Session X11: Focus Session: Graphene Structure, Stacking, Interactions: Twisting, Stretching, Folding, Wrinkling

Graphene Origami

Graphene, which features unparalleled in-plane strength and low out-of-plane bending energy, is an ideal material with which to tackle the challenge of building three-dimensional structures and moving parts at the nanoscale. Here we demonstrate laser-induced folding and scrolling of large-area monolayer graphene in solution. Monolayer graphene is typically well-adhered to its substrate, but we have achieved control of the adhesion using a combination of an aluminum sacrificial layer and surfactants. Once the graphene can move, local heating with an infrared laser and the interfacial tension of laser-nucleated bubbles allow us to lift, fold, and scroll the graphene. We have also formed a regular array of polymer dots on the graphene surface which can be easily imaged in three dimensions, allowing us to optically track the shape of the graphene as it moves. And finally, we establish graphene's viability as a strong but flexible sheet hinge by building and manipulating structures of rigid metallic panels connected by strips of graphene.   

Twisting Graphene into Carbon Nanotubes

Carbon nanotubes are usually described as being rolled up from graphene sheets; this process, however, have never been realized experimentally. We showed that graphene can indeed be transformed into nanotube by twisting [1]. Further, we showed that tube formation can be well-explained within classical theory of elasticity---in fact the very mechanism of tube formation can be observed by twisting a strap from one's backpack (try now!). Furthermore, we showed that nanotube chirality may not only be predicted, but can also be controlled externally. The quantum molecular dynamic simulations at T=300K were achieved thanks to the revised periodic boundary conditions (RPBC) approach [2-3]. The structures similar to simulated have been recently observed experimentally [4]. This novel rote for nanotube formation opens new opportunities in nanomaterial manipulation not restricted to carbon alone. In the presentation, I will describe tube formation, as well as outline the easy and efficient technique for distorted nanostructures simulation, the RPBC approach. \\[4pt] [1] O. O. Kit et al. arXiv:1108.0048\\[0pt] [2] P. Koskinen \& O. O. Kit PRL 105, 106401 (2010)\\[0pt] [3] O. O. Kit, L. Pastewka, P. Koskinen PRB 84, 155431 (2011)\\[0pt] [4] A. Chuvilin et al. Nature Materials 10, 687 (2011)   

Wrinkling instability in graphene supported on nanoparticle-patterned SiO$_{2}$

Atomically-thin graphene is arguably the thinnest possible mechanical membrane: graphene's effective thickness (the thickness of an isotropic continuum slab which would have the same elastic and bending stiffness) is significantly less than 1 {\AA}, indicating that graphene can distort out-of-plane to conform to sub-nanometer features. Here we study the elastic response of graphene supported on a SiO$_{2}$ substrate covered with SiO$_{2}$ nanoparticles. At a low density of nanoparticles, graphene is largely pinned to the substrate due to adhesive interaction. However, with increasing nanoparticle density, graphene's elasticity dominates adhesion and strain is relieved by the formation of wrinkles which connect peaks introduced by the supporting nanoparticles. At a critical density, the wrinkles percolate, resulting in a wrinkle network. We develop a simple elastic model allowing for adhesion which accurately predicts the critical spacing between nanoparticles for wrinkle formation. This work has been supported by the University of Maryland NSF-MRSEC under Grant No. DMR 05-20471 with supplemental funding from NRI, and NSF-DMR 08-04976.   

Molecular Dynamics Study of Ripples in Graphene and Bilayer Graphene

Transmission electron microscopy experiments have shown that suspended graphene is not perfectly flat, but displays ripples such that the surface normal of graphene varies by several degrees [1,2]. For multi-layered graphene, the ripples are suppressed with increasing numbers of layers. Recent experiments demonstrated that ripples in suspended graphene can also be controlled by mechanical and thermally induced strain [3]. Knowledge of and control over the ripples in graphene is desirable for fabricating and designing of strain-based devices. We show using molecular dynamics simulation that thermally induced ripples in suspended single and multi-layer graphene at room temperature result in deviations of the local surface normal by $\pm$ 7 $^{\circ}$ and $\pm$ 4 $^{\circ}$ for single and bilayer graphene, respectively. These angular deviations are in excellent agreement with transmission electron microscopy results [2] and confirm that these ripples can be dynamic and thermally induced. We also study how these angles change as a function of applied tensile and shear strain. [1] Meyer J. C., Geim A. K., et al. Solid State Communications, 143, 101 (2007). [2] Meyer J.C., Geim A.K., et al. Nature, 446, 60 (2007). [3] Bao W., Miao F., et al. Nature Nanotechnology, 4 (9), 562 (2009).   

Ideal strength of graphene

We have investigated the ideal strength of graphene by calculating the response under strain based on density functional theory. The strength of materials with usual contaminations and impurities is typically weaker than the ideal one. However, we have considered realistic factors and calculated several electromechanical properties of perturbed graphene showing that under certain conditions graphene can endure more strain than the pristine one. The interpretation of our result will be presented in the context of competitions among different energy scales under mechanical strains that eventually leads to the structure failure.   

Determination of Young's Modulus of Graphene by Raman Spectroscopy

The mechanical properties of graphene are interesting research subjects because its Young's modulus and strength are extremely high. Values of $\sim $1 TPa for the Young's modulus have been reported [Lee et al. Science, \textbf{321}, 385 (2008), Koenig et al. Nat. Nanotech. \textbf{6}, 543 (2011)]. We made a graphene sample on a SiO$_{2}$/Si substrate with closed-bottom holes by mechanical exfoliation. A pressure difference across the graphene membrane was applied by putting the sample in a vacuum chamber. This pressure difference makes the graphene membrane bulge upward like a balloon. By measuring the shifts of the Raman G and 2D bands, we estimated the amount of strain on the graphene membrane. By comparing the strain estimated from the Raman measurements with numerical simulations based on the finite element method, we obtained the Young's modulus of graphene.   

Role of the effective tensile strain in the electromechanical response of helical graphene nanoribbons with open and closed edges

There is a growing need to understand the electronic properties of non-ideal graphene nanoribbons. Using objective molecular dynamics [1] and a density-functional based tight-binding model, we investigate the effects of torsion on the electromechanical properties of graphene nanoribbons with armchair edges. We propose to characterize with an effective tensile strain scalar [2] the torsional mechanical response, including a reverse Poynting effect, and the fundamental band gap modulations. The demonstrated utility of this concept in both the mechanical and electrical domains provides a perspective for understanding electromechanical response in a unified way, and for designing NEMS devices with graphene components. [1] T. Dumitric? and R.D. James, J. Mech. Phys. Sol. 55, 2206-2236 (2007). [2] D.-B. Zhang and T. Dumitric?, Small 7, 1023 (2011) .   

Failure mechanisms of graphene under tension

Recent experiments established pure graphene as the strongest material known to mankind, further invigorating the question of how graphene fails. Using density functional theory, we reveal the mechanisms of mechanical failure of pure graphene under a generic state of tension at zero temperature. One failure mechanism is a novel soft-mode phonon instability of the $K_1$-mode, whereby the graphene sheet undergoes a phase transition and is driven towards isolated hexagonal rings resulting in a reduction of strength. The other is the usual elastic instability corresponding to a maximum in the stress-strain curve. Our results indicate that finite wave vector soft modes can be the key factor in limiting the strength of monolayer materials.   

Characterization of strain in CVD graphene on copper substrates

Strain plays an important role in controlling graphene's properties and induces significant changes in the electronic band structure. Strain and morphology of CVD (chemical vapor deposition) graphene layers grown on Cu substrates are studied by Raman spectroscopy and scanning tunneling microscopy (STM). We find that CVD graphene on Cu surfaces are subject to strain which depends on the orientation of the underlying Cu surfaces. The strain is compressive on Cu (111) surface and estimated to be on the order of 0.5 percent by molecular dynamics (MD) simulations. For graphene grown on Cu (100) surface the strain is highly nonuniform and includes both compressive and tensile components. MD simulations of graphene on Cu (100) show highly nonuniform strain patterns including linear superstructures, consistent with the patterns seen in STM. For graphene grown on Cu foil the strain is partially released after graphene is removed from Cu surfaces and transferred onto oxidized Si substrate.   

Local nanoscale frictional variations of graphene investigated with lateral force microscopy

Lateral force microscopy is used to investigate the local nanoscale frictional variations on single- and multi-layered graphene films. Employing novel calibration methods, quantitative frictional measurements are taken for a range of normal loads. The coverage of specific high-friction regions with a single layer of graphene shows a significant reduction in the frictional characteristics.   

Adsorption-induced Pore Expansion and Contraction in Activated Carbon

Adsorbent materials such as activated carbon and Metal-Organic Frameworks (MOFs) have received significant attention as a potential storage material for hydrogen and natural gas.1 Typically the adsorbent material is assumed to consist of rigid slit- or cylindrical-shaped pores. Recent work has revealed the importance of the mechanical response of the adsorbent in the presence of an adsorbate. Here, we first demonstrate the flexibility of pore walls in activated carbon and the effect this has on the pore structure of the bulk samples. The interaction is modeled as a competition between Van der Waals interactions between neighboring walls and a resistance to bending due to the rigidity of graphene. Minimal energy configurations were calculated analytically for a simplified potential and numerically for a more realistic potential. The pore structures are discussed in the context of pore measurements on activated carbon samples. Following recent work by Cole and Neimark, large pressures due to an adsorbed film are predicted in the narrow pores of activated carbon. The coverage-dependent nature of adsorbed-film pressure, indicating a pressure-variant pore structure, is discussed in terms of adsorption isotherms.   

Hierarchical graphene materials: from monolayers to papers and nanocomposites

Macroscopic graphene materials such as papers and nanocomposites consist of chemically modified graphene sheets and intersheet crosslinks of various types, which hold great promises in high-performance, multifunctional and light-weighted applications. In this talk, we will present a multiscale approach (density functional theory, molecular dynamics and continuum mechanics) to understand simultaneously atomistic mechanisms, microscale structures and microscopic performance of these hierarchical graphene materials, and provide general principles for materials design that are supported by experimental evidence. Hierarchical structures of graphene-based materials will be also discussed comparably with biological materials that are widely studied recently, such as bones, nacre and collagen fibrils, which possess similar materials hierarchies and inspire many novel concepts in new materials development.   

Layer Effects in Graphene NEMS Resonators

In this talk we will present new data on mono, bi, and tri-layer graphene nanoelectromechanical (G-NEMS) resonators.~ G-NEMS resonators utilize graphene's high mobility, high Young's modulus, Dirac-like dispersion relation, and other unique qualities to produce unusual physical phenomena at the intersection of electronics and mechanics on the quantum scale.~ We extend the work done on these devices with a study into the effects of layer number on temperature dependence, quality factor, tunability, and frequency amongst others.   

Ultrastrong 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 +/- 0.02 J m-2 for monolayer graphene and 0.31 +/- 0.03 J m-2 for samples containing two to five 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.   

Graphene coatings: An efficient protection from oxidation

We demonstrate that graphene coating can provide an efficient protection from oxidation by posing a high energy barrier to the path of oxygen atom, which could have penetrated from the top of graphene to the reactive surface underneath. Graphene bilayer, which blocks the diffusion of oxygen with a relatively higher energy barrier provides even better protection from oxidation. While an oxygen molecule is weakly bound to bare graphene surface and hence becomes rather inactive, it can easily dissociates into two oxygen atoms adsorbed to low coordinated carbon atoms at the edges of a vacancy. For these oxygen atoms the oxidation barrier is reduced and hence the protection from oxidation provided by graphene coatings is weakened. Our predictions obtained from the state of the art first-principles calculations of electronic structure, phonon density of states and reaction path will unravel how a graphene can be used as a corrosion resistant coating and guide further studies aiming at developing more efficient nanocoating materials.