Density functional theory for the description of spherical non-associating monomers in confined media using the SAFT-VR equation of state and weighted density approximations

Abstract

As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the “CG” approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the “FMT” extension version gives a good representation solely at low pressures. Hence, the “CG” version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.