Article pubs.acs.org/JPCC
Shape of Water−Air Interface beneath a Drop on a Superhydrophobic Surface Revealed: Constant Curvature That Approaches Zero Boris Haimov,†,‡ Sasha Pechook,†,‡ Orna Ternyak,§ and Boaz Pokroy†,‡,* †
Department of Materials Science & Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel Russell Berrie Nanotechnology Institute, Technion Israel Institute of Technology, Haifa 32000, Israel § Micro- and Nano- Fabrication Unit (MNFU) Department of Electrical Engineering, Technion Israel Institute of Technology, Haifa 32000, Israel ‡
ABSTRACT: The 3D interface between a sessile water drop that is found on a superhydrophobic microtextured surface has been directly imaged using a confocal microscope with an immersion lens. The local mean curvature of the water−air interface was derived and was shown to be constant and close to zero not only for the case of pure water, but also for cases of variable drop density and surface tension. Although the mean curvature is constant and close to zero, the standard deviation on the mean curvature increases with increasing drop density and lower surface tension. The resulting 3D image of the water−air interface at the bottom of a water drop demonstrates the possibility of investigating practical interfaces of water on given textures and confirms that no matter what the superhydrophobic surface characteristics are, the interface remains with a constant curvature of close to zero.
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curvature, C.16 The total curvature for a given point on a surface is given by C = R1−1 + R2−1 where R1 and R2 are the principle radii of a given point, giving: ΔP = γ(R1−1 + R2−1). Thus, in the simplest case of binary liquid interface, the predicted interface shape is one with a constant curvature, such as a section of a perfect sphere. Experimental observations agree with these predictions.15 A second case is that of a liquid−gas interface which is constrained by a solid substrate. The substrate might theoretically be perfectly smooth without any defects. In such a case, one should employ the Young relation,17 which relates the three possible interface tensions and the CA:18
INTRODUCTION For more than a decade, there has been an ever-increasing interest both scientifically as well as technologically in the phenomenon of superhydrophobicity.1 The applications of superhydrophobicity are manifold and some examples are as follows: self-cleaning surfaces2 (windows, building paints), windshields,3 antifouling applications,4 low water adhesion,5 anti-icing surfaces,6 and nonwetting textiles.7 Nature also demonstrates superhydrophobicity as a strategy for the selfcleaning of leaves and plants such as the famed lotus leaf,8 nonwetting bodies of insects such as butterflies,9 beetles,10 and even entire biofilms.11 Superhydrophobicity, by definition, is a state in which the apparent contact angle (CA) of water on a surface is over 150°.1b The only way to enhance a hydrophobic contact angle to a superhydrophobic state is by introducing surface roughness.1b,12 The two major models for superhydrophobic conditions are the Wenzel13 and the Cassie−Baxter14 states. In the former the water beneath a drop fills the asperities of the surface roughness, while in the latter air pockets are trapped beneath the water drop forming what is known as a composite interface. Many theoretical efforts have been carried out in order to explain and predict the behavior of liquid binary interfaces (liquid−gas and liquid−liquid interfaces). The simplest interface to this end, where no reaction occurs between the phases, will behave according to the Young−Laplace relation:15 the pressure difference, ΔP, on the interface is equal to the interfacial surface tension, γ, multiplied by the total interface © XXXX American Chemical Society
γSG = γSL + γLG cos θ0 where γSG, γSL, and γLG are the surface−gas, surface−liquid, and liquid−gas interfacial tensions, and θ0 is the intrinsic contact angle. In this case, practical observations also agree with the predictions of the Young relation. A third case which is most relevant to the current study is a constrained interface that is attained when the liquid phase is found on top of a textured solid substrate. These interfaces include the case in which a liquid phase resides on a rough surface, such as for example, hierarchically textured surface structures like those found on Lotus leaf and on numerous other natural and artificial interfaces. In these examples, Received: December 21, 2012 Revised: March 5, 2013
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Figure 1. Zeiss Ultra Plus (HR-SEM) High Resolution Scanning Electron Microscope micrograph of the epoxy positive replica (a) view with 30° tilt angle, (b) top view, and (c) indication of the relevant 1 μm diameter and 3 μm pitch.
used parameter optimized for obtaining dense high aspect ratio (1:10) silicon pillars and to avoid block etch. The etching process was terminated with C4F8 plasma (which is known to deposit a thin Teflon-like layer) in order to induce hydrophobic properties to the etched Silicon surface, followed by removal of residual photoresist in commercial solvent solution. Replication of the Microtextured Surface from Epoxy and Making Them Superhydrophobic. In order to reproduce the patterned surface from epoxy, we utilized a soft lithography technique as described elsewhere.25 The initial high-aspect-ratio silicon master was covered by Polydimethylsiloxane (PDMS), vacuum treated for residual air removal and cured at 80 °C for 3 h. This formed a negative replica which was removed gently. UV-initiated one-part epoxy UVO-114TM (Epoxy Technology) was poured over the negative replica followed by 20 min UV curing. Following full curing the epoxy positive replica was peeled off from the PDMS. The micro patterned epoxy surface was coated with a 20 nm gold layer by sputtering under 0.1 Torr. The gold surface was modified with a dodecanethiol (C12SH) self assembled monolayer26 in a 24 h process where the thiols are adsorbed via gaseous phase to the surface. In this way, the prepared surface became hydrophobic (θ0 > 90) and in combination with its microtextured structure, leads to superhydrophobic characteristics. Measuring the static contact angle of a water droplet on these epoxy surfaces revealed contact angles of 170°. Imaging the Water−Air Interface. A Leica DCM-3D confocal microscope was utilized in this experiment to directly image the water−air interface. An X63 Leica immersion lens was immersed within 1 mL drops (H2O, D2O, or water− ethanol mixtures), which were placed on the microtextured superhydrophobic epoxy substrate. The strong mismatch between the refractive indexes of water and air allowed the direct imaging of the water−air interface beneath the droplet. Fields of views of 128 × 128 pixels2 were imaged. With a lateral resolution of about 263 nm/pixel for the X63 immersion lens, the resulting images were of about 33 × 33 μm2. The bare substrate was imaged using the nonimmersion X50 lens with a
utilizing more complex relations such as those introduced by Wenzel,13 Cassie−Baxter,14 and their derivatives, is warranted. To date, very limited practical direct observation of such complex interfaces has been made and the 3D shape of such interfaces remains unclear. Luo et al.19 by utilizing confocal laser scanning microcopy from above and from outside of a drop in the Cassie−Baxter state could prove experimentally that indeed there is air trapping beneath a drop in the Cassie− Baxter state. They could also show the in situ transition from the Cassie−Baxter state to that of the Wenzel state. Papadopoulos et al.20 recently also imaged such a gradual transition. Boreyko et al., utilizing side view optical microscopy, could prove that indeed there is air trapped beneath a drop in the Cassie−Baxter state.21 Chen et al.22 by using Environmental Scanning Electron Microscopy (ESEM) and Atomic Force Microscopy (AFM) on a millimeter-sized water drop supported on a Lotus leaf surface, could also observe the air trapped below a drop on a superhydrophobic surface and the Cassie−Baxter Wenzel transition. Chen et al.22 could also show interesting quasi Wenzel states and partial air trapping in nano cavities. Rykaczewski et al.23 used in situ cryogenic SEM to image the water air interface after the water drop freezes. Rathgen et al. studied the dynamics of periodic arrays of micrometer-sized liquid−gas menisci formed at superhydrophobic surfaces.24
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EXPERIMENTAL SECTION
Fabrication of Silicon Microtextured Template. Si template is a square lattice array of 10 μm high, 1 μm diameter round pillars, and a 3 μm pitch. The fabrication was done on 2″ (100) oxidized Silicon wafers using standard photolithography and etching techniques. Samples were patterned with 1818 photoresist by GCA Autostep 200 DSW i-line Wafer Stepper UV exposure followed by TMAH development. The pattern was transferred into the silicon oxide layer, used as a hard mask, by CF4/O2 Reactive Ion Etching (RIE) in a 790 PlasmaTherm tool. The subsequent etching of Silicon pillars to the depth of 10 μm was carried out in a PlasmaTherm Versaline Inductively Coupled Plasma (ICP) system by a Deep Reactive Ion Etching (DRIE) process. We B
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Figure 2. Imaging the 3D water−air interface beneath a water drop on a superhydrophobic microtextured substrate. (a) Macro view of the confocal X63 immersion lens inside the water drop, the acquired 3D images of the (b) water-air interface, (c) 170° water CA on the supporting textured surface demonstrating it indeed induces superhydrophobicity, and (d) supporting substrate. The 3D image of the bare substrate was produced using a nonimmersion X50 lens.
of the interface and show that the local curvature at every point of the interface is constant and close to zero. We also demonstrate how the local curvature of the interface changes as a function of the liquid drop’s density and as a function of the liquid−air interfacial tension. Imaging the water−air interface beneath a drop in the Cassie−Baxter state was performed by a Leica DCM-3D confocal microscope with an immersion lens submerged within a 1 mL drop placed on a microtextured superhydrophobic surface (Figure 1). As is clearly observed in Figure 2, the resulting interface at the bottom of the water drop does not wet the substrate and is clearly in the Cassie−Baxter state with air pockets trapped beneath. Though the height of the substrate’s textural features (see Experimental Section) was 8 μm, the water−air interface beneath the drop dipped between the features by only about 150 nm (see Figure 2b). The Cassie−Baxter state was achieved due to the high surface roughness and the hydrophobic surface treatment of the substrate (also observed by contact angle of over 170° seen Figure 2c). In this situation, the Cassie−Baxter state is a thermodynamically preferred state.16,29 The water−air interface has clear periodic maxima and minima where the minima are between four substrate posts while the maxima seem to be above each substrate post. To further study the resulting 3D shape of the interface that is observed in Figure 3b, we exported the 3D data points (X, Y, and Z) of the water−air interface and transferred it to the Matlab program environment where we used the built-in “surfature” function that extracts the surface curvature at each point on a given 3D surface. This procedure provides a histogram of the local curvatures of the interface at each pixel. Such a histogram can be observed in Figure 3 for the case of pure water. The curvatures extracted by the Matlab surfature function are the mean curvature (H) values, that is H = (K1 + K2)/2, where K1 and K2 are the maximum and minimum of the normal curvature at a given point on a surface and are called the principal curvatures which are always orthogonal. These principal curvatures measure the maximum and minimum bending of a regular surface at each point on the
lateral resolution of about 328 nm/pixel, the resulting image was of about 42 × 42 μm2. Varying the Surface Tension and Density of the Drops. Variation in the surface tension of the aqueous drops was achieved by simply mixing water with ethanol.27 Since the surface tension of the ethanol−air interface is much lower (23 mN/m) than that of the water−air interface (75 mN/m), the resulting mixture of a small amount of ethanol with water yielded prominent lowering of the liquid’s surface tension while maintaining an almost constant drop density. Variation in the pressure difference between the top and the bottom of the drop was achieved by altering the density of the drop. Such alteration was achieved by using a mixture of “heavy water” (D2O) with distilled water (H2O). This maintains a constant surface tension of the drop while allowing for density variation (just above 10%). Surface Tension Measurements. Surface tension measurements were performed utilizing an Attension Theta LiteTM optical tensiometer by KSV instruments. The tool allows the measurement of the surface tension, contact angle; drop volume and some other relevant physical properties. The tool is based on a computer controlled CCD camera. A PC runs software that acquires the digital images from the CCD camera and extracts the surface tension and contact angle properties from the digital acquired image. The desired values are extracted from the digital image using fitting algorithms, which are based on the fact that the surface principal curvature reveals information on the surface tension.28
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RESULTS AND DISCUSSION Despite recent fundamental studies, there remain as yet two open questions which have not been fully answered, namely, what is the 3D shape of a water−air interface beneath a drop on a superhydrophobic surface and what is the local curvature of this shape? Herein, we directly image the water−air interface beneath a drop on a superhydrophobic surface from within the drop with excellent resolution so as to reveal the 3D shape of this interface. We were also able to calculate the local curvature C
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surface tension as compared to that of water (23 mN/m vs 75 mN/m), the surface tension was significantly lowered by the addition of the ethanol. Figure 4 presents the mean interface curvature histograms for the cases of variation in liquid density and surface tension,
Figure 3. Mean curvature histogram of the water−air interface beneath a drop on a superhydrophobic surface of pure water.
surface. The relation between the total curvature, C, and the mean curvature, H, is given by H = C/2. The Histogram in Figure 3 clearly reveals that the distribution of the resulting local curvatures is a normal distribution possessing a defined mean value, μ = 0.001 μm−1, and a standard deviation around the mean value, σ = 0.045 μm−1. The fact that the mean local 3D curvature is close to zero is not trivial and has never previously been proved experimentally. The reason one expects a mean curvature close to zero is that according to the Young−Laplace equation the pressure difference across the drop−air interface is proportional to the mean curvature. As the pressure difference is very small (see elaboration below) the mean local curvature should also be close to zero and this is exactly what we have obtained in this experiment. This has also been elegantly pointed out theoretically by Marmur.16 In order to prove that the curvature beneath a drop on a superhydrophobic surface should indeed be close to zero, we should calculate the pressure difference at the bottom of the drop. As we have rather large water drops in our experiments due to technical limitations (1 mL), the effect of gravity is stronger for very small droplets (beneath the capillary size). The pressure difference is given by ΔP = ρgh, where ρ is the density of the liquid, g is the gravity constant, and h is the height of the drop that was maintained constant at h ≈ 0.6 cm. Having ρ ≈ 1 gr/mL and g ≈ 10 N/kg we receive a pressure difference with close approximation to ΔP ≈ 60 Pa. This pressure difference is very small in comparison to the ambient atmospheric pressure of approximately 101 kPa. Since the local mean curvature of a given point on an interface is given by H = ΔP/2γ, it is straightforward to conclude that the expected mean curvature of all points on the resulting interface should be very small as graphically shown in Figure 2b and analytically presented in Figure 3. We further desired to investigate the shape and local curvature of the water−air interface beneath a drop on a superhydrophobic surface as a function of liquid density and surface tension. For the former, we performed similar experiments in which we kept the drop volume constant at 1 mL, however we mixed heavy water (D2O) with pure water at different ratios. For the latter we used ethanol/water mixtures (up to 10% ethanol). As ethanol has a considerably lower
Figure 4. (a) Mean curvature histograms of the water−air interface beneath a drop on a superhydrophobic surface of different relative mixtures between water and heavy water (variable density) and (b) mean curvature histograms of the water−air interface beneath a drop on a superhydrophobic surface of different relative mixtures between water and ethanol (variable surface tension).
respectively. Both plots presented in Figure 4a,b also show that the distribution of the resulting local mean curvatures are normal distributions with a mean value and a deviation around the mean value as for pure water (Figure 3). The calculation of the mean local curvature, μ, and the appropriate standard deviation, σ, are presented in Tables 1 and 2. It is clearly seen Table 1. H2O and D2O Mixture Drops Measurements Summary D2O
0%
25 %
50 %
75 %
100 %
H2O
100 %
75 %
50 %
25 %
0%
ST [mN/m] D [gr/mL] μ(C/2) [1/um] σ(C/2) [1/um]
73.7 1.011 0.001 0.045
74.0 1.039 −0.001 0.054
74.0 1.056 −0.001 0.067
74.1 1.086 −0.001 0.078
74.0 1.116 −0.003 0.087
that in all cases, the mean value is very close to zero, which again corroborates the fact that the change in pressure is Table 2. H2O and EtOH Mixture Drops Measurements Summary
D
EtOH
0%
2.5 %
5%
7.5 %
10 %
H2O
100 %
97.5 %
95 %
92.5 %
90 %
ST [mN/m] D [gr/mL] μ(C/2) [1/um] σ(C/2) [1/um]
73.7 1.011 0.001 0.045
69.3 1.002 −0.002 0.061
55.6 0.997 −0.003 0.101
50.7 0.990 0.014 0.199
45.9 0.985 0.002 0.228
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negligible. Another interesting trend that is clearly observed in both the case of the varying surface tension as well as the case of varying density, is that there is a considerable increase in the standard deviation of the mean curvature as one increases the drop’s density and lowers its surface tension (see Tables 1 and 2). The variable drop’s density plots (Figure 4a) suggest that the lower the pressure difference at the interface, the lower the standard deviation in mean curvature becomes. This may be explained intuitively by the concept that the pressure difference is the driving force that deforms the interface. Thus, the higher the pressure difference, the higher the deformation trend, and hence the higher the standard deviation in the mean curvature. The variable drop’s surface tension plots (Figure 4b) suggest that the lower the surface tension, the higher the deviation. This may be explained intuitively by the concept that the surface tension of a given interface is the resistive force to the interface deformation, thus the greater the surface tension, the greater the resistance to deformations, and hence the lower the standard deviation of the mean curvature. In conclusion, the resulting 3D imaging of the water−air interface beneath a water drop on a superhydrophobic surface allowed the measurement of the local mean curvature of this interface. Experimental curvature analysis coincides with the theoretical expectations that the interfaces’ mean curvature at every point is constant and close to zero. Since experimentally one is dealing with a real system, the results show the form of a Gaussian (Normal) distribution with a mean value that fits theoretical expectations of approximately zero curvature. The standard deviation of the resulting interfaces was proportional to the pressure difference on the given interface and also proportional to the inverse surface tension of the given interface. The simple and intuitive reason for such behavior of the standard deviation is that the surface tension resists the interface deformation, and the pressure difference acts as a driving force that deforms the interface. We believe that these results are important for the fundamental understanding of wetting phenomena and our technique will open up new opportunities to study different phenomena that take place at the water−air interface not only on synthetic materials, but also directly on biological materials.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding
Financial support by the Russell Berrie Nanotechnology Institute at the Technion. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS Very helpful discussions with Prof. A. Marmur from the Technion are greatly appreciated. We thank the Russell Berrie Nanotechnology Institute at the Technion for financial support. The fabrication was performed at the Micro-Nano Fabrication Unit (MNFU), Technion. E
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(21) Boreyko, J. B.; Baker, C. H.; Poley, C. R.; Chen, C.-H. Wetting and Dewetting Transitions on Hierarchical Superhydrophobic Surfaces. Langmuir 2011, 27 (12), 7502−7509. (22) Chen, P. P.; Chen, L.; Han, D.; Zhai, J.; Zheng, Y. M.; Jiang, L. Wetting Behavior at Micro-/Nanoscales: Direct Imaging of a Microscopic Water/Air/Solid Three-Phase Interface. Small 2009, 5 (8), 908−912. (23) Rykaczewski, K.; Landin, T.; Walker, M. L.; Scott, J. H. J.; Varanasi, K. K. Direct Imaging of Complex Nano- to Microscale Interfaces Involving Solid, Liquid, and Gas Phases. ACS Nano 2012, 6 (10), 9326−9334. (24) Rathgen, H.; Sugiyama, K.; Ohl, C. D.; Lohse, D.; Mugele, F., Nanometer-Resolved Collective Micromeniscus Oscillations through Optical Diffraction. Phys. Rev. Lett. 2007, 99 (21). (25) Pokroy, B.; Epstein, A. K.; Persson-Gulda, M. C. M.; Aizenberg, J. Fabrication of Bioinspired Actuated Nanostructures with Arbitrary Geometry and Stiffness. Adv. Mater. 2009, 21 (4), 463−. (26) Verho, T.; Bower, C.; Andrew, P.; Franssila, S.; Ikkala, O.; Ras, R. H. A. Mechanically Durable Superhydrophobic Surfaces. Adv. Mater. 2011, 23 (5), 673−678. (27) Vazquez, G.; Alvarez, E.; Navaza, J. M. Surface Tension of Alcohol Water + Water from 20 to 50 .degree.C. J. Chem. Eng. Data 1995, 40 (3), 611−614. (28) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. Determination of Surface-Tension and Contact-Angle from the Shapes of Axisymmetric Fluid Interfaces. J. Colloid Interface Sci. 1983, 93 (1), 169−183. (29) Marmur, A. Solid-Surface Characterization by Wetting. Annu. Rev. Mater. Res. 2009, 39, 473−489.
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