Interaction forces between a spherical nanoparticle and a flat surface†
Due to the breakdown of Derjaguin approximation at the nanoscale level apart from the neglect of the atomic discrete structure, the underestimated number density of atoms, and surface effects, the continuum Hamaker model does not hold to describe interactions between a spherical nanoparticle and a flat surface. In this work, the interaction forces including van der Waals (vdW) attraction, Born repulsion and mechanical contact forces between a spherical nanoparticle and a flat substrate have been studied using molecular dynamic (MD) simulations. The MD simulated results are compared with the Hamaker approach and it is found that the force ratios for one nanosphere interacting with a flat surface are different from those for two interacting nanospheres, both qualitatively and quantitatively. Thus two separate formulas have been proposed to estimate the vdW attraction and Born repulsion forces between a nanosphere and a flat surface. Besides, it is revealed that the mechanical contact forces between a spherical nanoparticle and a flat surface still can be described by the continuum Hertz model.