1706.08744v1.pdf (3.76 MB)
The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
journal contribution
posted on 2017-07-21, 10:50 authored by Andrew ArcherAndrew Archer, Blesson Chacko, Robert EvansIn 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.
Funding
B.C. is supported by an EPSRC studentship and R.E. by a Leverhulme Emeritus Fellowship: EM-2016-031.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Chemical PhysicsVolume
147Issue
3Citation
ARCHER, A.J., CHACK, B. and EVANS, R., 2017. The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect. Journal of Chemical Physics, 147 (3), 034501.Publisher
AIP © The AuthorsVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2017-06-26Publication date
2017-07-17Notes
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in ARCHER, A.J., CHACK, B. and EVANS, R., 2017. The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect. Journal of Chemical Physics, 147 (3), 034501 and may be found at http://dx.doi.org/10.1063/1.4993175.ISSN
0021-9606eISSN
1089-7690Publisher version
Language
- en