Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 06 eV This leads to a crossover to a direct-gap material in the limit of the single monolayer Unlike the bulk material, the MoS₂ monolayer emits light strongly The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 10⁴ compared with the bulk material

Atomically thin MoS2: a new direct-gap semiconductor

Graphene is a wonder material with many superlatives to its name. It is the thinnest known material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have zero effective mass, and can travel for micrometers without scattering at room temperature. Graphene can sustain current densities six orders of magnitude higher than that of copper, shows record thermal conductivity and stiffness, is impermeable to gases, and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a benchtop experiment. This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

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Graphene: Status and Prospects

Problems associated with large-scale pattern growth of graphene constitute one of the main obstacles to using this material in device applications. Recently, macroscopic-scale graphene films were prepared by two-dimensional assembly of graphene sheets chemically derived from graphite crystals and graphene oxides. However, the sheet resistance of these films was found to be much larger than theoretically expected values. Here we report the direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers, and present two different methods of patterning the films and transferring them to arbitrary substrates. The transferred graphene films show very low sheet resistance of approximately 280 Omega per square, with approximately 80 per cent optical transparency. At low temperatures, the monolayers transferred to silicon dioxide substrates show electron mobility greater than 3,700 cm(2) V(-1) s(-1) and exhibit the half-integer quantum Hall effect, implying that the quality of graphene grown by chemical vapour deposition is as high as mechanically cleaved graphene. Employing the outstanding mechanical properties of graphene, we also demonstrate the macroscopic use of these highly conducting and transparent electrodes in flexible, stretchable, foldable electronics.

Large-scale pattern growth of graphene films for stretchable transparent electrodes

There is intense interest in graphene in fields such as physics, chemistry, and materials science, among others. Interest in graphene's exceptional physical properties, chemical tunability, and potential for applications has generated thousands of publications and an accelerating pace of research, making review of such research timely. Here is an overview of the synthesis, properties, and applications of graphene and related materials (primarily, graphite oxide and its colloidal suspensions and materials made from them), from a materials science perspective.

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Graphene and Graphene Oxide: Synthesis, Properties, and Applications

We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and third-order elastic stiffnesses of 340 newtons per meter (N m(-1)) and -690 Nm(-1), respectively. The breaking strength is 42 N m(-1) and represents the intrinsic strength of a defect-free sheet. These quantities correspond to a Young's modulus of E = 1.0 terapascals, third-order elastic stiffness of D = -2.0 terapascals, and intrinsic strength of sigma(int) = 130 gigapascals for bulk graphite. These experiments establish graphene as the strongest material ever measured, and show that atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.

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Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

This research explores the nonlinear elastic properties of two-dimensional molybdenum disulfide. We derive a thermodynamically rigorous nonlinear elastic constitutive equation and then calculate the nonlinear elastic response of two-dimensional MoS${}_{2}$ with first-principles density functional theory (DFT) calculations. The nonlinear elastic properties are used to predict the behavior of suspended monolayer MoS${}_{2}$ subjected to a spherical indenter load at finite strains in a multiple-length-scale finite element analysis model. The model is validated experimentally by indenting suspended circular MoS${}_{2}$ membranes with an atomic force microscope. We find that the two-dimensional Young's modulus and intrinsic strength of monolayer MoS${}_{2}$ are 130 and 16.5 N/m, respectively. The results approach Griffith's predicted intrinsic strength limit of ${\ensuremath{\sigma}}_{\mathrm{int}}\ensuremath{\sim}\frac{E}{9}$, where $E$ is the Young's modulus. This study reveals the predictive power of first-principles density functional theory in the derivation of nonlinear elastic properties of two-dimensional MoS${}_{2}$. Furthermore, the study bridges three main gaps that hinder understanding of material properties: DFT to finite element analysis, experimental results to DFT, and the nanoscale to the microscale. In bridging these three gaps, the experimental results validate the DFT calculations and the multiscale constitutive model.

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Nonlinear elastic behavior of two-dimensional molybdenum disulfide

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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Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description

We descnbe studies of the elastic properties and frictional characteristics of graphene samples of varying thickness using an atomic force microscope. For tensile testing, graphene is suspended over micron-sized circular holes and indented by atomic force microscope (AFM) tips. Fitting of the force-displacement curves yields the prestress and elastic stiffness, while comparison of the breaking force to simulation gives the ultimate strength, which is the highest measured for any material. Experiments on samples with 1-3 atomic layers yield similar values for the intrinsic stiffness and strength of a single sheet, but also reveal differences in mechanical behavior with thickness. The frictional force between an AFM tip and graphene decreases with thickness for samples from 1 to 4 layers, and does not depend on the presence of a substrate. High-resolution friction force imaging in stick-slip mode shows the same trend, and allows direct imaging of the crystal lattice.

Elastic and frictional properties of graphene

Numerous theoretical and experimental studies on various species of natural composites, such as nacre in abalone shells, collagen fibrils in tendon, and spider silk fibers, have been pursued to provide insight into the synthesis of novel bioinspired high-performance composites. However, a direct link between the mechanical properties of the constituents and the various geometric features and hierarchies remains to be fully established. In this paper, we explore a common denominator leading to the outstanding balance between strength and toughness in natural composite materials. We present an analytical model to link the mechanical properties of constituents, their geometric arrangement, and the chemistries used in their lateral interactions. Key critical overlap length scales between adjacent reinforcement constituents, which directly control strength and toughness of composite materials, emerge from the analysis. When these length scales are computed for three natural materials-nacre, collagen molecules, and spider silk fibers-very good agreement is found as compared with experimental measurements. The model was then used to interpret load transfer capabilities in synthetic carbon-based materials through parametrization of in situ SEM shear experiments on overlapping multiwall carbon nanotubes.

Xiaoding Wei

Papers

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

Nonlinear elastic behavior of two-dimensional molybdenum disulfide

Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description

Elastic and frictional properties of graphene

Optimal length scales emerging from shear load transfer in natural materials: application to carbon-based nanocomposite design.