ARCHER, A.J. and EVANS, R., 2013. Relationship between local molecular field theory and density functional theory for non-uniform liquids. Journal of Chemical Physics, 138, 014502; http://dx.doi.org/10.1063/1.4771976 (14 pages)
The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful
for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating
LMF in terms of one-body direct correlation functions we recast the theory in the framework of
classical density functional theory (DFT). We show that the general LMF equation for the effective
reference potential φR(r) follows directly from the standard mean-field DFT treatment of attractive
interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere
reference fluid we determine φR(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall.
In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure
that can include damped oscillations at large distances from the wall as well as the repulsive hump
near the wall required to generate the low density “gas” layer characteristic of complete drying.
We argue that it would be difficult to obtain the same level of detail from other (non-DFT based)
implementations of LMF. LMF emphasizes the importance of making an intelligent division of the
interatomic pair potential of the full system into a reference part and a remainder that can be treated in
mean-field approximation.We investigate different divisions for an exactly solvable one-dimensional
model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure
factor and the equation of state of the uniform fluid show that including a significant portion of the
attraction in the reference system can be much more accurate than treating the full attractive tail in
mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.