Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene
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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TL;DR: A series of titanium dioxide and graphene sheets composites were synthesized with a sol-gel method using tetrabutyl titanate and graphite oxide (GO) as the starting materials.
Abstract: A series of titanium dioxide and graphene sheets (GSs) composites were synthesized with a sol–gel method using tetrabutyl titanate and graphite oxide (GO) as the starting materials. The obtained TiO2/GSs photocatalysts are characterized by X-ray diffraction, N2 adsorption analysis, Raman spectroscopy, transmission electron microscopy, X-ray photoelectron spectroscopy and ultraviolet-visible (UV-vis) diffuse reflectance spectroscopy. The photocatalytic activity of the as-prepared samples was evaluated by hydrogen evolution from water photo-splitting under UV-vis illumination. The influence of GSs content and calcinations atmosphere on the photocatalytic activity was also investigated. The results show that both GSs content and the calcinations atmosphere can affect the photocatalytic activity of the obtained composites.
985 citations
TL;DR: In this paper, a superparamagnetic graphene oxide-Fe3O4nanoparticles hybrid was prepared via a simple and effective chemical precipitation method, which was then loaded with doxorubicin hydrochloride (DXR) and the loading capacity was as high as 1.08 mg mg−1.6 wt% by atomic absorption spectrometry.
Abstract: A superparamagnetic graphene oxide –Fe3O4nanoparticles hybrid (GO–Fe3O4) was prepared via a simple and effective chemical precipitation method. The amount of loading of Fe3O4 on GO was estimated as 18.6 wt% by atomic absorption spectrometry. The hybrid was then loaded with doxorubicin hydrochloride (DXR) and the loading capacity was as high as 1.08 mg mg−1. Both of the GO–Fe3O4 hybrids before and after loading with DXR can be dispersed well in aqueous solution. They can congregate under acidic conditions and move regularly under the force of an external magnet. Furthermore, the aggregated hybrid can be redispersed to form a stable suspension under basic conditions. These properties make it a potential candidate for controlled targeted drug delivery and release.
979 citations
TL;DR: A highly strained ultrathin membrane of MoS2 could lead to the creation of a solar funnel, a new form of solar cell which absorbs a much broader range of the solar spectrum that a usual single junction device as discussed by the authors.
Abstract: A highly strained ultrathin membrane of MoS2 could lead to the creation of a solar funnel, a new form of solar cell which absorbs a much broader range of the solar spectrum that a usual single junction device.
978 citations
TL;DR: The novel AFM imaging and FEM-based mapping methods presented here are of general utility for obtaining the elastic modulus and prestress of thin membranes.
Abstract: Mechanical properties of ultrathin membranes consisting of one layer, two overlapped layers, and three overlapped layers of graphene oxide platelets were investigated by atomic force microscopy (AFM) imaging in contact mode. In order to evaluate both the elastic modulus and prestress of thin membranes, the AFM measurement was combined with the finite element method (FEM) in a new approach for evaluating the mechanics of ultrathin membranes. Monolayer graphene oxide was found to have a lower effective Young’s modulus (207.6 ± 23.4 GPa when a thickness of 0.7 nm is used) as compared to the value reported for “pristine” graphene. The prestress (39.7−76.8 MPa) of the graphene oxide membranes obtained by solution-based deposition was found to be 1 order of magnitude lower than that obtained by others for mechanically cleaved graphene. The novel AFM imaging and FEM-based mapping methods presented here are of general utility for obtaining the elastic modulus and prestress of thin membranes.
975 citations
Cites background or methods from "Measurement of the Elastic Properti..."
...0 TPa and the ultimate breaking strength of 130 GPa by indenting the center of a series of monolayer graphene membranes with a diamond-coated tip using atomic force microscopy (AFM).(2) Gomez-Navarro et al....
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...0 TPa, corresponding to E 342 30 N/m.(2) Therefore, E of the G O monolayer platelets studied here is about half that of graphene....
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...165, the value for graphite in the basal plane.(2,59) Displacements at the center of the membrane were calculated at 10 GPa and 2 MPa increments for elastic moduli and prestresses, respectively....
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...Monolayer graphene obtained from mechanically cleaved graphite has a measured Young’s modulus of 1.0 TPa, corresponding to E2D 342 30 N/m.2 Therefore, E2D of the G O monolayer platelets studied here is about half that of graphene....
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...Graphene can be modeled as a two-dimensional (2D) membrane with no bending stiffness.(2) However, the addition of oxygen atoms in G O...
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TL;DR: The extreme flexibility of graphene allows it to conform to the topography of even the smoothest substrates, thus making its interaction with the substrate more liquid-like than solid-like and comparable to solid-liquid adhesion energies.
Abstract: Pressurized blister tests show that the adhesion energies of graphene samples on silicon oxide are much higher than those measured in typical micromechanical structures.
973 citations
Additional excerpts
...In equation (1) the four terms represent, respectively, (1) stretching of the membrane due to the pressure difference across it, Dp1⁄4 pint 2 pext (we calculate this by equating the strain energy in the deformed membrane to the work done by the expanding gas during deformation, which is easier to directly calculate, and then simplifying the results using Hencky’s relations for the pressuredeflection and pressure-blister volume); (2) graphene/SiO2 adhesion; (3) expansion of the gas in the chamber from V0 to a final volume V0þ Vb(a); and (4) work done on the gas held at a fixed external pressure pext....
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References
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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
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
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
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