Line Tension and Drop Size Dependence of Contact Angle at the Nanoscale

Abstract

Despite considerable research efforts, the influence of contact line tension during wetting at the nanoscale and its experimental determination remain challenging tasks. So far, molecular dynamics simulations and atomic force microscope measurements have contributed to the understanding of these phenomena. However, a direct measurement of the size dependence of the contact angle and the magnitude of the apparent line tension has not been realized so far. Here, we show that the contact angle is indeed dependent on the drop size for small drop diameters and determine the magnitude of the apparent line tension via liquid-metal based measurements of advancing and receding contact angle inside a scanning electron microscope. For this purpose, a robotic setup inside an electron microscope chamber and oxide-free Galinstan droplets—produced via an electromigration-based and focused ion beam irradiation-assisted process—are employed. Using the first-order correction of Young’s equation, we find an apparent line tension value of 4.02 × 10−7 J/m for Galinstan© on stainless steel.

Fundamentals and Applications of Surface Wetting

“…Bridging the gap between these scales and developing a comprehensive understanding of wetting interactions is a significant challenge. Accordingly, followed by the traditional contact angle goniometry, currently, more advanced techniques like optical and confocal microscopy, − atomic force microscopy, scanning electron microscopy (SEM), and surface plasmon resonance (SPR), , etc. are being used to characterize multiscale wetting.…”

Salinity and pH effects on water–oil–calcite interfaces by using molecular dynamics

“…The cylindrical geometry of the droplets provides benefits to calculate the contact angle at the nanoscale by reducing the tension in the triple interface and the curvature of the droplet. 49,63,64 Furthermore, the periodic boundary conditions in the y-axis are exploited to reduce the simulation size and the computational cost. The cylindrical droplets had a radius of 22.5 Å and a width of 24.9500 Å.…”

Advances in assembled micro- and nanoscale mechanical contact probes

“…contact angle measurements (see Figures 9A,D a) for which a liquid metal sphere that is as unaffected as possible is required. This implementation resulted in successful applications such as probes for contact angle measurements (Kleist-Retzow et al, 2020;Klauser et al, 2022), probes for gripping processes with adjustable adhesion (Kleist-Retzow von et al, 2019b) or probes for printing liquid metal volumes (see Figure 9C) (Kleist-Retzow von et al, 2019b).…”

“…water droplets can only be used to a very Frontiers in Mechanical Engineering frontiersin.org limited extent due to rapid evaporation and offer hardly any possibilities to keep the volume of the sphere constant. With the use of liquid metal, this measurement method made it possible for the first time to experimentally determine the effect of the line tension and to determine contact angles in the nanometer range (Klauser et al, 2022). Manipulators to perform liquid metal based gripping procedures are mainly based on phase changing mechanisms.…”

“…The diameter of liquid metal droplets can be tailored by top-down processes such as using a blender (Tevis et al, 2014) and a simple syringe (Natalia Sobczak et al, 2010), or via bottom-up processes such as physical vapor deposition (PVD) (Kleist-Retzow and von, 2021) or by means of controlled electromigration (Kleist-Retzow von et al, 2019b). As the surface tension of the droplets determines its shape, when brought into contact with a substrate, its shape is entirely defined by the surface energies of the interface components (Klauser et al, 2022). After liquid metal spheres are formed with the desired diameter, they can be mounted on a manipulator or cantilever by controlled wetting processes.…”