Density functional theory: X-ray reflectivity studies of pure fluid liquid/vapour interfaces

Abstract

Although there are numerous model independent methods for the extraction of a density profile from X-ray reflectivity data, for many systems there are fundamental limitations to the uniqueness of profiles so determined owing to the limited range of scattering data and the nature of the inverse transformation. Based on density functional theory (DFT) of inhomogeneous fluids we model the liquid/vapour interface of some pure simple liquids (Ar, N₂, Kr, CCl₄). Attractive contributions to the Helmholtz free energy are treated by a mean-field approximation (MF). Both local density approximation (LDA) and smoothed density approximation (SDA) are applied to the repulsive reference system described by a hard sphere equation of state. A cut-off and shifted Lennard-Jones potential divided according to the Weeks–Chandler–Andersen (WCA)-prescription is used as intermolecular interaction force model. The potential parameters were determined by modelling saturated liquid densities of a pure fluid. Computed theoretical density profiles are used to predict X-ray specular reflectivities. Capillary waves models of Braslau etal. (Phys. Rev. A, 1998, 38, 2457), Evans etal. (Mol. Phys., 1981, 42, 1169) and of Meunier (J. Phys. (Paris), 1987, 48, 1819) are adopted to approximate these contributions to both specular reflectivities and surface tension. We propose a parameter free procedure based on the intrinsic interfacial thickness to calculate these terms. The agreement of predicted X-ray reflectivities with experimental data is good in the case where these terms are included. Similarly the surface tension is calculated from the intrinsic part plus contributions due to capillary wave roughening. All the calculations are based exclusively on potential parameters determined from saturated liquid densities.

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