The thickness dependence of surface energy and contact angle of water on ultrathin MoS$_{2}$ film

The properties of ultrathin 2D materials generally show a strong thickness dependence. Using first-principles methods, we have systematically calculated surface energy and surface stress of MoS$_{2}$ films as a function of thickness from one to 12 layers, using two van der Waals functional based approaches (vdW-DF and DFT-D2). Based on the calculated surface energies, which increases with the increasing thickness, we further analyze the surface contact angle of water droplet on MoS$_{2}$ film surface using Young's equation as a function of thickness, in comparison with experiments, from which the water-MoS$_{2}$ interfacial energy and its MoS$_{2}$ thickness dependence is derived. These results will be useful for future studies of physical and chemical properties of ultrathin MoS$_{2}$ films.