Critical nucleus composition in a multicomponent system

The properties of a critical nucleus are derived using the capillarity theory in the framework of classical nucleation. An analytical solution for the composition of a critical nucleus is given for low supersaturation. The theory is valid for any multicomponent systems. It is found that the deviation in nucleus composition from the equilibrium tie-line is mainly due to the difference in the Hessian of the Gibbs energy of the phases and the magnitude of the deviation in composition from equilibrium is order of the supersaturation. Despite our analysis strictly holds for low supersaturation, this suggests strong deviations near the spinodal line.