Layering and capillary waves in the structure factor of liquid surfaces

Within the extended Capillary Wave Theory (ECWT), to extract the bending modulus of a liquid surface from the total structure factor of the interfacial region requires to separate the capillary waves (CW) signal from a non-CW background. Some years ago, Höfling and Dietrich (HD), working in the strict grazing incidence limit q_z = 0, proposed a background that combines the liquid and vapor bulk structure factors in the amounts set by Gibbs's plane. We contrast that proposal with Molecular Dynamics (MD) simulations of the Lennard-Jones model analyzed with the Intrinsic Sampling Method (ISM). The study is extended to q_z ≠ 0, to test the stronger consistency requirements of the ECWT and the experimental conditions; it shows a good MD-ECWT matching although we need some fine tuning over HD proposal. Then, the agreement with the ISM result for the surface bending modulus is good and that provides an interpretation, in terms of the molecular layering at the liquid edge, for the fluctuating surface represented by the CW signal in the surface structure factor, both for MD simulations and surface diffraction experiments.