Monosized sphere packing approach in the nanoporous structure modeling

In many structural models atoms appear as hard monosized spheres. The properties of nanostructured porous matrix filled by adsorbed substance strongly depend on the density of atoms in nanochannels, those can be interpreted as cylinders. The problem of densest packing of monosized spheres in a cylindrical container is considered. It belongs to the optimization problems of Computational Geometry and is known to be NP-hard, i.e. its exact solution cannot be obtained in a polynomial time. Some approaches of the problem, which are applicable for modeling of nanoporous structures, are discussed. The classifications of packing models and known maximal densities are given. Three approaches represent different approximations in the modeling of packing´s. Those are: i) the numerical simulation, based on the geometrical properties, wall effects, and determination of stable position of spheres under gravity; ii) the Voronoi-Delaunay network, which models the channel structure in 3D space; and iii) the non-linear mathematical programming methods employed for densest packing search through cylinder height minimizing. These methods can be used for diverse nanoporous structure designs.