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Tuning wettability and getting superhydrophobic surface by controlling surface roughness with well-designed microstructures
Sensors and Actuators A 130–131 (2006) 595–600
Tuning wettability and getting superhydrophobic surface by controlling surface roughness with well-designed microstructures Liang Zhu, Yanying Feng ∗ , Xiongying Ye, Zhaoying Zhou Micro-Nano Technology Research Center, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China Received 4 June 2005; received in revised form 24 November 2005; accepted 5 December 2005 Available online 19 January 2006
Abstract We proposed a method to tune the wettability of a solid surface by changing its roughness. With specific designed micro square pillar arrays, the apparent contact angle of a hydrophobic surface can be continuously adjusted from the intrinsic contact angle. The samples were fabricated by combining silicon micromachining and self-assembled monolayer modification. The experimental results were closer to Cassie’s theoretical predictions on the superhydrophobic surfaces than that by Wenzel’s. The apparent contact angle (CA) can be tuned from the intrinsic CA to a superhydrophobic CA. The largest apparent CA in our experiments can be up to 162◦ , with pillars of 9.45 m × 9.45 m × 16 m (width × width × height), and the spacing of 26.34 m. By controlling the size and layout of the square micropillars, we also formed a surface with a certain roughness gradient, on which spontaneous movement of a droplet has been observed. © 2005 Elsevier B.V. All rights reserved. Keywords: Superhydrophobic surface; Roughness; Wettability; Micromaching
1. Introduction Wettability is one of the most important properties of a solid surface. Recently, superhydrophobic surfaces, with a water CA greater than 150◦ , have attracted great interest since the development of nanotechnology and the requirement of special material [1,2]. Because the wettability of a solid surface is determined by both the chemic component and microcosmic geometrical structure, it could be changed through surface roughening or adjustment of the surface energy on a flat surface. Only through lowering of the surface energy, however, the maximal CA on a flat surface is difficult to increase up to more than 120◦ [3]. Getting a rough surface is a method more effective to obtain a superhydrophobic surface with greater CA. It is useful to classify rough surfaces into three kinds for their characterization: a regular (designed) rough surface, a random (irregular), and a hierarchical one [3]. The random rough surfaces were commonly got by spontaneous reactions such as anode oxidation of metal surfaces, wax solidification [4], and
∗
Corresponding author. Tel.: +86 10 62796379. E-mail address: [email protected] (Y. Feng).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.12.005
nanomaterial alignment [5,6]. But it is hard to control the morphology of a random rough surface. Otherwise, highly regular rough surfaces are very useful for quantitative study of the equilibrium configuration of a droplet on rough substrate and its contact line dynamics. Generally, a regular surface is fabricated with micro protrusions by silicon-micromachining techniques. Then, the required surface chemistry is introduced to make the surface hydrophilic or hydrophobic [7–9]. On the other hand, one of motivations for wettability tuning of a solid surface is to control the droplet’s movement, which can find many applications in the fields of biology and microfluidics. If a spatial gradient of surface tension exists, a droplet may be able to move on the surface from the higher surface energy end towards the lower one by a net force, as a result of the imbalance of surface forces acting on the two opposite sides of the liquid–solid contact line. The gradient of surface tension had been formed by exposing the surface to the diffusing front of a vapor of chemical reagent [10,11]. Such surface energy gradient on a surface may be also produced by controlling its roughness in a controllable method. In this paper, we describe a method to control the surface wettability from the CA on a flat surface to superhydrophobic apparent CAs through tuning surface roughness using silicon
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L. Zhu et al. / Sensors and Actuators A 130–131 (2006) 595–600
micromachining and self-assembled monolayer modification. We try to verify theoretical predictions on the regular surface with micromachined microstructures from a point of experiment and get an apparent CA as large as possible. We also try to control the movement of a droplet by the surface with a certain roughness spatial gradient. 2. Theory and design The CA of a liquid on a flat solid surface, θ e , can be given by Young’s equation: cos θe =
(γsv − γsl ) γlv
(1)
where γ sv , γ sl , and γ lv are the interfacial free energies per unit area of the solid–liquid, the solid–gas, and the liquid–gas interface, respectively. If a droplet is small enough to neglect the influence of gravity, as is typically the case for a droplet with size of millimeter down to micrometer, it will have the shape of a spherical cap and the CA is called the intrinsic CA of the droplet. When the surface roughness is considered, two different models for predicting the apparent CA were proposed, respectively, by Wenzel [12] and Cassie [13]. Wenzel assumed that a liquid completely fills the depressions in the region where it contacts with the substrate, as shown in Fig. 1a. Hereafter it was referred to as the “wetted surface.” The apparent CA with Wenzel model, θrw , is given by: cos θrw
= r cos θe
Fig. 2. Top and cross-sectional schematic sketches of a roughness geometry of square pillars.
Cassie’s theory assumed that a composite surface is formed when a droplet contact with a rough surface and the liquid is completely lifted up by the roughness features, as shown in Fig. 1b. The apparent CA with Cassie model, θrc , is given by: cos θrc = fs (1 + cos θe ) − 1
where fs is the ratio of the area contacting with the droplet of the rough surface to the projected area. If a regular rough surface consists of a micro square pillar array with pillar size a × a, height H, and spacing b, as shown in Fig. 2, the r and fs in Eqs. (2) and (3) are given as: r =1+ fs =
(2)
where r is the ratio of the actual area of the rough surface to the projected area.
(3)
4A (a/H)
1 (b/a + 1)2
(4) (5)
where, A=
1 (b/a + 1)2
(6)
Therefore, the apparent CAs, according, respectively, to Wenzel’s and Cassie’s formulas, are given as the functions of the geometric parameters of the microstructures on the surface: 4A w (7) cos θe cos θr = 1 + (a/H) cos θrc = A(1 + cos θe ) − 1
(8)
Fig. 3 shows curves of the predicted apparent CAs according to Wenzel and Cassie formulas versus the geometric parameter b/a, with a given value of θ e . The low-energy segments (with the lower value of the apparent CA) and the high-energy segments are marked in Fig. 3. The intersection point of the Wenzel and the Cassie curves, which is called as critical point denotes the maximum value of the apparent CA in all the possible lower energy states. The apparent CAs from the two theories are same at the critical point, which means the energies of the composite and wetted surfaces are same, and: γsl [(a + b)2 + 4aH] Fig. 1. Sketch of drops on rough surfaces (a) wetting contact; (b) composite contact.
= γsl a2 + γlv (b2 + 2ab) + γsv (b2 + 2ab + 4aH)
(9)
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to form a surface with wettability gradient. In our design, each of the eight regions has a length of 3 mm and the same width for one sample, which changed from 260 to 1040 m for different samples. Table 1 listed the geometry parameters of the eight regions, which are corresponding to a sample of the region width of 520 m. The average theoretical predicted CA gradients are 13.46 and 5.56◦ /mm, respectively, from Cassie’s and Wenzel’s theories. 3. Fabrication and experiments
Fig. 3. Curves of the predicted CAs vs. the b/a.
Substituting Eq. (1) into Eq. (9), one can obtain: 1 cos θe = −1 (4A)/((a/H)(A − 1))
(10)
Eq. (10) gives the relationship between the intrinsic CAs of the rough surfaces and its geometric parameters at the critical point. It can be used to design a robust superhydrophobic surface with given values of θ e and a/H where the apparent CA does not change even if the wetting state transits between the composite and wetting contacts. On the other hand, the CA on the Cassie’s high-energy segment is higher than that at the critical point from Fig. 3. Therefore, we can also design a superhydrophobic surface with a larger value of b/a. In this case, the wetting state is difficult to change, because of the huge energy barrier between the composite and wetting contacts [13]. Based on Eqs. (7), (8) and (10), we have designed two groups of samples with the same height H. One group was designed to be just at the critical points at which both the Wenzel’s and Cassie’s models will predict the same value of apparent CAs. The other was designed to have the same size of micropillar and different spacings. We also designed a surface with certain roughness gradient, which leads to certain surface energy gradient, by controlling the spatial gradient of the size a and spacing b of the square micropillars on the same surface. The sample with the roughness gradient consists of eight regions, each of which has been design to be of a certain apparent CAs by adjusting geometry parameters of micropillar array based on Eq. (7) or (8) (Table 1). These eight regions were arranged together according to their apparent CAs
We fabricated rough surfaces with square pillars of different dimensions by silicon-micromachining technology. The fabrication process is illustrated in Fig. 4. First, a silicon substrate was etched by ICP after lithography to form square micropillar arrays. In this way, a regular surface can be obtained with precise size and shape. Then the regular rough surface was made to be hydrophobic by grafting a self-assembled monolayer of Octadecyltrichlorosilane (OTS, C18 H37 Cl3 Si), which has a CA against water of 110◦ .
Fig. 4. Fabrication process flow chart: (a) spin coating photoresist, (b) photolithography, (c) etching by ICP, and (d) grafting OTS.
Table 1 Designed geometric parameters of micropillars and theoretical predicted CAs Region
a (m)
b (m)
b/a
θrw (◦ )
θrc (◦ )
1 2 3 4 5 6 7 8
10 15 20 25 30 35 40 45
40 35 30 25 20 15 10 5
4.0000 2.3333 1.5000 1.0000 0.6667 0.4286 0.2500 0.1111
115.09 117.72 120.41 123.18 126.03 128.99 132.09 135.35
166.83 160.18 153.47 146.67 139.74 132.65 125.37 117.84
Fig. 5. SEM images of pillar structures made of silicon: (a) a = 3.45 m, b = 8.90 m; (b) a = 9.38 m, b = 6.97 m; (c) a = 30.1 m, b = 13.6 m; (d) a = 9.44 m, b = 31.2 m.
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to be hydrophobic by coating a Teflon AF1600 film on top of the surface, which has a CA against water of about 110◦ . Each sample is fabricated to have both a flat surface region and a rough one for contrast experiment. The CAs of the surfaces against deionized water were measured by a goniometer. The dosing needles of the goniometer were made to be hydrophobic by hydrophobe (HY-Kit Art. No. 2000394). Three points were measured for one surface and the mean of the three measured values was regarded as the CA value of the surface. 4. Results and discussion
Fig. 6. A roughness gradient surface with square pillars of eight kinds of different dimensions. (a) Photo picture, regions 1–8 in Table 1 is in turn from left side to the right; (b) SEM picture.
Fig. 5 shows SEM images of the pillar structures before OTS coating. Fig. 6 shows a surface with a certain roughness gradient composed of square micropillars with eight different size a and spacing b. Instead of grafting OTS, the gradient surface is made
The designed and measured geometric parameters of micropillar arrays were listed in the left part of Table 2. The depth of micropillars is designed to be 15 m and measured to be 15.985 m. In group 1, there are six different structures which have gradually increasing sizes of micropillars and spacings fitting to Eq. (10). The samples in group 2 have the same size of micropillars and gradually increasing spacing. In the group 2, samples 1–3 are on the left side of the critical point, sample 4 is at the critical point and samples 5–8 are on the right. In our experiment, the largest CA of 162.1◦ can be observed, as shown in Fig. 7, corresponding to which the micropillar array has geometry parameters of a = 9.45 m, b = 26.34 m, and H = 16 m. The theoretical and measured apparent CAs (θrw , θrc , θ r ), are listed in the right part of Table 2. The CA θ e is the measured CA on the flat surface of each sample. The average value of θ e with all samples is 111.8◦ , which is used in the theoretical calculation of apparent CAs. Fig. 8 showed curves of apparent CAs θ r versus b/a. Fig. 8a is corresponding to the first group of samples and Fig. 8b to the second. From Fig. 8a, it can be seen that the experimental θ r − b/a curve has the same trend with those predicted by Wenzel’s and Cassie’s formulas basically, the values of CAs will increase when b/a increases. And from Table 2 and Fig. 8a, we can see that the CA is the largest when the values of a and b
Table 2 Geometric parameters of micropillars and CAs of rough surfaces Sample
Original design (m)
Measured (m)
Theoretical CAs (◦ )
Experimental result (◦ )
a
b
b/a
a
b
b/a
θrw
θrc
θr
Group 1 1 2 3 4 5 6
10 15 20 25 30 85
10 11 12 12 13 15
1.00 0.73 0.60 0.50 0.43 0.18
9.22 15.08 19.99 25.08 30.1 85.8
10.83 11.44 12.53 12.89 13.6 15.2
1.17 0.76 0.63 0.51 0.45 0.18
151.94 148.12 142.42 139.37 136.27 123.97
150.11 142.81 139.68 136.53 134.56 123.11
151.94 152.78 148.30 146.01 149.20 141.36
Group 2 1 2 3 4 5 6 7 8
10 10 10 10 10 10 10 10
5 6 7 10 15 20 25 30
0.50 0.60 0.70 1.00 1.50 2.00 2.50 3.00
9.66 9.38 9.31 9.22 9.63 9.45 9.45 9.08
5.74 6.97 8.12 10.83 15.80 21.25 26.34 31.61
0.59 0.74 0.87 1.17 1.64 2.25 2.79 3.48
180 180 180 151.94 134.68 126.5 122.40 119.58
138.82 142.47 145.15 150.11 155.48 160.12 162.97 165.62
147.06 147.95 148.34 151.94 153.40 153.37 161.01 159.89
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Fig. 7. Pictures of drops on a flat surface (left, θ r = 111.8◦ , volume = 2 L) and a rough surface (right, θ r = 162.1◦ , volume = 4 L).
are the smallest ones in the group. Therefore, we should try to choose small values of a and b and fit them to Eq. (10), when we need a superhydrophobic surface where the apparent CA does not change even if the wetting state transits between the composite and wetting contacts. We also can find from Fig. 8a that the experimental CAs are always larger than those predictions. This
Fig. 9. Video frames of a droplet on a roughness gradient surface: (a) the droplet just placed and (b) the droplet after 80 ms.
maybe is caused by the difference of the designed geometric parameters and the measured. With the kind of surfaces, which has the CA on the critical point, the larger value of CA corresponds to the smaller size of pillars, which will be restricted by the fabrication technics. So if we need a higher apparent CA, we can choose a sample from group 2. From Fig. 8b, we can see that the values of b/a in group 2 are bigger than that in group 1, and the difference of measured values and the predictions from Cassie’s theory is smaller in group 2 than that in group 1 on the whole curve. Thus one can tune the surface wettability by changing surface roughness according to Cassie’s theory. We also tested the motion of droplets on the roughness gradient surface by placing droplets with a volume about 2–6 L. Fig. 9 shows video frames of a droplet motion. In the first frame (Fig. 9a) the droplet was just placed on the left side of the roughness gradient surface. After about 80 ms, in the second frame (Fig. 9b) the droplet moved to the right side and stopped. The speed of the motion is about 4–6 mm/s. 5. Conclusion Fig. 8. Apparent CAs as a function of b/a. The curves denoted by squares and triangles are Wenzel’s and Cassie’s prediction, respectively, and the points denoted by stars are measured values: (a) is corresponding to the first group of samples and (b) to the second.
In this paper, we described a method to control the wettability of a solid surface through fabricating a regular rough surface with a square pillar array by silicon micromachining and coating a hydrophobic layer. Two groups of samples were designed,
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fabricated and tested. The measured results were compared with Wenzel’s and Cassie’s theories. In our experiment, the largest CA of 162◦ was observed. This method tuning surface wettability by controllable changing surface roughness can be also used to transport microdroplets. The spontaneous movement of a droplet has been observed qualitatively on a surface with a certain roughness spatial gradient. But further experiments should be carried out for quantitative characterization of this phenomenon. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 50405001) and Doctoral Innovation Foundation of Tsinghua University. References [1] A. Nakajima, K. Hashimoto, T. Watanabe, Recent studies on superhydrophobic films, Monatsh. Chem. 132 (2001) 31–41. [2] A. Nakajima, A. Fujishima, K. Hashimoto, T. Watanabe, Preparation of transparent superhydrophobic boehmite and silica films by sublimation of aluminum acetylacetonate, Adv. Mater. (16) (1999) 1365– 1368. [3] R. Blossey, Self-cleaning surfaces — virtual realities, Nat. Mater. 2 (2003) 301–306. [4] T. Onda, S. Shibuichi, N. Satoh, K. Tsujii, Super-water-repellent fractal surfaces, Langmuir 12 (9) (1996) 2125–2127. [5] L. Feng, Y.L. Song, J. Zhai, B.Q. Liu, J. Xu, L. Jiang, D.B. Zhu, Creation of a superhydrophobic surface from an amphiphilic polymer, Angew. Chem. Int. Ed. 42 (7) (2003) 800–802. [6] T.L. Sun, G.J. Wang, L. Feng, B.Q. Liu, Y.M. Ma, L. Jiang, D.B. Zhu, Reversible switching between superhydrophilicity and superhydrophobicity, Adv. Mater. 43 (2004) 357–360. [7] J. Bico, C. Marzolin, D. Qu´er´e, Pearl drops, Europhys. Lett. 47 (2) (1999) 220–226. [8] C. Marzolin, S.P. Smith, M. Prentiss, G.M. Whitesides, Fabrication of glass microstructures by micro-molding of sol–gel precursors, Adv. Mater. 10 (8) (1998) 571–574.
[9] B. He, J. Lee, Dynamic wettability switching by surface roughness effect, in: Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems, Kyoto, Japan, 19–23 January, 2003, pp. 120–123. [10] M.K. Chaudhury, G.M. Whitesides, How to make water run uphill, Science 256 (1992) 1539–1541. [11] S. Daniel, M.K. Chaudhury, J.C. Chen, Fast drop movements resulting from the phase change on a gradient surface, Science 291 (2001) 633–636. [12] N.A. Patankar, On the modeling of hydrophobic contact angles on rough surfaces, Langmuir 19 (2003) 1249–1253. [13] B. He, N.A. Patankar, J. Lee, Multiple equilibrium droplet shapes and design criterion for rough hydrophobic surfaces, Langmuir 19 (2003) 4999–5003.
Biographies Liang Zhu received the B.S. degree in Precision Instruments and Mechanology from Tsinghua University, Beijing, China, in 2002. He is currently working towards the Ph.D. degree in microfluidic at Tsinghua University. His research includes work in the fabrication and design of microfluidics, simulation and measurement of micropump and microvalves. Yanying Feng received his B.S. and M.S. degrees in Mechanical Engineering from Harbin Institute of Technology in Harbin, China, respectively, in 1997 and 1999. In 2004, He received his Ph.D. degree in Department of Precision Instruments and Mechanology in Tsinghua University in Beijing, China. He is currently working as a postdoctoral member at Center for Micro/Nano Technology in Tsinghua University. His research interests include microfluidics for biomedical detection and atomic inferometry. Xiongying Ye is a professor of the Department of Precision Instruments and Mechanology, Tsinghua University. Her current research interests focus on micro fluidics, optical MEMS, micro/nano senser, measurement on MEMS, and so on. Zhaoying Zhou is a professor and chairman of academic committee, the MicrorNano Technology Research Center, Tsinghua University. He is the President of the Beijing Instrument Society and vice-president of the Chinese Instrument Society, and deputy chief editor of the Journal of Chinese Instrumentation. His research interest is in the fields of measurement, control, MEMS and NEMS.
Tuning wettability and getting superhydrophobic surface by controlling surface roughness with well-designed microstructures Liang Zhu, Yanying Feng ∗ , Xiongying Ye, Zhaoying Zhou Micro-Nano Technology Research Center, State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China Received 4 June 2005; received in revised form 24 November 2005; accepted 5 December 2005 Available online 19 January 2006
Abstract We proposed a method to tune the wettability of a solid surface by changing its roughness. With specific designed micro square pillar arrays, the apparent contact angle of a hydrophobic surface can be continuously adjusted from the intrinsic contact angle. The samples were fabricated by combining silicon micromachining and self-assembled monolayer modification. The experimental results were closer to Cassie’s theoretical predictions on the superhydrophobic surfaces than that by Wenzel’s. The apparent contact angle (CA) can be tuned from the intrinsic CA to a superhydrophobic CA. The largest apparent CA in our experiments can be up to 162◦ , with pillars of 9.45 m × 9.45 m × 16 m (width × width × height), and the spacing of 26.34 m. By controlling the size and layout of the square micropillars, we also formed a surface with a certain roughness gradient, on which spontaneous movement of a droplet has been observed. © 2005 Elsevier B.V. All rights reserved. Keywords: Superhydrophobic surface; Roughness; Wettability; Micromaching
1. Introduction Wettability is one of the most important properties of a solid surface. Recently, superhydrophobic surfaces, with a water CA greater than 150◦ , have attracted great interest since the development of nanotechnology and the requirement of special material [1,2]. Because the wettability of a solid surface is determined by both the chemic component and microcosmic geometrical structure, it could be changed through surface roughening or adjustment of the surface energy on a flat surface. Only through lowering of the surface energy, however, the maximal CA on a flat surface is difficult to increase up to more than 120◦ [3]. Getting a rough surface is a method more effective to obtain a superhydrophobic surface with greater CA. It is useful to classify rough surfaces into three kinds for their characterization: a regular (designed) rough surface, a random (irregular), and a hierarchical one [3]. The random rough surfaces were commonly got by spontaneous reactions such as anode oxidation of metal surfaces, wax solidification [4], and
∗
Corresponding author. Tel.: +86 10 62796379. E-mail address: [email protected] (Y. Feng).
0924-4247/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2005.12.005
nanomaterial alignment [5,6]. But it is hard to control the morphology of a random rough surface. Otherwise, highly regular rough surfaces are very useful for quantitative study of the equilibrium configuration of a droplet on rough substrate and its contact line dynamics. Generally, a regular surface is fabricated with micro protrusions by silicon-micromachining techniques. Then, the required surface chemistry is introduced to make the surface hydrophilic or hydrophobic [7–9]. On the other hand, one of motivations for wettability tuning of a solid surface is to control the droplet’s movement, which can find many applications in the fields of biology and microfluidics. If a spatial gradient of surface tension exists, a droplet may be able to move on the surface from the higher surface energy end towards the lower one by a net force, as a result of the imbalance of surface forces acting on the two opposite sides of the liquid–solid contact line. The gradient of surface tension had been formed by exposing the surface to the diffusing front of a vapor of chemical reagent [10,11]. Such surface energy gradient on a surface may be also produced by controlling its roughness in a controllable method. In this paper, we describe a method to control the surface wettability from the CA on a flat surface to superhydrophobic apparent CAs through tuning surface roughness using silicon
596
L. Zhu et al. / Sensors and Actuators A 130–131 (2006) 595–600
micromachining and self-assembled monolayer modification. We try to verify theoretical predictions on the regular surface with micromachined microstructures from a point of experiment and get an apparent CA as large as possible. We also try to control the movement of a droplet by the surface with a certain roughness spatial gradient. 2. Theory and design The CA of a liquid on a flat solid surface, θ e , can be given by Young’s equation: cos θe =
(γsv − γsl ) γlv
(1)
where γ sv , γ sl , and γ lv are the interfacial free energies per unit area of the solid–liquid, the solid–gas, and the liquid–gas interface, respectively. If a droplet is small enough to neglect the influence of gravity, as is typically the case for a droplet with size of millimeter down to micrometer, it will have the shape of a spherical cap and the CA is called the intrinsic CA of the droplet. When the surface roughness is considered, two different models for predicting the apparent CA were proposed, respectively, by Wenzel [12] and Cassie [13]. Wenzel assumed that a liquid completely fills the depressions in the region where it contacts with the substrate, as shown in Fig. 1a. Hereafter it was referred to as the “wetted surface.” The apparent CA with Wenzel model, θrw , is given by: cos θrw
= r cos θe
Fig. 2. Top and cross-sectional schematic sketches of a roughness geometry of square pillars.
Cassie’s theory assumed that a composite surface is formed when a droplet contact with a rough surface and the liquid is completely lifted up by the roughness features, as shown in Fig. 1b. The apparent CA with Cassie model, θrc , is given by: cos θrc = fs (1 + cos θe ) − 1
where fs is the ratio of the area contacting with the droplet of the rough surface to the projected area. If a regular rough surface consists of a micro square pillar array with pillar size a × a, height H, and spacing b, as shown in Fig. 2, the r and fs in Eqs. (2) and (3) are given as: r =1+ fs =
(2)
where r is the ratio of the actual area of the rough surface to the projected area.
(3)
4A (a/H)
1 (b/a + 1)2
(4) (5)
where, A=
1 (b/a + 1)2
(6)
Therefore, the apparent CAs, according, respectively, to Wenzel’s and Cassie’s formulas, are given as the functions of the geometric parameters of the microstructures on the surface: 4A w (7) cos θe cos θr = 1 + (a/H) cos θrc = A(1 + cos θe ) − 1
(8)
Fig. 3 shows curves of the predicted apparent CAs according to Wenzel and Cassie formulas versus the geometric parameter b/a, with a given value of θ e . The low-energy segments (with the lower value of the apparent CA) and the high-energy segments are marked in Fig. 3. The intersection point of the Wenzel and the Cassie curves, which is called as critical point denotes the maximum value of the apparent CA in all the possible lower energy states. The apparent CAs from the two theories are same at the critical point, which means the energies of the composite and wetted surfaces are same, and: γsl [(a + b)2 + 4aH] Fig. 1. Sketch of drops on rough surfaces (a) wetting contact; (b) composite contact.
= γsl a2 + γlv (b2 + 2ab) + γsv (b2 + 2ab + 4aH)
(9)
L. Zhu et al. / Sensors and Actuators A 130–131 (2006) 595–600
597
to form a surface with wettability gradient. In our design, each of the eight regions has a length of 3 mm and the same width for one sample, which changed from 260 to 1040 m for different samples. Table 1 listed the geometry parameters of the eight regions, which are corresponding to a sample of the region width of 520 m. The average theoretical predicted CA gradients are 13.46 and 5.56◦ /mm, respectively, from Cassie’s and Wenzel’s theories. 3. Fabrication and experiments
Fig. 3. Curves of the predicted CAs vs. the b/a.
Substituting Eq. (1) into Eq. (9), one can obtain: 1 cos θe = −1 (4A)/((a/H)(A − 1))
(10)
Eq. (10) gives the relationship between the intrinsic CAs of the rough surfaces and its geometric parameters at the critical point. It can be used to design a robust superhydrophobic surface with given values of θ e and a/H where the apparent CA does not change even if the wetting state transits between the composite and wetting contacts. On the other hand, the CA on the Cassie’s high-energy segment is higher than that at the critical point from Fig. 3. Therefore, we can also design a superhydrophobic surface with a larger value of b/a. In this case, the wetting state is difficult to change, because of the huge energy barrier between the composite and wetting contacts [13]. Based on Eqs. (7), (8) and (10), we have designed two groups of samples with the same height H. One group was designed to be just at the critical points at which both the Wenzel’s and Cassie’s models will predict the same value of apparent CAs. The other was designed to have the same size of micropillar and different spacings. We also designed a surface with certain roughness gradient, which leads to certain surface energy gradient, by controlling the spatial gradient of the size a and spacing b of the square micropillars on the same surface. The sample with the roughness gradient consists of eight regions, each of which has been design to be of a certain apparent CAs by adjusting geometry parameters of micropillar array based on Eq. (7) or (8) (Table 1). These eight regions were arranged together according to their apparent CAs
We fabricated rough surfaces with square pillars of different dimensions by silicon-micromachining technology. The fabrication process is illustrated in Fig. 4. First, a silicon substrate was etched by ICP after lithography to form square micropillar arrays. In this way, a regular surface can be obtained with precise size and shape. Then the regular rough surface was made to be hydrophobic by grafting a self-assembled monolayer of Octadecyltrichlorosilane (OTS, C18 H37 Cl3 Si), which has a CA against water of 110◦ .
Fig. 4. Fabrication process flow chart: (a) spin coating photoresist, (b) photolithography, (c) etching by ICP, and (d) grafting OTS.
Table 1 Designed geometric parameters of micropillars and theoretical predicted CAs Region
a (m)
b (m)
b/a
θrw (◦ )
θrc (◦ )
1 2 3 4 5 6 7 8
10 15 20 25 30 35 40 45
40 35 30 25 20 15 10 5
4.0000 2.3333 1.5000 1.0000 0.6667 0.4286 0.2500 0.1111
115.09 117.72 120.41 123.18 126.03 128.99 132.09 135.35
166.83 160.18 153.47 146.67 139.74 132.65 125.37 117.84
Fig. 5. SEM images of pillar structures made of silicon: (a) a = 3.45 m, b = 8.90 m; (b) a = 9.38 m, b = 6.97 m; (c) a = 30.1 m, b = 13.6 m; (d) a = 9.44 m, b = 31.2 m.
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to be hydrophobic by coating a Teflon AF1600 film on top of the surface, which has a CA against water of about 110◦ . Each sample is fabricated to have both a flat surface region and a rough one for contrast experiment. The CAs of the surfaces against deionized water were measured by a goniometer. The dosing needles of the goniometer were made to be hydrophobic by hydrophobe (HY-Kit Art. No. 2000394). Three points were measured for one surface and the mean of the three measured values was regarded as the CA value of the surface. 4. Results and discussion
Fig. 6. A roughness gradient surface with square pillars of eight kinds of different dimensions. (a) Photo picture, regions 1–8 in Table 1 is in turn from left side to the right; (b) SEM picture.
Fig. 5 shows SEM images of the pillar structures before OTS coating. Fig. 6 shows a surface with a certain roughness gradient composed of square micropillars with eight different size a and spacing b. Instead of grafting OTS, the gradient surface is made
The designed and measured geometric parameters of micropillar arrays were listed in the left part of Table 2. The depth of micropillars is designed to be 15 m and measured to be 15.985 m. In group 1, there are six different structures which have gradually increasing sizes of micropillars and spacings fitting to Eq. (10). The samples in group 2 have the same size of micropillars and gradually increasing spacing. In the group 2, samples 1–3 are on the left side of the critical point, sample 4 is at the critical point and samples 5–8 are on the right. In our experiment, the largest CA of 162.1◦ can be observed, as shown in Fig. 7, corresponding to which the micropillar array has geometry parameters of a = 9.45 m, b = 26.34 m, and H = 16 m. The theoretical and measured apparent CAs (θrw , θrc , θ r ), are listed in the right part of Table 2. The CA θ e is the measured CA on the flat surface of each sample. The average value of θ e with all samples is 111.8◦ , which is used in the theoretical calculation of apparent CAs. Fig. 8 showed curves of apparent CAs θ r versus b/a. Fig. 8a is corresponding to the first group of samples and Fig. 8b to the second. From Fig. 8a, it can be seen that the experimental θ r − b/a curve has the same trend with those predicted by Wenzel’s and Cassie’s formulas basically, the values of CAs will increase when b/a increases. And from Table 2 and Fig. 8a, we can see that the CA is the largest when the values of a and b
Table 2 Geometric parameters of micropillars and CAs of rough surfaces Sample
Original design (m)
Measured (m)
Theoretical CAs (◦ )
Experimental result (◦ )
a
b
b/a
a
b
b/a
θrw
θrc
θr
Group 1 1 2 3 4 5 6
10 15 20 25 30 85
10 11 12 12 13 15
1.00 0.73 0.60 0.50 0.43 0.18
9.22 15.08 19.99 25.08 30.1 85.8
10.83 11.44 12.53 12.89 13.6 15.2
1.17 0.76 0.63 0.51 0.45 0.18
151.94 148.12 142.42 139.37 136.27 123.97
150.11 142.81 139.68 136.53 134.56 123.11
151.94 152.78 148.30 146.01 149.20 141.36
Group 2 1 2 3 4 5 6 7 8
10 10 10 10 10 10 10 10
5 6 7 10 15 20 25 30
0.50 0.60 0.70 1.00 1.50 2.00 2.50 3.00
9.66 9.38 9.31 9.22 9.63 9.45 9.45 9.08
5.74 6.97 8.12 10.83 15.80 21.25 26.34 31.61
0.59 0.74 0.87 1.17 1.64 2.25 2.79 3.48
180 180 180 151.94 134.68 126.5 122.40 119.58
138.82 142.47 145.15 150.11 155.48 160.12 162.97 165.62
147.06 147.95 148.34 151.94 153.40 153.37 161.01 159.89
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Fig. 7. Pictures of drops on a flat surface (left, θ r = 111.8◦ , volume = 2 L) and a rough surface (right, θ r = 162.1◦ , volume = 4 L).
are the smallest ones in the group. Therefore, we should try to choose small values of a and b and fit them to Eq. (10), when we need a superhydrophobic surface where the apparent CA does not change even if the wetting state transits between the composite and wetting contacts. We also can find from Fig. 8a that the experimental CAs are always larger than those predictions. This
Fig. 9. Video frames of a droplet on a roughness gradient surface: (a) the droplet just placed and (b) the droplet after 80 ms.
maybe is caused by the difference of the designed geometric parameters and the measured. With the kind of surfaces, which has the CA on the critical point, the larger value of CA corresponds to the smaller size of pillars, which will be restricted by the fabrication technics. So if we need a higher apparent CA, we can choose a sample from group 2. From Fig. 8b, we can see that the values of b/a in group 2 are bigger than that in group 1, and the difference of measured values and the predictions from Cassie’s theory is smaller in group 2 than that in group 1 on the whole curve. Thus one can tune the surface wettability by changing surface roughness according to Cassie’s theory. We also tested the motion of droplets on the roughness gradient surface by placing droplets with a volume about 2–6 L. Fig. 9 shows video frames of a droplet motion. In the first frame (Fig. 9a) the droplet was just placed on the left side of the roughness gradient surface. After about 80 ms, in the second frame (Fig. 9b) the droplet moved to the right side and stopped. The speed of the motion is about 4–6 mm/s. 5. Conclusion Fig. 8. Apparent CAs as a function of b/a. The curves denoted by squares and triangles are Wenzel’s and Cassie’s prediction, respectively, and the points denoted by stars are measured values: (a) is corresponding to the first group of samples and (b) to the second.
In this paper, we described a method to control the wettability of a solid surface through fabricating a regular rough surface with a square pillar array by silicon micromachining and coating a hydrophobic layer. Two groups of samples were designed,
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fabricated and tested. The measured results were compared with Wenzel’s and Cassie’s theories. In our experiment, the largest CA of 162◦ was observed. This method tuning surface wettability by controllable changing surface roughness can be also used to transport microdroplets. The spontaneous movement of a droplet has been observed qualitatively on a surface with a certain roughness spatial gradient. But further experiments should be carried out for quantitative characterization of this phenomenon. Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 50405001) and Doctoral Innovation Foundation of Tsinghua University. References [1] A. Nakajima, K. Hashimoto, T. Watanabe, Recent studies on superhydrophobic films, Monatsh. Chem. 132 (2001) 31–41. [2] A. Nakajima, A. Fujishima, K. Hashimoto, T. Watanabe, Preparation of transparent superhydrophobic boehmite and silica films by sublimation of aluminum acetylacetonate, Adv. Mater. (16) (1999) 1365– 1368. [3] R. Blossey, Self-cleaning surfaces — virtual realities, Nat. Mater. 2 (2003) 301–306. [4] T. Onda, S. Shibuichi, N. Satoh, K. Tsujii, Super-water-repellent fractal surfaces, Langmuir 12 (9) (1996) 2125–2127. [5] L. Feng, Y.L. Song, J. Zhai, B.Q. Liu, J. Xu, L. Jiang, D.B. Zhu, Creation of a superhydrophobic surface from an amphiphilic polymer, Angew. Chem. Int. Ed. 42 (7) (2003) 800–802. [6] T.L. Sun, G.J. Wang, L. Feng, B.Q. Liu, Y.M. Ma, L. Jiang, D.B. Zhu, Reversible switching between superhydrophilicity and superhydrophobicity, Adv. Mater. 43 (2004) 357–360. [7] J. Bico, C. Marzolin, D. Qu´er´e, Pearl drops, Europhys. Lett. 47 (2) (1999) 220–226. [8] C. Marzolin, S.P. Smith, M. Prentiss, G.M. Whitesides, Fabrication of glass microstructures by micro-molding of sol–gel precursors, Adv. Mater. 10 (8) (1998) 571–574.
[9] B. He, J. Lee, Dynamic wettability switching by surface roughness effect, in: Proceedings of the IEEE International Conference on Micro Electro Mechanical Systems, Kyoto, Japan, 19–23 January, 2003, pp. 120–123. [10] M.K. Chaudhury, G.M. Whitesides, How to make water run uphill, Science 256 (1992) 1539–1541. [11] S. Daniel, M.K. Chaudhury, J.C. Chen, Fast drop movements resulting from the phase change on a gradient surface, Science 291 (2001) 633–636. [12] N.A. Patankar, On the modeling of hydrophobic contact angles on rough surfaces, Langmuir 19 (2003) 1249–1253. [13] B. He, N.A. Patankar, J. Lee, Multiple equilibrium droplet shapes and design criterion for rough hydrophobic surfaces, Langmuir 19 (2003) 4999–5003.
Biographies Liang Zhu received the B.S. degree in Precision Instruments and Mechanology from Tsinghua University, Beijing, China, in 2002. He is currently working towards the Ph.D. degree in microfluidic at Tsinghua University. His research includes work in the fabrication and design of microfluidics, simulation and measurement of micropump and microvalves. Yanying Feng received his B.S. and M.S. degrees in Mechanical Engineering from Harbin Institute of Technology in Harbin, China, respectively, in 1997 and 1999. In 2004, He received his Ph.D. degree in Department of Precision Instruments and Mechanology in Tsinghua University in Beijing, China. He is currently working as a postdoctoral member at Center for Micro/Nano Technology in Tsinghua University. His research interests include microfluidics for biomedical detection and atomic inferometry. Xiongying Ye is a professor of the Department of Precision Instruments and Mechanology, Tsinghua University. Her current research interests focus on micro fluidics, optical MEMS, micro/nano senser, measurement on MEMS, and so on. Zhaoying Zhou is a professor and chairman of academic committee, the MicrorNano Technology Research Center, Tsinghua University. He is the President of the Beijing Instrument Society and vice-president of the Chinese Instrument Society, and deputy chief editor of the Journal of Chinese Instrumentation. His research interest is in the fields of measurement, control, MEMS and NEMS.