Influence of surface energy on the elastic compression of nanosphere

The influence of surface energy on the elastic compression of nanosphere is addressed through the principle of minimum potential energy. By using the displacement potential approach, the elastic field of nanosphere under diametrical compression is derived analytically. Firstly, surface energy induces a uniform pre-existing hydrostatic compression in the entire nanosphere. More importantly, when the ratio of surface energy density to the radius of sphere is comparable with the elastic modulus, the response of nanosphere to external loading will be evidently distinct from the classical prediction. When the compressive load-depth curve is used to calculate the elastic modulus of nanosphere, the presence of surface energy predicts the size dependence of elastic modulus, which enhances significantly as the radius of sphere decreases below 100 nm. This study provides an efficient tool to analyze the elastic deformation of nanoparticles and measure their elastic properties.