Influence of Surface Stress on Bending Nanowires with Different Boundary Conditions

The influence of surface stress on the static and dynamic bending nanowires is investigated by incorporating the Young-Laplace equation into Euler-Bernoulli beam theory. The proposed theoretical approach gives explicit solutions for bending nanowires with two different boundary conditions - cantilever, and fixed-fixed. The solutions indicate that the nanowires behave as softer material for the cantilever structure and stiffer material for the fixed-fixed structure as the nanowire diameter decreases for a positive surface stress and a constant length. The surface stress influenced nanowire bending behavior is not only diameter dependent but also length dependent. Based on the proposed approach, nanowire overall Young´s modulus is calculated to exhibit the nanowire elastic bending behavior influenced by the surface stress. The theoretical calculations of the overall Young´s moduli agree with reported experiment results of Ag nanowires with diameter in the range of 38.7~135 nm and length in the range of 1-2.55 mum.