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Dynamic Effects of Bouncing Water Droplets on Superhydrophobic Surfaces Yong Chae Jung and Bharat Bhushan* Nanotribology Laboratory for Information Storage and MEMS/NEMS (NLIM), The Ohio State UniVersity, 201 West 19th AVenue, Columbus, Ohio 43210-1142 ReceiVed January 31, 2008. ReVised Manuscript ReceiVed March 12, 2008 Superhydrophobic surfaces have considerable technological potential for various applications due to their extreme water repellent properties. Superhydrophobic surfaces may be generated by the use of hydrophobic coating, roughness, and air pockets between solid and liquid. Dynamic effects, such as the bouncing of a droplet, can destroy the composite solid-air-liquid interface. The relationship between the impact velocity of a droplet and the geometric parameters affects the transition from the solid-air-liquid interface to the solid-liquid interface. Therefore, it is necessary to study the dynamic effect of droplets under various impact velocities. We studied the dynamic impact behavior of water droplets on micropatterned silicon surfaces with pillars of two different diameters and heights and with varying pitch values. A criterion for the transition from the Cassie and Baxter regime to the Wenzel regime based on the relationship between the impact velocity and the parameter of patterned surfaces is proposed. The trends are explained based on the experimental data and the proposed transition criterion. For comparison, the dynamic impact behavior of water droplets on nanopatterned surfaces was investigated. The wetting behavior under various impact velocities on multiwalled nanotube arrays also was investigated. The physics of wetting phenomena for bouncing water droplet studies here is of fundamental importance in the geometrical design of superhydrophobic surfaces.
1. Introduction It is well-known that water condensation from a humid environment may lead to the formation of menisci at the interface between solid bodies during sliding contact, which increases adhesion and friction. As a result of this, the friction force in a humid environment is greater than that in dry air, which is usually undesirable.1–4 Menisci also can lead to stiction, or the sticking together of two contacting components. Numerous applications, such as magnetic storage devices and micro-/nanoelectromechanical systems (MEMS/NEMS), require surfaces with low adhesion and stiction.3–8 As the size of these devices decreases, the surface forces tend to dominate over the volume forces, and adhesion and stiction constitute a challenging problem for proper operation of these devices. This makes the development of superhydrophobic surfaces crucial for many of these emerging applications. Superhydrophobic surfaces with low contact angle hysteresis have a low drag for fluid flow and low tilt angle. When these surfaces are tilted, even for a small angle, water droplets roll off (with some slip) the surface and take contaminants with them, providing a self-cleaning ability. These self-cleaning surfaces are of interest for various applications, including selfcleaning windows, windshields, exterior paints for buildings and * Corresponding author. E-mail:
[email protected]; tel.: (614) 2920651; fax: (614) 292-0325. (1) Bhushan, B. Handbook of Micro-/Nanotribology, 2nd ed.; CRC Press: Boca Raton, FL, 1999. (2) Bhushan, B. Introduction to Tribology; Wiley: New York, 2002. (3) Bhushan, B. J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.sProcess., Meas., Phenom. 2003, 21, 2262. (4) Bhushan, B. Nanotribology and NanomechanicssAn Introduction; Springer-Verlag: Berlin, 2005. (5) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature (London, U.K.) 1995, 374, 607. (6) Bhushan, B. Tribology and Mechanics of Magnetic Storage Systems, 2nd ed.; Springer-Verlag: Berlin, 1996. (7) Bhushan, B. Tribology Issues and Opportunities in MEMS; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1998. (8) Bhushan, B. Springer Handbook of Nanotechnology, 2nd ed.; SpringerVerlag: Berlin, 2007.
ships, utensils, roof tiles, textiles, and applications requiring a reduction of drag in fluid flow (e.g., in micro-/nanochannels). The primary parameter that characterizes wetting is the static contact angle, which is defined as the measurable angle that a liquid makes with a solid. The contact angle depends on several factors, such as roughness and the manner of surface preparation and its cleanliness.9,10 If the liquid wets the surface (referred to as a wetting liquid or hydrophilic surface), the value of the static contact angle is 0° e θ e 90°, whereas if the liquid does not wet the surface (referred to as a nonwetting liquid or hydrophobic surface), the value of the contact angle is 90° < θ e 180°. Hydrophobic (water-repellent) surfaces can be constructed by using low surface energy materials or coatings such as polytretafluoroethylene or wax. The hydrophobicity of a surface also can be increased by increasing the surface roughness and/or creating air pockets.11–14 A number of studies have been carried out to produce artificial biomimetic roughness-induced hydrophobic surfaces.15–25 Recent (9) Adamson, A. V. Physical Chemistry of Surfaces; Wiley: New York, 1990. (10) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, 1992. (11) Bhushan, B.; Jung, Y. C. J. Phys.: Condens. Matter 2008, 20, 225010. (12) Nosonovsky, M.; Bhushan, B. Mater. Sci. Eng., R 2007, 58, 162. (13) Nosonovsky, M.; Bhushan, B. J. Phys.: Condens. Matter 2008, 20, 225009. (14) Nosonovsky, M.; Bhushan, B. Langmuir 2008, 24, 1525. (15) Shibuichi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512. (16) Hozumi, A.; Takai, O. Thin Solid Films 1998, 334, 54. (17) Coulson, S. R.; Woodward, I.; Badyal, J. P. S. J. Phys. Chem. B 2000, 104, 8836. (18) Miwa, M.; Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. Langmuir 2000, 16, 5754. (19) Oner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (20) Feng, L.; Li, S.; Li, Y.; Li, H.; Zhang, L.; Zhai, J.; Song, Y.; Liu, B.; Jiang, L.; Zhu, D AdV. Mater. 2002, 14, 1857. (21) Erbil, H. Y.; Demirel, A. L.; Avci, Y. Science (Washington, DC, U.S.) 2003, 299, 1377. (22) Lau, K. K. S.; Bico, J.; Teo, K. B. K.; Chhowalla, M.; Amaratunga, G. A. J.; Milne, W. L.; Mckinley, G. H.; Gleason, K. K. Nano Lett. 2003, 3, 1701. (23) Burton, Z.; Bhushan, B. Nano Lett. 2005, 5, 1607. (24) Jung, Y. C.; Bhushan, B. Nanotechnology 2006, 17, 4970. (25) Bhushan, B.; Sayer, R. A. Microsyst. Technol. 2007, 13, 71.
10.1021/la8003504 CCC: $40.75 2008 American Chemical Society Published on Web 05/15/2008
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studies have investigated wetting behavior during condensation26 and evaporation27,28 and the stability of the composite interface of artificial superhydrophobic surfaces and the transition from composite to homogeneous interface under pressure,29,30 vertical vibration,31 and the effect of contact angle hysteresis.32 Nosonovsky and Bhushan33 suggested that destabilizing factors responsible for such a transition have different characteristic scale lengths, and thus, multiscale (hierarchical) roughness plays an important role in stabilizing the composite interface. Various criteria have been formulated to predict the transition from a metastable composite state to a wetted state, such as the contact line density,34 energy barrier,35 and spacing factor.36 In addition, Bhushan and Jung,37 Jung and Bhushan,27,28 and Reyssat et al.38 proposed a transition criterion obtained from the curvature of a droplet governed by the Laplace equation, which relates pressure inside the droplet to its curvature. Another important phenomenon related to wetting behavior is the bouncing of droplets. When a droplet hits a surface, it can bounce, spread, or stick. In practical applications of superhydrophobic surfaces, surfaces should maintain their ability to repel penetrating droplets under dynamic conditions. Many researchers have considered the dynamic effects of droplets on superhydrophobic surfaces. Richard et al.,39 Bartolo et al.,40 and Reyssat et al.41 showed that the transition can occur by the impact of a droplet on the patterned surface with a critical geometric parameter. Therefore, we believe that a criterion is needed to predict the transition based on the impact velocity and the geometric parameter of the patterned surface, and systematic investigations are needed to validate the transition criterion. This information is critical in designing a superhydrophobic surface for applications requiring water repellency. In this paper, a study of the dynamic impact behavior of a water droplet was conducted on micropatterned silicon surfaces with pillars of two different diameters and heights and with varying pitch values. We propose a criterion where the transition from the Cassie and Baxter regime to the Wenzel regime is determined from the relationship between the impact velocity, geometric parameters of patterned surfaces, and liquid properties. On the basis of the experimental data and transition criterion, trends are explained. For comparison, the dynamic impact behavior of a water droplet on nanopatterned surfaces was investigated. The wetting behavior under various impact velocities on multiwalled nanotube (MWNT) arrays also was investigated.
volume (with radius of a spherical droplet of about 1 mm) gently were deposited on the substrate using a microsyringe for the static contact angle. The image of the droplet was obtained by a digital camcorder (Sony, DCRSR100) with a 10× optical and 120× digital zoom. Images were analyzed using Imagetool software (University of Texas Health Science Center) for the contact angle. The process of the dynamic impact behavior was obtained by a high speed camera (Kodak Ektapro HS Motion Analyezer, Model 4540) operating at 500 frames/s for each experimental run and then measuring the dynamic impact behavior of the droplet as a function of time. The impact velocity was calculated by varying the droplet release height. The size of the droplet was the same as that of a droplet for the static contact angle. All measurements were made in a controlled environment at 22 ( 1 °C and 45 ( 5% relative humidity (RH). 2.2. Samples. Single-crystal silicon (Si) was used for micropatterned surfaces in this study. To create micropatterned Si, two series of nine samples each were fabricated using photolithography.42 Series 1 had 5 µm diameter and 10 µm height flat-top, cylindrical pillars with different pitch values (7, 7.5, 10, 12.5, 25, 37.5, 45, 60, and 75 µm), and series 2 had 14 µm diameter and 30 µm height flat-top, cylindrical pillars with different pitch values (21, 23, 26, 35, 70, 105, 126, 168, and 210 µm). Two different surface height maps were obtained using an optical profiler (NT-3300, Wyko Corp.) as can be seen for the micropatterned Si in Figure 1a. In each case, a 3-D map and a flat map along with a 2-D profile in a given location of the flat 3-D map are shown.28,37 The pitch is the spacing between the centers of two adjacent pillars. The Si chosen was initially hydrophilic, so to obtain a sample that was hydrophobic, a selfassembled monolayer (SAM) of 1,1,-2,2,-tetrahydroperfluorodecyltrichlorosilane (PF3) was deposited on the sample surfaces using a vapor phase deposition technique.42 For nanopatterned surfaces, two types of surface patterns were fabricated from PMMA: low aspect ratio asperities (LAR, 1:1 height/ diameter ratio) and high aspect ratio asperities (HAR, 3:1 height/ diameter ratio) (supplied by Dr. E. S. Yoon of KIST). Figure 1b shows SEM images of the two types of nanopatterned structures, LAR and HAR, on a PMMA surface.23,24 Nanopatterned structures were manufactured using soft lithography. To obtain a hydrophobic sample, a SAM of perfluorodecyltriethoxysilane (PFDTES) was deposited on the sample surfaces using a vapor phase deposition technique.43 Three different vertically aligned carbon nanotube arrays also were used (Figure 1c). The diameter and length of MWNT 1 were 15 nm and 1 mm, respectively (Cheap Tubes Inc.). The diameter and length of MWNT 2 were 35 nm and 50 µm, respectively (MER Corp.). The diameter and length of MWNT 3 were 30-40 nm and 30 µm, respectively (Sunnano Co.).
2. Experimental Procedures
3. Theoretical Background
2.1. Instrumentation. For the measurement of the static contact angle, the droplet size should be small but larger than the dimension of the structures present on the surfaces. Droplets of about 5 µL in
3.1. Contact Angle Analysis. We considered a rough solid surface where the typical size of the roughness structure was smaller than the size of the droplet (typically on the order of few hundred micrometers or larger). For a droplet in contact with a rough surface without air pockets, referred to as a homogeneous interface, the contact angle is given as44
(26) Narhe, R. D.; Beysens, D. A. Europhys. Lett. 2006, 75, 98. (27) Jung, Y. C.; Bhushan, B. Scripta Mater. 2007, 57, 1057. (28) Jung, Y. C.; Bhushan, B. J. Microsc. 2008, 229, 127. (29) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (30) Liu, B.; Lange, F. F. J. Colloid Interface Sci. 2006, 298, 899. (31) Bormashenko, E.; Pogreb, Y.; Whyman, G.; Erlich, M. Langmuir 2007, 23, 6501. (32) Ishino, C.; Okumura, K. Europhys. Lett. 2006, 76, 464. (33) Nosonovsky, M.; Bhushan, B. Microelectron. Eng. 2007, 84, 382. (34) Extrand, C. W. Langmuir 2004, 20, 5013. (35) Patankar, N. A. Langmuir 2004, 20, 7097. (36) Bhushan, B.; Nosonovsky, M.; Jung, Y. C. J. R. Soc. Interface 2007, 4, 643. (37) Bhushan, B.; Jung, Y. C. Ultramicroscopy 2007, 107, 1033. (38) Reyssat, M.; Yeomans, J. M.; Quere, D. Europhys. Lett. 2008, 81, 26006. (39) Richard, D.; Clanet, C.; Quere, D. Nature (London, U.K.) 2002, 417, 811. (40) Bartolo, D.; Bouamrirene, F.; Verneuil, E.; Buguin, A.; Silberzan, P.; Moulinet, S. Europhys. Lett. 2006, 74, 299. (41) Reyssat, M.; Pepin, A.; Marty, F.; Chen, Y.; Quere, D. Europhys. Lett. 2006, 74, 306.
cos θ ) Rf cos θ0
(1)
where θ is the contact angle for a rough surface, θ0 is the contact angle for a smooth surface, and Rf is a roughness factor defined as a ratio of the solid-liquid area ASL to its projection on a flat plane, AF. The model predicts that roughness enhances hydrophobicity if θ0 is greater than 90°. If θ0 is less than 90°, then the contact angle for the rough surface will decrease with increasing Rf values. (42) Barbieri, L.; Wagner, E.; Hoffmann, P. Langmuir 2007, 23, 1723. (43) Bhushan, B.; Hansford, D.; Lee, K. K. J. Vac. Sci. Technol., A 2006, 24, 1197. (44) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988.
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Figure 1. (a) Surface height maps and 2-D profiles of patterned Si surfaces coated with PF3 using an optical profiler. The diameter and height of the pillar are D and H, respectively. The pitch of the pillars is P. (b) SEM images of two nanopatterned polymer surfaces (shown using two magnifications to see both asperity shape and asperity pattern on the surface). (c) SEM images of the vertically aligned MWNT arrays. Diameter and length of MWNT 1 were 15 nm and 1 mm, respectively. Diameter and length of MWNT 2 were 35 nm and 50 µm, respectively. Diameter and length of MWNT 3 were 30-40 nm and 30 µm, respectively.
In a rough surface, a wetting liquid will be completely absorbed by the rough surface cavities, while a nonwetting liquid may not
penetrate into surface cavities, resulting in the formation of air pockets and leading to a composite solid-air-liquid interface.
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Cassie and Baxter45 extended the Wenzel equation for the composite interface, which was originally developed for the homogeneous solid-liquid interface. In this case, there are two sets of interfaces: a solid-liquid interface with an ambient environment surrounding the droplet and a composite interface involving liquid-air and solid-air interfaces. To calculate the contact angle for the composite interface, the Wenzel equation can be modified by combining the contribution of the fractional area of wet surfaces and the fractional area with air pockets (θ ) 180°)
cos θ ) Rf cos θ0 - fLA(Rf cos θ0 + 1)
(2)
where fLA is the fractional flat geometrical area of the liquid-air interfaces under the droplet. To show an application example of the Wenzel and Cassie and Baxter equations, we considered the geometry of flat-top, cylindrical pillars of diameter D, height H, and pitch P distributed in a regular square array as shown in Figure 1a. For the special case where the droplet size is much larger than P (of interest in this study), a droplet only contacts the flat-top of the pillars in the composite interface, and the cavities are filled with air. For this case, fLA ) 1 - {πD2}/{4P2} ) 1 - fSL. Let us further assume that the flat tops are smooth with Rf ) 1. Eqs 1 and 2 for this case reduce to37 Wenzel
(
cos θ ) 1 +
)
πDH cos θ0 P2
(3)
and Cassie and Baxter
cos θ )
πD2 (cos θ0 + 1) - 1 4P2
(4)
The Wenzel and Cassie and Baxter equations present two possible equilibrium states for a water droplet on the surface. This indicates that there is a critical pitch below which the composite interface dominates and above which the homogeneous interface dominates the wetting behavior. It should also be noted that even in cases where the liquid droplet does not contact the bottom of the cavities, the water droplet in a metastable state becomes unstable, and the transition from the Cassie and Baxter regime to the Wenzel regime occurs if the pitch is large. 3.2. Transition Criterion. A stable composite interface is essential for the successful design of superhydrophobic surfaces. However, the composite interface is fragile, and it may transform into a homogeneous interface. The dynamic effects affect the transition. Hence, we consider this factor in the model discussed next. When a droplet impacts a superhydrophobic surface with a certain velocity, it can either bounce off or wet the surface. The kinetic energy of the droplet is stored in the surface deformation during the impact. A deformed droplet has a higher surface area and therefore higher free surface energy. Therefore, during the impact when the droplet is deformed, it can accommodate the kinetic energy. We consider a water droplet hitting a superhydrophobic surface consisting of a regular array of circular pillars with diameter D, height H, and pitch P as shown in Figure 2. The curvature of a droplet is governed by the Laplace equation, which relates the pressure inside the droplet to its curvature.9 The curvature is the same at the top and at the bottom of the droplet.33,46 As the droplet hits the surface at velocity V, the liquid-air interface below the droplet is formed when the dynamic pressure is less than the Laplace pressure. For the patterned surface considered (45) Cassie, A.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (46) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457.
Figure 2. Small water droplet, hitting at a velocity V, suspended on a superhydrophobic surface consisting of a regular array of circular pillars: (a) plane view, maximum droop of droplet occurs in the center of the square formed by four pillars and (b) side view in section A-A, the maximum droop of droplet (δ) can be found in the middle of two pillars that are diagonally across.
here, the maximum droop of the droplet occurs in the center of the square formed by the four pillars as shown in Figure 2a. Therefore, the maximum droop of the droplet (δ) in the recessed region can be found in the middle of two pillars that are diagonally across as shown in Figure 2b, which is (2P - D)2/(8R). The Laplace pressure can be written as
pL ) 2γ ⁄ R ) 16γδ ⁄ (√2P - D)2
(5)
where γ is the surface tension of the liquid-air interface. The dynamic pressure of the droplet is equal to
1 pd ) FV2 2
(6)
where F is the mass density of the liquid droplet. If the maximum droop of the droplet (δ) is larger than the height of pillar (H), the droplet contacts the bottom of the cavities between pillars. Determination of the critical velocity at which the droplet touches the bottom is obtained by equating the Laplace pressure to the dynamic pressure. To develop a composite interface, the velocity should be smaller than the critical velocity given as
V
