MAXIMUM POSSIBLE DENSITIES OF RANDOM SPHERE PACKING WITHIN THE COMPOSITE

Abstract

The maximum possible densities of random packing of spheres with the same radius in space have been established. The maximum random packing densities Φ_n for spaces with dimensions n = 1–4 have been determined by numerical experiment based on the Monte Carlo simulation. If the established maximum possible density is exceeded, spatial correlations will occur in the system. They will be manifested as oscillation behavior of the pair correlation function at small distances and as significantly greater viscosity of the system of spheres. The application of the results to polymer matrices reinforced with glass or basalt microspheres is under discussion. In particular, it has been reasonably assumed that the compositions suitable for producing high-quality composites by die casting should not have packing density higher than Φ₃ = 0.359 obtained for a three-dimensional space.