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Atomic origami
Current Opinion in Solid State and Materials Science 24 (2020) 100882
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Atomic origami Marc Z. Miskin Dept. of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Origami-fabrication 2D materials Nanofabrication Meta-materials NEMS
Here we summarize recent experimental work in the field of atomic origami: the folding of 3D structures from sheets that are just atoms thick. We highlight current techniques for folding at the microscale and provide scaling arguments as to why some approaches work better than others at small sizes. Finally, we point out that for folding structures made from 2D materials, miniaturization can extend another three orders of magnitude: current state of the art devices are microns in size while, as a platform, atomic membranes should be foldable down to the nanoscale. The ability to scale folding structures over a wide range in size could open diverse ap plications, from microscopic robots to new interfaces with biology.
1. Introduction While today it’s possible to pattern 2D features with nearly nano meter precision, it remains a challenge to build small 3D objects. For micro and nano systems that are meant to interact with the physical world, this imposes a significant constraint. The real world is 3D, and the capacity to move, sense, or explore in three dimensions would open up tremendous new opportunities for nanotechnology ranging from meta materials [1–3] to sensors [45] to robots too small to be seen by the naked eye. The most direct route to take 2D patterns into 3D is arguably selffolding: make something that folds itself into a specific geometry. Indeed, a major body of work [6–8] has established self-folding and origami inspired fabrication as powerful techniques for building com plex mechanisms and structures at small sizes thanks to several key properties. First, origami fabrication is extremely well suited to micro/ nano systems because even complicated, dense patterns of folds can be built with massively parallel lithographic techniques [7]. Second, origami allows virtually any 3D shape to be built. For instance, several fold patterns are universal, meaning they can be used to approximate any 3D shape up to a voxel resolution [9–11]. In addition, there are now established CAD programs that can map arbitrary 3D surfaces into specific 2D patterns that form them [12], and libraries of origami mechanisms and linkages are coming into place, providing a route to engineering complex machines with folding elements [13]. Yet one of the most remarkable properties of origami fabrication is that it scales. By this we mean that the same origami structure can be built at a variety of different length scales without having to rethink the basic working principles. Instead, origami can be scaled up or down arbitrarily in size by adjusting the length, width, and thickness of the self-folding sheet appropriately [14–16]. Fig. 1 shows several
realizations of self-folding systems. While these devices are made from materials spanning roughly five orders of magnitude in thickness, they operate using similar design concepts and obey similar constraints. This stands in stark contrast to traditional approaches for mechanical control, such as wheels and gears, which struggle in sub-millimeter dimensions due to the dominance of surface forces and friction [17,18]. Scaling in origami is akin to scaling in microelectronics: devices can be increased or decreased in size by following simple design rules based on physical principles. Given scalability and the capacity to pattern 2D features with nanoscale precision, a natural question arises: how small can we make the smallest origami structure? To the extent that building smaller de vices requires thinner sheets, atomically thin materials set a funda mental limit to miniaturization. In other words, the smallest folded structures should be made from sheets of “paper” just one atom thick. From our perspective, this extreme limit represents an exciting challenge for the field of nanoscience. How do we make something that self-folds with the thinnest paper that nature allows? Remarkably, the materials needed to meet this goal are already in place: twenty years of research in 2D materials have brought a range of atomically thin “pa pers” like graphene, transition metal dichalcogenides [23,23] and membranes formed by atomic layer deposition [1,24–26]. Here we re view some recent work on folding these materials, which we call atomic origami. We point out that atomically thin materials provide a unique class well suited to self-folding: they can be deformed to large curvatures without fracture and provide useful properties like high stiffness and electrical, photonic, and chemical functionality. We review different methods that the field has developed for folding atomically thin mate rials and provide design rules that describe how folding mechanisms work when shrunk to smaller dimensions. We also show that as a plat form for origami, atomically thin materials provide a route towards
https://doi.org/10.1016/j.cossms.2020.100882 Received 10 August 2020; Received in revised form 27 October 2020; Accepted 1 November 2020 Available online 18 November 2020 1359-0286/© 2020 Elsevier Ltd. All rights reserved.
M.Z. Miskin
Current Opinion in Solid State & Materials Science 24 (2020) 100882
Fig. 1. Origami structures from millimeter scale paper down to atomically thin mem branes. At each size scale, similar concepts can be reused thanks to the scale invariance of origami inspired fabrication. From left to right: Panel (1) a folded bird made from laminated paper, pre-stretched polystyrene, and folded via Joule heating with internal coper circuits from Felton et al. 2013 [19]. Panel (2): an octet-truss pattern folded in crosslinked polymers from Na et al. 2014 [20], Panel (3): a cube folded using differen tial stresses in 100 nm thick metal layers from Leong et al. 2008 [21]. Panel (4) a cube fol ded from stresses in nanometer thick glass and graphene from Miskin et al. 2018 [22].
Fig. 2. Atomic membranes are well suited to origami. (A) Failure stress vs. Young’s modulus for different material classes. Good materials for origami maximize the ratio of σ3f /E2y . As shown by the guide lines, 2D materials like graphene and MoS2 stand out as excellent by this metric. Other outstanding choices include elastomers and ceramics, both of which are frequent material choices in the literature [1,22,26,27]. Reproduced from [22] (B) Folding graphene at the nanometer scale by hand, from Chen et al. [28]. A TEM tip is used to pick up graphene and controllably fold it over itself to produce true, nanoscale elastic folds.
building microscale machines, metamaterials, and microscopic robots. Finally, we point out that pushed to its logical conclusion, atomic origami could enable folded structures with nanoscale radii of curva ture, potentially allowing machines the size of cells, proteins and everything in between.
These two conditions, maximum bending resistance subject to stay ing within the elastic limit, can be used together to eliminate the thickness of the hinge altogether in favor of a single, material-based figure of merit. The result is that, for a given curvature set by the desired size of the origami device, the best material will be the one that maximizes σ3y /Ey 2. Fig. 2A shows a log-log plot of modulus and yield stress for different material classes and guidelines for different values for σ3y /Ey 2. By this metric, 2D materials stand out as excellent. Mechanically they can deform to high strains without fracture and yet possesses some of the highest moduli of any material available. This unique combination provides a nice payoff for microscale origami engineering: in principle one can build incredibly small structures with high mechanical resis tance by using atomically thin sheets. As a back of the envelope estimate, one can consider how far down a 3D structure could be scaled if 2D materials could be folded to their ultimate limits. Typically, 2D materials have a fracture strain in exper iment on the order of 10% [23]. Taking the thickness as 3 angstroms, an effective value estimated from the layer spacing in graphite, one expects graphene origami to scale to radii of curvatures on the order of nano meters, essentially a carbon nanotube. Recent work has demonstrated proof of concept for this vision, albeit by manual folding. In Chen et al. [28], researchers were able to pick up a sheet of graphene using an TEM tip and fold it over itself (Fig. 2B). The results were controllable, nanoscale folds with exotic electrical proper ties. Tiny folded structures like these show the potential of graphene as a folding material, mixing interesting electronic functionality with ultra-
2. Choosing the right material for microscale origami A good folding material is determined by the mechanics of a folding hinge and given their high strength and flexibility, atomic membranes turn out to be an exceptional choice. When a hinge bends from a flat shape, it experiences a stress, σ , on the order of Eyκt where t is the thickness of the hinge, Ey is the Young’s modulus, and κ is the curvature. Geometrically, κt is the strain required to deform the hinge while Ey provides the conversion from strain to stress. Because the material cannot deform beyond its yield stress, σy, without breaking, there is a maximum curvature that a given material sheet can achieve: tκ < σy/Ey. While the left-hand side expresses geometric factors, the right-hand side of the equation is essentially fixed by the material choices. Thus, once a material is selected, going to small radii of curvature requires a decrease in thickness. Just bending to small sizes isn’t enough: the hinge also needs to be able to resist forces from the external world. At thinner and thinner sizes this becomes a challenge since the hinge’s stiffness decreases dramati cally: the bending resistance scales like Ey t3. For the hinge to reliably hold its shape, this quantity needs to be maximized, subject to the constraint that the materials involved don’t fail. 2
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
continuum mechanics predicts that the material stack will bend to a curvature set by force and torque balance [31]: κ=
0 6
0
0
6E1 E2 (t1 + t2 )t1 t2 Δ∊ E12 t14 + 4E1 E2 t13 t2 + 6E1 E2 t12 t22 + 4E1 E2 t23 t1 +E22 t24
where Δε is the strain difference between the two layers and Ei and ti represent the modulus and thickness of the layers. Dimensional analysis of eqn. 1 shows that origami hinges folded by internal stresses are essentially scale invariant: one can simply increase or decrease the size of everything proportionally and the device will work in exactly the same way. Specifically, multiplying every thickness on the right-hand side of the above equation by a fixed factor of λ will produce a curvature scaled down by λ. In fact, the entire equation could be non-dimensionalized by simply multiplying both sides by the average layer thickness (t1 + t2). At the extreme end of this scaling are recent works using atomically thin materials for the layers. For example, Miskin et al. used graphene and nm-thick layers of glass to build self-folding bilayer actuators [22]. They showed that strain could be introduced in the glass layer by using either thermal expansion or chemically induced stresses (Fig. 3A). At just nm thick, these devices were able to easily fold to micron scale radii of curvature, enabling ~10 um self-folding origami structures. In another example, Xu et al. demonstrated self-folding with graphene and polymer bilayers (Fig. 3B) [27,32]. The resulting structures opened up new opportunities that leverage small 3D shapes and the unique mate rial properties of graphene like folded transistors and nonlinear re sistors. Finally, using pre-stresses in tri-layer stacks of ALD materials, Bircan et al. [26] demonstrated complex origami structures (Fig. 3C) including tiny folded birds and patterns upward of 100 folds in sheets just 10 nm thick. The work also included a complete process flow that maps arbitrary origami CAD files into corresponding lithographic masks. At the 10-µm scale, these small 3D structures are comparable in size to many cells, inviting new ways to sense or interact with biology. A significant step in this direction came from Xu et al. who demonstrated encapsulation of cells with self-folding graphene-polymer composites [33]. By integrating silver nanoparticles in the composite structure, they were able to perform surface-enhanced Raman spectroscopy on the surface of the cell. Indeed, this approach could be generalized into a platform technology, using atomically thin materials with understood, controllable surface chemistries (e.g. glass and polymers) to create 3D structures with specific biological or chemical functionality. Broadly, self-folding via internal elastic stress can be triggered in respond to a wide range of different stimuli. Linear responses couple strain to temperature, light, magnetic fields, and chemistry and all of these can be used to build self-folding structures. Origami structures coupling folds to fields can then be used as the building block of smart materials with microscale features or mechanisms that extract me chanical work from changes in their environment. In addition, working with extremely thin films leads to a dramatic increase in response time. For example, for chemical or thermally induced stresses, the response time is limited by the diffusion of chemistry/heat through the bilayer stack, scaling as ~t2. Thus, modes of motion control that are sluggish at the macroscale become rapid when miniaturized: examples include glass as a chemically active medium at the nanoscale [22], or DNA-based smart films [34].
Fig. 3. Self-folding with elastic stresses. (A) A tetrahedron made from graphene and glass folds and unfolds in a few hundred milliseconds when responding to changes in its chemical environment. Ions from the solution lead to swelling in the glass, producing bending. The rapid response time is a feature of working with extremely thin films. (From Miskin et al. [22]). (B) Self-folding with graphene-polymer bilayers (From Xu et al. [27]) in response to temperature changes. Specifically, the polymer layer swells in response to temperature changes, producing reversible actuation. (C) A bi-directional folding origami structure made from nanometer thick ALD films. Here the fabrication protocols allow for both mountain and valley folds, enabling generic origami structures (From Bircan et al. [26]).
small geometric structures. Yet an open question remains: how can atomic origami be done at scale, without having to pick and place each fold by hand? 3. How to fold small systems The main challenge for atomic origami is to actually produce the forces that drive bending and folding. Overcoming the elastic restoring force of the material requires something to act at each origami hinge, bending it to a desired shape. While many choices are possible, here we focus those that scale well to small sizes and can be parallelized to fold a large number of independent folds. To our knowledge, prior work with atomically thin sheets has demonstrated four main techniques that meet these criteria: internal stress, liquid capillary forces, solid surface stresses, and magnetic fields. Our discussion focuses on continuum descriptions, which are heu ristic for 2D materials, but have largely been a reliable basis for explaining self-folding experiments. Yet it should be noted that the mechanics of 2D materials is still under investigation [23]. For example, experimental values for the bending energy of graphene can differ by a factor of almost 10,000, depending on the details of the measurement, whether the sheet is crumpled, or even how big it is [2,23]. Similarly, new physics can dominate at smaller sizes, and continuum descriptions of self-folding may need to be augmented with atomistic simulations [29,30] or integrated into multiscale models [27].
3.2. Self-folding by capillary forces At small scales, surface forces tend to dominate, and as a conse quence, they can provide a robust way to fold tiny structures. This approach defines a second technique for self-folding called capillary origami [35]. Here the surface tension, γ, from a liquid interface is used to fold a thin sheet of elastic material. When the liquid tries to minimize its surface area, it folds up the attached solid sheet, creating a 3D shape. For sufficiently thin sheets, capillary-driven folding is essentially
3.1. Self-folding by internal elastic stress The most common way to build self-folding structures is internal stress: take two materials, layer them together, and find a way to introduce a strain in one material but not the other. For thin layers, 3
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
Fig. 4. Self-folding structures using capillary forces. Here MoS2 and graphene sheets are folded into targeted shapes set by the geometry of the sheet and the placement of rigid panels (Reproduced from Reynolds et al. [41]).
geometric due to a large separation in energy scales. As pointed out by Paulsen [36,37] and King [38], an elastic sheet at a liquid interface has three primary contributions to its energy: (I) a surface energy that scales as γL2, (II) an energy for stretching the sheet that scales as EytL2 and (III) a bending energy that scales as Ey t3. For sufficiently thin sheets, these energy scales are well separated: stretching the sheet is prohibitively expensive, bending is extremely low energy and surface energy falls somewhere in between. The resulting problem becomes geometric: minimize the available surface area subject to a “no-stretching” condi tion, fixing all the behavior to a single, geometric parameter comparing the size of the drop to the size of the sheet [36]. Take the specific example of a ten-micron wide graphene sheet floating at a water-oil interface. Here the surface tension is on the order of 30 mN/m. By contrast, the 2D Young’s modulus, defining the stretching energy, is on the order of 340 N/m [39]. Thus, the liquid interface can at most stretch the graphene by a strain on the order of 10− 4. Smaller still, the bending energy for a graphene sheet is 10− 15 J [2]. Until the sheet is deformed to a radius of curvature on the order of 100 nm, the surface energy provides a significantly larger contribution than bending. From an origami perspective, capillary forces possess a unique scaling behavior: provided the sheet is thin enough, it will always try to fold to a structure dictated by geometry. Again, the mechanism is scale invariant, but here, there is no need to even adjust the thickness of the sheet. The large separation in energy scales essentially locks the folding
shape once the sizes of the droplet and the sheet of material are defined. In practice, this constraint proves extremely useful. To our knowl edge, the smallest origami structures have been built using capillary forces acting on thin films. Specifically, Leong et al. demonstrated 100 nm e-beam patterned resonators folded by molten tin [40]. Recently, this idea was extended to operate on atomic membranes: working with films of graphene and MoS2, Reynolds et al. demonstrated self-folding capillary objects with micron dimensions (Fig. 4) [41]. In general, these capillary-folded structures show well-defined, precise angles at each of the folds, a consequence of the strong separation of energy scales involved in the folding process. Eventually, as the curvature in each hinge becomes large enough, new behavior onsets for capillary origami. At sufficiently small radii of curvature, the surface tension begins to compete with bending energy to set the shape of the structure. As an order of magnitude estimate, the surface and bending energies balance at a size l2 ~ t3Ey/γ. This length is known as the elastocapillarity length scale [35]. In effect, it provides a limit for self-folding with capillary forces: at smaller radii of curvature, the elastic energy is too large for surface energy to drive bending. Even atomistic simulations shown a balance between bending and surface energy dictates whether the system can self-fold for sheets just nano meters in size [29]. Taking a typical bending energy, t3Ey, for an atomically thin material on the order of 10− 17-10− 15 J [1,2,41] and a surface tension of approximately 10–100 mN/m, the electrocapillarity length is on the order of 10–100 nm. Going beyond this dimension 4
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
The simplest approach to folding with surface stresses is to func tionalize one side of a material, but not the other. The difference in surface stress between the two distinct faces causes the device to bend, minimizing energy [44]. Indeed, cantilever bending experiments based on this concept go back thirty years, detailing a wide range of chemical and material combinations that can be used to trigger and modulate surface stress stresses [45–48]. Furthermore, many of the surface stress differences are large, on the order of ~N/m. For instance, DNA func tionalization [49,50], biomolecule adsorption [46,48] and electro chemical adsorption/oxidation [42,47] are well known to produce large surface stresses, providing several routes to actuators and folds with small radii of curvature. Many of these experiments can be directly miniaturized by decreasing the thickness of the layers involved. Specifically, a cantilever of thickness t and modulus E experiencing a stress difference Δγ between its two interfaces will bend to a curvature [44,51]:
Surface with adsorbates
Bare surface Capping Layer
e-
Platinum
Reaction paths
Anion in solution
Oxidized reaction product
κ=
Note this expression can be derived from eqn. 1 by taking the limit where one of the material’s thicknesses vanishes and renormalizing all the remaining material properties of that layer into a single parameter, Δγ. In terms of scaling, surface-stress origami clearly favors miniaturi zation, with curvatures rapidly increasing for thin films: decreasing the overall thickness of the actuator, t, by a factor of λ leads to a curvature that is larger by a factor of λ2. Recently, Miskin et al. demonstrated that surface stresses can be used to fold atomically thin materials. The authors layered graphene with 7 nm thick sheets of platinum to create two material interfaces (Fig. 5) [52]. Placed in water, the surface stress difference between the two sides bends the device to micron radii of curvature. In addition, the same system provides a route to electronically controlled actuation. When biased relative to the electrolyte surrounding it, ions attach or remove themselves from the surface of the platinum, modulating the forces at the interface. The full span of voltages required for going from flat to folded is just 200 mV, using just nW of power to operate. Since silicon microelectronics operate at a comparable voltage and current density, the authors showed that these actuators can readily be combined with components for information processing, offering a route to small ma chines that move, sense, and compute.
8 μm
Lower Potential
6Δγ Et2
Higher Potential
Fig. 5. Self-folding via surface stresses. Miskin et al. showed that electro chemical adsorption could be used to modulate the surface stress on a platinumgraphene bilayer. The resulting sheet bends to micron-scale radii of curvature that can be controlled via small-scale (200 mV) electrical potentials. From Miskin et al. [52].
requires either increasing the surface tension beyond what is typical for liquids or finding a new mechanism of force generation. 3.3. Self-folding by surface stresses Surface tensions at the interface of liquids are only one form of surface-stress. Broadly, the boundary of any material has a different distribution of bonds as compared to the bulk, leading to excess forces. Indeed, surface forces arising from solid interfaces provide another mechanism that can bend materials. Yet unlike liquid interfaces, these forces can be much larger: solid interface surface stresses are typically N/m, about an order of magnitude larger than liquids [42,43].
Fig. 6. Folding via magnetic fields. (A) A nanometer thick platinum film folded via magnetic panels and applied fields (from Dorsey et al. [1]). (B) Programmability via magnetic fields from Cui et al. [53] Here the strengths and orientations of magnetic panels are chosen so a given device can be put into a “P” state (left panel) and an “X” state (right panel) when actuated by an external field. 5
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
Fig. 7. A walking, microscopic robot using origami design concepts. The overall robot is fabricated in a fully planer processing environment, and self-folds into its final 3D structure. At a total size under 100 µm, it is too small to see by the naked eye and walks when pulsed via laser light. From Miskin et al. [52].
3.4. Self-folding by magnetic fields
4. A Moore’s law for machines
As a final approach for self-folding, we point to magnetic fields. The idea is to pattern permanent magnets onto rigid panels on either side of a hinge. When an external magnetic field is applied, the in-built magnets generate a torque that folds the hinge. Torque balance between the elastic forces in the hinge and the applied magnetic field, B, gives the fold angle φ in terms of the field, the magnetic moment μs, the bending energy of the hinge, and its aspect ratio [1,53]:
Scaling is a powerful concept: for fifty years it drove a revolution in microelectronics, enabling new applications from cheaper, smaller, faster information systems. With scalable approaches like self-folding, many of these characteristics could carry over to machines. For instance, making folding layers thinner leads to lower strains in moving parts, even when bending to small sizes. Far from failure, these mech anisms can perform large numbers of cycles without accruing damage or showing hysteresis [1,2,22,52]. Moreover, many of the atomically thin materials discussed here (e.g. graphene, glass, platinum) can sustain harsh chemical environments or large temperature variations, giving extreme material robustness [1,22,52]. Finally, manufactured massively in parallel with lithographic techniques, self-folding machines get cheaper as they get smaller: smaller machines mean more per wafer, lowering the cost per device [52]. What will happen with the capacity to manufacture such machines, miniaturizing devices to ever smaller length scales? What kinds of technologies should we expect as origami structures push to smaller and smaller dimensions? At the 100-µm scale, origami with self-folding structures is already emerging as a powerful platform for metamaterials [1,2]. For example, with atomic origami, it is feasible to build photonic structures with submicron 3D features by leveraging small radii of curvature. Moreover, mechanical metamaterials made from atomically thin membranes can sustain large displacements or deformations by accomidating strain in bending parts [1,2]. This enables dramatic shape changes or broad tunability in compliance. Furthermore, it could become possible to create new kinds of smart, responsive metamaterials with self-folding: the stimulus used to trigger folding in one domain maps onto a phys ical property in another. Tailoring this relationship could lead to new breeds of functional, responsive, and adaptable materials. One order of magnitude smaller, at the ten-micron scale, origami with atomic membranes has recently enabled machines and robotic systems. Broadly, macroscale robot designs based on origami [54,55] can be ported to the microscale by exploiting scalability. Indeed, in a recent paper, Miskin et al. demonstrated how to turn simple folding structures for legs into electronically integrated, walking, microscopic robots [52], as shown in Fig. 7. By merging the information processing abilities of silicon electronics with the mechanical control of self-folding structures, origami-based microscopic robots could invite an entirely new way to shape and engineer the microworld. Further, this work demonstrates how small machines can be manufacturable and robust: the microrobots actuate for upwards of thousands of cycles without damage, survive harsh chemical environments and high temperatures, can be sucked in syringes and injected back out without damage, can be fabricated millions at a time, can be deployed at 90% yield, and cost fractions of a penny per machine [52]. While these results show great potential, self-folding systems are still
L μB ϕ/cos(ϕ) = s 3 w Ey t Written in this form, geometric factors are on the left-hand side, and material parameters are on the right. We note that since the magnetic moment on the right-hand side scales in proportion to the volume of the magnet, the full expression is again scale invariant: the whole origami structure works exactly the same way if every dimension, including the thickness of the sheets used and volume of the magnets, is changed proportionally. To our knowledge, the thinnest sheet folded via magnets was ach ieved by Dorsey et. al where magnets were used to actuate hinges made from nanometer thick sheets of glass and platinum [1] (Fig. 6A). As noted by the authors, the sheets possessed bending energies of 10− 15 J, comparable to experimental values for graphene [2]. The authors demonstrated that magnetic panels could be used to build a range of mechanisms and 3D structures that could be controlled by simple external knobs like magnetic field orientation and strength. Magnetic fields bring several unique features to self-folding. First, there is a well-established and powerful technology for reading and writing 2D magnetization patterns. In principle, the backbone technol ogy for magnetic data recording could be appropriated as a means to encoding folds into lithographically patterned 2D films. Second, mag nets can interact with one another, as well as with the elastic sheet they are imbedded in. This provides a distinct mechanism to encode multiple responses or switch between behaviors by repositioning magnets in free space. Concepts like programmability and shape morphing have started to emerge for origami structures developed by the microrobots commu nity. Using a similar platform of magnetic panels embedded between hinges Cui et al. demonstrated shape morphing origami structures at the microscale [53]. The authors demonstrated how modular units could be joined together to build programable pop-up structures (Fig. 6B) or selfactuating devices, in particular a microscale flapping bird. While this work was carried out using 50 nm thick silicon nitride sheets as the folding layer, the scale invariance of magnetic systems means it could potentially be imported to work at smaller dimensions by moving to atomically thin materials.
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largely micrometers in dimension, only scratching the surface of what’s possible with atomic origami. Pushed to its limit, an origami structure made using atomically thin materials could go at least three orders of magnitude smaller in size, becoming geometrically comparable to fol ded biological counterparts. Perhaps someday it will be possible to fold graphene into shapes small enough to hug the radius of a DNA strand (2 nm diameter), a single α-helix (1.5 nm diameter), or an actin filament (6 nm diameter). Made from synthetic materials, atomic origami at the nanoscale could potentially incorporate chemical, electronic, or pho tonic elements, blurring the lines between information technology and biology. While this represents a long-term goal, there is no physical limitation that prohibits folding atomic membranes at this size. Already, atomic origami offers a new way to build 3D nanotechnologies over an incredible range of scales. If it’s full potential can be realized, it could perhaps enable tiny machines and materials that range in size from just barely visible down to the smallest dimensions allowed by nature.
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] K.J. Dorsey, T.G. Pearson, E. Esposito, S. Russell, B. Bircan, Y. Han, M.Z. Miskin, D. A. Muller, I. Cohen, P.L. McEuen, Atomic layer deposition for membranes, metamaterials, and mechanisms, Adv. Mater. 31 (2019) 1901944. [2] M.K. Blees, A.W. Barnard, P.A. Rose, S.P. Roberts, K.L. McGill, P.Y. Huang, A. R. Ruyack, J.W. Kevek, B. Kobrin, D.A. Muller, et al., Graphene kirigami, Nature 524 (2015) 204–207. [3] E.T. Filipov, T. Tachi, G.H. Paulino, Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials, Proc. Natl. Acad. Sci. 112 (2015) 12321–12326. [4] Y.M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K.-J. Choi, Z. Liu, H. Park, C. Lu, R.-H. Kim, et al., Digital cameras with designs inspired by the arthropod eye, Nature 497 (2013) 95–99. [5] W. Xu, T. Li, Z. Qin, Q. Huang, H. Gao, K. Kang, J. Park, M.J. Buehler, J.B. Khurgin, D.H. Gracias, Reversible MoS2 origami with spatially resolved and reconfigurable photosensitivity, Nano Lett. 19 (2019) 7941–7949. [6] C.D. Santangelo, Extreme mechanics: self-folding origami, Annu. Rev. Condens. Matter Phys. 8 (2017) 165–183. [7] J. Rogers, Y. Huang, O.G. Schmidt, D.H. Gracias, Origami mems and nems, Mrs Bulletin 41 (2016) 123–129. [8] W. Xu, K.S. Kwok, D.H. Gracias, Ultrathin shape change smart materials, Acc. Chem. Res. 51 (2018) 436–444. [9] N. Benbernou, E. D. Demaine, M. L. Demaine, A. Ovadya, A universal crease pattern for folding orthogonal shapes. arXiv preprint arXiv:0909.5388 (2009). [10] N.M. Benbernou, E.D. Demaine, M.L. Demaine, A. Lubiw, in: Workshop on Algorithms and Data Structures, Springer, 2017, pp. 109–120. [11] B. An, N. Benbernou, E.D. Demaine, D. Rus, Planning to fold multiple objects from a single self-folding sheet, Robotica. 29 (2011) 87–102. [12] T. Tachi, Origamizing polyhedral surfaces, IEEE Trans. Visual Comput. Graphics 16 (2009) 298–311. [13] H. Greenberg, M.L. Gong, S.P. Magleby, L.L. Howell, Identifying links between origami and compliant mechanisms, Mech. Sci. 2 (2011) 217–225. [14] C.D. Santangelo, Theory and practice of origami in science, Soft Matter 16 (2020) 94–101. [15] Z.Y. Wei, Z.V. Guo, L. Dudte, H.Y. Liang, L. Mahadevan, Geometric mechanics of periodic pleated origami, Phys. Rev. Lett. 110 (2013), 215501. [16] A.A. Evans, J.L. Silverberg, C.D. Santangelo, Lattice mechanics of origami tessellations, Phys. Rev. E 92 (2015), 013205. [17] M. Wautelet, Scaling laws in the macro-, micro-and nanoworlds, Eur. J. Phys. 22 (2001) 601. [18] R.S. Fearing, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots, IEEE, 1995, vol. 2, pp. 212–217. [19] S.M. Felton, M.T. Tolley, B. Shin, C.D. Onal, E.D. Demaine, D. Rus, R.J. Wood, Selffolding with shape memory composites, Soft Matter 9 (2013) 7688–7694. [20] J.-H. Na, A.A. Evans, J. Bae, M.C. Chiappelli, C.D. Santangelo, R.J. Lang, T.C. Hull, R.C. Hayward, Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers, Adv. Mater. 27 (2015) 79–85. [21] T.G. Leong, C.L. Randall, B.R. Benson, A.M. Zarafshar, D.H. Gracias, Self-loading lithographically structured microcontainers: 3D patterned, mobile microwells, Lab Chip 8 (2008) 1621–1624. [22] M.Z. Miskin, K.J. Dorsey, B. Bircan, Y. Han, D.A. Muller, P.L. McEuen, I. Cohen, Graphene-based bimorphs for micron-sized, autonomous origami machines, Proc. Natl. Acad. Sci. 115 (2018) 466–470.
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Contents lists available at ScienceDirect
Current Opinion in Solid State & Materials Science journal homepage: www.elsevier.com/locate/cossms
Atomic origami Marc Z. Miskin Dept. of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Origami-fabrication 2D materials Nanofabrication Meta-materials NEMS
Here we summarize recent experimental work in the field of atomic origami: the folding of 3D structures from sheets that are just atoms thick. We highlight current techniques for folding at the microscale and provide scaling arguments as to why some approaches work better than others at small sizes. Finally, we point out that for folding structures made from 2D materials, miniaturization can extend another three orders of magnitude: current state of the art devices are microns in size while, as a platform, atomic membranes should be foldable down to the nanoscale. The ability to scale folding structures over a wide range in size could open diverse ap plications, from microscopic robots to new interfaces with biology.
1. Introduction While today it’s possible to pattern 2D features with nearly nano meter precision, it remains a challenge to build small 3D objects. For micro and nano systems that are meant to interact with the physical world, this imposes a significant constraint. The real world is 3D, and the capacity to move, sense, or explore in three dimensions would open up tremendous new opportunities for nanotechnology ranging from meta materials [1–3] to sensors [45] to robots too small to be seen by the naked eye. The most direct route to take 2D patterns into 3D is arguably selffolding: make something that folds itself into a specific geometry. Indeed, a major body of work [6–8] has established self-folding and origami inspired fabrication as powerful techniques for building com plex mechanisms and structures at small sizes thanks to several key properties. First, origami fabrication is extremely well suited to micro/ nano systems because even complicated, dense patterns of folds can be built with massively parallel lithographic techniques [7]. Second, origami allows virtually any 3D shape to be built. For instance, several fold patterns are universal, meaning they can be used to approximate any 3D shape up to a voxel resolution [9–11]. In addition, there are now established CAD programs that can map arbitrary 3D surfaces into specific 2D patterns that form them [12], and libraries of origami mechanisms and linkages are coming into place, providing a route to engineering complex machines with folding elements [13]. Yet one of the most remarkable properties of origami fabrication is that it scales. By this we mean that the same origami structure can be built at a variety of different length scales without having to rethink the basic working principles. Instead, origami can be scaled up or down arbitrarily in size by adjusting the length, width, and thickness of the self-folding sheet appropriately [14–16]. Fig. 1 shows several
realizations of self-folding systems. While these devices are made from materials spanning roughly five orders of magnitude in thickness, they operate using similar design concepts and obey similar constraints. This stands in stark contrast to traditional approaches for mechanical control, such as wheels and gears, which struggle in sub-millimeter dimensions due to the dominance of surface forces and friction [17,18]. Scaling in origami is akin to scaling in microelectronics: devices can be increased or decreased in size by following simple design rules based on physical principles. Given scalability and the capacity to pattern 2D features with nanoscale precision, a natural question arises: how small can we make the smallest origami structure? To the extent that building smaller de vices requires thinner sheets, atomically thin materials set a funda mental limit to miniaturization. In other words, the smallest folded structures should be made from sheets of “paper” just one atom thick. From our perspective, this extreme limit represents an exciting challenge for the field of nanoscience. How do we make something that self-folds with the thinnest paper that nature allows? Remarkably, the materials needed to meet this goal are already in place: twenty years of research in 2D materials have brought a range of atomically thin “pa pers” like graphene, transition metal dichalcogenides [23,23] and membranes formed by atomic layer deposition [1,24–26]. Here we re view some recent work on folding these materials, which we call atomic origami. We point out that atomically thin materials provide a unique class well suited to self-folding: they can be deformed to large curvatures without fracture and provide useful properties like high stiffness and electrical, photonic, and chemical functionality. We review different methods that the field has developed for folding atomically thin mate rials and provide design rules that describe how folding mechanisms work when shrunk to smaller dimensions. We also show that as a plat form for origami, atomically thin materials provide a route towards
https://doi.org/10.1016/j.cossms.2020.100882 Received 10 August 2020; Received in revised form 27 October 2020; Accepted 1 November 2020 Available online 18 November 2020 1359-0286/© 2020 Elsevier Ltd. All rights reserved.
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
Fig. 1. Origami structures from millimeter scale paper down to atomically thin mem branes. At each size scale, similar concepts can be reused thanks to the scale invariance of origami inspired fabrication. From left to right: Panel (1) a folded bird made from laminated paper, pre-stretched polystyrene, and folded via Joule heating with internal coper circuits from Felton et al. 2013 [19]. Panel (2): an octet-truss pattern folded in crosslinked polymers from Na et al. 2014 [20], Panel (3): a cube folded using differen tial stresses in 100 nm thick metal layers from Leong et al. 2008 [21]. Panel (4) a cube fol ded from stresses in nanometer thick glass and graphene from Miskin et al. 2018 [22].
Fig. 2. Atomic membranes are well suited to origami. (A) Failure stress vs. Young’s modulus for different material classes. Good materials for origami maximize the ratio of σ3f /E2y . As shown by the guide lines, 2D materials like graphene and MoS2 stand out as excellent by this metric. Other outstanding choices include elastomers and ceramics, both of which are frequent material choices in the literature [1,22,26,27]. Reproduced from [22] (B) Folding graphene at the nanometer scale by hand, from Chen et al. [28]. A TEM tip is used to pick up graphene and controllably fold it over itself to produce true, nanoscale elastic folds.
building microscale machines, metamaterials, and microscopic robots. Finally, we point out that pushed to its logical conclusion, atomic origami could enable folded structures with nanoscale radii of curva ture, potentially allowing machines the size of cells, proteins and everything in between.
These two conditions, maximum bending resistance subject to stay ing within the elastic limit, can be used together to eliminate the thickness of the hinge altogether in favor of a single, material-based figure of merit. The result is that, for a given curvature set by the desired size of the origami device, the best material will be the one that maximizes σ3y /Ey 2. Fig. 2A shows a log-log plot of modulus and yield stress for different material classes and guidelines for different values for σ3y /Ey 2. By this metric, 2D materials stand out as excellent. Mechanically they can deform to high strains without fracture and yet possesses some of the highest moduli of any material available. This unique combination provides a nice payoff for microscale origami engineering: in principle one can build incredibly small structures with high mechanical resis tance by using atomically thin sheets. As a back of the envelope estimate, one can consider how far down a 3D structure could be scaled if 2D materials could be folded to their ultimate limits. Typically, 2D materials have a fracture strain in exper iment on the order of 10% [23]. Taking the thickness as 3 angstroms, an effective value estimated from the layer spacing in graphite, one expects graphene origami to scale to radii of curvatures on the order of nano meters, essentially a carbon nanotube. Recent work has demonstrated proof of concept for this vision, albeit by manual folding. In Chen et al. [28], researchers were able to pick up a sheet of graphene using an TEM tip and fold it over itself (Fig. 2B). The results were controllable, nanoscale folds with exotic electrical proper ties. Tiny folded structures like these show the potential of graphene as a folding material, mixing interesting electronic functionality with ultra-
2. Choosing the right material for microscale origami A good folding material is determined by the mechanics of a folding hinge and given their high strength and flexibility, atomic membranes turn out to be an exceptional choice. When a hinge bends from a flat shape, it experiences a stress, σ , on the order of Eyκt where t is the thickness of the hinge, Ey is the Young’s modulus, and κ is the curvature. Geometrically, κt is the strain required to deform the hinge while Ey provides the conversion from strain to stress. Because the material cannot deform beyond its yield stress, σy, without breaking, there is a maximum curvature that a given material sheet can achieve: tκ < σy/Ey. While the left-hand side expresses geometric factors, the right-hand side of the equation is essentially fixed by the material choices. Thus, once a material is selected, going to small radii of curvature requires a decrease in thickness. Just bending to small sizes isn’t enough: the hinge also needs to be able to resist forces from the external world. At thinner and thinner sizes this becomes a challenge since the hinge’s stiffness decreases dramati cally: the bending resistance scales like Ey t3. For the hinge to reliably hold its shape, this quantity needs to be maximized, subject to the constraint that the materials involved don’t fail. 2
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
continuum mechanics predicts that the material stack will bend to a curvature set by force and torque balance [31]: κ=
0 6
0
0
6E1 E2 (t1 + t2 )t1 t2 Δ∊ E12 t14 + 4E1 E2 t13 t2 + 6E1 E2 t12 t22 + 4E1 E2 t23 t1 +E22 t24
where Δε is the strain difference between the two layers and Ei and ti represent the modulus and thickness of the layers. Dimensional analysis of eqn. 1 shows that origami hinges folded by internal stresses are essentially scale invariant: one can simply increase or decrease the size of everything proportionally and the device will work in exactly the same way. Specifically, multiplying every thickness on the right-hand side of the above equation by a fixed factor of λ will produce a curvature scaled down by λ. In fact, the entire equation could be non-dimensionalized by simply multiplying both sides by the average layer thickness (t1 + t2). At the extreme end of this scaling are recent works using atomically thin materials for the layers. For example, Miskin et al. used graphene and nm-thick layers of glass to build self-folding bilayer actuators [22]. They showed that strain could be introduced in the glass layer by using either thermal expansion or chemically induced stresses (Fig. 3A). At just nm thick, these devices were able to easily fold to micron scale radii of curvature, enabling ~10 um self-folding origami structures. In another example, Xu et al. demonstrated self-folding with graphene and polymer bilayers (Fig. 3B) [27,32]. The resulting structures opened up new opportunities that leverage small 3D shapes and the unique mate rial properties of graphene like folded transistors and nonlinear re sistors. Finally, using pre-stresses in tri-layer stacks of ALD materials, Bircan et al. [26] demonstrated complex origami structures (Fig. 3C) including tiny folded birds and patterns upward of 100 folds in sheets just 10 nm thick. The work also included a complete process flow that maps arbitrary origami CAD files into corresponding lithographic masks. At the 10-µm scale, these small 3D structures are comparable in size to many cells, inviting new ways to sense or interact with biology. A significant step in this direction came from Xu et al. who demonstrated encapsulation of cells with self-folding graphene-polymer composites [33]. By integrating silver nanoparticles in the composite structure, they were able to perform surface-enhanced Raman spectroscopy on the surface of the cell. Indeed, this approach could be generalized into a platform technology, using atomically thin materials with understood, controllable surface chemistries (e.g. glass and polymers) to create 3D structures with specific biological or chemical functionality. Broadly, self-folding via internal elastic stress can be triggered in respond to a wide range of different stimuli. Linear responses couple strain to temperature, light, magnetic fields, and chemistry and all of these can be used to build self-folding structures. Origami structures coupling folds to fields can then be used as the building block of smart materials with microscale features or mechanisms that extract me chanical work from changes in their environment. In addition, working with extremely thin films leads to a dramatic increase in response time. For example, for chemical or thermally induced stresses, the response time is limited by the diffusion of chemistry/heat through the bilayer stack, scaling as ~t2. Thus, modes of motion control that are sluggish at the macroscale become rapid when miniaturized: examples include glass as a chemically active medium at the nanoscale [22], or DNA-based smart films [34].
Fig. 3. Self-folding with elastic stresses. (A) A tetrahedron made from graphene and glass folds and unfolds in a few hundred milliseconds when responding to changes in its chemical environment. Ions from the solution lead to swelling in the glass, producing bending. The rapid response time is a feature of working with extremely thin films. (From Miskin et al. [22]). (B) Self-folding with graphene-polymer bilayers (From Xu et al. [27]) in response to temperature changes. Specifically, the polymer layer swells in response to temperature changes, producing reversible actuation. (C) A bi-directional folding origami structure made from nanometer thick ALD films. Here the fabrication protocols allow for both mountain and valley folds, enabling generic origami structures (From Bircan et al. [26]).
small geometric structures. Yet an open question remains: how can atomic origami be done at scale, without having to pick and place each fold by hand? 3. How to fold small systems The main challenge for atomic origami is to actually produce the forces that drive bending and folding. Overcoming the elastic restoring force of the material requires something to act at each origami hinge, bending it to a desired shape. While many choices are possible, here we focus those that scale well to small sizes and can be parallelized to fold a large number of independent folds. To our knowledge, prior work with atomically thin sheets has demonstrated four main techniques that meet these criteria: internal stress, liquid capillary forces, solid surface stresses, and magnetic fields. Our discussion focuses on continuum descriptions, which are heu ristic for 2D materials, but have largely been a reliable basis for explaining self-folding experiments. Yet it should be noted that the mechanics of 2D materials is still under investigation [23]. For example, experimental values for the bending energy of graphene can differ by a factor of almost 10,000, depending on the details of the measurement, whether the sheet is crumpled, or even how big it is [2,23]. Similarly, new physics can dominate at smaller sizes, and continuum descriptions of self-folding may need to be augmented with atomistic simulations [29,30] or integrated into multiscale models [27].
3.2. Self-folding by capillary forces At small scales, surface forces tend to dominate, and as a conse quence, they can provide a robust way to fold tiny structures. This approach defines a second technique for self-folding called capillary origami [35]. Here the surface tension, γ, from a liquid interface is used to fold a thin sheet of elastic material. When the liquid tries to minimize its surface area, it folds up the attached solid sheet, creating a 3D shape. For sufficiently thin sheets, capillary-driven folding is essentially
3.1. Self-folding by internal elastic stress The most common way to build self-folding structures is internal stress: take two materials, layer them together, and find a way to introduce a strain in one material but not the other. For thin layers, 3
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Current Opinion in Solid State & Materials Science 24 (2020) 100882
Fig. 4. Self-folding structures using capillary forces. Here MoS2 and graphene sheets are folded into targeted shapes set by the geometry of the sheet and the placement of rigid panels (Reproduced from Reynolds et al. [41]).
geometric due to a large separation in energy scales. As pointed out by Paulsen [36,37] and King [38], an elastic sheet at a liquid interface has three primary contributions to its energy: (I) a surface energy that scales as γL2, (II) an energy for stretching the sheet that scales as EytL2 and (III) a bending energy that scales as Ey t3. For sufficiently thin sheets, these energy scales are well separated: stretching the sheet is prohibitively expensive, bending is extremely low energy and surface energy falls somewhere in between. The resulting problem becomes geometric: minimize the available surface area subject to a “no-stretching” condi tion, fixing all the behavior to a single, geometric parameter comparing the size of the drop to the size of the sheet [36]. Take the specific example of a ten-micron wide graphene sheet floating at a water-oil interface. Here the surface tension is on the order of 30 mN/m. By contrast, the 2D Young’s modulus, defining the stretching energy, is on the order of 340 N/m [39]. Thus, the liquid interface can at most stretch the graphene by a strain on the order of 10− 4. Smaller still, the bending energy for a graphene sheet is 10− 15 J [2]. Until the sheet is deformed to a radius of curvature on the order of 100 nm, the surface energy provides a significantly larger contribution than bending. From an origami perspective, capillary forces possess a unique scaling behavior: provided the sheet is thin enough, it will always try to fold to a structure dictated by geometry. Again, the mechanism is scale invariant, but here, there is no need to even adjust the thickness of the sheet. The large separation in energy scales essentially locks the folding
shape once the sizes of the droplet and the sheet of material are defined. In practice, this constraint proves extremely useful. To our knowl edge, the smallest origami structures have been built using capillary forces acting on thin films. Specifically, Leong et al. demonstrated 100 nm e-beam patterned resonators folded by molten tin [40]. Recently, this idea was extended to operate on atomic membranes: working with films of graphene and MoS2, Reynolds et al. demonstrated self-folding capillary objects with micron dimensions (Fig. 4) [41]. In general, these capillary-folded structures show well-defined, precise angles at each of the folds, a consequence of the strong separation of energy scales involved in the folding process. Eventually, as the curvature in each hinge becomes large enough, new behavior onsets for capillary origami. At sufficiently small radii of curvature, the surface tension begins to compete with bending energy to set the shape of the structure. As an order of magnitude estimate, the surface and bending energies balance at a size l2 ~ t3Ey/γ. This length is known as the elastocapillarity length scale [35]. In effect, it provides a limit for self-folding with capillary forces: at smaller radii of curvature, the elastic energy is too large for surface energy to drive bending. Even atomistic simulations shown a balance between bending and surface energy dictates whether the system can self-fold for sheets just nano meters in size [29]. Taking a typical bending energy, t3Ey, for an atomically thin material on the order of 10− 17-10− 15 J [1,2,41] and a surface tension of approximately 10–100 mN/m, the electrocapillarity length is on the order of 10–100 nm. Going beyond this dimension 4
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The simplest approach to folding with surface stresses is to func tionalize one side of a material, but not the other. The difference in surface stress between the two distinct faces causes the device to bend, minimizing energy [44]. Indeed, cantilever bending experiments based on this concept go back thirty years, detailing a wide range of chemical and material combinations that can be used to trigger and modulate surface stress stresses [45–48]. Furthermore, many of the surface stress differences are large, on the order of ~N/m. For instance, DNA func tionalization [49,50], biomolecule adsorption [46,48] and electro chemical adsorption/oxidation [42,47] are well known to produce large surface stresses, providing several routes to actuators and folds with small radii of curvature. Many of these experiments can be directly miniaturized by decreasing the thickness of the layers involved. Specifically, a cantilever of thickness t and modulus E experiencing a stress difference Δγ between its two interfaces will bend to a curvature [44,51]:
Surface with adsorbates
Bare surface Capping Layer
e-
Platinum
Reaction paths
Anion in solution
Oxidized reaction product
κ=
Note this expression can be derived from eqn. 1 by taking the limit where one of the material’s thicknesses vanishes and renormalizing all the remaining material properties of that layer into a single parameter, Δγ. In terms of scaling, surface-stress origami clearly favors miniaturi zation, with curvatures rapidly increasing for thin films: decreasing the overall thickness of the actuator, t, by a factor of λ leads to a curvature that is larger by a factor of λ2. Recently, Miskin et al. demonstrated that surface stresses can be used to fold atomically thin materials. The authors layered graphene with 7 nm thick sheets of platinum to create two material interfaces (Fig. 5) [52]. Placed in water, the surface stress difference between the two sides bends the device to micron radii of curvature. In addition, the same system provides a route to electronically controlled actuation. When biased relative to the electrolyte surrounding it, ions attach or remove themselves from the surface of the platinum, modulating the forces at the interface. The full span of voltages required for going from flat to folded is just 200 mV, using just nW of power to operate. Since silicon microelectronics operate at a comparable voltage and current density, the authors showed that these actuators can readily be combined with components for information processing, offering a route to small ma chines that move, sense, and compute.
8 μm
Lower Potential
6Δγ Et2
Higher Potential
Fig. 5. Self-folding via surface stresses. Miskin et al. showed that electro chemical adsorption could be used to modulate the surface stress on a platinumgraphene bilayer. The resulting sheet bends to micron-scale radii of curvature that can be controlled via small-scale (200 mV) electrical potentials. From Miskin et al. [52].
requires either increasing the surface tension beyond what is typical for liquids or finding a new mechanism of force generation. 3.3. Self-folding by surface stresses Surface tensions at the interface of liquids are only one form of surface-stress. Broadly, the boundary of any material has a different distribution of bonds as compared to the bulk, leading to excess forces. Indeed, surface forces arising from solid interfaces provide another mechanism that can bend materials. Yet unlike liquid interfaces, these forces can be much larger: solid interface surface stresses are typically N/m, about an order of magnitude larger than liquids [42,43].
Fig. 6. Folding via magnetic fields. (A) A nanometer thick platinum film folded via magnetic panels and applied fields (from Dorsey et al. [1]). (B) Programmability via magnetic fields from Cui et al. [53] Here the strengths and orientations of magnetic panels are chosen so a given device can be put into a “P” state (left panel) and an “X” state (right panel) when actuated by an external field. 5
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Fig. 7. A walking, microscopic robot using origami design concepts. The overall robot is fabricated in a fully planer processing environment, and self-folds into its final 3D structure. At a total size under 100 µm, it is too small to see by the naked eye and walks when pulsed via laser light. From Miskin et al. [52].
3.4. Self-folding by magnetic fields
4. A Moore’s law for machines
As a final approach for self-folding, we point to magnetic fields. The idea is to pattern permanent magnets onto rigid panels on either side of a hinge. When an external magnetic field is applied, the in-built magnets generate a torque that folds the hinge. Torque balance between the elastic forces in the hinge and the applied magnetic field, B, gives the fold angle φ in terms of the field, the magnetic moment μs, the bending energy of the hinge, and its aspect ratio [1,53]:
Scaling is a powerful concept: for fifty years it drove a revolution in microelectronics, enabling new applications from cheaper, smaller, faster information systems. With scalable approaches like self-folding, many of these characteristics could carry over to machines. For instance, making folding layers thinner leads to lower strains in moving parts, even when bending to small sizes. Far from failure, these mech anisms can perform large numbers of cycles without accruing damage or showing hysteresis [1,2,22,52]. Moreover, many of the atomically thin materials discussed here (e.g. graphene, glass, platinum) can sustain harsh chemical environments or large temperature variations, giving extreme material robustness [1,22,52]. Finally, manufactured massively in parallel with lithographic techniques, self-folding machines get cheaper as they get smaller: smaller machines mean more per wafer, lowering the cost per device [52]. What will happen with the capacity to manufacture such machines, miniaturizing devices to ever smaller length scales? What kinds of technologies should we expect as origami structures push to smaller and smaller dimensions? At the 100-µm scale, origami with self-folding structures is already emerging as a powerful platform for metamaterials [1,2]. For example, with atomic origami, it is feasible to build photonic structures with submicron 3D features by leveraging small radii of curvature. Moreover, mechanical metamaterials made from atomically thin membranes can sustain large displacements or deformations by accomidating strain in bending parts [1,2]. This enables dramatic shape changes or broad tunability in compliance. Furthermore, it could become possible to create new kinds of smart, responsive metamaterials with self-folding: the stimulus used to trigger folding in one domain maps onto a phys ical property in another. Tailoring this relationship could lead to new breeds of functional, responsive, and adaptable materials. One order of magnitude smaller, at the ten-micron scale, origami with atomic membranes has recently enabled machines and robotic systems. Broadly, macroscale robot designs based on origami [54,55] can be ported to the microscale by exploiting scalability. Indeed, in a recent paper, Miskin et al. demonstrated how to turn simple folding structures for legs into electronically integrated, walking, microscopic robots [52], as shown in Fig. 7. By merging the information processing abilities of silicon electronics with the mechanical control of self-folding structures, origami-based microscopic robots could invite an entirely new way to shape and engineer the microworld. Further, this work demonstrates how small machines can be manufacturable and robust: the microrobots actuate for upwards of thousands of cycles without damage, survive harsh chemical environments and high temperatures, can be sucked in syringes and injected back out without damage, can be fabricated millions at a time, can be deployed at 90% yield, and cost fractions of a penny per machine [52]. While these results show great potential, self-folding systems are still
L μB ϕ/cos(ϕ) = s 3 w Ey t Written in this form, geometric factors are on the left-hand side, and material parameters are on the right. We note that since the magnetic moment on the right-hand side scales in proportion to the volume of the magnet, the full expression is again scale invariant: the whole origami structure works exactly the same way if every dimension, including the thickness of the sheets used and volume of the magnets, is changed proportionally. To our knowledge, the thinnest sheet folded via magnets was ach ieved by Dorsey et. al where magnets were used to actuate hinges made from nanometer thick sheets of glass and platinum [1] (Fig. 6A). As noted by the authors, the sheets possessed bending energies of 10− 15 J, comparable to experimental values for graphene [2]. The authors demonstrated that magnetic panels could be used to build a range of mechanisms and 3D structures that could be controlled by simple external knobs like magnetic field orientation and strength. Magnetic fields bring several unique features to self-folding. First, there is a well-established and powerful technology for reading and writing 2D magnetization patterns. In principle, the backbone technol ogy for magnetic data recording could be appropriated as a means to encoding folds into lithographically patterned 2D films. Second, mag nets can interact with one another, as well as with the elastic sheet they are imbedded in. This provides a distinct mechanism to encode multiple responses or switch between behaviors by repositioning magnets in free space. Concepts like programmability and shape morphing have started to emerge for origami structures developed by the microrobots commu nity. Using a similar platform of magnetic panels embedded between hinges Cui et al. demonstrated shape morphing origami structures at the microscale [53]. The authors demonstrated how modular units could be joined together to build programable pop-up structures (Fig. 6B) or selfactuating devices, in particular a microscale flapping bird. While this work was carried out using 50 nm thick silicon nitride sheets as the folding layer, the scale invariance of magnetic systems means it could potentially be imported to work at smaller dimensions by moving to atomically thin materials.
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largely micrometers in dimension, only scratching the surface of what’s possible with atomic origami. Pushed to its limit, an origami structure made using atomically thin materials could go at least three orders of magnitude smaller in size, becoming geometrically comparable to fol ded biological counterparts. Perhaps someday it will be possible to fold graphene into shapes small enough to hug the radius of a DNA strand (2 nm diameter), a single α-helix (1.5 nm diameter), or an actin filament (6 nm diameter). Made from synthetic materials, atomic origami at the nanoscale could potentially incorporate chemical, electronic, or pho tonic elements, blurring the lines between information technology and biology. While this represents a long-term goal, there is no physical limitation that prohibits folding atomic membranes at this size. Already, atomic origami offers a new way to build 3D nanotechnologies over an incredible range of scales. If it’s full potential can be realized, it could perhaps enable tiny machines and materials that range in size from just barely visible down to the smallest dimensions allowed by nature.
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