Using a new approach, Stauffer's expression for the rate of steady state binary nucleation and Trinkaus's expression for the steady state cluster concentrations f are derived directly from the diffusion equation that governs the evolution of f in composition space. The behavior of φ (≡f/N, where N is the equilibrium cluster concentration) is explored since this function provides a characterization of the nucleating binary system that, to lowest order, is independent of the actual composition of the mother phase. The angle ω that describes the direction of ▽ φ at the saddle point differs, in general, from the angle φ found by Stauffer for the direction of the nucleation current at the saddle point. These two angles are related by the formula: tan φ=r tan ω, where r is the ratio of impingement frequencies defined by Stauffer. In general, at the saddle point, ▽ φ also fails to lie in the direction of steepest descent on the free energy surface.
G. Wilemski, "Binary Nucleation Kinetics. IV. Directional Properties and Cluster Concentrations at the Saddle Point," Journal of Chemical Physics, vol. 110, no. 13, pp. 6451-6457, American Institute of Physics (AIP), Apr 1999.
The definitive version is available at http://dx.doi.org/10.1063/1.478547
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