Nonadditivity contribution to the surface tension of simple liquids

Abstract

The Kirkwood-Buff formula has been extended to include three-body interactions by differentiation of the partition function with respect to the area. Assuming a step-function density profile (Fowler) and the superposition approximation (Kirkwood) for the triplet correlation function, the nonadditivity correction ${\ensuremath{\gamma}}_{3}$ to the surface tension is expressed as a septuple integral whose integrand contains the three-body interaction potential ${u}_{123}$ and the radial distribution function of the liquid $g(r)$. We use the triple-dipole interaction (Axilrod-Teller) for ${u}_{123}$ and the neutron diffraction data of Yarnell etal for liquid Ar at 85\ifmmode^\circ\else\textdegree\fi{}K to represent $g(r)$. It is necessary to make several changes of variable and inversions of the order of integration in order to transform the integral into a sextuple integral which can be programmed without incurring large errors due to cancellation. The result for Ar at 85\ifmmode^\circ\else\textdegree\fi{}K is ${\ensuremath{\gamma}}_{3}=\ensuremath{-}4.5$ erg/${\mathrm{cm}}^{2}$, which is not negligible when compared with the experimental surface tension (13.1 erg/${\mathrm{cm}}^{2}$). When ${\ensuremath{\gamma}}_{3}$ is combined with ${\ensuremath{\gamma}}_{2}$ [the surface tension computed in the Kirkwood-Buff-Fowler approximation from realistic pair potentials for Ar using the same $g(r)$ data], the total surface tension is significantly smaller than the experimental value.