Session E41: Atomic Origami, Kirigami and Crumpling

Programmable folding triggered by temperature and DNA

Temperature and biomolecule responsive materials allow the creation of wireless devices that respond autonomously to physiological or environmental cues without the need for any external tethers of power sources. However, it can be challenging to realize the same level of control and programmability that can be achieved with wired electrical or pneumatic devices. In addition, controllable folding of atomically thin films using these stimuli has proven challenging, especially under conditions compatible with living systems. In this talk, the design, fabrication and characterization of temperature and DNA responsive soft shape change devices will be discussed including those that display programmability, multi-state and complex shape change. Gels and soft-material hybrids including those with ultra-stiff yet ultra-thin graphene are patterned using multilayer photolithography or 3D printing; the swelling or collapse of gels or stimuli responsive polymers drives folding. Experiments are guided by mechanics and mulstiscale simulations and this synergy enables a high level of design. In addition to the intellectual elements, potential applications of these shape change and self-folding devices in electronics, optics, biosensing and medicine will be highlighted.   

How to fold a magnet: distorted kagome antiferromagnets as topologically frustrated origami sheets

Frustration in condensed matter, the hard decision of choosing one ground state among many, is both delicate and robust. In frustrated antiferromagnets, its delicate side of lifting this degeneracy has been used to find exotic states of matter from nearly flat-band spin wave dispersions to quantum spin liquids of anyons. But we have only begun to understand its robust side. A recent discovery links their Hamiltonians to those of balls and springs networks now known to host topological and geometrical invariants. So the science of the robust frustration is waiting to be discovered just by mapping frustrated magnets onto metamaterials and back.

In this talk, I will present a theory of distorted kagome lattice antiferromagnets by mapping their ground states onto triangulated kirigami or origami. This map associates spin moment vectors to directed edges of triangle faces. We illustrate the theory with two ``spin-origami'' materials, ${\rm Cs}_2{\rm ZrCu}_3{\rm F}_{12}$ with flattenable (coplanar) origami ground states and ${\rm Cs}_2{\rm CeCu}_3{\rm F}_{12}$ with crumpled (non-flattenable, non-coplanar) origami. Remarkably, the zero modes are demanded by topological invariants, are exotic with a flat band in the former and a doubly degenerate topological ``Dirac   

From Atomic Origami, Towards Cell-Sized Machines

We are developing origami into a tool for fabricating autonomous, cell-sized machines. These devices can interact with their environment, be manufactured en masse, and carry the full power of modern information technology. Our approach starts with origami in the extreme limit of folding 2D atomic membranes. We make actuators that bend to micron radii of curvature out of atomically thin materials, like graphene. By patterning rigid panels on top of these actuators, we can localize bending to produce folds, and scale down existing origami patterns to produce a wide range of machines. These machines change shape in fractions of a second in response to environmental changes, and perform useful functions on time and length scales comparable to microscale biological organisms. Beyond simple stimuli, we demonstrate how to fabricate voltage responsive actuators that can be powered by on-board photovoltaics. Finally, we demonstrate that these actuation technologies can be combined with silicon-based electronics to create a powerful platform for robotics at the cellular scale.   

Perforations, disclination quadrapoles and crumpling of free-standing graphene

Understanding deformations of macroscopic thin plates and shells has a long and rich history, culminating with the Foeppl-von Karman equations in 1904, characterized by a dimensionless coupling constant (the ``Foeppl-von Karman number'') that can easily reach vK = 10$^{7}$ in an ordinary sheet of writing paper. These equations lead to highly nonlinear force-extension curves associated with the buckling of partial disclinations, even for the simple case of a square sheet punctured by a large square hole. However, thermal fluctuations in thin elastic membranes fundamentally alter the long wavelength physics. We discuss the remarkable properties of free-standing graphene sheets (with vK = 10$^{13}$!) at room temperature, where enhancements of the bending rigidity by factors of $\sim$4000 compared to T = 0 values have now been observed. Thermalized elastic membranes can undergo a crumpling transition when the microscopic bending stiffness is comparable to kT. We argue that the crumpling temperature can be dramatically reduced by inserting a regular lattice of laser-cut perforations. These expectations are confirmed by extensive molecular dynamics simulations, which also reveal a remarkable "frame crumpling transition" triggered by a single large hole inserted into a graphene sheet.   

Nanoscale Construction with DNA

I'll discuss how to use DNA to construct nanoscale structures. We have invented a general framework to program DNA/RNA strands to self-assemble into structures with user-specified geometry or dynamics. By interfacing these nanostructures with other functional molecules, we have introduced digital programmability into diverse application areas, e.g. fabrication of inorganic nanoparticles with arbitrary prescribed shapes, robust DNA probes with near optimal binding specificity, RNA-based translation regulators with unprecedented dynamic range and orthogonality, and a highly multiplexed optical imaging method. In this talk, I will focus on describing two recent advances in DNA nanoconstruction: the programmable self-assembly of three-dimensional nanostructures from 10,000 unique components and the programmable self-folding of a single DNA/RNA polymer into a compact user-defined shape. For more details of our work, see http://molecular.systems.