Method to Measure Surface Tension of Microdroplets Using Standard AFM Cantilever Tips

Surface tension is a physical property that is central to our understanding of wetting phenomena. One could easily measure liquid surface tension using commercially available tensiometers (e.g., Wilhelmy plate method) or by optical imaging (e.g., pendant drop method). However, such instruments are designed for bulk liquid volumes on the order of milliliters. In order to perform similar measurements on extremely small sample volumes in the range of femtoliters, atomic force microscope (AFM) is considered as a promising tool. It was previously reported that by fabricating a special “nanoneedle”-shaped cantilever probe, a Wilhelmy-like experiment can be performed with AFM. By measuring the capillary force between such special probes and a liquid surface, surface tension could be calculated. Here, we carried out measurements on microscopic droplets with AFM, but instead, using standard pyramidal cantilever tips. The cantilevers were coated with a hydrophilic polyethylene glycol-based polymer brush in a simple one-step process, which reduced its contact angle hysteresis for most liquids. Numerical simulations of a liquid drop interacting with a pyramidal or conical geometry were used to calculate surface tension from the experimentally measured force. The results on micrometer-sized drops agree well with bulk tensiometer measurement of three test liquids (mineral oil, ionic liquid, and glycerol), within a maximum error of 10%. Our method eliminates the need for specially fabricated “nanoneedle” tips, thus reducing the complexity and cost of measurement.


Figure S3
Detailed measurement data of surface tension of several liquid droplets, calculated using the AFM method as described in the main text. Here, each point represents a measurement done on a unique liquid drop. Calculations based on cone and pyramid approximation of the tip shape are shown separately as circles and crosses respectively. Summarized results of the presented data are reported in Table 1 and Figure 6

Eect of tip coating
Surface modication of the AFM cantilevers were performed to investigate the eectiveness of alternative coatings that are typically used to reduce the wettability of a surface. Here, we report PDMS-brush coated and uorosilane coated cantilevers.
RFESPA cantilever tips were coated with PDMS-brush by chemical vapour deposition (CVD) method. 0.1 ml of dichlorodimethylsilane (Sigma-Aldrich) was placed in a sealed 1 Litre chamber together with the plasma treated cantilever tips for 10 minutes. The cantilevers were subsequently rinsed in toluene before AFM measurements. Similarly, uorinated cantilever tips were also prepared by CVD method, but under vacuum. A small cup containing 0.05 ml of 1H,1H,2H,H-peruorooctyltrimethoxysilane (SigmaAldrich) was placed in a 5 Litre vacuum chamber (< 100 mm Hg) for 10 minutes to uorinate the tips by the CVD process. The tips were then heated to 150°C for 30 minutes before AFM experiments.
Mineral oil and glycerol droplet preparation and subsequent AFM measurement protocol were followed exactly as described in the main text.
Force distance curves ( Figure S1) indicate that mineral oil shows high capillary adhesion and little hysteresis when the tip is coated with PDMS-brush, which is a consequence of its low contact angle with the coated tip. Here, the approach and retract curves have a relatively smooth trend during drop contact, similar to our measurements with PEG-brush coated tips. However, for glycerol, the forces curves show a signicantly non-ideal trend, with several local pinning events. The measured adhesion force in this case is also quite low, due to the large contact angle that glycerol has with the hydrophobic tip. A similar problem is also seen with the uorinated tips, where even for mineral oil, the force curves show several pinning events as well as low adhesion. Thus hydrophobic coatings are not a good choice to obtain smooth force-distance curves with high adhesion on liquid droplets, which is necessary to reasonably model the tip-drop contact process for surface tension estimation. Our attempts to perform AFM experiments on water drops using the JPK NanoWizard 4 S4 AFM failed to give reasonable force curves ( Figure S2). The laser spot on the cantilever head was too large that it locally heats the water drop during image scanning, even though the measurements were done under sealed saturated vapour conditions at 5°C. Further, our custom made cooling stage introduced unwanted mechanical noise into the system, overall rendering such measurements unfeasible for volatile liquids like water.
On the other hand, our preliminary experiments using Cypher AFM (Asylum Research) gave us a rather smooth and stable force curve for water droplet, showing very little hysteresis ( Figure S2). Here, the Cypher AFM had a precisely engineered in-built sample chamber, where the temperature and humidity can be controlled under a sealed environment quite well without introducing noise. More importantly, the laser spot on the cantilever head was focused to a much smaller area in this particular AFM, which signicantly minimized droplet evaporation during imaging and force measurements. Based on the measured force curve shown here, using the cone approximation of the tip shape, the surface tension of water was calculated to be ≈ 67 mN/m, quite close to the expected macroscopic value of 72 mN/m.
Thus our reported method could potentially be extended to other volatile liquid droplets using an appropriate AFM instrument. A proper cooling system and a focused cantilever laser spot are essential for the system to inhibit droplet evaporation during measurements.
S5 retract approach Cypher JPK Figure S2: AFM force-distance curves on water drops performed on the JPK NanoWizard 4 (Bruker) attached with a custom made sample stage cooling system (blue) and Cypher AFM (Asylum Research), which has an in-built cooling system (orange). Measurements were performed using AC200TS cantilever tips (9 N/m, 150 kHz) coated with PEG-brush.

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Surface tension data Figure S3: Detailed measurement data of surface tension of several liquid droplets, calculated using the AFM method as described in the main text. Here, each point represents a measurement done on a unique liquid drop. Calculations based on cone and pyramid approximation of the tip shape are shown separately as circles and crosses respectively. Summarized results of the presented data are reported in Table 1 and Figure 6 of the main text.

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Glycerol: eect of contact angle Figure S4: Surface tension calculation for glycerol are shown by assuming a tip-liquid contact angle of 10°and 40°. The values are reported for both cone and pyramid tip approximations.
Here, the tip is coated with PEG-brush.

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Contact angle measurements Figure S5: Silicon wafer was coated with PEG-brush as described in the main text. Dynamic liquid contact angles were measured for mineral oil, ionic liquid, glycerol and water by observing the drop sliding over the substrate tilted by 10°. The obtained receding contact angle values here were used as the basis for AFM tip-liquid contact angle assumption for surface tension measurement of each given liquid (reported in Table 1 of the main text). Note that mineral oil and ionic liquid shows a very small contact angle below 10°, where optical measurement of the angle is no longer precise.

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Glycerol droplet evaporation Figure S6: Glycerol droplet was imaged before and after force measurements (≈10 mins apart) to track its evaporation. The drop volume does not change signicantly during this time span, going from 119 fL to 114 fL (4.2% decrease). This corresponds to less than 0.1 mN/m change in calculated surface tension value. Thus, the droplet evaporation rate here can be assumed to not inuence the AFM measurements. S10 Simulation plots Figure S7: Simulation curves showing normalized surface tension,γ = γh/F adh as a function of normalized drop contact diameter,D = D/h for cone (left) and regular square pyramid (right) tip geometries for various tip-liquid contact angles (see colour legend) and tip half angle, α.