Mapping micrometer-scale wetting properties of superhydrophobic surfaces

Significance

The functional properties of surfaces are often dictated by their wettability. For example, to minimize smudging on a surface, it should be able to repel and not be wetted by oil easily. The most common approach to quantify the surface wettability is to measure the contact angle of a droplet. While easy to perform, such measurements are crude and imprecise. Here, we report a technique to measure the interaction forces between a small microdroplet and a surface with nanonewton resolution and spatially map the local wetting properties at the micrometer scale. The insight generated by the technique can then inform future design of functional coatings.

Abstract

There is a huge interest in developing superrepellent surfaces for antifouling and heat-transfer applications. To characterize the wetting properties of such surfaces, the most common approach is to place a millimetric-sized droplet and measure its contact angles. The adhesion and friction forces can then be inferred indirectly using Furmidge’s relation. While easy to implement, contact angle measurements are semiquantitative and cannot resolve wetting variations on a surface. Here, we attach a micrometric-sized droplet to an atomic force microscope cantilever to directly measure adhesion and friction forces with nanonewton force resolutions. We spatially map the micrometer-scale wetting properties of superhydrophobic surfaces and observe the time-resolved pinning–depinning dynamics as the droplet detaches from or moves across the surface.

Water droplets can easily bounce and roll off superhydrophobic surfaces, enabling many important applications, ranging from water-repellent coatings to drag reduction in ships (1, 2). Since Thomas Young first proposed the concept in his seminal 1805 paper (3), contact angle measurements have become the gold standard to characterize a surface wetting property. In fact, superhydrophobic surfaces are often defined by their high contact angles θ > 150 ° (1, 4, 5).

There are a few reasons for the popularity of contact angle measurements. First, they are easy to implement, requiring only good lighting and a high-resolution camera. Moreover, the adhesion and friction forces can be inferred, albeit indirectly, from the advancing and receding contact angles ${\theta }_{\text{adv, rec}}$ (6, 7). There is, however, a growing debate as to whether contact angles adequately describe the surface wetting properties (8–10). They do not, for example, capture the local wetting variations due to chemical heterogeneity or surface texture (11). Moreover, for large contact angles (e.g., in superhydrophobic surfaces), a small error in the positioning of the droplet base (as small as a single pixel) translates to a large error in the contact angle value (of more than 10 °) (12, 13).

To overcome these limitations, there have been several attempts to develop more sensitive surface characterization techniques. The most common approach is to use a cantilever force sensor to directly measure the friction and adhesion forces (with a typical 0.1-$\mathrm{\mu }$N resolution) acting on a millimetric droplet (14–16). Recently, by greatly suppressing the environmental noise, our group has improved the resolution of such an instrument (which we named the Droplet Force Apparatus) to about 5 nN (17). More impressively, by combining a sensitive force sensor with a motorized sample stage, Ras and coworkers were not only able to achieve a similar nanonewton force resolution, but also able to map wetting variations with a lateral resolution of $10\hspace{0.17em}\mathrm{\mu }$m (11).

Since its invention in 1986, atomic force microscopy (AFM) has become a standard and powerful surface characterization tool (18). AFM was used to characterize surface wetting properties by measuring the tip–surface interactions (19–23); however, the AFM tip is typically made of solid silicon/silicon nitride and has a pyramidal geometry, which poorly approximates droplet–surface interactions.

In this paper, we replace the solid tip with a microdroplet and use this modified droplet probe AFM technique to map local wetting properties of superhydrophobic surfaces. Previously, droplet probe AFM was used to study droplet–surface interactions, but only in limited contexts (e.g., the effects of surfactants) for liquid–liquid or bubble–liquid systems and never in ambient air (24–26). Here, by attaching a 40-wt$\%$ glycerin–water droplet of diameter 20 to 50 $\mathrm{\mu }$m onto the AFM cantilever, we are able to measure the friction and adhesion forces with much improved force and lateral resolutions (at least 1 nN and 1 $\mathrm{\mu }$m, respectively) and observe the fast pinning–depinning dynamics (millisecond timescale) as the droplet detaches from or moves across the surface.

Results and Discussion

We first investigated the wetting properties of the Morpho butterfly wings, well known for their brilliant blue color and excellent water repellency (Fig. 1 A–C) (27, 28). The wings are covered with scales with intricate micro- and nanostructures (see SI Appendix, Fig. S1 for detailed scanning electron micrographs), which trap a stable air layer, resulting in superhydrophobicity and a high static contact angle of 160 ° ± 10 ° for millimetric water droplets (Fig. 1D).

Fig. 1.

(A and B) Millimetric-sized water droplets bead up on the wings of a Morpho butterfly, which are covered by (C) superhydrophobic scales. (Scale bars, 4 cm, 3 mm, and 150 $\mathrm{\mu }$m, respectively.) (D) The scales of the butterfly wing trap an air layer, resulting in a high contact angle of 160 ° ± 10 ° for millimetric droplets. (Scale bar, 0.5 mm.) (E) On an individual scale, it is difficult to measure the contact angles of a micrometric droplet. (Scale bar, 50 $\mathrm{\mu }$m.)

Conventionally, the forces required to remove the droplets are inferred indirectly from the advancing and receding contact angles ${\theta }_{\text{adv, rec}}$ (12, 13, 29). For example, the friction force $F_{\text{fric}}$ required to move the droplet laterally is given by Furmidge’s relation

$$F_{\text{fric}}=\pi \gamma r\mathrm{\Delta }\cos \theta =\pi \gamma r\left(\cos {\theta }_{\text{rec}}-\cos {\theta }_{\text{adv}}\right),$$ [1]

where $r$ is the droplet’s base radius, $\gamma$ is the surface tension, and $\mathrm{\Delta }\cos \theta$ is the contact angle hysteresis (6, 7, 30). Contact angle measurements can be performed relatively easily for millimetric droplets, but become very challenging for micrometric droplets (SI Appendix, Figs. S2 and S3). Moreover, the droplet’s base can be obscured on uneven surfaces, further complicating the measurements (Fig. 1E).

To overcome the limitations outlined above, we use droplet probe AFM to quantify the local surface wetting properties (24–26). We attached a 40-wt$\%$ glycerin–water droplet of diameter 20 to 50 $\mathrm{\mu }$m onto a tipless cantilever probe with a flexular spring constant of $k_z=2$ N/m. The addition of glycerol suppresses the evaporation rate of the microdroplet, without greatly changing its surface tension or viscosity (69 mN/m and 4 mPa$\cdot$s, compared to 73 mN/m and 1 mPa$\cdot$s for pure water).

The vertical force acting on the droplet $F$ is linearly proportional to the flexular deflections of the AFM cantilever $\mathrm{\Delta }z$; i.e., $F=k_z\mathrm{\Delta }z$ (Fig. 2A). $\mathrm{\Delta }z$ is detected by shining a laser light (infrared, wavelength of 980 nm) onto the cantilever, which is reflected into a 4-quadrant sensor. To convert the raw voltage signals $V_{\text{vert}}$ into force $F$, we use Sader’s method (SI Appendix, Figs. S4 and S5) (31–34).

Fig. 2.

(A) The adhesion force $F_{\text{adh}}$ on individual scales of the butterfly wing can be measured accurately with droplet probe AFM, as shown by the schematic. (B) Top–down view of the setup, showing one droplet attached to an AFM cantilever and another one sitting on a wing scale. Outlines of several wing scales are marked by dashed lines. (Scale bar, 50 $\mathrm{\mu }$m.) (C) Force spectroscopy of a 30-$\mathrm{\mu }$m–sized droplet on a wing scale. Dashed and solid lines are the approach and retract curves. The droplet position $z$ has been corrected for cantilever deflection. By solving the Young–Laplace equation, we can (D) deduce the droplet geometry and (E and F) obtain the base radius $r$ and the contact angle $\theta$ at different time points.

Since the microdroplet is smaller than the size of the wing scale, we are able to quantify local wetting properties of individual scales (Fig. 2B). Fig. 2C is the force spectroscopy results for a 30-$\mathrm{\mu }$m–diameter droplet with volume $V$ = 20 $\pm$ 2 pL approaching and retracting from one of the wing scales at $U$ = 10 $\mathrm{\mu }$m/s. The droplet’s size and volume were obtained by optical microscopy and using Cleveland’s method (SI Appendix, Fig. S6) (34).

When the droplet is far from the surface, the AFM did not detect any force, i.e., $F$ = 0; however, upon contact, there is a sudden attractive snap-in force $F_{\text{snap}}$ = 132 nN. We continue to press onto the microdroplet to the maximum normal force $F_{\text{N}}$ = 10 nN, before retracting (Fig. 2C, solid line). For the droplet to be completely detached from the surface, there is a maximum adhesion force that must be overcome, $F_{\text{adh}}$ = 720 nN. By integrating under the retract curve, we can also obtain the amount of work required to remove the droplet, $W_{\text{adh}}$ = 5.6 pJ, which is a fraction of the total surface energy of the droplet $4\pi R^2\gamma \approx$ 200 pJ, reflecting the liquid-repellent nature of the surface.

It is also possible to relate the force spectroscopy measurement with the evolution of the microdroplet’s contact angle with time. The shape of the droplet $u\left(z\right)$ is described by the axisymmetric Young–Laplace equation

$$\begin{array}{cc}\hfill \frac{u″}{{\left(1+u^{\prime 2}\right)}^{3/2}}-\frac{1}{u\sqrt{1+u^{\prime 2}}}& =-\mathrm{\Delta }P/\gamma \hspace{0.17em}\mathrm{f}\mathrm{o}\mathrm{r}\hspace{0.17em}z\in \left(0,h\right),\hfill \\ \hfill u\left(h\right)& =w/2\hfill \\ \hfill u\left(0\right)& =r\hfill \\ \hfill {\int }_0^h\pi u^{2}dz& =V\hfill \\ \hfill F=-2\pi \gamma r\sin \theta +\pi r^2\mathrm{\Delta }P.\end{array}$$ [2]

The droplet contact area on the cantilever is fixed by the cantilever’s width $w$ = 28 $\mathrm{\mu }$m (SI Appendix, Fig. S7), while the droplet height $h$ and the force $F$ can be deduced from the position of the piezomotor and the cantilever deflection, respectively. By solving Eq. 2 numerically, we can deduce the droplet’s geometry and in particular the Laplace pressure inside the droplet $\mathrm{\Delta }P$, the base radius $r$, and the contact angle $\theta$ at different time points.

For example, during snap-in (time point 1), the droplet has a base radius of $r$ = 4.5 $\mathrm{\mu }$m and contact angle of $\theta$ = 161.3 ° (Fig. 2D); whereas at the maximum $\left|F\right|=F_{\text{adh}}$, $r$ = 3.2 $\mathrm{\mu }$m and $\theta$ = 137.0 °. See SI Appendix, Figs. S7 and S8 for details of the numerical method implemented in Python (35). Movie S1 shows the full simulation of the droplet geometry during the force spectroscopy measurement.

Since the flexular deflections can be monitored with high speeds (up to hundreds of kilohertz), we can resolve the fast pinning–depinning dynamics with submillisecond time resolutions and probe the resultant stick–slip contact-line motions with unprecendented detail. See SI Appendix, Fig. S9 for a discussion on the achievable time resolutions. As the droplet retracts, both $r$ and $\theta$ decrease gradually, except at certain time points (which correspond to discrete force jumps $\delta F\sim$ nN), where there are sudden discontinuities in $r$ and $\theta$ over a timescale $\mathrm{\Delta }t\sim$ ms. The magnitudes of the discontinuities $\delta r,\delta \theta$ can be as small as fractions of a micrometer and a degree, respectively (Fig. 2 E and F). The sensitivity achieved with droplet probe AFM will allow us potentially to verify the accuracy of different depinning models (36, 37). Note that $r$ and $\theta$ should be taken as effective, radially averaged values, since we made the assumption of an axisymmetric droplet’s shape, even though the contact line is likely to be jagged and discontinuous (10).

We also note that there is no single value of ${\theta }_{\text{rec}}$ for the microdroplet. If we consider the retraction curve up to $F_{\text{adh}}$, where the contact line retracts at a relatively constant speed of $|\mathrm{d}r/\mathrm{d}t|\approx$ 0.7 $\mathrm{\mu }$m/s, ${\theta }_{\text{rec}}$ varies between 137 ° and 150 ° (shaded area in Fig. 2E), which translates to a contact angle hysteresis value of $\mathrm{\Delta }\cos \approx 1+\cos {\theta }_{\text{rec}}$ = 0.13 to 0.27, which is slightly higher than the $\mathrm{\Delta }\cos =0.05$ to 0.21 measured for a millimetric-sized droplet using a conventional tilting-plate method (SI Appendix, Fig. S2). This could be explained by the fact that the overlapping wing scales are able to trap an additional air layer, resulting in a lower solid surface fraction for millimetric droplets.

We repeated the force spectroscopy measurements for a total of 66 different wing scales and the resulting 670 depinning events (Fig. 3A). There are significant wetting variations between scales. For example, $F_{\text{snap}}$ can be as small as a few nanonewtons to more than 300 nN for the same 20-pL microdroplet; similarly $F_{\text{adh}}$ can vary between 84 and 943 nN, while $W_{\text{adh}}$ varies between 0.1 and 7.6 pJ. During droplet retraction, the magnitude of the force jumps $\delta F$ can vary between a couple of nanonewtons and more than 60 nN. Since $\delta F\sim a_{\text{p}}\gamma n_{\text{p}}$ where $a_{\text{p}}$ is the typical size and $n_{\text{p}}$ is the number of pinning points contributing to the depinning event, the probability density of $\delta F$ decreases rapidly with increasing $\left|\delta F\right|$; larger $\delta F$ is less likely to occur, because it involves simultaneous depinning from multiple points. In general, higher $F_{\text{adh}}$ translates also to higher $F_{\text{snap}}$ and $W_{\text{adh}}$ values, although there are large variations (Fig. 3 B and C). For example, when $F_{\text{adh}}$ = 500 nN, $F_{\text{snap}}$ varies between 50 and 200 nN, while $W_{\text{adh}}$ varies between 1 and 5 pJ.

Fig. 3.

(A) Histogram of $\delta F$, $F_{\text{snap, adh}}$, and $W_{\text{adh}}$ for a total of 66 different scales and 670 depinning events. (B and C) Plots of $F_{\text{adh}}$ against the snap-in force $F_{\text{snap}}$ and $W_{\text{adh}}$, with each point representing a different scale.

The force spectroscopy measurements therefore provide us with a wealth of information not easily obtained using conventional contact angle measurements. Note that while the results vary between wing scales, the force spectroscopy curves for each scale are reproducible (SI Appendix, Fig. S10). Experimentally, we also found that the results do not depend on the applied $F_{\text{N}}$ or the speed $U$; i.e., viscous effects are not important (SI Appendix, Figs. S11 and S12).

The raster scanning capability of the AFM also allows us to perform force spectroscopy measurements over a grid array of points to map micrometer-scale wetting variations on surfaces. To illustrate this, we chose a superhydrophobic surface with well-defined micro-/nanostructures, which consists of a square array of 10-$\mathrm{\mu }$m–diameter pillars decorated with smaller 2-$\mathrm{\mu }$m pillars, spaced $L$ = 20 $\mathrm{\mu }$m and $l$ = 3.5 $\mathrm{\mu }$m apart, and with a total height $H$ = 2.5 $\mathrm{\mu }$m (Fig. 4A). See SI Appendix, Fig. S13 for scanning electron micrographs and AFM images.

Fig. 4.

(A) $F_{\text{adh}}$ of a microdroplet on a structured surface can be mapped with micrometer-scale resolution. The surface consists of a square array of 10-$\mathrm{\mu }$m–diameter pillars with smaller 2-$\mathrm{\mu }$m pillars on them. (B) Force maps for a 30-$\mathrm{\mu }$m–sized droplet. (Scale bar, 10 $\mathrm{\mu }$m.) (C) A more detailed force map with the outline of the micropillars superimposed. (Scale bar, 2 $\mathrm{\mu }$m.) (D) Force spectroscopy curves on top (area 1) and in between pillars (area 2).

Fig. 4B is an adhesion map for an array of 3 $\times$ 3 pillars (70 $\times$ 70 $\mathrm{\mu }$m, 100 $\times$ 100 px). The force spectroscopy measurements were performed with a 30-$\mathrm{\mu }$m–sized droplet and at a relatively high speed $U$ = 150 $\mathrm{\mu }$m$\cdot {\mathrm{s}}^{-1}$ to minimize the scanning time to about 20 min. The adhesion is greatest when the droplet is in the gap between 4 neighboring pillars (marked 1 in Fig. 4B), where $F_{\text{adh}}$ can reach almost 800 nN (Fig. 4D). In contrast, when the droplet is on top of the micropillar (marked 2 in Fig. 4B), $F_{\text{adh}}$ is only about 150 nN.

It is likely that the 30-$\mathrm{\mu }$m–sized droplet is touching the base at area 1, where the gap between the pillars is the largest. In fact, when the experiment is repeated on a micropillar surface with the exact same lateral dimensions but taller $H$ = 12 $\mathrm{\mu }$m, there are no longer high-adhesion areas in area 1 (SI Appendix, Fig. S14). A closer look at the adhesion map also reveals the 4-fold and 6-fold symmetries that reflect the underlying positional symmetries of the micropillars (Fig. 4C).

We have therefore demonstrated the ability of droplet probe AFM to map wetting variations in the micrometer scale, despite the droplet’s size being much larger. This is because the lateral resolution is determined by the droplet’s base diameter $2r\sim$ 1 $\mathrm{\mu }$m (rather than its outer diameter $2R$) just before it detaches (Movie S1).

We can measure the friction force $F_{\text{fric}}$ by moving the droplet laterally in contact mode and monitoring the resultant torsional deflection of the cantilever $\mathrm{\Delta }\varphi$, since $F_{\text{fric}}=k_{\varphi }\mathrm{\Delta }\varphi /h$, where $k_{\varphi }=69.3$ nN$\cdot$m is the torsional spring constant (Fig. 5A). The torsional deflection is captured as voltage signal $V_{\text{lat}}$ by the 4-quadrant sensor and we used Sader’s method to relate $V_{\text{lat}}$ to $F_{\text{fric}}$ (SI Appendix, Figs. S4 and S5).

Fig. 5.

(A) $F_{\text{fric}}$ of a microdroplet moving on the micropillar surface can be measured accurately with droplet probe AFM. (B and C) Depinning due to individual 10-$\mathrm{\mu }$m and 2-$\mathrm{\mu }$m micropillars (spaced $L$ = 20 $\mathrm{\mu }$m and $l$ = 3.5 $\mathrm{\mu }$m apart, respectively) can be clearly distinguished.

Fig. 5B shows the lateral force measured for an array of 5 pillars (labeled 1 to 5), as we move a 30-$\mathrm{\mu }$m–sized droplet back and forth over a 100-$\mathrm{\mu }$m distance twice. During the motion of $U$ = 5 $\mathrm{\mu }$m$\cdot {\mathrm{s}}^{-1}$, the normal force is kept at $F_{\text{N}}$ = 5 nN. The force measured is positive one way and negative the other way, because the torsional deflections are in the opposite directions. Note also that since the spacing between pillars is $L$ = 20 $\mathrm{\mu }$m, the droplet is in contact with only one pillar at any one time.

The force required to detach from one pillar can vary between $F_{\text{fric}}=1.3\pm 0.3\hspace{0.17em}\mathrm{\mu }$N (pillar 1) and 2.7 $\pm$ 0.2 $\mathrm{\mu }$N (pillar 5). A closer look at the force spectroscopy measurements also reveals force jumps spaced $l=3.5\hspace{0.17em}\mathrm{\mu }$m apart, due to depinning from the smaller 2-$\mathrm{\mu }$m–sized pillars (Fig. 5C). Experimentally, we also found that $F_{\text{fric}}$ is independent of $U$, consistent with previous reports (SI Appendix, Fig. S15) (10). See also the friction force measurement results for the Morpho butterfly wing scale, where force jumps due to submicrometer features can clearly be seen (SI Appendix, Fig. S16).

While we have confined our discussion to superhydrophobic surfaces, the technique described in this paper can be adapted for other liquid probes (e.g., an oil droplet) and other liquid-repellent surfaces (e.g., an underwater superoleophobic surface). The force and lateral resolutions of the technique can also be easily improved by using a softer cantilever and a smaller droplet. Our technique will greatly complement other ultrasensitive surface wetting characterization tools previously reported, such as the Droplet Force Apparatus (16, 17) and the Scanning Droplet Adhesion Microscope (11). However, unlike previous approaches, our approach does not require any specialized instrument beyond a conventional AFM setup, which is available to many research groups.

Conclusion

In short, the potential of droplet probe AFM as a surface wetting characterization tool remains largely unexplored and we hope this work will stimulate further development of the technique and result in additional insights in wetting science. The technique developed here has direct relevance in many applications, e.g., in developing antifogging surfaces, in understanding surface condensation processes, and in emulsion science, where the wetting properties are dominated by droplets that are micrometers or even smaller in size.

Materials and Methods

Materials.

IP-Dip photoresist was purchased from Nanoscribe Inc. Propylene glycol monomethyl ether acetate (PGMEA) ($>$99.5$\%$), (3-aminopropyl)triethoxysilane (APTES), perfluorodecyltrichlorosilane (FDTS), glycerin, isopropyl alcohol, and ethanol were purchased from Sigma-Aldrich. Chromium (Cr) target (99.994$\%$) was purchased from Kurt J. Lesker Company. Aluminum (Al) target (99.99$\%$) was purchased from Zhongnuo Advanced Material Technology Co. Ltd. All chemicals were used without further purification, unless otherwise stated. The tipless AFM cantilever was purchased from NanoWorld and has dimensions of 225 $\times$ 28 $\times$ 1 $\mathrm{\mu }$m (length, width, and thickness).

Micropillar Fabrication.

The hierarchical micropillar surface is created by direct-write, 2-photon lithography using the Nanoscribe Photonic Professional instrument (Nanoscribe Inc.). The photoresist used (IP-Dip) is a proprietary negative-tone resin from Nanoscribe that can be used to create the submicrometer feature.

To improve the adhesion of the resin to the fused silica substrate, we first cleaned the substrate with oxygen plasma for 5 min at 100 W. The silica substrates were then submerged in 2$\%$ (vol/vol) APTES in ethanol for 5 min, followed by rinsing with a 50$\%$ (vol/vol) water/ethanol mixture. Subsequently, the substrates were blown dry with nitrogen gas and dried in an oven at 65 °C.

The micropillars were designed using computer-aided design (CAD) software SolidWorks and their dimensions were defined using the DEScribe software. The structures then written on fused silica substrate by direct laser writing (DLW), using an inverted microscope with an oil-immersion lens (Zeiss Plan Apochromat, 63$\times$, NA 1.4) and a computer-controlled piezoelectric stage. The DLW process was performed with an erbium-doped, femtosecond laser source with a center wavelength of 780 nm, pulse repetition rate of 80 MHz, and pulse length of 100 fs. The average laser power was around 40 mW and writing speed was 30 mm/s. After writing, sample substrates were developed in PGMEA, followed by isopropyl alcohol for 30 min each, and then air dried.

Surface Treatment of Micropillar.

Two nanometers of Cr film was coated on the substrates, followed by deposition of Al film up to 100 nm with a thermal evaporator system (Syskey) operating under high vacuum of $10^{-6}$ to $10^{-7}$ Torr. The micropillar with the Al coating was then boiled in DI water close to 100 °C for 20 min. This converts the Al coating into a nanostructured boehmite layer.

We then submerge the surface in a solution of 1 wt$\%$ FS-100, 5 wt$\%$ water in ethanol for 1 h at 70 °C. This fluorinates the boehmite layer and hence renders the micropillar surface superhydrophobic (38).

Droplet Probe AFM.

To create the microdroplets, we forced the 40-wt$\%$ glycerin solution through the nozzle of a conventional spray bottle onto a superhydrophobic surface. This generates multiple droplets with diameters between 10 and 80 $\mathrm{\mu }$m.

To ensure that the microdroplet does not spread on the AFM cantilever, we hydrophobize the surface by vapor-phase silanization with fluorinated silane FDTS. Once the cantilever is fluorinated, we can then pick up a microdroplet of the desired size to perform force spectroscopy measurements on another surface of interest. Note that the microdroplet is attached to the cantilever much more strongly than to the superhydrophobic surfaces. As described in the main text, there is little or no evaporation of the glycerin droplet.