Cassie-State Wetting Investigated by Means of a Hole-to-Pillar Density

pubs.acs.org/Langmuir © 2010 American Chemical Society

Cassie-State Wetting Investigated by Means of a Hole-to-Pillar Density Gradient Doris M. Spori,† Tanja Drobek,‡ Stefan Z€urcher,†,§ and Nicholas D. Spencer*,† †

Laboratory for Surface Science and Technology, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland, ‡Department Earth and Environmental Sciences, Section Crystallography, LMU Munich, Theresienstrasse 41/III, 80333 Munich, Germany, and § SuSoS AG, Lagerstrasse 14, 8600 D€ ubendorf, Switzerland Received December 15, 2009. Revised Manuscript Received March 7, 2010 The superhydrophobicity of rough surfaces owes its existence to heterogeneous wetting. To investigate this phenomenon, density gradients of randomly placed holes and pillars have been fabricated by means of photolithography. On such surfaces, drops can be observed in the Cassie state over the full range of f1 (fraction of the drop’s footprint area in contact with the solid). The gradient was produced with four different surface chemistries: native PDMS (polydimethylsiloxane), perfluorosilanized PDMS, epoxy, and CH3-terminated thiols on gold. It was found that f1 is the key parameter influencing the static water contact angle. Advancing and receding contact angles at any given position on the gradient are sensitive to the type of surface feature;hole or pillar;that is prevalent. In addition, roll-off angles have been measured and found to be influenced not only by the drop weight but also by suction events, edge pinning, and f1.

Introduction Since the superhydrophobic, self-cleaning properties of the lotus leaf1 were attributed to its rough surface structure, many different approaches have been developed to produce similar superhydrophobic surfaces artificially (see e.g. the review by Roach et al.2). While both natural and industrially produced superhydrophobic surfaces generally have a stochastic distribution of surface features, most investigations that have sought to determine which parameters lead to stable self-cleaning properties have been performed on micrometer-sized, photolithographically fabricated, periodically arranged pillars.3-6 This approach does not take into account the possibility that the inherently strong anisotropy of periodic structures, or even the periodicity itself, may have an effect on the wettability of a surface. It is therefore of interest to examine controlled, aperiodic surfaces, which are also better analogues for technically relevant systems. Gradients are very helpful tools7 for the investigation of a system’s sensitivity to specific parameters over a given range, since they constitute an inherently high-throughput approach. On surface gradients, one parameter is changed along the length of the sample, and therefore all other conditions, such as temperature, pressure, or surface energy, can be maintained constant while multiple measurements are made simultaneously over the parameter range selected. The parameter investigated in the present study was stochastically distributed pillar/hole density. This substrate allows models from the literature to be tested as to their validity on surfaces that resemble technically relevant systems. *Corresponding author. E-mail: [email protected]. (1) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1–8. (2) Roach, P.; Shirtcliffe, N. J.; Newton, M. I. Soft Matter 2008, 4, 224–240. (3) Barbieri, L.; Wagner, E.; Hoffmann, P. Langmuir 2007, 23, 1723–1734. (4) Bico, J.; Marzolin, C.; Quere, D. Europhys. Lett. 1999, 47, 220–226. (5) Callies, M.; Chen, Y.; Marty, F.; Pepin, A.; Quere, D. Microelectron. Eng. 2005, 78-79, 100–105. (6) Quere, D. Annu. Rev. Mater. Res. 2008, 38, 71–99. (7) Morgenthaler, S.; Zink, C.; Spencer, N. D. Soft Matter 2008, 4, 419–434.

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Generally, on a rough, somewhat hydrophobic substrate two different wetting states are possible: Either the drop completely conforms to the surface topography, or it bridges from asperity to asperity, spanning the air gaps beneath. The first case can be denoted as the Wenzel8 state and the second case as the Cassie and Baxter (CB) state.9 Both states can be associated with very high contact angles, but only in the CB state are very low roll-off angles in evidence, along with the concomitant self-cleaning effect. In this work, most drops described are in the CB state, but only few have low roll-off angles (e10°). On rough surfaces, as a consequence of contact-line pinning, there is not a single contact angle that describes wetting. In fact, the contact angle can adopt any value between a minimum (receding contact angle, θr) and a maximum (advancing contact angle, θa) value. The difference between θa and θr is known as the hysteresis. Findings on Regular Pillar Surfaces. Among other parameters, Barbieri et al.3 have investigated the influence of pitch distance (in hexagonal, square, and honeycomb periodic patterns) and pillar-top perimeter on the static contact angle of water drops atop perfluorinated silicon pillars. They generally found that the drop resides in the CB state much longer than would be predicted by calculating the thermodynamic transition to the Wenzel state. Pattern parameters, such as symmetry, pitch distance, and the pillar perimeter, only influenced the stability of the CB drop near the transition point, hexagonal and long perimeters favoring the CB state. € 10 and Dorrer11 have shown that the advancing contact Oner angle of a drop suspended on pillars in the CB state for a given f1 (fraction of the area under the drop in contact with the solid) is independent of the shape or spacing of the pillars. Dorrer and R€uhe11 proposed that the receding motion of the contact line is (8) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988–994. (9) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 0546–0550. € (10) Oner, D.; McCarthy, T. Langmuir 2000, 16, 7777–7782. (11) Dorrer, C.; R€uhe, J. Langmuir 2006, 22, 7652–7657.

Published on Web 05/20/2010

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governed by a jumping motion from one post to another, starting at the outermost post that inhibits the drop in assuming its preferred spherical shape. By holding f1 constant, they showed that increasing the pillar-top dimensions reduces the receding contact angle (thus increasing hysteresis), whereas increasing the pitch distance leads to an increase in the receding contact angle and € 10 suggests that the contact-angle hystereduced hysteresis. Oner resis on a surface of random roughness should be smaller than that on a regular surface with the same f1 due to the higher distortion of the contact line. Callies et al.5 measured constant advancing contact angles on perfluorinated silicon pillars for f1 values from 1% up to 25% and additionally showed how, for low pillar densities, it is possible to have drops in both the Wenzel and CB state, depending on the way in which the drop was put on the surface. Several frequently used models for wetting have been tested with the acquired data. The models investigated were the CassieBaxter approximation,9 the Furmidge equation for roll-off angles,12 and a proposition from Patankar13 for receding contact angles. Models Tested on the Pillar-Density Gradients. On an ideal surface, surface tensions γXY (where the subscripts X and Y refer to the phases at the corresponding X-Y interface: solid (S), liquid (L), or air (A)) in balance lead to one specific contact angle, the Young’s14 contact angle θY: cos θY = (|γBSA| - |γBSL|)/|γBLA|. However, most surfaces are not ideal and have a certain degree of roughness. Roughness generally increases the contact angle,15 unless surface energy is high enough to induce hemiwicking.16 Wenzel8 introduced an area roughness factor r to modify Young’s equation, which takes into account the increased surface area and its influence on contact angle (θW): cos θW = r cos θY. Concerns about this equation have been expressed, from both a theoretical17 and an experimental15,18 standpoint, but Wenzel’s description of the conformal wetting state is a useful one. On certain surfaces the roughness is so profound that the surface tension of the liquid is sufficiently high to bridge from asperity to asperity and enclose air beneath the drop. Cassie and Baxter9 modified Wenzel’s equation to take the behavior of this composite surface into account: cos θCB ¼ f1 cos θ - f2

ð1Þ

f1 and f2 describe the area fractions of the drop’s footprint in contact with the solid and in contact with air, respectively. f1 corresponds to the solid surface area wetted by the drop and f2 to the area where the drop spans over air enclosures. Since both parameters are normalized by the analyzed projected area, f1 þ f2 g 1. For small drops where gravity can be neglected and the Laplace pressure in the liquid is assumed to be constant,6 sagging of the drop can be neglected and the area fraction constituting f2 is assumed to be flat. When working with flat-top pillars, the area fraction of f1 can also be assumed to be flat, and then f1 þ f2 = 1. There remains a controversy in the field18,19 that can be summarized by the phrase “area vs line”. The models of Wenzel and CassieBaxter are based on area considerations. If they are tested by freeenergy calculations and free-energy barriers, they correctly predict (12) Furmidge, C. G. J. Colloid Sci. 1962, 17, 309–324. (13) Patankar, N. A. Langmuir 2003, 19, 1249–1253. (14) Young, T. Philos. Trans. R. Soc. London 1805, 95, 65–87. (15) Spori, D. M.; Drobek, T.; Z€urcher, S.; Ochsner, M.; Sprecher, C.; M€uhlebach, A.; Spencer, N. D. Langmuir 2008, 24, 5411–5417. (16) Quere, D. Physica A (Amsterdam, Neth.) 2002, 313, 32–46. (17) Gray, V. R. Chem. Ind. 1965, 23, 969. (18) Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 3762–3765. (19) Gao, L.; McCarthy, T. J. Langmuir 2009, 25, 7249–7255.

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the equilibrium contact angles for the noncomposite (Wenzel) and the composite (Cassie-Baxter) state.20 Nevertheless, the shape of the drop is also determined by the interaction at the three-phase-contact line; sharp edges influence the contact angle via pinning phenomena that are not considered in the thermodynamic approach.18,21 Surprisingly, the CB approximation has not prompted as many criticisms regarding its validity as the Wenzel equation, even though they are based on similar principles. In 1962, Furmidge12 was looking into the conditions necessary for drop retention on inclined surfaces and, by equating all the forces involved, defined a correlation between the inclination R of the surface with the drop weight m, drop diameter perpendicular to the sliding direction w, advancing and receding contact angles (θa, θr), and the surface tension γBLA of the liquid. f mg sin R ¼ wjγ LA jðcos θr - cos θa Þ

ð2Þ

Furmidge assumed the footprint of the drop to be rectangular during sliding, which may be a source of error, but the equation is sufficiently accurate to be able to account for sliding drops on a flat surface. The Cassie-Baxter model was designed to describe drops in thermodynamic equilibrium. Advancing and receding contact angles deviate from the equilibrium contact angles. Therefore, Patankar13 deduced, via energy considerations, a condition that would describe the case of the receding drop if it would not leave a dry, but a wet, surface behind. In this case, the θr should obey the following rule: cos θPr ¼ 2f1 - 1

ð3Þ

In this work, a novel, rapid method has been developed to explore the influence of quasi-randomly placed pillars and holes on the wetting of surfaces over a controlled range of f1 values. In order to investigate a large parameter range, hole-to-pillar density gradients have been prepared that span the range from isolated holes to isolated pillars, both of 20-30 μm diameter. A systematic study of the wetting mechanisms and the effect of the real contact area on static and dynamic contact angles and roll-off angles has been carried out on hole-to-pillar density gradients prepared with four different surface chemistries. In contrast to earlier systematic studies,3,5,22 this gradient approach covers the full range of f1 (0-100%) and is, by the choice of the pillar distribution, a useful model for technically relevant surfaces.

Materials and Methods A variety of morphological gradients with identical topography and different surface chemistry was prepared, following the procedure summarized in Figure 1. Masks. The design of the mask is based on a 900 dpi bitmap (28.2 μm/pixel) with a random distribution of black and white pixels, which was printed on a foil mask. Photoshop CS (Version 8.0 for Macintosh) was used to create an 8-bit grayscale image. The image of the black-to-white gradient was modified with the linear gradient tool, which was set to span from black (gray value of 0) to white (gray value of 255) for the whole range of pillar density. Afterwards, the image was transformed to a binary image of black and white pixels by using the option “diffusion dither” in the image mode menu. The resulting image was used for the printing process. For technical reasons the whole range of pillar densities was split onto two samples, thus giving a higher accuracy (20) Li, W.; Amirfazli, A. Adv. Colloid Interface Sci. 2007, 132, 51–68. (21) Extrand, C. W. Langmuir 2002, 18, 7991–7999. (22) Priest, C.; Albrecht, T. W. J.; Sedev, R.; Ralston, J. Langmuir 2009, 25, 5655–5660.

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Figure 1. Scheme of experimental setup: A pixel image of a grayscale gradient going from black to white was prepared and then converted into a black-and-white bitmap. Printing this bitmap on a transparency foil leads to a “pixel” mask for standard photolithography. A topographical gradient master was prepared by using standard photolithography of SU-8 on silicon. In a twostep replication process, copies of the master were prepared from epoxy or PDMS. These substrates were functionalized with hydrophobic surface coatings. The wetting properties were analyzed by measuring dynamic and static water contact angles and roll-off angles. for positioning the water drops. Each substrate was 42 mm long and 12 mm wide. The gradient covered 35 mm of the substrate, leaving 7 mm of microstructure-free area for handling of the substrate and measuring the reference contact angles (f1 =100%). The microstructure-free area is flat, only exhibiting the nanoscale roughness possibly created during the photolithographic step and thus having the same surface topography as the flat-top pillars. Because of the presets of gamma correction in the color workspace of the computer used to generate the gradient mask, the distribution of black and white pixels along the gradient shows a distinct nonlinearity. A detailed analysis of the pixel distribution on the mask is shown in Supporting Information 1. The mask manufacturing (Fotosatz Salinger AG, Z€ urich) was carried out with a drum exposure system (3810 dpi resolution) on a polyester foil of 0.1 mm thickness. Masters. The photolithographic masks were used to prepare the masters for the replica technique. Standard photolithography was performed on 4 in. silicon wafers. After wafer cleaning, SU-8 2025 negative photoresist (MicroChem, USA) was spin-coated for 60 s at 2000 rpm to a thickness of 30 μm and soft-baked on a hot plate for 2 min at 65 °C and 3 min at 95 °C. Subsequently, the wafer was exposed to UV light (MA6, S€ uss MicroTec, Germany) with constant intensity (total energy 180 mJ/cm2) through the photolithographic mask described above. After postbaking for 2 min at 65 °C and 3 min at 95 °C, the wafers were developed for 5 min in SU-8 developer (MicroChem, USA). Finally, the wafer was hard baked at 190 °C for 10 min. Replicas. In order to facilitate the replica process, the masters were exposed to air plasma for 2 min and then functionalized with fluorosilanes (1H,1H,2H,2H-perfluorooctyltrichlorosilane, ABCR GmbH, Germany) by vapor phase deposition in a desiccator (rough vacuum) for 1 h. Then, a mixture of polydimethylsiloxane (PDMS, 1:10 curing agent to base, SYLGARD 184 silicone elastomer, base and curing agent, Dow Corning, USA) was cast over the master and allowed to cure overnight at 70 °C. The cured PDMS replica represented the negative of the master. Langmuir 2010, 26(12), 9465–9473

Article After that, the PDMS negative replica was exposed to 2 min air plasma (RF level high, 0.1 Torr, PDC-32G, Harrick Plasma, USA) and functionalized with a layer of fluorosilanes. Again, a 10:1 mixture of PDMS was cast and cured overnight at 70 °C to yield a positive replica of the master. Contact angles were measured on the bare PDMS positive and on its surface following subsequent functionalization with fluorosilanes. Epoxy positive replicas were produced as substrates for surface functionalization by self-assembled monolayers (SAMs) with thiol headgroups, similar to the procedure described in our previous publication.15 The PDMS negatives were used as molds to cast an epoxy blend (EPO-TEK 302-3; Epoxy Technology, USA). The epoxy was mixed according to the protocol provided by the producer (4.5 g of Part A with 10 g of Part B), cast from the negative under vacuum, allowed to cure at 60 °C overnight, and postcured at 150 °C for 1 h. Later, these epoxy replicas were cleaned by ultrasonication for 10 min in a 2 vol % aqueous solution of Hellmanex (Hellma, Germany) and subsequently rinsed five times with ultrapure water (resistance 18.2 MΩ, TKA-GenPure, Huber & Co. AG, Switzerland). Contact angle measurements were performed after this step. By resistance evaporation (MED 020 coating system, BALTEC, Liechtenstein) the samples were coated with a layer of 10 nm Cr and 50 nm Au (purity >99.99%, Umicore, Liechtenstein). During coating, the stage was rotated and tilted by 25°. Directly after coating, the samples were immersed in a 0.1 mM solution of dodecylthiol (Aldrich Chemicals, USA) in ethanol for 20 min, rinsed with ethanol, and blown dry under a stream of nitrogen. Contact angles were measured on the freshly prepared samples. Contact Angle and Roll-Off Angle Measurements. Static and dynamic contact angle measurements were performed on a Kr€ uss DSA 100 (Kr€ uss, Germany). Static contact angles (θs) were usually measured with drop volumes of 6 or 9 μL on surfaces with contact angles above 140°. The drop was produced, still hanging on the syringe, and then the stage with the substrate was slowly lifted until the substrate touched the drop. Upon lowering the stage again, the drop detached, and after it came to rest, an image was taken. Thus, the history of the contact line was a purely advancing motion. The drop volume had to be increased to 9 μL for contact angles above 140°, since otherwise the drop would not detach from the syringe. For dynamic contact angles (advancing (θa) and receding (θr)) measurements the drop volume was increased and decreased with a speed of 15 μL/min. This leads to low-rate contact-angle measurements with advancing contact-line speeds below 0.012 mm/s. Receding contact-line speeds are slightly higher on strongly pinning surfaces, at around 0.03 mm/s. For the advancing drop, two movies with 200 frames and, for the receding drop, one movie with 250 frames were recorded. In cases where the drop was pinned on one side, only the moving side of the drop was taken into account for the evaluation.15 All drops were fitted with the tangent method 2 routine, a fourth-order polynomial function, of the DSA3 software (Kr€ uss, Germany). This routine has difficulty in fitting drops with large contact angles in the Cassie regime, leading to a systematic underestimation of a few degrees. Therefore, all drops with contact angles higher than 135° were fitted in ImageJ. Static contact angles were evaluated by means of the drop-analysis23 plug-in and dynamic contact angles with the simple angle tool delivered with ImageJ. The reasons are more closely described in Supporting Information 2. Roll-off angles were measured on a home-built device. It consists of a stage that is fixed on one side to a spindle and a goniometer that indicates the angle of the stage. The substrate is placed on the stage, and a drop of 6-9 μL is placed onto the sample surface. The stage is tilted until the drop starts to move, and the roll-off angle is recorded. (23) Stalder, A. F.; Kulik, G.; Sage, D.; Barbieri, L.; Hoffmann, P. Colloids Surf., A 2006, 286, 92–103.

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Scanning Electron Microscopy. The epoxy substrates were analyzed in a Gemini 1530 FEG SEM (Zeiss, Germany) at 3-5 kV, at room temperature, gold-coated as described above. Extraction of f1 and f2. The grayscale SEM images were imported into the ImageJ program and then transformed into black-and-white bitmaps. These bitmaps can be analyzed with the “analyze particles” tool, yielding pillar-top area and perimeter for each pillar on the image. Summing this pillar-top area and then dividing the sum by the total analyzed (projected) area results in a value of f1. For f2 it is assumed that f1 þ f2 =1, since the pillar tops are flat, exhibiting no significant roughness. The analyzed areas were 1.88  1.27 mm2, except for the positions at 51, 56, 61, and 66 mm (corresponding to f2 values of 80.2, 85.9, 88.2, and 94.4%), where the pillar density fell below 1000 pillars per analyzed area. Below this pillar density the contrast in gray values was too low for the program to distinguish between pillar and background. Therefore, the contrast had to be enhanced by hand by coloring the pillar tops white, and the analyzed area was reduced to 0.39  0.26 mm2.

Results and Discussion By the use of standard photolithography, the original bitmap from the Adobe Photoshop program was transferred into a morphological gradient by adding the third dimension (height) to the 2D pattern (see Figure 2). By using a negative photoresist, such as SU-8, all white pixels are cross-linked while the black pixels are etched away. This led to a morphology containing hole features on the “white” side of the gradient, gradually merging to larger holes, until islands were isolated, ending up as single pillars on the “black” side of the gradient. The same parameters for the photolithographic step were used as in our former publication,15 leading to all features being flat on top and slightly undercut, similar to golf tees. The undercut shape helps to support the drop in the Cassie state24 and ensures that the drop only wets the tops of the pillars. By choosing different materials (PDMS and epoxy) and surface coatings (perfluorinated silanes and CH3-terminated thiols on gold/epoxy), the surface chemistry of the substrates was varied. In Figure 3a the distribution of the black pixels (black dots) along the gradient extracted from the bitmap is compared to the f2 measured on SEM images on the positive (epoxy) replica (gray dots). The spots chosen for the SEM analysis were the same spots as used for the contact-angle measurements. The dotted line is a guide to the eye to show a gradient of black and white pixels having an entirely linear increase of black pixels along the distance. As already mentioned in the Materials and Methods section, the black pixels do not increase linearly along the gradient due to presets of the color workspace. The slight deviations between the bitmap and the topography occur during the printing and photolithography steps of the master fabrication. In the middle range (20-45 mm), where f2 is higher than the bitmap data, color bleeding in the printing process led to larger black areas on the mask. At positions 0-20 mm, f2 is actually lower than expected because of the cross-linking of the SU-8 epoxy. On an ideal substrate the corners of diagonally neighbored pixels would only touch, but on our master, the SU-8 actually forms narrow bridges across the corners. At the other end of the gradient (positions 45-70 mm) the larger printing of the black pixels compensates the bridges formed between the single, neighboring white pixels (f1). Figure 3b is a correlation graphic. It shows f2 extracted from the SEM analysis plotted versus f2 calculated from the contact (24) Tuteja, A.; Choi, W.; Ma, M. L.; Mabry, J. M.; Mazzella, S. A.; Rutledge, G. C.; McKinley, G. H.; Cohen, R. E. Science 2007, 318, 1618–1622.

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Figure 2. SEM-image composite of the gold-coated epoxy replica, containing 16 images that have been sampled every 5 mm along the gradient. The original white-to-black gradient on the photolithographic mask stretched from the top, white end, to the bottom, black end. The top end of the gradient contains isolated holes, whereas the bottom part is dominated by isolated pillars. In the central part of the gradient, the pixels grow together to yield more complex structures. Langmuir 2010, 26(12), 9465–9473

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Figure 3. Statistical analysis and static contact angles. (a) f2 distribution along the gradient. Black circle shows the data of a black pixel analysis on the initial gradient bitmap, and gray circle shows the extracted f2 from the SEM analysis on the epoxy replica and the dotted line represents a linear increase of f2 along the substrate. The error bars for the extraction of f2 from the SEM images of the epoxy replica were smaller than the circles used for the data presentation. (b) Correlation between f2 measured on the epoxy replica and f2 calculated from the static contact angle data by solving the Cassie-Baxter equation. (c) The static water contact angle measurements on all four substrates and the corresponding Cassie-Baxter approximation (dashed lines): perfluorinated PDMS, gold- and dodecylthiol-coated epoxy, native PDMS, native epoxy. The contact angles at high f2 values after the steep drop are in the Wenzel state. There, the pillars are set too far apart from each other to suspend the drop in the CB state.

angle data, solving the CB approximation (eq 1) for f2: f2 ¼

cos θY - cos θCB cos θY þ 1

ð4Þ

This calculation was performed for all available surface chemistries and the obtained data entered into the graph. Since, in principle, the same parameter (f2) is plotted on both axes, the data should exactly follow the bisector. The data show some scattering around the bisector but do not display a significant deviation that would imply another (or no) correlation. At f2 values exceeding 70%, the scattering pattern changes slightly, which we suspect to be due to gravitational influences on the drop (see Supporting Information 3). Influence of f1/f2 on Contact Angle. When plotting static contact angle data versus distance on the replicate substrates (Figure 3c), the data clearly show the same trend as depicted in the statistical analysis of the distribution of the initial black pixels (and f2) versus distance (Figure 3a). The shoulder in the black and white distribution occurs at the same position in the contact angle data. This is an indication that on our quasi-random substrates f1 and f2 are indeed the significant parameters influencing the contact angle of drops in the CB state. Since the static measurement is closest to thermodynamic equilibrium, it is justifiable to compare the data with the predictions calculated according to the CB approximation (eq 1). In the first part of the gradient in Figure 3c, with f2 going from 0 to 70% (equal to the distance of 0-41 mm) θs shows a good correlation to the Cassie-Baxter approximation. At the black end, where f2 approaches 100%, θs drops down to the angle measured on a flat sample with the same surface chemistry. Here, the distance between the pillars gets Langmuir 2010, 26(12), 9465–9473

so large that the drop cannot span from one pillar top to the next and wets in the Wenzel state. At the position of f2 equal to 97.3% the drop on the sample coated with thiols on gold/epoxy is metastable. Drops were observed to be in both states: Wenzel and CB state. Just before this transition at f2 values between 70 and ∼90% (positions between 41 and ∼61 mm), a deviation from the CB prediction occurs, which may be due to gravitational and discretization effects (see Supporting Information 3). “Line vs Area”. The question arises as to how the parameters f1/f2, which are area fractions, can be the main parameters influencing the contact angle in the CB state after it was shown18,25 that the contact angle of a drop is only defined by what is in the vicinity of the contact line and not by what is to be found underneath the drop. The explanation is quite simple: Since the topographical features are small compared to the base diameter of the drop (pillar side length of ∼30 μm versus drop base diameter of >1 mm), the value of f1 determined as an area fraction is equivalent to the fraction of the contact line in contact with the solid. In this case, f1 is actually a line parameter, not an area parameter. The question as to where the contact line truly contacts the pillars is irrelevant for this consideration, since the pillar tops are small compared to the footprint of the drop and deviations from the ideal circular footprint are negligible. Dynamic Contact Angle Data. Many equations describing wetting phenomena on rough surfaces such as eqs 1 and 3 include a cosine function. Therefore, plotting the cosine rather than the pure contact angle data versus f2 yields a straight line, if the data (25) Extrand, C. W. Langmuir 2003, 19, 3793–3796.

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Figure 4. Comparison of dynamic-contact-angle data on different surface chemistries with the prediction by Cassie and Baxter (two lines: advancing slope always lower than receding slope) and Patankar: (a) perfluorinated PDMS surface, (b) gold and CH3-terminated SAM on epoxy substrate, (c) native PDMS surface, and (d) native epoxy surface. Symbols: open symbols=advancing; full symbols=receding; dashed gray lines=corresponding Cassie predictions; dotted gray line=Patankar prediction (only for the graph of the native PDMS since its shape is the same for all other chemistries). The alternating dashed black lines are linear fits to the data.

follow the CB predictions. Thus, Figure 4 shows the cosine of the dynamic contact angle data measured on all four substrates versus f2 (perfluorinated PDMS, PDMS; CH3-terminated thiols and the pure epoxy surface). Additionally, the CB predictions for the dynamic case were calculated, using the f2 extracted from the SEM images. The condition for receding contact angles as proposed by Patankar (eq 3) was also computed. Since eq 3 is only dependent on f1 and not on surface chemistry, it looks the same for all data sets. In order to keep Figure 4 readable, it is only added to the graph of the native PDMS because there the strongest correlation between Patankar’s prediction and the receding contact angle can be seen. Supporting Information 4 shows the same figure with the raw measured contact-angle data rather than the cosines. Similarly to the static contact angles, the advancing and receding contact angles show a distinct dependence on f2. A detailed analysis shows that the gradients can be split into different regimes: For values of f2 larger than 95%, the distance between neighboring pillars is too large to be spanned by the drop, and therefore the drop is in the Wenzel state, showing contact angles close to those found on a flat surface. For smaller f2 values the drop only touches the pillar tops. In Figure 4, linear fits were added to selected data points (alternating dashed black lines). In the central region of the gradients, advancing as well as receding contact angles rise as air enclosure increases. For the perfluorinated PDMS surface, this region ranges from f2 = 0% to 75% for advancing angles and f2 =28% to 95% for receding angles. Receding angles show a tendency to level off for low values of f2, whereas for advancing angles, a plateau is visible for large f2. Qualitatively, the behavior is the same for all the materials investigated, although 9470 DOI: 10.1021/la904714c

the transitions from one regime to the other occur at different positions on the gradient. Looking at the advancing contact angles, they rise with increasing hole density. The rise can be approximated by a linear trend line and in the case of the PDMS and the fluorinated PDMS even follows the CB prediction exactly. As the features increasingly resemble single pillars, the θa levels off at about 160° (150° for the more hydrophilic epoxy substrate), and no change is detectable with decreasing pillar density. The phenomenon of leveling off at high advancing contact angles (around 160°) has also been reported by others,5,22 working with periodically distributed micrometer-sized pillars (4-fold symmetry). In this work, stagnation starts between 60% and 80% of air, and not at the same location for all substrates, even though they are replicates of the same master. Clearly, surface energy plays a role in the onset of stagnation. Additionally, since the sequence (CH3-terminated thiols, perfluorinated PDMS, PDMS, epoxy) does not strictly follow surface energy, other properties of the material can apparently play a role. For example, PDMS, an elastomer, has a much lower elastic modulus than epoxy, which is a thermoset. The low modulus of PDMS is also the reason why the advancing contact angle on the flat part of PDMS is larger than that on the perfluorinated PDMS: the y-component of the liquid-air surface tension cannot be fully compensated and thus forms a rim around the base perimeter of the drop. This rim acts as surface roughness and slightly increases the contact angle.26,27 During plasma (26) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1996, 184, 191–200. (27) Shanahan, M. E. R.; De Gennes, P. G. Equilibrium of the Triple Line Solid/ Liquid/Fluid of a Sessile Drop; Elsevier Applied Science: New York, 1987.

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treatment of the PDMS, which is necessary to functionalize the surface with perfluorinated silanes, a silica-like layer is formed.28 This layer is stiffer than the bulk PDMS. Therefore, the perfluorinated PDMS has a surface coating that is both more hydrophobic and stiffer than the native PDMS; thus, no rim formation occurs on these samples (see Supporting Information 5). The receding contact angles mirrored this behavior to some extent. On the holey side they first stagnate or even decrease, again until the holes become larger and the features resemble pillars, at which point the θr begins to increase. The rise starts at around 10% of air for the consistently hydrophobic substrates (CH3-terminated thiols and perfluorinated PDMS) and at 50% of air for the more hydrophilic substrates (PDMS and epoxy). PDMS is known to change the orientation of its methyl groups upon contact with water, making it more hydrophilic in this situation.29,30 This change of orientation and the aforementioned rim formation are the reason for the high contact angle hysteresis; even on flat PDMS; besides the roughness of the rim, the advancing contact line encounters a more hydrophobic surface than the receding contact line. The CB equation generally greatly overestimates θr, and the Patankar derivation strongly underestimates the measured θr of the hydrophobic substrates and clearly overestimates the θr of the epoxy surface. Only in the case of PDMS does the θr rise follow the Patankar prediction from 45% to 80% of air. This phenomenon is not yet a proof that a water film is actually left behind (the Patankar assumption), since other factors such as reorientation could be playing a role. Priest et al.22 showed in their investigations on substrates consisting only of holes or of pillars that the contact-angle hysteresis actually indicates on what type of feature the drop sits. Stagnation of the advancing and linear increasing of the receding contact angle with an increasing amount of air enclosure is a characteristic of the pillar surface. A linear increase of the advancing (a rather close agreement with the CB approximation) and stagnation or even decrease of the receding contact angle is found on holey surfaces. On our gradient surface where holes slowly merge together and pillars are formed, this behavior is also observed. However, although all four substrates exhibit the same topography, the transition point at which the behavior changes from hole contact to pillar contact cannot be found at the same f2 value (see Figure 4, intercepts of the linear regressions (alternating dashed lines)). Most probably, between air percentages of 20-70% the effects of topography intermingle and surface energy starts to play a more important role. In Figure 5, the cosine of the contact-angle hysteresis (Δ cos θ= cos θr - cos θa) vs f2 is shown. With increasing air content the hysteresis increases for all substrates up to about ∼50% air. Beyond this point, the hysteresis decreases rapidly until it reaches its minimum, before the collapse into the Wenzel state (indicated by a sharp increase in hysteresis at large f2 values). For the two consistently hydrophobic substrates (CH3-terminated thiols and the perfluorinated PDMS) a plateau in hysteresis can be distinguished between 20% and 50% of air. Nevertheless, all curves show a minimum at around 45% of air. Dividing the data sets into two parts (0 to 45% and 45 to ∼100% for all drops in CB state), the first part is predominantly governed by the mechanism originating from the hole structure and the second part is mostly governed by the presence of pillars. Each part can be fitted (28) Hillborg, H.; Sandelin, M.; Gedde, U. W. Polymer 2001, 42, 7349–7362. (29) Chen, C.; Wang, J.; Chen, Z. Langmuir 2004, 20, 10186–10193. (30) Morra, M.; Occhiello, E.; Marola, R.; Garbassi, F.; Humphrey, P.; Johnson, D. J. Colloid Interface Sci. 1990, 137, 11–24.

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Figure 5. Contact-angle hysteresis (cos θr - cos θa) as a function of f2 (f2 = 1 - f1). The curves have been separated for clarity. The slopes of the linear regressions are a measure for the pinning energy22 (circles=perfluorinated PDMS; triangles=thiols on gold/epoxy; squares = native PDMS; pyramids = epoxy). Table 1. Slopes of the Linear Fit in Figure 5 (Dashed Lines) Are Compared to the Values Found by Priest et al. on Homogeneous Substrates Epin/γLA 22

Priest et al. perfluorinated PDMS CH3-terminated thiols PDMS epoxy

holes

pillars

0.4 0.6 0 0.6 1.2

1.2 0.8 1.1 1 1.2

by a linear curve fit. According to Priest et al.,22 the slope in this linear fit is a measure for the pinning energy Epin and equal to Epin/γLA (see eq 5): Δ cos θ ¼ Δ cos θ0 þ fD

Epin γLA

ð5Þ

fD corresponds to the area fraction of the “defect”. A surface consisting of holes can be considered as a matrix of substrate with very low-energy defect patches (air enclosures). Therefore, fD corresponds to f2 on the holey side of the substrate. Similarly, a pillar surface consists of a matrix of air with high-energy defects (pillars; even a hydrophobic surface has a higher interaction with the liquid than air). Thus, on the pillar side, fD corresponds to f1. The slopes found on the substrates used in this work clearly show the same tendency: pinning energy of the pillars is significantly higher than the pinning energy of the holes (Table 1). On the holey surface the contact line is mostly in contact with the solid. In this way the energy barriers to adopting the contact angle corresponding to the lowest-free-energy state are lowered because of increased flexibility in the positioning of the contact line on the substrate. By being able to meander between the defects, the contact line does not have to follow the shape of the defects exactly, as it does on the pillar side, but can actually average over the defects on the surface, as was assumed in the CB approximation. This averaging might also be the reason why the CB approximation fits the data of the θa better on the holey side than on the pillar side. But, as mentioned above, the difference between the values of Epin/γLA (Table 1, holes vs pillars) is not quite as profound as in the work of Priest et al., most probably due to the fact that both features are present in the middle of the gradient. The differences in Epin/γLA between the present work (stochastic) DOI: 10.1021/la904714c

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Figure 6. Sine of the roll-off angles of all analyzed surfaces. Only data points are shown where a roll-off angle could actually be measured. All positions where the drop did not move up until a tilt angle of 90° are not displayed. Drops on the pure epoxy surface did not roll off at any angle. The dotted line shows the prediction by the Furmidge equation for each surface.

and that of Priest et al. (periodic) for similar features and surface chemistries could also be an effect of the greater contact line dis10 € tortion in the stochastic case, as was suggested by Oner. Despite the strong hysteresis, all drops evaluated were still in the CB state. In Supporting Information 6, examples of light microscopy images taken through a water drop are presented and clearly show the air enclosure over the full gradient. Despite its lower hydrophobicity, the epoxy surface is clearly in the CB state, since it shows qualitatively the same behavior as observed on the more hydrophobic substrates, which would not be the case if it were in the Wenzel state.31 Figure 6 shows the sine of the roll-off angles measured on the four different substrates together with the approximation calculated by the Furmidge equation (see eq 2, dashed lines). All parameters occurring in the Furmidge equation were measured independently from the roll-off angle (drop weight m, drop diameter w, advancing and receding contact angles θa, θr). Positions where no roll-off angles occurred are not displayed in that graph. For the pure epoxy surface no roll-off angle at any position could be observed for the given drop volumes. The native PDMS does not show any roll-off on the flat area due to the high hysteresis induced by the reorientation of the polymer side chains upon contact with water. For the two consistently hydrophobic substrates (perfluorinated PDMS and CH3-terminated thiols on gold), on the holey side of the gradient the roll-off angle increases with increasing hole density, until no movement is observable even up to 90°. Movement is only possible again when the topography changes from holes to pillars. There, the sine of the roll-off decreases linearly with f2 (R2 of the linear regression >97%). As observed in Figure 5, the holey side shows a lower pinning energy than the pillar side. But in Figure 6 the drop rolls off far more easily on the pillar side. One reason for this is that the contact line has far more contact (low f2) on the holey side than on the pillar side. Therefore, the inherent contact-angle hysteresis on the material plays a bigger role on the adhesion of the drop. At first this adhesion is increased by the introduction of pinning defects such as holes. Additionally, there is a range on the holey side of the gradient where the drop could not roll off at all. Two reasons may explain this phenomenon: (1) the receding contact line was strongly pinned, possibly aided by the finite curvature of the edges, at the front end of the holes;22 (2) due to the suction (31) Fetzer, R.; Ralston, J. J. Phys. Chem. C 2009, 113, 8888–8894. (32) Wang, S.; Jiang, L. Adv. Mater. 2007, 19, 3423–3424. (33) Steinberger, A.; Cottin-Bizonne, C.; Kleimann, P.; Charlaix, E. Nat. Mater. 2007, 6, 665–668.

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induced by the sealed air cushions,32,33 the drop was held on the surface. We therefore conclude that there are at least three different influences beyond f2 that determine whether a drop can roll off a surface consisting of holes (sealed air cushions): one, the size and with it the weight of the drop defines the driving energy for downward motion (as seen by Reyssat et al.34); two, pinning at the front edge of the drop; and three, the magnitude of the suction effect. On the pillar side the drop started moving at an air content of 56.2% (CH3-terminated thiols and perfluorinated PDMS) and for the PDMS at 71.4%. The onset of drop movement for the consistently hydrophobic substrates coincides with the position chosen to divide the data for the linear regressions in Figure 5, probably indicating a change in the prevalent pinning mechanism. The Furmidge equation is able to predict the general behavior of the roll-off angles. It is an equation consisting only of measured values. Since no distinct deviation of the measured values can be observed, it can be concluded that all necessary parameters to describe the behavior were identified. The suction or pinning events mentioned above also influence the receding contact angle and are therefore taken into account in the equation.

Conclusions A novel, rapid method for creating photolithographic masks has proven invaluable for the fabrication of gradients of 3D structures. Pseudo-random hole-to-pillar density gradients, covering the total f1 range of 0-1, have been shown to be a useful tool for investigating the influence of structural effects on a variety of different wetting phenomena, such as static and dynamic contact angles and roll-off angle. By the use of a gradient surface consisting of nearly randomly placed pillars slowly agglomerating into holes, different wetting mechanisms of drops in the CB state could be identified. Static contact angles increase more or less linearly with f2, clearly indicating the importance of f1 and f2 for the wetting behavior of a drop in the CB state. Since the topographical structures here are small compared to the drop diameter, the area parameters f1 and f2 can also be considered as line parameters influencing the contact line. When measuring advancing and receding contact angles, analyzing the hysteresis can distinguish whether holes or pillars are the predominant topographical feature. Dynamic measurements have shown that pinning energy is higher on pillared than on holey surfaces. Wetting behavior is consistent with that reported in previous (nongradient) studies,22 which utilized periodic surface structures, and thus the degree of periodicity appears to be of secondary importance to that of the f1 value. Drops of 6 μL were found to be pinned so strongly on holey structures that they do not roll off at all. Two potential causes were identified: pinning at the front edge of the drop and suction events of sealed air cushions. Acknowledgment. The authors thank Ciba Speciality Chemicals for their generous financial assistance and Electron Microscopy ETH Zurich, EMEZ, for their support. Additionally, we thank Rene T€olke for help with the photolithography, Cathrein H€uckst€adt for fruitful discussions, and Martin Elsener for building the roll-off angle goniometer. Financial support of TD by BMBF grant “Geotechnologien” 03G0709A is gratefully acknowledged. (34) Reyssat, M.; Quere, D. J. Phys. Chem. B 2009, 113, 3906–3909.

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Supporting Information Available: Supporting Information 1: more information on the mask characterization; Supporting Information 2: the difficulties in analyzing very high contact angles by testing different analysis tools; Supporting Information 3: discussion of the possibility that for drops in the CB state (showing very high contact angles) gravitational effects may occur at smaller volumes than is generally assumed by calculating the capillary length;

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Supporting Information 4: contact angle data acquired on the gradient vs f2; Supporting Information 5: discussion of how the modulus of an elastomer can influence contact angle hysteresis; Supporting Information 6: light microscopy study showing that the drops were in a CB state over the full range of the topographical gradient. This material is available free of charge via the Internet at http://pubs. acs.org.

DOI: 10.1021/la904714c

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