Langmuir 2008, 24, 2921-2928
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Control of Wettability of Molecularly Thin Liquid Films by Nanostructures Kenji Fukuzawa* Department of Micro/Nano Systems Engineering, Nagoya UniVersity, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan, and JST-PRESTO, 4-1-8 Hon-cho, Kawaguchi 332-0012, Japan
Takanori Deguchi, Yasuhiro Yamawaki, and Shintaro Itoh Department of Micro/Nano Systems Engineering, Nagoya UniVersity, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Takuro Muramatsu and Hedong Zhang Department of Complex Systems Science, Nagoya UniVersity, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan ReceiVed October 8, 2007. In Final Form: NoVember 24, 2007 The patterning of liquid thin films on solid surfaces is very important in various fields of science and engineering related to surfaces and interfaces. A method of nanometer-scale patterning of a molecularly thin liquid film on a silicon substrate using the lyophobicity of the oxide nanostructures has recently been reported (Fukuzawa, K.; Deguchi, T.; Kawamura, J.; Mitsuya, Y.; Muramatsu, T.; Zhang, H. Appl. Phys. Lett. 2005, 87, 203108). However, the origin of the lyophobicity of the nanostructure with a height of around 1 nm, which was fabricated by probe oxidation, has not yet been clarified. In the present study, the change in thickness of the liquid film on mesa-shaped nanostructures and the wettability for the various combinations of the thickness of the liquid films and the height of ridge-shaped nanostructures were investigated. These revealed that lyophobicity is caused by a lowering of the intermolecular interaction between the liquid and silicon surfaces by the nanostructure and enables the patterning of a liquid film along it. The tendency of the wettability for a given liquid film and nanostructure size can be predicted by estimating the contributions of the intermolecular interaction and capillary pressure. In this method, the height of the nanostructure can control the wettability. These results can provide a novel method of nanoscale patterning of liquid thin films, which will be very useful in creating new functional surfaces.
1. Introduction Patterning or distribution control of liquid thin films on solid surfaces is very important in various fields of science and engineering related to surfaces and interfaces, such as colloid and interface science, tribology, microfluidics, and soft lithography. In addition, fine patterning of liquid films on solid surfaces is facing strongly growing demand. Printing-based techniques1 have been used in recently emerging polymer-based electronics because the devices are made from polymer liquid. Polymer electronics can provide devices that are much more flexible and cheaper than conventional silicon devices. In addition, patterning of liquid film can provide new types of microfluidic devices such as micro-total-analysis systems or lab-on-a-chip. A recently developed liquid-liquid fluidic device, where microdroplets floating on another liquid are dielectrophoretically driven, can deliver materials without them adhering to the wall.2 In computer hard disk drives (HDDs), the control of liquid films is also indispensable to improving the recording density. High-density HDDs require a very low flying height for a head, less than 10 nm. To meet this demand, the current thickness of liquid lubricant films, which are necessary for good durability and reliability of HDDs, is molecularly thin and on the order of 1 nm. Therefore, * Corresponding author. E-mail:
[email protected]. Tel: +81-52-789-2747. Fax: +81-52-789-3129. (1) Service, R. F. Science 1997, 278, 383-384. (2) Velev, O. D.; Prevo, B. G.; Bhatt, K. H. Nature 2003, 426, 515-516.
the distribution control of molecularly thin lubricant films is indispensable to high-density recording.3 Many methods have been reported for controlling the distribution of liquids on solids with laterally varying wettabilities by using chemically patterned surfaces. However, the pattern size was on the order of micrometers because they aimed at patterning rather thick liquids.4,5 Nanometer-scale patterning requires the same order of thickness. Recently, nanometer-thick liquid stripes have been formed on a chemically patterned surface using monolayers with different end groups.6-8 In refs 6 and 7, lyophilic regions on a lyophobic monolayer formed by probe oxidation and nanopatterning of liquid thin films have been achieved. In these methods, a surface with locally different wettability was created by forming the regions consisting of different chemical materials. In the method in refs 6 and 7, a surface with different wettability was created by forming two regions with apolar -CH3 (lyophobic) and polar -COOH (lyophilic) groups. We reported another type of patterning of a nanometer-thick liquid film not by using a chemically patterned surface but by (3) Mate, C. M.; Toney, M. F.; Leach, K. A. IEEE Trans. Magn. 2001, 37, 1821-1823. (4) Lopez, C. P.; Biebuyck, H. A.; Frisbie, C. D.; Whitesides, G. M. Science 1993, 260, 647-649. (5) Gau, H.; Heminguhaus, S.; Lenz, P.; Lipowsky, R. Science 1999, 283, 46-49. (6) Hoeppener, S.; Maoz, R.; Sagiv, J. Nano Lett. 2003, 3, 761. (7) Chowdhury, D.; Maoz, R.; Sagiv, J. Nano Lett. 2007, 7, 1770. (8) Checco, A.; Gang, O.; Ocko, B. M. Phys. ReV. Lett. 2006, 96, 056104.
10.1021/la703106s CCC: $40.75 © 2008 American Chemical Society Published on Web 02/01/2008
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Figure 1. Patterning of a thin liquid film on a silicon surface by an oxide nanostructure. (a) AFM image of fabricated nanostructures with a height of about 2.5 nm. (b) AFM image of the liquid film on the nanostructures with a thickness of about 10 nm. (c) Crosssectional view of the dotted line of b.
using a physically patterned surface.9 In this method, a surface with locally different wettability was created by forming regions with different physical properties, although all of the regions consisted of the same materials. In thin liquid films, wettability is determined not only by the surface energy of the liquid/air and liquid/solid interfaces but also by the intermolecular interaction between the surfaces of liquid and solids. The contribution of the intermolecular interaction is frequently treated as the interface potential or disjoining pressure.10-13 Oxide nanostructures with a height of around 1 nm, which were fabricated by the probe oxidation of a silicon surface,14,15 lowered the wettability of the nanometer-thick liquid film on silicon surfaces, and the liquid films could be patterned along the nanostructures. An example of a patterned thin liquid film taken by atomic force microscopy (AFM) is shown in Figure 1. In this experiment, patterns with various shapes were drawn on a silicon surface using a nanooxide ridge (nanostructure) with a height of about 2.5 nm (Figure 1a), and a 10-nm-thick liquid perfluoropolyether lubricant film was applied to it (Figure 1b). Figure 1c shows the cross-sectional view of Figure 1b. The details of the experiment are described in the Materials and Methods section of this article. The Figure shows that a liquid thin film can be patterned along the nanostructure because of its lyophobicity. This means that patterns of liquid thin films of any desired shape can be produced by using a nanostructure as a template. Although the minimum size that the method can provide has not yet been clarified, a line of the thin liquid film with a width of less than 100 nm was possible. (9) Fukuzawa, K.; Deguchi, T.; Kawamura, J.; Mitsuya, Y.; Muramatsu, T.; Zhang, H. Appl. Phys. Lett. 2005, 87, 203108. (10) de Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827-863. (11) de Gennes, P. G.; Brochard-Wyart, F.; Que´re´, D. Gouttes, Bulles, Perles et Ondes; Berlin, 2002. (12) Derjaguin, B. V.; Chouraev, N. V. J. Colloid Interface Sci. 1978, 66, 389-398. (13) Israelachivili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, 1992. (14) Dagata, J. A.; Perez-Murano, F.; Martin, C.; Kuramochi, H.; Yokoyama, H. Appl. Phys. Lett. 1990, 56, 2001-2003. (15) Dagata, J. A. Science 1995, 270, 1625-1626.
Figure 2. Patterning of a 5-nm-thick liquid film by a ridge-shaped oxide nanostructure. The ridge height is about 1.9 nm. (a) AFM image of the liquid film on the nanostructure. (b) Cross-sectional views of the dotted line of a.
In the example shown in Figure 2, the minimum line width of 5-nm-thick perfluoropolyether lubricant films was about 72 nm.9 This patterning method can provide a novel functional surface for various fields in science and engineering. However, the origin of the lyophobicity of the nanostructure has not yet been fully clarified, although it was suggested that the lyophobicity is related to the intermolecular interaction between the liquid and solid surfaces. In this article, we report a detailed investigation of the mechanism of the lyophobicity, focusing on the intermolecular interaction.
2. Origin of the Lyophobicity of Nanostructures In this section, the origin of the lyophobicity of nanostructures is theoretically investigated. In a nanostructure with an area A (Figure 3), the difference in surface energy between surfaces covered and not covered with a liquid film is10,11,13,16
∆γA ) (γsa - γla - γsl - P(hr))A
(1)
Here, γsa, γla, and γsl are the interface energies of solid/air, liquid/ air, and solid/liquid; P(hr) is the interface potential between the (16) Adamson, W.; Gast. A. Physical Chemistry of Surfaces; Wiley: New York, 1997.
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the interface energy γna of nanostructure/air is equal to that of silicon/silicon oxide/air. In the same way, the interface energy γnl of nanostructure/liquid is equal to that of silicon/silicon oxide/ liquid. For apolar liquids,
γna ) γso + γoa +
Figure 3. Schematic liquid patterning by ridge-shaped nanostructure. The dotted line shows the case when a solid surface is covered with a liquid thin film.
liquid and solid surfaces; and hr is the thickness of the liquid film on the nanostructure. The nanostructure shows lyophobicity when ∆γ < 0. Using the spreading coefficient S ) γsa - γla - γsl, we can write this condition as
S < P(hr)
(2)
When thickness hr is the critical thickness hc (S ) P(hc)), the surface tension of the solid balances that of the liquid. Therefore, liquid-film covered and uncovered areas coexist when hr ) hc. In addition, when P(hr) is a monotonically decreasing function, the solid surface shows lyophobicity for liquid films with a thickness of hr < hc. If a liquid film with a thickness of hr < hc is applied to the nanostructure, then the film is unstable on the nanostructure. When the liquid is apolar and the intermolecular interaction between the liquid and solid is the van der Waals interaction, P(hr) of the silicon/silicon oxide/liquid/air interface is given by17
P(hr) )
Aola 12πhr2
+
Asla - Aola 12π(hr + D)2
(3)
where D is the thickness of the silicon oxide layer and Asla and Aola are Hamaker constants of silicon/liquid/air and silicon oxide/ liquid/air interfaces. There is a well-known relationship between the disjoining pressure Π(hr) and the interface potential P(hr), as shown below.12,13
Π(hr) ) -
∂P(hr) ∂hr
(4)
In this experiment, a buried oxide layer was formed by probe oxidation, as shown in Figure 3, and the ratio of the depth of the buried layer to the height of the nanostructure was almost constant at about 0.4.20 Therefore, the thickness of the oxide layer is written as D ) D0 +1.4H, where H is the height of the nanostructure and D0 is the thickness of the native oxide layer. Using this relation and eq 3, when the liquid thickness is the critical one, we get
S ) P(hc) )
Aola 12πhc
2
+
Asla - Aola 12π(hc + D0 + 1.4H)2
(5)
Considering that the substrate without a liquid film consists of three layers (i.e., silicon, silicon oxide, and air layers (Figure 3)), (17) Seemann, R.; Herminghaus, S.; Jacobs, K. Phys. ReV. Lett. 2001, 86, 5534-5537. (18) Teletzke, G. F.; Davis, H. T.; Scriven, L. E. Chem. Eng. Commun. 1987, 55, 41-81. (19) Kim, H. I.; Mate, C. M.; Hannibal, K. A.; Perry, S. S. Phys. ReV. Lett. 1999, 82, 3496-3499. (20) Fukuzawa, K.; Deguchi, T.; Muramatsu, T.; Zhang, H.; Mitsuya, Y. Microsyst. Technol. 2007, 13, 1219-1225.
γnl ) γso + γol +
Asoa
(6)
12π(D0 + 1.4H)2 Asol
(7)
12π(D0 + 1.4H)2
Here, γso, γoa, and γol are the interface energies of the silicon/ silicon oxide, silicon oxide/air, and silicon oxide/liquid interfaces. The third terms of eqs 6 and 7 are contributions of the van der Waals interaction. Asoa and Asol are the Hamaker constants of the silicon/silicon oxide/air and silicon/silicon oxide/liquid interfaces. Using eqs 6 and 7, we obtain the relationship between S and D as
S ) γna - γla - γnl ) S0 +
Asoa - Asol 12πD2 S0 +
) Asoa - Asol 12π(D0 + 1.4H)2
(8)
where S0 ) γoa - γol - γla. Equation 8 indicates that a higher nanostructure lowers the wettability by weakening the intermolecular interaction between the liquid and solid surfaces, which corresponds to the second term on the right side of the equation. Using the relation S ) P(hc) when the liquid film takes the critical thickness hc (eq 5) and eq 8, we get
S0 +
Asoa - Asol 12π(D0 + 1.4H)
) 2
Aola
+ 2
12πhc
Asla - Aola 12π(hc + D0 + 1.4H)2 (9)
Thus, the critical thickness hc can be obtained by eq 9. The nanostructure is covered with the liquid film when hr > hc whereas it is not covered with the liquid film when hr < hc. The thickness of a liquid film on the flat substrate hf is easier to obtain experimentally than that on the nanostructure hr (Figure 3). hf is not always equal to hr because the intermolecular interaction and the curvature of the surface of the liquid on the nanostructure are different from those on the flat substrate. hf can be converted to hr as follows. When the liquid film on the nanostructure is in hydrodynamic equilibrium, the pressures of the liquid film on the flat substrate and nanostructure are balanced.18,19 Therefore,
Aola 3
6πhr
+
Asla - Aola 6π(hr + D0 + 1.4H)
3
-
γLA ) R Aola 6πhf
+ 3
Asla - Aola 6π(hf + D0)3
(10)
where R is the radius of the nanostructure. In eq 10, the first and second terms on the left side are the disjoining pressure of the liquid on the nanostructure, and the third term is the capillary or Laplace pressure. The right side is the disjoining pressure of the liquid film on the flat substrate. Here, the disjoining pressure was obtained using eqs 3 and 4. Thus, hf can be converted to hr using eq 10. 3. Materials and Methods In this experiment, 〈100〉 silicon wafers were used as a substrate. The silicon wafers were N-type silicon whose dopant was phosphorus, and the resistivity was about 10 Ω cm. The roughness of the wafer
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was about 0.1 nm. The silicon substrates were cleaned with an aqueous solution of hydrogen peroxide and sulfuric acid and stored in a desiccator. Before probe oxidation, the wafer was cleaned with a fluorocarbon solvent (HFE-7200, 3M). A metallized probe for AFM (Nanoscope IV, Veeco), which was negatively biased, was placed in contact with the substrate surface, and oxide was produced by electrochemical reaction in the minute water meniscus formed between the probe tip and the substrate. The probe was a Pt/Ircoated silicon probe whose spring constant was about 0.2 N/m. Nano-oxide structures shaped in desired patterns can be fabricated by scanning the probe using contact AFM mode. The scanning speed of the probe was set at around 1 µm/s, and the bias voltage was from 5 to 11V. To observe the fabricated nanostructures, we used silicon probes with a smaller tip radius and selected a dynamic (tapping) AFM mode. In this measurement, microfabricated silicon cantilevers whose spring constants were about 20-100 N/m and whose tip radii were less than 10 nm were used. The probe oxidation created ridge and buried structures because silicon oxide has a lower density than silicon (Figure 3), and the ratio of ridge height to the depth of the buried structure was about 0.4 in this experiment, as explained above. Using metallized probes with a tip radius of about 20 nm, we were able to produce a surface structure with a width of several tens of nanometers and a height on the order of 1 nm. The average difference in the height of the ridge-shaped nanostructures just after fabrication and after leaving for 1 week was about 10%. Nanostructures with heights from 0.3 to 2.4 nm were investigated in this experiment. It is difficult to measure the exact same point just after fabrication and after 1 week because a probe is withdrawn from the samples. Therefore, we think that the difference is mainly due to a measurement error. This result shows that fabricated oxide nanostructures are stable. Details of the fabrication conditions are described in ref 21. Perfluoropolyether (PFPE) lubricant (FOMBLIN-Z03, Solvey Solexis), which is used for hard disk drives, was used as a sample liquid. It is an apolar liquid and a linear-chain polymer with a molecular weight of about 4000 and a length of about 14 nm. The estimated radius of gyration rG in the bulk is about 1.4 nm. Its surface energy is 23 × 10-3 J/m2. The molecular structure of the lubricant is given by CF3-[(O-CF2-CF2)p-(O-CF2)q]O-CF3
(11)
where the ratio p/q is typically between 0.5 and 2. The lubricant has very low volatility: its evaporation loss at 149 °C is 6% according to the manufacturer. A nonvolatile liquid was used in this study because the liquid film thickness is an important factor that determines the pattern formation, as mentioned below. It was experimentally confirmed that the interaction between the liquid lubricant and silicon substrate can be described by the van der Waals interaction, as shown in eq 3.21 Moreover, the Hamaker constants of eq 3 and the thickness of the native oxide layer were also experimentally obtained as Aola ) 9.1 × 10-21 J and Asla - Aola ) 7.0 × 10-20 J and D0 ) 1.0 nm.21 In this method, a microgroove on a silicon surface was fabricated, and a liquid film was applied to it by dip coating. A liquid meniscus was formed in the microgroove whereas a flat film was formed on the flat substrate surface. The radius of curvature of the meniscus of the thin film in the microgroove was measured by AFM, and the capillary pressure of the liquid in the microgroove was obtained. The disjoining pressure of the liquid film on the flat surface is balanced with the capillary pressure of the liquid in the microgroove. Therefore, the disjoining pressure is obtained from the capillary pressure. The Hamaker constants in eq 10 were obtained from the measured disjoining pressure. The liquid lubricant was applied to the silicon surface with nanostructures by dip coating. In this method, which is used for the commercial production of hard disk drives of computers, the substrate was immersed and then pulled out of the fluorocarbon solution (HFE7200) at a constant speed. The speed of pulling out was from 0.5 to 2 mm/s, and the density of solution was from 0.2 to 0.8 wt %. (21) Fukuzawa, K.; Kawamura, J.; Deguchi, T.; Zhang, H.; Mitsuya, Y. J. Chem. Phys. 2004, 121, 4358-4363.
The thickness of the liquid film on the substrate could be changed with subnanometer resolution by adjusting the removal speed and the lubricant solution density. To observe the liquid distribution, we used silicon probes with a smaller tip radius and selected a dynamic (tapping) AFM mode.21 In this measurement, microfabricated silicon cantilevers whose spring constants were about 2.8 N/m and whose tip radii were less than 10 nm were used. In dynamic mode AFM, the morphology of the surface is imaged by maintaining the vibration amplitude at a set point while placing the vibrating cantilever so close to a sample surface that the cantilever contacts the sample surface intermittently. To reduce adhesion of the liquid to the probe tip, the probe was fluoride coated.22 The probe was dipped into a fluoride coating solution. After heating the probe to 130 °C, an excess coating material was rinsed off by dipping the probe in the fluorocarbon solvent (HFE-7200). Then, the probe was heated again to adhere the coating material to the probe tightly.
4. Results and Discussion A. Relationship between Nanostructure and Intermolecular Interaction. To clarify the effect of nanostructures on the intermolecular interaction, mesa-shaped nanostructures with various heights were fabricated, and thin liquid films with various thicknesses were applied to them. To eliminate the effect of capillary pressure, a nanostructure without the curvature was used, as shown in Figure 4a. Here, this type of nanostructure, which has a flat part on the top and steep steps at the ends, is called a mesa-shaped nanostructure because it is similar in shape to a landform called “mesa”. Mesa-shaped structures were fabricated by narrowing the pitch of the probe scanning lines. The height of the mesa shown in Figure 4 is about 0.9 nm. Topography and phase AFM images of the liquid on the mesa are shown in Figure 4b,c. The thickness of the liquid was about 10.3 nm. Figure 4d-f shows cross-sectional views of Figure 4a-c, respectively. In Figure 4e,f, the averaged height or phase values over the vertical axis (y axis) are plotted to show the difference in height between the liquids on the mesa and flat substrate. Figure 4b,e shows that the liquid on the mesa is thinner than that on the flat substrate. This agrees qualitatively with the theory described in section 2. In eq 10, hr should be smaller than hf for a nonzero value of H because the right side of the equation is constant, which corresponds to the disjoining pressure of the liquid on the substrate without the mesa. R is infinite in this case. To confirm the validity of eq 10, the pressures of the liquid films on the nanostructure and the flat substrate were investigated. Let the difference in the thickness between the liquid films on the nanostructures and flat substrate be δh. Using the thicknesses of hf and δh obtained by AFM observation and the relationship hr ) hf - δh - H (Figure 3), we obtained the liquid thickness on the nanostructure hr. To obtain accurate data, the average height difference δh was obtained in the same manner as shown in Figure 4e. Some samples have small holes in the liquid film on the nanostructure. In this case, we directly obtained hr. By substituting hr and H into eq 10, we obtained the pressure on the nanostructure Πn and that on the flat substrate Πf. The imbalance |Πn - Πf|/Πn is shown in Figure 5. The average of the imbalance |Πn - Πf|/Πn is 4.3%. This means that the pressure balance of the liquids is almost valid and the eq 10 is also valid in this experiment. Moreover, by substituting hf and H into eq 10, we theoretically estimated hr. The theoretically obtained thickness hrt and experimental one hre are plotted in Figure 6. The standard deviation of |hrt - hre| is 0.26 nm. This result supports the validity of the effect of the nanostructure on the intermolecular interaction described in section 2. Here, the ratio of the depth of the buried layer to the height of the nanostructure was assumed to be 0.4, (22) Tani, H. IEEE Trans. Magn. 1999, 35, 2397.
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Figure 4. AFM images of a mesa-shaped nanostructure and a liquid film on it. (a) Mesa-shaped nanostructure fabricated by probe oxidation. The height of the nanostructure is about 0.9 nm, and the scan area is 6.3 × 2.3 µm2. (b) Thin liquid film on the nanostructure. The thickness of the liquid is about 10.3 nm. (c) Phase image of b. The scan area is 6.3 × 2.4 µm2 for both images. (d) Cross-sectional view of a. (e) Cross-sectional view of b. (f) Cross-sectional view of c. Averaged values over the vertical direction of b and c were plotted in e and f, respectively.
although the relation was experimentally confirmed only for the ridge-shaped nanostructure. However, we believe that the assumption is appropriate in this case because the mesa-shaped nanostructure was formed by fabricating the ridge-shaped ones with a very close pitch and theoretical estimations based on the assumption agree well with the experimental results as shown in Figures 5 and 6. B. Relationship between Wettability and Nanostructure. An example of liquid patterning by line- or ridge-shaped nanostructures is shown in Figure 7. Figure 7a,b shows AFM images of the fabricated nanostructure and about a 7.7-nm-thick liquid film applied to the nanostructure. Cross-sectional views of Figure 7a,b are shown in Figure 7c. These results indicate that a lower nanostructure has lower lyophobicity, which leads to coverage by the liquid film. To clarify the relationship between the height of nanostructure and the lyophobicity, we applied liquid films of various thicknesses onto ridge-shaped nanostruc-
tures with various heights. Figure 8 shows the relationship between the height of the nanostructure H and the liquid thickness on the nanostructure hr when the thickness on the flat substrate hf ) 3.8, 7.4, and 11.6 nm. In the same manner as in section 4A, using the thicknesses hf and δh obtained by AFM observation, we obtained hr as hf - δh - H. When hf ) 3.8 and 7.4 nm, hr drastically changed at H ) 1.0 and 1.4 nm, respectively. This means that the wettability changed at these heights. Conversely, hr did not drastically change within the height range in this experiment when hf ) 11.6 nm. This indicates that the wettability of the liquid film with hf ) 11.6 nm did not change within this height range and the nanostructure did not exhibit lyophobicity. Letting the nanostructure height where hr drastically changes be the critical height Hc, the nanostructure is covered with the liquid film when H < Hc, whereas it is not covered when H > Hc. For various combinations of hf and H, Hc was obtained, and the wettability results were plotted in Figure 9. The result indicates
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Figure 5. Relation between the pressure imbalance and the thickness of the liquid film on the mesa-shaped nanostructure. Πf and Πn are the disjoining pressures of the liquid on the flat substrate surface and mesa structure, respectively.
Figure 6. Relationship between theoretically and experimentally obtained thicknesses of the liquid film on the mesa-shaped nanostructure for various film thicknesses.
that the nanostructure shows lyophobicity when the liquid film is thin and the nanostructure is high. To confirm the validity of the theory described in section 2, the boundary of the film coverage shown in Figure 9 was estimated using the theory. When the film thickness hf takes the value at the boundary, the thickness on the nanostructure hr takes the critical thickness hc. Letting hf on the boundary be hfb, we get hr ) hc. By estimating the critical thickness hc for the nanostructure with a height of H by eq 9 and converting hc to hfb using eq 10, we can obtain the theoretical boundary. For this estimation, S0 and (Asoa - Asol) in eq 9 should be experimentally obtained. These parameters were determined as follows. Two representative points on the boundary of (hfb, H) ) (6.5 nm, 1.3 nm) and (hfb, H) ) (8.0 nm, 1.6 nm) were selected. Using eq 10, we converted hfb to hr () hc). The radius of curvature of the ridge-shaped nanostructure was obtained as
w2 R) 8(hr + H - hf)
(12)
where w is the width of the nanostructure, which was about 100 nm in this experiment. Substituting (hc, H) of the two repre-
Figure 7. Nanoscale patterning by ridge-shaped nanostructures. (a) AFM image of ridge-shaped nanostructures fabricated by probe oxidation. The scan area is 5.3 × 2.8 µm2. (b) AFM image of the liquid thin film on the nanostructure. The scan area is 5.3 × 2.8 µm2. (c) Cross-sectional views of a and b.
sentative points into eq 9 and solving the simultaneous equations, we obtained S0 and (Asoa - Asol) as S0 ) -1.1 × 10-5 J/m2 and (Asoa - Asol) ) 1.5 × 10-20 J. Using these values, we obtained the theoretically predicted boundary, which is shown as a solid line in Figure 9. The tendency of the theoretical boundary agrees with the experimental data. The validity of the estimated value of (Asoa - Asol) is discussed below. In general, the order of the Hamaker constant of the interface of medium1/medium 2/medium 3 is approximated as11
A123 ≈ π2k(R1 - R2)(R2 - R3)
(13)
where Ri is the polarizability per unit volume for medium i. Using eq 13, we can write the relationship between (Asla - Aola) and (Asoa - Asol) as
Asla - Aola ≈ Asoa - Asol ≈ π2k(RSi - RSiO)(Rl - Ra) (14)
Wettability of Molecularly Thin Liquid Films
Figure 8. Relationship between the height of the ridge-shaped nanostructure and the thickness of the liquid film on it.
Figure 9. Effect of the height of the nanostructure and the thickness of the liquid film on the wettability.
where RSi, RSiO, Rl, and Ra are the polarizabilities of the silicon, silicon oxide, liquid, and air, respectively. As described in section 3, (Asla - Aola) was experimentally obtained as (Asla - Aola) ) 7.0 × 10-20 J. Therefore, the order of (Asoa - Asol) should be 10-20 J. (Asoa - Asol) was obtained as 1.5 × 10-20 J in the above estimation. This result supports the validity of the theory described in section 2. It is important to discuss the effect of confinement of the liquid film. The thickness of the liquid film was very small, which was on the order of the radius of gyration of the molecule in the bulk (rG ) 1.4 nm). The liquid may be in a confined condition. Although a liquid thin film is assumed to be a continuous body in the theory described in section 2, the theoretical estimations show good agreement with the experimental results. Moreover, in ref 21, the pressure balance equation (eq 10), which is based on continuum theory, is valid for the liquid film with a thickness of more than 3 nm. The sample liquid and silicon substrate in ref 21 were the same as those in the experiment reported in this article. These results indicate that the effect of the confined condition is not remarkable and the liquid can be treated as a continuous body. This may be due to the fact that the liquid used in this experiment was aploar. In addition, it is also important to discuss the effect of the curvature of the nanostructure. In this study, the width of the nanostructure was almost constant at around 100 nm. Using eqs
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Figure 10. Estimated boundary of the wettability for the ridges with various widths.
Figure 11. Estimated relationship between the capillary pressure of the liquid on the ridge-shaped nanostructure Pr and the disjoining pressure of the liquid on the flat substrate Πf.
9, 10, and 12, the boundaries of the film coverage were obtained for the ridge-shaped nanostructures with w ) 10 and 1000 nm. The results are shown in Figure 10, and the boundary for w ) 100 nm, which is already shown in Figure 9, is plotted again as a solid line. The results indicate that the ridge width does not significantly affect the boundary. This implies that the condition of the film coverage is mainly determined by disjoining pressure, in other words, the intermolecular interaction between the liquid and solid surface, not by the capillary pressure. Figure 11 shows the ratio of the capillary pressure of the liquid on the ridge Pr and the disjoining pressure on the flat surface Πf. The results were estimated for the liquid films whose film thicknesses were critical ones (hr ) hc) by calculating each term shown in eq 10. In the Figure, the results when w ) 10, 100, and 100 nm are shown. These results indicates that the contribution of the capillary pressure is much smaller than that of the disjoining pressure. This means that the wettability is mainly controlled by the ridge height because the disjoining pressure is determined by the height. In Figure 12, the capillary pressure is compared with the pressure when the liquid surface is along the ridge and the curvature of the liquid surface is equal to that of the ridge surface. The capillary pressure is much smaller than the pressure when the liquid is along the ridge. This implies that the liquid is not along the ridge and is almost flat. Moreover, in Figure 1b,c, liquid films with different thicknesses coexist inside and outside the nanoridgebased circle. Because both of the liquid films are on the substrate
2928 Langmuir, Vol. 24, No. 6, 2008
Figure 12. Comparison between the capillary pressures estimated from experiment shown in Figure 9 and estimated for the liquid film along the ridge surface.
surface, the liquid films should take the same thickness because of the pressure balance (eq 10) if the liquids connect at the nanostructure. These results suggest that the liquid film just after application onto the ridge is almost flat and it becomes unstable and leaves the ridge when the film thickness is less than the critical thickness as shown in Figure 9. The instability is mainly caused by the intermolecular interaction between the liquid and solid surface as described in section 2. Moreover, Figure 11 implies the profile of the liquid on the ridge. The sign of the capillary pressure Pr is positive when H < 1.5 nm but is negative when H > 1.5 nm. Positive pressure means a convex surface, and negative pressure means a concave surface. Therefore, the result suggests that the liquid surface is convex when H < 1.5 nm but concave when H > 1.5 nm. Thus, the lyophobicity of the nanostructure is caused by a lowering of the intermolecular interaction between the liquid and solid surfaces and enables patterning of the liquid film along the nanostructure. The wettability tendency for a given liquid and solid can be predicted using the procedure for obtaining the theoretical boundary in Figure 9, which includes the contributions of the intermolecular interaction and capillary pressure. In this
Fukuzawa et al.
method, the height of the nanostructure can control the wettability. This height is a physical quantity and is easier to adjust than the chemical properties of the surface in a conventional surface coating. This is quite different from a conventional surface coating. Although probe oxidation was used for the fabrication of nanostructures in this study, other methods such as the photolithography-based fabrication used in microelectronics may also be used to fabricate the oxide nanostructure, which would be more suitable for mass production. Moreover, the results in this study can be applied to many liquid/solid systems because the liquid used here was a simple liquid, which is governed by van der Waals interaction and does not have any special interfacial properties. Our method can provide a novel route to device fabrication such as the fine patterning of circuits of polymer electronic devices, the fabrication of nanochannels and reactors for micro-total-analysis systems, or wettability-controlled surfaces for biomedical applications. In addition, it can also provide a novel method for new subjects in science such as the physical properties of a nanoliquid under 3D confinement or chemical reactions in the nanoliquid.
5. Conclusions The origin of the lyophobicity of an oxide surface nanostructure, which was fabricated by probe oxidation on silicon surfaces, was theoretically and experimentally investigated. The lyophobicity was caused by a lowering of the intermolecular interaction between the liquid and silicon surfaces and enables the patterning of a liquid thin film along the nanostructure. The wettability for a given liquid and nanostructure can be predicted using a procedure that includes the contributions of the intermolecular interaction and capillary pressure. In this method, the height of the nanostructure can control the wettability. This is easier to adjust than the chemical properties of the surface in a conventional surface coating. This method is expected to be very useful in creating new functional surfaces in science and engineering related to surfaces and interfaces. Acknowledgment. This work was supported in part by the Japanese Ministry of Education, Culture, Sports, Science and Technology under grant no. 17206014 and by the Storage Research Consortium. We also thank Dr. H. Tani for his advice about the AFM observation of the liquid films. LA703106S
