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The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

Research output: Contribution to journalArticle

Original languageEnglish
Article number034501
Number of pages8
JournalJournal of Chemical Physics
Volume147
Issue number3
Early online dateJul 2017
DOIs
DateSubmitted - 24 Apr 2017
DateAccepted/In press - 26 Jun 2017
DateE-pub ahead of print - Jul 2017
DatePublished (current) - 21 Jul 2017

Abstract

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

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