Distribution function theory for inhomogeneous fluids

Abstract

A theory for inhomogeneous fluids is presented. It is derived by an approach that is inspired by the cluster variation method for lattice systems. A systematic expansion of the free-energy functional is generated, which is then truncated and minimized to obtain integral equations for the density profile and the pair distribution function. The theory can be simplified by an additional approximation that serves to decouple the integral equations. Numerical results from this simplified theory show promising agreement with computer simulations.

A simple theory of weakly inhomogeneous fluids

“…(15a) for a bulk fluid), but ran into numerical problems for the Lennard-Jones fluid. Some results for hard spheres have been reported by Schlijper and Harris (1991). Figure 1 shows the density profile of the hard-sphere fluid at bulk density p,03=0.5 in a slit where the distance L between the walls is 4.50, with 0 the molecular diameter.…”

“…This set of equations has an asymptotic form that is valid for N + 00, V + = with p = NN fixed. The calculation of the asymptotic form involves a considerable amount of algebra and is given in (Schlijper & Harris, 1991). For a system without three-particle interactions, i.e.…”

“…In previous publications an adaptation of this CVM formalism to the theory of fluids was presented (Schlijper & Kikuchi, 1990;Schlijper & Harris, 1991). Here the formalism is used to derive a simple theory for weakly inhomogeneous fluids.…”

“…The difference and major technical difficulty is that the equations involve the system size in a non-trivial way; it is necessary to extract the large N behaviour, while the average density p = N/V is kept fixed. This takes a significant calculational effort that is not reproduced here but can be found in (Schlijper & Harris, 1991).…”

Positional ordering of hard adsorbate particles in tubular nanopores

“…Note that if a two-body density based DF would be available then the two-body density profile would reflects the effect of the system finiteness along the perimeter has on transverse particle correlations despite the unchanged value of the density profile along the perimeter. On lattice systems this kind of DF has been worked out [68][69][70], so it is mandatory its extension to the continuum. A promising route to take into account the finiteness of the system along one spatial direction at the level of one-body density based DF could consist on the extension of the formalism developed in Ref.…”