A 3D non-local density functional theory for any pore geometry

Abstract

A general framework of classical non-local density functional theory (NLDFT) is presented, in order to consider the adsorption of spherical molecules in porous materials of any geometry. Fluid-fluid interactions and fluid-solid interactions can be repulsive or attractive. Some techniques that have been developed for the computation of weighted densities of hard-spheres are extended to attractive ones, in order to deal with an arbitrary pore geometry. This way, the computation method introduced in this work is validated by a comparison with analytical results for simple cases, and is directly applied to more complex systems. Density distributions depending on multi-dimensional effects are presented, and some radial distribution functions are recovered from NLDFT computations. Finally, the case of attractive continuous curved walls is detailed, which represents a large variety of real systems (e.g. micro and mesoporous silica, zeolites, carbonaceous nanoporous materials, etc.). With the new way of computation proposed, a general solution is presented, valid for any shape of continuous pore surface, by considering mathematical properties of discrete geometry due to the discretisation of the computational space with FFT computations.

GRAPHICAL ABSTRACT

Keywords:

• Density functional theory
• fundamental-measure theory
• discrete geometry

Acknowledgments

M.M.P. acknowledges CESGA (www.cesga.es) for providing access to computing facilities We acknowledge G. Jackson for the useful discussions on fluid-solid interaction modelling and for the use of its RHNC code.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

M.M.P. acknowledges financial support by Ministerio de Economía y Competitividad, in Spain (Grant Ref. FIS2015-68910-P). T.B. acknowledges the Ministère de l'Éducation, de l'Enseignement Supérieur et de la Recherche, in France, for his MENRT Ph.D. Grant and Total SA for additional funding. C. Miqueu acknowledges the E2S UPPA hub Newpores supported by the "Investissements d'Avenir" French programme managed by ANR (ANR-16-IDEX-0002) for funding.