Letter www.acsami.org
Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX-XXX
Superhydrophobic, Low-Hysteresis Patterning Chemistry for WaterDrop Manipulation Ting Dong†,‡ and Thomas J. McCarthy*,‡ †
College of Textiles, Donghua University, Shanghai 201620, China Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003, United States
‡
S Supporting Information *
ABSTRACT: A method for preparing superhydrophobic surfaces containing guiding lines that control water motion is described. The background surfaces exhibit contact angles of θA/θR = 173°/171°, and the guiding lines are also hydrophobic (θA/θR = 104°/102°). The low-contact-angle hysteresis allows facile water motion. The sequence of steps used to prepare these surfaces is central to their success, is designed to minimize defects, and involves only two inexpensive and fluorine-free reagents: methyltrichlorosilane and dimethyldichlorosilane. Examples of patterned surfaces that direct water motion are described. The disparity in receding contact angles is identified as the key parameter for guided motion. KEYWORDS: open microfluidics, drop transportation, low hysteresis, superhydrophobic, 3-phase contact line guiding lines. All of these substrates required wind flow to initiate and sustain water-drop motion, and “tails”, wetting of the guiding tracks, appeared behind moving drops on all three surfaces. The tails became long and broke off (Rayleigh instabilities) on the more hydrophilic (glass and PET) lines but were much shorter and did not break off on the more hydrophobic PDMS lines. The wind-induced drop motion on the PDMS-patterned superhydrophobic surfaces was described as “no-loss transportation.” This Letter also concerns the motion of water drops (and streams) on patterned surfaces, but our emphasis is on the chemistry of the background and guiding line preparation and, in particular, the synthesis of hydrophobic guiding lines that exhibit low-contact-angle hysteresis. We applaud the work of Hu, Yu, and Song,11 which used commercially available PDMS (Dow Corning Sylgard 184) for guiding lines, Ultra-Ever Dry as a background, and a shadow mask for lithography, but we wanted to develop a convenient laboratory route to defect-free devices that perform much better than those prepared by this “off-the-shelf” method. We also want to emphasize that contactangle hysteresis is responsible for water that is left behind on guiding tracks and that the PDMS (Sylgard 184) surfaces described in the prior report,11 although they appear to exhibit “no-loss” behavior, most certainly have nonvisible water left behind by the drops that move on them. The advancing and receding water-contact angles on the PDMS reported by Hu, Yu, and Song11 are θA/θR = 110°/64° (significant hysteresis). The reports of Kota et al.12 and Balu et al.13 warrant mention. The former team12 prepared patterned surfaces that controlled water-drop transport by patterning a texture on stainless steel
urfaces that exhibit extreme water repellency or “superhydrophobicity” have been developed over the past ∼20 years and are used or are argued to be useful in a wide range of technologies beyond simple repellency, including self-cleaning,1 antifog,2 drag-reduction,3 and anti-icing technologies.4 Of particular concern to this report is the range of applications envisioned that involve drop manipulation and guided liquid transportation, which require the preparation of anisotropic or patterned surfaces with nonuniform chemical compositions.5 There are numerous successful demonstrations that use hydrophilic lines or regions on water repellent backgrounds and involve various preparative methods, including UVstimulated photocatalytic decomposition of TiO2 nanostructures,6 electrochemical etching and lithography of aluminumalloy surfaces,7 selective ablation using lasers,8 photodefinable mixtures of a UV-curable epoxy resin and polytetrafluoroethylene nanoparticles,9 and UV exposure of hydrophobized silicon nanowire arrays.10 Drops of water, particularly small drops, do not readily move (slide) on most surfaces, thus making superhydrophobic surfaces appealing for water repellency. Many surfaces of this type are now easily prepared by a wide variety of methods, and several that work quite well are commercially available.11 Water drops that are placed on horizontal surfaces with this property do not come to rest and move spontaneously in directions that are caused by slight initial momentum. Guiding the motion of drops or streams of water on these surfaces requires destroying this superhydrophobicity by introducing defects. The strategy of using thin hydrophilic lines as guiding tracks, although it functions in the experiments reported in the papers mentioned above, has an inherent problem: water is “left behind” on the tracks. This was recognized by Hu, Yu, and Song,11 who described experiments that used a commercially available sprayon superhydrophobic coating and glass, PET, and PDMS
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© XXXX American Chemical Society
Received: October 16, 2017 Accepted: November 14, 2017 Published: November 14, 2017 A
DOI: 10.1021/acsami.7b15739 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
Figure 1. (a) Procedure for preparing low-hysteresis guiding lines on superhydrophobic surfaces. (b) SEM image of a silicon-wafer-supported, CH3SiCl3-derived, superhydrophobic surface. (c) SEM micrographs illustrating the resolution of the photolithography, showing concentric, alternating, superhydrophobic and hydrophilic rings varying from 50 (upper left) to 400 μm (lower right) in width. (d) Frames of video recordings (Movie S1) of advancing and receding contact-angle measurements on background (upper images) and guiding-line (lower images) areas.
permeates rapidly in cross-linked methylsilicones;22 thus, drops moving on surfaces of this material have an additional mechanism for liquid loss. Figure 1a shows our approach to superhydrophobic surfaces containing low hysteresis guiding lines. We emphasize that this was carried out in a standard preparative lab with access to an oxygen-plasma cleaner, a spin coater, and a UV lamp (not a clean room). Photolithography was carried out on silicon-wafer sections using photoresist spin coating, illumination, and development procedures that have previously been reported.23 After area-selective development, which yielded a resist-coated guiding line and an environment-contaminated Si/SiO2 background (θA/θR = ∼56°/∼24°), the wafer section was exposed to 20 min, 100 mTorr, O2-plasma treatment (Harrick PDC001). This treatment cleans the background and oxidizes the outer few nanometers of the ∼1.3 μm thick resist. We point out that this treatment does not clean the Si/SiO2 background as well as it does a wafer section that contains no photoresist; the oxidation of the photoresist “pollutes” the O2 plasma to some extent, which is evidenced by finite advancing contact angles (θA/θR = ∼15°/0°). This surface was then treated with CH3SiCl3 using a procedure which is now well established24−27 for introducing silicone nanofilaments that impart superhydrophobicity. These contorted nanofilaments with diameters of tens of nanometers (Figure 1b) distort the 3-phase (solid/ liquid/vapor) circular contact line, making it dynamic at room temperature. A dynamic contact line constantly advances or recedes at different points on the line and this micrometerlength-scale motion reduces macroscopic hysteresis. After resist removal, the wafer section contained a superhydrophobic background (θA/θR = 172°/164°) and an environmentcontaminated Si/SiO2 guiding line (θA/θR = ∼56°/∼24°). We have reported25 the preparation of perfectly hydrophobic (θA/θR = 180°/180°) surfaces on plasma-cleaned Si/SiO2 substrates using this chemistry with a finite (70%) success rate. We ascribe the lower (θA/θR = 172°/164°) contact angles reported here to impurities introduced during the plasma and photolithography steps. Figure 1c demonstrates the resolution of this photolithography and chemistry procedure with SEM
with a laser engraver and subsequently adding surface modifications with a perfluoroalkyl-containing trichlorosilane. The water-contact angles of the smooth (nontextured) functionalized guiding lines were reported12 as θA/θR = 89°/ 74° (significant hysteresis). The latter group13 laser printed dots and lines (Microsoft Word 2007) on superhydrophobic paper, which was prepared by sequential oxygen- and pentafluoroethane-plasma treatments of specially prepared hardwood and softwood papers. Their superhydrophobic background and features exhibited θA/θR = 165°/135° and θA/θR = 114°/85°, respectively. These authors took advantage of this significant hysteresis to pin drops in desired locations. They also used lines to initially pin and then mix droplets. The barrier to sessile drop motion on surfaces is controlled by contact-angle hysteresis, the difference between advancing and receding contact angles.14 This was understood and quantified in the early 1960s, and the expression derived by Furmidge,15 which relates the sliding angle to the receding and advancing contact angles, is shown as eq 1 mg (sin α)/w = γLV(cos θR − cos θA)
(1)
where m is the mass of the drop, g is gravitational acceleration, α is the sliding angle, w is the width of the drop, and γLV is the liquid surface tension. Without hysteresis (θA = θR), sessile drops move without applied force and without changing shape. Several authors have proposed16−19 that hysteresis is due to events at the receding contact line that lead to a liquid film being left behind moving drops. These proposals are supported by observations20,21 of droplets and sodium chloride crystals left behind drops of a (nonvolatile) ionic liquid or aqueous NaCl moving on superhydrophobic surfaces. There is no appearance of liquid left behind pure water drops on these surfaces. The significant hysteresis values exhibited by the guiding lines on the surfaces reported by Hu, Yu, and Song11 (θA/θR = 110°/64°) and Kota12 (θA/θR = 89°/74°) argue that liquid must be left behind on these guiding lines as well. The thin water films or small water droplets, however, evaporate rapidly and are not visible. The PDMS used as a guiding line (Sylgard 184) has an additional complication: water vapor B
DOI: 10.1021/acsami.7b15739 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
Figure 2. (a) Water drop sliding down a guiding line upon slight tilting of the sample. (b) Water drop rotating around a circular ring with slight oscillation from the horizontal. (c) Water streams from a squirt bottle being directed by guiding lines along a straight path, a curve, and a sharp curve. (d) Water stream from a squirt bottle being guided by a sinusoidal guiding line (left) and the dropwise addition of water to a sinusoidal guiding line (right).
varying tilt angles) from the video recording (Movie S2). Velocities of 1.25 ± 0.07 and 3.18 ± 0.21 m/s were calculated for movement between the first and third and the third and fifth frames, respectively, shown in Figure 2a. The velocity between the first and fifth frames is 1.75 ± 0.15 m/s. These data need to be regarded as qualitative, but we contrast this rapid, accelerating motion with the very slow motion observed for sessile drops on low-hysteresis backgrounds being guided by curbs of higher contact angle.30 Figure 2b and Movie S3 (Supporting Information) show a 20 μL drop of water rotating around an 8 mm diameter ring on a 0.9 mm guiding line. The dark image in the background at the right of the frames in Figure 2b is the right shoe of one of the authors (T.D.). This gives perspective to this experiment, particularly in Movie S3. This movie can be directly compared with one of a similar experiment on a surface with greater hysteresis, which is available as Supporting Information in ref 12. Figure 2c and Movies S4, S5, and S6 (Supporting Information) show that a stream of water from a squirt bottle can be directed along a straight guiding line, around a bend, or even around a tight curve. Figure 2d and Movies S7 and S8 (Supporting Information) show water-stream and multiple-droplet motion along a sinusoidal guiding line that is 1 mm in width with a drift angle of 20°. The stream breaks (Rayleigh instabilities) into individual droplets when the stream slows because of resistance at the corners in the path. An additional movie, Movie S9, is included as Supporting Information that shows a stream of water being directed by a sinusoidal hydrophilic path. This sample was prepared via the first stage of Figure 1a, and the guiding line and background had contact angles of θA/θR = ∼56°/∼24° and 172°/164°, respectively. The stream does not break into drops on this surface; however, this hydrophilic guiding line is not significantly more effective at guiding the water than the low hysteresis (θA/θR = 104°/102°) line. Some comments concerning the stability and durability of these patterned surfaces are in order. Samples were stored with no apparent degradation in air (in closed Petri dishes) for many months (some for more than a year) and were cleaned multiple times with strong streams of water from squirt bottles. We have not tested their resistance to abrasion but note that the scale-up
micrographs that show concentric, alternating, superhydrophobic and hydrophilic (environment-contaminated silicon wafer) rings from 50 to 400 μm in width. Oxygen-plasma treatment of this surface for 20 min rendered a hydrophilic guiding line and a “superhydrophilic” background, which were exposed to (CH3)2SiCl2 vapor. This reaction is now a well-established method for preparing low hysteresis, covalently attached, liquidlike PDMS monolayers.28,29 We emphasize that this final vaporphase reaction of a plasma-cleaned surface, which creates both the background and the guiding line chemistries in a single step, is key to the preparation of defect-minimized surfaces. We note that Zhang and Seeger have shown that O2-plasma-treated, CH3SiCl3-derived nanofibers exhibit silica-surface reactivity.26 The contact angles of the guiding-line region and the background were determined to be θA/θ R = 104°/102° and 173°/171°, respectively. Low hysteresis is imparted to both the background and guiding-line regions by the liquid-like, covalently attached, oligomeric PDMS. Frames from video recordings (Supporting Information, Movie S1) of advancing and receding water drops on these surfaces are shown in Figure 1d. These surfaces were prepared dozens of times, and a fraction (∼30%) of the samples prepared contained defects and were discarded. The contact-angle values reported are averages of values determined on a number of samples, and we include, as Supporting Information, contact-angle data for a number of individual surfaces as well as mean and standard-deviation values. Surfaces prepared using this method are very effective at guiding both water drops and streams of water, and Figure 2 shows photographs of several samples, which were prepared to demonstrate control of motion. These are all frames from video recordings that are included as Supporting Information, and we emphasize that the video recordings capture the ease with which guiding motion occurs much better than these still photographs. Figure 2a shows a 20 μL drop of water sliding down a 1 × 20 mm guiding line upon slight tilting. The video recording (Supporting Information, Movie S2) shows the drop moving back and forth along the line and indicates that the drop moves upon very slight tilting and accelerates at a tilt angle of ∼4°. We did not measure drop velocities in any controlled manner, but they can be determined (albeit with C
DOI: 10.1021/acsami.7b15739 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Letter
ACS Applied Materials & Interfaces
θR = 173°/171°) “Cassie” contact lines. Figure 3c1,c2 is a photograph and a schematic of a sessile drop tilted ∼30° around the guiding line. The drop is pinned because the contact angle would have to decrease to 102° for the drop to recede across the line. The 500 μm wide line supports both 3 and 5 μL drops when the surface is tilted perpendicular to the plane of the floor; a 10 μL drop depins from the line at ∼75° from the plane of the floor. In summary, a combination of surface chemistry and photolithography was used to prepare surfaces that contain low-hysteresis guiding lines on superhydrophobic backgrounds. We reiterate and re-emphasize that low hysteresis is required and that defects, which pin receding contact lines, cannot be present. There are few preparative methods that can prepare defect-free surfaces of this quality on even rigorously cleaned silicon wafers, and incorporating these techniques into (messy) procedures that involve photolithography and selective resist development is difficult. The key to the success of the preparative method was the sequence of reactions: the vaporphase reaction that formed both the guiding lines and background was the final step. The difference between the receding contact angles of the background (θR = 171°) and the guiding line (θR = 102°) is responsible for the retention of water on the guiding lines. Low hysteresis is responsible for the facile motion.
work reported27 for CH3SiCl3-derived nanofiber surfaces suggests practical superhydrophocity. It is not obvious that low-hysteresis, water-repellent, very hydrophobic (θA/θR = 104°/102°) guiding lines should direct water motion as well as they do, and an analysis of the structure of water on superhydrophobic and low-hysteresis patterned surfaces is warranted. Figure 3 shows several photographs and
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.7b15739. Contact angle data for MeSiCl3-derived surfaces (Table S1), Me2SiCl2-treated background areas (Table S2), and Me2SiCl2-treated guiding-line areas (Table S3) (PDF) Movie S1. Contact-angle measurements on background and guiding-line areas (AVI) Movie S2. Water drop sliding on a straight guiding line (AVI) Movie S3. Water drop rotating on a circular guiding line (AVI) Movie S4. Water stream on a straight guiding line (AVI) Movie S5. Water stream on a curved guiding line (AVI) Movie S6. Water stream on a sharply curved guiding line (AVI) Movie S7. Water stream on a sinusoidal guiding line (AVI) Movie S8. Water droplets on a sinusoidal guiding line (AVI) Movie S9. Water stream on a hydrophilic, sinusoidal guiding line (AVI)
Figure 3. (a) Photographs of water drops viewed from the side of the guiding line. (b) Photographs (b1,b2) and schematic (b3) of water drops viewed along the guiding line. (c) Photograph (c1) and schematic (c2) of a droplet on a surface that was rotated ∼30° around the guiding line. (d) Schematic of a view from above a water drop on a superhydrophobic surface containing a guiding line. The solid black line indicates the contact line with the guiding line, and the dotted lines indicate dynamic contact lines on the superhydrophobic background.
schematic diagrams of ∼10−20 μL water drops on a 500 μm guiding line that is the shape of the structure shown in Figure 1a. Figure 3a1,a2 shows views of drops from the side of the guiding line, and Figure 3b1,b2 shows views along the guiding line. To balance Laplace pressure at all points on the surface and retain contact angles between the advancing and receding values (which vary by only 2°), the drops adjust to the shapes imaged. The side views indicate that “proboscises” emerge from the spheroidal drops to wet the lower-contact-angle guiding lines and also that they do not emerge as far as the maximum diameter of the sessile drop (they are not visible from above). The end-on views (Figure 3b1,b2) show that small-enough (stationary) drops barely advance onto the background, and that larger drops (distorted by gravity to ellipsoidal shapes) interact with the background in a “Cassie” fashion. Figure 3d captures these features in a diagram. The solid contact line (θA/ θR = 104°/102°) with the smooth, liquid-like guiding line is much more stable than the mobile, discontinuous (dotted, θA/
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Thomas J. McCarthy: 0000-0003-0414-010X Author Contributions
T.D. performed all of the experimental work. The manuscript was written through the contributions of both authors. Both authors have given approval to the final version of the manuscript. D
DOI: 10.1021/acsami.7b15739 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
(19) Roura, P.; Fort, J. Comment on “Effects of the Surface Roughness on Sliding Angles of Water Droplets on Superhydrophobic Surfaces. Langmuir 2002, 18, 566−569. (20) Krumpfer, J. W.; Bian, P.; Zheng, P.; Gao, L.; McCarthy, T. J. Contact Angle Hysteresis on Superhydrophobic Surfaces: An Ionic Liquid Probe Fluid Offers Mechanistic Insight. Langmuir 2011, 27, 2166−2169. (21) Krumpfer, J. W.; McCarthy, T. J. Dip-Coating Crystallization on a Superhydrophobic Surface: A Million Mounted Crystals in a 1 cm2 Array. J. Am. Chem. Soc. 2011, 133, 5764−5766. (22) Robb, W. L. Thin Silicone Membranes − Their Permeation Properties and Some Applications. Ann. N. Y. Acad. Sci. 1968, 146, 119−137. (23) Cheng, D. F.; McCarthy, T. J. Using the Fact that Wetting Is Contact Line Dependent. Langmuir 2011, 27, 3693−3697. (24) Artus, G. R. J.; Jung, S.; Zimmermann, J.; Gautschi, H.-P.; Marquardt, K.; Seeger, S. Silicone Nanofilaments and Their Application as Superhydrophobic Coatings. Adv. Mater. 2006, 18, 2758−2762. (25) Gao, L.; McCarthy, T. J. A Perfectly Hydrophobic Surface (θA/ θR= 180°/180°). J. Am. Chem. Soc. 2006, 128, 9052−9053. (26) Zhang, J.; Seeger, S. Superoleophobic Coatings with Ultralow Sliding Angles Based on Silicone Nanofilaments. Angew. Chem., Int. Ed. 2011, 50, 6652−6656. (27) Artus, G. R. J.; Seeger, S. Scale-Up of a Reaction Chamber for Superhydrophobic Coatings Based on Silicone Nanofilaments. Ind. Eng. Chem. Res. 2012, 51, 2631−2636. (28) Fadeev, A. Y.; McCarthy, T. J. Self-Assembly Is Not the Only Reaction Possible between Alkyltrichlorosilanes and Surfaces: Monomolecular and Oligomeric Covalently Attached Layers of Dichloro- and Trichloroalkylsilanes on Silicon. Langmuir 2000, 16, 7268−7274. (29) Flagg, D. H.; McCarthy, T. J. Rapid and Clean Covalent Attachment of Methylsiloxane Polymers and Oligomers to Silica Using B(C6F5)3 Catalysis. Langmuir 2017, 33, 8129−8139. (30) Wier, K. A.; Gao, L.; McCarthy, T. J. Two-Dimensional Fluidics Based on Differential Lyophobicity and Gravity. Langmuir 2006, 22, 4914−4916.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the China Scholarship Council and Gelest, Inc., for financial support.
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REFERENCES
(1) Zamuruyev, K. O.; Bardaweel, H. K.; Carron, C. J.; Kenyon, N. J.; Brand, O.; Delplanque, J.-P.; Davis, C. E. Continuous Droplet Removal upon Dropwise Condensation of Humid Air on a Hydrophobic Micropatterned Surface. Langmuir 2014, 30, 10133− 10142. (2) Gao, X.; Yan, X.; Yao, X.; Xu, L.; Zhang, K.; Zhang, J.; Yang, B.; Jiang, L. The Dry-Style Antifogging Properties of Mosquito Compound Eyes and Artificial Analogues Prepared by Soft Lithography. Adv. Mater. 2007, 19, 2213−2217. (3) Shirtcliffe, N. J.; McHale, G.; Newton, M. I.; Zhang, Y. Superhydrophobic Copper Tubes with Possible Flow Enhancement and Drag Reduction. ACS Appl. Mater. Interfaces 2009, 1, 1316−1323. (4) Kreder, M. J.; Alvarenga, J.; Kim, P.; Aizenberg, J. Design of AntiIcing Surfaces: Smooth, Textured or Slippery? Nature Rev. Mater. 2016, 1, 1−15. (5) Ju, J.; Zheng, Y.; Jiang, L. Bioinspired One-Dimensional Materials for Directional Liquid Transport. Acc. Chem. Res. 2014, 47, 2342− 2352. (6) Zhang, X.; Jin, M.; Liu, Z.; Tryk, D. A.; Nishimoto, S.; Murakami, T.; Fujishima, A. Superhydrophobic TiO2 Surfaces: Preparation, Photocatalytic Wettability Conversion, and Superhydrophobic-Superhydrophilic Patterning. J. Phys. Chem. C 2007, 111, 14521−14529. (7) Yang, X.; Liu, X.; Li, J.; Huang, S.; Song, J.; Xu, W. Directional Transport of Water Droplets on Superhydrophobic Aluminium Alloy Surface. Micro Nano Lett. 2015, 10, 343−346. (8) Xing, S.; Harake, R. S.; Pan, T. Droplet-Driven Transport on Superhydrophobic-Patterned Surface Microfluidics. Lab Chip 2011, 11, 3642−3648. (9) Hong, L.; Pan, T. Surface Microfluidics Fabricated by Photopatternable Superhydrophobic Nanocomposite. Microfluid. Nanofluid. 2011, 10, 991−997. (10) Seo, J.; Lee, S.; Lee, J.; Lee, T. Guided Transport of Water Droplets on Superhydrophobic-Hydrophilic Patterned Si Nanowires. ACS Appl. Mater. Interfaces 2011, 3, 4722−4729. (11) Hu, H.; Yu, S.; Song, D. No-Loss Transportation of Water Droplets by Patterning a Desired Hydrophobic Path on a Superhydrophobic Surface. Langmuir 2016, 32, 7339−7345. (12) Pendurthi, A.; Movafaghi, S.; Wang, W.; Shadman, S.; Yalin, A. P.; Kota, A. K. Fabriction of Nanostructured Omniphobic Surfaces with Inexpensive CO2 Laser Engraver. ACS Appl. Mater. Interfaces 2017, 9, 25656−25661. (13) Balu, B.; Berry, A. D.; Hess, D. W.; Breedveld, V. Patterning of Superhydrophobic Paper to Control the Mobility of Micro-Liter Drops for Two-Dimensional Lab-on-Paper Applications. Lab Chip 2009, 9, 3066−3075. (14) Gao, L.; McCarthy, T. J. Contact Angle Hysteresis Explained. Langmuir 2006, 22, 6234−6237. (15) Furmidge, C. G. Studies at Phase Interfaces. I. The Sliding of Liquid Drops on Solid Surfaces and a Theory for Spray Retention. J. Colloid Sci. 1962, 17, 309−324. (16) Li, X.; Ma, X.; Lan, Z. Dynamic Behavior of the Water Droplet Impact on a Textured Hydrophobic/Superhydrophobic Surface: The Effect of the Remaining Liquid Film Arising on the Pillars’ Tops on the Contact Time. Langmuir 2010, 26, 4831−4838. (17) Patankar, N. A. On the Modeling of Hydrophobic Contact Angles on Rough Surfaces. Langmuir 2003, 19, 1249−1253. (18) Chibowski, E. Surface free energy of a solid from contact angle hysteresis. Adv. Colloid Interface Sci. 2003, 103, 149−172. E
DOI: 10.1021/acsami.7b15739 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
