Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface

Abstract

We study the density-density correlation function $G(\mathbf{r},{\mathbf{r}}^{\prime })$ in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform $G(z,z^{\prime };q)$ and local structure factor $S(z;q)$ separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension $\sigma (q)$, and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of $G(z,z^{\prime };q)$ and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that "float" with the surface and show that this describes the full $q$ and $z$ dependence of the excess contributions to both $G$ and $S$. However, neither the "crossing-criterion" nor the new "floating interface" definition of $\sigma (q)$ are quantities directly measurable from the total structure factor $S^{tot}(q)$ which contains additional $q$ dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret $\sigma (q)$.

11 pages, 1 figure

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• Non-locality and short-range wetting phenomena
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• Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study
• Finite-size corrections for the static structure factor of a liquid slab with open boundaries
• Four-point interfacial correlation functions in two dimensions. Exact results from field theory and numerical simulations
• Structure of liquid--vapor interfaces: perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence X-ray diffraction
• Curvature corrections to the nonlocal interfacial model for short-ranged forces
• Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry
• Correlation function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations