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Growth Dynamics of Water Drops on a Square-Pattern Rough Hydrophobic Surface R. D. Narhe† and D. A. Beysens*,†,‡ Equipe du Supercritique pour l’EnVironnement, les Mate´ riaux et l’Espace, Laboratoire de Physique et Me´ canique des Milieux He´ te´ roge` nes, Ecole Supe´ rieure de Physique et Chimie Industrielle et UniVersite´ s Paris 6 et Paris 7, 10 rue Vauquelin, 75231 Paris Cedex 05, France, and SerVice des Basses Tempe´ ratures, CEA-Grenoble, Grenoble, France ReceiVed July 12, 2006. In Final Form: December 15, 2006 Condensation on rough or superhydrophobic substrates can induce wetting behavior that is quite different from that of deposited or impinging drops. We investigate the growth dynamics of water drops in a well-controlled condensation chamber on a model rough hydrophobic surface made of square pillars. After having followed growth laws similar to those observed on flat surfaces, a transition to an air-pocket-like state occurred because of the bridging of the drops between the pillars. Another transition to the more stable Wenzel state is later ensured by a noticeable pillar self-drying process. Condensation ends up in a few large drops in a mixed Wenzel penetration regime. The drops are fed by neighboring channels and the adjacent pillars stay almost dry, a remarkable and seemingly general property of rough hydrophobic substrates.
Introduction Self-cleaning surfaces (e.g., lotus leaves)1-7 are naturally superhydrophobic and super-water-repellent. Depending on how water reaches the surface, the lotus leaves can behave as hydrophilic, hydrophobic, or superhydrophobic.1 This phenomenon has stimulated the scientific and industrial community to create an artificial superhydrophobic surface and to investigate the behavior of water drops on such a surface. Although many studies have been devoted to the wetting behavior of drops deposited on a surface,3 very few have delved into the condensation process even though it is a key phenomenon in both fundamental and applied studies. Condensation on superhydrophobic substrates can indeed induce wetting behavior that is quite different from that of deposited or impinging drops1,4-5 because during condensation the drops grow on all surfaces of the substrate. In addition, the drops coalesce with each other. This drop-drop interaction and the fact that the drop sizes cover a broad range of length scales, both smaller and larger than that of the pattern, makes the condensation situation quite different from the generally considered case of drop deposition. In this letter, we investigated the main features of water condensation on a rough hydrophobic model surface made of square pillars. Whereas some of the features of superhydrophobicity are maintained during growth, quite unexpected phenomena were observed (pillar bridging, self-drying) that can be easily generalized to other surface geometries and could lead to interesting applications or developments. A superhydrophobic surface, where the contact angle of water is very large (typically >150° but this is not a strict definition), is basically a rough surface. Rough/superhydrophobic surfaces * Corresponding author. E-mail:
[email protected]. † Ecole Supe ´ rieure de Physique et Chimie Industrielle et Universite´s Paris 6 et Paris 7. ‡ CEA-Grenoble. (1) Cheng, Y. T.; Rodak, D. E.; Angelopoulos, A.; Gacek, T. Appl. Phys. Lett. 2005, 87, 194112. (2) Cheng, Y. T.; Rodak, D. E. Appl. Phys. Lett. 2005, 86, 144101. (3) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457. (4) Narhe, R. D.; Beysens, D. A. Europhys. Lett. 2006, 75, 98. (5) Narhe, R. D.; Beysens, D. A. Phys. ReV. Lett. 2004, 93, 076103. (6) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1. (7) Otten, A.; Herminghaus, S. Langmuir 2004, 20, 2405.
can be produced by various methods8-15 (e.g., by molding solgel, chemical vapor deposition, micromachining, lithography, plasma-enhanced chemical vapor deposition, self-organization, etc.). Artificial superhydrophobic surfaces can consist of different configurations (e.g., triangular spike,3,4 pillars,9,11-14 pin cushion (or needle),14,16 fractal,17 striped pattern,5,14 carbon nanotubes,18,19 etc.). Surface roughness and air trapped on the surface increase the drying properties of superhydrophobic surfaces. When a drop is deposited on such a surface, the liquid can be arranged in one of the following geometrical configurations corresponding to different wetting states: (i) Cassie-Baxter (CB) or air pocket, where air remains trapped below the drop (e.g., when the drop is gently put onto the substrate), (ii) Wenzel (W), where the interpillar space below the drop is filled with liquid (e.g., when the drop is pushed toward the substrate), and (iii) penetration (e.g., the drop is firmly pushed onto the substrate), where the drop is in the Wenzel state but also fills the region of the substrate around the drop. The apparent contact angle θ* in the CB state is given20 by
cos θ* ) φs(1 + cos θ) - 1
(1)
(8) Feng, L.; Li, S.; Li, Y.; Li, H.; Zhang, L.; Zhai, T.; Song, J. Y.; Liu, B.; Jaing, L.; Zhu, D. AdV. Mater. 2002, 14, 1857. (9) Bico, J.; Marzolin, C.; Que´re´, D. Europhys. Lett. 1999, 47, 220. (10) Wu, Y.; Sugimura, H.; Inoue, Y.; Takai, O. Chem. Vap. Deposition 2002, 8, 47. (11) O ¨ ner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (12) Fu¨rstner, R.; Barthlott, W.; Neinhuis, C.; Walzel, P. Langmuir 2005, 21, 956. (13) Patankar, N. A. Langmuir 2004, 20, 8209. Patankar, N. A. Langmuir 2004, 20, 7097. Patankar, N. A. Langmuir 2003, 19, 1249. He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999. (14) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (15) Yabu, H.; Takebayashi, M.; Tanaka, M.; Shimomura, M. Langmuir 2005, 21, 3235. (16) Miwa, M.; Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. Langmuir 2000, 16, 5754. (17) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2125. (18) Lau, K. K. S.; Bico, J.; Teo, K. B. K.; Chhowalla, M.; Amaratunga, G. A. J.; Milne, W. I.; McKinley, G. H.; Gleason, K. K. Nano Lett. 2003, 3, 1701. (19) Journet, C.; Moulinet, S.; Ybert, C.; Purell, S. T.; Bocquet, L. Europhys. Lett. 2005, 71, 104. (20) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546.
10.1021/la062021y CCC: $37.00 © 2007 American Chemical Society Published on Web 05/02/2007
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Here, φs is the solid-liquid interface area fraction, and θ is the equilibrium contact angle on the same flat surface. In the W state, the apparent contact angle is given21 by
cos θ* ) r cos θ
(2)
where r is the surface roughness defined as the ratio of the actual area to the projected area. The equilibrium state depends on whether, for given θ, r, and φs, the minimum energy is W or CB.3,13,14,22 With a critical contact angle such as
θc ) cos-1
( ) φs - 1 r - φs
(3)
when θ > θc, the most stable state is CB, whereas when θ < θc, it is W.3 It is not guaranteed, however, that a drop will always exists in the lower-energy state because the state in which the drop will settle depends on how the drop is formed.13 In general, the transition from a higher-energy CB state to a lower-energy W state is possible only if the required energy barrier is overcome by the drop (e.g., by lightly pressing the drop, releasing the drop from some height, etc.).3,13 During steady condensation, while the volume of individual drops grows proportionally with time leading to a drop radius of R ≈ t1/3, drop interactions via coalescence are the key to the dynamics. On a flat surface, coalescence events rescale the average drop radius evolution as 〈R〉 ≈ t. On a patterned substrate, such coalescence greatly modifies the growth dynamics. What is essential is the presence of a crossover between the early and late stages that leads to very particular geometry-dependent phenomena. During the early stages, the drop sizes remain smaller than the typical length scales of the surface pattern, and drops basically visit a plane surface. During the late stages, the drop size is much larger than the typical length scales of the surface pattern. Superhydrophobicity holds only in this stage, and the CB and W states can be observed. However, this energy description is not sufficient to describe the growth. Drops indeed continue to nucleate, grow, and interact at all length scales as a recent investigation of condensation on a 2D superhydrophobic surface5 has shown. Experimental Section In the present study, we address a general substrate geometry consisting of a pillar-type rough hydrophobic surface model. For this purpose, a square-pillar silicon substrate was used. A 2 × 1 cm2 piece of silicon wafer was used with half of the substrate (1 × 1 cm2) containing grooves to form square pillars of width a ) 32 ( 2 µm, separation b ) 32 ( 2 µm, height c ) 62 ( 2 µm, and bottom diameter d ) 22 ( 2 µm (Figure 1). The contact angle of silicon was changed by a silanization method23,24 and measured by the sessile drop method.25 We arbitrarily define the equilibrium value of the contact angle by θ ) (θa + θr)/2, where θa (θr) is the advancing (receding) angle. From the shape of a deposited drop, θ was 90 ( 2° on the unpatterned part of the substrate (θa ) 95° and θr ) 85°). The contact angle hysteresis is not very large (∼10°) on the smooth surface, so the phenomena discussed below (growth stages and growth laws) will not be changed even if there is little variation in the equilibrium contact angle. On the square-pillarpatterned part, the contact angle is 138 ( 2° (θa ) 142° and θr ) 134°). This last value is in agreement with a CB state. However, the most stable state is W: from the roughness factor r ) 1 + [4ac/(a (21) Wenzel, R. Ind. Eng. Chem. 1936, 28, 988. (22) Ishino, C.; Okumura, K.; Que´re´, D. Europhys. Lett. 2004, 68, 419. (23) Chaudhury, M. K.; Whitesides, G. M. Science 1992, 256, 1539. (24) Elwing, H.; Welin, S.; Askendal, A.; Nilsson, U.; I. Lustro¨m, J. Colloid Interface Sci. 1987, 119, 203. (25) Narhe, R.; Beysens, D.; Nikolayev, V. S. Langmuir 2004, 20, 1213.
Figure 1. Optical microscope image of a square-pillar-patterned silicon substrate: (a) top view, (b) bottom view, and (c) side view (a ) 32 µm, b ) 32 µm, c ) 62 µm, d ) 22 µm). In part d, a 1 µL drop was deposited using a microsyringe on the square-pillar substrate coated by decyltrichlorosilane, and it has a contact angle of θ ) 138°. + b)2] ) 2.93 and the solid-liquid interface area fraction φs ) a2/(a + b)2 ) 0.25, the critical angle is θc ≈ 106° > θ ) 90°, a value taken by both the Wenzel and the equilibrium contact angles in the present study. The technique used for making such square-pillar superhydrophobic surfaces is the same as used by Yoshimitsu et al.14 (microsaw milling). Figure 1a-c shows an optical microscope picture of a top view, bottom view, and side view of the substrate, respectively. A cleaned substrate was fixed on a thick electrolytic copper plate of the condensation chamber by a thin liquid water film in order to ensure good thermal contact. A gas flow of pure nitrogen, saturated with water vapor by bubbling into pure water, was sent to the chamber with a rate kept fixed at 0.6 L min-1 for all experiments. The chamber is closed with a cover so that the space (∼5 mm) between the substrate and the cover is filled with N2 saturated with water vapor. The temperature difference between the supersaturated water vapor (at room temperature ) 23 ( 0.5 °C) and the substrate is 8 ( 0.5 °C. Heterogeneous dropwise nucleation of liquid water takes place on the substrate inhomogeneities. The growth of drops was observed with a CCD camera attached to an optical microscope (resolution ∼0.5 µm) and recorded on a video recorder. Video images were digitized and then analyzed by Image Tool software.
Results and Discussions We observed the following stages of growth: Initial (Nucleation) Stage (2R < a, b, c). In the beginning, the nucleation of tiny drops takes place on the top surface of pillars, on all sides of the pillars, and in the bottom channels (Figure 2a,b; stage i; t ) 2.43 min). On the scale of the drop, this stage corresponds to the growth of drops with contact angle θ () 90°) on a planar substrate. The drops on the top surface, on the sides of pillars, and on channels grow by condensation and coalescence. The average drop radius initially follows a t1/3 growth law and, at later times, a self-similar growth of ∼t. (See below and Figure 3 for a quantitative analysis.) Bridge-Formation Stage (2R ≈ a, b). The drops on the top surface cover the entire surface of each pillar (Figure 2a,b; stage ii). We observe that the drops on the top surface grow faster than the drops in the bottom channel and side of the square pillars. One would expect that the drops on the top surface coalesce with nearby neighboring drops on the sides of the pillars. Instead, the top surface drops coalesce with another neighboring top surface
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Figure 2. (a) Time sequence of different growth stages of condensed water drops on a square-pillar substrate. (b) Sketch of growth stages.
drop. In addition, the drops on the side of the pillars coalesce with neighboring side drops and form bridges (provided that c > b). In this sense, such bridging is quite an unexpected situation. At the end of this stage, a few drops are formed that cover several pillars as a result of the coalescence of top surface drops with other top surface drops. These drops grow over the air present in incompletely filled channels in a state that resemble the CB state. (However, the CB state is defined only for a drop that is much larger than the roughness scale of the substrate.) Drying Stage (2R > a, b, c). When the above drops on the top surface of pillars come into contact with either neighboring drops or bridges or drops in the channel, the coalescence process takes place. A composite drop covering many pillars in a CB state is formed (Figure 2a, stage iii, t ) 86.3 min). Strikingly, this drop later flows down into the channel in a very short time ( a/2. The time origin is taken at drop-formation time. The straight line corresponds to a power law.
a single drop on a flat surface R ≈ t1/3. (The experimental exponent in Figure 3 is 0.29 ( 0.03.) In stage i, the growth dynamics of the drop can be studied by measuring the average radius of drops 〈R〉 at the top surface of the pillars. Figure 3 shows the time dependence of 〈R〉. In the initial stage (t < 20 min), the surface coverage is low, and the rescaling effect of coalescence is negligible. The growth law is 〈R〉 ≈ tR with R ) 0.39 ( 0.007 (uncertainty of 1 SD), a value that compares relatively well with the expected t1/3 growth. In a later stage (t > 20 min), crossover is observed to 〈R〉 ≈ tβ, where β ) 0.96 ( 0.14 (uncertainty of 1 SD). The surface coverage (2) increases with time and reaches unity so that the entire pillar surface is covered by the drop. Once this value is reached, stage i is succeeded by stage ii, where the coalescence of drops with
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neighboring drops or bridges results in a large CB (metastable) drop. The latter is later sucked down into the channels; the surface coverage of the pillar surface then again becomes zero. This drying phenomenon has also been observed with 2D grooved patterns5 and seem to be a general property of rough hydrophobic substrates. Condensation on a superhydrophobic lotus leaf1 presents differences and similarities with the present case. The geometric structure of the lotus leaf is characterized by two roughness scales (hairs and bumps). The contact angle of a water drop is small on the side of the bump and large on the top. Thus, after an initial stage where water nucleates between the bumps or on the sides of the bumps, the drops rise up to the top of the bumps. We then observe drop coalescence and bridging between bumps with drops eventually sitting on many bumps, a situation that is also encountered in the present pillar case. In both cases, the final stage is always the most energetically favorable (CB for lotus leaf, W for the present pillar case). The drying transition between the CB to W state as observed with pillars is not detected with the lotus leaf because CB is the most stable state.
Conclusions As expected, condensation on rough hydrophobic substrates can induce wetting behavior that is quite different than that with
deposited or impinging drops. Phenomena that are particularly interesting with respect to potential applications take place during growth on such pillar substrates. A stage resembling air-pocket superhydrophobicity, although a metastable state, is indeed produced during intermediate times thanks to the bridging of drops between pillars. A pillar self-drying process then proceeds where droplets are sucked into the channels. In this particular stage, droplets leave a metastable air pocket state to enter the Wenzel equilibrium state. In the very last stages, condensation proceeds in a few large drops fed by neighboring channels, where droplets continue to nucleate, grow, and coalesce. The large drops are in a penetration or Wenzel regime (the most stable state for this surface). Some interesting features are nevertheless still present because the tops of pillars that are not covered by large drops remain almost dry. These phenomena can be easily generalized to surface geometries similar to pillars (columns, grooves, etc.). Acknowledgment. We are indebted to V. Nikolayev and S. Berkowicz for useful comments and the critical reading of the manuscript. LA062021Y
