pubs.acs.org/Langmuir © 2009 American Chemical Society
Contact Line Pinning on Microstructured Surfaces for Liquids in the Wenzel State Pontus S. H. Forsberg,† Craig Priest,† Martin Brinkmann,‡ Rossen Sedev,† and John Ralston*,† †
Ian Wark Research Institute, ARC Special Research Centre for Particle and Material Interfaces, University of South Australia, Mawson Lakes, South Australia 5095, Australia, and ‡Max Planck Institute for Dynamics and Self-Organization, Bunsenstrasse 10, G€ ottingen D37073, Germany Received June 26, 2009. Revised Manuscript Received July 27, 2009 The wettability of surfaces microstructured with square pillars was studied, where the static advancing contact angle on the planar surface was 72. We observed elevated advancing angles (up to 140) on these structures for droplets in the Wenzel state. No air was trapped in the structured surfaces beneath the liquid, ruling out the well-known Lotus leaf effect. Instead, we show that the apparent hydrophobicity is related to contact line pinning at the pillar edges, giving a strong dependence of wetting hysteresis on the fraction of the contact line pinned on pillars. Simulating the contact line pinning on these surfaces showed similar behavior to our measurements, revealing both strong pinning at the edges of the pillars as well as mechanistic details.
Introduction The wettability of structured surfaces is of great importance in macroscopic applications, e.g., self-cleaning1 and water-repellency,2 and, recently, in the rapidly advancing field of microfluidics,3 where the reduced dimensions enhance the importance of surface effects, e.g., interfacial tension and slip properties. It has long been known that surface roughness plays a crucial role in determining the wetting properties of a surface;4-7 however, there remains much to study in this regard. Many studies have been dedicated to the fabrication and characterization of special interfaces modeled on naturally occurring surfaces for their functionality, including the well-known superhydrophobic Lotus leaf.8 Other work has focused on elucidating the parameters that dictate the state of a liquid resting on a structured interface.9-11 Two physically different wetting states exist on structured surfaces.9 A droplet may fully wet the structured surface, i.e. completely fill the crevices of the surface, or, alternatively, rest on top of the structure with air trapped below the droplet. The former case is referred to as the Wenzel state,9 as the droplet (1) Blossey, R. Nat. Mater. 2003, 2, 301. (2) Callies, M.; Quere, D. Soft Matter 2005, 1, 55. (3) Baroud, C. N.; Willaime, H. C. R. Phys. 2004, 5, 547. Choi, C.-H.; Ulmanella, U.; Kim, J.; Ho, C.-M.; Kim, C.-J. Phys. Fluids 2006, 18, 087105. Huang, T. T.; Mosier, N. S.; Ladisch, M. R. J. Sep. Sci. 2006, 29, 1733. Zhao, B.; Moore, J. S.; Beebe, D. J. Science 2001, 291, 1023. Zhang, J.; Kwok, D. Y. Langmuir 2006, 22, 4998. Joseph, P.; Cottin-Bizonne, C.; Benot, J.-M.; Ybert, C.; Journet, C.; Tabeling, P.; Bocquet, L. Phys. Rev. Lett. 2006, 97, 156104. (4) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (5) Shuttleworth, R.; Bailey, G. L. J. Discuss. Faraday Soc. 1948, 3, 16–22. Johnson, R. E. J.; Dettre, R. H. Adv. Chem. Ser. 1964, 43, 112–135. (6) Huh, C.; Mason, S. G. J. Colloid Interface Sci. 1977, 60, 11. Eick, J. D.; Good, R. J.; Neumann, A. W. J. Colloid Interface Sci. 1975, 53, 235. (7) Johnson, R. E. J.; Dettre, R. H. J. Phys. Chem. 1964, 68, 1744. (8) Garrod, R. P.; Harris, L. G.; Schofield, W. C. E.; McGettrick, J.; Ward, L. J.; Teare, D. O. H.; Badyal, J. P. S. Langmuir 2007, 23, 689. Sun, T.; Feng, L.; Gao, X.; Jiang, L. Acc. Chem. Res. 2005, 38, 644. Zhai, L.; Berg, M. C.; Kim, C. F. C, Y.; Milwid, J. M.; Rubner, M. F.; Cohen, R. E. Nano Lett. 2006, 6, 1213. Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1. Bliznakov, S.; Liu, Y.; Dimitrov, N.; Garnica, J.; Sedev, R. Langmuir 2009, 25, 4760. (9) Lafuma, A.; Quere, D. Nat. Mater. 2003, 2, 457. (10) Liu, B.; Lange, F. F. J. Colloid Interface Sci. 2006, 298, 899. Barbieri, L.; Wagner, E.; Hoffmann, P. Langmuir 2007, 23, 1723. (11) Marmur, A. Langmuir 2008, 24, 7573. Bahadur, V.; Garimella, S. V. Langmuir 2009, 25, 4815.
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senses a rough but homogeneous surface, while the latter case is referred to as the Cassie state,9 as the droplet senses a flat but heterogeneous surface. These two wetting states and related intermediate states (partial penetration of the liquid into the surface structure) have been studied extensively, driven largely by the very different wetting behaviors observed. Characteristic of the Wenzel state is a high degree of contact angle hysteresis,9,12,13 while droplets in the Cassie state may exhibit superhydrophobicity, where advancing and receding contact angles both exceed 150 with low contact angle hysteresis, i.e., droplets easily roll off of the surface.9,14 Superhydrophobicity arising from the Cassie state is generally employed for applications in water-repellency and self-cleaning surfaces and is the subject of a many studies.1,2 In fact, recent work has demonstrated repellency using other liquids, including oils, on carefully structured surfaces.15 Transitions between Cassie and Wenzel states may also be triggered, providing a switchable surface wettability.10,16 Despite this large body of research, the wetting behavior of liquids resting in the Wenzel state has not been studied in such great detail and is, therefore, the focus of this study. The wettability of an ideal surface can be expressed as a balance of the liquid-vapor, γ, solid-liquid, γSL, and solidvapor, γSV, interfacial tensions, according to the well-known Young equation,17 provided the solid surface is rigid, flat, homogeneous and inert to both fluid phases. However, direct use of Young’s equation is restricted in the presence of roughness and/or chemical heterogeneity, which are present at all real surfaces. (12) Yeh, K.-Y.; Chen, L.-J.; Chang, J.-Y. Langmuir 2008, 24, 245. (13) McHale, G.; Shirtcliffe, N. J.; Newton, M. I. Langmuir 2004, 20, 10146. (14) Dorrer, C.; Ruehe, J. Soft Matter 2009, 5, 51. (15) Tuteja, A.; Choi, W.; Ma, M.; Mabry, J. M.; Mazzella, S. A.; Rutledge, G. C.; McKinley, G. H.; Cohen, R. E. Science 2007, 318, 1618. Ahuja, A.; Taylor, J. A.; Lifton, V.; Sidorenko, A. A.; Salamon, T. R.; Lobaton, E. J.; Kolodner, P.; Krupenkin, T. N. Langmuir 2008, 24, 9. (16) Bahadur, V.; Garimella, S. V. Langmuir 2007, 23, 4918. Krupenkin, T.; Taylor, J.; Schneider, T.; Yang, S. Langmuir 2004, 20, 3824. Sun, T.; Wang, G.; Feng, L.; Liu, B.; Ma, Y.; Jiang, L.; Zhu, D. Angew. Chem., Int. Ed. 2004, 43, 357. Wang, S.; Liu, H.; Liu, D.; Ma, X.; Fang, X.; Jiang, L. Angew. Chem., Int. Ed. 2007, 46, 3915. Bahadur, V.; Garimella, S. V. Langmuir 2008, 24, 8338. (17) Young, T. Phil. Trans. R. Soc. London 1805, 95, 65.
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Wenzel accounted for the additional solid-liquid and solidvapor interfacial energies at a rough surface using a roughness factor, r, given by the ratio of the actual surface area to the projected surface area.4 Introducing the roughness factor into Young’s equation on the assumption the liquid fills the underlying surface structure gives the Wenzel equation: cos θ ¼ r 3 cos θ0
ð1Þ
where θ is the observed contact angle on the structured surface and θ0 is the Young angle on the planar surface. According to eq 1, θ > θ0 whenever θ0 > π/2, and θ < θ0 whenever θ0 < π/2. Wenzel’s equation has since been applied to studies of roughened and structured surfaces with some success.18 However, if air is trapped in the surface structure, the surface is effectively a composite comprising hydrophobic regions (air, θ = 180). Where the surface features have flat tops in the same plane and there is zero penetration of liquid into a surface structure, the Cassie equation can be used, describing the observed wettability as a weighted average of the surface components: cos θ ¼ φ1 cos θ1 þ ð1 - φ1 Þ cos θ2
ð2Þ
where θ is the observed contact angle on the heterogeneous surface, φ1 is the surface area fraction of component 1, and θ1 and θ2 are the Young contact angles for components 1 and 2, respectively. Of particular importance to applications of wettability is the extent of wetting hysteresis, for which there is clearly no account in either the Wenzel or Cassie equation. To account for wetting hysteresis on chemically heterogeneous surfaces, Pease19 considered the average wettability existing locally at the contact line. In this case, the contact angle is only affected by surface components encountered in the immediate vicinity of the advancing or receding contact line. Similar arguments can be applied to rough surfaces.20 Thus, the average surface condition in the immediate vicinity of the contact line (i.e., line fraction, instead of the traditional area fraction) is, on occasion, considered in place of the average surface properties, i.e., in place of φ and r in Cassie and Wenzel’s equations, respectively. However, it should be noted that the importance of the local wettability and structure was established long before the recent discussions in literature.5 In addition, the use of line fraction is complicated, as the shape of the contact line itself is strongly dependent on the nature of the local surface heterogeneity, e.g., domain size and shape, and is seldom used to describe wetting on real surfaces. We have previously studied the influence of microscopic chemical heterogeneity21 and hydrophobic, periodic roughness22 on the contact angle and hysteresis for droplets resting in the Cassie state. Now we address droplets in the Wenzel state resting on a periodic roughness at a relatively hydrophilic substrate, i.e., the inherent contact angle is less than 90. According to Wenzel’s equation, the observed wettability should increase with increasing surface roughness, i.e. increasing roughness factor r, since θ0 < 90.4 However, we have observed remarkably different behavior on these surfaces. In our experiments, the advancing contact angle is elevated substantially, approaching that generally observed (18) Fabretto, M.; Sedev, R.; Ralston, J. Contact Angle, Wettability Adhes. 2003, 3, 161. Boyes, A. P.; Ponter, A. B. J. Appl. Polym. Sci. 1972, 16, 2207. (19) Pease, D. C. J. Phys. Chem. 1945, 49, 107–110. (20) Extrand, C. W. Langmuir 2003, 19, 3793. (21) Priest, C.; Sedev, R.; Ralston, J. Phys. Rev. Lett. 2007, 99, 026103. (22) Priest, C.; Albrecht, T. W. J.; Sedev, R.; Ralston, J. Langmuir 2009, 25, 5655.
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Figure 1. Optical and scanning electron microscopy of microstructured surfaces. (a) Top-view of square pillars. (b) Schematic showing the dimensions of the individual pillars: height, h, width, w, and lattice spacing, d. (c) Profile of the pillars showing welldefined edges and vertical side-walls. (d) Three dimensional scanning electron microscopy view.
when a droplet rests in the Cassie state, while the receding contact angle decreases sharply. We have explored this non-Wenzel wetting behavior from an experimental perspective, with support from Surface Evolver simulations, paying particular attention to the role of contact line pinning on the structured surface.
Experimental Section Arrays of microscopic pillars were prepared by structuring SU8 photoresist using UV-photolithography. SU8 is an epoxy-based negative photoresist with excellent structural integrity and chemical resistance after hard bake (200 C, 5 min).23 The SU8 monomer is an aromatic hydrocarbon with eight epoxy functional groups available for cross-linking.23 The root-mean-square (rms) roughness of a flat, cross-linked SU8 layer is less than 1 nm (1 μm2 scan size), as measured by atomic force microscopy (Digital Instruments Nanoscope III) using NSG10 cantilevers (NTMDT). All samples were hard-baked after structuring. The static advancing, θa, and receding, θr, contact angles of water on the flat, hard-baked SU8 surface were 72 and 59, respectively, which reflects that expected for aromatic surface chemistry24 and similar to that measured elsewhere on SU8 surfaces.22,25 The microstructured surfaces were prepared on Æ100æ silicon wafers (Si-Mat), which were precoated with a flat, hard-baked SU8 underlayer to ensure that the inherent wettability of the pillars and underlying substrate was identical. Every sample included an unstructured region, allowing us to check the inherent wettability, θ0, of the photoresist. The width, w, of the square pillars was fixed at 20 μm while the height, h, was varied from 7 to 30 μm. The lattice constant, d, was also varied to adjust the pillar density, w/d. Each sample was carefully examined by optical microscopy to ensure that the pillars exhibited sharp edges and the desired pillar height. A representative scanning electron microscopy and optical microscopy image is shown in Figure 1. The hydrophobization of the microstructures was carried out as described elsewhere22,25 under slightly adjusted conditions. Samples were immersed in a stirred aqueous solution of 10 wt % hydrophobizing agent (Granger’s Extreme Wash In) for 1 h at room temperature. Samples were then rinsed in water, dried with (23) Feng, R.; Farris, R. J. J. Micromech. Microeng. 2003, 13, 80. (24) Moineau, J.; Granier, M.; Lanneau, G. F. Langmuir 2004, 20, 3202. (25) Shirtcliffe, N. J.; Aqil, S.; Evans, C.; McHale, G.; Newton, M. I.; Perry, C. C.; Roach, P. J. Micromech. Microeng. 2004, 14, 1384.
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compressed air, and cured at 50 C for 17 h. After treatment, the advancing contact angle on the planar surface was (105 ( 10). The advancing contact angles were always greater than 90, sufficient to induce the Cassie state. Droplets on these surfaces were used for qualitative comparisons with droplets resting in the Wenzel state. Advancing and receding contact angles were measured using the sessile drop method, based on observation of the profile of the droplet (Dataphysics OCA-20). Droplets conformed to the square lattice of the pillar array, and, therefore, all contact angles were measured for contact lines pinned along the lattice dimension, d. The initial droplet volume (∼ 2 μL) was increased slowly (0.06 μL/s) until the contact line advanced/receded. When the contact line came to rest, the contact angle was measured by fitting the profile of the droplet close to the contact line. This procedure was repeated (4) on different regions of each sample to yield more than 12 measurements per sample. For the structured samples, the advancing/receding motion was captured by video, and the contact angles were measured immediately prior to depinning of the contact line. In addition to the experiments, we calculated the shape of the liquid-air interface in the vicinity of the pillars for various pillar heights and lattice spacings by numerically minimizing the interfacial energy. The inherent contact angle on the flat surface is set by the three surface energies. Throughout this work we used the software Surface Evolver developed by Brakke,26 which employs a free triangulation of the liquid-vapor interface. In this method, the liquid-vapor interface is represented by a mesh of small triangles spanning between N nodes. The interfacial energy is a function of the 3N Cartesian coordinates of the nodes and can be minimized using standard numerical methods. Nodes lying on the contact line are subject to a geometric constraint because they have to be located in the surfaces of the substrate. The interfacial energies of the substrate being exposed to the liquid and vapor, respectively, are calculated from appropriate line integrals along the contact line. Owing to the particular symmetry of the surface topography, we considered only a small stripe of the liquid-air interface between the center of a pillar and the center of the interstice between two adjacent pillars. A virtual surface opposing the topographically structured surface was introduced to fix the apparent contact angle of the liquid-air interface. The deformations of the liquid-vapor interface, caused by the topography, decay exponentially on a length scale that is given by the pillar height and distance. To ensure that the extension of the system does not affect our results, we chose a separation between the substrate and the virtual surface of 20 times the height of the pillars. The minimization was stopped once the interfacial configuration was sufficiently close to a local minimum of the energy. Using the final configuration of the previous run as the initial configuration for the following run, the apparent contact angle was increased in small steps until the liquid-air interface became unstable. This interfacial instability is accompanied by a sharp decrease of the interfacial energy.
Results and Discussion Figure 2 shows the remarkable wettability difference observed on the planar and structured SU8 surfaces. On the structured surface (w/d = 0.63), the advancing contact angle approached 140, representing a large increase from the advancing contact angle on the planar surface, 72. In the receding case, the contact angle on the structured surface was much lower than for the planar surface. In fact, for high pillar densities, a liquid film remained trapped between the pillars before evaporating, indicating no dewetting at all (θr = 0). The liquid film is evidenced by the (26) Brakke, K. Exp. Math. 1992, 1, 141.
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Figure 2. Native photoresist: images showing the advancing and receding contact angles (water) for planar and microstructured surfaces. The structured surface is covered with 20 μm square pillars at a lattice constant of 32 μm. The surface structure increases the advancing contact angle, while in the receding measurement liquid remains in the surface structure behind the receding contact line. Inset (Pillars, Rec): the edge of the liquid film trapped in the microstructure. The film hides the pillars to the right, so that only the dry pillars are observed in the zoomed image. Hydrophobized photoresist: images showing the advancing contact angle on a structured surface for a lattice constant of 120 μm, and a typical image of air trapped under a “sliding” droplet (right image) traveling to the right. Fingers of liquid can be seen pinned on individual pillars at the receding contact line.
inability to image the profile of the pillars, as shown in the inset. Thus, there is a remarkable, structure-induced wetting hysteresis (up to 140), which is much greater than that observed on the planar surface (13). It must be noted here that the behavior observed on the native SU8 surfaces is not indicative of the Cassie state. Air entrapment in the Cassie state can normally be observed by optical inspection of the solid-liquid interface through the droplet, but optical microscopy of the solid-liquid interface showed no evidence of air trapped between pillars. Furthermore, for high pillar densities where air entrapment is more likely, optical microscopy behind the receding contact line revealed liquid trapped between the pillars. These results indicate that we were observing the Wenzel state in our measurements. In order to unequivocally show that this was the case, we also hydrophobized the structured surfaces to induce the Cassie state and compare the wetting behavior with the native structured SU8 surfaces. Figure 2 shows a droplet resting on a hydrophobized microstructured surface. On this surface, the pillars can be clearly distinguished below the droplet, and no liquid entrapment was observed when the droplet was receded, giving advancing and receding contact angles larger than 90 and hysteresis between 15 and 50, depending on the pillar density. The distinct transition from high to low contact angle hysteresis after hydrophobization is consistent with a Wenzel-to-Cassie state transition. Thus, our measurements on the native SU8 surfaces were indeed in the Wenzel state, and the remainder of this paper deals Langmuir 2010, 26(2), 860–865
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Figure 3. (a) Left: schematic (top view) of meniscus wetting the pillars with symbols relating to eq 3. Right: optical microscopy image of contact line pinned on pillars (d = 120 μm). (b) Calculated meniscus profile using Surface Evolver for water pinning on a pillar, w/d = 0.5 and h/w = 1. The apparent and inherent contact angles are 150 and 72, respectively. (c) As per panel b, except the inherent contact angle is 55 and a liquid protrusion wets a finite fraction of the front face. (d) Advancing (filled symbols) and receding (open symbols) contact angles for microstructured surfaces containing 7 μm (circles) and 30 μm (squares) square pillars as a function of the pillar density, w/d. Cassie (dashed gray line) and Wenzel’s (dashed black line, for h = 30 μm) predictions, shown for advancing data, are qualitatively different from our experiments. Taking into account pinning behavior, eq 6 is in excellent agreement with the data for the short pillars (7 μm).
exclusively with droplets in the Wenzel state on native SU8 surfaces, unless otherwise stated. Having established that we observe the Wenzel state in our wettability measurements on the native photoresist (θa,r = 72, 59), we now consider the influence of pillar density. Figure 3d shows advancing and receding contact angles for two pillar heights, 7 and 30 μm, at various pillar densities. The pillar density is defined here as the ratio of the pillar width, 20 μm, to the pillar lattice constant, d. Thus, the pillar density, w/d, can be approximated by the line fraction (on the pillars), if the contact line on the vertical walls of the pillars are to be ignored and lateral bending of the contact line is negligible. On the basis of the advancing contact angles measured on the planar photoresist, we have calculated the contact angles predicted by Wenzel and Cassie’s equation (eqs 1 and 2, respectively), which are shown for comparison in Figure 3d. The Cassie angles were calculated (using eq 2) for comparison only, since, as discussed earlier, the droplets rest on the surface in the Wenzel state. It is evident from Figure 3d that the wetting behavior observed on the microstructured surfaces is not described even qualitatively by either Cassie or Wenzel’s equations. Both theories predict a decrease in the advancing Langmuir 2010, 26(2), 860–865
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and receding contact angles with increasing pillar density; however, the trend for our advancing measurements is quite the opposite. This behavior was evident for the pillar heights studied here, although the taller pillars (30 μm) gave significantly higher contact angles, and these data tended to bow away from our measurements on the shorter pillars (7 μm). Increasing the pillar density also influences the receding contact angles (open symbols), which approach the limit of complete wetting for both data sets. For the taller pillars, dewetting does not occur beyond the limit w/d ∼ 0.25, while for the shorter pillars the dewetting limit was w/d ∼ 0.5, according to extrapolation of the data to θr = 0. From these data, it is clear that the hysteresis increases with pillar density, suggesting that the Wenzel equation (which is derived by free energy minimization) is no longer appropriate. Therefore, to explain this wetting behavior, the contortion and movement of the contact line over individual pillars must be considered. Using optical microscopy and high-speed imaging, we observed stick-slip motion, where the contact line periodically slips between and sticks on consecutive rows of pillars. A pinned contact line is shown in Figure 2 for both advancing and receding contact lines. In the advancing case, the image is captured through the liquid phase (due to the high contact angle, θ > 90), while, in the receding case, the image is captured through the vapor phase (due to the low contact angle, θ < 90). The advancing liquid engulfs the pillars, until the contact line comes to rest at the trailing edges of the pillars, so that the contact line is prevented from traveling down the face of the pillar. In the receding case, fingers of liquid remain trapped between the pillars (a capillarity effect), while the top surface of the pillars is dewetted by the liquid. For high pillar densities, the liquid may remain trapped within the microstructure as a continuous film, which is thinner than the height of the pillars, i.e., the tops of the pillars are dry. These advancing and receding mechanisms appear to operate on all the surfaces studied here. To explain this behavior, we first consider an advancing contact line. In a mechanically stable configuration of the liquid-air interface, one can assume a continuity of stresses being transmitted between the substrate and the surface. The components of the interfacial stress caused by the presence of the liquid-air interface can be evaluated close to the substrate or at any distance which is small compared with the dimensions of the droplet. For simplicity we will consider only a stripe of the liquid-air interface of width equal to the lattice spacing of the structured surface. Furthermore, we assume short pillars, i.e., the ratio of pillar height to pillar width is small compared to one. Hence, the contact line lies in the plane of the substrate, i.e., the x-y plane. The component of the force in the plane of the substrate and normal to the row of pillars (we chose to be the x component, cf. the schematic in Figure 3a) can be calculated from the line integral Z Fx ¼ γ dlex 3 n cos θ Γ
ð3Þ
where γ is the interfacial tension of the liquid-vapor interface, Γ is the contact line, l is the arc length parameter on the contact line, ex is the unit vector pointing into the x direction, n is the normal unit vector of the contact line (in the x-y plane), and θ is the local contact angle with respect to the x-y plane. The contact line Γ can be split into a pinned segment, Γp, and into an unpinned segment, Γo, lying on the base between the pillars. Recalling that the contact angle on the unpinned segment DOI: 10.1021/la902296d
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Γo equals Young’s contact angle θ0, and that n = ex on Γp, we may rewrite eq 3 in the form Z Z Fx ¼ γ cos θ0 dlex 3 n þ γ dl cosθ p ð4Þ Γo
Γp
where the local contact angle on the pinned segment Γp is denoted θhp. Using the same approach at a distance from the substrate where the interface is unperturbed, we find the relation Fx ¼ dγ cos θ
ð5Þ
with θ, the apparent (macroscopic) contact angle of the liquid-air interface, and the periodicity d of the substrate topography. The first term on the right-hand side of eq 4 yields exactly (d - w)γ cos θ0, which is the length of the contact line segment Γo projected onto the y direction. At the point of instability, i.e., the moment the contact line depins from the top edge of the pillar, one may assume that the pinning criterion θhp = θ0 þ π/2 holds everywhere on Γp.6 As a consequence, the second term in eq 4 can be simplified to w γ cos(θ0 þ π/2). Combining eqs 4 and 5, one finally arrives at cos θ ¼ ð1 -w=dÞ cos θ0 þ ðw=dÞ cosðθ0 þ π=2Þ
ð6Þ
Equation 6 is in excellent agreement with our static advancing contact angle measurements on the shorter pillars (7 μm) over the full range of pillar densities (see Figure 3d). Since the pinning is related to the surface geometry, we expect that this treatment would be equally appropriate for liquids other than water, although the magnitude of the pinning energy may differ. In contrast, the taller pillars (30 μm) show very different behavior, giving contact angles greatly in excess of those predicted by eq 6. The measurements bow away from eq 6 toward higher contact angles, with the difference maximized at intermediate pillar densities. This difference can be attributed to increasingly significant contributions from the pillar walls and/or deviation from θ0 on the underlying surface between the pillars. The magnitude of these effects is difficult to ascertain from our experiments. It should be noted however, that where w/d > 0.4, the height of the pillars, h, exceeds the spacing between the pillars and closely corresponds to a distinct change in slope in the data. This condition is only met for the 7 μm high pillars at w/d g 0.74, where there is too little data to draw any direct comparison. In order to gain further insight into the shape of the liquid front and pinning of the contact line, we carried out a numerical minimization of the interfacial energy using Surface Evolver.26 In contrast to the method of Dorrer et al.,27 we consider a liquid-air interface spanning between the topographic surface and a perfectly plane surface, which is aligned parallel to the base of the topographic surface. While increasing the apparent contact angle in small steps, the liquid-air interface may become unstable (i) as a result of depinning from the top edge of a pillar or (ii) when the liquid-air interface touches a pillar in the next row. For the particular values of pillar height and pillar spacing used in our minimizations, instabilities caused by scenario (ii) never occurred. A generic equilibrium configuration for a liquid-air interface on one-half of the wetted pillar is shown in Figure 3b for an inherent contact angle of 72. The shape of the liquid-vapor interface was indeed found to distort around the pinned contact line at the edge of the pillars, as observed in our experiments and (27) Dorrer, C.; R€uhe, J. Langmuir 2007, 24, 1959.
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Figure 4. Measurements (points) replotted with data from Surface Evolver simulations (lines) against pillar density, w/d.
in simulations carried out by Dorrer et al.27 As Young’s contact angle is smaller than 90, we observe a liquid protrusion into the gap between two neighboring pillars. This protrusion also wets part of the base between a row of pillars partially wet by liquid and the next row of dry pillars. A close view of the shape of the liquid-air interface reveals that the contact line makes an excursion onto the front face of the pillar close to the point where the horizontal top edge and vertical front edge of the pillar meet. As the apparent contact angle increases during the minimization, these parts of the contact line grow at the expense of the parts being pinned to the pillar’s top and side edge. In the case of high aspect ratio pillars (h = 30 μm) the fraction of the contact line being pinned to the top edge of the pillar drops to almost zero at the point of instability, i.e., when the contact line starts to travel down the front face of the pillar. For low aspect ratio pillars (h = 5 μm), this depinning transition appears to be discontinuous. At high aspect ratios, we observed a gradual downward movement of the contact line on the front face of the pillar after complete detachment from the top edge. This may be an effect of the finite extension of the system in the z direction. In addition to the depinning transition, we checked that the configuration of the equilibrium liquid-vapor interface for a given apparent contact angle was consistent with the geometric constraints of the microstructured surface. For a material contact angle of 72 and the aspect ratio of the pillars in our simulation (h/w = 0.25 and h/w = 1.5), the liquid interface does not come into contact with the next row of dry pillars, provided the contact line is partially pinned at the top edge of the wet pillars. Rather, the liquid-vapor interface only contacts the next row of dry pillars when the contact line has detached completely from the top edge and traveled down the face of the wet pillars. From these energy minimizations, we have extracted the advancing contact angle observed macroscopically immediately prior to depinning from the pillars. These values are compared with our experiments in Figure 4. There is qualitative agreement in the trends of the two data sets, with the exception of the data for the short pillars at high pillar densities, w/d g 0.5, for which the simulations predict higher contact angles than those measured. However, other aspects, such as the divergence of the data for the two pillar heights at low pillar densities and the convergence at high pillar densities, are predicted. It is worth noting that the simulated results approach 162 in the simulations, which is in excellent agreement with our earlier assumption that the local contact angle on the edge of the pillar can be approximated by the maximum θ0 þ π/2 = 162. Thus, eq 4 may indeed be quite appropriate where the height of the pillars is small and the separation between the pillars is large. In our experiments, the 7 and 30 μm pillar data sets converge as w/d f 1 at a lower Langmuir 2010, 26(2), 860–865
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Figure 5. Contact angle hysteresis increases linearly as a function of pillar density for both the Wenzel state (filled symbols) and for the Cassie state, i.e., hydrophobized surfaces (open symbols). As expected, the intercept for the Wenzel state corresponds to the inherent hysteresis on the planar surface, while, for superhydrophobic surfaces, the intercept is at zero hysteresis, as expected for a surface fraction of air of unity.
maximum contact angle (140-150, depending on how the data is extrapolated). This observation is consistent with Dorrer and R€ uhe’s27 suggestion that the rounded edges of the pillars (radius ∼ 1 μm) reduce the pinning force and, therefore, the measured contact angles. The simulation data allow us to reconsider the influence, if any, of the aspect ratio of the valley between pillars. Earlier we proposed that, as the aspect ratio of the valley between the pillars, h/(d - w), reduces below unity, there is a change in the gradient of the data. This condition is met for the short and tall pillars when w/d g 0.74 and 0.35, respectively, and seems consistent with the simulation data. Although this is only speculation, our simulation results appear to support this concept, as both data sets seem to plateau beyond these critical values toward the limit of θ0 þ π/2. This is a strong indication that the aspect ratio of the valleys between the pillars plays a role in determining the measured contact angle on microstructured surfaces, the details of which are yet to be clarified. Numerical minimizations carried out at values of Young’s contact angle different from 72 point to the possibility of different instability mechanisms leading to an advancement of the contact line. In a certain range of hydrophilic contact angles, it may happen that two neighboring protrusions fuse at the obtuse edge formed by the front face of the pillar and the bottom surface of the substrate. This is shown for an inherent contact angle of 55 in Figure 3c. The liquid clasping around the base of the pillars will lead to an advance of the contact line that is not triggered by the detachment of the contact line from the top edge of a pillar. On the basis that there is a finite pinning force associated with each pillar, one would expect contact angle hysteresis on these structured surfaces to increase proportionally with pillar density, w/d. In fact, this expectation is fulfilled for all of the structured surfaces presented here, as shown in Figure 5, and is similar to the observations of Yeh et al. on similar topographies.12 For both
Langmuir 2010, 26(2), 860–865
Article
the 7 and 30 μm structures, linear fits of the data intercept at the inherent hysteresis of the planar surface, as one would expect. The proportionality of the hysteresis with w/d was also observed for the hydrophobized surfaces described earlier; however, the intercept is now at zero hysteresis, which is entirely consistent with the notion of trapped air under the droplet approaching a surface fraction of 1, i.e., zero adhesion. However, when we considered the symmetry of the hysteresis from the equilibrium contact angle on the flat surfaces (equilibrium angle estimated in Figure 3d by the dashed line), we found that the deviation from this value was largely symmetrical, i.e., the hysteresis energy contributes equally to the advancing and receding departure from the equilibrium angle. This suggests that the hysteretic behavior on these microstructured surfaces differs fundamentally from the asymmetric hysteresis observed recently on chemically heterogeneous surfaces.21 This conclusion could also be drawn from the results of Yeh et al.12 Considering these results together, we conclude that asymmetric hysteresis on chemically heterogeneous surfaces is due to the discontinuous wettability of the flat surface. This is in stark contrast to the structured surfaces studied here, for which the surface wettability is continuous and the contact angle hysteresis is symmetrical.
Conclusions We have investigated the wettability of a solid surface with a regular microscopic roughness. With increasing pillar density, advancing contact angles approached those expected for a superhydrophobic surface (140), despite no air entrapment, while receding contact angles reduced to zero. This wetting behavior is inexplicable in terms of the Cassie state (as there is no air trapped) or Wenzel’s law, since θ0 < π/2. In contrast, we show that this behavior can be directly related to contact line pinning at each row of pillars. The proposed model is in good agreement with our advancing contact angle measurements in the limit of short pillar heights (7 μm). Our contact angle measurements are in close agreement with Surface Evolver simulations, which revealed the microscopic pinning behavior in greater detail. Inspection of the contact angle hysteresis on these surfaces revealed symmetric wetting hysteresis, which was proportional to the pillar density. The symmetry differs remarkably from the asymmetric hysteresis observed in our previous study of microscopic chemical heterogeneity. As roughness and chemical heterogeneity are ubiquitous to both natural and synthetic surfaces, we expect that these findings will be broadly relevant, with specific implications for surface design and advanced wetting applications. Acknowledgment. Photolithography masks and microstructured surfaces were prepared at the Macquarie/ATP and University of South Australia nodes of the Australian National Fabrication Facility, respectively, under the National Collaborative Research Infrastructure Strategy to provide nano- and microfabrication facilities for Australia’s researchers. Financial support from the Australian Research Council (ARC) Special Research Centre Scheme, ARC Linkage and Linkage International Schemes, AMIRAInternational, and State Governments of South Australia and Victoria is gratefully acknowledged.
DOI: 10.1021/la902296d
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