Size‐Dependent Contact Angles of Microscopic Droplets on Ultra‐Smooth Silanized Surfaces Probed by Atomic Force Microscopy

Abstract Microscale wetting phenomena are of great technological and fundamental importance. Challenging questions arise in the growth process of nanometer to micrometer‐sized droplets. Atomic force microscopy is used to study the size dependence of the contact angle in microscopic droplets. At this scale, droplets are small enough to neglect gravitational forces and large enough for line tension to become relevant. Thus, interfacial tension and contact line friction control droplet wetting. To minimize contact line friction caused by pinning, smooth surfaces are used with minimal heterogeneities, created by a post‐silanization technique known as peel‐off. Irrespective of the liquid, the contact angle as a function of droplet size has a monotonous nonlinear relationship, plateauing at the macroscopic value beyond a certain size. To explain this, a theoretical model based on the energy balance is developed for coalescing droplets. Essentially, an energy balance is sought where capillary, pinning, and viscous energies reach an equilibrium where the net available energy is zero. Based on this analysis, a physics‐based equation is derived to predict the size dependence of microscale wetting. The characteristic length scales from this modeling match the experimentally observed size. Results show that minimal heterogeneities have a significant impact on the wetting of micrometer‐sized droplets.