Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes

The small mass and atomic-scale thickness of graphene membranes make them highly suitable for nanoelectromechanical devices such as e.g. mass sensors, high frequency resonators or memory elements. Although only atomically thick, many of the mechanical properties of graphene membranes can be described by classical continuum mechanics. An important parameter for predicting the performance and linearity of graphene nanoelectromechanical devices as well as for describing ripple formation and other properties such as electron scattering mechanisms, is the bending rigidity, {\kappa}. In spite of the importance of this parameter it has so far only been estimated indirectly for monolayer graphene from the phonon spectrum of graphite, estimated from AFM measurements or predicted from ab initio calculations or bond-order potential models. Here, we employ a new approach to the experimental determination of {\kappa} by exploiting the snap-through instability in pre-buckled graphene membranes. We demonstrate the reproducible fabrication of convex buckled graphene membranes by controlling the thermal stress during the fabrication procedure and show the abrupt switching from convex to concave geometry that occurs when electrostatic pressure is applied via an underlying gate electrode. The bending rigidity of bilayer graphene membranes under ambient conditions was determined to be $35.5^{+20}_{-15}$ eV. Monolayers have significantly lower {\kappa} than bilayers

Nanoscale Mechanical Drumming Visualized by 4D Electron Microscopy

With four-dimensional (4D) electron microscopy, we report in situ imaging of the mechanical drumming of a nanoscale material. The single crystal graphite film is found to exhibit global resonance motion that is fully reversible and follows the same evolution after each initiating stress pulse. At early times, the motion appears “chaotic” showing the different mechanical modes present over the micron scale. At longer time, the motion of the thin film collapses into a well-defined fundamental frequency of 1.08 MHz, a behavior reminiscent of mode locking; the mechanical motion damps out after ∼200 μs and the oscillation has a “cavity” quality factor of 150. The resonance time is determined by the stiffness of the material, and for the 75 nm thick and 40 μm square specimen used here we determined Young’s modulus to be 1.0 TPa for the in-plane stress−strain profile. Because of its real-time dimension, this 4D microscopy should have applications in the study of these and other types of materials structures

Ripple Texturing of Suspended Graphene Atomic Membranes

Graphene is the nature's thinnest elastic membrane, with exceptional mechanical and electrical properties. We report the direct observation and creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene sheets, using spontaneously and thermally induced longitudinal strains on patterned substrates, with control over their orientations and wavelengths. We also provide the first measurement of graphene's thermal expansion coefficient, which is anomalously large and negative, ~ -7x10^-6 K^-1 at 300K. Our work enables novel strain-based engineering of graphene devices.Comment: 15 pages, 4 figure

Ultra-strong Adhesion of Graphene Membranes

As mechanical structures enter the nanoscale regime, the influence of van der Waals forces increases. Graphene is attractive for nanomechanical systems because its Young's modulus and strength are both intrinsically high, but the mechanical behavior of graphene is also strongly influenced by the van der Waals force. For example, this force clamps graphene samples to substrates, and also holds together the individual graphene sheets in multilayer samples. Here we use a pressurized blister test to directly measure the adhesion energy of graphene sheets with a silicon oxide substrate. We find an adhesion energy of 0.45 \pm 0.02 J/m2 for monolayer graphene and 0.31 \pm 0.03 J/m2 for samples containing 2-5 graphene sheets. These values are larger than the adhesion energies measured in typical micromechanical structures and are comparable to solid/liquid adhesion energies. We attribute this to the extreme flexibility of graphene, which allows it to conform to the topography of even the smoothest substrates, thus making its interaction with the substrate more liquid-like than solid-like.Comment: to appear in Nature Nanotechnolog

Strain- and Adsorption-Dependent Electronic States and Transport or Localization in Graphene

The chapter generalizes results on influence of uniaxial strain and adsorption on the electron states and charge transport or localization in graphene with different configurations of imperfections (point defects): resonant (neutral) adsorbed atoms either oxygen- or hydrogen-containing molecules or functional groups, vacancies or substitutional atoms, charged impurity atoms or molecules, and distortions. To observe electronic properties of graphene-admolecules system, we applied electron paramagnetic resonance technique in a broad temperature range for graphene oxides as a good basis for understanding the electrotransport properties of other active carbons. Applied technique allowed observation of possible metal-insulator transition and sorption pumping effect as well as discussion of results in relation to the granular metal model. The electronic and transport properties are calculated within the framework of the tight-binding model along with the Kubo-Greenwood quantum-mechanical formalism. Depending on electron density and type of the sites, the conductivity for correlated and ordered adsorbates is found to be enhanced in dozens of times as compared to the cases of their random distribution. In case of the uniaxially strained graphene, the presence of point defects counteracts against or contributes to the band-gap opening according to their configurations. The band-gap behaviour is found to be nonmonotonic with strain in case of a simultaneous action of defect ordering and zigzag deformation. The amount of localized charge carriers (spins) is found to be correlated with the content of adsorbed centres responsible for the formation of potential barriers and, in turn, for the localization effects. Physical and chemical states of graphene edges, especially at a uniaxial strain along one of them, play a crucial role in electrical transport phenomena in graphene-based materials.Comment: 16 pages, 10 figure

Ab-initio structural, elastic, and vibrational properties of carbon nanotubes

A study based on ab initio calculations is presented on the estructural, elastic, and vibrational properties of single-wall carbon nanotubes with different radii and chiralities. We use SIESTA, an implementation of pseudopotential-density-functional theory which allows calculations on systems with a large number of atoms per cell. Different quantities like bond distances, Young moduli, Poisson ratio and the frequencies of different phonon branches are monitored versus tube radius. The validity of expectations based on graphite is explored down to small radii, where some deviations appear related to the curvature effects. For the phonon spectra, the results are compared with the predictions of the simple zone-folding approximation. Except for the known defficiencies of this approximation in the low-frequency vibrational regions, it offers quite accurate results, even for relatively small radii.Comment: 13 pages, 7 figures, submitted to Phys. Rev. B (11 Nov. 98

Selective Molecular Sieving through Porous Graphene

Membranes act as selective barriers and play an important role in processes such as cellular compartmentalization and industrial-scale chemical and gas purification. The ideal membrane should be as thin as possible to maximize flux, mechanically robust to prevent fracture, and have well-defined pore sizes to increase selectivity. Graphene is an excellent starting point for developing size selective membranes because of its atomic thickness, high mechanical strength, relative inertness, and impermeability to all standard gases. However, pores that can exclude larger molecules, but allow smaller molecules to pass through have to be introduced into the material. Here we show UV-induced oxidative etching can create pores in micrometre-sized graphene membranes and the resulting membranes used as molecular sieves. A pressurized blister test and mechanical resonance is used to measure the transport of a variety of gases (H2, CO2, Ar, N2, CH4, and SF6) through the pores. The experimentally measured leak rates, separation factors, and Raman spectrum agree well with models based on effusion through a small number of angstrom-sized pores.Comment: to appear in Nature Nanotechnolog

The influence of size effect on the electronic and elastic properties of diamond films with nanometer thickness

The atomic structure and physical properties of few-layered oriented diamond nanocrystals (diamanes), covered by hydrogen atoms from both sides are studied using electronic band structure calculations. It was shown that energy stability linear increases upon increasing of the thickness of proposed structures. All 2D carbon films display direct dielectric band gaps with nonlinear quantum confinement response upon the thickness. Elastic properties of diamanes reveal complex dependence upon increasing of the number of layers. All theoretical results were compared with available experimental data.Comment: 16 pages, 5 figures, 3 table

Mechanical cleaning of graphene using in situ electron microscopy

Avoiding and removing surface contamination is a crucial task when handling specimens in any scientific experiment. This is especially true for two-dimensional materials such as graphene, which are extraordinarily affected by contamination due to their large surface area. While many efforts have been made to reduce and remove contamination from such surfaces, the issue is far from resolved. Here we report on an in situ mechanical cleaning method that enables the site-specific removal of contamination from both sides of two dimensional membranes down to atomic-scale cleanliness. Further, mechanisms of re-contamination are discussed, finding surface-diffusion to be the major factor for contamination in electron microscopy. Finally the targeted, electron-beam assisted synthesis of a nanocrystalline graphene layer by supplying a precursor molecule to cleaned areas is demonstrated