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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