Mechanism for Stripe Pattern Formation on Hydrophilic Surfaces by

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Mechanism for Stripe Pattern Formation on Hydrophilic Surfaces by Using Convective Self-Assembly Satoshi Watanabe, Koji Inukai, Shunsuke Mizuta, and Minoru T. Miyahara* Department of Chemical Engineering, Kyoto University, Katsura, Nishikyo, Kyoto 615-8510, Japan Received January 24, 2009. Revised Manuscript Received April 15, 2009 We have studied the formation of stripe patterned films of ordered particle arrays on completely solvophilic substrates by using a self-organization technique. In this method, a substrate immersed in a suspension is withdrawn vertically at a controlled temperature. We have also systematically examined the effects of several experimental parameters. Well-defined stripes spontaneously form at the air-solvent-substrate contact line because of a very dilute suspension in a quasi-static process. The stripe width depends on particle concentration, withdrawal rate, and surface tension, while the stripe spacing depends on the thickness of stripes, surface tension, and type of substrate. A stripe width and the adjacent spacing show a clear correlation, strongly indicating the synchronized formation of a stripe and the next spacing. The evaporation rate does not affect stripe width and spacing but determines the growth rate of stripe patterned films. Based on these results, we propose a new mechanism for stripe formation, which is neither a stick-slip motion of the contact line nor dewetting but a negative feedback of particle concentration caused by a concavely curved shape of the meniscus, demonstrating not only its qualitative but also its quantitative validity.

1. Introduction The ordered arrays of colloidal particles or colloidal crystals have received substantial attention because of the wide range of potential applications, which include optical,1,2 chemical, and biosensing,3-6 data storage,7,8 and photonic band gap materials9,10 as well as templates for the creation of nanostructured11,12 or ordered porous materials.13-16 From an industrial point of view, it is important to have the colloidal particles self-organized. Extensive efforts along this line have been devoted to prepare continuous films of ordered arrays by using several methods such *Corresponding author. E-mail: [email protected]. (1) Weissman, J. M.; Sunkara, H. B.; Tse, A. S.; Asher, S. A. Science 1996, 274, 959–963. (2) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. Adv. Mater. 2000, 12, 693–713. (3) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829–832. (4) Asher, S. A.; Alexeev, V. L.; Goponenko, A. V.; Sharma, A. C.; Lednev, I. K.; Wilcox, C. S.; Finegold, D. N. J. Am. Chem. Soc. 2003, 125, 3322–3329. (5) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 3693–3698. (6) Lu, Y.; Liu, G. L.; Kim, J.; Mejia, Y. X.; Lee, L. P. Nano Lett. 2005, 5, 119–124. (7) Sun, S.; Murray, C. B.; Weller, D.; Folks, L.; Moser, A. Science 2000, 287, 1989–1992. (8) Pham, H. H.; Gourevich, I.; Oh, J. K.; Jonkman, J. E. N.; Kumacheva, E. Adv. Mater. 2004, 16, 516–520. (9) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. Nature 1997, 386, 143–149. (10) T
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opez, C. Langmuir 1999, 15, 4701–4704. (19) Jiang, P.; McFarland, M. J. J. Am. Chem. Soc. 2004, 126, 13778–13786. (20) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303–1311. (21) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132–2140. (22) Wong, S.; Kitaev, V.; Ozin, G. A. J. Am. Chem. Soc. 2003, 125, 15589– 15598.

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as the sedimentation of particles,17 filtration,14 electrophoretic deposition,18 spin coating,19 convective self-assembly,20-22 and drying of a suspension droplet.23-25 Among these techniques, convective self-assembly is the most widely employed method. In this method, a substrate is immersed in a suspension vertically or with a certain tilting angle. Then, a colloidal crystal film forms on the substrate due to the particle transfer to the tip of a meniscus induced by solvent evaporation. The method is being refined in order to improve the quality of colloidal crystals and increase the efficiency of the formation process.26-30 Meanwhile, another important topic of study is the precise control of particle positions to fabricate “higher-order” patterned films of ordered particle arrays. Although complex patterned structures can be formed using top-down approaches such as prepatterning of substrates31-34 and soft lithography,35-37 a self-organization process is strongly desired; the convective assembly method is a possible candidate because, in this method, unlike other methods, the nucleation of colloidal crystals occurs only around the tip of the meniscus. Further, patterned structures can be formed by controlling the meniscus motion. Masuda et al. fabricated stripe patterned particle arrays on silicon wafers treated with a monolayer of octadecyltrichlorosilane (23) Micheletto, R.; Fukuda, H.; Ohtsu, M. Langmuir 1995, 11, 3333–3336. (24) Wang, C.; Zhang, Y.; Dong, L.; Fu, L.; Bai, Y.; Li, T.; Xu, J.; Wei, Y. Chem. Mater. 2000, 12, 3662–3666. (25) Fudouzi, H. J. Colloid Interface Sci. 2004, 275, 277–283. (26) Zhou, Z.; Zhao, X. S. Langmuir 2004, 20, 1524–1526. (27) Prevo, B. G.; Velev, O. D. Langmuir 2004, 20, 2099–2107. (28) Zheng, Z. Y.; Liu, X. Z.; Luo, Y. H.; Cheng, B. Y.; Zhang, D. Z.; Meng, Q. B.; Wang, Y. R. Appl. Phys. Lett. 2007, 90, 051910. (29) Wang, L. K.; Zhao, X. S. J. Phys. Chem. C 2007, 111, 8538–8542. (30) Cademartiri, L.; Sutti, A.; Calestani, G.; Dionigi, C.; Nozar, P.; Migliori, A. Langmuir 2003, 19, 7944–7947. (31) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718–8729. (32) Yang, S. M.; Mı´ guez, H.; Ozin, G. A. Adv. Funct. Mater. 2002, 12, 425–431. (33) Xia, D.; Biswas, A.; Li, D.; Brueck, S. R. J. Adv. Mater. 2004, 16, 1427–1432. (34) Bae, C.; Shin, H.; Moon, J. Chem. Mater. 2007, 19, 1531–1533. (35) Xia, Y.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 550–575. (36) Yao, J.; Yan, X.; Lu, G.; Zhang, K.; Chen, X.; Jiang, L.; Yang, B. Adv. Mater. 2004, 16, 81–84. (37) Lee, B. H.; Shin, H.; Sung, M. M. Chem. Mater. 2007, 19, 5553–5556.

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by using the convective assembly method.38 Ghosh et al. prepared stripe patterns on gold-coated silicon wafers immersed in water suspension by using the convective assembly method and examined the effects of the withdrawal rate of substrates onto the stripe width, stripe spacing, and degree of order of structures, demonstrating the existence of a transition withdrawal velocity at which the trend of the stripe width and spacing changes dramatically.39 Lee et al. applied the convective assembly method to anisometric nanoparticles and observed the formation of stripe patterns when the concentration was quite low.40 In cases where partially wet substrates with a large contact angle of solvent are used, the formation of stripe patterns is basically governed by a gravitydriven “stick-slip” motion of the air-solvent-substrate contact line. Huang et al. excellently utilized the stick-slip motion to fabricate one-dimensional lines of a width of a single particle in their modified Langmuir-Blodgett type of experiments.41 However, a critical problem of the stick-slip process lies in the difficulty to predict the stripe width and spacing because the time for a meniscus to remain “stuck” until the next slip is not available a priori. As a similar phenomenon, ring-shaped patterns of particles were observed when a suspension droplet dried on a horizontally placed substrate;42,43 these patterns are known as “coffee stains.”44 Although Adachi et al. succeeded in formulating a mathematical model for this process, the equations still contain some fitting parameters.45 Another problem in the stick-slip process is that the resultant stripes often show distorted shapes and a low degree of periodicity, although Xu et al. improved the process by evaporating a suspension in a “sphere-on-flat” restricted geometry.46 When substrates with a charge opposite to that of the particles are used, that is, there exists electrostatic attraction between a substrate and particles, a mechanism different from the stick-slip phenomenon seems to work in the formation of stripelike patterns by using the convective assembly method. Przerwa et al. suggest that the formation of particle aggregates is strongly affected by the shape of the meniscus in the vicinity of the substrate surface,47 and Ray et al. successfully calculated stripe spacing assuming a wedge-shaped liquid film around the tip of the meniscus.48 However, the stripe patterns formed in this process are not well-defined because the strong adhesive force between the substrate and the particles hinders the rearrangement of particles on the substrate. Dewetting of thin liquid films has also been used to produce patterned layers of particles owing to the “fingering instability.”49 Stripe patterns in the dewetting process are typically perpendicular to the three-phase contact line. In contrast, in the stickslip process, stripes are formed parallel to the contact line, as demonstrated by Huang et al.50 and Sawadaishi and (38) Masuda, Y.; Itoh, T.; Itoh, M.; Koumoto, K. Langmuir 2004, 20, 5588–5592. (39) Ghosh, M.; Fan, F.; Stebe, K. J. Langmuir 2007, 23, 2180–2183. (40) Lee, J. A.; Meng, L.; Norris, D. J.; Scriven, L. E.; Tsapatsis, M. Langmuir 2006, 22, 5217–5219. (41) Huang, J. X.; Tao, A. R.; Connor, S.; He, R.; Yang, P. Nano Lett. 2006, 6, 524–529. (42) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Chem. Phys. Lett. 1993, 204, 455–460. (43) Shmuylovich, L.; Shen, A. Q.; Stone, H. A. Langmuir 2002, 18, 3441–3445. (44) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (45) Adachi, E.; Dimitrov, A. S.; Nagayama, K. Langmuir 1995, 11, 1057–1060. (46) Xu, J.; Xia, J. F.; Lin, Z. Q. Angew. Chem., Int. Ed. 2007, 46, 1860–1863. (47) Przerwa, E.; Sosnowski, S.; Slomkowski, S. Langmuir 2004, 20, 4684–4689. (48) Ray, M. A.; Kim, H.; Jia, L. Langmuir 2005, 21, 4786–4789. (49) Cazabat, A. M.; Heslot, F.; Troian, S. M.; Carles, P. Nature 1990, 346, 824–826. (50) Huang, J. X.; Kim, F.; Tao, A. R.; Connor, S.; Yang, P. D. Nat. Mater. 2005, 4, 896–900.

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Shimomura.51 The dewetting process can form not only stripe patterns but also “spoke”-like radial shapes,50 polygonal patterns, and parallel-chain arrays.52 However, the resulting structures are quite sensitive to experimental conditions, and controlling these structures is difficult. The difficulty in modeling the stick-slip and the dewetting processes comes from the fact that they involve an uncertainty due to the instability of the meniscus. However, stripe patterns can be formed even on completely wetting surfaces on which fluids spread readily, as demonstrated by Giraldo et al. who prepared stripe patterns of manganese oxide particles on hydrophilic glass substrates.53 The use of well wet substrates for a pattern formation process would open up the possibility of modeling the process, avoiding the uncertainty caused due to meniscus motion. However, the formation mechanism of stripes on wetting substrates is unclear. On the other hand, although the stripes are formed parallel to the contact line, it is at least clear that the mechanism would not be based on stick-slip motion, which is observed only on partially wet substrates as stated by Huang et al.41 Systematic investigation into the formation process is thus strongly required. In the present study, we explore the formation of stripe patterned layers on completely solvophilic substrates by using the convective assembly method, systematically examining the effects of several experimental parameters, including the particle concentration, velocities of substrate withdrawal and solvent evaporation, surface tension of solvents, and material of substrates, on the stripe width and spacing. Well-defined stripe patterns form spontaneously on the substrates. The stripe width depends on particle concentration, withdrawal rate, and surface tension, while the spacing is affected by the thickness of stripes, surface tension, and substrates. After a detailed analysis of the results, we propose a new mechanism for stripe formation, demonstrating the quantitative validity of the mechanism with excellent agreement between the experiment and model calculation of stripe spacing.

2. Experimental Section Materials. The particles used were silica spheres (Cataloid SI80P, Catalysts & Chemicals Ind. Co., Ltd., Japan), and their mean particle diameter as measured by dynamic light scattering (ELS-8000, Otsuka Electronics Co., Ltd., Japan) was 123 nm with a coefficient of variation of 13.3%. The silica particles were suspended in ultrapure, deionized water with a resistivity of 18 MΩ 3 cm-1 that was passed through a water purifier system (Millipore Corp., Bedford, MA) and ethanol (99.5%, Kishida Chemical Co., Ltd., Japan) at volume fractions in the order of 10-2-10-6. The substrates used were mica sheets (Okenshoji Co., Ltd., Japan), glass plates with dimensions of 18
18 mm2 (Micro cover glass, Matsunami Glass Ind., Ltd., Japan), and silicon wafers with (100) crystal orientation (SUMCO Corp., Japan). Mica sheets and silicon wafers were cut into squares of approximately 10 mm
30 mm. Before use, the cut mica plates were cleaved, washed with deionized water in an ultrasonic bath, and dried in a stream of nitrogen gas. The glass and silicon plates were washed with acetone (99.5%, Wako Pure Chemical Ind., Ltd., Japan), ethanol, and deionized water in an ultrasonic bath, as a preliminary cleaning procedure. Then, they were immersed for 15 min in a 5:1:1 mixture of deionized water, ammonium hydroxide (28%, Kishida Chemical), and hydrogen peroxide (30%, Kishida Chemical) set in an oven at 70 °C. This process (51) Sawadaishi, T.; Shimomura, M. Colloids Surf., A 2005, 257-258, 71–74. (52) Rezende, C. A.; Lee, L.-T.; Galembeck, F. Langmuir 2007, 23, 2824–2828. (53) Giraldo, O.; Durand, J. P.; Ramanan, H.; Laubernds, K.; Suib, S. L.; Tsapatsis, M.; Brock, S. L.; Marquez, M. Angew. Chem., Int. Ed. 2003, 42, 2905–2909.

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Figure 1. Schematic drawing of the experimental setup. is called the SC-1 [Standard Clean #1] process.54,55 It was followed by rinsing the plates thoroughly with deionized water and drying them in a stream of nitrogen gas. The SC-1 process removes organic and metallic contaminants from surfaces, resulting in completely wetting the glass and silicon surfaces. A nonionic surfactant, polyethylene glycol mono-4-nonylphenyl ether (Tokyo Chemical Industry Co., Ltd., Japan) was used to vary the surface tension of the water suspension. The surface tension of surfactant solutions with concentrations of 1.1
10-6 and 1.1
10-5 mol/L, which are below the critical micelle concentration of approximately 1.4
10-4 mol/L, was measured by a ring tensiometry technique and found to be 6.2
10-2 and 5.2
10-2 N/m, respectively, at room temperature. Fabrication of Particle Films. Figure 1 illustrates a schematic of the experimental setup. A substrate was attached to a driving piston of a syringe pump (KD Scientific Inc., Holliston, MA) by a nonelastic string through a small aperture drilled through the top wall of an incubator (IS600, Yamato Scientific Co., Ltd., Japan) in which the internal temperature Ti was controlled. A glass vessel (20 mL beaker, diameter = approximately 3 cm) containing a colloidal suspension with the given volume fraction of φ was set in the incubator after preheating the suspension in a water bath at the same Ti. The substrate was immersed vertically in the suspension and then slowly withdrawn from it with a controlled pulling rate, vw, if necessary. Because the liquid level falls with an increase in the evaporation rate, ve, the relative rate of the substrate to the liquid surface, vr, is accordingly given by the sum of the withdrawal and evaporation rates. The evaporation rate ve was estimated to be 0.03-0.3 μm/s from the total amount of solvent that evaporated during the experiment, which in turn depends on the internal temperature Ti that was varied from 25 to 60 °C. The withdrawal rate vw was varied from 0 to 0.9 μm/s, which is in the order of the evaporation rate. Sample Characterization. The microscopic structures of stripe patterned layers were observed using a field emission scanning electron microscope (JSM-6340FS, JEOL Ltd., Japan). Prior to imaging, a thin gold layer was sputtered onto the samples after they were dried in vacuum. A larger area was observed with an optical microscope (Keyence, Japan). A confocal laser microscope (VK-8500, Keyence) was used to investigate the thickness of the stripes.

3. Results and Discussion 3.1. Formation of Stripe Patterned Layers. Figure 2 shows variations in the film structure of particles deposited on a mica substrate with varying particle concentrations of the ethanol suspension at Ti = 40 °C. As shown in Figure 2a, a thick continuous film was prepared from the suspension of φ = 1.0
10-2. The decrease in the concentration to 10-4 led to the formation of a stripe patterned layer (Figure 2c) via a transition structure between the continuous film and a stripe pattern (54) Kern, W. Handbook of semiconductor wafer cleaning technology: Science, technology, and applications; William Andrew Publishing: Norwich, NY, 1993. (55) Kern, W.; Puotinen, D. A. RCA Rev. 1970, 31, 187–206.

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Figure 2. SEM images of particle film morphology on mica substrates from ethanol suspensions of (a) φ = 1.0
10-2, (b) φ = 3.0
10-4, (c) φ=1.0
10-4, and (d) φ =1.0
10-6 without being withdrawn (vw=0) at Ti=25 °C.

(Figure 2b). Stripes were formed in the direction parallel to the contact line. Further decrease in the particle concentration resulted in the random deposition of isolated particles and particle clusters as shown in Figure 2d. The same trend was confirmed when water was used as the solvent, although the water suspension had a slightly lower limit for the stripe formation than the ethanol suspension. The typical range of particle concentration for the formation of stripe patterns was found to be of the order 10-4-10-6 in volume fraction. It was thus concluded that a low particle concentration is critical to stripe formation. Figure 3a shows a representative scanning electron microscopy (SEM) image of stripe patterned layers, which was prepared on a silicon wafer immersed in the water suspension. The white band is a stripe composed of particles which form a close-packed array as shown in the magnified image of the stripe (Figure 3b). The gray band indicates a bare part of the substrate where almost no particles are deposited. Because the stripe width and stripe spacing are typically in the order of micrometers, the stripe patterns interestingly realize the coexistence between micrometer-scale periodicity and nanoscale ordering. In contrast to the water suspension, the ethanol suspension tends to result in stripes composed of rather disordered aggregates of particles, which would result from weaker capillary forces acting between particles for ethanol than those for water (see the Supporting Information, Figure S1). When observed with an optical microscope, the stripes exhibit various brilliant colors (Figure 3c), which would be due to the interference of light depending on the thickness of the particle film.56 In fact, our cross-sectional analysis using a confocal laser microscope confirmed that the color change corresponds to the thickness difference in the stripes (see the Supporting Information, Figure S2). From the sharp color transition in the optical images of the stripes, it is concluded that these stripes have an asymmetric structure in the growth direction; in the upper portion of a single stripe, the number of layers increases stepwise with an interval of several micrometers. Further, the number of layers decreases suddenly in the bottom (56) Dushkin, C. D.; Nagayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695–3701.

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Figure 4. (a) SEM image of stripes composed of monolayer particle arrays prepared on a mica substrate from the water suspension of φ = 2.5
10-5 with Ti = 25 °C and vw =0.22 μm/s. (b) Magnified image of a stripe in (a).

Figure 5. Stripe width and spacing as a function of the particle concentration. The substrate and solvent are glass and water under the condition of Ti = 60 °C and vw = 0. Error bars indicate the standard deviation of the data.

Figure 3. (a) Representative image of stripe patterns. Black arrow indicates the direction of liquid level descent, that is, the stripe growth direction. Stripes are prepared on a silicon wafer from a water suspension of φ=2.5
10-5 with Ti=60 °C and vw=0. (b) Magnified image of a stripe in (a). (c) Optical image of stripes in (a).

portion as if a multilayered particle film were “cut off” during the steady growth of the film. The asymmetry of the thickness gradient is characteristic of the assembly technique applied in the present study and is closely related to the formation mechanism of the stripe patterns, which is discussed later. The thickness of the stripes can vary from one layer (Figure 4) to a maximum of five layers (Figure 3), and the stripe width can vary from 3 to 60 μm depending on experimental conditions such as the particle concentration, withdrawal rate of a substrate, evaporation rate, solvents, and substrates. The effects of these experimental conditions are examined in the following sections. 3.2. Effect of Particle Concentration. Figure 5 shows stripe width and spacing as a function of particle concentration within the concentration range required for the formation of stripe patterns. Error bars reported in Figure 5 and the subsequent figures indicate the standard deviation of the data sampled from at least 15 stripes of a sample. The stripe width increases almost linearly against the particle concentration, and the number of layers also increases with an increase in particle concentration. This is qualitatively natural because a higher concentration drives 7290 DOI: 10.1021/la900315h

Figure 6. Dependence of the stripe spacing on the thickness of stripes formed on different substrates from water suspension with Ti=60 °C and vw=0. Error bars indicate the standard deviation of the data.

more particles to the tip of the meniscus, where a particulate film is growing, resulting in thicker and wider stripes. Particle concentration thus determines the particle flux supplied to the stripe growing region, which is directly related to the width and thickness of the stripes. On the other hand, stripe spacing does not seem to depend directly on particle concentration but on the number of layers of stripes. In order to examine this dependence, the relation between stripe spacing and the number of layers of stripes for three different substrates is plotted in Figure 6. It is observed that the stripe spacing increases with the number of layers in the stripes. The dependency is quite clear for the silicon wafer and glass substrates, while it is rather small for the mica substrate. Although, at present, the reason is not clear why the mica substrate shows a small difference in the stripe spacing especially between the monolayer and bilayer cases, it is certain that the Langmuir 2009, 25(13), 7287–7295

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Figure 7. Stripe width and spacing as a function of the relative rate for two temperatures prepared on mica substrates from ethanol suspensions of φ =1.0
10-4. Numbers inside the closed plots denote the number of layers of stripes. Error bars indicate the standard deviation of the data.

stripe spacing depends on the number of layers of the stripe for three different substrates and that the dependency is not linear but mild. As for the width of the stripe spacing, the silicon wafer gives longer spacing than the glass and mica substrates. 3.3. Effect of the Withdrawal Rate. The stripe width and spacing from ethanol suspensions are plotted in Figure 7 against the relative rate vr, which is varied by changing the withdrawal rate under a constant evaporation rate at each temperature. The substrate used is mica. The numbers inside the closed plots indicate the number of layers of stripes. The stripe width is almost inversely proportional to the relative rate with the slope of -0.8 and -1.0 for 25 and 60 °C, respectively. Furthermore, the number of layers decreases from two to one with an increase in the withdrawal rate. Faster withdrawal would allow fewer particles to be deposited on a substrate, leading to shorter and thinner stripes. The same trend was confirmed for water suspension with a slope of -0.9. On the other hand, the effect of the withdrawal is not recognized in Figure 7 for stripe spacing; the spacing is almost constant against the increase in the withdrawal rate for each temperature condition for the same number of layers (monolayer for Ti = 25 °C and bilayer for Ti = 60 °C). This result suggests that a single mechanism controls the stripe formation within the range of withdrawal rates applied in the present study, while Ghosh et al. demonstrated that the increase in the withdrawal rate changes the formation mechanism abruptly at a transition velocity from the gravity-driven stick-slip to the thin-film entrainment regime.39 The withdrawal rates in the present study are so low that the meniscus shape is not forced to be entrained by the substrate moving upward but maintained as described by the Laplace equation in static mechanics.57 In fact, the viscous drag due to substrate motion is calculated to have negligible contribution to the meniscus shape.47 The formation process of stripe patterned films can therefore be regarded as a quasi-static one in the present condition. 3.4. Effect of the Evaporation Rate. Figure 8 shows the dependence of the stripe width and spacing on the evaporation rate, which is sampled from the stripes composed of two layers. As seen, the stripe width is almost constant regardless of the evaporation rate. The increase in the evaporation rate means a faster descent of the liquid level, and in that sense the evaporation rate plays a role similar to that played by the withdrawal rate. However, increasing the evaporation rate also increases the convective transfer of particle flux from the bulk suspension (57) Landau, L. D.; Lifshitz, E. M. Fluid mechanics, 2nd ed.; ButterworthHeinemann: Oxford, 1987.

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Figure 8. Stripe width and spacing as a function of the evaporation rate of ethanol suspensions of φ = 1.0
10-4 using mica substrates without being withdrawn (vw = 0). Error bars indicate the standard deviation of the data.

Figure 9. Effect of surface tension on stripe width and spacing prepared on silicon wafers without being withdrawn (vw= 0) at Ti = 60 °C. Particle concentration was adjusted so that stripes were composed of two layers in thickness. Error bars indicate the standard deviation of the data.

to the tip of the meniscus. Therefore, these two opposite effects caused by the increased evaporation balance each other out; this results in a constant width of stripes over the entire range of the evaporation rates. The stripe spacing also remains constant against the evaporation rate. This result is consistent with the dependence of stripe width on the withdrawal rate because the evaporation rate is equivalent to the withdrawal rate in the sense that both increase the relative rate. Although the evaporation rate has little effect on the resultant stripe structures, the time needed to form stripe patterns decreases with increasing evaporation rate. The evaporation rate thus determines the growth rate of stripes. 3.5. Effect of Solvent and Surface Tension. We compared the stripe spacing resulting on a silicon wafer immersed in water and ethanol suspension under the same temperature and having the same stripe thickness (bilayer). The water suspension was confirmed to result in longer spacing than the ethanol suspension (37.0 μm for water and 24.9 μm for ethanol). This result suggests that the periodicity of the stripe pattern can be controlled by changing solvents probably due to the difference in surface tension. In order to clarify the effect, we varied the surface tension by adding a small amount of nonionic surfactant in the water suspension. As shown in Figure 9, the stripe spacing decreases with the decrease in the surface tension, indicating that the surface tension of the solvent is a controlling factor for the spacing. In addition, the stripe width also decreases with a decrease in surface tension, indicating a correlation between the stripe width and spacing. 3.6. Correlation between Stripe Width and Spacing. Upon investigating the correlation accurately, it was noted that averaged stripe width and spacing would not work; the relation DOI: 10.1021/la900315h

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Figure 10. Relation between the stripe width and spacing prepared on silicon wafers at Ti = 60 °C for different particle concentrations.

between individual widths and spacing was required. We thus examined a stripe width and the adjacent spacing in the growing direction as a pair and plotted about 20 consecutive pairs for each of the four different particle concentrations in Figure 10, where a definite correlation can be recognized; a wider stripe yields a wider spacing, and the correlation becomes stronger with increasing particle concentration. It should be noted that no clear correlation was observed between a stripe width and the previous spacing. This correlation strongly indicates that the formation of a stripe and the next spacing are synchronized with each other.

4. Mechanism of Stripe Pattern Formation Previously proposed mechanisms for the stripe formation are based on stick-slip motion and fingering instability. However, the gravity-driven periodic jump of a meniscus would not explain the mild dependence of stripe spacing on the thickness of stripes (Figure 6) and the correlation between the stripe width and spacing (Figure 10) if the stick-slip motion occurred on completely wet surfaces. The fingering instability of the tip of a meniscus would result in stripes that are perpendicular to the contact line. A new model is thus required to give a reasonable explanation for the experimental results shown above. After unsuccessful attempts to elucidate the mechanism of stripe formation on the basis of, for example, energy balance and force balance of the meniscus, we have finally devised a new mechanism for the formation of stripe patterns on a hydrophilic surface. Figure 11 presents a schematic of the proposed mechanism. The key idea of the breakthrough is that the meniscus can form a concave surface against the substrate (concave rightward in Figure 11) because its top edge can be attached to the outermost particle layer that is at a certain distance from the substrate, which is in contrast to the meniscus usually being attached to a bare substrate with a zero contact angle. In step (i), the top edge of the meniscus vertically touches the tail end of the particulate film, whose length is growing due to the particle flux from underneath. When the particle concentration is high, the particle flux can be sufficiently large to maintain a steady growth of the particle film, resulting in the formation of a continuous film as seen in Figure 2a, because the growth rate of the particulate film balances with the relative rate of the substrate to the liquid level. However, under the present condition of a reasonably low concentration, the particle flux is so small that the growth rate of the particulate film becomes lower than the relative rate of the substrate. This rate difference accordingly increases the distance between the liquid surface and the tail end of the particulate film. The shape of the meniscus must satisfy the Laplace equation in static mechanics, because the process is quasistatic as discussed in section 3.3. In order to satisfy the Laplace equation, the meniscus shape must become concave against the 7292 DOI: 10.1021/la900315h

substrate, as shown in the schematic of step (ii), by adjusting the angle at the point of contact of the meniscus with the spherical surface of a particle. In step (ii), the particle flux to region (A) decreases because the “path” of the thin liquid film connecting the two regions (A) and (B) narrows. On the other hand, region (B) has a higher particle concentration temporarily due to the partial stagnation of particles. The smaller particle flux to region (A) slows the growth rate of the particulate film to further elongate and curve the meniscus shape. The elongation naturally involves an increase in the particle concentration in region (B), squeezing the particle suspension and arranging the particles into a dense structure. Simultaneously, the path width (the separation of this part from the substrate surface) also narrows as shown in step (iii). The growth of the particulate film ceases when no particles pass through the path into region (A), which would happen when the path width becomes, for example, less than the particle size as an extreme case. After a certain time, the meniscus stops the elongation and cuts at a certain threshold of the path width hc, resulting in the formation of a stripe and the adjacent spacing as shown in step (iv). Because region (B) has a high concentration of particles with a dense structure, the next stripe is ready to form and grow stably. In this manner, the negative feedback of particle concentration around regions (A) and (B) plays a critical role in the formation of stripe patterns. This formation process is supported by the fact that the very first stripe shows a different structure from the following stripes (see the Supporting Information, Figure S3). This mechanism would be characteristic of easily wettable substrates on which a thin liquid film can remain stable. According to the proposed mechanism, the stripe spacing corresponds to the distance between the tail end of the particulate film and the position of the headmost particle in region (B). A meniscus stuck to a thicker film can be elongated further, and accordingly gives a longer distance than that stuck to a thinner film, which results in the dependence of the stripe spacing on the thickness of the stripe (Figure 6). Moreover, a meniscus with a lower surface tension has a higher curvature, leading to shorter stripe spacing (Figure 9). The width of stripes, on the other hand, is determined by the total number of particles brought to region (A) by the time the meniscus elongation stops. Further, because the increase in the withdrawal rate linearly decreases the stripe formation period at a certain particle concentration, the stripe width is inversely proportional to the withdrawal rate (Figure 7). The increase in particle concentration increases the particle flux to region (A) and at the same time decreases the rate difference between the film growth and descent rates, both of which lead to an increase in the stripe formation period, resulting in a linear relation between the stripe width and the particle concentration (Figure 5). The correlation between the stripe width and spacing is, though somewhat complicated, explained as follows. Suppose, for instance, that the particle flux to region (A) is smaller than the average flux, the stripe width becomes narrower and the concentration of region (B) becomes greater than average. More particles in region (B) make it difficult to be dragged downward, due to a larger friction between particles and the substrate during the meniscus elongation in step (iii), resulting in a shorter spacing as well as a shorter stripe. In contrast, a wider spacing follows a wider stripe when more particles than the average are brought to region (A), and region (B) has a lower concentration. In this manner, the fluctuation in the particle flux to region (A) gives rise to the correlation between the stripe width and spacing, inevitably resulting in the scattering widths of stripe spacing (Figure 10). Langmuir 2009, 25(13), 7287–7295

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Figure 11. Schematic representation of the proposed mechanism of the stripe pattern formation on completely wet substrates.

Quantitatively, the stripe spacing is calculated on the basis of the shape of the meniscus defined by the Laplace equation for a static system57 because the formation process is regarded as quasistatic. Setting the x-axis along the horizontal surface of the suspension and the z-axis along the substrate surface as shown in Figure 11, the meniscus shape is described by the combination of the Laplace equation

a certain path width hc. It should be noted that angle θ was calculated to be a maximum of 2° to make the meniscus shape curved in order to attain the stripe formation. Assuming a close-packed structure, the stripe thickness t is given by ! rffiffiffi 2 ðn -1Þ ð5Þ t ¼d 1 þ 3

1 ðFs - Fair Þg ¼ z R γ

where d indicates the particle diameter and n is the number of layers of the stripe. The width of stripe spacing ws is obtained by the following equation:

ð1Þ

and the definition of the curvature 1 dj ¼ R ds

ws ¼ zðtÞ - zðdÞ ð2Þ

where R is the curvature radius, Fs is the density of solvent, Fair is the density of air, g is the gravitational constant, γ is the surface tension of the solvent, j is the angle between a horizontal line and a tangent line of the meniscus, and s is the length along the meniscus. By solving the above two equations, we obtain the following equation that represents the meniscus shape: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a x ¼ - 2a2 -z2 þ pffiffiffi arccosh 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 2a2 -h2 þ t

pffiffiffi pffiffiffi a 2a 2a - pffiffiffi arccosh z h 2 ð3Þ

with a2 ¼

2γ ðFs - Fair Þg

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and h ¼ a 1 - sin θ

ð4Þ

where t is the thickness of the stripe and θ is the angle between the z-axis and the tangent line of the meniscus at the point of contact with the particle surface. Because the particle surface is spherical, angle θ is assumed to be flexible and uniquely determined for Langmuir 2009, 25(13), 7287–7295

ð6Þ

During the elongation of a meniscus, the meniscus gradually approaches the substrate surface to narrow the path between regions (A) and (B), or, in other words, the thickness of a thin liquid film, and stops at a certain thickness hc. We can assume the following two extreme situations when the meniscus elongation stops. One possibility is that the meniscus stops at a thickness that is the same as the particle diameter, that is, hc = d, because a particle is stuck at the path and prevents further growth of the stripe and elongation of the meniscus, which results in the minimum estimate of stripe spacing for a given thickness of a stripe. The other possibility is that the meniscus further elongates and stops at the point of its contact with the substrate surface, that is, hc =0, leading to the maximum estimate of the spacing. However, the calculated maximum and minimum widths of stripe spacing can vary by 30 μm because of the two “extreme” situations. In particular, it would be impossible to realize the condition of hc =0 because of the stability limit of a thin liquid film.45 To limit the uncertainty involved in setting the limit path width hc, we compared the calculated spacing for various values of hc with experimental results and found that the calculation describes the general trend of the experiments when the limit path width is set to be hc= Rd with R of 0.5-0.8. As an example, the calculated spacing widths for R=0.65 (hc=80 nm) are shown DOI: 10.1021/la900315h

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Figure 12. Shape evolution of the meniscus that attaches to the bottom-right edge of a glass slide when the liquid level descends gradually, obtained by aspirating the solvent with a syringe. Solvent used is water, and thickness of the glass slide is 1 mm.

in Figures 6 and 9. In the calculation, the parameters used for water at 25 °C were Fs =997 kg/m3 and γ=7.2
10-2 N/m and that used for air was Fair = 1.2 kg/m3. The value of R=0.65 gives good fits for the silicon wafer, while a somewhat larger value of R (∼0.8) is required for other substrates (glass and mica). To further examine the performance of the model calculation, we conducted similar experiments with different particle sizes (316 and 607 nm) using silicon wafers as substrate and compared with the proposed model. We found that the proposed model with R = 0.65 agrees well with the experimental data for different diameters with an accuracy of approximately 9%, which demonstrates the validity of the proposed model. In the case of ethanol, the calculated spacing is 28.6 μm for a bilayered stripe and R= 0.65 (hc=80 nm) with Fs=785 kg/m3 and γ=2.2
10-2 N/m at 25 °C, demonstrating agreement with the experimental result of 24.9 μm as described in section 3.5. Although introducing the temperature dependence of the density and surface tension might improve the accuracy of the prediction, the important thing is that the model can grasp the general trend of the resultant stripe spacing for variations in several experimental parameters. The concavely curved meniscus against the substrate is thus crucial in the mechanism but might appear unreasonable because of its novelty. Thus, in order to confirm further the validity of the mechanism, we attempt to directly observe the shape of the meniscus that is attached to the outermost particle layer away from the substrate. As a model system for the observation, we use a slide glass with a thickness of 1 mm as a substitute for the particulate film and capture a side view of the behavior of the meniscus shape attached to the bottom-right edge of the slide glass, when the liquid level descends gradually (Figure 12). As for the difference in scale, please note the following: If the matter is on the nanoscale, its phenomena would naturally differ from bulk phenomena because nanomaterials do not exhibit bulk properties. However, the present matter of interest is typically on the submicrometer or micrometer scale, which is sufficiently large to exhibit bulklike behavior; the physical properties of water are the same for its contact with both micrometer-scale and millimeterscale materials. Therefore, we believe that this observation is surely adequate to test the mechanism. From the shape that 7294 DOI: 10.1021/la900315h

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is similar to the shape of the meniscus attached to a vertical flat surface (Figure 12a), the meniscus shape indeed starts deforming into a concave shape as the liquid level descends (Figure 12b). A further descent of the liquid level curves the meniscus further such that the shape can be described by the Laplace equation, as shown by the dashed line (Figure 12c); finally, the descent of the liquid level is sufficient to cut off the meniscus (Figure 12d). Therefore, this observation strongly supports our proposed mechanism of the stripe pattern formation in which a concavely shaped meniscus plays a crucially important role. The effect of substrates needs to be discussed here because the limit path width is closely related to substrate properties. Two factors would be possible candidates to determine the limit of the meniscus elongation. One is the surface energy of substrates by which the stability of a thin liquid film spread on a substrate is affected; larger surface energy would result in small R, leading to wider stripe spacing. The other is the friction between a substrate and particles which acts against the force involved in the meniscus elongation to drag particles downward in region (B) as seen in the process of Figure 11 (iii). Considering the experimental facts that the surface energy is almost the same among the three hydrophilic substrates used and that the limit path width hc depends on the particle size, the latter is the more important factor in determining the stripe spacing than the former, as long as well wet substrates are used. At this point, it is difficult to quantify the effect of the friction on the value of R, although R depends on substrate type (R ∼ 0.65 for silicon wafer and R ∼ 0.8 for glass and mica as mentioned above). However, we again emphasize that the most important point of stripe formation on completely wet surfaces is the concept of the concavely curved meniscus, and it is surprising that all the experimental results are reasonably explained by introducing this simple concept.

5. Conclusion We have successfully prepared stripe patterned films composed of ordered particle arrays on hydrophilic surfaces by the convective assembly method and investigated the formation process systematically by varying several experimental parameters such as particle concentration, withdrawal and evaporation rates, solvents, and substrates. Stripe patterns are spontaneously formed only when the particle concentration is in the order of 10-4-10-6 in a volume fraction of particles. Given that the typical concentration for continuous particle films in convective assembly is in the order of 10-2, a very low concentration is required for stripe formation. Although the evaporation rate, unlike other experimental factors, has only a little effect on the periodicity of stripe patterns, it determines the formation period of the stripes. Stripe width increases linearly with particle concentration and the reciprocal of the withdrawal rate and shows a slight dependence on the surface tension, while stripe spacing depends on the thickness of stripes, surface tension, and type of substrates. Furthermore, there is a strong correlation between the widths of a stripe and the adjacent spacing; a wider stripe is followed by a wider spacing, and vice versa, indicating a synchronized formation of a stripe and the next spacing. In order to explain these results, we propose a possible mechanism for stripe formation, in which a meniscus is elongated and concavely curved due to a rate difference between the stripe growth and evaporation rates, inducing a negative feedback of particle concentration around the tip of the meniscus where a particulate film is growing. The curved shape of the meniscus plays a key role in stripe formation and also determines stripe spacing. The proposed mechanism not only accounts reasonably Langmuir 2009, 25(13), 7287–7295

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for the experimental results but also demonstrates its quantitative performance in predicting the stripe spacing for various conditions. Stripe patterns prepared in the present study show a quite high degree of order especially when the water suspension is used, the quality of which is as high as that of the pattern structures prepared through top-down approaches. The convective assembly method with the use of well wet surfaces is thus promising as a facile, lithography-free technique to fabricate particulate films with the control of film morphology ranging from patterned to continuous.

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Acknowledgment. This work was supported in part by Kyoto Prefecture Collaboration of Regional Entities for the Advancement of Technological Excellence, JST, Japan, and Nippon Sheet Glass Foundation for Materials Science and Engineering. Supporting Information Available: SEM images of stripe patterns prepared from an ethanol suspension, cross-sectional analysis of a stripe using a confocal laser microscope, and optical image to show the difference between the structure of the very first stripe and that of others. This material is available free of charge via the Internet at http://pubs.acs.org.

DOI: 10.1021/la900315h

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