6004
Langmuir 2007, 23, 6004-6010
Design of a Superhydrophobic Surface Using Woven Structures Stephen Michielsen* and Hoon J. Lee College of Textiles, North Carolina State UniVersity, 2401 Research DriVe, Raleigh, North Carolina 27695-8301 ReceiVed October 27, 2006. In Final Form: March 23, 2007 The relationship between surface tension and roughness is reviewed. The Cassie-Baxter model is restated in its original form, which better describes the most general cases of surface roughness. Using mechanical and chemical surface modification of nylon 6,6 woven fabric, an artificial superhydrophobic surface was prepared. A plain woven fabric mimicking the Lotus leaf was created by further grafting 1H,1H-perfluorooctylamine or octadecylamine to poly(acrylic acid) chains which had previously been grafted onto a nylon 6,6 woven fabric surface. Water contact angles as high as 168° were achieved. Good agreement between the predictions based on the original Cassie-Baxter model and experiments was obtained. The version of the Cassie-Baxter model in current use could not be applied to this problem since the surface area fractions in this form is valid only when the liquid is in contact with a flat, porous surface. The angle at which a water droplet rolls off the surface has also been used to define a superhydrophobic surface. It is shown that the roll-off angle is highly dependent on droplet size. The roll-off angles of these superhydrophobic surfaces were less than 5° when a 0.5 mL water droplet was applied.
1. Introduction Technologies related to superhydrophobic treatments have recently attracted considerable attention due to their potential applications in medical devices, as well as industrial materials. The idea of superhydrophobicity was introduced six decades ago by A. Cassie who, working for the British Council of the Wool Industries, was interested in enhanced water repellency.1 This amazing water repellency has been used in the textile industry ever since. A superhydrophobic surface is defined as having a water contact angle greater than 150° and a roll-off angle lower than 5°.2-3 The high contact angle is obtained by a combination of surface chemistry and surface roughness, while the roll-off angle depends on the droplet size and the contact angle hysteresis, which is the difference between the advancing and the receding contact angles.4 A water droplet easily rolls off a superhydrophobic surface, washing dirt off in the process and effectively cleaning the surface. This unusual wetting behavior is called the Lotus effect or self-cleaning.5 The Lotus effect is obtained by two criteria: a low surface energy and a well-designed surface roughness.6-10 Over the past 15 years, many studies of superhydrophobicity and contact angle hysteresis have been performed. Recently, Zhu et al. developed a superhydrophobic surface by electrospinning using a hydrophilic material, poly(hydroxybutyrateco-hydroxyvalerate) (PHBV).11 Gao and McCarthy made artificial superhydrophobic surfaces with conventional polyester and * To whom correspondence should be addressed. Phone: +1 (919) 515 1414. Fax: +1 (919) 515 3057. E-mail:
[email protected]. (1) Cassie, A. B. D.; Baxter, S. Nature (London) 1945, 155, 21. (2) Wu, X.; Shi, G. J. Phys. Chem. B 2006, 110, 11247. (3) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1. (4) Neinhuis, C.; Barthlott, W. Annals Botany 1997, 79, 667. (5) Tavana, H.; Amirafazli, A.; Neumann, W. Langmuir 2006, 22, 5556. (6) Nosonovsky, M.; Bhushan, B. Microsyst. Tech. 2006, 12, 231. (7) Zhang, J.; Kwok, D. Y. Langmuir 2006, 22, 4998. (8) Dupuis, A.; Yeomans, J. M. Langmuir 2005, 21, 2624. (9) Lee, J.; He, B.; Patankar, N. A. J. Micromech. Microeng. 2005, 15, 591. (10) Baldacchini, T.; Carey, J. E.; Zhou, M.; Mazur, E. Langmuir 2006, 22, 4917. (11) Zhu, M.; Zuo, W.; Yu, H.; Yang, W.; Chen, Y. J. Mater. Sci. 2006, 41, 3793.
microfiber polyester fabrics rendered hydrophobic by using a simple patented water-repellent silicone coating procedure.12 Lee and Michielsen developed superhydrophobic surfaces via the flocking process and achieved contact angles as high as 178°.13 Hennig et al. demonstrated that the contact angle hysteresis of a smooth film depends on the contact time with water.14 Dorrer and Ruehe proved that the advancing contact angle on a superhydrophobic surface is not affected by the surface roughness and reaches to 180° during the advancing motion; in contrast, the receding contact angle is strongly influenced by several geometric parameters such as the shape, size, and spacing of the protuberances of the surface.15 Yoshimitsu et al. showed that the roll-off angles are in inverse proportion to the weight of a water droplet and the proper design of a rough surface is more important than increasing roughness to obtain a better sliding behavior.16 According to Brandon et al., the contact angle hysteresis decreases as the volume of the drop increases.17 In the study described below, we have used treated nylon fibers and yarns. The characterization of the surface energies between two interacting liquid and solid surfaces is the key to understanding the wetting behaviors of solid materials.18-19 Contact angles between a liquid with a known surface tension and the solid are measured for the evaluation of the surface energy of a solid since it is easier to measure its contact angle than to measure its surface energy directly. The relationship between the surface tensions and the contact angle is obtained by a modified Young’s equation, when the solid is made of organic compounds:20 (12) Gao, L.; McCarthy, T. J. Langmuir 2006, 22, 5998. (13) Lee, H. J.; Michielsen, S. J. Polym. Sci., Part B 2007, 45, 253. (14) Hennig, A.; Eichhorn, K. J.; Staudinger, U.; Sahre, K.; Rogalli, M.; Stamm, M.; Neumann, A. W.; Grundke, K. Langmuir 2004, 20, 6685. (15) Dorrer, C.; Ruehe, J. Langmuir 2006, 22, 7652. (16) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (17) Brandon, S.; Haimovich, N.; Yeger, E.; Marmur, A. J. Colloid Interface Sci. 2003, 263, 237. (18) Fowkes, F. M. Ind. Eng. Chem. 1964, 56, 40. (19) Santiago, J. M.; Keffer, D. J.; Counce, R. M. Langmuir 2006, 22, 5358. (20) Balkenede, A. R.; Van de Boogaard, H. J. A. P.; Scholten, M.; Willard, N. P. Langmuir 1998, 14, 5907.
10.1021/la063157z CCC: $37.00 © 2007 American Chemical Society Published on Web 04/28/2007
Superhydrophobic Surfaces with WoVen Structures
cos θe )
γS - γSL γL
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(1)
where θe is an equilibrium contact angle on a flat surface, γ is the surface tension, and S, L, and SL are a solid-air, a liquidair, and a solid-liquid interface. The Young equation is valid only for the wetting of a flat surface. Wenzel showed that roughness makes a significant contribution to the wetting behavior of a solid surface.21 Wenzel defined the surface roughness, r, to obtain an apparent contact angle for a liquid that completely covers the rough surface. He defined r as the ratio of the true, wetted area of the surface divided by the projected surface area below the droplet. He then showed that the apparent liquid contact angle at a rough surface, θrW, is related to Young’s equilibrium contact angle by
cos θrW ) r cos θe
(2)
Since r > 1 for a rough surface, Wenzel’s model leads to two different behaviors. If θe < 90°, cos θrW goes toward 1, θrW goes toward 0°, and the liquid is sucked into contact with the rough surface. In the same manner, when θe > 90°, cos θrW goes toward -1 and θrW goes toward 180°. Cassie and Baxter extended the Wenzel model to include porous surfaces. In this model, a liquid sits on a composite surface made of a solid and air. Therefore, the liquid does not fill the grooves of a rough solid. In their paper published in 1944, Cassie and Baxter suggested that22
cos θrCB ) f1 cos θe - f2
(3)
where f1 is the surface area of the liquid in contact with the solid divided by the projected area and f2 is the surface area of the liquid in contact with air trapped in the pores of the rough surface divided by the projected area. According to Cassie and Baxter:
f1 )
area in contact with liquid projected area
f2 )
area in contact with air projected area
(4)
When there is no trapped air, f1 is identical to the value of r in the Wenzel model. Recognizing this, eq 3 has recently been rewritten as follows23
f1 ) rf f
(5)
f2 ) 1 - f
(6)
cos θrCB ) rf f cos θe + f - 1
(7)
where f is the fraction of the projected area of the solid surface in contact with the liquid and rf is the roughness of the portion of the solid that is in contact with water. When f ) 1, rf ) r in the Wenzel model. It is important to note that rf in eq 7 is not the roughness ratio of the total surface, but only that in contact with the liquid. In this form of the Cassie-Baxter equation, the contributions of surface roughness and of trapped air are much clearer than in the other forms of the equation. (21) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (22) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (23) Marmur, A. Langmuir 2003, 19, 8343.
In recent literature, the Cassie-Baxter model is often described using the apparent contact angle on a rough surface by the following equation:24-26
cos θrCB ) ΦS(cos θe + 1) - 1
(8)
where ΦS is the ratio of the rough surface area in contact with a liquid drop to the apparent surface area covered by a liquid drop. Note that the form of the Cassie-Baxter equation given in eq 8 is not generally valid. In fact, comparing eq 8 to eq 7, it is obvious that eq 8 is only valid when rf ) 1, i.e., when the liquid is in contact with a flat, porous surface. The use of eq 8 should be restricted, and the complete Cassie-Baxter equation in either the form given in eq 3 or the form given in eq 7 should be used. In the study discussed below, a superhydrophobic rough surface is designed using a plain woven structure and prepared by grafting low surface tension materials such as 1H,1H-perfluorooctylamine or octadecylamine to poly(acrylic acid) (PAA)-grafted nylon 6,6 woven fabric consisting of multifilament yarns. The woven fabrics consist of conventional nylon fibers whose diameters are greater than 15 µm, which is much larger than the microfibers (diameter of 73 118 e θ e 134
93 e θ e 110 130 e θ e 138
θ > 73 120 e θ e 127
95 e θ e 102 125 e θ e 134
-
-
-
-
123 e θ e 138
b
125 e θ e 131
b
θ)0
θ)0
θ)0
θ)0
146 e θ e 158
160 e θ e 168
147 e θ e 152
155 e θ e 168
θ)0
θ)0
θ)0
θ)0
112 e θ e 127
109 e θ e 113
114 e θ e 120
107 e θ e 110
a
Measured after the contact angles reach the equilibrium statement. b Not measured.
2.3. Grafting of 1H,1H-Perfluorooctylamine on PAA-Grafted Nylon 6,6 Surfaces. 1H,1H-Perfluorooctylamine (0.05 g) was dissolved in 10 mL of methanol at 20 °C. Then, 0.15 g of PAAgrafted nylon film (5 × 6 cm2) and 0.3 g of each PAA-grafted nylon woven fabric (5 × 6 cm2) were immersed in the 1H,1Hperfluorooctylamine solution for 24 h with stirring to allow adsorption of 1H,1H-perfluorooctylamine. DMTMM (0.03 g) was dissolved in methanol with vigorous stirring at 20 °C. 1H,1H-Perfluorooctylamine-adsorbed PAA-grafted nylon materials were immersed in the DMTMM solution to graft 1H,1Hperfluorooctylamine to the PAA on nylon 6,6 surfaces. The reaction proceeded for 2 h. The 1H,1H-perfluorooctylamine-grafted PAAgrafted nylon materials were rinsed in methanol for 8 h (repeated twice with fresh solvent), rinsed in distilled water for 8 h (repeated twice with fresh solvent), wiped with Kimwipes, and air-dried. 2.4. Grafting of Octadecylamine on PAA-Grafted Nylon 6,6 Surfaces. Octadecylamine (0.03 g) was dissolved in 10 mL of methanol at 20 °C. Then, 0.15 g of PAA-grafted nylon film and 0.3 g of each PAA-grafted nylon woven fabric were immersed in the octadecylamine solution for 24 h with stirring to allow adsorption of octadecylamine. DMTMM (0.03 g) was dissolved in methanol with vigorous stirring at 20 °C. Octadecylamine-adsorbed PAA-grafted nylon materials were immersed in the DMTMM solution to graft octadecylamine to the PAA on nylon 6,6 surfaces. The reaction proceeded for 2 h. The octadecylamine-grafted PAA-grafted nylon materials were rinsed in methanol for 8 h (repeated twice with fresh solvent), rinsed in distilled water for 8 h (repeated twice with fresh solvent), wiped with Kimwipes, and air-dried. 2.5. Scanning Electron Microscopy. The surfaces of nylon woven fabrics were examined with a scanning electron microscope (SEM), Hitachi S-3200N, operated at 5 kV and magnification from 25× to 200×. For the analysis of SEM pictures, Image J 1.34s (National Institute of Health) was used. 2.6. Contact Angle Measurements. The contact angles on the prepared surfaces were examined with sessile water drops using a lab-designed goniometer at 20 °C. The contact angle images were obtained using a charge-coupled device camera. The weights of the applied droplets of distilled water were 10, 20, and 50 mg. Mean values were calculated from at least four individual measurements each on a new spot. The roll-off angles were measured by placing a specimen on a level platform mounted on a Newport 495 rotation stage and inclining the specimen. Water droplets (10, 20, 50, 100, and 500 mg) were placed onto the surface, and the angle of the stage was recorded when the drops began to roll off.
3. Results and Discussion The wetting behavior of a solid surface is controlled by both the surface tension and the geometric structure of the surface. To form a superhydrophobic surface, the surface has to have a low surface tension and an appropriate roughness. First, we
verified that the chemical procedure described in the Experimental Section resulted in a low surface energy on smooth nylon 6,6 films. 3.1. Wetting Properties of Hydrophilic and Hydrophobic Films. A water droplet (γLd ) 21.8, γLp ) 1.4, and γLH ) 49.6 dyn/cm) placed upon a clean, smooth nylon surface (γSd ) 40.8 and γSH ) 6.2 dyn/cm) should have a contact angle θe ) 72°.31 After cleaning the surface of a smooth nylon 6,6 film, we measured the water contact angles to be 65° e θe e 73°, as shown in Table 1. This is in good agreement with the predicted contact angle. To make the nylon surface hydrophobic, θe > 90°, the surface was treated with a low-surface-energy material. Since nylon has few reactive sites, it was first modified to increase the number of reactive sites. This was done by grafting PAA onto nylon film using the procedure developed by Tobiesen and Michielsen32 as modified by Thompson.30 Since PAA is more hydrophilic than nylon due to the carboxylic acid groups along the backbone, θe should be less than 65°. When water was placed on a PAAgrafted nylon film, the measured contact angles were 43° e θe e 50°, in good agreement with those found by Thompson.30 In order to make the film surface hydrophobic, 1H,1H-perfluorooctylamine or octadecylamine was grafted onto the PAA-grafted nylon films as described in the Experimental Section. Since 1H,1H-perfluorooctylamine and octadecylamine are more hydrophobic than nylon due to the fluoroalkyl groups or alkyl groups, respectively, θe should be greater than 73°. The water contact angles measured on the 1H,1H-perfluorooctylamine-grafted PAAgrafted nylon film and the octadecylamine-grafted PAA-grafted nylon film were 93° e θe e 110° and 95° e θe e 102°, respectively, as shown in Table 1. Thus, the first criterion for making a superhydrophobic surface has been achieved. 3.2. Preparation of Superhydrophilic Rough Surfaces. As mentioned in the Introduction, since cos θrW ) r cos θe, θrW goes toward 0° when θe < 90°, and the liquid is sucked into contact with the rough surface. In other words, a hydrophilic surface becomes more hydrophilic when roughness, r, increases. Figure 1 shows a cross-sectional view of a model of a plain woven fabric made from monofilament yarns. The surface area of a single round monofilament yarn in the unit fabric can be calculated based on Figure 1. The circumference of a yarn is 2πR. The length of the yarn in a unit cell is 4R, so the surface area of a single round, monofilament yarn in the unit cell is 8πR2. There are two yarns in a unit cell, one warp and one weft. Thus, the true surface area for the entire thickness of a monofilament plain woven fabric is 16πR2. Thus, the true surface area is (31) Lee, H. J.; Michielsen, S. J. Textile Institute 2006, 97, 455. (32) Tobiesen, F. A.; Michielsen, J. Polym. Sci., Part A 2002, 40, 719.
Superhydrophobic Surfaces with WoVen Structures 2 Areal fabric ) Amono ≈ 16πR
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(9)
The apparent surface area is just equal to the area of a plane tangent to the top surface. 2 Aapparent fabric ) 2 x3R × 2 x3R ) 12R
(10)
Finally, the roughness, r, is just the ratio of these areas:
r)
Areal fabric
4 ≈ π ) 4.19 Aapparent 3
(11)
fabric
We use the measured contact angles 65° e θe e 73° for the flat nylon film or 43° e θe e 50° for the flat PAA-grafted nylon film. On substituting r ) 4.19 into eq 2, θrW ) 0° for both fabrics. The predicted values are in good agreement with the measured angles shown in Table 1. Next, we look at a plain woven fabric made with multifilament yarns. Clearly, a multifilament yarn will have even higher values of r, since the space between the fibers will increase the real surface area while the apparent surface area remains the same. In this case, eq 9 becomes
Areal fabric ) Amulti ≈ NRf × 16πR
(12)
where N is the number of filament fibers, R is the radius of the yarn, and Rf is the radius of the filament fibers. Substituting eq 12 into eq 11 yields
r)
Areal fabric Aapparent fabric
≈
4πNRf NRf ) 4.19 3R R
(13)
When N ) 1, Rf ) R. Otherwise, Rf < R but NRf > R. Equations 12 and 13 are only valid when N ) 1 or N . 1. Figure 2 shows a plain woven fabric consisting of nylon 6,6 multifilament yarns. For this fabric, R ) 150 µm, N > 70, and Rf ) 10 µm. Substituting these values into eq 13 gives r > 19.55. Since r > 19.55 for the multifilament fabric, we again expect that θrW ) 0° for both the nylon fabric and the PAA-grafted fabric. Again, the predicted values are in good agreement with the measured angles, as shown in Table 1. Thus, we can easily create Wenzel-type behavior with complete wetting by having θe < 90° and sufficient roughness. 3.3. Preparation of Superhydrophobic Rough Surfaces. To make a superhydrophobic surface, we first need to make the surface hydrophobic and create the appropriate roughness. According to Cassie and Baxter22 and Marmur23 and as is evident from eqs 3 and 7, the Wenzel model is a special case of the Cassie-Baxter equation where f ) 1 and rf ) r (eq 7). For a material with a smooth surface water contact angle of 93° (as above), the Wenzel surface roughness, r, must be greater than 16.5 for the apparent contact angle to exceed 150°. However, according to Marmur, the minimization of the free energy requires that, for a hydrophobic surface with f ) 1, θe ) 180°. Since the only material known with θe ) 180° is air or vacuum, f cannot be equal to 1. In order to develop superhydrophobic surfaces, we need to use a different approach, namely the Cassie-Baxter model. We begin with an analysis of f, the fraction of the projected area in contact with the water droplet. For parallel cylinders viewed normal to the cylinders’ axes, as shown in Figure 3, there are two cases (a) the cylinders are packed tightly together or (b) they are separated by some distance. In case (a), the distance from the center on one cylinder to the center of the next is 2R,
Figure 1. Cross-section views of a plain woven fabric at (a) the warp yarn direction and (b) the weft yarn direction.
where R is the radius of the cylinder. For parallel cylinders, Marmur showed that f is the length of the dotted line in Figure 3 divided by the radius of the cylinder; f ) R sin R/R ) sin R, where R is the angle between the top of the cylinder and the liquid contact line. In case (b), by analogy, the center-to-center distance is 2(R + d). Then, f ) R sin R/(R + d). In both cases, the roughness of the surface in contact with water, rf, is the length of the chord in contact with water, RR, divided by the projected area of the chord in contact with water, R sin R, i.e., rf ) R/sin R. Following Marmur’s derivation, d(rf f )/d f ) (cos R)-1 and d2(rf f )/d f 2 > 0. Under these conditions, Marmur showed that there was a minimum in the surface free energy on each surface such that R ) π - θe.23 Substituting f and rf for case (b) into eq 7 results in
cos θCB r )-
(R +R d)R cos R + (R +R d)sin R - 1
(14)
On substituting π - θe for R, we obtain
cos θCB r )
(R +R d)(π - θ )cos θ + (R +R d)sin θ - 1 (15) e
e
e
For θe > 90°, θCB r increases with increasing d. For example, when θe ) 120° and d ) 0, the fibers are closely packed and CB CB θCB r ) 131°; for d ) R, θr ) 146°; and for d ) 2R, θr ) 152°. We consider two cases for solving eq 15. First, we solve it for a monofilament plain woven fabric shown in Figure 1. According to Pythagorean’s theorem, the angle that a weft yarn (or warp yarn) makes with the fabric plane in traveling from one warp yarn (or weft yarn) to another is 30°. Therefore, the distance from the top of a weft yarn (or warp yarn) to the top of an adjacent warp yarn (or weft yarn) is 2 x3 R. From this geometric consideration, the center-to-center distance of adjacent cylinders in eq 15, 2(R + d), is equal to 2 x3 R, and f ) sin θe/x3. Substituting these values into eq 15 along with the measured contact angles from the flat nylon films, we find 118° e θCB r e 134° for the 1H,1H-perfluorooctylamine-grafted monofilament woven fabric and 120° e θCB r e 127° for the octadecylaminegrafted monofilament woven fabric. These values are in good agreement with the measured values shown in Table 1. In the second case, we again extend the analysis to a multifilament fabric. We begin by determining the apparent contact angle of the liquid with the multifilament yarns. From Figure 2, it is seen that the fiber spacing is approximately equal to the fiber diameter, i.e., 2d ≈ 2Rf, where Rf is the fiber radius. Substituting Rf for R and d into eq 15, as shown in Table 1, we obtain θCB r ranging from 123° to 138° for the 1H,1H-perfluorooctylamine-grafted single fiber, and from 125° to 131° for the octadecylamine-grafted single fiber. Then, using these values as the effective contact angles for the yarns in the woven structure and re-solving eq 15 with R being the yarn radius and d ) R(x3 - 1) such that 2(R + d) ) 2 x3 R as before. We obtain
6008 Langmuir, Vol. 23, No. 11, 2007
Michielsen and Lee
Figure 2. SEM micrographs of a multifilament plain woven fabric.
yarns of Figure 2, d ) R(x3 - 1), θe ≈ 100° giving f1 ) 0.81 and f2 ) 0.43 since
f1 )
R (π - θe) R+d
f2 ) 1 -
Figure 3. Liquid drop sitting on (a) cylinders packed tightly and (b) cylinders separated by a distance, 2d. R ) π - θ. The dotted line represents the projected area of the cylinders in contact with water, while the dashed line is the interfacial area between air and water.
Figure 4. Water droplet on the multifilament plain woven fabric. The apparent water contact angle on this rough surface is 168°.
146° e θCB r e 158° for the 1H,1H-perfluorooctylamine-grafted fabric, and 147° e θCB r e 152° for the octadecylamine-grafted fabric. As seen in Table 1, the measured values are slightly larger than our predicted values. This is probably due to the real value of d being larger than the values chosen in this analysis. For example, the surface of the fabric shown in Figure 2 clearly has loose fibers on the surface that are not entrained in the yarn. These surface fibers are separated from the remainder of the fibers by distances d > R. As shown earlier, larger values of d CB result in larger values of θCB r . Thus the measured values of θr are greater than the predicted values. Figure 4 shows a water droplet sitting on this surface; the apparent water contact angle on this surface is 168°. Others have reported the Cassie-Baxter model using eq 8. This form of the Cassie-Baxter equation is valid only when a surface is perfectly smooth (i.e., ΦS ) r ) 1) or when the top of a rough surface is flat. Comparing eq 8 to eqs 3 and 7 shows that eq 8 is only correct when f1 + f2 ) 1. However, f1 + f2 > 1 on general rough surfaces. For example, in the multifilament
R sin θe R+d
(16) (17)
Thus, in this case, f1 + f2 ) 1.24. This is clearly not equal to 1, and eq 8 cannot be applied in this case. Rather, the original Cassie-Baxter equation is preferred. As can be seen from eq 7, eq 8 is invalid for a typical rough surface unless the top is perfectly flat. The second portion of the definition of superhydrophobic materials is that they have a water roll-off angle of less than 5°. To understand the relationship between roll-off angle and contact angle hysteresis, Dorrer and Ruehe prepared square pillars protruding from a substrate with varying sizes and spacings of pillars.15 Then, they showed that the advancing contact angle approached 180° when the droplet rolled of the surface, regardless of post size or spacing. However, the receding contact angle depended on the post spacing and inversely on the post size. In their studies, receding contact angles varied from 80° to 150° for the same value of θe. It is important to note that the droplet size must be much larger than the underlying structure to have a low roll-off angle. For our samples, the advancing contact angles of the 1H,1H-perfluorooctylamine-grafted or octadecylaminegrafted multifilament fabric surface also became very close to 180° when the droplet began to move. However, the receding contact angles were affected by the local structures of fabric such as protruding yarns, yarn size, and yarn spacing on the surface. Although the receding contact angles were as small as 90°, the roll-off angles of these superhydrophobic surfaces were less than 5° when a 0.5 g water droplet was applied as shown in Figure 5. However, when 10, 20, 50, and 100 mg drops were applied, the roll-off angles were greater than 5° since the roll-off angle was influenced by the weight of a water droplet and local yarn or fabric geometry. Yoshimitsu et al. also showed that the roll-off angle depended on the weight of a water drop, i.e., on its size. They showed that the roll-off angle exceeded 90° for small droplets and decreased to 15° for large droplets on their materials. An additional surface structure was analyzed using flattened fibers, which resulted in a smoother fabric. Figure 6 shows another woven fabric made of monofilament yarns that have been calendared. In this case, the fraction of the surface in contact with water, f1, must be larger than that of round fibers since water will contact more of the surface of these flattened yarns. f1 + f2 is also greater than 1 on this rough surface. Since it is
Superhydrophobic Surfaces with WoVen Structures
Langmuir, Vol. 23, No. 11, 2007 6009
is wet by the liquid and rf is the roughness ratio of the wet area, we obtain
f)
4b + 4R sin R 4b + 2d + 4R
(18)
rf )
4b + 4RR 4b + 4R sin R
(19)
where R is the angle between the top of the cylinder and the liquid contact line (R ) π - θe), Again, according to Marmur, the surface has a minimum surface free energy for θCB r , when d(rf f )/df ) (cos R)-1 and d2(rf f )/df 2 > 0. We obtained Figure 5. Dependence of roll-off angles on the weights of water droplets.
4b + 4RR d(rf f ) d 4b + 4R + 2d d(b + RR) 1 ) (20) ) ) df 4b + 4R sin R d(b + R sin R) cos R d 4b + 4R + 2d
( (
d2(rf f ) df 2
Figure 6. SEM micrograph of a calendared monofilament woven fabric. The solid line shows the warp direction, and the dotted line shows the weft direction.
)
) )
d(cos R)-1 ) 4b + 4R sin R d 4b + 4R + 2d
(
)
sin R > 0 (21) R(4b + 4R + 2d)cos3 R
Again, following Marrmur’s analysis, the surface can have minimum free energy at the Cassie-Baxter apparent contact angle when eqs 20 and 21 are satisfied on the surface. On substituting eqs 18 and 19 into eqs 5 and 6, f1 and f2 are obtained as
f 1 ) rf f )
4b + 4RR 4b + 4R + 2d
f2 ) 1 - f ) 1 -
4b + 4R sin R 4b + 4R + 2d
(22) (23)
On substituting eqs 22 and 23 into eq 3 Figure 7. Cross-section view of a calendared woven fabric when it is cut in the warp direction shown in Figure 6.
difficult to measure f1 and f2 of calendared fabric directly or to compute it from a simple fabric model, we estimated them through analyzing rf and f from eqs 5 and 6. The arrangement of the flattened fibers in this woven fabric is anisotropic. There are two types of fibers which can be regarded as flattened cylinders in this structure: cylinders passing through the warp direction shown as a solid line in Figure 6 and cylinders passing through the weft direction shown as a dotted line. As shown in Figure 6, only the cylinders passing through weft direction reside on the top of this rough surface. Thus, only these fibers are considered to obtain f and rf. These top fibers have shorter center-to-center distance when measured in the warp direction (solid line) than when measured in the weft direction (dotted line). We measure R, b, and d, which are defined in Figure 6, to obtain only the warp directional f and rf. R is the radius of rounded part of a flattened cylinder, 2d is the spacing between the edges of the fibers, and 2b is the width of the flattened portion of the fiber. Figure 7 presents the cross view of the unit structure of the fabric when it is cut through the solid line in Figure 6. In the warp direction, two flattened cylinders are placed on the top of the rough surface at a distance, 2d, with the adjacent cylinders lying in the same direction. Thus, the unit center-tocenter distance is 4(R + b) + 2d, as shown in Figure 7. Since f is the fraction of the projected area of the rough surface that
cos θCB r )
b + R(π - θe) cos θe + b + R + 0.5d b + R sin(π - θe) - 1 (24) b + R + 0.5d
Using the SEM image of the rough surface, b, R, and d were measured at 10 locations on the surface: baverage ) 60 µm, Raverage ) 40 µm, and daverage ) 100 µm. Applying the measured θe, b, e 127° for the 1H,1HR, and d to eq 24 gives 112° e θCB r perfluorooctylamine-grafted nylon calendared monofilament fabric and 114° e θCB r e 120° for the octadecylamine-grafted nylon calendared monofilament fabric. Although d of the rough surface has a large coefficient of variation, ∼30%, the predicted values show good agreement with the measured values, 109° e CB θCB r e 113° and 107° e θr e 110°, respectively. As predicted by eq 24, this surface is not superhydrophobic due to the short distances between adjacent fibers and high portion of flat top surfaces.
4. Conclusion A superhydrophobic surface is obtained by two criteria: a low surface energy and an appropriate surface roughness which result in water detaching from the surface at a low roll-off angle. In order to make nylon 6,6 superhydrophobic, a low-surface-tension material, 1H,1H-perfluorooctylamine or octadecylamine, was grafted onto nylon 6,6 woven fabric consisting of multifilament
6010 Langmuir, Vol. 23, No. 11, 2007
yarns. We modeled the multifilament, plain woven fabric as consisting of monofilaments whose water contact angle was equal to the apparent water contact angle of the multifilament yarn. We approximated the fabric as parallel cylinders with radii equal to that of the multifilament yarns. From the water contact angles measured on flat, modified nylon films, we predicted the apparent contact angle of the woven fabrics. Good agreement between the predicted values and the observed contact angles was obtained. Apparent water contact angles of the multifilament woven fabric as high as 168° were obtained. A flattened fabric was also modeled and the predicted and measured values for this fabric also were
Michielsen and Lee
in good agreement. The roll-off angles of our superhydrophobic surfaces were less than 5° when a 0.5 g water droplet was placed on the surfaces. However, when small drops were applied, the roll-off angles were greater than 5° since the roll-off angle was influenced by the droplet size and local yarn or fabric geometry. It is also important to note that the form of the Cassie-Baxter equation in common use today (eq 8) is, in general, invalid. The original Cassie-Baxter equation (eq 3) or the reformed CassieBaxter equation by Marmur (eq 7) should be used instead. LA063157Z
