Comparison of different approaches to the determination of the work of critical cluster formation

A comparative analysis of the results of determination of the work of criti cal cluster formation in nucleation theory for three different methods of e valuation-Gibbs' method, the van der Waals-Cahn and Hilliard, and a newly d eveloped modified Gibbs' approach-is given. As a model system for compariso n, regular solutions are chosen. In addition to the work of critical cluste r formation, the composition of the critical clusters, their characteristic sizes and the values of the surface tension are determined in dependence o n the initial supersaturation in the system or, equivalently, on the size o f the critical clusters. It is found, in particular, that, for regular solu tions, Tolman's equation cannot serve as a first approximation for the desc ription of the curvature dependence of the surface tension even for large c luster sizes and an alternative formula is developed. It is shown that the latter two mentioned methods of determination of the work of critical clust er formation (the van der Waals-Cahn and Hilliard and the modified Gibbs' a pproach) lead-at least for the model system considered-to qualitatively and partly quantitatively equivalent results. Nevertheless, differences remain which may lead to quantitative deviations when applied to the determinatio n of the steady-state nucleation rates. The possible origin of such deviati ons is discussed and some further directions of analysis are anticipated. ( C) 2000 Academic Press.