Wetting at nanoscale: Effect of surface forces and droplet size

Despite being intensively investigated, wetting at the nanoscale leaves a manifold of questions unresolved. In particular, the dependence of a contact angle on a droplet size for the droplets of the height of the order of a few nanometers is intensively debated. This effect is believed to be related to intermolecular (surface) forces. In the present work, we use the disjoining pressure concept and solve the Derjaguin equation numerically and analytically to model profiles of the sessile droplets of heights comparable with the range of the surface force action. We show that values of the contact angle are dramatically dependent on the droplet height as well as the way the contact angle is defined. For the axisymmetric droplets, the contact angle increases with increasing droplet height, and this dependency becomes universal for different disjoining pressure isotherms when plotted dimensionless with respect to the surface force action range. We demonstrate that for cylindrical droplets, different contact angle definitions can lead to opposite dependencies on the droplet size. We show as well that varying orders of magnitude of the apparent line tension reported can be additionally explained by the contact angle definition chosen.