Atomistic potential for graphene and other sp2 carbon systems.

We introduce a torsional force field for sp2 carbon to augment an in-plane atomistic potential of a previous work [G. Kalosakas et al., J. Appl. Phys., 2013, 113, 134307] so that it is applicable to out-of-plane deformations of graphene and related carbon materials. The introduced force field is fit to reproduce density-functional-theory calculation data of appropriately chosen structures. The aim is to create a force field that is as simple as possible so it can be efficient for large scale atomistic simulations of various sp2 carbon structures without significant loss of accuracy. We show that the complete proposed potential reproduces characteristic properties of fullerenes and carbon nanotubes. In addition, it reproduces very accurately the out-of-plane acoustic and optical modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1000 cm-1.

Biaxial Tensile Strain Enhances Electron Mobility of Monolayer Transition Metal Dichalcogenides.

Strain engineering can modulate the properties of two-dimensional (2D) semiconductors for electronic and optoelectronic applications. Recent theory and experiments have found that uniaxial tensile strain can improve the electron mobility of monolayer MoS2, a 2D semiconductor, but the effects of biaxial strain on charge transport are not well characterized in 2D semiconductors. Here, we use biaxial tensile strain on flexible substrates to probe electron transport in monolayer WS2 and MoS2 transistors. This approach experimentally achieves ∼2× higher on-state current and mobility with ∼0.3% applied biaxial strain in WS2, the highest mobility improvement at the lowest strain reported to date. We also examine the mechanisms behind this improvement through density functional theory simulations, concluding that the enhancement is primarily due to reduced intervalley electron-phonon scattering. These results underscore the role of strain engineering in 2D semiconductors for flexible electronics, sensors, integrated circuits, and other optoelectronic applications.

Phonon and structural changes in deformed Bernal stacked bilayer graphene.

We present the first Raman spectroscopic study of Bernal bilayer graphene flakes under uniaxial tension. Apart from a purely mechanical behavior in flake regions where both layers are strained evenly, certain effects stem from inhomogeneous stress distribution across the layers. These phenomena such as the removal of inversion symmetry in bilayer graphene may have important implications in the band gap engineering, providing an alternative route to induce the formation of a band gap.

High pressure Raman scattering of silicon nanowires.

We study the high pressure response, up to 8 GPa, of silicon nanowires (SiNWs) with ∼ 15 nm diameter, by Raman spectroscopy. The first order Raman peak shows a superlinear trend, more pronounced compared to bulk Si. Combining transmission electron microscopy and Raman measurements we estimate the SiNWs' bulk modulus and the Grüneisen parameters. We detect an increase of Raman linewidth at ∼ 4 GPa, and assign it to pressure induced activation of a decay process into LO and TA phonons. This pressure is smaller compared to the ∼ 7 GPa reported for bulk Si. We do not observe evidence of phase transitions, such as discontinuities or change in the pressure slopes, in the investigated pressure range.

Uniaxially Strained Graphene: Structural Characteristics and G-Mode Splitting.

The potential use of graphene in various strain engineering applications requires an accurate characterization of its properties when the material is under different mechanical loads. In this work, we present the strain dependence of the geometrical characteristics at the atomic level and the Raman active G-band evolution in a uniaxially strained graphene monolayer, using density functional theory methods as well as molecular dynamics atomistic simulations for strains that extend up to the structural failure. The bond length and bond angle variations with strain, applied either along the zigzag or along the armchair direction, are discussed and analytical relations describing this dependence are provided. The G-mode splitting with strain, as obtained by first principles' methods, is also presented. While for small strains, up to around 1%, the G-band splitting is symmetrical in the two perpendicular directions of tension considered here, this is no longer the case for larger values of strains where the splitting appears to be larger for strains along the zigzag direction. Further, a crossing is observed between the lower frequency split G-mode component and the out-of-plane optical mode at the Γ point for large uniaxial strains (>20%) along the zigzag direction.

Width Dependent Elastic Properties of Graphene Nanoribbons.

The mechanical response of graphene nanoribbons under uniaxial tension, as well as its dependence on the nanoribbon width, is presented by means of numerical simulations. Both armchair and zigzag edged graphene nanoribbons are considered. We discuss results obtained through two different theoretical approaches, viz. density functional methods and molecular dynamics atomistic simulations using empirical force fields especially designed to describe interactions within graphene sheets. Apart from the stress-strain curves, we calculate several elastic parameters, such as the Young's modulus, the third-order elastic modulus, the intrinsic strength, the fracture strain, and the Poisson's ratio versus strain, presenting their variation with the width of the nanoribbon.

Efficient Mechanical Stress Transfer in Multilayer Graphene with a Ladder-like Architecture.

We report that few graphene flakes embedded into polymer matrices can be mechanically stretched to relatively large deformation (>1%) in an efficient way by adopting a particular ladder-like morphology consisting of consecutive mono-, bi-, tri-, and four-layer graphene units. In this type of flake architecture, all of the layers adhere to the surrounding polymer inducing similar deformation on the individual graphene layers, preventing interlayer sliding and optimizing the strain transfer efficiency. We have exploited Raman spectroscopy to quantify this effect from a mechanical standpoint. The finite element method and molecular dynamics simulations have been used to interpret the above experimental findings. The results suggest that a step pyramid-like architecture of a flake can be ideal for efficient loading of layered materials embedded into a polymer and that there are two prevailing mechanisms that govern axial stress transfer, namely, interfacial shear transfer and axial transmission through the ends. This concept can be easily applied to other two-dimensional materials and related van der Waals heterostructures fabricated either by mechanical exfoliation or chemical vapor deposition by appropriate patterning. This work opens new perspectives in numerous applications, including high volume fraction composites, flexible electronics, and straintronic devices.

Structural Defects Modulate Electronic and Nanomechanical Properties of 2D Materials.

Two-dimensional materials such as graphene and molybdenum disulfide are often subject to out-of-plane deformation, but its influence on electronic and nanomechanical properties remains poorly understood. These physical distortions modulate important properties which can be studied by atomic force microscopy and Raman spectroscopic mapping. Herein, we have identified and investigated different geometries of line defects in graphene and molybdenum disulfide such as standing collapsed wrinkles, folded wrinkles, and grain boundaries that exhibit distinct strain and doping. In addition, we apply nanomechanical atomic force microscopy to determine the influence of these defects on local stiffness. For wrinkles of similar height, the stiffness of graphene was found to be higher than that of molybdenum disulfide by 10-15% due to stronger in-plane covalent bonding. Interestingly, deflated graphene nanobubbles exhibited entirely different characteristics from wrinkles and exhibit the lowest stiffness of all graphene defects. Density functional theory reveals alteration of the bandstructures of graphene and MoS2 due to the wrinkled structure; such modulation is higher in MoS2 compared to graphene. Using this approach, we can ascertain that wrinkles are subject to significant strain but minimal doping, while edges show significant doping and minimal strain. Furthermore, defects in graphene predominantly show compressive strain and increased carrier density. Defects in molybdenum disulfide predominantly show tensile strain and reduced carrier density, with increasing tensile strain minimizing doping across all defects in both materials. The present work provides critical fundamental insights into the electronic and nanomechanical influence of intrinsic structural defects at the nanoscale, which will be valuable in straintronic device engineering.

Temperature-induced valence transition and associated lattice collapse in samarium fulleride.

The different degrees of freedom of a given system are usually independent of each other but can in some materials be strongly coupled, giving rise to phase equilibria sensitively susceptible to external perturbations. Such systems often exhibit unusual physical properties that are difficult to treat theoretically, as exemplified by strongly correlated electron systems such as intermediate-valence rare-earth heavy fermions and Kondo insulators, colossal magnetoresistive manganites and high-transition temperature (high-T(c)) copper oxide superconductors. Metal fulleride salts-metal intercalation compounds of C60--and materials based on rare-earth metals also exhibit strong electronic correlations. Rare-earth fullerides thus constitute a particularly intriguing system--they contain highly correlated cation (rare-earth) and anion (C60) sublattices. Here we show, using high-resolution synchrotron X-ray diffraction and magnetic susceptibility measurements, that cooling the rare-earth fulleride Sm2.75C60 induces an isosymmetric phase transition near 32 K, accompanied by a dramatic isotropic volume increase and a samarium valence transition from (2 + epsilon) + to nearly 2 +. The negative thermal expansion--heating from 4.2 to 32 K leads to contraction rather than expansion--occurs at a rate about 40 times larger than in ternary metal oxides typically exhibiting such behaviour. We attribute the large negative thermal expansion, unprecedented in fullerene or other molecular systems, to a quasi-continuous valence transition from Sm(2+) towards the smaller Sm((2+epsilon)+), analogous to the valence or configuration transitions encountered in intermediate-valence Kondo insulators like SmS (ref. 3).

Diameter-selective solubilization of carbon nanotubes by lipid micelles.

The one-step dispersion of HiPco single-walled carbon nanotubes in aqueous media with the use of a synthetic lyso-phosphatidylcholine was studied. Solubilization occurs through wrapping of lipid molecules around the circumference of the tubes, yielding lipid monolayers on the graphitic sidewalls as evidenced by atomic force microscopy imaging and dynamic light scattering measurements. Raman spectroscopy showed that the dispersion and centrifugation process leads to an effective enrichment of the stable aqueous suspension in carbon nanostructures with smaller diameters.

An Evaluation of Graphene as a Multi-Functional Heating Element for Biomedical Applications.

Graphene has been found to be an excellent heat-conductor due to the high speed of acoustic phonons in its lattice. In this work, we examine in depth a commercial graphene-based waist protector which uses graphene as a heating element. By employing thermal imaging in tandem with Raman microscopy, the thermal characteristics and performance of this device is fully assessed. It will be shown that no pronounced variation in its function is observed up to 3 hours of continuous operation and that the device seems to work effectively as an IR emitter at low power consumption. Temperature fluctuations, associated with a decrease of its electrical resistance are observed after 12 hours uptime and a temperature difference of 15 °C was recorded after 5 days of uninterrupted operation. These effects are thought to be due to the loss of graphene/polymer adhesion resulting from thermal fatigue. Overall, it is demonstrated that graphene can indeed be incorporated as an effective and operational thermal heating system in similar biomedical devices.

Strain Engineering in Highly Wrinkled CVD Graphene/Epoxy Systems.

Chemical vapor deposition (CVD) is regarded as a promising fabrication method for the automated, large-scale, production of graphene and other two-dimensional materials. However, its full commercial exploitation is limited by the presence of structural imperfections such as folds, wrinkles, and even cracks that downgrade its physical and mechanical properties. For example, as shown here by means of Raman spectroscopy, the stress transfer from an epoxy matrix to CVD graphene is on average 30% of that of exfoliated monolayer graphene of over 10 µm in dimensions. However, in terms of electrical response, the situation is reversed; the resistance has been found here to decrease by the imposition of mechanical deformation possibly due to the opening up of the structure and the associated increase of electron mobility. This finding paves the way for employing CVD graphene/epoxy composites or coatings as conductive "networks" or bridges in cases for which the conductivity needs to be increased or at least retained when the system is under deformation. The tuning/control of such systems and their operative limitations are discussed here.

Wrinkled Few-Layer Graphene as Highly Efficient Load Bearer.

Multilayered graphitic materials are not suitable as load-bearers due to their inherent weak interlayer bonding (for example, graphite is a solid lubricant in certain applications). This situation is largely improved when two-dimensional (2D) materials such as a monolayer (SLG) graphene are employed. The downside in these cases is the presence of thermally or mechanically induced wrinkles which are ubiquitous in 2D materials. Here we set out to examine the effect of extensive large wavelength/amplitude wrinkling on the stress transfer capabilities of exfoliated simply supported graphene flakes. Contrary to common belief we present clear evidence that this type of "corrugation" enhances the load-bearing capacity of few-layer graphene as compared to "flat" specimens. This effect is the result of the significant increase of the graphene/polymer interfacial shear stress per increment of applied strain due to wrinkling and paves the way for designing affordable graphene composites with highly improved stress-transfer efficiency.

Mechanical Stability of Flexible Graphene-Based Displays.

The mechanical behavior of a prototype touch panel display, which consists of two layers of CVD graphene embedded into PET films, is investigated in tension and under contact-stress dynamic loading. In both cases, laser Raman spectroscopy was employed to assess the stress transfer efficiency of the embedded graphene layers. The tensile behavior was found to be governed by the "island-like" microstructure of the CVD graphene, and the stress transfer efficiency was dependent on the size of graphene "islands" but also on the yielding behavior of PET at relatively high strains. Finally, the fatigue tests, which simulate real operation conditions, showed that the maximum temperature gradient developed at the point of "finger" contact after 80 000 cycles does not exceed the glass transition temperature of the PET matrix. The effect of these results on future product development and the design of new graphene-based displays are discussed.

Phonon properties of graphene derived from molecular dynamics simulations.

A method that utilises atomic trajectories and velocities from molecular dynamics simulations has been suitably adapted and employed for the implicit calculation of the phonon dispersion curves of graphene. Classical potentials widely used in the literature were employed. Their performance was assessed for each individual phonon branch and the overall phonon dispersion, using available inelastic x-ray scattering data. The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures. The temperature dependence of the phonon dispersion curves has been examined with emphasis on the doubly degenerate Raman active Γ-E2g phonon at the zone centre, where experimental results are available. The potentials used show diverse behaviour. The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

Graphene flakes under controlled biaxial deformation.

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm(-1)/%, and 148.2 ± 6 cm(-1)/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E2g shifts with strains and the Grüneisen parameter was observed.

Suspended monolayer graphene under true uniaxial deformation.

2D crystals, such as graphene, exhibit the higher strength and stiffness of any other known man-made or natural material. So far, this assertion has been primarily based on modelling predictions and on bending experiments in combination with pertinent modelling. True uniaxial loading of suspended graphene is not easy to accomplish; however such an experiment is of paramount importance in order to assess the intrinsic properties of graphene without the influence of an underlying substrate. In this work we report on uniaxial tension of graphene up to moderate strains of ∼0.8%. This has been made possible by sandwiching the graphene flake between two polymethylmethacrylate (PMMA) layers and by suspending its central part by the removal of a section of PMMA with e-beam lithography. True uniaxial deformation is confirmed by the measured large phonon shifts with strain by Raman spectroscopy and the indication of lateral buckling (similar to what is observed for thin macroscopic membranes under tension). Finally, we also report on how the stress is transferred to the suspended specimen through the adhesive grips and determine the value of interfacial shear stress that is required for efficient axial loading in such a system.

Stress transfer mechanisms at the submicron level for graphene/polymer systems.

The stress transfer mechanism from a polymer substrate to a nanoinclusion, such as a graphene flake, is of extreme interest for the production of effective nanocomposites. Previous work conducted mainly at the micron scale has shown that the intrinsic mechanism of stress transfer is shear at the interface. However, since the interfacial shear takes its maximum value at the very edge of the nanoinclusion it is of extreme interest to assess the effect of edge integrity upon axial stress transfer at the submicron scale. Here, we conduct a detailed Raman line mapping near the edges of a monolayer graphene flake that is simply supported onto an epoxy-based photoresist (SU8)/poly(methyl methacrylate) matrix at steps as small as 100 nm. We show for the first time that the distribution of axial strain (stress) along the flake deviates somewhat from the classical shear-lag prediction for a region of ∼ 2 µm from the edge. This behavior is mainly attributed to the presence of residual stresses, unintentional doping, and/or edge effects (deviation from the equilibrium values of bond lengths and angles, as well as different edge chiralities). By considering a simple balance of shear-to-normal stresses at the interface we are able to directly convert the strain (stress) gradient to values of interfacial shear stress for all the applied tensile levels without assuming classical shear-lag behavior. For large flakes a maximum value of interfacial shear stress of 0.4 MPa is obtained prior to flake slipping.

Deformation of wrinkled graphene.

The deformation of monolayer graphene, produced by chemical vapor deposition (CVD), on a polyester film substrate has been investigated through the use of Raman spectroscopy. It has been found that the microstructure of the CVD graphene consists of a hexagonal array of islands of flat monolayer graphene separated by wrinkled material. During deformation, it was found that the rate of shift of the Raman 2D band wavenumber per unit strain was less than 25% of that of flat flakes of mechanically exfoliated graphene, whereas the rate of band broadening per unit strain was about 75% of that of the exfoliated material. This unusual deformation behavior has been modeled in terms of mechanically isolated graphene islands separated by the graphene wrinkles, with the strain distribution in each graphene island determined using shear lag analysis. The effect of the size and position of the Raman laser beam spot has also been incorporated in the model. The predictions fit well with the behavior observed experimentally for the Raman band shifts and broadening of the wrinkled CVD graphene. The effect of wrinkles upon the efficiency of graphene to reinforce nanocomposites is also discussed.