Introducing a novel coefficient on mixed-nanoparticles material: relationship between the theoretical and experimental densities

Nanoparticles (NPs) indicating a unique potential in bioradiation and nuclear reactor shielding are employed in many fields due to their particular specifications leading improving the mechanical properties as well as pore structure of the concrete-shield. The aim was to introduce a novel coefficient ([Formula: see text]), namely the experimental to theoretical density ratio for mixed-NPs material at various nanoparticles percent concentrations ([Formula: see text]) based on pure mathematical aspects along with the some suitable physical purposes by Monte Carlo method. The change in the mixture density to the change in [Formula: see text] is always proportional to the [Formula: see text] value. The density will become maximum at the [Formula: see text] in which the physical, morphological and chemical features of NPs along with the amounts of voids in the material have a key role over estimating porosity percentage. The NPs’ separation probability as born-cascaded-pairs towards very small radii may be formulated as [Formula: see text] where [Formula: see text] and [Formula: see text] are constant values. In conclusion, the theoretical results may be experimentally used in future work for different applications such as designing shield at a nuclear facility.