Langmuir 2007, 23, 8747-8751
8747
Surface Tension-Driven Self-Folding Polyhedra Timothy G. Leong,† Paul A. Lester,† Travis L. Koh,† Emma K. Call,§ and David H. Gracias*,†,‡ Department of Chemical and Biomolecular Engineering and Department of Chemistry, Johns Hopkins UniVersity, 3400 North Charles Street, Baltimore, Maryland 21218, and Baltimore Polytechnic Institute, 1400 West Cold Spring Lane, Baltimore, Maryland 21209 ReceiVed March 29, 2007. In Final Form: June 2, 2007 We discuss finite element simulations and experiments involving the surface tension-driven self-folding of patterned polyhedra. Two-dimensional (2D) photolithographically patterned templates folded spontaneously when solder hinges between adjacent faces were liquefied. Minimization of interfacial free energy of the molten solder with the surrounding fluidic medium caused the solder to ball up, resulting in a torque that rotated adjacent faces and drove folding. The simulations indicate that the folding process can be precisely controlled, has fault tolerance, and can be used to fold polyhedra composed of a variety of materials, ranging in size from the millimeter scale down to the nanometer scale. Experimentally, we have folded metallic, arbitrarily patterned polyhedra ranging in size from 2 mm to 15 µm.
Introduction It is extremely difficult to fabricate and pattern 3D submillimeter-scale objects. The challenge lies in the inherent twodimensionality of photolithography that is used to pattern small structures. Although it is possible to pattern top and bottom faces of 3D structures such as polyhedra, it is virtually impossible to pattern side faces using conventional photolithography. Novel strategies such as stereolithography, laser micromachining, and ion beam milling overcome this challenge,1-5 but because of the serial nature of these fabrication processes, the structures are expensive and time-consuming to make. In the last 15 years, self-assembly based on folding a 2D template to form a 3D structure has been suggested as a strategy for constructing patterned sub-millimeter-scale 3D structures. The strategy is reminiscent of the ancient Japanese art of paper folding, origami. Several strategies for self-assembly based on folding have been explored, including the use of electroactive polymers,6 magnetic forces,7-9 stress-induced forces,10-13 and surface forces.14-28 Of these, the utilization of surface forces is especially attractive because there is no need for active actuation. The highlight of this self-assembly process is that it retains all of the advantages of conventional microfabrication while enabling 3D fabrication in a highly parallel and cost-effective manner. * Corresponding author. E-mail:
[email protected]. † Department of Chemical and Biomolecular Engineering, Johns Hopkins University. ‡ Department of Chemistry, Johns Hopkins University. § Baltimore Polytechnic Institute. (1) Hruby, J. MRS Bull. 2001, 26, 337-340. (2) Howe, R. T. Technical Digest: 13th Sensor Symposium, Tokyo, Japan, 1993. (3) Varadan, K.; Vasundara, V. Proceeding of SPIE: The International Society for Optical Engineering, Yokohama, Japan, 2001. (4) Markus, K. W.; Koester, D. A.; Cowen, A.; Mahadevan, R.; Dhuler, V. R.; Robertson, D.; Smith, L. Proceedings of SPIE: The International Society for Optical Engineering, Austin, TX, 1999. (5) Rogers, M. S.; Sniegowski, J. J.; Miller, S. L.; Barron, C. C.; McWhorter, P. J. Proceedings of SPIE: The International Society for Optical Engineering, Austin, TX, 1997. (6) Smella, E.; Ignana¨s, O.; Lundstro¨m, I. Science 1995, 268, 1735-1738. (7) Boncheva, M.; Andreev, S. A.; Mahadevan, L.; Winkleman, A.; Reichman, D. R.; Prentiss, M. G.; Whitesides, S.; Whitesides, G. M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3924-3929. (8) Yi, Y. W.; Liu, C. J. Microelectromech. Syst. 1999, 8, 10-17. (9) Iwase, E.; Shimoyama, I. J. Microelectromech. Syst. 2005, 14, 12651271.
Moreover, surface forces scale linearly with the characteristic length, but gravitational forces scale with the length cubed. This scaling allows interfacial forces to dominate at small length scales. If engineered correctly, miniaturized structures can be assembled with these forces over a wide range of sizes, ranging from the millimeter scale down to the nanoscale. Our research is unique in its focus on the fluidic assembly of hollow, free-standing (i.e., untethered), patterned polyhedra. We believe that these structures could be used in a wide range of applications as precisely engineered “patterned hollow particles”. We have previously reported on the fabrication of the polyhedra, with a primary focus on their applications as nanoliter, controlledporosity containers for use in reconfigurable microfluidics, spatially controlled chemistry, and remote-controlled release of chemicals.29-31 However, we provided limited details on the actual self-folding process. In this article, we outline theoretical (10) In, H. J.; Arora, W.; Buchner, T.; Jurga, S. M.; Smith, H. I.; Barbastathis, G. IEEE Conference on Nanotechnology, Munich, Germany, 2004. (11) Kubota, K.; Fleischmann, T.; Saravanan, S.; Vaccaro, P. O.; Aida, T. Jpn. J. Appl. Phys. 2003, 42, 4079-4083. (12) Ho Y.; Wu, M.; Lin, H.; Fang, W. Proceeding of the IEEE/LEOS International Conference on Optical MEMS, Lugano, Switzerland, 2002. (13) Sasaki, M.; Briand, D.; Noell, W.; de Rooij, N. F.; Hane, K. IEEE J. Sel. Top. Quant. Electron. 2004, 10, 455-461. (14) Syms, R. R. A.; Yeatman, E. M. Electron. Lett. 1993, 29, 662-664. (15) Syms, R. R. A. J. Microelectromech. Syst. 1995, 4, 177-184. (16) Green, P. W.; Syms, R. R. A.; Yeatman, E. M. J. Microelectromech. Syst. 1995, 4, 170-176. (17) Harsh, K.; Lee, Y. C. Proceedings of SPIE, San Jose, CA, 1998. (18) Syms, R. A. A. J. Microelectromech. Syst. 1999, 8, 448-455. (19) Harsh, K. F.; Bright, V. M.; Lee, Y. C. Proceedings of the IEEE Electron. Comp. Technology Conference, Las Vegas, NV, 2000. (20) Hui, E. E.; Howe, R. T.; Rodgers, M. S. IEEE 13th International Conference on Microelectromechanical Systems, Miyazaki, Japan, 2000. (21) Syms, R. R. A. IEEE Photon. Tech. Lett. 2000, 12, 1519-1521. (22) Linderman, R. J.; Kladitis, P.; Bright, V. M. Sens. Actuators, A 2002, 95, 135-142. (23) Dahlmann, G. W.; Yeatman, E. M.; Young, P.; Robertson, I. D.; Lucyszyn, S. Sens. Actuators, A 2002, 97-98, 215-220. (24) Patterson, P. R.; Hah, D.; Nguyen, H.; Toshiyoshi, H.; Chau, R.; Wu, M. C. 15th IEEE International Conference on MEMS, Las Vegas, NV, 2002. (25) McCarthy, B.; Bright, V. M.; Neff, J. A. Sens. Actuators, A 2003, 103, 187-193. (26) Hong, Y. K.; Syms, R. R. A.; Pister, K. S. J.; Zhou, L. X. J. Micromech. Microeng. 2005, 15, 663-672. (27) Gracias, D. H.; Kavthekar, V.; Love, J. C.; Paul, K. E.; Whitesides, G. M. AdV. Mater. 2002, 14, 235. (28) Syms, R. R. A.; Yeatman, E. M.; Bright, V. M.; Whitesides, G. M. J. MEMS 2003, 12, 387-417. (29) Gimi, B.; Leong, T.; Gu, Z.; Yang, M.; Artemov, D.; Bhujwalla, Z. M.; Gracias, D. H. Biomed. MicrodeV. 2005, 7, 341-345.
10.1021/la700913m CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007
8748 Langmuir, Vol. 23, No. 17, 2007
Leong et al.
and experimental design specifications of the surface tensiondriven self-folding process in order to facilitate a conceptual understanding of the interfacial driving forces, provide insight into size scaling of the process, and understand factors that minimize defects and increase fault tolerance. Additionally, this article provides a generalized framework that can be used to design and fabricate 3D millimeter-to-nanoscale, patterned, untethered, polyhedral structures composed of a wide range of materials.
Fabrication of Patterned Polyhedra The first step in the process involved the fabrication of 2D templates composed of patterned faces and solder hinges that would eventually fold up into 3D hollow polyhedra. We spincoated a polymeric sacrificial layer made of polymethyl methacrylate onto a silicon (Si) substrate to facilitate the subsequent release of the 2D templates. A metallic seed layer was then evaporated onto the sacrificial layer to create wafer-scale electrical contact for subsequent electrodeposition steps. The faces were patterned using photolithography and fabricated using electrodeposition. Because we utilized conventional photolithography to pattern faces, any arbitrary pattern could be incorporated. We fabricated faces composed of either copper (Cu) or nickel (Ni); our choice of metals was determined by cost, etch selectivity with respect to the seed layer, ease of deposition, and the need for magnetic functionality. A second layer of photolithography was used to pattern the solder hinge templates. After hinge patterning, the exposed seed layer in the hinge region bounded by the faces was etched to disconnect the underlying seed layer only between the faces while retaining electrical continuity with the rest of the seed layer at the face corners. The solder hinges were electrodeposited, and then the 2D template was released from the substrate by etching the remaining seed layer and dissolving the sacrificial layer. A template composed of six square faces, arranged in a cruciform and held together by solder hinges, was used to form a cube. Apart from the solder in between faces, there is no other tether. Self-folding was carried out in a high-boiling-point solvent, N-methylpyrrolidone (NMP), which was heated above the melting point of the solder (∼188 °C). A small amount of Indalloy flux 5RMA (rosin, mildly activated) was added to the solvent to clean and dissolve any oxide layers on the solder and thereby ensure good solder reflow.
Design Considerations In our design, Ni was always used as the topmost surface layer of the face in contact with the hinges. Even for the Cu polyhedra, the tops of the faces were coated with a thin layer of Ni prior to hinge deposition. Solder does not wet Ni surfaces well, so the solder stays in the region where it is electrodeposited and does not spread across the entire surface of the face during folding (which occurs when solder is in contact with Cu). When the Ni coating was absent, we still observed folding; however, the yields were poor. The low yield was a result of the solder migrating away from the regions where it was deposited, thereby making it very difficult to control the volume of solder in the hinge region between faces (which ultimately determines the final folding angle). The design of the 2D template determined the final shape and porosity of the polyhedra. Shown in Figure 1A is a typical 2D (30) Leong, T. G.; Gu, Z.; Koh, T.; Gracias, D. H. J. Am. Chem. Soc. 2006, 128, 11336-11337. (31) Ye, H.; Randall, C. L.; Leong, T. G.; Slanac, D. A.; Call, E. K.; Gracias, D. H. Angew. Chemie 2007, 46, 4991-4994.
Figure 1. Comparison of finite simulation and experimental results for the self-assembly process. (A) Top view (drawn to scale) with dimensions of the faces and gap widths of the 2D template used to self-assemble the cube. (B) Side view of two adjacent faces of the cruciform (as fabricated) with variables used in the finite element simulation. (C) Side view of adjacent faces at the onset of reflow of the folding hinge. (D-F) Finite element snapshots showing (D) underfolded, (E) right-angle folded, and (F) overfolded faces. (GI) Optical microscope images of experimentally fabricated 200 µm cubes exhibiting the underfolded, right-angle folded, and overfolded faces. Note that B-F are not drawn to scale in order to illustrate important dimensions.
layout of the faces and hinges. We used Autodesk AutoCAD 2005 to generate the layout file used to fabricate two photomasks (one for the faces, one for the hinges). To fabricate a cube, we typically used square faces separated by a gap, g, of 10-15% of the face dimension, L, in Figure 1A. We observed some tolerance in the gap width as the molten solder tends to draw the faces laterally toward each other during folding. It should also be noted that because the gap width is 10-15% of L it was often the minimum feature size of the photomask and lithography process (e.g., for 15 µm cubes, the required gap width of 1.5-2 µm represented the smallest lithographically patterned feature). In contrast with prior surface tension-based self-folding work,14,16-26 we utilized two types of hinges: internal ones between faces (folding hinges) and external ones at the periphery of the faces (locking hinges). The folding hinge width (shown as W in Figure 1B) was 25% of L, and the hinge length was 80-90% of L. If the folding hinge lengths were smaller (90%) were unnecessary because neighboring hinges would overlap at the corners. Additionally, hinge lengths of 100% were incompatible with the fabrication process; these hinge patterns resulted in the complete removal
Surface Tension-DriVen Self-Folding Polyhedra
of the seed layer at the perimeter of the 2D templates during the etch step after photolithography of the faces. This removal formed an electrically discontinuous seed layer that prevented subsequent electrodeposition of the hinges. Reflow of the folding hinges provided the torque to rotate adjacent faces. Locking hinges that had the same length but half the width of the folding hinges played a secondary role in the folding of the 2D template; they functioned as a stabilizing stop, increased fault tolerance in folding, and ensured a final fold angle of 90°.15 Additionally, locking hinges increased the mechanical strength and sealed the edges of the polyhedra when two half-sized locking hinges fused and formed a single hinge containing the equivalent volume of a folding hinge. Folding was complete within seconds when the locking hinges met and fused with each other.32 The fusion occurred as a result of the minimization of interfacial free energy between the molten locking solder hinge on each face and the surrounding liquid. On cooling, the solder hinges solidified, and the polyhedral structure was locked into place.
Langmuir, Vol. 23, No. 17, 2007 8749
Figure 2. Simulation results of the dependence of the fold angle on solder volume for a 200 micron cube. The results demonstrate that the folding angle can be precisely engineered by controlling the solder volume at the hinge.
Finite Element Simulations To understand the self-assembly process better, we performed finite element simulations using the Surface Evolver33 software program. Surface Evolver determines the minimum energy surface for a given initial surface and a set of physical constraints such as gravity, density, and surface tension. The iterations for evolving a minimum surface are controlled manually by the user. We developed scripts to automate the task of varying parameters and evolving multiple surfaces. In our simulations, we have included only two adjacent square faces held together by a single solder folding hinge, because this captured the essential function of the folding hinges that play a critical role in forming a well-folded structure. One face was assumed to be fixed, and the other was allowed to rotate freely around the solder hinge; this assumption parallels what was observed in experiments.32 To determine the equilibrium fold angle for a given geometry, we used the following strategy:17 Minimum-energy surfaces were generated for angles of rotation (out of the 2D plane) between 0° (flat) and 120° (overfolded) in incremental steps of 5°. The equilibrium angle corresponding to the global minimum energy was then determined from the minimum of the surface energy trend line versus angle plot for a particular given face dimension. Shown in Figure 1B-F are illustrations of the finite element simulation for the folding process. In the 2D template, the folding hinge solder is in the form of a T-shaped right prism. On reflow, the solder liquefies and forms a rounded contour (Figure 1C). Because of the high interfacial tension of the liquid solder (∼481 mJ/m2),34 there is a strong driving force to minimize the exposed interfacial area between the molten solder and the surrounding fluidic liquid. This driving force causes the solder to ball up, which results in the rotation of adjacent faces. The fold angle is primarily controlled by the solder volume. We observed evidence for this control in both simulations and experimental observations. Different solder volumes generated underfolded (Figure 1D,G), correctly folded (Figure 1E,H), or overfolded (Figure 1F,I) structures. A plot of the dependence of the fold angle on solder volume (generated by simulations, Figure 2) shows that the fold angle decreases with increasing solder volume. Experimentally, the solder volume that determines the (32) Supplemental Video 1 featuring real-time video of 500 µm cubical polyhedron folding, encoded using DivX 6.2.2 Codec. (33) Surface Evolver was developed by Ken Brakke from the Susquehanna University Department of Mathematics. The latest Windows version (v2.26c, updated September 13, 2005) was used. (34) White, D. W. G. Metall. Trans. 1971, 2, 3067-3070.
Figure 3. Normalized total energy curves (finite element simulations) plotted as a function of fold angle for faces with lengths ranging from 6 mm to 50 nm. The curves show that folding is spontaneous on small size scales with stable minima. As the scale increases, gravitational forces increase, folding is no longer spontaneous (initial slope changes from negative to positive), and there are no minima present at 6 mm.
equilibrium fold angle was manipulated by controlling the height of the electrodeposited solder for a given hinge geometry. Because we were interested in the scaling properties of the process, we accounted for the gravitational potential energy of both the solder and the faces, in addition to the interfacial surface energy of the solder. It has been shown by others15,17,18 and verified in our simulations that the magnitude of gravitational effects are essentially negligible compared to the interfacial surface energy until the sizes become large (i.e., millimeter scale). However, our inclusion of a gravitational energy term allowed us to determine the relative magnitudes of each of the forces as
8750 Langmuir, Vol. 23, No. 17, 2007
Figure 4. (A) Optical image showing free-standing polyhedra fabricated (experimental results) with a wide range of sizes all the way from 2 mm to (B) 15 µm and with different shapes (e.g., (C) square pyramid).
the feature sizes were scaled up or down. The fact that surface forces scale favorably with decreasing size is an attractive feature of surface tension-driven self-assembly and has the potential to provide widespread utility in the assembly of microfabricated microscale and nanoscale structures. To determine the effect of size scaling on the folding process, we performed simulations for 2D templates with faces sized from the millimeter scale to the nanometer scale for a given solder volume. In each case, all dimensions (height, width, and length) were linearly scaled by the same constant factor. We observe that there is an energy landscape (Figure 3) that drives the folding process and that there are different energies for different fold angles (for a given geometry and solder volume). The initial slope of the energy curves indicates the magnitude of the rotational force of the faces and determines whether the folding process is spontaneous. A negative initial slope (Figure 3, 50 nm to 200 microns curves) results in a spontaneous folding process whereas a positive initial slope (Figure 3, 2-6 mm curves) indicates a nonspontaneous process. The minima in the curves (Figure 3, 50 nm to 4 mm) around 100° are indicative of a stable, equilibrium folded configuration. The absence of a minimum in the curve for 6 mm faces implies the absence of any stable folded configuration (i.e., the two faces prefer to remain flat). These results can be explained by noting that as the size of the faces increases, the weight increases and gravitational forces begin to dominate, compared to the surface tension forces on the millimeter scale. Hence, the initial slope of the energy landscape becomes positive in the millimeter range, and the process becomes nonspontaneous. At smaller sizes, surface forces overcome gravitational forces, and the process becomes spontaneous all
Leong et al.
Figure 5. (A) Optical image of cubes with a range of sizes formed in large numbers. (B) Enlarged image of the outlined region in A featuring 100 µm cubes sitting on top of and among 500 µm cubes.
the way down to the nanoscale. It should be noted that in our simulations we assumed bulk properties for the materials and the solder and ignored effects such as phase segregation, intermetallic formation, and diffusion within the solder; if these assumptions hold, then it appears that the self-folding process would work on the nanoscale. For our standard geometry, material densities, and solder surface tension, our simulations show the maximum spontaneous folding size to be L ≈ 1400 µm. Simulations also show that in an extreme case of a low-surface-energy hinge (10 dynes/cm, e.g., a liquid polymer) and heavy faces (20 g/cm3, e.g., a dense metal) folding is still spontaneous for polyhedra as large as 165 µm. This implies that it should be possible to fold structures with faces composed of almost any solid material and with hinges composed of virtually any liquefiable material up to a size scale of around 165 µm for our particular geometry.
Experimental Results We have folded cubic polyhedra ranging in size from 15 µm up to 2 mm (Figure 4). We have also been able to fold polyhedra of other shapes (Figure 4C). Although we believe that smaller polyhedra can be fabricated, we have been limited by our photolithographic capabilities. Below tens of micrometers, hinge gap widths approach the sub-micrometer size scale, and alternative patterning techniques, such as electron beam lithography, are required to fabricate the 2D templates. Our theoretical simulations show that the folding of smaller polyhedra is spontaneous as a result of the large magnitude of the surface forces on small size scales. Although simulations show that the folding of polyhedra with large faces (i.e., 2 mm faces) is a nonspontaneous process, experimentally we were able to fold 2 mm cubes. We rationalize this result on the basis of two observations. First, agitation due
Surface Tension-DriVen Self-Folding Polyhedra
to convection currents in the heated fluid occurs experimentally. This agitation can provide the initial driving force to lift faces marginally over the activation barrier for folding. Second, it should be noted that whereas we proportionally scaled all size variables in the simulations (e.g., a 2 mm face was simulated with a thickness of 80 µm) it was not possible to do so experimentally. Because of restrictions on the height of the photoresist and resolvable aspect ratios, we electrodeposited a thickness of only 12 µm for 2 mm cubes; the faces of the experimental templates thus had a substantially lower weight, increasing the threshold at which folding became nonspontaneous to larger sizes. Accounting for this fixed frame thickness in our simulation, we determined that the largest size for which the self-folding process would work for the materials used in our process is ∼7 mm. Although we do not expect to use a lithographic process to fabricate structures as large 7 mm, the process of self-folding may still be relevant on this size scale, especially in the packaging of electronic devices. Tolerance of the Process. Wafer-scale patterning of the 2D templates is highly parallel (e.g., we pack approximately 1000 (L ) 100 µm) and 100 000 (L ) 15 µm) 2D cruciforms on a 3 in. wafer). The folding process is also highly parallel, and large numbers of 2D templates can be folded at once. Experimentally, the folding process also appears to be considerably fault-tolerant, and we have often been able to achieve yields in excess of 90% and fabricate large numbers of polyhedra (Figure 5). We have also observed that folding occurred even when the hinge registry was not perfectly centered across adjacent faces. Experimentally, to increase fault tolerance, we targeted our solder volume to result in a slight overfold (∼100° of rotation from the horizontal). Because we used locking hinges, this overfold ensured that the faces met, allowing the locking hinges to fuse, thereby increasing the tolerance of the process15 and sealing the cubes at the edges and corners. Additionally, convection currents existed in the hot solution during the folding process. These convection currents
Langmuir, Vol. 23, No. 17, 2007 8751
agitated the 2D templates and increased the folding-angle tolerance by encouraging the edges of the faces to collide; this allowed the locking solder hinges to fuse and hold the faces together with considerable strength.35,36
Conclusions We have described a surface tension-based folding process that can be utilized to fabricate untethered, hollow and patterned polyhedra with a wide range of sizes from the millimeter to the nanometer scale. By leveraging well-established lithographic methods in microelectronics, our fabrication process provides a route to incorporate precisely engineered monodisperse porosity, transistors, sensors, and other information-processing devices on the polyhedra to create “smart particles”. Using simulations, we have demonstrated that the folding would work with a wide range of face materials and liquefiable hinges. We believe that our research also demonstrates that the utilization of interfacial forces, which scale favorably at small sizes, is a useful paradigm that should be further explored in microfabrication and nanofabrication. Acknowledgment. We acknowledge funding support from the National Science Foundation Career Award (DMI-0448816), the Beckman Foundation, and the Camille and Henry Dreyfus Foundation. Supporting Information Available: A video featuring realtime folding of a 500 µm cube. The video was encoded using the DivX 6.2.2 Codec. This material is available free of charge via the Internet at http://pubs.acs.org. LA700913M (35) Jacobs, H. O.; Tao, A. R.; Schwartz, A.; Gracias, D. H.; Whitesides, G. M. Science 2002, 296, 323-325. (36) Gracias, D. H.; Tien, J.; Breen, T. L.; Hsu, C.; Whitesides, G. M. Science 2000, 289, 1170-1172.
