Measurement of line tension on droplets in the submicrometer range

Wetting is a universal phenomenon in nature and of interest in fundamental research as well as in engineering sciences. Usually, wetting of solid substrates by liquid drops is described by Young's equation, which relates the contact angle between the liquid and the substrate to the three interfacial tensions. This concept has been widely used and confirmed for macroscopic droplets. On the contrary, it is still matter of debate to what extent this concept is able to explain relations on the micrometer scale and below. The so-called extended Young's equation, which takes account of the specific arrangement of the molecules in the three-phase contact line by implementing a term called "line tension", is frequently used to characterize deviations from the "ideal" Young's case. In this work we tried to look into the dependence of measured contact angles of droplets on their size for a close to ideal system. We measured contact angles of ionic liquid droplets with radii between some tens and some hundreds of nanometers by atomic force microscopy on an ideally flat silicon wafer. We found that the contact angles decreased with decreasing droplet size: smaller droplets showed stronger wetting. This dependence of the contact angle on the droplet radius could not be described with the concept of line tension or the modified Young's equation. We propose simple arguments for a possible alternative concept.