On the cluster compositions in the classical binary nucleation theory

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Abstract
The classical binary nucleation theory is considered. It is shown that as a consequence of the Gibbs–Duhem equation and the Gibbs adsorption isotherm, an equation emerges which can be used together with the interior (bulk) mole fraction and radius of the critical cluster given by the theory to calculate the total numbers of molecules of both species in the cluster. Accordingly the overall (average) composition of the critical cluster is determined. Furthermore, it is noted that it is possible to use this equation to determine the interior (bulk) mole fraction of any sufficiently large spherical cluster with known total numbers of molecules, which allows the construction of a free energy surface within the framework of the classical nucleation theory. However, numerical calculations for the water–ethanol system result in strange predictions at some typical experimental conditions. Possible reasons for the unsuccessful predictions by the classical theory are discussed.