Nonadditivity contribution to the surface energy of a simple liquid

The nonadditivity contribution to the surface energy (excess internal energy per unit area of the surface) is derived from statistical mechanics as an integral involving intermolecular potentials and molecular distribution functions. Using Fowler's step-function density profile for the vapor-liquid system, Kirkwood's superposition approximation for the triplet-correlation function, Axilrod-Teller's triple-dipole potential for the three-body interaction potential $u_{123}$, and neutron-diffraction data of Yarnell et al. for the radial distribution function, one can calculate a sextuple integral to obtain the three-body correction $U_3^{\mathrm{}\left(s\right)\mathrm{}}$, which is about -2.4±0.1 erg/${\mathrm{cm}}^2$ for liquid Ar at 85°K (near the triple point). This contribution is opposite in sign to the correction needed to improve the two-body contribution $U_2^{\mathrm{}\left(s\right)\mathrm{}}$ obtained from Fowler's formula with the same $g\left(r\right)\mathrm{}$ data and Barker's realistic potential. Thus the combined value 23.9 erg/${\mathrm{cm}}^2$ of $U_2^{\mathrm{}\left(s\right)\mathrm{}}$ and $U_3^{\mathrm{}\left(s\right)\mathrm{}}$ is in worse disagreement with the experimental value of 34.9 erg/${\mathrm{cm}}^2$ than $U_2^{\mathrm{}\left(s\right)\mathrm{}}$ itself.