Classical Density Functional Theory Consistent with the SAFT-VR Mie Equation of State: Development of Functionals and Application to Confined Fluids

Classical density functional theory has provided a robust and consistent framework to thermodynamically describe systems with local density variations. The development of functionals that are consistent with homogeneous equations of state allows us to investigate inhomogeneous systems applying the same models used for homogeneous ones. Particularly for adsorption, this is extremely desirable since one ought to apply a consistent modeling for both bulk and adsorbed phases. In this work, new functionals for the Helmholtz energy are proposed by combining the Statistical Associating Fluid Theory for potentials of variable range of Mie type (SAFT-VR Mie) with the weighted density approximation (WDA) formalism of classical density functional theory. As a result, the SAFT-VR Mie equation of state is extended to inhomogeneous fluids and is applied in the prediction of density profiles of linear alkanes adsorbed in carbon slit pores. The density profiles of the adsorbed phases are compared to the results of molecular simulations performed with the Monte Carlo method in the grand-canonical ensemble. An example involving capillary condensation and hysteresis is also investigated. Despite the intrinsic differences between molecular simulation and the analytical model with regard to the representation of the molecular structure, a qualitative agreement and, to some extent, quantitative agreement are obtained.