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Journal ArticleDOI

Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene

Changgu Lee1, Xiaoding Wei1, Jeffrey W. Kysar1, James Hone1, James Hone2 
18 Jul 2008-Science (American Association for the Advancement of Science)-Vol. 321, Iss: 5887, pp 385-388
TL;DR: Graphene is established as the strongest material ever measured, and atomically perfect nanoscale materials can be mechanically tested to deformations well beyond the linear regime.
Abstract: 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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Citations
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Journal ArticleDOI
TL;DR: T theoretical and experimental developments in the emerging field of nanoporous atomically thin membranes are discussed, focusing on the fundamental mechanisms of gas- and liquid-phase transport, membrane fabrication techniques and advances towards practical application.
Abstract: Graphene and other two-dimensional materials offer a new approach to controlling mass transport at the nanoscale. These materials can sustain nanoscale pores in their rigid lattices and due to their minimum possible material thickness, high mechanical strength and chemical robustness, they could be used to address persistent challenges in membrane separations. Here we discuss theoretical and experimental developments in the emerging field of nanoporous atomically thin membranes, focusing on the fundamental mechanisms of gas- and liquid-phase transport, membrane fabrication techniques and advances towards practical application. We highlight potential functional characteristics of the membranes and discuss applications where they are expected to offer advantages. Finally, we outline the major scientific questions and technological challenges that need to be addressed to bridge the gap from theoretical simulations and proof-of-concept experiments to real-world applications.

551 citations

Journal ArticleDOI
TL;DR: A comprehensive review on the application of metal oxide/graphene composites in water treatment and their role as photocatalyst, adsorbent and disinfectant in water remediation is presented in this article.
Abstract: With a rapidly growing population, development of new materials, techniques and devices which can provide safe potable water continues to be one of the major research emphases of the scientific community. While the development of new metal oxide catalysts is progressing, albeit at a slower pace, the concurrent and rapid development of high surface area catalyst supports such as graphene and its functionalised derivatives has provided unprecedented promise in the development of multifunctional catalysts. Recent works have shown that metal oxide/graphene composites can perform multiple roles including (but not limited to): photocatalysts, adsorbents and antimicrobial agents making them an effective agent against all major water pollutants including organic molecules, heavy metal ions and water borne pathogens, respectively. This article presents a comprehensive review on the application of metal oxide/graphene composites in water treatment and their role as photocatalyst, adsorbent and disinfectant in water remediation. Through this review, we discuss the current state of the art in metal oxide/graphene composites for water purification and also provide a comprehensive analysis of the nature of interaction of these composites with various types of pollutants which dictates their photocatalytic, adsorptive and antimicrobial activities. The review concludes with a summary on the role of graphene based materials in removal of pollutants from water and some proposed strategies for designing of highly efficient multifunctional metal oxide/graphene composites for water remediation. A brief perspective on the challenges and new directions in the area is also provided for researchers interested in designing advanced water treatment strategies using graphene based advanced materials.

551 citations

Journal ArticleDOI
TL;DR: It is shown here that GB strength can either increase or decrease with the tilt, and the behaviour can be explained well by continuum mechanics.
Abstract: Graphene is often referred to as the strongest material in existence. That may be so for a perfect crystal, but most graphene sheets are polycrystalline, and the grain boundaries affect their mechanical properties. A new study reveals that both the density and detailed arrangement of the defects that form the grain boundaries play a significant part in determining the strength of a polycrystalline graphene sheet.

550 citations

Journal ArticleDOI
TL;DR: It is reported that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp(3)-type defects, which provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.
Abstract: It is important from a fundamental standpoint and for practical applications to understand how the mechanical properties of graphene are influenced by defects. Here we report that the two-dimensional elastic modulus of graphene is maintained even at a high density of sp(3)-type defects. Moreover, the breaking strength of defective graphene is only ~14% smaller than its pristine counterpart in the sp(3)-defect regime. By contrast, we report a significant drop in the mechanical properties of graphene in the vacancy-defect regime. We also provide a mapping between the Raman spectra of defective graphene and its mechanical properties. This provides a simple, yet non-destructive methodology to identify graphene samples that are still mechanically functional. By establishing a relationship between the type and density of defects and the mechanical properties of graphene, this work provides important basic information for the rational design of composites and other systems utilizing the high modulus and strength of graphene.

549 citations


Cites background from "Measurement of the Elastic Properti..."

  • ...The result resembles a cumulative Weibull distribution with the following three distinct regimes: (1) incubation period, (2) an intermediate regime and (3) a terminal regime....

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Journal ArticleDOI
TL;DR: This work opened a pathway for investigating the mechanical properties of monolayers and bilayers of other MXenes and extends the already broad range of MXenes’ applications to structural composites, protective coatings, nanoresonators, and membranes that require materials with exceptional mechanical properties.
Abstract: Two-dimensional (2D) transition metal carbides and nitrides, known as MXenes, are a large class of materials that are finding numerous applications ranging from energy storage and electromagnetic interference shielding to water purification and antibacterial coatings. Yet, despite the fact that more than 20 different MXenes have been synthesized, the mechanical properties of a MXene monolayer have not been experimentally studied. We measured the elastic properties of monolayers and bilayers of the most important MXene material to date, Ti3C2T x (T x stands for surface termination). We developed a method for preparing well-strained membranes of Ti3C2T x monolayers and bilayers, and performed their nanoindentation with the tip of an atomic force microscope to record the force-displacement curves. The effective Young's modulus of a single layer of Ti3C2T x was found to be 0.33 ± 0.03 TPa, which is the highest among the mean values reported in nanoindentation experiments for other solution-processed 2D materials, including graphene oxide. This work opens a pathway for investigating the mechanical properties of monolayers and bilayers of other MXenes and extends the already broad range of MXenes' applications to structural composites, protective coatings, nanoresonators, and membranes that require materials with exceptional mechanical properties.

548 citations

References
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Journal ArticleDOI
TL;DR: This work shows that graphene's electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers, and allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area.
Abstract: Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the number of layers The D peak second order changes in shape, width, and position for an increasing number of layers, reflecting the change in the electron bands via a double resonant Raman process The G peak slightly down-shifts This allows unambiguous, high-throughput, nondestructive identification of graphene layers, which is critically lacking in this emerging research area

13,474 citations

Journal ArticleDOI
TL;DR: By using micromechanical cleavage, a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides are prepared and studied.
Abstract: We report free-standing atomic crystals that are strictly 2D and can be viewed as individual atomic planes pulled out of bulk crystals or as unrolled single-wall nanotubes. By using micromechanical cleavage, we have prepared and studied a variety of 2D crystals including single layers of boron nitride, graphite, several dichalcogenides, and complex oxides. These atomically thin sheets (essentially gigantic 2D molecules unprotected from the immediate environment) are stable under ambient conditions, exhibit high crystal quality, and are continuous on a macroscopic scale.

10,586 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
Abstract: In the course of an investigation of the effect of surface scratches on the mechanical strength of solids, some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion. The original object of the work, which was carried out at the Royal Aircraft Estab­lishment, was the discovery of the effect of surface treatment—such as, for instance, filing, grinding or polishing—on the strength of metallic machine parts subjected to alternating or repeated loads. In the case of steel, and some other metals in common use, the results of fatigue tests indicated that the range of alternating stress which could be permanently sustained by the material was smaller than the range within which it was sensibly elastic, after being subjected to a great number of reversals. Hence it was inferred that the safe range of loading of a part, having a scratched or grooved surface of a given type, should be capable of estimation with the help of one of the two hypotheses of rupture commonly used for solids which are elastic to fracture. According to these hypotheses rupture may be expected if (a) the maximum tensile stress, ( b ) the maximum extension, exceeds a certain critical value. Moreover, as the behaviour of the materials under consideration, within the safe range of alternating stress, shows very little departure from Hooke’s law, it was thought that the necessary stress and strain calculations could be performed by means of the mathematical theory of elasticity.

10,162 citations

Book
01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.

8,520 citations

Journal ArticleDOI
28 Jan 2000-Science
TL;DR: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a "nanostressing stage" located within a scanning electron microscope and a variety of structures were revealed, such as a nanotube ribbon, a wave pattern, and partial radial collapse.
Abstract: The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus E of the outermost layer varied from 270 to 950 gigapascals. Transmission electron microscopic examination of the broken nanotube fragments revealed a variety of structures, such as a nanotube ribbon, a wave pattern, and partial radial collapse.

5,011 citations