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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: The combined experiment and modelling verify the applicability of the classic Griffith theory of brittle fracture to graphene and quantifies the essential fracture properties of graphene and provides mechanistic insights into the mechanical failure of graphene.
Abstract: While the intrinsic strength of graphene has previously been demonstrated to be high, the fracture toughness remains unknown. Here, the authors perform in situ testing of graphene in a scanning electron microscope and report a critical stress intensity factor of ~4.0 MPa√m.

624 citations

Journal ArticleDOI
TL;DR: In this paper, a review of recent work in this area is presented, focusing on results from the author's group, and it is concluded that functionalized nanotubes can be exfoliated to the greatest degree.
Abstract: Many applications of carbon nanotubes require the exfoliation of the nanotubes to give individual tubes in the liquid phase. This requires the dispersion, exfoliation, and stabilization of nanotubes in a variety of liquids. In this paper recent work in this area is reviewed, focusing on results from the author's group. It begins by reviewing stabilization mechanisms before exploring research into the exfoliation of nanotubes in solvents, by using surfactants or biomolecules and by covalent attachment of molecules. The concentration dependence of the degree of exfoliation in each case will be highlighted. In addition research into the dispersion mechanism for each dispersant type is discussed. Most importantly, dispersion quality metrics for all dispersants are compared. From this analysis, it is concluded that functionalized nanotubes can be exfoliated to the greatest degree. Finally, the extension of this work to the liquid phase exfoliation of graphite to give graphene is reviewed.

621 citations

Journal ArticleDOI
TL;DR: In this article, the authors present an overview on electrochemical characteristics of graphene by summarizing the recent research trend on graphene for energy conversion and storage applications, such as fuel, and present an analysis of the potential of this material for next generation energy conversion devices.

616 citations

Journal ArticleDOI
TL;DR: This work investigates the interactions of graphene and few-layer graphene (FLG) microsheets with three cell types and with model lipid bilayers by combining coarse-grained molecular dynamics (MD), all-atom MD, analytical modeling, confocal fluorescence imaging, and electron microscopic imaging and proposed mechanism allows cellular uptake of even large multilayer sheets of micrometer-scale lateral dimension.
Abstract: Understanding and controlling the interaction of graphene-based materials with cell membranes is key to the development of graphene-enabled biomedical technologies and to the management of graphene health and safety issues. Very little is known about the fundamental behavior of cell membranes exposed to ultrathin 2D synthetic materials. Here we investigate the interactions of graphene and few-layer graphene (FLG) microsheets with three cell types and with model lipid bilayers by combining coarse-grained molecular dynamics (MD), all-atom MD, analytical modeling, confocal fluorescence imaging, and electron microscopic imaging. The imaging experiments show edge-first uptake and complete internalization for a range of FLG samples of 0.5- to 10-μm lateral dimension. In contrast, the simulations show large energy barriers relative to kBT for membrane penetration by model graphene or FLG microsheets of similar size. More detailed simulations resolve this paradox by showing that entry is initiated at corners or asperities that are abundant along the irregular edges of fabricated graphene materials. Local piercing by these sharp protrusions initiates membrane propagation along the extended graphene edge and thus avoids the high energy barrier calculated in simple idealized MD simulations. We propose that this mechanism allows cellular uptake of even large multilayer sheets of micrometer-scale lateral dimension, which is consistent with our multimodal bioimaging results for primary human keratinocytes, human lung epithelial cells, and murine macrophages.

615 citations


Cites background or methods or result from "Measurement of the Elastic Properti..."

  • ...A series of calculations with different interaction parameters between graphene and lipid molecules are also performed to demonstrate that the corner entry mode is robust within a broad range of dissipative particle dynamics (DPD) parameters (SI Text)....

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  • ...Following Groot and Rabone (2), the parameters for the bending constant and the equilibrium angle among three consecutive lipid tail beads or three consecutive lipid head beads in a lipid molecule are k1 = 6 and θ= 180°; for the head bead connected to the lipid tails and the first beads in the tails (beads 3, 4, and 9 in Fig....

    [...]

  • ...The coarse-grained simulations in this paper are based on DPD, which is a Lagrangian method derived from coarse graining of molecular dynamics (51) widely used as a mesoscopic simulation method for biomembrane systems (52–55)....

    [...]

  • ...G is a 2D plate-like material consisting of a single layer of hexagonally arranged carbon atoms with extraordinary electrical (1), mechanical (2), and thermal properties (3)....

    [...]

  • ...The simulations are based on the method of dissipative particle dynamics (DPD) (1, 2)....

    [...]

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