We investigate the mechanical strength and properties of graphene under uniaxial tensile test as a function of size and chirality using the orthogonal tight-binding method and molecular dynamics simulations with the AIREBO potential. Our results on Young's modulus, fracture strain, and fracture strength of bulk graphene are in reasonable agreement with the recently published experimental data. Our results indicate that fracture strain and fracture strength of bulk graphene under uniaxial tension can have a significant dependence on the chirality. Mechanical properties such as Young's modulus and Poisson's ratio can depend strongly on the size and chirality of the graphene nanoribbon.

In this letter, we investigate the mechanical properties of graphene under shear deformation. Specifically, using molecular dynamics simulations, we compute the shear modulus, shear fracture strength, and shear fracture strain of zigzag and armchair graphene structures at various temperatures. To predict shear strength and fracture shear strain, we also present an analytical theory based on the kinetic analysis. We show that wrinkling behavior of graphene under shear deformation can be significant. We compute the amplitude to wavelength ratio of wrinkles using molecular dynamics and compare it with existing theory. Our results indicate that graphene can be a promising mechanical material under shear deformation.

A fundamental understanding of chemical sensing mechanisms in graphene-based chemical field-effect transistors (chemFETs) is essential for the development of next generation chemical sensors. Here we explore the hidden sensing modalities responsible for tailoring the gas detection ability of pristine graphene sensors by exposing graphene chemFETs to electron donor and acceptor trace gas vapors. We uncover that the sensitivity (in terms of modulation in electrical conductivity) of pristine graphene chemFETs is not necessarily intrinsic to graphene, but rather it is facilitated by external defects in the insulating substrate, which can modulate the electronic properties of graphene. We disclose a mixing effect caused by partial overlap of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of adsorbed gas molecules to explain graphene's ability to detect adsorbed molecules. Our results open a new design space, suggesting that control of external defects in supporting substrates can lead to tunable graphene chemical sensors, which could be developed without compromising the intrinsic electrical and structural properties of graphene.

Social scientists are rarely able to gather data from the full range of contexts to which they hope to generalize (Shadish, Cook, and Campbell 2002). Here we suggest that debates about the generality of causal inferences in the social sciences can be informed by quantifying the conditions necessary to invalidate an inference. We begin by differentiating the target population into two subpopulations: a potentially observed subpopulation from which all of a sample is drawn and a potentially unobserved subpopulation from which no members of the sample are drawn but which is part of the population to which policymakers seek to generalize. We then quantify the robustness of an inference in terms of the conditions necessary to invalidate an inference if cases from the potentially unobserved subpopulation were included in the sample. We apply the indices to inferences regarding the positive effect of small classes on achievement from the Tennessee class size study and then consider the breadth of external validity. We use the statistical test for whether there is a difference in effects between two subpopulations as a baseline to evaluate robustness, and weThe authors with to acknowledge the helpful comments of two anonymous reviewers, as well as Wei Pan. The opinions expressed in this paper are solely those of the authors. Direct correspondence to Kenneth Frank, 349 350 FRANK AND MIN consider a Bayesian motivation for the indices and compare the use of the indices with other procedures. In the discussion we emphasize the value of quantifying robustness, consider the value of different quantitative thresholds, and conclude by extending a metaphor linking statistical and causal inferences.

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