Method for Measuring Surface Tension of Microscopic Droplets Using Standard AFM Cantilever Tip

The influence of surface tension is ubiquitous in our daily lives, whether it is the water droplets breaking off from the showerhead, the bubbles formed when we use soap, or the sand particles sticking to our wet feet during a fun beach holiday. This concept is central to our current understanding of wetting phenomena, which has evolved over the past centuries, starting with Leonardo da Vinci, who sought to explain the counterintuitive rise of water inside a partially vertical capillary tube. The famous studies by von Segner, Young, Laplace, and Gauss subsequently formalized our current understanding of capillarity, where surface tension is introduced into the model as a key liquid-related parameter.

Surface tension is often intuitively thought of as the net constant tension experienced by a liquid surface in all directions, similar to the stretching of a rubber membrane of a balloon. This tension is the result of an imbalance of net intermolecular forces near the liquid interface. Several measurement techniques have since been developed to measure the surface tension of macroscopic liquids. One commonly used approach is to directly measure the surface tension of a liquid using appropriate force measurement devices. A classic example is the Wilhelmy plate method, where the maximum force required to pull a thin plate vertically from the liquid surface is measured.

The surface tension can then be obtained by dividing the measured force by the wet perimeter of the plate. On the other hand, methods such as the suspended droplet method, rotating droplet method, and oscillating droplet method rely on optical observation of the droplet shape under specific conditions, and surface tension is evaluated by solving the Young-Laplace or Rayleigh equations.

Although measuring the surface tension of bulk liquids using commercial instruments based on these techniques is straightforward, these methods are unsuitable for microscopic measurements, where the available liquid sample volume is very small, in the range of micron-sized droplets. Such small-scale measurements are especially useful for enhancing our understanding of certain important natural phenomena, such as how atmospheric aerosols influence climate change processes and human health, or the properties of tiny secretions on certain insect legs that allow them to adhere to most surfaces.

One of the initial attempts to make such measurements was the use of Atomic Force Microscopy (AFM) in a Wilhelmy-like experiment. McGuiggan and Wallace connected a cylindrical quartz rod with a diameter of approximately 100 μm to a blunt AFM cantilever probe to measure liquid adhesion force and calculate surface tension.

Although their method gave reasonable values for low surface tension liquids like tetradecane, it underestimated the value of water by 44% compared to macroscopic results. This discrepancy was attributed to the shape defect of the rod and water contamination. Yazdanpanah et al. reported an improvement of this method by growing "nano-needles" of a gallium-silver alloy on the tip of the standard AFM cantilever.

These nano-needles (approximately 100 nm in diameter) had a more defined cylindrical geometry, allowing precise measurement of surface tension for liquids including water. Similar methods using colloidal probe AFM have also been shown to form capillary-condensed liquid bridges between spherical probes and substrates. Another approach involves tracking droplet oscillations caused by the polymer-induced vibrations using optical tweezers or by spraying droplets through inkjet nozzles. The resonant frequency modes of these oscillations, which depend on the liquid surface tension based on Rayleigh theory, can then be analyzed using high-speed optical detectors.

Similar experiments can also be conducted using AFM on hemispherical droplets without a handle, by measuring the oscillations at the liquid interface when it contacts a hydrophobic colloidal probe.

To enable surface tension measurements using a standard AFM conical tip, the tip surface must be modified to have a low contact angle hysteresis with any liquid to be detected, even when the tip is superhydrophobic. In principle, this can minimize any local pinning or sticking events when the liquid contacts the tip during measurement, thus providing force curves closely related to the ideal theoretical scenario. For example, hydrophobic coatings of fluorinated polymers can reduce hysteresis to some extent, but they perform poorly against low surface tension liquids.

Pranav Sudersan et al. proposed a method for balancing surface tension measurements on AFM using a polymer-brush-coated standard conical tip for microdroplets. A simple one-step process adapted from previously reported studies allows for a hydrophilic polymer brush coating on the tip surface. The low contact angle hysteresis of the coated tip prevents the droplets from sticking to the AFM tip, despite the tip being hydrophilic.

Additionally, we numerically simulated the configuration where a droplet sits on a flat surface and interacts with the pyramid or conical tip above using Surface Evolver software. The simulated force-distance curves were compared with AFM experimental data to calculate the surface tension. This method attempts to simplify microscale surface tension measurements and aids in the scientific understanding of various processes controlled by wetting phenomena at small scales. All involved lengths and forces were normalized with respect to (h) and (\gamma h), where (h) is the undisturbed height of the droplet that does not contact the tip (Figure 1).

Figure 1:(a) Schematic of the AFM experiment for depositing a microdroplet on a mica surface.(b) Magnified view of the interaction between the AFM tip and the droplet (highlighted region in (a)). Initially, the droplet is fixed on the surface with a contact diameter of 𝐷 and a height of ℎ. During the force measurement, the droplet forms a contact angle 𝜃 with the tip surface.

Figure 2:Procedure for measuring surface tension.

For example, a glycerol droplet height image was captured with a scanning line speed of 0.7 Hz and a 22 × 22 μm scanning area, with the cantilever adjusted to a target amplitude of 40 nm (Figure 2). Since the droplet size is comparable to the scanning area, high image resolution was not necessary for analysis. Two common strategies to make the surface superhydrophobic are to coat it with a nanostructured layer or a lubricating layer. However, both methods are unsuitable for our needs because these superhydrophobic layers are typically a few microns thick, and if we choose a lubricating coating method, it may alter the tip shape or contaminate our sample liquid. Recent studies show that polymer brushes can provide surfaces with very low contact angle hysteresis (less than 5°) due to the dense brush layers, which exhibit high chemical and physical uniformity and behave like a thin lubricating liquid film. These polymer brushes have nanoscale coating thicknesses, making them an ideal choice for modifying tip surfaces.

1.Sudersan, P.; Müller, M.; Hormozi, M.; Li, S.; Butt, H.-J.; Kappl, M., Method to Measure Surface Tension of Microdroplets Using Standard AFM Cantilever Tips. Langmuir 2023, 39 （30）, 10367-10374.