Criticality of a liquid-vapor interface from an inhomogeneous integral equation theory.

A microscopic theory is developed to study the liquid-vapor interfacial properties of simple fluids with ab initio treatment of the inhomogeneous two-body correlation functions, without any interpolation. It consists of the inhomogeneous Ornstein-Zernike equation coupled with the Duh-Henderson-Verlet closure and the Lovett-Mou-Buff-Wertheim equation. For the liquid-vapor interface of the Lennard-Jones fluid, we obtained the density profile and the surface tension, as well as their critical behaviour. In particular, we identified non-classical critical exponents. The theory accurately predicts the phase diagram and the interfacial properties in a very good agreement with simulations. We also showed that the method leads to true capillary-wave asymptotics in the macroscopic limit.