Geometry, mechanics, and electronics of singular structures and wrinkles in graphene

Design of advanced porous graphene materials: from graphene nanomesh to 3D architectures

In order to make full utilization of the high intrinsic surface area of graphene, recently, porous graphene materials including graphene nanomesh, crumpled graphene and graphene foam, have attracted tremendous attention and research interest, owing to their exceptional porous structure (high surface area, and high pore volume) in combination with the inherent properties of graphene, such as high electronic conductivity, good thermal stability, and excellent mechanical strength. Interestingly, porous graphene materials and their derivatives have been explored in a wide range of applications in the fields of electronic and photonic devices, energy storage, gas separation/storage, oil absorption and sensors. This article reviews recent progress in the synthesis, characterization, properties, and applications of porous graphene materials. We aim to highlight the importance of designing different porous structures of graphene to meet future challenges, and the trend on future design of porous graphene materials is analyzed.

Flower-shaped domains and wrinkles in trilayer epitaxial graphene on silicon carbide

Trilayer graphene is of particular interest to the 2D materials community because of its unique tunable electronic structure. However, to date, there is a lack of fundamental understanding of the properties of epitaxial trilayer graphene on silicon carbide. Here, following successful synthesis of large-area uniform trilayer graphene, atomic force microscopy (AFM) showed that the trilayer graphene on 6H-SiC(0001) was uniform over a large scale. Additionally, distinct defects, identified as flower-shaped domains and isolated wrinkle structures, were observed randomly on the surface using scanning tunneling microscopy and spectroscopy (STM/STS). These carbon nanostructures formed during growth, has different structural and electronic properties when compared with the adjacent flat regions of the graphene. Finally, using low temperature STM/STS at 4K, we found that the isolated wrinkles showed an irreversible rotational motion between two 60° configurations at different densities of states.

Mechanics of graphyne crumpling

As the deformation of 2D materials can strongly affect properties such as diffusion, electrical conductivity, and mechanical performance, it is worthwhile to explore the potentiality of crumpling as a method to tailor the properties of 2D materials while maintaining the surface area.

Electric field-controlled rippling of graphene

Metal-graphene interfaces generated by electrode deposition induce barriers or potential modulations influencing the electronic transport properties of graphene based devices. However, their impact on the local mechanical properties of graphene is much less studied. Here we show that graphene near a metallic interface can exhibit a set of ripples self-organized into domains whose topographic roughness is controlled by the tip bias of a scanning tunneling microscope. The reconstruction from topographic images of graphene bending energy maps sheds light on the local electro-mechanical response of graphene under STM imaging and unveils the role of the stress induced by the vicinity of the graphene-metal interface in the formation and the manipulation of these ripples. Since microscopic rippling is one of the important factors that limit charge carrier mobility in graphene, the control of rippling with a gate voltage may have important consequences in the conductance of graphene devices where transverse electric fields are created by contactless suspended gate electrodes. This opens up also the possibility to dynamically control the local morphology of graphene nanomembranes.

Wide-gap semiconducting graphene from nitrogen-seeded SiC

All carbon electronics based on graphene have been an elusive goal. For more than a decade, the inability to produce significant band-gaps in this material has prevented the development of graphene electronics. We demonstrate a new approach to produce semiconducting graphene that uses a submonolayer concentration of nitrogen on SiC sufficient to pin epitaxial graphene to the SiC interface as it grows. The resulting buckled graphene opens a band gap greater than 0.7 eV in the otherwise continuous metallic graphene sheet.

Graphene wrinkling: formation, evolution and collapse

In this paper we focus on the studies of graphene wrinkling, from its formation to collapse, and its dependence on aspect ratio and temperature using molecule dynamics simulation. Based on our results, the first wrinkle is not formed on the edge but in the interior of graphene. The fluctuations of edge slack warps drive the wrinkling evolution in graphene which is distinguished from the bifurcation in continuum film. There are several obvious stages in wrinkling progress, including incubation, infancy, youth, maturity and gerontism periods which are identified by the atomic displacement difference due to the occurrences of new wrinkles. The wrinkling progress is over when the C-C bonds in highly stretched corners are broken which contributes to the wrinkling collapse. The critical wrinkling strain, the wrinkling pattern and extent depend on the aspect ratio of graphene, the wrinkling level and collapsed strains do not. Only the collapsed strain is sensitive to the temperature, the other wrinkling parameters are independent of the temperature. Our results would benefit the understanding of the physics of graphene wrinkling and the design of nanomechanical devices by tuning the wrinkles.

Multifunctionality and control of the crumpling and unfolding of large-area graphene

Crumpled graphene films are widely used, for instance in electronics, energy storage, composites and biomedicine. Although it is known that the degree of crumpling affects graphene's properties and the performance of graphene-based devices and materials, the controlled folding and unfolding of crumpled graphene films has not been demonstrated. Here we report an approach to reversibly control the crumpling and unfolding of large-area graphene sheets. We show with experiments, atomistic simulations and theory that, by harnessing the mechanical instabilities of graphene adhered on a biaxially pre-stretched polymer substrate and by controlling the relaxation of the pre-strains in a particular order, graphene films can be crumpled into tailored self-organized hierarchical structures that mimic superhydrophobic leaves. The approach enables us to fabricate large-area conductive coatings and electrodes showing superhydrophobicity, high transparency, and tunable wettability and transmittance. We also demonstrate that crumpled graphene-polymer laminates can be used as artificial-muscle actuators.

Selective molecular transport through intrinsic defects in a single layer of CVD graphene

We report graphene composite membranes with nominal areas more than 25 mm(2) fabricated by transfer of a single layer of CVD graphene onto a porous polycarbonate substrate. A combination of pressure-driven and diffusive transport measurements provides evidence of size-selective transport of molecules through the membrane, which is attributed to the low-frequency occurrence of intrinsic 1-15 nm diameter pores in the CVD graphene. Our results present the first step toward the realization of practical membranes that use graphene as the selective material.

Charge inhomogeneity determines oxidative reactivity of graphene on substrates

Single-layer graphene (SLG) supported on SiO(2) shows anomalously large chemical reactivity compared to thicker graphene, with charge inhomogeneity-induced potential fluctuations or topographic corrugations proposed as the cause. Here we systematically probe the oxidative reactivity of graphene supported on substrates with different surface roughnesses and charged impurity densities: hexagonal boron nitride (hBN), mica, thermally grown SiO(2) on Si, and SiO(2) nanoparticle thin films. SLG on low charge trap density hBN is not etched and shows little doping after oxygen treatment at temperatures up to 550 °C, in sharp contrast with oxidative etching under similar conditions of graphene on high charge trap density SiO(2) and mica. Furthermore, bilayer graphene shows reduced reactivity compared to SLG regardless of its substrate-induced roughness. Together the observations indicate that graphene's reactivity is predominantly controlled by charge inhomogeneity-induced potential fluctuations rather than surface roughness.

Stress defocusing in anisotropic compaction of thin sheets

We address the crumpling of thin sheets in between large scale curved cylinders. In contrast with the usual crushing of a paper ball, one curvature of the sheet is fixed here by the cylinders radius, yielding an anisotropic compaction. As compaction proceeds, it is found that sheets first develop singular folds involving ridges or developable cones, but eventually turn to regular folds free of any geometrical singularities, without ever having entered the plastic regime. This surprising uncrumpling transition corresponds to a stress defocusing. It is understood from a balance between bending and stretching energies on regular states.

Interplay of wrinkles, strain, and lattice parameter in graphene on iridium

Following graphene growth by thermal decomposition of ethylene on Ir(111) at high temperatures we analyzed the strain state and the wrinkle formation kinetics as function of temperature. Using the moiré spot separation in a low energy electron diffraction pattern as a magnifying mechanism for the difference in the lattice parameters between Ir and graphene, we achieved an unrivaled relative precision of ±0.1 pm for the graphene lattice parameter. Our data reveals a characteristic hysteresis of the graphene lattice parameter that is explained by the interplay of reversible wrinkle formation and film strain. We show that graphene on Ir(111) always exhibits residual compressive strain at room temperature. Our results provide important guidelines for strategies to avoid wrinkling.

Synergistic toughening of composite fibres by self-alignment of reduced graphene oxide and carbon nanotubes

The extraordinary properties of graphene and carbon nanotubes motivate the development of methods for their use in producing continuous, strong, tough fibres. Previous work has shown that the toughness of the carbon nanotube-reinforced polymer fibres exceeds that of previously known materials. Here we show that further increased toughness results from combining carbon nanotubes and reduced graphene oxide flakes in solution-spun polymer fibres. The gravimetric toughness approaches 1,000 J g(-1), far exceeding spider dragline silk (165 J g(-1)) and Kevlar (78 J g(-1)). This toughness enhancement is consistent with the observed formation of an interconnected network of partially aligned reduced graphene oxide flakes and carbon nanotubes during solution spinning, which act to deflect cracks and allow energy-consuming polymer deformation. Toughness is sensitive to the volume ratio of the reduced graphene oxide flakes to the carbon nanotubes in the spinning solution and the degree of graphene oxidation. The hybrid fibres were sewable and weavable, and could be shaped into high-modulus helical springs.

Slow dynamics of stress and strain relaxation in randomly crumpled elasto-plastic sheets

Stress and strain relaxation in randomly folded paper sheets under axial compression is studied both experimentally and theoretically. Equations providing the best fit to the experimental data are found. Our findings suggest that, in an axially compressed ball folded from an elastic or elasto-plastic material, the relaxation dynamics is ruled by activated processes of an energy foci rearrangement in the crumpling network. The dynamics of relaxation is discussed within a framework of Edwards's statistical mechanics. The functional forms of the activation barrier between admissible jammed folding configurations of the crumpling network under axial compression are derived. It is shown that relaxation kinetics can be mapped to activated dynamics of depinning and creep of elastic interface in a disordered medium.

Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

Anisotropic surface tension of buckled fluid membranes

Thin solid sheets and fluid membranes exhibit buckling under lateral compression. Here it is revealed that buckled fluid membranes have anisotropic mechanical surface tension contrary to solid sheets. Surprisingly, the surface tension perpendicular to the buckling direction shows stronger dependence on the projected area than that parallel to it. Our theoretical predictions are supported by numerical simulations of a meshless membrane model. This anisotropic tension can be used to measure the membrane bending rigidity. It is also found that phase synchronization occurs between multilayered buckled membranes.