Multiply Folded Graphene

The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material, folding may transform it to complex shapes with new and distinct properties. Here, we present experimental results that folded structures in graphene, termed grafold, exist, and their formations can be controlled by introducing anisotropic surface curvature during graphene synthesis or transfer processes. Using pseudopotential-density functional theory calculations, we also show that double folding modifies the electronic band structure of graphene. Furthermore, we demonstrate the intercalation of C60 into the grafolds. Intercalation or functionalization of the chemically reactive folds further expands grafold's mechanical, chemical, optical, and electronic diversity.Comment: 29 pages, 10 figures (accepted in Phys. Rev. B

Active swarms on a sphere

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.Comment: 5 pages, 4 figures plus Supporting Informatio

Mechanics of large folds in thin interfacial films

A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, self-adhesion and energy dissipation.Comment: 5 pages, 3 figure

Folding Large Antenna Tape Spring

This paper presents a novel concept for a low-mass, 50-m^2-deployable, P-band dual polarization antenna that can measure terrestrial biomass levels from a spacecraft in a low Earth orbit. A monolithic array of feed and radiating patches is bonded to a transversally curved structure consisting of two Kevlar sheets. The first sheet supports the array and the other sheet supports a ground plane. The two sheets are connected by a compliant Kevlar core that allows the whole structure to be folded elastically and to spring back to its original, undamaged shape. Test pieces have been made to demonstrate both the radio frequency and mechanical aspects of the design, particularly the radio frequency performance before and after folding the structure. It is concluded that the proposed design concept has high potential for large, low-frequency antennas for low-cost missions