We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

Graphene: a new emerging lubricant ☆

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

Semiconducting transition metal dichalcogenides (TMDs) are emerging as the potential alternatives to graphene. As in the case of graphene, the monolayer of TMDs can easily be exfoliated using mechanical or chemical methods, and their properties can also be tuned. At the same time, semiconducting TMDs (MX2; M = Mo, W and X = S, Se, Te) possess an advantage over graphene in that they exhibit a band gap whose magnitude is appropriate for applications in the opto-electronic devices. Using ab initio simulations, we demonstrate that this band gap can be widely tuned by applying mechanical strains. While the electronic properties of graphene remain almost unaffected by tensile strains, we find TMDs to be sensitive to both tensile and shear strains. Moreover, compared to that of graphene, a much smaller amount of strain is required to vary the band gap of TMDs. Our results suggest that mechanical strains reduce the band gap of semiconducting TMDs causing an direct-to-indirect band gap and a semiconductor-to-metal...

Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains.

Using micro-Raman spectroscopy and scanning tunneling microscopy, we study the relationship between structural distortion and electrical hole doping of graphene on a silicon dioxide substrate. The observed upshift of the Raman G band represents charge doping and not compressive strain. Two independent factors control the doping: (1) the degree of graphene coupling to the substrate and (2) exposure to oxygen and moisture. Thermal annealing induces a pronounced structural distortion due to close coupling to SiO2 and activates the ability of diatomic oxygen to accept charge from graphene. Gas flow experiments show that dry oxygen reversibly dopes graphene; doping becomes stronger and more irreversible in the presence of moisture and over long periods of time. We propose that oxygen molecular anions are stabilized by water solvation and electrostatic binding to the silicon dioxide surface.

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Atmospheric Oxygen Binding and Hole Doping in Deformed Graphene on a SiO2 Substrate

There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold but they are characterized by a $s{p}^{3}$ orbital hybridization, have different crystal symmetry, and otherwise behave upon loading. By first-principles calculations we determine their structural and phonon properties, as well as we establish their relative stability. Through continuum elasticity we define a simulation protocol addressed to measure by a computer experiment their linear and nonlinear elastic moduli and we actually compute them by first principles. We argue that all graphane conformers respond to any arbitrarily oriented extension with a much smaller lateral contraction than the one calculated for graphene. Furthermore, we provide evidence that boat-graphane has a small and negative Poisson ratio along the armchair and zigzag principal directions of the carbon honeycomb lattice (axially auxetic elastic behavior). Moreover, we show that chair-graphane admits both softening and hardening hyperelasticity, depending on the direction of applied load.

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Elastic properties of hydrogenated 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.

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Nonlinear elasticity of monolayer graphene

We exploit the concept of strain-induced band-structure engineering in graphene through the calculation of its electronic properties under uniaxial, shear, and combined uniaxial-shear deformations. We show that by combining shear deformations to uniaxial strains it is possible modulate the graphene energy-gap value from zero up to 0.9 eV. Interestingly enough, the use of a shear component allows for a gap opening at moderate absolute deformation, safely smaller than the graphene failure strain.

Gap opening in graphene by shear strain

Using a tight-binding atomistic simulation, we simulate the recent atomic-force microscopy experiments probing the slipperiness of graphene flakes made slide against a graphite surface. Compared to previous theoretical models, where the flake was assumed to be geometrically perfect and rigid, while the substrate is represented by a static periodic potential, our fully-atomistic model includes quantum mechanics with the chemistry of bond breaking and bond formation, and the flexibility of the flake. These realistic features, include in particular the crucial role of the flake rotation in determining the static friction, in qualitative agreement with experimental observations.

Atomistic simulations of the sliding friction of graphene flakes

While the unique elastic properties of monolayer graphene have been extensively investigated, less knowledge has been developed so far on folded graphene. Nevertheless, it has been recently suggested that fold-induced curvature (without in-plane strain) could possibly affect the local chemical and electron transport properties of graphene, envisaging a material-by-design approach where tailored membranes are used in enhanced nanoresonators or nanoelectromechanical devices. In this work we propose a novel method combining apparent strain analysis from high-resolution transmission electron microscopy (HREM) images and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations to map and measure the nanoscale curvature of graphene folds and wrinkles. If enough contrast and resolution in HREM images are obtained, this method can be successfully applied to provide a complete nanoscale geometrical and physical picture of 3D structure of various wrinkle and fold configurations.

Emiliano Cadelano

Papers

Elastic properties of hydrogenated graphene

Nonlinear elasticity of monolayer graphene

Gap opening in graphene by shear strain

Atomistic simulations of the sliding friction of graphene flakes

Folded graphene membranes: mapping curvature at the nanoscale.