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

A. O. Parry, C. Rascón, G. Willis, R. Evans

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)

Abstract

We study the density-density correlation function G(r, r') 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'; 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 σ(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'; 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 σ(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 σ(q).

Original languageEnglish
Article number355008
JournalJournal of Physics Condensed Matter
Volume26
Issue number35
DOIs
Publication statusPublished - 3 Sep 2014

Keywords

  • correlation function
  • liquid-vapour interface
  • surface tension

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