Measurement of the elastic properties and intrinsic strength of monolayer graphene

Dirac electrons in graphene-based quantum wires and quantum dots

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots. We show that due to the formation of sub-bands in the ribbons it is possible to spatially localize some of the electronic modes using a p-n-p junction. We also show that scattering of confined Dirac electrons in a narrow channel by an infinitely massive wall induces mode mixing, giving a qualitative reason for the fact that an analytical solution to the spectrum of Dirac electrons confined in a square box has not yet been found. A first attempt to solve this problem is presented. We find that only the trivial case k = 0 has a solution that does not require the existence of evanescent modes. We also study the spectrum of quantum dots of graphene in a perpendicular magnetic field. This problem is studied in the Dirac approximation, and its solution requires a numerical method whose details are given. The formation of Landau levels in the dot is discussed. The inclusion of the Coulomb interaction among the electrons is considered at the self-consistent Hartree level, taking into account the interaction with an image charge density necessary to keep the back-gate electrode at zero potential. The effect of a radial confining potential is discussed. The density of states of circular and hexagonal quantum dots, described by the full tight-binding model, is studied using the Lanczos algorithm. This is necessary to access the detailed shape of the density of states close to the Dirac point when one studies large systems. Our study reveals that zero-energy edge states are also present in graphene quantum dots. Our results are relevant for experimental research in graphene nanostructures. The style of writing is pedagogical, in the hope that newcomers to the subject will find this paper a good starting point for their research.

Implantation and growth of dendritic gold nanostructures on graphene derivatives: electrical property tailoring and Raman enhancement

Interfacing electron-rich metal nanoparticles with graphene derivatives can sensitively regulate the properties of the resultant hybrid with potential applications in metal-doped graphene field-effect transistors (FETs), surface-enhanced Raman spectroscopy, and catalysis. Here, we show that by controlling the rate of diffusion and catalytic reduction of gold ions on graphene oxide (GO), dendritic "snowflake-shaped" gold nanostructures (SFGNs) can be templated on graphene. The structural features of the SFGNs and their interfacing mechanism with GO were characterized by microscopic analysis and Raman-scattering. We demonstrate that (a) SFGNs grow on GO-surface via diffusion limited aggregation; (b) SFGN's morphology (dendritic to globular), size (diameter of 150-500 nm and a height of 45-55 nm), coverage density, and dispersion stability can be controlled by regulating the chemiophysical forces; (c) SFGNs enhance the Raman signal by 2.5 folds; and (d) SFGNs act as antireduction resist during GO-SFGN's chemical reduction. Further, the SFGNs interfacing with graphene reduces the apparent band gap (from 320 to 173 meV) and the Schottky barrier height (from 126 to 56 meV) of the corresponding FET.

Evolving properties of two-dimensional materials: from graphene to graphite

We have studied theoretically, using density functional theory, several material properties when going from one C layer in graphene to two and three graphene layers and on to graphite. The properties we have focused on are the elastic constants, electronic structure (energy bands and density of states), and the dielectric properties. For any of the properties we have investigated the modification due to an increase in the number of graphene layers is within a few per cent. Our results are in agreement with the analysis presented recently by Kopelevich and Esquinazi (unpublished).

A simple route to enhance the interface between graphite oxide nanoplatelets and a semi-crystalline polymer for stress transfer

This report shows that thermal treatment is a simple and effective approach to create a polymer crystalline layer on the surface of graphite oxide nanoplatelets (GONPs) in polycaprolactone (PCL) melts. It was found that the crystallization temperature of the PCL increased significantly by nearly 9 degrees C with the incorporation of 2 wt% GONPs. As the composite melts isothermally crystallized at the temperature that was 14 degrees C higher than the crystallization temperature, the polymer crystalline layer was optimized on the surface of the GONPs. At 2 wt% GONPs, the Young's modulus of the composite was nearly 1.5 times greater than for the pure PCL. In comparison with untreated composites, the improvement in the Young's modulus of treated composites nearly doubled. It confirmed that a non-covalent interface for stress transfer can be enhanced by the formation of the polymer crystalline layer bridging the GONPs and the polymer matrix.

Structural transformations in graphene studied with high spatial and temporal resolution

Graphene has remarkable electronic properties, such as ballistic transport and quantum Hall effects, and has also been used as a support for samples in high-resolution transmission electron microscopy and as a transparent electrode in photovoltaic devices. There is now a demand for techniques that can manipulate the structural and physical properties of graphene, in conjunction with the facility to monitor the changes in situ with atomic precision. Here, we show that irradiation with an 80 kV electron beam can selectively remove monolayers in few-layer graphene sheets by means of electron-beam-induced sputtering. Aberration-corrected, low-voltage, high-resolution transmission electron microscopy with sub-ångström resolution is used to examine the structural reconstruction occurring at the single atomic level. We find preferential termination for graphene layers along the zigzag orientation for large hole sizes. The temporal resolution can also be reduced to 80 ms, enabling real-time observation of the reconstruction of carbon atoms during the sputtering process. We also report electron-beam-induced rapid displacement of monolayers, fast elastic distortions and flexible bending at the edges of graphene sheets. These results reveal how energy transfer from the electron beam to few-layer graphene sheets leads to unique structural transformations.

Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension

We investigate the mechanical strength and properties of graphene under uniaxial tensile test as a function of size and chirality using the orthogonal tight-binding method and molecular dynamics simulations with the AIREBO potential. Our results on Young's modulus, fracture strain, and fracture strength of bulk graphene are in reasonable agreement with the recently published experimental data. Our results indicate that fracture strain and fracture strength of bulk graphene under uniaxial tension can have a significant dependence on the chirality. Mechanical properties such as Young's modulus and Poisson's ratio can depend strongly on the size and chirality of the graphene nanoribbon.

Spin gapless semiconductor-metal-half-metal properties in nitrogen-doped zigzag graphene nanoribbons

The geometries, formation energies, and electronic and magnetic properties of N-doping defects, including single atom substitution and pyridine- and pyrrole-like substructures in zigzag graphene nanoribbons (ZGNRs), were investigated by means of spin-unrestricted density functional theory computations. The edge carbon atoms are more easily substituted with N atoms, and three-nitrogen vacancy (3NV) defect and four-nitrogen divacancy (4ND) defect also prefer the ribbon edge. Single N atom substitution and pyridine- and pyrrole-like N-doping defects can all break the degeneracy of the spin polarization of pristine ZGNRs. One single N atom substitution makes the antiferromagnetic semiconducting ZGNRs into spin gapless semiconductors, while double edge substitution transforms N-doped graphenes into metals. Pyridine- and pyrrole-like N-doping defects make ZGNRs into half-metals or spin gapless semiconductors. These results suggest the potential applications of N-doped ZGNRs in nanoelectronics.

Mesomorphic lamella rolling of au in vacuum

Lamellar nanocondensates in partial epitaxy with larger-sized multiply twinned particles (MTPs) or alternatively in the form of multiple-walled tubes (MWTs) having nothing to do with MTP were produced by the very energetic pulse laser ablation of Au target in vacuum under specified power density and pulses. Transmission electron microscopic observations revealed (111)-motif diffraction and low-angle scattering. They correspond to layer interspacing (0.241-0.192 nm) and the nearest neighbor distance (ca. 0.74-0.55 nm) of atom clusters within the layer, respectively, for the lamella, which shows interspacing contraction with decreasing particle size under the influence of surface stress and rolls up upon electron irradiation. The uncapped MWT has nearly concentric amorphous layers interspaced by 0.458-0.335 nm depending on dislocation distribution and becomes spherical onions for surface-area reduction upon electron dosage. Analogous to graphene-derived tubular materials, the lamella-derived MWT of Au could have pentagon-hexagon pair at its zig-zag junction and useful optoelectronic properties worthy of exploration.

Mechanical properties of graphene nanoribbons

Herein, we investigate the structural, electronic and mechanical properties of zigzag graphene nanoribbons in the presence of stress by applying density functional theory within the GGA-PBE (generalized gradient approximation-Perdew-Burke-Ernzerhof) approximation. The uniaxial stress is applied along the periodic direction, allowing a unitary deformation in the range of ± 0.02%. The mechanical properties show a linear response within that range while a nonlinear dependence is found for higher strain. The most relevant results indicate that Young's modulus is considerable higher than those determined for graphene and carbon nanotubes. The geometrical reconstruction of the C-C bonds at the edges hardens the nanostructure. The features of the electronic structure are not sensitive to strain in this linear elastic regime, suggesting the potential for using carbon nanostructures in nano-electronic devices in the near future.

Electromechanical properties of suspended graphene nanoribbons

Graphene nanoribbons present diverse electronic properties ranging from semiconducting to half-metallic, depending on their geometry, dimensions, and chemical composition. Here we present a route to control these properties via externally applied mechanical deformations. Using state-of-the-art density functional theory calculations combined with classical elasticity theory considerations, we find a remarkable Young's modulus value of approximately 7 TPa for ultranarrow graphene strips and a pronounced electromechanical response toward bending and torsional deformations. Given the current advances in the synthesis of nanoscale graphene derivatives, our predictions can be experimentally verified opening the way to the design and fabrication of miniature electromechanical sensors and devices based on ultranarrow graphene nanoribbons.

Photoconductivity of bulk-film-based graphene sheets

Time-resolved photoconductivity measurements are carried out on graphene films prepared by using soluble graphene oxide. High photocurrent generation efficiency is observed for these graphene-based films, and the relationships between their photoconductivity and different preparation methods, incident light intensity, external electric field, and photon energies are investigated. Higher photoconductivity is observed with higher photon energy at same incident light intensity. By fitting the experimental data to the Onsager model, the primary quantum yields for charge separation to generate bound electron-hole pairs and the initial ion-pair thermalization separation distance are calculated.

The macroscopic delamination of thin films from elastic substrates

The wrinkling and delamination of stiff thin films adhered to a polymer substrate have important applications in "flexible electronics." The resulting periodic structures, when used for circuitry, have remarkable mechanical properties because stretching or twisting of the substrate is mostly accommodated through bending of the film, which minimizes fatigue or fracture. To date, applications in this context have used substrate patterning to create an anisotropic substrate-film adhesion energy, thereby producing a controlled array of delamination "blisters." However, even in the absence of such patterning, blisters appear spontaneously, with a characteristic size. Here, we perform well-controlled experiments at macroscopic scales to study what sets the dimensions of these blisters in terms of the material properties and explain our results by using a combination of scaling and analytical methods. Besides pointing to a method for determining the interfacial toughness, our analysis suggests a number of design guidelines for the thin films used in flexible electronic applications. Crucially, we show that, to avoid the possibility that delamination may cause fatigue damage, the thin film thickness must be greater than a critical value, which we determine.

Two- and one-dimensional honeycomb structures of silicon and germanium

First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, honeycomb structures. Similar to graphene, these puckered structures are ambipolar and their charge carriers can behave like a massless Dirac fermion due to their pi and pi(*) bands which are crossed linearly at the Fermi level. In addition to these fundamental properties, bare and hydrogen passivated nanoribbons of Si and Ge show remarkable electronic and magnetic properties, which are size and orientation dependent. These properties offer interesting alternatives for the engineering of diverse nanodevices.

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.

Defect scattering in graphene

Irradiation of graphene on SiO2 by 500 eV Ne and He ions creates defects that cause intervalley scattering as is evident from a significant Raman D band intensity. The defect scattering gives a conductivity proportional to charge carrier density, with mobility decreasing as the inverse of the ion dose. The mobility decrease is 4 times larger than for a similar concentration of singly charged impurities. The minimum conductivity decreases proportional to the mobility to values lower than 4e(2)/pih, the minimum theoretical value for graphene free of intervalley scattering. Defected graphene shows a diverging resistivity at low temperature, indicating insulating behavior. The results are best explained by ion-induced formation of lattice defects that result in midgap states.

In situ observation of graphene sublimation and multi-layer edge reconstructions

We induced sublimation of suspended few-layer graphene by in situ Joule-heating inside a transmission electron microscope. The graphene sublimation fronts consisted of mostly {1100} zigzag edges. Under appropriate conditions, a fractal-like "coastline" morphology was observed. Extensive multiple-layer reconstructions at the graphene edges led to the formation of unique carbon nanostructures, such as sp(2)-bonded bilayer edges (BLEs) and nanotubes connected to BLEs. Flat fullerenes/nanopods and nanotubes tunneling multiple layers of graphene sheets were also observed. Remarkably, >99% of the graphene edges observed during sublimation are BLEs rather than monolayer edges (MLEs), indicating that BLEs are the stable edges in graphene at high temperatures. We reproduced the "coastline" sublimation morphologies by kinetic Monte Carlo (kMC) simulations. The simulation revealed geometrical and topological features unique to quasi-2-dimensional (2D) graphene sublimation and reconstructions. These reconstructions were enabled by bending, which cannot occur in first-order phase transformations of 3D bulk materials. These results indicate that substrate of multiple-layer graphene can offer unique opportunities for tailoring carbon-based nanostructures and engineering novel nano-devices with complex topologies.

Free-standing nanoparticle superlattice sheets controlled by DNA

Free-standing nanoparticle superlattices (suspended highly ordered nanoparticle arrays) are ideal for designing metamaterials and nanodevices free of substrate-induced electromagnetic interference. Here, we report on the first DNA-based route towards monolayered free-standing nanoparticle superlattices. In an unconventional way, DNA was used as a 'dry ligand' in a microhole-confined, drying-mediated self-assembly process. Without the requirement of specific Watson-Crick base-pairing, we obtained discrete, free-standing superlattice sheets in which both structure (inter-particle spacings) and functional properties (plasmonic and mechanical) can be rationally controlled by adjusting DNA length. In particular, the edge-to-edge inter-particle spacing for monolayered superlattice sheets can be tuned up to 20 nm, which is a much wider range than has been achieved with alkyl molecular ligands. Our method opens a simple yet efficient avenue towards the assembly of artificial nanoparticle solids in their ultimate thickness limit--a promising step that may enable the integration of free-standing superlattices into solid-state nanodevices.

Quantum manifestations of graphene edge stress and edge instability: a first-principles study

We have performed first-principles calculations of graphene edge stresses, which display two interesting quantum manifestations absent from the classical interpretation: the armchair edge stress oscillates with a nanoribbon width, and the zigzag edge stress is noticeably reduced by spin polarization. Such quantum stress effects in turn manifest in mechanical edge twisting and warping instability, showing features not captured by empirical potentials or continuum theory. Edge adsorption of H and Stone-Wales reconstruction are shown to provide alternative mechanisms in relieving the edge compression and hence to stabilize the planar edge structure.

Phonon softening and crystallographic orientation of strained graphene studied by Raman spectroscopy

We present a systematic study of the Raman spectra of optical phonons in graphene monolayers under tunable uniaxial tensile stress. Both the G and 2D bands exhibit significant red shifts. The G band splits into 2 distinct subbands (G(+), G(-)) because of the strain-induced symmetry breaking. Raman scattering from the G(+) and G(-) bands shows a distinctive polarization dependence that reflects the angle between the axis of the stress and the underlying graphene crystal axes. Polarized Raman spectroscopy therefore constitutes a purely optical method for the determination of the crystallographic orientation of graphene.

Graphene at the edge: stability and dynamics

Although the physics of materials at surfaces and edges has been extensively studied, the movement of individual atoms at an isolated edge has not been directly observed in real time. With a transmission electron aberration-corrected microscope capable of simultaneous atomic spatial resolution and 1-second temporal resolution, we produced movies of the dynamics of carbon atoms at the edge of a hole in a suspended, single atomic layer of graphene. The rearrangement of bonds and beam-induced ejection of carbon atoms are recorded as the hole grows. We investigated the mechanism of edge reconstruction and demonstrated the stability of the "zigzag" edge configuration. This study of an ideal low-dimensional interface, a hole in graphene, exhibits the complex behavior of atoms at a boundary.

Chemical methods for the production of graphenes

Interest in graphene centres on its excellent mechanical, electrical, thermal and optical properties, its very high specific surface area, and our ability to influence these properties through chemical functionalization. There are a number of methods for generating graphene and chemically modified graphene from graphite and derivatives of graphite, each with different advantages and disadvantages. Here we review the use of colloidal suspensions to produce new materials composed of graphene and chemically modified graphene. This approach is both versatile and scalable, and is adaptable to a wide variety of applications.

Intrinsic response of graphene vapor sensors

Graphene is a two-dimensional material with extremely favorable chemical sensor properties. Conventional nanolithography typically leaves a resist residue on the graphene surface, whose impact on the sensor characteristics has not yet been determined. Here we show that the contamination layer chemically dopes the graphene, enhances carrier scattering, and acts as an absorbent layer that concentrates analyte molecules at the graphene surface, thereby enhancing the sensor response. We demonstrate a cleaning process that verifiably removes the contamination on the device structure and allows the intrinsic chemical responses of the graphene monolayer to be measured. These intrinsic responses are surprisingly small, even upon exposure to strong analytes such as ammonia vapor.

The formation of atomic nanoclusters on graphene sheets

The formation of atomic nanoclusters on suspended graphene sheets has been investigated by employing a molecular dynamics simulation at finite temperature. Our systematic study is based on temperature-dependent molecular dynamics simulations of some transition and alkali atoms on suspended graphene sheets. We find that the transition atoms aggregate and make various size nanoclusters distributed randomly on graphene surfaces. We also report that most alkali atoms make one atomic layer on graphene sheets. Interestingly, the potassium atoms almost deposit regularly on the surface at low temperature. We expect from this behavior that the electrical conductivity of a suspended graphene doped by potassium atoms would be much higher than in the case doped by the other atoms at low temperature.

Colloidal suspensions of highly reduced graphene oxide in a wide variety of organic solvents

We report that homogeneous colloidal suspensions of chemically modified graphene sheets were readily produced in a wide variety of organic solvent systems. Two different sets of solubility parameters are used to rationalize when stable colloidal suspensions of graphene oxide sheets and, separately, of reduced graphene oxide sheets in a given solvent type are possible and when they are not. As an example of the utility of such colloidal suspensions, "paperlike" materials generated by very simple filtration of the reduced graphene oxide sheets had electrical conductivity values as high as 16,000 S/m.

Nano-indentation studies on polymer matrix composites reinforced by few-layer graphene

The mechanical properties of polyvinyl alcohol (PVA) and poly(methyl methacrylate) (PMMA)-matrix composites reinforced by functionalized few-layer graphene (FG) have been evaluated using the nano-indentation technique. A significant increase in both the elastic modulus and hardness is observed with the addition of 0.6 wt% of graphene. The crystallinity of PVA also increases with the addition of FG. This and the good mechanical interaction between the polymer and the FG, which provides better load transfer between the matrix and the fiber, are suggested to be responsible for the observed improvement in mechanical properties of the polymers.

Probing charged impurities in suspended graphene using Raman spectroscopy

Charged impurity (CI) scattering is one of the dominant factors that affects the carrier mobility in graphene. In this paper, we use Raman spectroscopy to probe the charged impurities in suspended graphene. We find that the 2D band intensity is very sensitive to the CI concentration in graphene, while the G band intensity is not affected. The intensity ratio between the 2D and G bands, I(2D)/I(G), of suspended graphene is much stronger compared to that of nonsuspended graphene, due to the extremely low CI concentration in the former. This finding is consistent with the ultrahigh carrier mobility in suspended graphene observed in recent transport measurements. Our results also suggest that at low CI concentrations that are critical for device applications, the I(2D)/I(G) ratio is a better criterion in selecting high quality single layer graphene samples than is the G band blue shift.

The importance of edge effects on the intrinsic loss mechanisms of graphene nanoresonators

We utilize classical molecular dynamics simulations to investigate the intrinsic loss mechanisms of monolayer graphene nanoresonators undergoing flexural oscillations. We find that spurious edge modes of vibration, which arise not due to externally applied stresses but intrinsically due to the different vibrational properties of edge atoms, are the dominant intrinsic loss mechanism that reduces the quality (Q) factors. We additionally find that while hydrogen passivation of the free edges is ineffective in reducing the spurious edge modes, fixing the free edges is critical to removing the spurious edge-induced vibrational states. Our atomistic simulations also show that the Q factor degrades inversely proportional to temperature; furthermore, we also demonstrate that the intrinsic losses can be reduced significantly across a range of operating temperatures through the application of tensile mechanical strain.

Effective elastic mechanical properties of single layer graphene sheets

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

The ultimate strength of glass silica nanowires

In the past decade nanowires have attracted an increase interest because of their extraordinary mechanical strength. In fact, material properties in the nanoregime are extremely different from those found in macroscopic samples: few crystalline materials have shown a tensile strength in excess of 10 GPa in the form of nanowires. Still the length of defect-free crystalline nanowires is limited to a few millimeters and the strength of long nanowires is compromised by defects. The strength of glass nanowires is less affected by single defects. In this paper we present the ultimate strength of glass silica nanowires manufactured by a top-down fabrication technique; this is the highest value reported for glass materials. The measured ultimate strength is in excess of 10 GPa and increases for decreasing nanowire diameters. Scanning electron micrographs of the broken fragments showed a fragile rupture.

Finite temperature lattice properties of graphene beyond the quasiharmonic approximation

The thermal and mechanical stability of graphene is important for many potential applications in nanotechnology. We calculate the temperature dependence of the lattice parameter, elastic properties, and heat capacity by means of atomistic Monte Carlo simulations that allow us to go beyond the quasiharmonic approximation. We predict an unusual, nonmonotonic, behavior of the lattice parameter with a minimum at T approximately 900 K and of the shear modulus with a maximum at the same temperature. The Poisson ratio in graphene is found to be small approximately 0.1 in a broad temperature interval.

Bending properties of single functionalized graphene sheets probed by atomic force microscopy

We probe the bending characteristics of functionalized graphene sheets with the tip of an atomic force microscope. Individual sheets are transformed from a flat into a folded configuration. Sheets can be reversibly folded and unfolded multiple times, and the folding always occurs at the same location. This observation suggests that the folding and bending behavior of the sheets is dominated by pre-existing kink (or even fault) lines consisting of defects and/or functional groups.

Strong anomalous optical dispersion of graphene: complex refractive index measured by Picometrology

We introduce spinning-disc Picometrology which is designed to measure complex refractive index of ultra-thin and size-limited sample deposited on a solid surface. Picometrology is applied to measure the refractive index of graphene on thermal oxide on silicon. The refractive index varies from ñg = 2.4-1.0i at 532 nm to ñg = 3.0-1.4i at 633 nm at room temperature. The dispersion is five times stronger than bulk graphite (2.67- 1.34i to 2.73-1.42i from 532 nm to 633 nm).

Actuation of a suspended nano-graphene sheet by impact with an argon cluster

Using a molecular dynamics simulation, we examine the actuation of nanodrums consisting of a single graphene sheet. The membrane of the nanodrum, which contains 190 carbon atoms, is bent by collision with a cluster consisting of 10 argon atoms. The choice of an appropriate cluster velocity enables nanometre deformation of the membrane in sub-picosecond time without rupturing the graphene sheet. Theoretical results predict that, if an adsorbed molecule exists on the graphene sheet, the quick deformation due to the impact with the cluster can break the weak bonding between the adsorbed molecule and the graphene sheet and release the molecule from the surface; this suggests that this system has attractive potential applications for purposes of molecular ejection.

4D imaging of transient structures and morphologies in ultrafast electron microscopy

With advances in spatial resolution reaching the atomic scale, two-dimensional (2D) and 3D imaging in electron microscopy has become an essential methodology in various fields of study. Here, we report 4D imaging, with in situ spatiotemporal resolutions, in ultrafast electron microscopy (UEM). The ability to capture selected-area-image dynamics with pixel resolution and to control the time separation between pulses for temporal cooling of the specimen made possible studies of fleeting structures and morphologies. We demonstrate the potential for applications with two examples, gold and graphite. For gold, after thermally induced stress, we determined the atomic structural expansion, the nonthermal lattice temperature, and the ultrafast transients of warping/bulging. In contrast, in graphite, striking coherent transients of the structure were observed in both image and diffraction, directly measuring, on the nanoscale, the longitudinal resonance period governed by Young's elastic modulus. The success of these studies demonstrates the promise of UEM in real-space imaging of dynamics.

Edge-stress-induced warping of graphene sheets and nanoribbons

We show that edge stresses introduce intrinsic ripples in freestanding graphene sheets even in the absence of any thermal effects. Compressive edge stresses along zigzag and armchair edges of the sheet cause out-of-plane warping to attain several degenerate mode shapes. Based on elastic plate theory, we identify scaling laws for the amplitude and penetration depth of edge ripples as a function of wavelength. We also demonstrate that edge stresses can lead to twisting and scrolling of nanoribbons as seen in experiments. Our results underscore the importance of accounting for edge stresses in thermal theories and electronic structure calculations for freestanding graphene sheets.

Continuum elastic modeling of graphene resonators

Starting from an atomistic approach, we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. We find that already for deflections of the order of 0.5 A a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated, and we find good agreement with recent experimental findings.

Reversible basal plane hydrogenation of graphene

We report the chemical reaction of single-layer graphene with hydrogen atoms, generated in situ by electron-induced dissociation of hydrogen silsesquioxane (HSQ). Hydrogenation, forming sp3 C--H functionality on the basal plane of graphene, proceeds at a higher rate for single than for double layers, demonstrating the enhanced chemical reactivity of single sheet graphene. The net H atom sticking probability on single layers at 300 K is at least 0.03, which exceeds that of double layers by at least a factor of 15. Chemisorbed hydrogen atoms, which give rise to a prominent Raman D band, can be detached by thermal annealing at 100-200 degrees C. The resulting dehydrogenated graphene is "activated" when photothermally heated it reversibly binds ambient oxygen, leading to hole doping of the graphene. This functionalization of graphene can be exploited to manipulate electronic and charge transport properties of graphene devices.