critical cluster formation in nucleation theory and, in general, considerably.