Is There Really a Size effect on the Surface Energy of Nanoparticles ?

Surface energy is a key quantity that controls many physical properties of materials, yet determining its value at the nanoscale remains challenging. By using $N$-body interatomic potentials and performing analytical calculations, we develop a robust approach to determine the surface energy of metallic nanoparticles as a function of particle size and temperature. A strong increase in the surface energy is obtained when the size of the nanoparticle decreases, both in the solid and liquid states. However, we show how the use of the classical spherical approximation to characterise the surface area of a nanoparticle leads to an almost constant surface energy with size as usually done to characterize the thermodynamic and kinetic properties of NPs in many works. We then propose a correction of the spherical approximation that is particularly useful for small size nanoparticles to improve the different models developed in the literature so far.Surface energy is a key quantity that controls many physical properties of materials, yet determining its value at the nanoscale remains challenging. By using $N$-body interatomic potentials and performing analytical calculations, we develop a robust approach to determine the surface energy of metallic nanoparticles as a function of particle size and temperature. A strong increase in the surface energy is obtained when the size of the nanoparticle decreases, both in the solid and liquid states. However, we show how the use of the classical spherical approximation to characterise the surface area of a nanoparticle leads to an almost constant surface energy with size as usually done to characterize the thermodynamic and kinetic properties of NPs in many works. We then propose a correction of the spherical approximation that is particularly useful for small size nanoparticles to improve the different models developed in the literature so far