Surface Energy of Au Nanoparticles Depending on Their Size and Shape

Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to the value for facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface energy is hugely reduced, if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.