Porous Polymer Films Templated by Marangoni Flow-Induced Water

May 21, 2009 - can be dependently controlled by tuning the humidity of the airflow. The ordered arrays of water droplets on the substrate are then uti...
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Porous Polymer Films Templated by Marangoni Flow-Induced Water Droplet Arrays Yangjun Cai and Bi-min Zhang Newby* Department of Chemical and Biomolecular Engineering, The University of Akron, Akron, Ohio 44325-3906 Received January 23, 2009 In this article, we report the development of a novel, simple, and cost-effective method for fabricating porous polymer films with controllable interpore distances, pore sizes, and arrangements using water droplets induced by Marangoni flow as templates. First, a spread-thin ethanol film on a partially water-wettable substrate is exposed to a humid airflow, facilitating the evaporation and recession of the ethanol film. Meanwhile, water in the airflow condenses on the ethanol film and accumulates near the receding contact line, which induces the formation of water fingers at the receding contact line and, finally, ordered arrays of water droplets after detachment. The formation of the hexagonal and square arrays of water droplets is due to the pinning and sliding of the water fingers on the silicone oxide (SiOx) and silicon (Si) substrates, respectively. By varying the thickness of the ethanol film spread on the Si substrate, the sliding velocity of water fingers can be tuned, subsequently leading to the fabrication of other arrangements. The interdroplet distance and droplet size can be dependently controlled by tuning the humidity of the airflow. The ordered arrays of water droplets on the substrate are then utilized to fabricate porous polymer films by dip-coating the substrate with a polystyrene solution. Films with hexagonal and square (and other arrangements) arrays of pores are fabricated on the silicon oxide (SiOx) and silicon (Si) substrates, respectively. The pore size can also be independently tuned by further condensation or evaporation of formed water droplets, leading to porous polymer films with both close- and non-close-packed arrays of pores. The ordered porous polymer films can be further used as templates for fabricating metal post patterns.

Introduction Porous polymer films with uniform pores receive vast attention because of their wide applications in membranes,1-3 template materials,4,5 immobilization of biomolecules,6-9 scaffolds for sensors10 and catalysts,11 and microelectronic and optical devices.12 Porous films are primarily fabricated by conventional top-down lithography approaches.13,14 Alternatively, nonlithography approaches based on self-assembled templates of block copolymers,15,16 colloidal particles,17 and emulsions,18,19 have been extensively utilized for fabricating porous polymer films. However, the templates used in these methods are sacrificed during the fabrication of porous films and, in most cases, not *Corresponding author. E-mail: [email protected]. (1) Xu, H.; Goedel, W. A. Angew. Chem., Int. Ed. 2003, 42, 4694. (2) Park, S. H.; Xia, Y. Adv. Mater. 1998, 10, 1045. (3) Yan, F.; Goedel, W. A. Adv. Mater. 2004, 16, 911. (4) Yabu, H.; Shimomura, M. Langmuir 2005, 21, 1709. (5) de Boer, B.; Stalmach, U.; Nijland, H.; Hadziioannou, G. Adv. Mater. 2000, 12, 1581. (6) Zhang, Y.; Wang, C. Adv. Mater. 2007, 19, 913–916. (7) Zhang, G.; Yan, X.; Hou, X.; Lu, G.; Yang, B.; Wu, L.; Shen, J. Langmuir 2003, 19, 9850. (8) Batra, D.; Vogt, S.; Laible, P. D.; Firestone, M. A. Langmuir 2005, 21, 10301. (9) Sunami, H.; Ito, E.; Tanaka, M.; Yamamoto, S.; Shimomura, M. Colloids Surf., A 2006, 284 + 285, 548. (10) Steiner, G.; Zimmerer, C.; Salzer, R. Langmuir 2006, 22, 4125. (11) Ha, J.-M.; Wolf, J. H.; Hillmyer, M. A.; Ward, M. D. J. Am. Chem. Soc. 2004, 126, 3382. (12) Wijnhoven, J. E. G. J.; Vos, W. L. Science 1998, 281, 802. (13) Campbell, M.; Sharp, D. N.; Harrison, M. T.; Denning, R. G.; Turberfield, A. J. Nature 2000, 404, 53. (14) Xia, Y.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 550. (15) Templin, M.; Franck, A.; Du Chesne, A.; Leist, H.; Zhang, Y.; Ulrich, R.; Schadler, V.; Wiesner, U. Science 1997, 278, 1795. (16) Hayakawa, T.; Horiuchi, S. Angew. Chem., Int. Ed. 2003, 42, 2285. (17) Li, J.; Zhang, Y. Chem. Mater. 2007, 19, 2581. (18) Imhof, A.; Pine, D. J. Nature 1997, 389, 948. (19) Ham, H. T.; Chung, I. J.; Choi, Y. S.; Lee, S. H.; Kim, S. O. J. Phys. Chem. B 2006, 110, 13959.

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easily prepared, removed, or both. One convenient and inexpensive template for fabricating porous films would be the use of ordered arrays of water droplets, which can be easily removed by simple evaporation. Ordered water droplet arrays can be produced by condensation of water on chemical patterns, which then are used as templates to fabricate a porous film by dip-coating in a polymer solution.7,20,21 This approach still requires soft lithography to pattern the substrate. Alternatively, ordered water droplet arrays are formed by direct condensation on a polymer solution, the phenomenon is known as “breath figures”.22-25 The breath figure method is simple, fast, and cost-effective, producing honeycombed macroporous polymer films. The pore sizes of the porous films (typically ranging from 0.2 to 10 μm) can be controlled by varying cast conditions and polymer properties. It must be noted, however, that the breath figure method has its own limitations. First, this method normally produces porous films with close-packed pores, which are not applicable when nonclose-packed patterns are preferred.26 Second, the pore size and interpore distance are sensitive to the properties of the polymers (e.g., structure and molecular weight), type of solvents, and processing environment,23,24 which make the pore size unpredictable. Third, because of the coalescence of water droplets, the preparation of large pore sizes (>10 μm) is limited. The larger pores are important for patterning biomolecules such as cells, (20) Braun, H. G.; Meyer, E. Thin Solid Films 1999, 345, 222. (21) Lu, G.; Li, W.; Yao, J.; Zhang, G.; Yang, B.; Shen, J. Adv. Mater. 2002, 14, 1049. (22) Sirringhaus, H.; Tessler, N.; Friend, R. H. Science 1998, 280, 1741. (23) Bunz, U. H. F. Adv. Mater. 2006, 18, 973. (24) Stenzel, M. H.; Barner-Kowollik, C.; Davis, T. P. J. Polym. Sci., Part A: Polym. Chem. 2006, 44, 2363. (25) Widawski, G.; Rawiso, M.; Francois, B. Nature 1994, 369, 387. (26) Ren, Z.; Li, X.; Zhang, J.; Li, W.; Zhang, X.; Yang, B. Langmuir 2007, 23, 8272.

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which typically have a size ranging from 10 to 50 μm.27,28 Finally, the breath figure method produces primary hexagonal patterns, whereas square patterns are observed only occasionally.29 The square patterns are preferred in the semiconductor industry’s integrated circuit design, software, and fabrication process.30 Herein, we report a convenient, nonlithography technique for fabricating porous polystyrene (PS) films using water droplet arrays as templates. The water droplet arrays are created through the combination of Marangoni flow between an evaporating ethanol film and a condensed water layer and the fingering instability of the water layer. This technique could address some limitations of the breath figure method. First, by controlling the humidity of the airflow during the Marangoni flow, the interdroplet (or interpore) distance and the droplet (or pore) size can be controlled dependently. Second, by further water condensation on the droplets, or water evaporation of the droplets, the droplet (pore) size can also be controlled independently, which makes the pore size predictable and allows the fabrication of not only closepacked but also non-close-packed porous films. This technique is suitable for any water-immiscible polymers. The pore size and interpore distance, which are both predetermined before the formation of porous films, are independent of the polymer used. Porous films with both hexagonal and square pore arrays can be fabricated on substrates with different wettabilities. In addition, array arrangements other than hexagonal and square are possible.

Experimental Section Materials. Test silicon wafers of P(100) were purchased from Silicon Quest International. PS (Mw = 60 000 g/mol) was purchased from Polymer Source. Hydrofluoric acid (48-50%) was the product of Fisher Scientific. HPLC-grade ethanol and chloroform were the products of Fluka. Deionized (DI) water was purified in house and had a conductivity of ∼0.1 S or less. Preparation of Substrates. Silicon wafers (typically 1  1 cm2) with a native silicon oxide (SiOx) layer were sonicated first in a 1/1 (v/v) mixture of DI water and ethanol and then in a 1/1 (v/v) mixture of toluene and acetone for 5 min each. The samples were then rinsed with acetone, ethanol, and copious amounts of DI water and dried with a stream of N2 (SiOx substrates). For the preperation of hydrogen-terminated silicon substrates (Si substrate), the SiOx substrates were further treated with the piranha solution (70/30 (v/v) 98% concentrated H2SO4 and 30% H2O2) at 80 C for 1 h. After being rinsed with a copious amount of DI water, the substrates were treated in a hydrofluoric acid (HF) solution (1/20 HF/H2O) for 2 min and rinsed once with water and then dried with a stream of N2 (Si substrates). The water contact angles of the SiOx and Si substrates were measured by the sessile drop technique using a Rame-Hart contact angle goniometer (model 100-00) under ambient conditions (1 atm, ∼24 C). Advancing (θA), receding (θR), and static (θ0) contact angles were measured on two randomly chosen spots of each sample, and a total of three samples were used. θA, θR, and θ0 are 41.2 ( 0.6, 21.9 ( 0.7, and 37.1 ( 0.4 for the SiOx substrate and 81.7 ( 1.3, 35.1 ( 1.9, and 76.3 ( 0.6 for the Si substrate, respectively.

Formation of Water Droplet Arrays and Porous Polystyrene Films. To reduce the evaporation rate of the formed

water droplets in the subsequent step, ∼0.1 vol % of ethylene glycol (EG) was added to ethanol in advance. To achieve a uniform spreading of ethanol and a straight contact line (CL), 1 μL of ethanol containing EG was carefully dispensed from a (27) Ostuni, E.; Chen, C. S.; Ingber, D. E.; Whitesides, G. M. Langmuir 2001, 17, 2828. (28) Rettig, J. R.; Folch, A. Anal. Chem. 2005, 77, 5628. (29) Li, J.; Peng, J.; Huang, W.; Wu, Y.; Fu, J.; Yang, C.; Xue, L.; Han, Y. Langmuir 2005, 21, 2017. (30) Tang, C.; Lennon, E. M.; Fredrickson, G. H.; Kramer, E. J.; Hawker, C. J. Science 2008, 322, 429.

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Article micropipet into a line in the middle of the substrate, which then spread horizontally outward toward the edge of the substrate at room temperature (∼24 C). As the spreading CL almost reached the edge of the substrate, a carrier airflow was flown over a DI water bath and blown toward the CL of the spread ethanol film with an angle of ∼30 with respect to the substrate. The humid air flowed through a tube (cross-sectional area: ∼0.25  2.0 cm2), and its flow rate (∼2.0 L/min) was controlled by a needle valve and measured with a flow meter. The relative humidity (RH) of the airflow, which was controlled by the amount of DI water in the water bath, was monitored with a hygrometer. When the ethanol film evaporated and its CL receded, the water in the airflow condensed and formed ordered arrays of water droplets behind the receding CL. After the ethanol film was completely dried, the substrate was immediately mounted on a cold stage (∼10 C) and maintained for ∼30 s. Then, the substrate was dipped in a PS solution in chloroform (5-75 mg/mL) and withdrawn quickly. Upon complete evaporation of chloroform and water, a porous PS film formed on the substrate. The formation process of the water droplet arrays near the CL was videotaped in real time using an optical microscope video system. Control of Pore Arrangements. To control the arrangements of pores in the porous films, we varied the volume of ethanol (0.7 to 2.3 μL) spread on the 1  1 cm2 Si substrates. The receding CL during the formation of water droplets was monitored and videotaped, and we measured its receding velocity by playing back the video tape and using Image J 1.41 software. Control of Pore Sizes. To control the size of the pores independently, we further exposed the substrate with formed water droplet arrays on the cold stage (∼10 C) to a gentle humid airflow (flow rate ∼0.2 LPM) with a high (∼44%) or low (∼36%) RH, which induced a growth or shrinkage of water droplets because of further condensation or evaporation, respectively. Upon dip-coating the substrate containing water droplet arrays, a porous film with a certain size of pores formed. The real-time condensation and evaporation processes were also videotaped. Fabrication of Aluminum Post Arrays. To fabricate aluminum posts, we washed the porous film with ethanol to remove the residual EG in the pore, and then a layer of aluminum (∼55 nm) was vapor-phase-deposited on the porous film. After the PS film was removed by annealing at 400 C for 2 h and sonicating in toluene for 20 min, aluminum post arrays were left on the substrate. Characterization. The porous polymer films and aluminum post arrays were examined by an optical microscope (Olympus IX70) fitted with appropriate filters and a Sony CCD camera, and images were taken using the Dazzle media and its software. The aluminum post arrays were also characterized by a tapping-mode atomic force microscopy (AFM, Veeco MultiMode).

Results and Discussion Fabrication of Porous Polymer Film. Figure 1 outlines the schematic procedure of fabricating porous polymer films. First, a thin film of ethanol is spread on the substrate and exposed to a humid airflow (Figure 1a). As the ethanol film evaporates and recedes along the direction of the airflow, water condenses from the airflow and forms instability fingers that detach to form ordered arrays of water droplets behind the three-phase CL (top view of Figure 1a). We utilize the ordered arrays of water droplets as templates for fabricating porous polymer films by dipping the substrate in a PS solution in chloroform (Figure 1b).7,20,21 After withdrawing, water droplets are covered with a film of PS solution (Figure 1c). Upon evaporation of chloroform, a PS film forms, encircling the water droplets. As water subsequently evaporates, arrays of circular pores in the polymer film result (Figure 1d). DOI: 10.1021/la901335w

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Figure 1. Schematic illustration of the procedure for fabricating a porous polystyrene (PS) film using the Marangoni flow-induced arrays of water droplets as templates. (a) Details of the formation of the water droplets resulting from the combined evaporation of ethanol and condensation of water, followed by the Marangoni flow from the ethanol phase to the water phase. A maximum evaporation of ethanol and hence a maximum condensation of water occur near the contact line; a surface tension gradient (arrow in the boxed scheme) and hence a Marangoni flow develops and drives the condensed water toward the contact line to form a water rim. The instability of this water rim initiates and develops into water fingers, which finally detach from the contact line to form water droplets on the substrate as the contact line recedes. (b) The substrate containing the droplet arrays is then dip-coated in a PS/chloroform solution and quickly withdrawn. (c,d) Upon the evaporation of chloroform and water, a porous PS film forms on the substrate.

Figure 2. Optical microscopic (OM) images of water droplet arrays induced by Marangoni flow and the corresponding porous PS films by dip-coating with a PS solution in chloroform (40 mg/mL). (a) Hexagonal arrays of water droplets on the SiOx substrate of exposing a spread 1 μL/cm2 ethanol film to an airflow with ∼45% RH and (b) the corresponding porous PS film. (c) Square arrays of water droplets on the Si substrate of exposing a spread 1 μL/cm2 ethanol film to an airflow with ∼30% RH, and (d) the corresponding porous PS film. Insets in parts a and c show the associated fast Fourier transforms (FFTs) of the water droplet arrays. (e) Representative AFM topographic image (50  50 μm2, z scale: 0-2000 nm) of a porous PS film and (f) sectional profile (z: -1000 to 1000 nm). 7640 DOI: 10.1021/la901335w

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Figure 2 shows the optical microscopy (OM) images of the ordered arrays of water droplets on both substrates (SiOx and Si) and their corresponding porous PS films after dip-coating. The fast Fourier transform (FFT) images (insets in Figure 2a,b) indicate the formation of hexagonal and square arrays of water droplets on the SiOx and Si substrates, respectively. Because the pores in the porous film are replicas of the water droplets,20 the corresponding pores have identical periodicity (L = ∼55.5 and ∼49.4 μm for hexagonal and square arrays, respectively) and a hexagonal or square distribution. In addition, the pore size matches the size of the water droplets immediately prior to film formation.20 Figure 2 shows that the diameters (D) of the resulting pores (20.2 ( 0.5 and 16.6 ( 1.3 μm for hexagonal and square arrays, respectively) agree well with those of the initial water droplets (21.2 ( 0.6 and 17.2 ( 0.7 μm for hexagonal and square arrays, respectively). The slight reduction in diameter is mainly due to the evaporation of water droplets prior to (i.e., transferring substrate) and during dip-coating. In an attempt to reduce water evaporation and subsequent droplet shrinkage, less-volatile EG is added to the ethanol (0.1 vol %). During the Marangoni flow process, the EG is transferred into the water droplets, reducing the evaporation of water.31 Moreover, immediately after the formation of the water droplets, the substrate is quickly mounted onto a cold stage with a temperature close to the dew point (∼10 C) of the ambient humidity (∼40% RH). The entire substrate and the water droplets on it are cooled down to allow the droplets to reach the equilibrium state (i.e., no evaporation or condensation). The addition of EG and the cooling process also allow the water droplets to remain stable during dip-coating. Therefore, the resulting pore size is almost the same as the size of the water droplets (Figure 2). It is observed that without the addition of EG and the cooling process, the resulting pore size is greatly reduced, or sometimes no pore even forms in the PS film because of complete evaporation of the water droplets before the formation of the polymer film. The AFM topographic image (Figure 2e) and the crosssectional profile (Figure 2f) show that the film thickness in between the pores varies with the location. In general, the film thickness at the edge of the pores is largest and decreases progressively toward the middle of two pores. The concave shape profile of the thickness in between two pores could simply be the result of transporting the PS/chloroform solution on top of the water droplet to the surrounding of the droplet as the solution evaporates. The cross-sectional profile also reveals that the bottom surface of the pore is flat. Formation Mechanism of Hexagonal and Square Water Droplet Arrays. The formation of ordered water droplets behind the receding three-phase CL is due to the combination of ethanol evaporation and water condensation, the subsequent Marangoni flow between the ethanol phase and the water phase, and the detachment of fingering instability of the water layer accumulated near the CL (Figure 1a).32 Exposing the evaporative ethanol film to humid airflow results in a reduced ethanol film temperature. When the temperature of the ethanol film is lower than the water dew point of the humid airflow applied over the film, water in the airflow condenses on the ethanol film. A maximum evaporation normally occurs at the meniscus near the three-phase CL because of its maximum curvature, which induces a maximum temperature reduction (Figure 1a).33,34 Therefore, more water condenses (31) Rusdi, M.; Moroi, Y.; Nakahara, H.; Shibata, O. Langmuir 2005, 21, 7308. (32) Cai, Y.; Zhang Newby, B.-m. J. Am. Chem. Soc. 2008, 130, 6076. (33) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (34) Hohmann, C.; Stephan, P. Exp. Therm. Fluid Sci. 2002, 26, 157.

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near the CL as compared with the bulk of the relatively flat ethanol film. Because of the large difference in surface tensions between ethanol and water (22.4 and 72.9 mN/m at 20 C),35 a surface tension gradient is generated between the bulk ethanol film and the CL, leading to a horizontal Marangoni flow from the lower (e.g., bulk) to higher (e.g., CL) surface tension regions. The thermocapillary flow36,37 also occurs because of an increased surface tension with decreasing temperature near the CL. However, the surface tension difference induced by the temperature difference (dγ/dT ≈ -0.086 and -0.138 mN/m 3 K for ethanol and water, respectively) is much smaller when compared with that induced by concentration difference. Therefore, in this case, the Marangoni flow is mainly attributed to the surface tension difference between ethanol and water, which is responsible for the formation of the ordered water droplet arrays. This is further confirmed by three separate experiments, where an ethanol film is exposed to a dry airflow and a thin water film is exposed to a dry and humid airflow. For all cases, no water droplet arrays result (Figure S1 in the Supporting Information). The Marangoni flow, for the case of a spread ethanol film exposed to a humid airflow, carries ethanol mixed with the condensed water on the ethanol film toward the CL. As ethanol evaporates first, because of its higher volatility, a thin rim of liquid, mostly water, accumulates near the CL (Figure 1a). The accumulated liquid rim, under the influence of the Rayleigh instability and Marangoni instability, initiates and forms water fingers at the CL.32,38-41 When the fingers continue to grow as the CL recedes, a second Rayleigh instability in the direction of the water finger occurs,42,43 which detaches the fingers from the CL to form arrays of water droplets. Depending on the wettabilities of the substrates, hexagonal and square arrays of water droplets form on the SiOx and Si substrates, respectively. It should be noted that disordered water droplet arrays and variations in droplet sizes are observed occasionally (e.g., Figure S2 in the Supporting Information). This may be due to irregular distributions of the fingers (unequal interfinger distance, droplet size, or both) along the CL, which are induced by the nonuniform evaporation rate, thickness, or both of ethanol film along the CL or the curved receding CL. Hexagonally arranged water droplets formed from Marangoni flow on the SiOx substrate are likely due to the alternative detachment of the neighboring water fingers from the CL.32 Figure 3a,d and Video S1 in the Supporting Information show the formation process of the hexagonal water droplet arrays on the SiOx substrate. C marked in Figure 3a indicates the initiation of a new water finger, which occurs almost immediately after the detachment of the previous droplet (A) and before the detachment of the neighboring finger (B). Because the regions surrounding the fingers on the CL are thinner than the fingers themselves, the water flows from the thinner regions into the thicker water fingers (curved arrows in Figure 3a),36 leading to the growth of fingers A and B. As the CL recedes, finger B, and subsequently (35) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997; p 36. (36) Gonuguntla, M.; Sharma, A. Langmuir 2004, 20, 3456. (37) Hu, H.; Larson, R. G. J. Phys. Chem. B 2006, 110, 7090. (38) Maillard, M.; Motte, L.; Pileni, M.-P. Adv. Mater. 2001, 13, 200. (39) Huang, J.; Kim, F.; Tao, A. R.; Connor, S.; Yang, P. Nat. Mater. 2005, 4, 896. (40) Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P. Nature 1990, 346, 824. (41) Lyushnin, A. V.; Golovin, A. A.; Pismen, L. M. Phys. Rev. E 2002, 65, 021602/1. (42) Karthaus, O.; Grasjo, L.; Maruyama, N.; Shimomura, M. Chaos 1999, 9, 308. (43) Carvalho, A. J. F.; Pereira-da-Silva, M. A.; Faria, R. M. Eur. Phys. J. E 2006, 20, 309.

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Figure 3. Video sequence of the formation process of (a-d) the hexagonal and (e-h) the square arrays of water droplets on the SiOx and Si substrates, respectively. C marked in parts a-d indicates the initiation, growth, and detachment of a water finger and the relaxation of the detached finger into a circular water droplet, respectively. The curved arrows in parts a and b indicate the local flow of water near the CL. The vertical dashed line across parts a-d is a guide to show that water finger/droplet C maintains its original location. The average receding velocity of the CL (a-d) is ∼1580 μm/s. (e) The formation of a “line” of water fingers (dotted line) on the CL following the previous “line” of detached droplets (dashed line). The longer and shorter arrows indicate the receding direction and the potential sliding direction of the water finger, respectively. (f) Detachment of the water fingers in part e into a “line” of water droplets and the formation of a new “line” of water fingers on the CL, with one circled to show the details. (g) Repeation behaviors of part e. (h) Variation of shape angle (ψ) with the receding velocity of the CL. ds in part e is the sliding distance of the water fingers during their growth. λ and d are the distances between two neighboring “lines” of water droplets parallel and perpendicular to the CL. The resulting array shapes are quantified with the shape angle (ψ) sketched in parts c and g. L is defined as the interdroplet distance. It should be worth noting that interference fringes are observed near the receding CL, which are caused by the thickness difference near the receding CL (See the Supporting Information.)

finger C, detach from the CL to form droplets (Figure 3b,c). To quantify the arrangement, the distances between two neighboring “lines” of the detached droplets parallel and perpendicular to the CL are defined as d and λ, respectively (Figure 3d). As a result, A and B are on the same “line”, which is almost parallel to the CL, whereas C is on the subsequent “line”. It is observed that the subsequently detached water droplet, C, has a shift (λ ≈ 100 μm) along the CL, located in the middle of two preceding droplets DOI: 10.1021/la901335w

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(A and B). By comparing the locations of finger/droplet C (dashed line across Figure 3a,d), it is also observed that finger/droplet C maintains its original location, which is likely caused by the pinning of the water finger/droplet on the SiOx substrate. The distance between the two proceeding “lines” of droplets, that is, droplet C and droplets A and B, along the receding direction of the CL (i.e., perpendicular to the CL) is √ defined as d (∼57 μm), which results in a d/λ ratio of 0.57 (∼1/ 3) and a shape angle (ψ =—ACB = 2 cot-1(d/λ)) of ∼120 (Figure 3c,d). These values are indicative of a hexagonal arrangement of water droplets. It is noteworthy that the water fingers are tilted to the receding CL instead of perpendicular to the CL (Figure 3a,d).39 The tilted fingers have also been observed at the receding CL of an evaporating polymer solution, which suggests that fingering is induced by the combination of Rayleigh instability and local concentration gradient at the CL.42,43 Therefore, the tilted fingers in this case confirm the existence of the Marangoni flow induced by the concentration gradient of ethanol/water. The occurrence of the tilted fingers with an elongated shape also indicates that the CL of the water fingers can pin on the SiOx substrate during growth, which otherwise would relax to be perpendicular to the CL. After detachment, the elongated water droplet relaxes into a spherical capped droplet to minimize its total surface area/energy (Figure 3d).44,45 Consequently, circular pores are resulted in the porous films. Figure 3e-h and Video S2 in the Supporting Information show the formation process of the square water droplet arrays on the Si substrate. Similarly, a new “line” of water fingers (dotted line in Figure 3e) forms immediately after the detachment of the preceding “line” of fingers (dashed line in Figure 3e) and has a shift (λ) parallel to the CL from the preceding “line”. Different from the SiOx substrate, in which the water fingers/droplets maintain their original locations, this new “line” of water fingers slides a distance (ds) along the receding direction on the Si substrate (left dashed line in Figure 3f). As a result, the interdroplet distance along the receding direction increases, resulting in a d/λ ratio of ∼1 (d ≈ 72 μm and λ ≈ 70 μm) and ψ of ∼90. Therefore, the resulting water droplets appear to have a square arrangement. This square arrangement can be regarded as a stretched hexagon, which has a larger d/λ ratio than the perfect hexagon (sketches in Figure 3c,g). It is observed that one particular droplet (circled in Figure 3g) still remains on the location of the original finger (circled in Figure 3f) after detachment instead of sliding along the receding direction like other droplets detached from the same “line” (left dashed line in Figure 3g). One possible reason could be contamination or defects on the substrate surface preventing the finger from sliding along the receding direction of the CL. Therefore, a clean substrate is necessary to obtain ordered water droplet arrays. In addition, most water fingers are almost perpendicular to the CL (Figure 3e-h), which results from sliding of the fingers with the CL during their growth. We believe that local concentration gradient within the liquid exists near the CL on the Si substrate because some fingers are slightly tilted to the CL (Figure 3e,f). Therefore, the pinning and sliding of the water fingers are responsible for the hexagonal and square arrangements of water droplets on the SiOx and the Si substrates, respectively. The sliding of water fingers on the Si substrate could be the result of unbalanced forces acting on each predetached finger. The sliding occurs before detachment (i.e., during growth) because the detached droplets are “pinned” on the Si substrate under the (44) Andrieu, C.; Beysens, D. A.; Nikolayev, V. S.; Pomeau, Y. J. Fluid Mech. 2002, 453, 427. (45) Narhe, R.; Beysens, D.; Nikolayev, V. S. Int. J. Thermophys. 2005, 26, 1743.

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Figure 4. Schematic illustration of the forces exerted on: (a) a stabilized water droplet after detachment. θA and θR are the advancing and receding contact angles, respectively, that vary with the force from the airflow (Fflow); (b) a predetached water finger.

airflow (i.e., the hydrodynamic force (Fflow)46 from airflow is balanced by the hysteresis force (FH)47 of water experienced on the substrate, Figure 4a). Before detachment, forces experienced by the water finger mainly include the unbalanced Young’s force (FY),48 Fflow, the viscous force (Fv),48 and the Marangoni force (FMF)49 (Figure 4b). Fflow and FMF are independent of the substrate properties and Fv is much smaller than FY, and thus the overall force acting on the water finger on the SiOx and on the Si substrate differs mainly in FY. By neglecting the effect of EG transferred into the finger, we can estimate FY for the water finger per unit length of the three-phase line48,50 from FY = γH2O + γS/H2O - γS = γH2O(1 - cos θ0), where γH2O, γS/H2O, and γS are interfacial tensions of water/air, substrate/water, and substrate/ air and θ0 is the static water contact angle on the substrate. FY for the water finger on the Si substrate (∼55.6 mN/m) is much greater than that on the SiOx substrate (∼15.4 mN/m). Therefore, water fingers slide on the Si substrate but pin on the SiOx substrate. Control of the Arrangements of Water Droplet Arrays. In Figure 3h, d (∼72 μm) and λ (∼70 μm) at the left region of the image are different from those at the right region (d ≈ 84 μm and λ ≈ 64 μm), resulting in an increase in the d/λ ratio from ∼1 to ∼1.31 (i.e., ψ from ∼90 to ∼75). The corresponding receding velocity of the CL (νCL) increases from ∼1710 μm/s at the right region to ∼2050 μm/s at the left region (Video S2 in the Supporting Information). On the contrary, when νCL decreases from ∼2120 to ∼840 μm/s, the d/λ ratio decreases from 1.31 to 0.58 (i.e., ψ from ∼75 to ∼120) (Figure S3 and Video S3 in the Supporting Information). This indicates that the arrangement of water droplets varies with νCL because the predetached fingers appear to slide more with a greater νCL. The change in νCL is likely caused by a variation of the ethanol layer thickness at the region. When receding of the ethanol layer is mainly due to evaporation, a thicker ethanol film will result in a lower receding velocity (vCL  (1/hethanol-layer)).51 As a result, it is possible to control the arrangements of the water droplets by simply varying the thickness of the ethanol film spread on the Si substrate with all other experimental conditions kept the same. Figure 5a shows that νCL decreases with an increasing volume of ethanol spread on the Si substrate (1  1 cm2) (i.e., an increasing thickness of ethanol film). The d/λ ratio decreases or ψ increases with decreasing νCL (Figure 5b). Therefore, water droplet arrays and porous films with different arrangements can be fabricated (Figure 5c-j). (46) Basu, S.; Nandakumar, K.; Masliyah, J. H. J. Colloid Interface Sci. 1997, 190, 253. (47) Daniel, S.; Chaudhury, M. K. Langmuir 2002, 18, 3404. (48) Carre, A.; Eustache, F. Langmuir 2000, 16, 2936. (49) Nikolov, A. D.; Wasan, D. T.; Chengara, A.; Koczo, K.; Policello, G. A.; Kolossvary, I. Adv. Colloid Interface Sci. 2002, 96, 325. (50) Redon, C.; Brzoska, J. B.; Brochard-Wyart, F. Macromolecules 1994, 27, 468. (51) Berteloot, G.; Pham, C. T.; Daerr, A.; Lequeux, F.; Limat, L. Europhys. Lett. 2008, 83, 14003/1.

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Figure 5. (a) CL receding velocity (vCL) is determined by the volume (V) of ethanol spread on a 1  1 cm2 Si substrate. (b) Experimentally obtained dependency of the shape angle (ψ) and the d/λ ratio (in parentheses) of the water droplet arrays on vCL. (c-f) Representing still video images of the receding CLs with a spread ethanol layer thickness of 2.0, 1.5, 1.0, and 0.7 μL/cm2, respectively, exposed to an airflow with an RH of ∼40% and formed water droplet arrays having different ψ values. (g-j) Representative OM images of the porous films with the corresponding shape angle in parts c-f, respectively.

Other parameters, such as airflow rate, can be adjusted to vary the receding velocity of the ethanol layer, however the resulting arrays are either less controllable or less ordered, and hence no further investigation was followed in this study. It is noticed that water droplet arrays or pores in porous films with a shape angle of ψ have the same arrangement as those with a shape angle of (180 - ψ). For example, when the receding velocity increases to ∼3000 μm/s, ψ decreases to 60, which also results in a hexagonal arrangement (Figure 5e,f). Additionally, it should be noted that regardless of the ethanol film thickness on the SiOx substrate, the resulting water droplet arrays are hexagonal because the water fingers always pin on the SiOx substrate. A thinner ethanol film on the SiOx substrate only results in a smaller λ and smaller droplet size because less ethanol evaporated induces less water condensation. Control of Pore Size and Interpore Distance. Figure 6 shows that L of both hexagonal and square arrays increases with the RH of the airflow. The interdroplet distance (L) of the water droplet arrays is determined by the characteristic wavelength (λ) of the Marangoni instability of the condensed water layer at the CL (L = λ/sin(ψ/2)). λ depends on the dimensionless Marangoni number (Ma),38,52 that is, λ = (2πh)/(Ma/8)1/2, where Ma = [(Δγ/ l)h2]/(Fνκ), h is the liquid thickness, Δγ/l is the surface tension gradient, l is the horizontal distance along which surface tension varies, and F, ν, and κ are the density, kinematic viscosity, and thermal diffusivity, respectively, of the liquid (i.e., mixture of water and ethanol). When the airflow with a lower RH is applied, less water condenses near the CL, leading to a smaller L and hence a smaller λ. The calculated values of λ are in a good agreement with the experimental values. (See the Supporting Information.) (52) Smith, M. K.; Davis, S. H. J. Fluid Mech. 1983, 132, 119.

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Comparison of L on both substrates reveals that at the same RH, L on the Si substrate is ∼1.5 times (or ∼1.2 times for λ) that on the SiOx substrate. The liquid near the receding CL is the mixture of water and ethanol. Because of the wettability difference between the SiOx and Si substrates, the meniscus curvature on the Si substrate is higher than that on the SiOx substrate, resulting in more water condensed (i.e., a greater h) on the Si substrate.53 The resulting pore diameter (D) also increases with RH of the airflow (Figure 6). In this case, the resulting D/L ratios are close to 0.33, indicating that L and D can be controlled dependently by varying RH of the airflow. The pore size is determined by the water droplet size immediately before dip-coating. The water droplet size depends on the size of the droplets initially detached and the subsequent evaporation rate prior to dip-coating. Although the addition of EG and the cooling process after the formation of the water droplets can successfully retain the size of the water droplets during the dip-coating process, evaporation of water inevitably occurs prior to the cooling process (i.e., during the Marangoni flow and transferring the substrate onto the cold stage), which results in a shrinkage of water droplets. Under the fixed ambient condition (∼24 C and ∼40% RH), the size reduction is almost the same for different water droplets formed under different RHs. Therefore, the resulting water droplet size still increases with the increasing size of the water fingers initially detached, which depends on the overall volume (Vo) of the condensed water and the number (nd, and nd = w/λ with w and λ being the length of the CL and interfinger distance, respectively) of the detached water fingers on the CL for each “line” (i.e., Vd = Vo/nd = Voλ/w). Both Vo and λ increase with the increase in RH, (53) Starov, V.; Sefiane, K. Colloids Surf., A 2009, 333, 170.

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Figure 6. Interpore distance (L: 0 and 9 symbolize hexagonal and square arrays, respectively) and diameter (D: O for hexagonal arrays) of the pores in the porous PS films are tuned by the relative humidity (RH) of the airflow applied during the Marangoni flow. Four typical OM images of porous PS films with hexagonal (upper two images) and square (bottom two images) arrays of pores formed on the SiOx and Si substrates, respectively, are presented. The upper right corner of each image shows the associated RH value of the airflow applied.

whereas w remains constant. Therefore, the initial and resulting water droplet size increases with RH of the airflow applied. In addition, it is observed that as L or λ increases, the water droplet arrays or pore arrays in the porous films retain their original arrangements (Figure 6). This may be due to the fact that the initial size of the water droplets increases proportionally with L or λ. In the case of hexagonal arrays on the SiOx substrate, d increases linearly √ with λ, and the water droplet arrays have the same d/λ (∼1/ 3) ratio and retain the hexagonal arrangement for all λ values. In the case of square arrays on the Si substrate, d correlates with the sliding distance, which is determined by the forces acting on the water finger. These forces also increase with the size of the finger (i.e., D). As a result, as D increases with the increase in λ, the sliding distance increases correspondingly. Therefore, the water droplet arrays on the Si substrate are also likely to have the same d/λ ratios of ∼1 (i.e., square arrangements) for all λ values if the volume (i.e., thickness) of ethanol spread on the substrates is fixed (∼1 μL/cm2). The pore size can also be independently tuned after the formation of water droplets by further condensation or evaporation of water to or from the droplets. When the substrate on the cold stage (∼10 C) is exposed to a gentle airflow with a RH higher (e.g., ∼44%) than that of the ambient air (∼40%), water preferentially condenses on the existing water droplets, resulting in a growth of water droplets (Figure 7a-c,e (region I)). No visible droplets nucleate in between these existing water droplets. This preferential condensation is likely due to the curvature-dependent equilibrium vapor pressure of water 7644 DOI: 10.1021/la901335w

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Figure 7. A representative set shows that the diameter of pores in the porous PS films (L ≈ 22.5 μm) can be tuned by further condensation or evaporation of water droplets on the SiOx substrate. (a-d) Time sequence of the formation of the water droplet arrays increasing (a-c) and decreasing (c-d) in size by exposing the water droplet arrays to a humid airflow with 44 and 36% RH for further condensation and evaporation of water, respectively. (e) Diameter (D) of water droplets during the condensation (region I) and evaporation (region II) processes. The insets show OM images of three typical porous PS films with a constant L of ∼22.5 μm and D of ∼11.8, ∼7.4, and ∼1.0 μm, respectively (scale bar: 20 μm).

droplets. According to Laplace and Kelvin equations,54 the equilibrium vapor pressure of a water droplet is proportional to 1/r (r is the radius of the water droplet). Therefore, the vapor pressure for the newly nucleated droplets on the substrate is much higher than that of the existing water droplets (r > 2.5 μm in this case). When the humid airflow has a water vapor pressure in between the equilibrium vapor pressures of the existing large water droplets and the nucleated small droplets, water from the humid airflow preferentially condenses on the existing droplets. The maximum droplet size that can be obtained by further condensation is the size immediately prior to droplet coalescence, leading to close-packed water droplet arrays (circled in Figure 7c). Therefore, porous films with close-packed pores can be fabricated (Figure S4 in the Supporting Information). Conversely, when a low-humidity airflow (e.g., ∼36% RH) is applied, water droplets shrink because of evaporation (Figure 7c-d,e (region II)). Once the droplets reach a certain desired size, the airflow is removed and hence, again, the water droplets reach the equilibrium state. After dip-coating the substrate containing water droplets having a desired size, a porous PS film having a desired pore size could be fabricated. The insets in Figure 7e show porous films with identical L but different D values. Similarly, the porous film with square pore arrays having (54) Butt, H. J.; Graf, K.; Kappl, M. Physics and Chemistry of Interface; 2nd ed.; Wiley-VCH: Weinheim, Germany, 2006; pp 16-25.

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the polymer films, which are revealed by the cross-sectional profile of the porous film (Figure 2f). Therefore, the resulting shallow aluminum cylindrical posts have a uniform thickness (∼55 nm) and rest directly on the substrate (Figure 8c,d). When porous films with square arrays and other arrangements of pores are used as templates, corresponding post patterns are fabricated (Figure 8e,f). These micrometer-sized arrays of metal posts’ D/L ratios can be readily tuned for different applications. Clearly, this method could be easily extended to other metals, metal oxides, or both, including gold patterns for cell patterning. The porous films can also be utilized as masters to fabricate PDMS stamps, which can be used for soft-lithography-based applications.

Conclusions

Figure 8. OM images of (a) a porous PS film with a deposited aluminum film and (b) the corresponding arrays of shallow aluminum posts after removing the PS film and the aluminum film on it. (c) AFM topographic image (100  100 μm2, z scale: 0-120 nm) of the aluminum posts in part b. (d) Sectional profile (-60 to 60 nm) as indicated by the dashed line in part c. (e,f) Aluminum post arrays with a shape angle (ψ) of ∼90 (i.e., square) and ∼100, respectively.

the same L but different D values can be generated by further condensation and evaporation of water droplets (Figure S5 in the Supporting Information). Applications of Porous Polymer Film. The porous PS films fabricated by this nonlithographic technique can be utilized as pattern masks for fabricating metal patterns by depositing metal layer on the films.5,55-57 Figure 8a shows an optical microscopy image of a thin layer (∼55 nm) of vapor-deposited aluminum on a porous PS film. By thermally decomposing the PS film and removing the aluminum layer on it, aluminum in the pores remains on the substrate, resulting in ordered arrays of aluminum posts (Figure 8b). The L and D of the aluminum posts are ∼22.5 and ∼13.0 μm, respectively, which correspond well to the pores of the original porous PS film. Porous films from breath figures have been utilized as templates to fabricate bowl-like metal dots resulting from the spherical dimples in the film.5 In the Marangoni flow-induced approach, the pores are all the way through (55) Haupt, M.; Miller, S.; Sauer, R.; Thonke, K.; Mourran, A.; Moeller, M. J. Appl. Phys. 2004, 96, 3065. (56) Yabu, H.; Shimomura, M. Langmuir 2006, 22, 4992. (57) Yabu, H.; Hirai, Y.; Shimomura, M. Langmuir 2006, 22, 9760.

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In conclusion, we have developed a facile, fast, and costeffective technique for fabricating porous polymer films over a large area. It can be performed in a common laboratory without sophisticated instruments. It is different from the breath figure method; not only hexagonal arrays but also square arrays and other arrangements of pores in the films can be fabricated by varying the substrate wettability, the receding velocity of the CL and the thickness of the spread ethanol film. The interpore distance (L) and pore size (D) can be dependently controlled by tuning the humidity of the airflow during the formation process of the water droplet arrays. Moreover, the pore sizes can be readily tuned by further water condensation or evaporation, leading to porous polymer films with pore arrays having different D/L ratios. Because the interdroplet distance and droplet size are predetermined before dip-coating the polymer films, the resulting interpore distance and pore size will not vary with the properties of the polymer used, allowing the fabrication of the porous films with predictable interpore distance and pore size. This approach opens a novel and simple route to fabricate highly ordered porous structures and meanwhile greatly broadens the diversity of the porous structures, which can be used for lithography masks, biomolecular patterning, and fabrication of metal or metal oxide patterns. Acknowledgment. We acknowledge Mr. Ruofeng Wang and Dr. Edward A. Evans for assisting with vapor deposition of aluminum. Supporting Information Available: No droplet formation without Marangoni flow, disordered droplet arrays, droplet array variations on the Si substrate, estimation of inter instability finger distance, and independent control of pore size. This material is available free of charge via the Internet at http://pubs.acs.org.

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