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Shape-Gradient Composite Surfaces: Water Droplets Move Uphill Jilin Zhang and Yanchun Han* State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Graduate UniVersity of the Chinese Academy of Sciences, Changchun 130022, P. R. China ReceiVed NoVember 20, 2006. In Final Form: March 8, 2007 The approach of water droplets self-running horizontally and uphill without any other forces was proposed by patterning the shape-gradient hydrophilic material (i.e., mica) to the hydrophobic matrix (i.e., wax or low-density polyethylene (LDPE)). The shape-gradient composite surface is the best one to drive water droplet self-running both at the high velocity and the maximal distance among four different geometrical mica/wax composite surfaces. The driving force for the water droplets self-running includes: (1) the great difference in wettability of surface materials, (2) the low contact angle hysteresis of surface materials, and (3) the space limitation of the shape-gradient transportation area. Furthermore, the average velocity and the maximal distance of the self-running were mainly determined by the gradient angle (R), the droplet volume, and the difference of the contact angle hysteresis. Theoretical analysis is in agreement with the experimental results.
1. Introduction The spontaneous motion of a liquid droplet on a solid surface has attracted great interest in relation to energy transduction by surface materials, i.e., to convert surface energy to mechanical energy for achieving the liquid self-transportation, micro-fluidic devices, etc. The possibility of droplet movement due to a surface tension gradient was first predicted by Greenspan1 in 1978 and experimentally demonstrated by Chaudhury and Whitesides2 in 1992. Since then several approaches to drive droplet motion by surface tension gradient have been reported,3-16 where the surface tension gradient was given by an initial2,3 or an external4,5 asymmetry in a surface condition. The surfaces with gradient surface tension were realized by several different approaches, i.e., wetting gradient surfaces are prepared by chemical,2,3,6-9 thermal,10 electrochemical,11,12 and photochemical4,5,13 methods and so on. For example, Chaudhury and Whitesides2 prepared a gradient self-assembled monolayer (SAM) of decyltrichlorosilane molecules on the silicon surface. The chemical gradient surface can make water droplets self-run uphill at a velocity of 1 to 2 mm/s. Lee et al. used noncovalent molecular adsorption to achieve the movement of drops on the patterned surfaces.6 * To whom correspondence should be addressed. E-mail: ychan@ ciac.jl.cn. Tel.: +86-431-85262175. Fax: +86-431-85262126. (1) Greenspan, H. P. J. Fluid Mech. 1978, 84, 125. (2) Chaudhury, M. K.; Whiteside, G. M. Science 1992, 256, 1539. (3) Bain, C. D.; Burnett-Hall, G. D.; Montgomerie, R. R. Nature 1994, 372, 414. (4) Ichimura, K.; Oh, S. K.; Nakagawa, M. Science 2000, 288, 1624. (5) Oh, S. K.; Nakagawa, M.; Ichimura, K. J. Mater. Chem. 2002, 12, 2262. (6) Lee, W.; Laibinis, P .E. J. Am. Chem. Soc. 2000, 122, 5395. (7) Sumino, Y.; Kitahata, H.; Yashikawa, K.; Nagayama, M.; Nomura, S. M.; Magome, N.; Mori, Y. Phys. ReV. E 2005, 72, 041603. (8) Sumino, Y.; Magome, N.; Hamada, T.; Yashikawa, K. Phys. ReV. Lett. 2005, 94. 068301. (9) Nagai, K.; Sumino, Y.; Kitahata, H.; Yashikawa, K. Phys. ReV. E 2005, 71, 065301(R). (10) Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P. Nature 1990, 346, 824. (11) Gallardo, B. S.; Gupta, V. K.; Eagerton, F. D.; Jong, L. I.; Craig, V. S.; Shah, R. R.; Abbott, N. L. Science 1999, 283, 57. (12) Yamada, R.; Tada, H. Langmuir 2005, 21, 4254. (13) Abbott, N. L.; Ralston, J.; Reynolds, G.; Hayes, R. Langmuir 1999, 15, 8923. (14) Bico, J.; Que´re´, D. Europhys. Lett. 2000, 51, 546. (15) Daniel, S.; Chuadhury, M. K.; Chen, J. C. Science 2001, 291, 633. (16) Daniel, S.; Chuadhury, M. K. Langmuir 2002, 18, 3404.
Recently, Yamada et al.12 fabricated a ferrocenyl alkanethiol monolayer, on which droplets can self-run reversibly by using electrochemical reactions. On the other hand, Sumino et al.7,8 prepared chemosensitive running droplets, which can selfrun periodically and circularly by a chemical Marangoni effect.17-18 All of these artificial surfaces have achieved energy transduction at the proper conditions. However, in most cases, the surface energy cannot be converted to mechanical energy of liquid drops directly, and some other powers, such as photoenergy,4,5 chemical energy,3,6-9 and electric energy11,12 are need. Therefore, strictly speaking, they are not true energy transduction surfaces. Furthermore, the liquid drops are driven at a relatively low velocity, which limits its applications. Here, we propose a simple yet efficient approach to realize the water droplets self-running horizontally and uphill without any other forces by patterning the shape-gradient hydrophilic material (i.e., mica) to the hydrophobic matrix (i.e., wax or lowdensity polyethylene (LDPE)). We believe there are three key factors to govern this self-running uphill process, i.e., the great difference in wettability of the two solid materials, the shapegradient transportation area, and the low contact angle hysteresis of surface materials. Furthermore, we also find that the average velocity and the maximal distance of the self-running are influenced by the gradient angle (R), the droplet volume, and the difference of the contact angle hysteresis. In the proposed approach, the surface energy can be converted into mechanical energy, which may be find applications in many fields, such as in liquid transportation and the microfluidic system. 2. Experimental Section The fresh-cleaved mica (0.05 mm in thickness) was cut into a trapezium piece (0.6 mm (width) × 17 mm (length) × 3.0 mm (width)) with a square end (7 mm (width) × 7 mm (length)). Then the prepared mica piece was put on a soft paraffin wax (C20H42∼C30H62) surface (60 °C; mp 65 °C;19 Figure 1a). Subse(17) Magome, N.; Yoshikawa, K. J. Phys. Chem. 1996, 100, 19102. (18) Shioi, A.; Katano, K.; Onodera, Y. J. Colloid Interface Sci. 2003, 266, 415. (19) Lewin, M.; Mey-Marom, A.; Frank, R. Polym. AdV. Technol. 2005, 16, 429.
10.1021/la063376k CCC: $37.00 © 2007 American Chemical Society Published on Web 04/20/2007
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Figure 1. (a-c) Schematic illustrations of the preparation of the shape-gradient composite surfaces; (d) mica/paraffin wax and (e) mica/LDPE shape-gradient composite surfaces (the width (at the gradient start) ) 0.6 mm, the length (transportation area) ) 17 mm, R ) 8°, the storage area is 7 mm × 7 mm).
Figure 2. Photographs of mica/wax composite surfaces with different geometries. (a) trapezia, (b) triangle, (c) rectangle, and (d) meniscus. Table 1. Sessile Contact Angles and Contact Angle Hysteresis of Mica, Wax, and LDPE materials
mica
wax
LDPE
contact angle (θ) advancing contact angle (θa) receding contact angle (θr) contact angle hysteresis (θa - θr)
7° 11° 6° 5°
109° 111° 100° 11°
102° 104° 68° 36°
quently, a cleaned silicon wafer (the silicon wafer was cleaned with a 70/30 v/v solution of 98% H2SO4/30% H2O2 at 80 °C for 30 min and then thoroughly rinsed with deionized water and dried by N2) was covered onto the cut mica piece with a pressure of ∼500 Pa (Figure 1b). After the wax was cooled to room temperature, the silicon wafer was lifted off carefully (Figure 1c). Thus, the relatively smooth shape-gradient mica/wax composite surface was prepared (Figure 1d). The shape-gradient surfaces contain three important areas to achieve the water self-running process: gradient start, transportation area, and storage area. In order to investigate the effects of the material properties (Table 1) and the gradient angle (R) on the water droplet self-running process, wax was replaced by LDPE ((-CH2-CH2-)n) to prepare the same scale shape-gradient mica/LDPE composite surface (Figure 1e). Herein, the LDPE piece was softened at 180 °C under N2 protection. We also prepared a series of shape-gradient mica/wax composite samples (0.6 ( 0.05 mm (width of the gradient start) × 40 ( 0.07 mm (length)) with different R (0°, 8°, 14°, 16°, 18.5°, 22°, 30°, 35°, 40°, and 45°, the error is 0.5°), and four different geometries of mica/wax composite samples ((0.6 ( 0.05 mm (width of the gradient start) × 40 ( 0.07 mm (length)) including trapezia, triangle, rectangle, and meniscus (Figure 2) by the method described in Figure 1a-c. Contact angles of three materials were determined using a Kru¨ss DSA10-MK2 (Germany) contact angle measuring system at ambient temperature. The probe fluid was deionized water, and the droplet volume was 2 µL. The average contact angle value was obtained
Figure 3. Water droplet self-running on the horizontal (I and II) and uphill (III and IV; inclined at an angle of 25° with respect to the horizon) mica/wax and mica/LDPE shape-gradient composite surfaces, respectively. The water droplet was (a) dripped at the gradient start; (b) spreading from the hydrophobic area to the hydrophilic area; (c) elongating along the transportation area; (d) shrinking to the storage area. Scale bar: 1 cm. by measuring the same sample at 5 different positions. The advancing contact angles and the receding contact angles of wax and LDPE were measured by using the reported method.20 Furthermore, the imbalance contact angles (θ′mica ) 40 ( 3°) of Figure 3 (I)b, (II)b, (III)b, and (IV)b were roughly measured by a protractor and a ruler. The moving of the water droplets on the composite surface was performed at the horizontal and uphill (inclined at an angle of 25° with respect to the horizon) conditions. To observe the movement of water droplets easily, we used 5 ppm KMnO4 water solution instead of pure water. The droplets (8∼50 µL) were continuously dripped at the gradient start, and the movement process was caught by a Sony digital camera (T5 made in Japan). Here, the average velocity of the moving process is described by the ratio of the moving distance to the end time. (20) Erbil, H. Y.; Demirel, A. L.; Avci, Y.; Mert, O. Science 2003, 299, 1377.
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3. Results and Discussion 3.1. Water Droplets Self-Run on the Shape-Gradient Composite Surfaces. The water contact angle (θ), the advancing contact angles (θa), the receding contact angles (θr), and the contact angle hysteresis (θa - θr) of mica, wax, and LDPE are listed in Table 1. Mica surface is mainly composed of the hydrophilic chemical group (-OH), in contrast, wax and LDPE surfaces mainly contain hydrophobic ones (-CH2-, -CH3). So, mica, wax, and LDPE are strong hydrophilic and hydrophobic materials with water contact angles (θ) of 7°, 109°, and 102°, respectively. Herein, three common wetting phenomena should be noted. (1) When the water droplets are dripped at the contact line of the smooth composite mica/wax or mica/LDPE surfaces, the droplets can spontaneously spread from hydrophobic area to hydrophilic area, i.e., from wax or LDPE surfaces to mica surfaces by the interfacial force. (2) When a water droplet is dripped on a hydrophilic surface with a limited area, the droplet can spontaneously spread on the surface among the hydrophilic or more hydrophilic area. (3) On a solid surface, water droplets tend to be spherical instead of other irregular shapes. According to these three common wetting phenomena, we fabricate the shape-gradient mica/wax and mica/LDPE composite surfaces to achieve the surfaces on which the water droplets can self-run (Figure 1). Here, the composite surfaces contain three important areas to achieve the water droplets self-running process: the gradient start, the transportation area, and the storage area. In our experiment, these areas are employed to transport and storage water droplets, respectively. Figure 3, panels I and II, shows the self-running process of a water droplet on the above-mentioned horizontal shape-gradient mica/wax and mica/LDPE composite surfaces, respectively. (The gradient start is 0.6 mm (width), the transportation area 17 mm (length) × 3 mm (width), the storage area 7 mm (width) ×7 mm (length) and the gradient angle (R) 8°.) When a water droplet is dripped at the gradient start (Figure 3, panels I(a) and II(a)), surprisingly, it spreads from wax and LDPE surfaces to mica surface immediately (Figure 3, panels I(b) and II(b)) and then elongates itself along the transportation area (Figure 3, panels I(c) and II(c)). Finally, the elongated droplet shrinks from the transportation area to the storage area (Figure 3 panels I(d) and II(d)). This self-running process finishes 1.7 cm length within ∼0.17 and ∼0.25 s, and the average velocities are as high as ∼10.0 ( 0.1 cm/s (see the Supporting Information, movie S1) and ∼6.8 ( 0.4 cm/s, respectively. Water droplets can even self-run uphill without any other forces on both shape-gradient composite surfaces that are inclined at an angle of 25° with respect to the horizon (Figure 3, panels III and IV). This process also includes the spreading stage (Figure 3, panels III(b) and IV(b)), the elongating stage (Figure 3, panels III(c) and IV(c)), and the shrinking stage (Figure 3, panels III(d) and IV(d)). The finish times of the 1.7 cm length are 0.45 and 0.75 s, and the average velocities are ∼3.8 ( 0.2 (see the Supporting Information, movie S2) and ∼2.3 ( 0.4 cm/s, respectively. However, when the inclined angle is larger than 28°, we will not see any uphill water movement (droplet size: 8 µL) on the shape-gradient composite surfaces. To investigate the effect of the composite surface geometries to self-running, we prepared four different geometrical mica/ wax composite surfaces: trapezia, triangle, rectangle, and meniscus (Figure 2). The velocities and the maximal distances of self-running on all composite surfaces are listed in Table 2. In Table 2, it shows that on the trapeziform composite surface, i.e., on the shape-gradient composite surface, water droplets can self-run at high velocities horizontally (∼10.0 ( 0.1 cm/s) and
Zhang and Han Table 2. Average Velocities and the Maximal Distance of the Water Droplet Self-running on Different Geometrical Mica/wax Composite Surfaces
horizontal
uphill (25° with respect to the horizon)
geometries of composite surfaces
average velocity (cm/s)
maximal distance (mm)
average velocity (cm/s)
maximal distance (mm)
trapezia triangle rectangular meniscus
10.0 ( 0.1 6.7 ( 0.4 2.4 ( 0.4 13.1 ( 0.5
24.5 ( 0.5 24.0 ( 0.5 26.0 ( 0.5 16.3 ( 2.0
3.8 ( 0.2 2.3 ( 0.5 0 6.4 ( 0.5
24.5 ( 0.5 24.0 ( 0.5 0 14.0 ( 2.5
uphill (∼3.8 ( 0.2 cm/s) without any other forces about 24.5 ( 0.5 mm in distance. On the triangular composite surface, the area of the gradient start is small. So, the spreading process is much slower than that on the trapeziform composite surface. However, water droplets can self-run both at the horizontal (∼6.7 ( 0.4 cm/s) and the uphill (∼2.3 ( 0.5 cm/s) conditions at the relatively lower velocities about 24.0 ( 0.5 mm in distance. On the rectangular composite surface, the space limitation of the transportation area is big, which deeply affects the elongating stage of the self-running process. So a water droplet can only self-run horizontally in a low velocity (∼2.4 ( 0.4 cm/s) around 26.0 ( 0.5 mm in distance. However, at the uphill condition (the inclined angle ) 25°), the water droplet self-running is impossible in our experiments. On the meniscus composite surface, i.e., on the composite surface with continuous increase of the gradient angle. The selfrunning process is approximately same to the one on the trapeziform composite surface. In contrast to the self-running on the trapeziform composite surface, the water droplets can selfrun in higher velocities horizontally (∼13.1 ( 0.5 cm/s) and uphill (∼6.4 ( 0.5 cm/s) without any other forces. However, the maximal distance (horizontal: ∼16.3 ( 2.0 mm; uphill: ∼14.0 ( 2.5 mm) of water droplet self-running decreases because of the continuous increase of the gradient angle. Looking at the experimental results, we can conclude that the trapeziform composite surface, i.e., the shape-gradient composite surface, is the best one to drive water droplet self-running at both the high velocity and the maximal distance. In addition, the gradient angle (R) and the droplet volume are both important to accomplish the self-running of water droplets. To investigate the relationship between the gradient angle (R) and the self-running process, we study the self-running of water droplets on a series of shape-gradient mica/wax composite surfaces (0.6 ( 0.05 mm (width of the gradient start) × 40 mm (length of the transportation area)) with different R (0°, 8°, 14°, 16°, 18.5°, 22°, 30°, 35°, 40°, and 45°, the error is 0.5°). In Figure 4, with R increasing from 0° to 45°, the self-running velocity enhances from 2.4 ( 0.4 to 15.2 ( 0.1 cm/s obviously. However, the maximal distance of water droplets self-running decreases from ∼26 to 4 mm unavoidably. On the other hand, we also investigated the effect of water droplet size (Figure 5) on the maximal water droplets self-running. On the horizontal mica/wax and mica/LDPE composite surfaces, water droplets can self-run from the gradient start to storage area even though the size of the water droplet is as large as 50 µL. With the increase of droplets volume, the average velocities of self-running decrease from 10.0 ( 0.1 and 6.8 ( 0.4 cm/s to 1.8 ( 0.3 and 0.6 ( 0.3 cm/s, respectively. However, on the composite surfaces that are inclined at an angle of 25° with respect to the horizon, the water droplet cannot self-run uphill when the water
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angle (R) of the shape-gradient transportation area on the composite surface. As a common wetting phenomenon, when a water droplet is dripped on a composite solid surface, it may spontaneously spread against the force of contact angle hysteresis from the hydrophobic area to the hydrophilic area.21,22 In other words, to achieve the spreading process, the driving force must be larger than the resistant force. The driving force comes from the difference of interfacial tensions between the water droplet and the solid materials and the resistant force from the contact angle hysteresis of solid surface. Herein, the rule plays an important role in our experiments. When a water droplet is dripped at the gradient start of the mica/wax or mica/LDPE composite surfaces, an imbalance force (δF1) can be obtained by eq 16,24 Figure 4. Average velocities and the maximal distance of the water droplet self-running on the horizontal surfaces at different gradient angle (R). (The gradient start width of all samples is 0.6 ( 0.05 mm.)
δF1 ) γwater (cos θmica - cos θx)
where γwater is the surface tension of water and θmica and θx are the water contact angles on the smooth mica and wax or LDPE surfaces, respectively. The resistant force (δf) which comes from the contact angle hysteresis of wax or LDPE can be obtained by eq 26,24
δf ≈ γwater (cos θrx - cos θax)
Figure 5. Average velocities of the water droplet self-running on the horizontal and uphill (the inclined angle ) 25°) mica/wax and mica/LDPE composite surfaces with different droplet volume.
droplet size is larger than 15 µL because of the increase of the gravitational force. 3.2. Driving Forces for the Water Droplets Self-Running. From the above experimental results, three interesting phenomena can be addressed. First, on the shape-gradient mica/wax or mica/ LDPE composite surfaces, the water droplet self-running is composed of three stages: (1) spreading at the gradient start, (2) elongating along the transportation area, and (3) shrinking to the storage area. Second, the wettability of the materials has an effect on the self-running velocities. In contrast to the mica/wax composite surface, the average velocity of a water droplet selfrunning on the mica/LDPE surface is less both at the horizontal and the uphill conditions (Table 3). Third, the gradient angle can affect the self-running velocity and the maximal distance. On the shape-gradient mica/wax composite surfaces, with the gradient angle (R) increasing from 0° to 45°, the average velocity of water droplets self-running increases from 2.4 ( 0.4 to 15.2 ( 0.1 cm/s. However, the maximal distance of water droplets selfrunning decreases from ∼26 to ∼4 mm. In our opinion, these interesting phenomena are mainly due to three factors: (1) the wettability of the composite surface materials, (2) the contact angle hysteresis, and (3) the gradient
(1)
(2)
where θax and θrx are the advancing and the receding water contact angles won the smooth wax or LDPE surfaces, respectively. From eq 1 and Table 1, the imbalance force (δF1) coming from the great wettability difference of the surface materials can be calculated around 97.2 and 87.4 mN/m on the mica/wax and mica/LDPE surfaces, respectively (Table 3). The resistant force (δf) is around 12.3 and 44.9 mN/m on the mica/wax and mica/ LDPE surfaces (from eq 2 and Table 1), respectively. The driving force (δF1) exceeds the resistant one (δf), i.e., δF1 - δf ) 84.9 mN/m and 42.5 mN/m > 0 (Table 3) on both the mica/wax and mica/LDPE surfaces, which means the resultant force (δF1 - δf) can drive the droplet to spread from wax or LDPE surfaces to mica surface at the gradient start. However, the water droplet cannot reach the balance water contact angle ( θmica ) 7°) at the gradient start because the confinement by the limited area of the gradient start (0.6 mm in width). Therefore, the droplet has an imbalance water contact angle (θ′mica ≈ 40° ( 3°) temporarily, (Figure 3, panels I(b), II(b), III(b), and IV(b)), resulting another imbalance force (δF2) which can be calculated by eq 36,24
δF2 ≈ γwater (cos θmica - cos θ′mica)
(3)
Here, the force (δF2) is around 16.5 mN/m on both mica/wax and mica/LDPE surfaces (Table 3). Driving by δF2, the droplet elongates itself along the transportation area immediately so as to approach the balance water contact angle (θmica ) 7°) on the mica surface (Figure 3, panels I(c) and II(c)). It should be noted here, on the surfaces that are inclined at an angle of 25° with respect to the horizon, that the elongating process is prevented from the droplet gravitational force (δG ≈ 7.5 mN/m; Table 3). In our experiments, the driving force (δF2) exceeds the droplet gravitational force (δG ≈ 7.5 mN/m) by 9.0 mN/m, i.e., δF2 δG ) 9.0 mN/m > 0 (Table 3). So the droplet can elongate uphill against the gravitational force (Figure 3, panels III(c) and IV(c)). (21) Raphae¨l, E. C. R. Acad. Sci. Paris, Ser. II 1988, 306, 751. (22) Ondarc¸ uhu, T.; Veyssie´, M. J. Phys. II 1991, 1, 75. (23) Zhang, J.; Xue, L.; Han, Y. Langmuir 2005, 21, 5667. (24) Que´re´, D. Rep. Prog. Phys. 2005, 68, 2495.
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Table 3. Driving and the Resistant Forces of the Water Droplets in the Self-Running Process water dr oplets self-running on shape-gradient composite surfaces average velocity spreading stage
δF1 δf δF1 - δf δF2 δG δF2 - δG δF3 δG δF3 - δG
elongating stage shrinking stage
mica/wax (horizontal)
mica/LDPE (horizontal)
mica/wax (uphill)
mica/LDPE (uphill)
10.0 cm/s 97.2 mN/m 12.3 mN/m 84.9 mN/m 16.5 mN/m 0 16.5 mN/m 10.0 mN/m 0 10.0 mN/m
6.8 cm/s 87.4 mN/m 44.9 mN/m 42.5 mN/m 16.5 mN/m 0 16.5 mN/m 10.0 mN/m 0 10.0 mN/m
3.8 cm/s 97.2 mN/m 12.3 mN/m 84.9 mN/m 16.5 mN/m 7.5 mN/m 9.0 mN/m 10.0 mN/m 7.5 mN/m 2.5 mN/m
2.3 cm/s 87.4 mN/m 44.9 mN/m 42.5 mN/m 16.5 mN/m 7.5 mN/m 9.0 mN/m 10.0 mN/m 7.5 mN/m 2.5 mN/m
Table 4. End Time of Different Stage in the Water Droplets Self-Running Process Obtained from Figure 3, Panels I, II, III, and IV water droplets self-running on composite surfaces spreading elongating and shrinking total end time
mica/wax (horizontal)
mica/LDPE (horizontal)
mica/wax (uphill)
mica/LDPE (uphill)
0.05′′ 0.12′′
0.10′′ 0.15′′
0.15′′ 0.30′′
0.40′′ 0.35′′
0.17′′
0.25′′
0.45′′
0.75′′
However, this driven force (δF2) cannot make the elongated water droplet to shrink to the storage area. To shrink the elongated water droplet to the storage area completely, the surface energy (E) plays the key role. Commonly, the droplets tend to have a spherical shape instead of any irregular one so as to keep the lowest surface energy (E). In our experiments, when the water droplet elongates to the storage area (7 mm × 7 mm), the space limitation disappears. The elongated droplet spontaneously shrinks from the transportation area to the storage area to keep a spherical shape instead of the irregular one. This shrinking process can decrease the system surface energy (∆E), which can be expressed by eq 423-25
∆E ) (γmica/water - γmica) × ∆Smica/water + γwater × ∆Swater ) γwater (∆Swater - ∆Smica/water cos θmica)
(4)
where γmica/water is the interfacial tension between mica and water, γmica is the surface tension of mica, ∆Smica/water is the variation of the interfacial area between mica and water, and ∆Swater is the variation of surface area of water in air. Herein, ∆Swater almost equates to ∆Smica/water because of the low water contact angle of mica ( θmica ) 7°). According to eq 4, ∆E can be calculated around 10.0 × 10-6 mJ. So, the shrinking force (δF3 ≈ 10.0 mN/m) can be calculated by the change of surface energy of unit area (mm2; Table 3). Driven by this force, the droplet can shrink itself along the transportation area toward the storage area (Figure 3, panels I(d) and II(d)). It should be noted that on the inclined uphill composite surfaces (inclined angle is around 25° with respect to the horizon) the shrinking process is also prevented from the droplet gravitational force (δG ≈ 7.5 mN/m). However, the driving force (δF3) exceeds the droplet gravitational force (δG ≈ 7.5 mN/m) by 2.5 mN/m, i.e., δF3 - δG ) 2.5 mN/m > 0 (Table 3). So the shrinking process can spontaneously finish (Figure 3, panels III(d) and IV(d)). With the shrinking stage, the droplet can self-transport entirely, and the self-transportation process has a perfect finish. (25) Young, T. Philos. Trans. R. Soc. London 1805, 95, 65.
In summary, we can find that the three stages (spreading stage, elongating stage, and shrinking stage) are controlled by different factors. (1) The spreading velocity is controlled by the different wettability and the contact angle hysteresis of surface materials. (2) The elongating velocity is controlled by the shape of transportation area, i.e., the gradient angle (R). (3) The shrinking stage is driven by the surface energy of water droplets. So the self-running velocity rests with the surface materials and the gradient angle (R), i.e., spreading and elongating stages. Because of the above-mentioned conclusions, we can understand the difference of velocities on the same scale mica/wax and mica/LDPE surfaces to be due to the surface materials. Furthermore, the different velocities on the same mica/wax surfaces with different gradient angles (R) are due to the elongating stage. On the same scale shape-gradient mica/wax and mica/LDPE surfaces, i.e., on the same gradient angle (R ) 8°) surfaces with different surface materials, the average velocity of a water droplet self-running on the mica/LDPE surface is less both at the horizontal and the uphill conditions in contrast to the mica/wax composite surface. At the spreading stage, the driving force (δF1 - δf) of the mica/LDPE surface decreases (42.5 < 84.9 mN/m) obviously (Table 3) because of the lower WCA (102° < 110°) and the higher contact angle hysteresis (36° > 11°; Table 1). However, the δF2 and δF3 are stable. That proves that the decrease of the velocity is mainly due to the spreading stage, and the elongating and the shrinking stages have no effect on it. This conclusion can also be proved by our experimental results. In Table 4, it shows that the difference of total end time is mainly due to the spreading stage, and the elongating and shrinking stages are relatively stable. On the mica/LDPE surface, the end times of the spreading stage are 0.10′′ and 0.40′′ at the horizontal and the uphill conditions, respectively, which is larger than that on the mica/wax surface (0.05′′ and 0.15′′). However, the end times of the elongating and shrinking stages are approximately equal at the horizontal (0.12′′ ≈ 0.15′′) and the uphill (0.30′′ ≈ 0.35′′) conditions. So the decrease of the velocity is mainly due to the spreading stage, and the elongating and the shrinking stages have no effect on it. In addition, on the shape-gradient mica/wax surfaces with different gradient angles (R), i.e., on the different gradient angle surfaces composed by the same surface materials, the space limitations of the transportation area are different. Herein, a bigger gradient angle (R) means a sharper decrease of space limitation of the transportation area. With the space limitation decreasing sharply, the self-running process can be accelerated because the surface energy decreases sharply too. Correspondingly, the maximal distance of self-running shortens with the space limitation disappearing quickly.
Water Droplets MoVe Uphill
4. Conclusion In summary, we proposed a simple method to fabricate a shapegradient mica/paraffin wax and mica/LDPE composite surfaces. On the composite surfaces, the water droplets can self-run at high velocities horizontally and uphill without any other forces. The shape-gradient composite surface is the best one to drive water droplet self-running both at the high velocity and the maximal distance among the trapezia, triangle, rectangle, and meniscus composite surfaces. From our experimental results, we believe there are three key factors to achieve this self-running uphill process. The first is the great difference in wettability of surface materials, the second is the space limitation of the shapegradient transportation area, and the last is the low contact angle hysteresis of surface materials. Furthermore, the high contact angle hysteresis can decrease the self-running average velocity, and the water droplets self-running depends not only on the gradient angle (R) but also on the droplet volume. With the gradient angle (R) increasing from 0° to 45°, the average velocity
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of self-running enhances from 2.4 ( 0.4 to 15.2 ( 0.1 cm/s obviously. However, the maximal distance of water droplets self-running decreases from ∼26 to 4 mm unavoidably. On the other hand, with the droplet volume increase, the average velocities of self-running decrease on all samples. When the water droplet size is larger than 15 µL, the water droplet cannot self-run uphill on the composite surfaces that are inclined at an angle of 25° with respect to the horizon because of the increase of the gravitational force. Acknowledgment. This work is subsidized by the National Natural Science Foundation of China (20334010, 20621401, and 50573077). Supporting Information Available: Movies of water droplets self-run on the horizontal and uphill shape-gradient mica/wax composite surfaces. This information is available free of charge via the Internet at http://pubs.acs.org. LA063376K
