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"chunk": "# Spontaneous Pattern Formation Induced by Bénard−Marangoni Convection for Sol−Gel-Derived Titania Dip-Coating Films: Effect of Co-solvents with a High Surface Tension and Low Volatility \n\nHiroaki Uchiyama,\\* Tadayuki Matsui, and Hiromitsu Kozuka Department of Chemistry and Materials Engineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan \n\n\\*S Supporting Information \n\n \n\nABSTRACT: Evaporation-driven surface tension gradient in the liquid layer often causes the convective flow, i.e., Bénard− Marangoni convection, resulting in the formation of cell-like patterns on the surface. Here, we prepared sol−gel-derived titania films from $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}^{~i})_{4}$ solutions by dip coating and discussed the effect of the addition of co-solvents with a high surface tension and low volatility on the spontaneous pattern formation induced by Bénard−Marangoni convection. Propylene glycol (PG, with a surface tension of $38.6\\mathrm{\\dot{m}N\\ m^{-1}},$ ) and dipropylene glycol (DPG, with a surface tension of $33.9\\ \\mathrm{mN\\m^{-1}}$ ) were added to the coating solutions containing 2-propanol $(2\\mathrm{-Pr},$ with a surface tension of $22.9\\ \\mathrm{mN\\m^{-1}}$ ) for controlling the evaporationdriven surface tension gradient in the coating layer on a substrate. During dip coating at a substrate withdrawal speed of $50\\ \\mathrm{cm}$ $\\operatorname*{min}^{-1}$ in a thermostatic oven at $60\\ {}^{\\circ}{\\bf C},$ , linearly arranged cell-like patterns on a micrometer scale were spontaneously formed on the titania gel films, irrespective of the composition of coating solutions. Such surface patterns remained even after the heat treatment at 200 and $600^{\\circ}\\mathrm{C},$ where the densification and crystallization of the titania films progressed. The width and height of the cell-like patterns increased with increasing PG and DPG contents in the coating solutions, where the addition of PG resulted in the formation of cells with a larger height than DPG.",
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"category": " Abstract"
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"id": 2,
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"chunk": "# INTRODUCTION \n\nSelf-assembly and self-organization triggered by solvent evaporation are very attractive techniques for making thinfilm materials with highly ordered surface patterns.1−15 Solvent evaporation from solutions containing non-volatile solutes (e.g., colloidal solutions, suspensions, and polymer solutions) often induces a convective flow in the solution layer, leading to the spontaneous assembly and organization of the solutes. “Marangoni effect” is widely known as an evaporation-driven convection phenomenon.16−22 Temperature or concentration gradients in the solution layer result from solvent evaporation, creating the local surface tension gradient. The evaporationdriven surface tension gradient leads to the convective flow of solutions, i.e., “Bénard−Marangoni convection”. The Bénard− Marangoni convection can be characterized by the Marangoni number, Ma, which is a measure of the occurrence tendency of convection, as described below21−23 \n\n$$\nM a=\\frac{-(\\partial\\gamma/\\partial T)H^{2}\\nabla T}{\\mu\\alpha}\n$$ \n\n$$\nM a=\\frac{-(\\partial\\gamma/\\partial C)H^{2}\\nabla C}{\\mu D}\n$$ \n\nwhere $\\partial\\gamma/\\partial T$ is the temperature derivative of the surface tension, $\\nabla T$ is the temperature gradient near the solution surface, $\\partial\\gamma/\\partial C$ is the concentration derivative of the surface tension, $\\nabla C$ is the concentration gradient near the solution surface, $H$ is the thickness of the solution layer, $D$ is the mass diffusivity of the component, and $\\mu$ and $\\alpha$ are the viscosity and thermal diffusivity of the solution, respectively. Generally, Bénard−Marangoni convection occurs when Ma is high; Ma increases with increasing temperature or concentration gradients near the solution surface, with increasing thicknesses of the solution layer, and with decreasing solution viscosities, as shown in eqs 1 and 2. When Bénard−Marangoni convection is activated, micrometer-scaled cell-like patterns (i.e., Bénard cells) often appear on the surface of the solution layer. Such pattern formation attributed to the “Marangoni effect” is commonly seen in many kinds of solutions and, thus, can be applicable as the self-assembly and self-organization techniques for thin-film materials. \n\nThe spontaneous pattern formation induced by Bénard− Marangoni convection can be also found on sol−gel-derived inorganic and organic−inorganic hybrid films.2 35 The thickness variations of sol−gel coating films are reported to be caused by the Bénard−Marangoni convection.24,25,27 In the case of polymer films, the solvent depletion from the surface of the coating layer often creates solute-rich skins, providing the local surface tension gradient.36 Birnie et al. investigated the thickness variations in sol−gel-derived spin-coating films and suggested that the surface tension gradient as a result of the solute-rich skins leads to the lateral flow of solutions toward the higher surface tension area (i.e., solute-rich area) and then the skins become thicker with time, resulting in surface roughening.25 They also found that striation defects observed after the spin coating is attributed to the connection of cell-like Bénard−Marangoni convections along the radial solution flow on a spinning substrate.24 Our group has also observed the striation defects on alkoxide-derived spin-coating layers28−30 and, furthermore, found that the striations and cell-like patterns as a result of the Marangoni effect appeared even on a droplet of alkoxide solutions on a stationary substrate.28,34 Moreover, we have reported that the linearly arranged striations and celllike patterns were formed on sol−gel-derived dip-coating films,32,33,35 where the size and shape of the periodic patterns depend upon the substrate withdrawal speed,35 the viscosity of coating solutions,3 and the coating temperature (i.e., the temperature of substrates, solutions, and atmosphere).33 We attributed the highly ordered surface patterns on sol−gelcoating films to the fixing of the local surface elevation as a result of Bénard−Marangoni convection by the gelation of the coating layer.33,34 Figure 1 shows the schematic illustration of the pattern formation as a result of the Marangoni effect. The rapid solvent evaporation from the coating layer during the deposition process can lead to the evaporative concentration of the solutes and the cooling at the surface, which makes a locally higher surface tension area (Figure 1a), leading to the local surface elevation as a result of Bénard−Marangoni convection (Figure 1b). The surface elevation is fixed by the rapid gelation of the coating layer as a result of the solvent evaporation, resulting in the formation of periodic surface patterns.33 Such pattern formation accompanied by the fixing of the coating layer has also been reported in organic polymer films.37 The spontaneous pattern formation induced by Bénard−Marangoni convection in the sol−gel-coating process is expected as a novel fabrication technique of highly ordered surface patterns in metal oxide film materials, and thus, it is highly desirable to achieve the precise control of the size, shape, and arrangement of the patterns. \n\nIn this work, we focused on the influence of the surface tension of solvents on the pattern formation induced by Bénard−Marangoni convection for sol−gel-derived metal oxide thin films. The surface tension is a definitely essential factor for Bénard−Marangoni convection, because the convection phenomenon is caused by the evaporation-driven surface tension gradient in the solution layer (Figure 1). The solvent selection strategy for preventing the thickness inhomogeneity on sol−gel-coating films as a result of the Marangoni effect has been discussed by Birnie et al., which suggests that the thickness inhomogeneity can be prevented by the addition of co-solvents that can reduce the surface tension gradient in the coating layer during solvent evaporation.24−26 When the lowvolatile co-solvent with a lower surface tension is added to the coating layer, the co-solvent is left together with the solutes during the evaporation of the major solvent. Birnie et al. proposed that such an evaporative concentration of the cosolvent with a lower surface tension causes the local decrease in the surface tension, which reduces the local surface tension gradient that is induced by the evaporative concentration of the solutes and the cooling of the coating layer, suppressing the occurrence of Bénard−Marangoni convection.24,25 Here, we attempted to use such a solvent selection strategy to enhance the evaporation-driven pattern formation on sol−gel-coating films. If the co-solvent with a higher surface tension and lower volatility exists in the evaporating coating layer, the co-solvent would remain there and enhance the local increase in the surface tension as a result of the evaporative loss of the major solvent, creating a higher surface tension gradient. The higher surface tension gradient would provide a stronger convective flow in the coating layer, resulting in the larger surface elevation. We prepared sol−gel-derived titania films by dip coating from $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}{}^{i})_{4}$ solutions containing 2-propanol (2- $\\mathrm{Pr}_{\\mathbf{\\lambda}}$ ) as the major solvent and propylene glycol (PG) and dipropylene glycol (DPG) as the co-solvents. The PG and DPG contents were varied for controlling the surface tension gradient in the coating layer, and the effect of the co-solvents on the spontaneous pattern formation induced by Bénard− Marangoni convection was systematically discussed. \n\n \nFigure 1. Schematic illustration of the pattern formation as a result of the Marangoni effect: (a) evaporation-driven surface tension gradient and (b) surface elevation.",
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"category": " Introduction"
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"id": 3,
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"chunk": "# 2. EXPERIMENTAL SECTION \n\n2.1. Materials. The starting materials were $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}^{~i})_{4}$ (Wako Pure Chemical Industries, Osaka, Japan), nitric acid ${\\mathrm{(HNO}}_{3},$ 69 mass $\\%$ , Wako Pure Chemical Industries, Osaka, Japan), $2{\\cdot}\\mathrm{Pr}$ $(2\\mathrm{-}C_{3}\\mathrm{H}_{7}\\mathrm{OH},$ Wako Pure Chemical Industries), PG $\\mathrm{\\small{[CH_{3}C H(O H)C H_{2}O H_{3}}}$ , Wako Pure Chemical Industries], DPG $\\big[\\big(\\mathrm{HOC}_{3}\\mathrm{H}_{6}\\big)_{2}\\mathrm{O}_{\\cdot}$ , Wako Pure Chemical Industries], and ion-exchanged water $\\left(\\mathrm{H}_{2}\\mathrm{O}\\right)$ . The surface tension, viscosity, and boiling point of the solvents are listed in Table 1. \n\nTable 1. Surface Tension, Viscosity, and Boiling Point of Solvents \n\n\n<html><body><table><tr><td>solvent</td><td>surface tension (mN m-l)</td><td>viscosity (mPa s)</td><td> boiling point (°C)</td></tr><tr><td>2-Pr</td><td>22.9</td><td>1.77</td><td>82.4</td></tr><tr><td>PG</td><td>38.6</td><td>61.7</td><td>188.2</td></tr><tr><td>DPG</td><td>33.9</td><td>75.3</td><td>230.0</td></tr></table></body></html> \n\n2.2. Preparation of Titania Films. The compositions of starting solutions are listed in Table 2. Starting solutions of molar compositions, $\\mathrm{Ti}(\\mathrm{OC_{3}H_{7}}^{i})_{4}/\\mathrm{H_{2}O}/\\mathrm{HNO_{3}}/\\mathrm{\\bar{2}}\\mathrm{-Pr}/\\mathrm{PG}$ or DPG $\\mathbf{\\Sigma}=\\mathbf{\\Sigma}$ $1{:}2{:}0.2{:}40{:}x$ or $y$ $\\dot{}_{x}$ or $y=0{-}1.50)$ , were prepared by the following procedure. First, $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}{}^{i})_{4}$ was added in a half of the prescribed amount of $2{\\cdot}\\mathrm{Pr}$ . The remaining amount of $2{\\cdot}\\mathrm{Pr}$ was mixed with $_\\mathrm{H}_{2}\\mathrm{O}$ and ${\\mathrm{HNO}}_{3}$ . The solution containing 2-Pr, $\\mathrm{H}_{2}\\mathrm{O},$ , and ${\\mathrm{HNO}}_{3}$ was added dropwise to the $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}^{~i})_{4}$ solution under stirring. The solutions were kept standing at room temperature in a sealed glass container for $30~\\mathrm{{min},}$ , and then PG or DPG was added under stirring. The solutions were, furthermore, kept standing at room temperature for $3\\mathrm{~h~}$ and served as coating solutions. \n\nTitania gel films were deposited on Si(100) substrates $(20\\times40\\times$ $0.85\\ \\mathrm{mm},$ ) using a dip coater (portable dip coater DT-0001, SDI, Kyoto, Japan), where the substrates were withdrawn at $50.0\\ \\mathrm{cm\\min^{-1}}$ . The dip coating was performed in a thermostatic oven, as shown in Figure S1 of the Supporting Information. The coating temperature (i.e., the temperature of substrates, solutions, and atmosphere) was kept at $60~^{\\circ}\\mathrm{C},$ where the solutions and substrates were heated at the coating temperature for $30\\ \\mathrm{min}$ before the dip coating. After the deposition, the gel films were kept at $60~^{\\circ}\\bar{\\mathrm{{C}}}$ for $3~\\mathrm{min}$ in the thermostatic oven. Then, the gel films were heated at 200 or $600~^{\\circ}\\mathrm{C}$ for $10\\ \\mathrm{min}$ in air, where the films were transferred to an electric furnace held at the prescribed temperature. \n\n2.3. Characterizations. The viscosity of the coating solutions was measured using an oscillating-type viscometer (VM-1G, Yamaichi Electronics, Tokyo, Japan). Microscopic observation of the film samples was made using an optical microscope (KH-1300, HiROX, Tokyo, Japan). The crystalline phases were identified by X-ray diffraction (XRD) measurement by ordinary $2\\theta/\\theta$ mode using an Xray diffractometer (model Rint 2550V, Rigaku, Tokyo, Japan) with Cu $\\mathrm{K}\\alpha$ radiation operated at $40\\ \\mathrm{kV}$ and $300~\\mathrm{{mA}}$ . \n\nTwo-dimensional (2D) and three-dimensional (3D) surface profiles of the film samples were measured using a contact probe surface profilometer (SE-3500K31, Kosaka Laboratory, Tokyo, Japan). The measurement was conducted at the center of the films, as shown in Figure 2a. Surface roughness parameters, S (mean spacing of local peaks) and $R_{z}$ (ten point height of irregularities), were automatically calculated from the 2D profile (the definitions of S and $R_{z}$ are shown in Figure S2 of the Supporting Information). S and $R_{z}$ represent the width and height, respectively, of the surface patterns, as shown in Figure 2b. \n\n \nFigure 2. (a) Schematic illustration of the test line and area employed in 2D and 3D surface roughness measurements and (b) definition of the film thickness and width and height of the surface pattern. \n\nTable 2. Compositions and Viscosity of the Coating Solutions \n\n\n<html><body><table><tr><td colspan=\"6\"> mole ratio</td><td colspan=\"2\">co-solvent volume per gram of Ti(OCH7)4 (mL)</td><td></td></tr><tr><td>Ti(OCH)4</td><td>HO</td><td>HNO3</td><td> isopropanol</td><td>PG (x)</td><td>DPG (y)</td><td> PG</td><td>DPG</td><td>viscosity (mPa s)</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2.05</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>0.25</td><td></td><td>0.064</td><td></td><td>2.27</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>0.50</td><td></td><td>0.13</td><td></td><td>2.33</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>0.75</td><td></td><td>0.19</td><td></td><td>2.48</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>1.00</td><td></td><td>0.26</td><td></td><td>2.42</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>1.25</td><td></td><td>0.32</td><td></td><td>2.46</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td>1.50</td><td></td><td>0.39</td><td></td><td>2.50</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>0.25</td><td></td><td>0.12</td><td>2.14</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>0.50</td><td></td><td>0.23</td><td>2.11</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>0.75</td><td></td><td>0.35</td><td>2.30</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>1.00</td><td></td><td>0.46</td><td>2.25</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>1.25</td><td></td><td>0.58</td><td>2.45</td></tr><tr><td>1</td><td>2</td><td>0.2</td><td>40</td><td></td><td>1.50</td><td></td><td>0.69</td><td>2.43</td></tr></table></body></html> \n\nFilm thickness was measured by the profilometer (the definitions of the thickness are shown in Figure 2b). A part of the thin film was scraped off with a surgical knife immediately after the film deposition, and the level difference between the coated part and the scraped part was measured after drying.",
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"category": " Materials and methods"
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"id": 4,
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"chunk": "# 3. RESULTS AND DISCUSSION \n\n3.1. Preparation of Titania Films with Surface Patterns. Colorless, transparent $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}{}^{i})_{4}$ solutions were obtained at room temperature, irrespective of PG and DPG contents $[\\mathrm{PG}/\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{\\bar{H}}_{7}{}^{i})_{4}$ mole ratio $(x)\\ =\\ 0{-}1.50,$ and $\\mathrm{DPG}/\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}{}^{i})_{4}$ mole ratio $\\left(y\\right)=0{-}1.50]$ . The viscosity of the coating solutions slightly increased with increasing PG and DPG contents, as shown in Table 2, which could be caused by the high viscosity of PG and DPG (Table 1). \n\nTitania gel films were prepared from the coating solutions of $x$ or $y=0{-}1.50$ by dip coating at a substrate withdrawal speed of $5\\dot{0}\\ \\mathrm{cm\\min^{-1}}$ in a thermostatic oven at $60~^{\\circ}\\mathrm{C}$ . Crack-free, transparent gel films were obtained from all of the solutions. Figure 3 shows the optical micrographs of the as-deposited gel air, where the gel films were transferred to an electric furnace held at the prescribed temperature after dip coating. Crack-free, transparent titania films were basically obtained for all of the conditions, while a few small cracks were only occasionally observed on the surface after heating at $600^{\\circ}\\mathrm{C}.$ Anatase phases were detected in the XRD patterns of the titania films heated at $600^{\\circ}\\mathrm{C},$ irrespective of the addition of PG and DPG, while all of the films heated at $200~^{\\circ}\\mathrm{C}$ were composed of the amorphous phase (the XRD patterns are shown in Figure S3 of the Supporting Information). \n\n \n\nFigure 4 shows the dependence of the thickness upon the PG and DPG contents in the coating solutions for the heat-treated films. Cell-like patterns of $20-50~\\mu\\mathrm{m}$ in width were observed on the surface, irrespective of the composition of coating solutions, where the surface patterns were linearly arranged parallel to the substrate withdrawal direction. The formation of linearly arranged cell-like patterns during dip-coating agreed with our previous work,33,35 which could be attributed to Bénard−Marangoni convection triggered by solvent evaporation. During the dip coating at ${\\bf\\bar{60}}\\ {}^{\\circ}{\\bf C},$ $2{\\cdot}\\mathrm{Pr}$ as the major solvent of the coating solutions could rapidly evaporate from the coating layer on the substrate, leading to the evaporationdriven pattern formation on the surface. However, the gelation of the coating layers containing PG and DPG did not complete without the heat treatment as a result of the high boiling point of the co-solvents (Table 1). Thus, the thickness and surface roughness measurements with a contact probe surface profilometer could not be carried out for the as-deposited gel films, because the coating layers was scraped off by the contact probe during the measurements. \n\n \nFigure 3. Optical micrographs of the as-deposited gel films obtained (a) without co-solvents $\\dot{\\boldsymbol{x}}$ and $y=0$ ) and with (b) PG $\\stackrel{\\prime}{x}=0.75$ ) and (c) DPG $\\left(y=0.75\\right)$ , dried at $60~^{\\circ}\\mathrm{C}$ . \nFigure 4. Dependence of film thickness upon PG and DPG volumes in the coating solutions for the titania films heated at 200 and $600^{\\circ}\\mathrm{C}$ ( $\\mathbf{\\Phi}_{x}$ or $y=0{-}\\mathrm{\\bar{1}}.50_{,}^{\\cdot}$ ). The error bars represent the standard deviations. The lines are a guide to the eye. \n\nTo obtain rigid coating layers, we heated the as-deposited gel films. Heat-treated titania films were obtained from the gel films of $x$ or $y=0{-}1.50$ by heating at 200 or $600~^{\\circ}\\mathrm{C}$ for $10~\\mathrm{min}$ in titania films, where the co-solvent contents are described with the co-solvent volume per gram of $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}^{~i})_{4}$ in the solutions (Table 2). Generally, the thickness of dip-coating layers is known to be influenced by the viscosity of the coating solutions. The higher viscosities suppress the downward flow of the coating solution on the substrate, resulting in the formation of thicker films. The thickness of the titania films heated at 200 $^{\\circ}\\mathrm{C}$ increased from ca. $150~\\mathrm{nm}$ ( $x$ or $y=0,$ ) to ca. $370~\\mathrm{nm}$ ( $\\overset{\\cdot}{x}=$ 1.50) and ca. $340~\\mathrm{nm}$ $(y=1.50)$ with increasing PG and DPG volumes, respectively. The slight increase in the thickness was also observed for the films heated at $600~^{\\circ}\\mathrm{C},$ where the thickness increased from ca. $110\\ \\mathrm{nm}$ ( $x$ or $y=0$ ) to ca. $140~\\mathrm{nm}$ $\\left(x=1.50\\right)$ and ca. $130~\\mathrm{nm}$ $\\left(y=1.50\\right)$ . The increase in the film thickness with rgw addition of PD and DPG could be caused by the higher viscosity of the coating solutions containing the cosolvents (Table 2). The solutions containing PG possessed higher viscosity than DPG, resulting in the slightly larger film thickness. Moreover, the heat treatment at higher temperatures resulted in a smaller thickness, which may be caused by the burning of organic species and the densification of the films. \n\nFigure 5 shows the optical micrographs and 3D surface profiles of the titania films heated at $200~^{\\circ}\\mathrm{C}$ . Cell-like patterns of $20-50\\ \\mu\\mathrm{m}$ in width remained after the heat treatment at 200 $^{\\circ}\\mathrm{C}$ (Figure 5a), and the 3D surface profiles show that the center of the patterns was depressed (Figure 5b). The surface patterns became clear with the addition of the co-solvents, especially PG. Figure 6 shows the optical micrograph and 3D surface profile of the titania films obtained with PG $\\stackrel{\\prime}{x}=1.00\\stackrel{\\cdot}{,}$ ) after the heat treatment at $600~^{\\circ}\\mathrm{C}$ [the surface patterns of the films obtained without co-solvents ( $x$ and $y=0$ ) and with DPG $\\left(y=1.00\\right)$ after the heat treatment at $600~^{\\circ}\\mathrm{C}$ are shown in \n\n \nFigure 5. (a) Optical micrographs and (b) 3D surface profiles of the titania films obtained without co-solvents ( $x$ and $y=0$ ) and with PG $(x=1.00)\\$ ) and DPG $\\left(y=1.00\\right)$ , heated at $200~^{\\circ}\\mathrm{C}$ . \n\n \nFigure 6. (a) Optical micrograph and (b) 3D surface profile of the titania films obtained with PG $\\mathit{\\check{x}}=1.00\\check{},$ , heated at $600~^{\\circ}\\mathrm{C}$ . \n\nFigure S4 of the Supporting Information]. The cell-like patterns did not collapse even after the crystallization and densification of the films, while the height of the patterns after the heating at $600~^{\\circ}\\mathrm{C}$ was small in comparison to $200~^{\\circ}\\mathrm{C}$ (Figures $5\\mathbf{b}$ and $6\\ensuremath{\\mathbf{b}}$ ). \n\n3.2. Influence of the Co-solvent Contents on the Size of Cell-like Patterns. The surface roughness parameters, S and $R_{z},$ of the heat-treated titania films were measured for the quantitative evaluation of the size of cell-like patterns, where S and $R_{z}$ represent the width and height, respectively, of the patterns (Figure 2b). Figure 7 shows the dependence of the width and height of the surface patterns on the PG and DPG volumes in the coating solutions for the heat-treated titania films. The width of the cell-like patterns monotonically increased with increasing the co-solvent volume (Figure 7a), which indicates the reduction of the number of convection cells per area. On the other hand, the height of the patterns increased with increasing the co-solvent volume up to ca. 0.30 mL and reduced with further addition of the co-solvents (Figure 7b). The initial increase in the height suggests the enhancement of evaporation-driven surface elevation by the addition of the co-solvents, despite the decrease in the number of convection cells. It should also be noted that no significant difference in the width between PG and DPG was observed (Figure 7a), while the titania films obtained with PG exhibited a larger height than DPG (Figure 7b). \n\nThe decrease in the number of convection cells per area (i.e., the increase in the width of the cell-like patterns) with the addition of PG and DPG is deduced to be caused by the high boiling point and high viscosity of the co-solvents. The presence of the co-solvents with a high boiling point, i.e., low volatility, and high viscosity in the coating layer can inhibit the evaporation-driven convective phenomenon, which means the reduction of the frequency of the occurrence of Bénard− \n\n \nFigure 7. Dependence of (a) width and (b) height of the surface patterns upon PG and DPG volumes in the coating solutions for the titania films heated at 200 and $600~^{\\circ}\\mathrm{C}$ ( $\\dot{\\boldsymbol{x}}$ or $y=0{-}1.50)$ . The error bars represent the standard deviations. The lines are a guide to the eye. \n\nMarangoni convection. Thus, the addition of PG and DPG could decrease the number of the convection cells per area, leading to the formation of wider cell-like patterns. Because the boiling point of PG and DPG is high enough to disturb the occurrence of Bénard−Marangoni convection at $60~^{\\circ}\\mathrm{C}$ (the boiling point of PG, $188.2\\ ^{\\circ}\\mathrm{C};$ DPG, $230.0\\ ^{\\circ}\\mathrm{C})$ , PG and DPG could similarly influence the number of convection cells, providing the surface patterns with a similar width. \n\nOn the other hand, the addition of small amounts of PG and DPG [below $0.30\\mathrm{mL}/\\mathrm{g}$ of $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}{}^{i})_{4}]$ led to a larger surface elevation (Figure 7b), while the addition of the co-solvents reduced the number of convection cells. As shown in eqs 1 and 2, Bénard−Marangoni convection is activated with an increasing coating layer thickness. In fact, we have investigated the influence of the film thickness on the pattern formation induced by Bénard−Marangoni convection for sol−gel-derived titania films, where the height of cell-like patterns increased with increasing film thickness.35 In the present case, the addition of PG and DPG also resulted in the increase in the film thickness (Figure 4), and thus, the larger thickness of the coating layer may contribute to the increase in the height of the patterns. \n\nHowever, the larger surface elevation observed in the present case cannot be explained only by the influence of the thickness. Figure 8 shows the ratio of the height of cell-like patterns to the thickness for the heat-treated titania films. The height/thickness ratio increased with an increasing co-solvent volume up to ca. $0.30~\\mathrm{mL}$ and reached 0.62 and 0.40 by the addition of PG and DPG, respectively. Table 3 shows the height/thickness ratio for the sol−gel-derived titania films reported in the present and previous works, the latter of which were all prepared without co-solvents. It is seen that the titania films obtained with PG and DPG exhibited a higher height/thickness ratio than that without the co-solvents, irrespective of the film thickness. These suggest that the surface elevation induced by Bénard− Marangoni convection is more strongly activated by the addition of the co-solvents, especially PG. The enhancement of the evaporation-driven surface elevation could be attributed to the higher surface tension gradient as a result of the addition of the co-solvents with a high surface tension and low volatility. \n\n \nFigure 8. Dependence of the height/thickness ratio on PG and DPG volumes in the coating solutions for the titania films heated at 200 and $600~^{\\circ}\\mathrm{C}$ ( $x$ or $y=0{-}1.50\\rangle$ . The lines are a guide to the eye. \n\nBénard−Marangoni convection may have resulted from the surface tension gradient in the coating layer as a result of the evaporation of $2{\\cdot}\\mathrm{Pr}$ during dip coating at $60\\ ^{\\circ}\\mathrm{C},$ where PG and DPG are thought to remain in the coating layer during the solvent evaporation, creating a much higher surface tension gradient. A higher surface tension gradient could provide a stronger convective flow of solutions, resulting in a larger surface elevation. The larger surface elevation provided by PG than that provided by DPG may be due to the higher surface tension of PG than that of DPG (Figure 7b and Table 3). \n\nFurther addition of PG and DPG over $0.30~\\mathrm{mL}$ led to the decrease in the height (Figure 7b), where the height/thickness ratio became smaller than that of the films obtained without the co-solvents (Figure 8). Previously, we reported that the slow gelation of the coating layer leads to the disappearance of the surface patterns via solution flow before the completion of the gelation.30,34 The presence of the large amounts of co-solvents with low volatility is thought to suppress the gelation of the coating layer, resulting in the reduction of the height of cell-like patterns. \n\n3.3. Influence of the Heating Temperature on the Size of Cell-like Patterns. The heat treatment at $600~^{\\circ}\\mathrm{C}$ resulted in the cell-like patterns with a smaller height than $200~^{\\circ}\\mathrm{C}$ (Figure 7b), which could be attributed to the densification of the films. However, the heat-treatment temperature did not influence the height/thickness ratio (Figure 8). On the other hand, the width did not depend upon the heat-treatment temperature (Figure 7a) because the films are contained by the substrate and not allowed to shrink in the in-plane direction.",
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"category": " Results and discussion"
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},
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{
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"id": 5,
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"chunk": "# 4. CONCLUSION \n\nSpontaneous pattern formation induced by Bénard−Marangoni convection was observed for the sol−gel-derived titania films prepared from $\\mathrm{Ti}(\\mathrm{OC}_{3}\\mathrm{H}_{7}^{~i})_{4}$ solutions, where micrometerscaled cell-like patterns were formed on the surface during dip coating. The height and width of the patterns were controlled by the addition of co-solvents with a high surface tension and low volatility. The width of the patterns increased with increasing PG and DPG contents, which could be attributed to the reduction of the number of convection cells. On the other hand, the addition of PG and DPG resulted in the increase in the height of the surface patterns, which was thought to be provided by the higher surface tension gradient in the coating layer generated during solvent evaporation and the consequent activation of the surface elevation via the convective flow of solutions. The surface patterns remained even after the heat treatment, and anatase thin films with periodic surface patterns could be obtained. \n\nTable 3. Height/Thickness Ratio for the Pattern Formation Induced by Bénard−Marangoni Convection on Sol−Gel-Derived Titania Films \n\n\n<html><body><table><tr><td>film </td><td> solvent</td><td> pattern height (nm)</td><td>thickness (nm)</td><td>height/thickness</td></tr><tr><td colspan=\"5\">Present Work, Heated at 200 °C</td></tr><tr><td>titania</td><td>2-Pr</td><td>42</td><td>148</td><td>0.28</td></tr><tr><td>titania</td><td>2-Pr + PG (0.26 mL of PG)</td><td>213</td><td>346</td><td>0.62</td></tr><tr><td>titania</td><td>2-Pr + DPG (0.35 mL of DPG)</td><td>130</td><td>322</td><td>0.40</td></tr><tr><td colspan=\"3\">Previous Work34 a</td><td></td><td></td></tr><tr><td>titania</td><td>2-Pr</td><td>49</td><td>140</td><td>0.35</td></tr><tr><td>titania-PVPb (Ti/PVP = 0.3)c</td><td>2-Pr</td><td>103</td><td>410</td><td>0.25</td></tr><tr><td>titania-PVPb (Ti/PVP = 0.7)c</td><td>2-Pr</td><td>145</td><td>460</td><td>0.32</td></tr></table></body></html>\n\naAll samples were dried at the coating temperature (without heating). $\\ensuremath{^b}\\ensuremath{\\operatorname{PVP}}=\\ensuremath{\\operatorname{poly}}$ (vinylpyrrolidone). cMole ratio.",
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"category": " Conclusions"
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},
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{
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"id": 6,
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"chunk": "# ASSOCIATED CONTENT",
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"category": " References"
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},
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{
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"id": 7,
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"chunk": "# $\\otimes$ Supporting Information \n\nThe Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b02929. \n\nSchematic illustration of our experimental methods (Figure S1), definitions of surface roughness parameters, including S (mean spacing of local peaks of the profile) and $R_{z}$ (ten point height of irregularities) (Figure S2), XRD patterns of heat-treated thin-film samples (Figure S3), and optical micrographs and 3D surface profiles of thin films heated at $600~^{\\circ}\\mathrm{C}$ (Figure S4) (PDF)",
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"category": " Materials and methods"
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},
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{
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"id": 8,
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"chunk": "# AUTHOR INFORMATION",
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"category": " References"
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},
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{
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"id": 9,
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"chunk": "# Corresponding Author \n\n\\*Telephone: $+81$ -6-6368-1121, ext. 5638. Fax: +81-6-6388- 8797. E-mail: h_uchi@kansai-u.ac.jp.",
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"category": " References"
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},
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{
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"id": 10,
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"chunk": "# Notes \n\nThe authors declare no competing financial interest.",
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"category": " Conclusions"
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},
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{
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"id": 11,
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"chunk": "# ACKNOWLEDGMENTS \n\nThis work was financially supported by the Sumitomo Foundation Grant-in-Aid for Basic Science Research.",
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"category": " References"
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},
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{
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"id": 12,
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"chunk": "# REFERENCES \n\n(1) Adachi, E.; Dimitrov, A. S.; Nagayama, K. Stripe patterns formed on a glass-surface during droplet evaporation. Langmuir 1995, 11 (4), 1057−1060. (2) Brinker, C. J.; Lu, Y. F.; Sellinger, A.; Fan, H. Y. Evaporationinduced self-assembly: Nanostructures made easy. Adv. Mater. 1999, 11 (7), 579−585. (3) Brinker, C. J. Evaporation-induced self-assembly: Functional nanostructures made easy. MRS Bull. 2004, 29 (9), 631−640. (4) Chen, J.; Liao, W.-S.; Chen, X.; Yang, T.; Wark, S. E.; Son, D. H.; Batteas, J. D.; Cremer, P. S. Evaporation-Induced Assembly of Quantum Dots into Nanorings. ACS Nano 2009, 3 (1), 173−180. (5) Fan, F. $\\mathrm{Q.;}$ Stebe, K. J. Assembly of colloidal particles by evaporation on surfaces with patterned hydrophobicity. Langmuir 2004, 20 (8), 3062−3067. (6) Gibaud, A.; Grosso, D.; Smarsly, B.; Baptiste, A.; Bardeau, J. F.; Babonneau, F.; Doshi, D. A.; Chen, Z.; Brinker, C. J.; Sanchez, C. 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(33) Uchiyama, H.; Mantani, Y.; Kozuka, H. Spontaneous Formation of Linearly Arranged Microcraters on Sol-Gel-Derived Silica-Poly(vinylpyrrolidone) Hybrid Films Induced by Benard-Marangoni Convection. Langmuir 2012, 28 (27), 10177−10182. \n(34) Uchiyama, H.; Miki, Y.; Mantani, Y.; Kozuka, H. Spontaneous Formation of Micrometer-Scaled Cell-like Patterns on AlkoxideDerived Silica Gels Induced by Benard-Marangoni Convections. J. Phys. Chem. C 2012, 116 (1), 939−946. \n(35) Uchiyama, H.; Namba, W.; Kozuka, H. Spontaneous Formation of Linear Striations and Cell-like Patterns on Dip-Coating Titania Films Prepared from Alkoxide Solutions. Langmuir 2010, 26 (13), 11479−11484. \n(36) de Gennes, P. G. Solvent evaporation of spin cast films: ″crust″ effects. Eur. Phys. J. E: Soft Matter Biol. Phys. 2002, 7, 31−34. \n(37) Weh, L. Surface structures in thin polymer layers caused by coupling of diffusion-controlled Marangoni instability and local horizontal temperature gradient. Macromol. Mater. 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"category": " References"
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}
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