An EQT-based cDFT approach for thermodynamic properties of confined fluid mixtures.

We present an empirical potential-based quasi-continuum theory (EQT) to predict the structure and thermodynamic properties of confined fluid mixtures. The central idea in the EQT is to construct potential energies that integrate important atomistic details into a continuum-based model such as the Nernst-Planck equation. The EQT potentials can be also used to construct the excess free energy functional, which is required for the grand potential in the classical density functional theory (cDFT). In this work, we use the EQT-based grand potential to predict various thermodynamic properties of a confined binary mixture of hydrogen and methane molecules inside graphene slit channels of different widths. We show that the EQT-cDFT predictions for the structure, surface tension, solvation force, and local pressure tensor profiles are in good agreement with the molecular dynamics simulations. Moreover, we study the effect of different bulk compositions and channel widths on the thermodynamic properties. Our results reveal that the composition of methane in the mixture can significantly affect the ordering of molecules and thermodynamic properties under confinement. In addition, we find that graphene is selective to methane molecules.