Generalization of the Fundamental-Measure Theory Beyond Hard Potentials: The Square-Well Fluid Case

Abstract

The fundamental-measure theory (FMT) developed at the end of the 1980s for hard-sphere inhomogeneous fluids has revolutionized density functional theories (DFTs), allowing one to describe accurately for the first time highly confined fluids. However, in order to apply DFTs to real fluids, less rigorous coarse-graining approaches have always been used for perturbative contributions in addition to the FMT hard-sphere treatment. With the aim to propose a formally consistent description avoiding this duality, a possible route is the generalization of the fundamental-measure theory for potentials different from the purely hard repulsive term. This is the main purpose of this work, achieved considering the square-well fluid as initial case test. As a reference for the bulk fluid, the statistical associating fluid theory for the square-well monomer has been selected, and a suitable functional has been developed and validated through comparison against Monte Carlo molecular simulations. This opens up a new class of efficient non-local DFTs directly applicable to mixtures of complex fluids.

Effect of structural considerations on the development of free energy functionals for the square-well fluid

“…Because the function used to compute these coefficients is defined for an homogeneous fluid, an approximation is performed when using them in an inhomogeneous fluid formalism. However, one can assume that this approximation does not alter the main behaviour of the fluid microstructure, as shown in our previous publication [9] or with stronger but physical approximations (see the MF approximation below). Hence, in the following, we consider the pair correlation function at contact and at the effective density, g HS i j,eff .…”

“…(this notation was introduced in the work [9]). In the KR-FMT, all of these weights are used to define weighted densities of a specie i for the hard-sphere,…”

“…for a homogeneous fluid, named the local compressibility approximation. Contrarily to our previous paper [9], we do not use this approximation in this work, because we will consider some further expressions for which this local description has no sense for inhomogeneous systems. Now, the square-well potential is chosen for the attractive contribution between two molecules i and j.…”

“…In reference [9], we applied the FMT formalism to this functional, and derived it to compute the inhomogeneous chemical potential. In this work, the functional is first derived to define the attractive contribution of the chemical potential…”

“…The effective pair correlation function considered in this section is the bulk one. This approach was developed in our previous work [9] and rests upon the idea of using the bulk SAFT-VR treatment only on the bulk pair correlation function, and use this homogeneous result directly into the functional.…”