Comparison of Different Approaches to the Determination of the Work of Critical Cluster Formation

Abstract

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation—Gibbs' method, the van der Waals-Cahn and Hilliard, and a newly developed modified Gibbs' approach—is given. As a model system for comparison, regular solutions are chosen. In addition to the work of critical cluster formation, the composition of the critical clusters, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is found, in particular, that, for regular solutions, Tolman's equation cannot serve as a first approximation for the description of the curvature dependence of the surface tension even for large cluster sizes and an alternative formula is developed. It is shown that the latter two mentioned methods of determination of the work of critical cluster formation (the van der Waals-Cahn and Hilliard and the modified Gibbs' approach) 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 determination of the steady-state nucleation rates. The possible origin of such deviations is discussed and some further directions of analysis are anticipated.