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NANO LETTERS Patterning Lines by Capillary Flows Saurabh Vyawahare, Kate M. Craig, and Axel Scherer* 2006 Vol. 6, No. 2 271-276 Thomas J. Watson, Sr. Laboratories of Applied Physics, California Institute of Technology, Pasadena, California 91125 Received November 15, 2005; Revised Manuscript Received December 7, 2005 ABSTRACT We report that capillary flows in an evaporating thin film create line patterns, with widths ranging from a few micrometers to less than 100 nm. Deliberate patterning of such lines requires contact-line pinning and the presence of foaming surfactants. Large-scale photolithography can guide and control these structures by creating pinning points and steering evaporation. We provide demonstrations of this process by making self-assembling lines of colloidal quantum dots and microspheres. Looking at a soap bubble, one can appreciate how capillary forces cause unexpected patterns and shapes.1 Surface tension is involved in the coffee-drop effect,2-4 fingering patterns in Hele-Shaw cells,5,6 microsphere ordering to form two-dimensional crystals,7,8, combing of DNA,9 and skeleton formation in marine creatures called radiolarians.10 Although it is common, using surface tension as a practical lithographic tool is beset with problems involving control of the process.11 Here, we report a new general method for depositing controlled line patterns, based on capillary flows in thin films of liquids.12,13 When a coffee drop evaporates on a table, ring-shaped coffee stains remain on drying. In this case, the boundary between air, solid, and liquid, the contact line,14 is pinned, that is, immobilized on surface defects. Then, capillary flows push coffee particles to the boundary.2 In experiments described in this paper, we find, under certain conditions, instead of rings, lines are formed. Three main conditions are necessary: (1) evaporating solutions between partially wetting surfaces, (2) the presence pinning points, and (3) the presence of foaming surfactants, molecules with a lyophilic or solvent-liking and lyophobic or solvent-repulsing part. Surfactant molecules prefer to aggregate at surfaces15 and tend to lower surface tension. Our initial experiments used solutions containing foaming protein surfactant16,17 bovine serum albumin (BSA), which belongs to a class of sticky proteins found in large quantities in blood and milk. An aqueous solution of BSA is sandwiched between either two cover glasses or two silicon wafers. The liquid spreads until it balances the weight on top of it (Figure 1a). If this solution is left to evaporate for a few hours, then wire-like patterns stick out of the receding boundary (Figure 1b), growing perpendicular to the contact line. Each line starts with a small clump of BSA that * Corresponding author. E-mail: [email protected]. Tel: 1-626-3954691. Fax: 1-626-577-8442. Correspondence and requests for materials should be addressed to M/C 200-36, Caltech, Pasadena, CA 91125. 10.1021/nl0522678 CCC: $33.50 Published on Web 01/05/2006 © 2006 American Chemical Society crystallized or formed a gel at the tip, creating a self-pinning point.18 The lines can stretch many millimeters and are a few micrometers wide. They stop growing only by breaking from the contact line, this is usually due to another clump of BSA nearby, causing depinning. This process is not very sensitive to concentration, and solutions of BSA from 10 nM to 10 mM all formed lines. Higher concentrations render the solution gellike because of an increase in viscosity; lower concentrations are too dilute and waterlike, unable to form stable lines. The two surfaces may be peeled apart. This leaves a pattern on one surface that is the mirror of the pattern on the other surface; the lines seem to break at the center, leaving behind material on each surface with approximately half the height (Figures 1c and 4a) This allows access to the lines directly. As mentioned earlier, a thin film of liquid between parallel plates is necessary; a drop of BSA solution on a surface will leave ring-shaped patterns. The main difference between the two geometries is that liquid cannot evaporate in the third dimension, perpendicular to the plane, when sandwiched. Also, in the sandwich geometry, pure water will form short lines that snap and reduce to a series of drops because of Rayleigh’s instability.19 A random impurity or a designed pinning point, described later in the paper, does the pinning in this case. And if the substrate, silicon or glass, is chemically treated to increase wetting, fewer BSA lines result, showing that partially wet surfaces are required. To better visualize this process, we added quantum dots to the solution. Quantum dots got concentrated in the lines, which could be seen by the photoluminescence intensity. We find that the shape of the contact line near the wire can be fitted to a second-order polynomial (Figure 2a and b). The shape is a parabola or a catenary (which is a parabola to the first approximation). This is different from three-dimensional pinned drops, where the shape of the contact line has been shown to be exponential.20 bubble appears near the receding contact line. Quantum dots tend to collect at its edges. Eventually, the bubble pinches off from the contact line and becomes a pinning point for a new line. Solution in the lines is constantly evaporating, and a new supply of liquid must be maintained to prevent lines from drying up. This flow brings with it additional solutes that tend to concentrate in these lines. The pressure gradient created by the parabolic shape, combined with the flows due to the receding contact line, creates a flow pattern as shown in Figure 2d (see Supporting Information video 1). Why are the lines stable, and what determines their width? A complete theoretical analysis is still a work in progress and will not be described in this paper. But, qualitatively, we believe that the physics of this process is analogous to that of soap bubbles and foams.22 Soap bubbles have film thickness between 5 nm and a few micrometers.23 These lines are similar to the thin film between two coalescing bubbles, the bubbles in this case being the air that surrounds the line on either side. Two effects keep soap bubbles from shrinking: one, the repulsion between molecules, also known as the disjoining pressure.24 We believe that this force prevents these lines from collapsing to zero width. Second, although poorly understood, the Gibbs-Marangoni effect plays a major role in foam formation.1 In these lines, this effect should provide a restoring force acting against change in width of the lines, resulting in lines whose widths are constant throughout, as observed. Surfactants are essential for this process, they energetically prefer to be at the air-liquid interface and increase the Gibbs film elasticity25,26 E E) Figure 1. Line formation. (a) Cartoon of the geometry showing fluid sandwiched between two parallel plates. Surfactant molecules tend to collect at the interface. (b) BSA line formation self-pinning. The clump at the tip of the line is the self-pinning point made up of a BSA clump that precipitated out. The dark area in the upper right is the evaporating liquid. Note that the lines are remarkably straight over small distances. (c) SEM image of two BSA lines that are pulled together to form a junction. In foams, the junction is called a plateau and the radiating arms are called lamellae. The growth rate of lines was measured on the scale of a few minutes, and it varied linearly with time (Figure 2c). This was true, irrespective of the solution used. We believe that the rate-determining factor is simply the evaporation rate, which, if constant, makes the contact line recede at constant velocity. Besides lines, other patterns are also present. Two nearby lines can coalesce if nonuniform contact-line motion forces them closer, and this leads to pronglike structures (Figures 1c and 3a). The angle between the arms of the prong is found to be close to 120° every time, which represents an energy minimum.21 Bubbles in the solution lead to the formation of structures shaped like “lollipops”. Figure 3b-e shows a sequence of images showing the formation of lollipops. The 272 dσ d ln A (1) where σ is the surface tension and A is the surface area. Growth of a line requires an increase in surface area, and surface tension forces oppose this change. In the presence of surfactants, an increase in area is also accompanied by the diffusion of surfactants from the bulk to the surface, which compensates for the energy loss due to change in area, making the process more energetically favorable. There are other similarities between these lines and foams, junctions between two wires, described earlier, are similar to structures formed when two bubbles coalesce; the junction is called the plateau, and the bubble films leading to it are called lamellae1 (Figure 1c). When two lines combine, they tend to suck in colloidal particles (see Supporting Information video 2). This behavior is very similar to that of a foam bubble plateau; the negative pressure in the plateau tends to suck in fluids and is one of the main mechanisms for drainage of bubbles. Also like soap films, the lines are metastable and increase in viscosity (for instance, by the concentration of solutes) and stability. The lines formed by BSA (Figure 4a) are spaced randomly, depending on self-pinning points at the boundary. Instead, we would like to be able to exert more control over areas where lines are created. This is possible by making artificial Nano Lett., Vol. 6, No. 2, 2006 Figure 2. Flow patterns, shape, and growth rate of lines. (a) A line formed by BSA solution with 200-nm fluorescent microspheres. (b) Parabolic fit for the shape of the curve joining the line to the bulk fluid. (c) Line growth measured over a period of a few minutes is linear and depends only on how fast the receding contact line moves. All of these experiments were done at 23 °C and 33% humidity. (d) A cartoon of the flow patterns that are set up with the contact line receding and the lines growing. Please see the Supporting Information for a video of the flow patterns with quantum dots. pinning points using photolithography. Various shapes were created on a silicon wafer surface using photoresist SU8, including squares, circles, and triangles of different sizes. Spinning photoresist at varying speeds varied the height of these shapes. A cover glass, placed on top of the resist, provided a viewing window to see the motion of the contact line. As the contact line recedes, lines are formed as expected (Figure 5a). The shape of the pinning point does not seem to matter; circles, squares, and triangles all produce single lines (Figure 5a-c). Specially designed structures with two prongs result only in a single line. Our conclusion is that the shape of the pinning point does not play an important role in this system, as long as the fluid continues to touch both surfaces. Moreover, the width of the line does not depend on the pinning point. Pinning structures can be much larger that the width of the line. Greater distance between the two parallel surfaces leads to wider lines. When the contact line moves across two pinning points, it leaves behind line deposits that connect the two pinning points (Figure 5c). This provides a way to make interconnection wires. The creation of pinning points allows precise control over the location of deposited lines. Because the pinning points may be much larger than the line widths, photolithography does Nano Lett., Vol. 6, No. 2, 2006 not need to have the same resolution as the structures that are produced by the process. Additionally, photolithography allows us to steer evaporation in the direction we want. Besides using evaporation, we also attempted dip-coating27 of substrates with pinning points; but we were unable to form lines. With the ability to create pinning points, the next step was to test other foaming surfactants; we find that sodium dodecyl sulfate (SDS), sodium oleate, Triton X-100 (octyl phenol ethoxylate), zonyl fluoro-surfactants FSN and FS300 (DuPont), and tween-20 all cause formation of continuous lines. The most stable lines had high concentrations of surfactants, exceeding the critical micelle concentration. Coffee, known to form ring stains when evaporating from a drop,2 will form lines in this geometry too. Thus, we believe that any foaming surfactant can form lines in this geometry. The lines formed by these surfactants are different from BSA lines. First, there is no self-pinning and pinning points have to be artificially created to obtain lines. Second, soap films are classified as rigid or mobile24 and compared to BSA, these surfactants form lines that tend to be less rigid and more fluidlike.28 This also explains the formation of droplets in place of lines, if it is cut off from the contactline boundary, stopping flow (Figure 4b). The lines formed 273 Figure 3. Quantum dots and other shapes. (a) When the contact line evaporates nonuniformly, two nearby lines can meet. This results in a prong formation. The angle between the three lines is usually close to 120°. This solution contained quantum dots that emit at a peak wavelength of 565 nm. (b-e) A bubble at the edge of the contact line results in the formation a “lollipop” shape. The pictures were taken at t ) 0, 9, 18, and 27 min. Here the solution contains quantum dots that emit at a peak wavelength of 605 nm. Figure 4. BSA and other surfactants. (a) SEM image of BSA forming a junction after drying. The line consists of a thin layer of BSA with a wall at the center. (b) A line of Triton X-100 surfactant breaking into droplets when flow was stopped. Unlike BSA, this surfactant forms nonrigid lines. are initially wide, tens of micrometers and then they tend to thin down, eventually becoming drops, when flow stops. With BSA, the rigidity slows down droplet formation by Rayleigh instability19 once flow stops. Scanning electron micrographs of the BSA lines after drying show a dark and 274 bright region (Figures 1c and 4a). We believe that the dark region is a thin film on the surface and the bright region is the BSA line. The base of the line is wider than the center. Lines can be made more rigid by simply adding other solutes or colloids, increasing viscosity, and slowing formation of a series of drops. Thus, adding solutes allows other surfactants to form stable lines similar to BSA. To test whether we can insert other kinds of colloids into the lines, besides quantum dots, we added microspheres to the solution. The beads used were made of polystyrene or silica. The surface was either plain or with an amine/carboxyl group. The beads were 50 nm to 3 μm in diameter. We find that beads enter the lines; this is confirmed both by visualizing using fluorescent beads and by scanning electron micrographs (Figure 5d and e). Smaller microspheres had a greater tendency to precipitate out of the receding contact line. Larger beads tend to form lines of the best quality. In BSA solution with smaller beads, we observe the phenomena of bridging, where the line is bridged by a bead. The BSA line formed in this case can be smaller than the size of the bead (Figure 5e). In conclusion, we have demonstrated a new way to create and control line patterns using capillary flow. This method is quite general, and may be used for creating a variety of lines. The fact that different types of surfactants can be used provides considerable flexibility for applications. Also, the patterning depends on flows, largely independent of the solute, and a variety of colloidal particles and protein molecules may be used, demonstrated by making lines of BSA, quantum dots, and microspheres. We believe that this method will find use in many future micro- and nanofabrication procedures. Further work on this subject will involve testing more surfactants, colloids, and substrates as well as developing a complete theory for the process. Nano Lett., Vol. 6, No. 2, 2006 Figure 5. Various types of pinning points, surfactants and microspheres. (a) Circular pinning points with a solution containing BSA. (b) Triangular pinning points with a solution containing surfactant Triton X-100. (c) A quantum-dot line forming between two pinning points. This could provide a way of making interconnect wires. (d) SEM image of 2-μm silica beads in a aqueous Zonyl FSN solution that have assembled into a line. There are two defects in the periodic structure with one bead out of place and another missing. (e) Small-sized beads can sometimes act as bridge between lines of BSA. Small particles are often antifoaming agents, and this is one of the mechanisms by which they operate. Methods. Materials and Instruments. Beads were obtained from Bangs Laboratories (Fisher, IN) or PolySciences Inc. (Warrington, PA), borate buffer kit from Pierce Biotechnology (Rockford, IL), and strepavidin-coated quantum dots from Quantum Dot Corporation (Hayward, CA). All other chemicals were obtained from Sigma Aldrich (St. Louis, MO) and used as obtained. Most experiments used no. 1 Cover glass from VWR (West Chester, PA) or silicon test wafer from Silicon Quest International (Santa Clara, CA). SU8 Nano Lett., Vol. 6, No. 2, 2006 2010 and 2025 photoresist from Microchem (Newton, MA) was spun at different speeds to obtain pinning points of various sizes. Imaging was done with a Nikon TE200 inverted microscope (fluorescence imaging) and a Zeiss MAX ERB (bright field imaging). SEM imaging was done using Hitachi S4500 or FEI Sirion. Experimental Protocols and Imaging. All experiments were done at room temperature (∼23°). Borate buffer at pH 8 was used with BSA protein. The humidity was kept 275 constant in some experiments by the use of a special humidity chamber. A typical experiment involved putting a 1-μL drop on a substrate that was then covered with another surface and then observed under a microscope. RCA cleaning procedure 129 was done on cover glass or silicon if we needed to make it more hydrophilic. We measured the change in weight of the samples to check if the evaporation rate was constant and found it to be so for substantial periods of time. Acknowledgment. We thank Heun Jin Lee for helping with optics, Koichi Okamoto for SEM training, and Chris Lacenere, Mike Van Dam, Todd Squires, Sandra Troian, Michael Cross, and Steve Quake for helpful discussions. K.M.C. thanks Caltech for a summer undergrad research fellowship. Funding for this work was provided by the DARPA Optofluidics Center. Supporting Information Available: Video 1 shows flow patterns and line formation. Line-pattern formation in a solution of quantum dots and BSA. The pinning of contact lines creates a flow pattern, which pumps quantum dots into the line. Solutes can also be seen moving parallel to the contact line as it recedes. This video has been sped up 2x compared to real time. Video 2 shows two lines forming a junction. Because of nonuniform evaporation, two lines may be brought together. They form a “plateau” that sucks in more solutes. The end result is a pronglike structure. This material is available free of charge via the Internet at http:// pubs.acs.org. 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