Curvature dependence of the interfacial tension in binary nucleation

The curvature dependence of the interfacial tension in binary nucleation was formulated by employing Tolman’s [J. Chem. Phys. 16, 758 (1948)] idea for the variation of state and the thermodynamics of inhomogeneous systems due to Cahn and Hilliard [J. Chem. Phys. 28, 258 (1958); 30, 1121 (1959); 31, 688 (1959)] and Hart [Phys. Rev. 113, 412 (1959)]. To investigate the numerical significance of the curvature dependence, the inhomogeneous regular solution model due to Cahn and Hilliard was employed. The interfacial tension was found to decrease with curvature and to be about 20% smaller than the value of the flat interface at a radius of 3 or 6 intermolecular distance for T=0.5$T_c$ or 0.8656$T_c$, respectively. The reversible work to form a critical nucleus predicted by the present theory is significantly lower than that obtained by neglecting the curvature dependence of the interfacial tension. Thus, neglect of the curvature dependence may severely underestimate the nucleation rate.