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 conformational phase diagram for rectangular graphene sheets, defined by their geometry (size and aspect ratio), boundary conditions, and the environmental conditions such as supporting substrates and chemical modifications, as well as changes in temperature is presented.
Abstract: Graphene features a two-dimensional structure, where applications from electronic building blocks to reinforced composites are emerging, enabled through the utilization of its intriguing electrical, mechanical, and thermal properties. These properties are controlled by the structural makeup of graphene, which is known to display multiple morphologies that change under thermal fluctuations and variations of its geometry. However, as of now, a systematic understanding of the relationship between the conformation of graphene and its geometry remains unknown, preventing rational bottom-up design of materials, structures, and devices. Here, we present a conformational phase diagram for rectangular graphene sheets, defined by their geometry (size and aspect ratio), boundary conditions, and the environmental conditions such as supporting substrates and chemical modifications, as well as changes in temperature. We discover the occurrence of three major structural arrangements in membrane, ribbon, and scroll phases as the aspect ratio of the graphene nanoribbon increases. A theoretical and computational analysis of governing mechanisms for each conformation is provided.
234 citations
TL;DR: In this paper, a modified two-step in-situ reduced method is used to synthesize reduced graphene oxide (r-GO), whose conductivity can reach to 600 S/cm.
234 citations
26 Aug 2014-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the GNFs were mixed with aluminum alloy powders through ball milling and followed by hot isostatic pressing, and the green body was then hot extruded to obtain the final GNFs reinforced aluminum alloy nanocomposite.
Abstract: As one of the most important engineering materials, aluminum alloys have been widely applied in many fields. However, the requirement of enhancing their mechanical properties without sacrificing the ductility is always a challenge in the development of aluminum alloys. Thanks to the excellent physical and mechanical properties, graphene nanoflakes (GNFs) have been applied as promising reinforcing elements in various engineering materials, including polymers and ceramics. However, the investigation of GNFs as reinforcement phase in metals or alloys, especially in aluminum alloys, is still very limited. In this study, the aluminum alloy reinforced by GNFs was successfully prepared via powder metallurgy approach. The GNFs were mixed with aluminum alloy powders through ball milling and followed by hot isostatic pressing. The green body was then hot extruded to obtain the final GNFs reinforced aluminum alloy nanocomposite. The scanning electron microscopy and transmission electron microscope analysis show that GNFs were well dispersed in the aluminum alloy matrix and no chemical reactions were observed at the interfaces between the GNFs and aluminum alloy matrix. The mechanical properties׳ testing results show that with increasing filling content of GNFs, both tensile and yield strengths were remarkably increased without losing the ductility performance. These results not only provided a pathway to achieve the goal of preparing high strength aluminum alloys with excellent ductilitybut they also shed light on the development of other metal alloys reinforced by GNFs.
234 citations
TL;DR: Graphene/cellulose nanocomposite paper with high mechanical and electrical performances was reported in this paper by combining reduced graphene oxide sheets (RGO) and amine-modified nanofibrillated cellulose (A-NFC) in a well-controlled manner.
Abstract: Graphene/cellulose nanocomposite paper with high mechanical and electrical performances was reported in this study by combining reduced graphene oxide sheets (RGO) and amine-modified nanofibrillated cellulose (A-NFC) in a well-controlled manner. By adjusting the GO content, various graphene/cellulose nanocomposites with 0.1–10 wt% content of graphene were obtained. The RGO/A-NFC nanocomposite synthesized by the developed method exhibits an electrical percolation threshold of 0.3 wt% with an electrical conductivity of 4.79 × 10−4 S m−1, which is well above the antistatic value. Furthermore, with 10 wt% of graphene, a high conductivity of 71.8 S m−1 was measured for the nanocomposite. Moreover, it was found that on addition of only 0.3 wt% of graphene, the tensile strength increased by 1.2 fold and 2.3 folds compared to that of the neat cellulose and graphene oxide paper, respectively, revealing an excellent reinforcement of graphene sheets. Moreover, the elongation at break of the composite with graphene content was 8.5%, which is similar to that of A-NFC paper and much higher than that of GO paper. It is noteworthy to mention that with 5 wt% of graphene, the RGO/A-NFC composite paper showed a significantly enhanced tensile strength of 273 MPa that is 1.4 fold and 2.8 folds higher than that of the cellulose papers and graphene oxide paper, respectively. Such a high enhancement of electrical and mechanical properties in cellulose paper by graphene has never been reported before for any carbon-based material/cellulose composite paper.
233 citations
TL;DR: In this article, the structural and mechanical properties of various 2D nanomaterials, different experimental strategies to induce strain and modify properties, and applications of strained 2DNMs are discussed.
233 citations
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