Langmuir 2008, 24, 245-251
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Contact Angle Hysteresis on Regular Pillar-like Hydrophobic Surfaces Kuan-Yu Yeh and Li-Jen Chen* Department of Chemical Engineering, National Taiwan UniVersity, Taipei 10617, Taiwan
Jeng-Yang Chang Department of Optics and Photonics, National Central UniVersity, Chung-Li 32001, Taiwan
Langmuir 2008.24:245-251. Downloaded from pubs.acs.org by UNIV OF TEXAS AT EL PASO on 10/30/18. For personal use only.
ReceiVed July 9, 2007. In Final Form: September 8, 2007 A series of pillar-like patterned silicon wafers with different pillar sizes and spacing are fabricated by photolithography and further modified by a self-assembled fluorosilanated monolayer. The dynamic contact angles of water on these surfaces are carefully measured and found to be consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Wenzel state, its contact angle hysteresis increases along with an increase in the surface roughness. While the surface roughness is further raised beyond its transition roughness (from the Wenzel state to the Cassie state), the contact angle hysteresis (or receding contact angle) discontinuously drops (or jumps) to a lower (or higher) value. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction and has nothing to do with the surface roughness. Even for a superhydrophobic surface, the contact angle hysteresis may still exhibit a value as high as 41° for the solid fraction of 0.563.
Introduction Superhydrophobic surfaces are very important for many biological processes and industrial applications. The definition of a superhydrophobic surface is a surface with a water contact angle greater than 150°. The dominant factors of water repellency are surface energy and surface roughness. The functional group -CF3 on top of a surface has the lowest surface energy. The surface energy for a surface with a substitution of fluorine atoms is in the following order: -CF3 < -CF2H < -CF2 < -CH3 < -CH2.1 However, even a surface covered with regularly aligned closest hexagonal packed -CF3 groups gives a water contact angle of only 119° when the surface is flat.2 Thus, enhancement of surface roughness is an undoubted requirement of a superhydrophobic surface. The earliest work to model liquid drops on a roughness surface can be contributed to Wenzel3 and Cassie.4 In 1963, Wenzel described the contact angle θw at a rough surface as follows:3
cos θw ) r cos θe
(1)
where the symbol r is the surface roughness defined as the ratio of the actual area of liquid-solid contact to the projected area, and θe is the equilibrium contact angle on a flat surface. In this case, liquid fills up the rough surface to form a completely wetted contact with the surface, as illustrated in Figure 1a, and this phenomenon is known as the Wenzel state. On the other hand, a liquid droplet sits on a composite surface composed of solid and air, as illustrated in Figure 1b, which is also known as the Cassie state. The Cassie model can be formulated as
cos θc ) Φs cos θe - (1 - Φs)
(2)
where Φs is the solid-liquid contact (or solid) fraction of the surface. * To whom correspondence should be addressed. E-mail address:
[email protected]. (1) Hare, E. F.; Shafrin, E. G.; Zisman, W. A. J. Phys. Chem. 1954, 58, 236. (2) Nishino, T.; Meguro, M.; Nakamae, K.; Matsushita, M.; Ueda, Y. Langmuir 1999, 15, 4321. (3) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (4) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546.
Figure 1. Schematic illustrations of a liquid droplet at the Wenzel state (a) and at the Cassie state (b).
Many experiments have been performed to fabricate and to understand superhydrophobic surfaces. Onda and co-workers5 prepared a super-repellent surface with fractal structure, and the contact angle was reported to be greater than 170°. Erbil et al.6 used p-xylene as a good solvent and methyl ethyl ketone as a nonsolvent to produce a porous polypropylene surface with a water contact angle of 160°. There are many other methods to create superhydrophobic surfaces such as sublimation of aluminum acetylacetonate, plasma fluorination of polybutadiene, silicon oxide nanowires, and so on.7-9 Note that all these methods7-9 are involved in the enhancement of surface roughness. Although the methods described above successfully fabricated superhydrophobic surfaces, the topologies of these surfaces are too complicated to calculate their geometrical parameters, such as Φs and r, to compare to the theoretical value of contact angle, as described by eqs 1 and 2. On the other hand, some well-designed surfaces with regular structures have been fabricated to explore the connection between the contact angle and surface topography.10-13 According to the results of Bico et al.,10 contact angle only depends on the solid fraction of the surface and is independent of the profile of the (5) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2125. (6) Erbil, H. Y.; Demirel, A. L.; Avci, Y.; Mert, O. Science 2003, 299, 1377. (7) (a) Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. AdV. Mater. 1999, 11, 1365. (b) Ferrari, M.; Ravera, F.; Liggieri, L. Appl. Phys. Lett. 2006, 88, 203125. (8) Woodward, I.; Schofield, W. C. E.; Roucoules, V.; Badyal, J. P. S. Langmuir 2003, 19, 3432. (9) (a) Coffinier, Y.; Janel, S.; Addad, A.; Blossey, R.; Gengembre, L.; Payen, E.; Boukherroub, R. Langmuir 2007, 23, 1608. (b) Callies, M.; Que´re´, D. Soft Matter 2005, 1, 55.
10.1021/la7020337 CCC: $40.75 © 2008 American Chemical Society Published on Web 12/08/2007
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patterns. Yoshimitsu et al.11 found that a transition between the Wenzel state and the Cassie state occurs at a small roughness, and the droplet weight is an important factor governing the sliding angle on the pattern surface. O ¨ ner and McCarthy12 reported that regularly structured superhydrophobic surfaces have high advancing and receding contact angles, and a water droplet easily rolls off a slightly tilted surface. Regular nanopatterns produced by Martines et al.13 demonstrated that the shape and curvature of every single structure play an important role in determining the advancing contact angle, and a forest of hydrophobic slender pillars is the most effective water-repellent configuration. It is well understood that there is no unique contact angle to characterize any given surface. The observed equilibrium contact angles always fall between the advancing and receding contact angles.10b The contact angle hysteresis ∆θ, defined as the difference between advancing and receding contact angles (∆θ ) θadv - θrec), can be used to conclude the state of a liquid droplet. If the contact angle hysteresis is small, then the droplet would be at the Cassie state. On the other hand, if the contact angle hysteresis is large, then the droplet would be at the Wenzel state. For an ideal superhydrophobic surface, the hysteresis must be small, and a water droplet rolls easily on it. It was pointed out decades ago that the minimum tilting angle θslide of a surface at which a liquid droplet with surface tension σ will spontaneously slide down can be directly related to the advancing/receding contact angles by the following equation:
mg sin θslide ) σ(cos θrec - cos θadv) w
(3)
where g is the gravitational force, and m and w are the mass and width of the droplet, respectively. This implies that the contact angle hysteresis is responsible for the pinning of liquid droplets on a surface. However, only few experiments have been made to discuss the relationship between hysteresis and surface topography12,14 and the transition between the Wenzel and Cassie15-17 states. O ¨ ner and McCarthy12 reported the advancing/receding contact angles on regularly structured superhydrophobic surfaces; however, the solid fractions and roughnesses of these patterned surface were not given to further examine the Cassie and Wenzel states. Some studies16,17 applied the static contact angle, instead of the advancing/receding contact angle, to explore the transition between the Wenzel and Cassie states. In this study, a series of pillar-like structures of different sizes and spacings on silicon wafers are fabricated. These pattern surfaces are further modified by grafting a self-assembled fluorosilanated monolayer. The wettability of these surfaces, including advancing and receding contact angles, is examined to develop a systematic analysis of the effect of microstructures on hydrophobic surfaces. It is found that the experimental results of the advancing and receding contact angles of water on these (10) Bico, J.; Marzolin, C.; Que´re´, D. Europhys. Lett. 1999, 47, 220. (11) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (12) (a) O ¨ ner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (b) Chen, W.; Fadeev, A. Y.; Hsieh, M. C.; O ¨ ner, D.; Youngblood, J. P.; McCarthy, T. J. Langmuir 1999, 15, 3395. (c) Youngblood, J. P.; McCarthy, T. J. Macromolecules 1999, 32, 6800. (13) Martines, E.; Seunarine, K.; Morgan, H.; Gadegaard, N.; Wilkinson, C. D. W. Nano Lett. 2005, 5, 2098. (14) Dorrer, C.; Ru¨he, J. Langmuir 2006, 22, 7652. (15) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457. (16) Barbieri, L.; Wagner, E.; Hoffmann, P. Langmuir 2007, 23, 1723. (17) Zhu, L.; Feng, Y.; Ye, X.; Zhou, Z. Sens. Acuators, A 2006, 130-131, 595.
patterned surfaces are consistent with the theoretical predictions of the Cassie model and the Wenzel model. Experimental Section Materials and Sample Preparation. Surfaces with regular structures were prepared by photolithography in 4 in. silicon wafers and then cut into 1 × 2 cm2 pieces. The surface topology was observed by using either an atomic force microscope (Nanoscope IIIa, Digital Instruments) or a surface profiler (Dektak). Isooctane (Merck, >99%) was purified by percolating through a column of anhydrous aluminum oxide (Merck). This percolating process also removed a certain amount of water in isooctane (Merck). The water content of isooctane was then determined by Karl Fischer titration (MKC-210, Kyoto Electronics Co., Japan) and found to always be smaller than 10 ppm. Isooctane was then used as a solvent to prepare the octadecyltrichlorosilane (OTS) (Aldrich) and (tridecanfluoro-1,1,2,2- tetrahydrooctyl)-1-trichlorosilane (FTS) (Gelest) solutions. The FTS (or OTS) solution in isooctane was freshly prepared right before the silanation reaction. The pattern substrates were cleaned by Piranha solution (a 7:3 mixture (v/v) of 98% H2SO4 and 30% H2O2) at 120 °C for 30 min before use. These substrates were then exposed to steam for around 30 s until water drops formed on the surface, and then blown dry with nitrogen gas. The hydrated substrates were immersed in an 1 wt % solution of FTS (or OTS) for 5 min at room temperature and then removed and rinsed by dichloromethane (Merck, 99.5%) and trichloromethane (Merck, 99%99.4%) to remove any unadsorbed FTS (or OTS) molecules. All the preparations of the adsorbate (FTS or OTS) solution and silanation reactions were conducted in a glovebag filled with dry nitrogen to exclude the amount of water traces in the surrounding atmosphere.18 A flat substrate with no pattern was prepared in the same way as the reference surface. Advancing/Receding Contact Angle Measurements. The advancing/receding contact angle measurements of water were performed by a homemade enhanced video-microscopy system incorporated with a digital image analysis. The schematic setup is illustrated in Figure 2a. The light of a fiber optic illuminator (DolanJenner) with a constant light intensity is collimated by a set of pinhole and plano-convex lenses, goes through a water droplet on a substrate enclosed in a constant temperature (25 °C) environmental chamber (Rame´-Hart Instrument Co.) and an objective lens, and finally forms an image of the water droplet onto a solid-state charge coupled device (CCD) camera.19 The experimental procedure was as follows: A silica substrate was initially placed in the environmental chamber, and a needle was positioned inside the chamber in the path of the parallel light beam. Then a syringe pump (Orion, Sage, model M362) was turned on to generate a water droplet on the substrate, as illustrated in Figure 2b. After the drop-forming step, water was continuously and slowly pumped into (or sucked from) the droplet, and the evolution of the water droplet was recorded simultaneously by a frame grabber (Data Translation) at a rate of 10 frames per second. Matlab commercial software was applied to digitalize the image to determine the profile of the water droplet as well as the three-phase (air-water-solid) contact point. The tangent line was determined right at the threephase contact point. Finally, the contact angle was then calculated by the angle spanned at the intersection of the tangent line and the baseline of the substrate. Figure 3a illustrates a typical result of an advancing contact angle measurement from our image analyses. When water was continuously pumped into the droplet, the contact angle initially increased at a fixed contact diameter d, which is the diameter of water/substrate contact area, as defined in Figure 2b. In our measurement, the contact diameter d falls in the range between 0.5 and 1.5 mm. As more liquid was injected, the three-phase contact line suddenly extended as a result of an increase in the contact diameter, as shown in Figure (18) Chen, L.-J.; Tsai, Y.-H.; Liu, C.-S.; Chiou, D.-R.; Yeh, M.-C. Chem. Phys. Lett. 2001, 346, 241. (19) Yeh, M.-C.; Chen, L.-J.; Lin, S.-Y.; Hsu, C.-T. J. Chin. Inst. Chem. Eng. 2001, 32, 109.
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Figure 2. (a) Schematic setup of the contact angle measurement apparatus: A, light source; B, pinhole lens; C, plano-convex lens; D, thermostated chamber; E, prepared sample; F, droplet; G, syringe; H, syringe pump; I, objective lens; J, CCD camera; K, monitor and personal computer; L, vibrationless table. (b) An image of a water droplet on a solid surface with a contact diameter d. 3b. Note that the sudden movement was accompanied by a maximum contact angle, as shown in Figure 3a, which was identified as the advancing contact angle. On the other hand, the contact angle kept decreasing and reached a minimum, as illustrated in Figure 3c, right before the contraction of the three-phase contact line as water was continuously and slowly sucked out of the water droplet. The advancing/receding contact angles were measured for more than five different positions on each substrate. The standard deviation of advancing/receding contact angles was around 2° at different positions. In addition, the substrate is sturdy enough to exhibit the same advancing/receding contact angle even after 1 year. It should be noted that our enhanced video-microscopy system still has a problem measuring contact angles larger than 160°, since the liquid droplet is slightly flattened as a result of gravity, and the drop profile near three-phase (gas-liquid-solid) contact point is not sharp enough to be easily located. We are in the process of improving the system to be able to measure contact angles larger than 160° by fitting the profile of a sessile drop on a tilting surface to the Young-Laplace equation.
Results and Discussion The regular pillar-like structure used in this study is schematically illustrated in Figure 4. The notation Pa-d(h) is applied to describe the microstructure with a µm × a µm square pillars separated by a distance d µm and the pillar height h µm. Figure 5a also shows the scanning electron microscope (SEM) image of a pattern surface to define the parameters a, d, and h. All the detail dimensions of these microstructures determined by atomic force microscopy or surface profile are listed in the Supporting Information. These parameters could be used for calculating the surface roughness r and the solid fraction Φs by assuming a smooth cutting surface and using the following relations:
r)
(a + d)2 + 4ah (a + d)2
Φs )
a2 (a + d)2
(4)
(5)
All the calculated surface roughness and solid fractions for different patterns are also listed in the Supporting Information. It should be noted that there exists a ripple structure along the vertical surface of pillars, as shown in Figure 5b. This ripple structure would enhance the surface roughness. However, there
is no way to exactly evaluate the surface roughness due to this ripple structure. Since eq 4 is based on the assumption of smooth cutting surfaces, it would underestimate the surface roughness. In addition, the corners and edges of square pillars are not very sharp, as shown in Figure 5b, which makes the solid fraction, eq 5, slightly overestimated. Both OTS and FTS are used to hydrophobize the silica surfaces with a structure of P10-10 at different pillar heights, and the advancing contact angles of water on these pillar-like structure surfaces are listed in Table 1. The advancing contact angle of water on the FTS-modified flat surface (120°) is larger than that of the OTS-modified one (110°), as expected. Obviously, the advancing contact angle increases with the increase in the surface roughness introduced into the system by raising the pillar height, especially when the pillar height h is less than 4.5 µm. In contrast, when the pillar height is h g 4.5 µm, the advancing contact angle remains constant for both OTS- and FTS-modified surfaces. Note that the advancing contact angle on the OTS-modified surface with large pillar heights is almost equal to that of the FTSmodified surface, in accord with the finding of O ¨ ner and McCarthy.12 The advancing contact angles on flat wafers coated with FTS and OTS are larger than 90°. When a drop rests on a composite surface of air and the hydrophobic coated wafer, the three-phase contact line is pinned at the corner. As the drop expands, the contact line inclines continuously till it reaches the one side of the next pillar and then slips to the corner. During this process, the maximum contact angle on any composite surface is almost 180° no matter the surface topography and chemistry, but contact angle measurements are limited by images from the optical method.14 None of the angles in our experiments is larger than 160°, which also reveals the limitation of our measurement system. Consider the systems at constant solid fraction, Φs ) 0.250. Figure 6a shows the variation of advancing/receding contact angles for three different structures, P3-3, P6-6, and P9-9, as a function of surface roughness r by simply using different pillar heights. The variation of advancing/receding contact angles can be divided into two regions: (1) 1 < r < 1.35: the advancing contact angle increases along with the surface roughness, and the receding contact angle decreases along with the surface roughness, i.e., the system falls into the Wenzel state. It should be noted that most of the advancing contact angles are larger than the theoretical predictions of the
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Figure 5. SEM images of pillar-like microstructures: (a) low magnification (3000×) and (b) high magnification (10 000×). Table 1. Experimental Advancing Contact Angle Data for Hydrophobic OTS- and FTS-Modified Surfaces with P10-10 Structure at Different Pillar Heights
Figure 3. Dynamic contact angle analysis of a water droplet on a hydrophobic surface. The advancing contact angle (a) and the contact diameter (b) vary with time (in terms of frame numbers). The receding contact angle (c) and the contact diameter (d) vary with time (in terms of frame numbers). The image is captured at a rate of 10 frames per second.
Figure 4. Schematic illustration of designed microstructures.
Wenzel state, as illustrated by the black dashed curve in Figure 6a, because of the underestimated surface roughness and the metastable part of the Cassie regime. The theoretical curves are
h (µm)
θa (OTS)
θa (FTS)
flat surface 2.1 3.2 4.5 5.5 6.9 9.4 19.9
110 132 145 152 154 153 153 155
120 142 143 154 154 155 155 156
simply the outcome of replacing the equilibrium contact angle in eq 1 by the advancing (or receding) contact angle. It is believed that the Wenzel eq 1 should well describe both the advancing and receding contact angles if the underestimated surface roughness is taken into account. (2) r > 1.35: both the advancing and receding contact angles remain constant, i.e., the system falls into the Cassie state. The average experimental receding contact angles are 136°, 132°, and 133° for the microstructures P3-3, P6-6, and P9-9, respectively, consistent with the theoretical prediction of the Cassie model 135°, shown as the red line in Figure 6a. Note that the receding contact angle predicted by the Cassie model (eq 2) is calculated by replacing the equilibrium contact angle by the receding contact angle 81°. On the other hand, the average experimental advancing
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Figure 6. (a) Variation of the advancing/receding contact angle of water droplet on pattern surfaces at a fixed solid fraction (Φs ) 0.25) as a function of the surface roughness. (a) The filled symbols stand for the advancing contact angle and open symbols for the receding contact angle: P3-3 (circle), P6-6 (triangle), and P9-9 (square). The dashed and solid lines represent theoretical predictions based on the Wenzel and Cassie models, respectively. The black and red lines represent theoretical predictions of the advancing and receding contact angels, respectively. (b) Variation of the contact angle hysteresis of a water droplet on patterned surfaces at a fixed solid fraction (Φs ) 0.25) as a function of the surface roughness.
contact angles are 157°, 155°, and 157° for the microstructures P3-3, P6-6, and P9-9, respectively, consistently slightly higher than the theoretical prediction of the Cassie model (151°), shown as the black line in Figure 6a. The advancing contact angle predicted by the Cassie model, eq 2, is calculated by replacing the equilibrium contact angle by the advancing contact angle 120°. The experimental result is slightly higher than the prediction of the Cassie model, which can be attributed to the overestimated solid fraction. There exists a transition between the Wenzel and Cassie states. The transition roughness of this transition point, rc, can be determined by the intersection of eqs 1 and 2:20
rc ) Φs -
1 - Φs cos θadv
(6)
Note that the advancing contact angle θadv is applied to the equilibrium contact angle θe in eqs 1 and 2. When r < rc, water penetrates between pillars and fully contacts the surface; i.e., the system belongs to the Wenzel state. On the other hand, when r g rc, a water droplet suspends on a composite surface of air and solid; i.e., the system belongs to the Cassie state. Note that the transition roughness rc for microstructures P3-3, P6-6, and P9-9 is 1.75, since the solid fraction is fixed (Φs ) 0.250) for these three microstructures. The experimental transition roughness, rc (20) Bico, J.; Thiele, U.; Que´re´, D. Colloids Surf., A 2002, 206, 41.
Figure 7. (a) Variation of the contact angle hysteresis at the Cassie state with a fixed pillar spacing d (3 µm, b; 6 µm, 1; and 9 µm, 9) as a function of the pillar width a. (b) Variation of the contact angle hysteresis at the Cassie state with a fixed pillar width a (3 µm, b; 6 µm, 1; and 9 µm, 9) as a function of the pillar spacing d.
) 1.35, is lower than the theoretical one (1.75) because of the underestimated surface roughness and overestimated solid fraction. Note that the advancing and receding contact angles are independent of the surface roughness at the Cassie state. On the other hand, the advancing (or receding) contact angle increases (or decreases) with an increase in the surface roughness at the Wenzel state. There is a dramatic change in the receding contact angle from the Wenzel state to the Cassie state. When the water droplet is at the Wenzel state (r < 1.35), the receding contact angle slightly decreases with an increase in the pillar height (or roughness), as shown in Figure 6a, consistent with the findings of Dettre and Johnson.21 However, there was no information about surface roughness in the latter study21 to further examine the Wenzel and Cassie equations. On the other hand, when the water droplet is at the Cassie state, the receding contact angle almost remains constant around 135°. There is a discontinuity of the receding contact angle when the transition between the Wenzel state and the Cassie state occurs. As a consequence, there is also a discontinuity of the hysteresis right at the transition point between the Wenzel state and the Cassie state. It is interesting to note that the hysteresis ∆θ () θadv - θrec) remains almost constant for these microstructures P3-3, P6-6, and P9-9 when the system is at the Cassie state. In addition, the contact angle hysteresis ∆θ increases with an increase in the pillar height (or surface roughness) when the system is at the Wenzel state, as shown in Figure 6b. It should be noted that both the Wenzel and (21) Dettre, R. H.; Johnson, R. E. AdV. Chem. Ser. 1964, 43, 112, 136.
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Figure 8. (a) Variation of the advancing/receding contact angle of a water droplet on patterned surfaces at the Cassie state as a function of solid fraction: P3-3 (blue circle), P3-6 (blue triangle), P3-9 (blue square), P3-20 (blue diamond), P6-3 (red circle), P6-6 (red triangle), P6-9 (red square) P6-20 (red diamond), P9-3 (green circle), P9-6 (green triangle), P9-9 (green square), and P9-20 (blue diamond). The filled symbols stand for the advancing contact angles, and the open symbols stand for the receding contact angle. (b) Variation of the contact angle hysteresis of a water droplet on patterned surfaces at the Cassie state as a function of solid fraction. The black and red lines are theoretical predictions of the Cassie model for the advancing and receding contact angles, respectively.
Cassie models, eqs 1 and 2, can be applied to either advancing or receding contact angles. Now, consider the systems of a fixed pillar size, say a ) 6 µm. The microstructures of four different spacing distances are fabricated: P6-3(h), P6-6(h), P6-9(h), and P6-20(h). For each microstructure, at least eight different pillar heights are prepared to produce a wide range of surface roughnesses (1-6.437). When the water droplet on this patterned surface falls into the Wenzel state, the advancing (or receding) contact angle increases (or decreases) with an increase in the surface roughness for the systems of these microstructures. The advancing and receding contact angles are independent of the surface roughness when the system belongs to the Cassie state. It is interesting to note that the contact angle hysteresis decreases as the spacing d increases, as shown in Figure 7b. In addition, two more systems of a fixed pillar size are also prepared. They are pillar sizes of a ) 3 µm and a ) 9 µm. The variation of the hysteresis as a function of the spacing d for these two different pillar sizes is also shown in Figure 7b, consistent with the finding of Dorrer and Ru¨he.14 It is obvious that the contact angle hysteresis decreases along with an increase in the spacing d. On the other hand, we can examine the contact angle hysteresis of the systems under the condition of a fixed spacing d at the Cassie state. It is obvious that the contact angle hysteresis increases
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Figure 9. (a) Variation of the advancing/receding contact angle of a water droplet on patterned surfaces at the Wenzel state as a function of solid fraction: P3-3 (blue circle), P3-6 (blue triangle), P3-9 (blue square), P3-20 (blue diamond), P6-3 (red circle), P6-6 (red triangle), P6-9 (red square) P6-20 (red diamond), P9-3 (green circle), P9-6 (green triangle), P9-9 (green square), and P9-20 (blue diamond). The filled symbols stand for the advancing contact angles, and open symbols stand for the receding contact angle. (b) Variation of the contact angle hysteresis of a water droplet on patterned surfaces at the Wenzel state as a function of solid fraction. The black and red dashed lines are theoretical predictions of the Cassie model for the advancing and receding contact angles, respectively.
along with the pillar size at a fixed spacing d, as shown in Figure 7a, consistent with the finding of Dorrer and Ru¨he.14 It is believed that the movement of a drop on a surface is strongly associated with the movement of the three-phase (airliquid-solid) contact line. Extrand proposed that the receding contact angle is a linear combination of the receding contact angle on the flat solid surface and that on air, when the liquid drop is at the Cassie state.22 In this study, there is no way to directly measure the three-phase contact line. However, the solid fraction is an index for the fraction of the three-phase contact line on the solid surface when the water drop is at the Cassie state. Figure 8a shows the variation of the advancing/receding contact angles as a function of the solid fraction under the condition of the Cassie state. Indeed, both the receding/advancing contact angles monotonically decrease with an increase in the solid fraction. It should be noted that Dorrer and Ru¨he14 pointed out that the variation of the receding contact angle is not a function of the solid fraction when the water drop is at the Cassie state. That is, the receding contact angle cannot be predicted from the solid fraction solely.14 As one can see in Figure 4 in ref 14 the receding contact angle varies from 110° to 130° when Φs ) (22) Extrand, C. W. Langmuir 2002, 18, 7991.
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0.25. However, in this study, the receding contact angle for Φs ) 0.25 is 134 ( 2°, consistent with the Cassie prediction of 135°. Note that the decrease in the advancing contact angle is not pronounced. It is expected to get the advancing contact angle as high as 173° at low solid fractions, as shown in Figure 8a. Recall that the limitation of our contact angle measurement is restricted to 160°. Therefore our advancing contact angle is smaller than the prediction of the Cassie model (simply replacing the equilibrium contact angle by the advancing contact angle on a flat surface, 120°, in eq 2) at low solid fractions. On the other hand, the advancing contact angle is larger than the prediction of the Cassie model at high solid fractions as a result of the overestimation of the solid fraction, as mentioned above. The trend of the receding contact angle is similar to that of the advancing contact angle. That is, the receding contact angle is smaller (or larger) than the prediction of the Cassie model (simply replacing the equilibrium contact angle by the receding contact angle on a flat surface, 80°, in eq 2) at low (or high) solid fraction. As a consequence, the contact angle hysteresis increases monotonically as a function of the solid fraction, as shown in Figure 8b, when the system is at the Cassie state. While the solid fraction is increased to 0.563, the contact angle hysteresis is enhanced up to 41°. Note that it is not necessary that the superhydrophobic surface (for the surface with an advancing contact angle larger than 150°) always have low hysteresis. On the other hand, the contact angle hysteresis is around 11° when the solid fraction is as low as 0.063. It is well understood that the criterion of a “superhydrophobic surface” is a surface with large contact angles and low hysteresis. Therefore, the rule of thumb for the fabrication of superhydrophobic surfaces is to increase the surface roughness (to ensure the system at the Cassie state) and to reduce the solid fraction as much as possible. Many of our pattern surfaces exhibit large advancing contact angles (>150°) but significant hysteresis (10-40°). A water drop forms an almost spherical bead on this kind of surface and rolls off easily. It is very difficult to grab a clear photo of the water droplet on a surface with such a large contact angle. When a water droplet forms a contact angle larger than 150° in our contact angle measurement, the droplet vibrates easily and rolls off with a slight tilt of the surface. Finally, we would like to examine the advancing/receding contact angles as a function of the surface roughness when the
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water droplet is at the Wenzel state. All the experimental results are shown in Figure 9a. The advancing/receding contact angle increases/decreases with an increase in the surface roughness at the Wenzel state. When the three-phase contact line expands, the water drop has to sweep across whole pillars.12 It should be noted that most of the advancing contact angles are larger than the theoretical predictions of the Wenzel state, as illustrated by the black dashed curve in Figure 9a, as a result of the underestimated surface roughness. The surface roughness has complex influence on the receding process because some water may be left behind in the grooves after the contraction of the water drop.23 The receding contact angle measurement demonstrates larger uncertainty, as one can see in Figure 9a. Nevertheless, the receding contact angle can be well described by the theoretical predictions of the Wenzel state, as illustrated by the red dashed curve in Figure 9(a). Consequently, the contact angle hysteresis increases along with an increase in the surface roughness, as shown in Figure 9b, when the system is at the Wenzel state. Note that the contact angle hysteresis could be as large as 80° when the surface roughness is only 1.25.
Conclusions In this study, a series of pillar-like pattern surfaces are applied to explore the effect of surface topography on dynamic contact angles. It is found that the experimental results of the advancing and receding contact angles of water on pillar-like patterned surfaces are consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction, as shown in Figure 8b. On the other hand, when a water drop is at the Wenzel state, its advancing and receding contact angles depend on the surface roughness, as shown in Figure 9, as well as the contact angle hysteresis. Supporting Information Available: Experimental data of advancing/receding contact angles on silane-modified surfaces with pillarlike microstructures. This information is available free of charge via the Internet at http: //pubs.acs.org. LA7020337 (23) Patankar, N. A. Langmuir 2003, 19, 1249.
