One approximate generic equation for calculating inter-nanoparticle forces

In this work, interaction forces between two identical silicon or dissimilar silicon-diamond nanospheres are calculated using molecular dynamics simulation. Modified formulas for van der Waals (vdW) attraction and Born repulsion forces have been proposed, respectively. Two different function forms are taken after particle's contact deformation, depending on the atomic discrete structure and mechanical properties of the materials. A second-order Fourier expansion is applied to two interacting identical silicon nanospheres, and a simplified linear functional form is used for two interacting dissimilar silicon-diamond nanospheres. Moreover, the constant asymptotic ratios of both vdW attraction and Born repulsion have been correlated to the additional material properties including the ratio k_ρ of the true number density of atoms to that determined from Hamaker approach and refractive index n₀. Upon the analysis of four different nanospheres (i.e., silica, amorphous carbon, diamond, and silicon), one approximate but generic equation is put forward for inter-nanosphere vdW attraction and Born repulsion forces, respectively.