The surface energy density of nanoparticles exhibits an obviously size-dependent behavior. However, how the surface energy density changes with the diameter of nanoparticles is still ambiguous. Based on a recently developed continuum theory considering the size effect in nanomaterials, theoretical analysis is carried out for various fcc metallic nanoparticles. Surface lattice contractions of nanoparticles are predicted and compared with the existing experimental data. As a result, the surface energy density decreases with the increase of nanoparticle diameter. Such a variation trend of surface energy density is contrary to the prediction of existing theoretical models but well consistent with the previously atomistic simulations and density functional calculations. The results in this paper provide a further understanding of the surface effect of nanoparticles, which should be helpful for the design of nanoscale devices or nanomaterials related to nanoparticles, such as NEMs and nanoparticlereinforced composites.

The surface energy density of nano-sized elements exhibits a significantly size-dependent behavior. Spherical nanoparticle, as an important element in nano-devices and nano-composites, has attracted many interesting studies on size effect, most of which are molecular dynamics (MD) simulations. However, the existing MD calculations yield two opposite size-dependent trends of surface energy density of nanoparticles. In order to clarify such a real underlying problem, atomistic calculations are carried out in the present paper for various spherical face-centered-cubic (fcc) metallic nanoparticles. Both the embedded atom method (EAM) potential and the modified embedded atom method (MEAM) one are adopted. It is found that the size-dependent trend of surface energy density of nanoparticles is not governed by the chosen potential function or variation trend of surface energy, but by the defined radius of spherical nanoparticles in MD models. The finding in the present paper should be helpful for further theoretical studies on surface/interface effect of nanoparticles and nanoparticle-reinforced composites.