The nonlinear in-plane elastic properties of graphene are calculated using density-functional theory. A thermodynamically rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. Upon accounting for the symmetries of graphene, a total of fourteen nonzero independent elastic constants are determined by least-squares fit to the ab initio calculations. The nonlinear continuum description is valid for infinitesimal and finite strains under arbitrary in-plane tensile loading in circumstance for which the bending stiffness can be neglected. The continuum formulation is suitable for incorporation into the finite element method.

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It is commonly accepted that the addition of spherical nanoparticles (NPs) cannot simultaneously improve the elastic modulus, the yield stress, and the ductility of an amorphous glassy polymer matrix. In contrast to this conventional wisdom, we show that ductility can be substantially increased, while maintaining gains in the elastic modulus and yield stress, in glassy nanocomposite films composed of spherical silica NPs grafted with polystyrene (PS) chains in a PS matrix. The key to these improvements are (i) uniform NP spatial dispersion and (ii) strong interfacial binding between NPs and the matrix, by making the grafted chains sufficiently long relative to the matrix. Strikingly, the optimal conditions for the mechanical reinforcement of the same nanocomposite material in the melt state is completely different, requiring the presence of spatially extended NP clusters. Evidently, NP spatial dispersions that optimize material properties are crucially sensitive to the state (melt versus glass) of the polymeric material.

A reproducible route for tuning localized surface plasmon resonance in scattering type near-field optical microscopy probes is presented. The method is based on the production of a focused-ion-beam milled single groove near the apex of electrochemically etched gold tips. Electron energy-loss spectroscopy and scanning transmission electron microscopy are employed to obtain highly spatially and spectroscopically resolved maps of the milled probes, revealing localized surface plasmon resonance at visible and near-infrared wavelengths. By changing the distance L between the groove and the probe apex, the localized surface plasmon resonance energy can be fine-tuned at a desired absorption channel. Tip-enhanced Raman spectroscopy is applied as a test platform, and the results prove the reliability of the method to produce efficient scattering type near-field optical microscopy probes.

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Single-step nano-lithography was performed on graphene sheets using a helium ion microscope. Parallel “defect” lines of ∼1 μm length and ≈5 nm width were written to form nanoribbon gratings down to 20 nm pitch. Polarized Raman spectroscopy shows that crystallographic orientation of the nanoribbons was partially maintained at their lateral edges, indicating a high-fidelity lithography process. Furthermore, Raman analysis of large exposure areas with different ion doses reveals that He ions produce point defects with radii ∼ 2× smaller than do Ga ions, demonstrating that scanning-He+-beam lithography can texture graphene with less damage.

The nanoscale friction between an atomic force microscopy tip and graphene is investigated using friction force microscopy (FFM). During the tip movement, friction forces are observed to increase and then saturate in a highly anisotropic manner. As a result, the friction forces in graphene are highly dependent on the scanning direction: under some conditions, the energy dissipated along the armchair direction can be 80% higher than along the zigzag direction. In comparison, for highly-oriented pyrolitic graphite (HOPG), the friction anisotropy between armchair and zigzag directions is only 15%. This giant friction anisotropy in graphene results from anisotropies in the amplitudes of flexural deformations of the graphene sheet driven by the tip movement, not present in HOPG. The effect can be seen as a novel manifestation of the classical phenomenon of Euler buckling at the nanoscale, which provides the non-linear ingredients that amplify friction anisotropy. Simulations based on a novel version of the 2D Tomlinson model (modified to include the effects of flexural deformations), as well as fully atomistic molecular dynamics simulations and first-principles density-functional theory (DFT) calculations, are able to reproduce and explain the experimental observations.

In this work, we clarify the features of the lateral damage of line defects in single layer graphene. The line defects were produced through well-controlled etching of graphene using a Ga(+) focused ion beam. The lateral damage length was obtained from both the integrated intensity of the disorder induced Raman D band and the minimum ion fluence. Also, the line defects were characterized by polarized Raman spectroscopy. It was found that graphene is resilient under the etching conditions since the intensity of the defect induced Raman D peak exhibits a dependence on the direction of the lines relative to the crystalline lattice and also on the direction of the laser polarization relative to the lines. In addition, electrical measurements of the modified graphene were performed. Different ion fluences were used in order to obtain a completely insulating defect line in graphene, which was determined experimentally by means of charge injection and electric force microscopy measurements. These studies demonstrate that a Ga+ ion column combined with Raman spectroscopy is a powerful technique to produce and understand well-defined periodic arrays of defects in graphene, opening possibilities for better control of nanocarbon devices.