Surface effects on the self equilibrium, self bending and symmetry lowering of nanofilms

A continuum theoretical scheme for self equilibrium, self bending and symmetry lowering of nanofilms was obtained by considering surface elasticity, surface stress and the corresponding surface slice thickness. When surface stress and surface elasticity are both balance, the nanofilm is simply compressed (or expanded). When the surface stress or surface elasticity is imbalance, the nanofilm will bend. On the other hand, surface stress and surface elasticity imbalances induce a nanofilm to curl into a nanotube when the nanofilm is very thin. The surface stress and surface elasticity balances induce uniform in-plane strain (the overall film relaxation), while the vertical direction of the nanofilm relaxes reversely due to Poisson's effect. And then, the crystal lattice constants of in-plane and vertical directions are different from each other, the ratio of these two lattice constants decrease with film thickness increase. Hence, the symmetry of the nanofilm is lowered by the overall film relaxation.