A 3D non-local density functional theory for any pore geometry
Thomas Bernet, Manuel M. Piñeiro, Frédéric Plantier, Christelle Miqueu
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.