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: The equivalent continuum elasticity representation is reconstructed, providing the full set of elastic moduli for carbyne, showing its extreme mechanical performance (e.g., a nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of 0.772 Å).
Abstract: We report an extensive study of the properties of carbyne using first-principles calculations. We investigate carbyne's mechanical response to tension, bending, and torsion deformations. Under tension, carbyne is about twice as stiff as the stiffest known materials and has an unrivaled specific strength of up to 7.5*10^7 Nm/kg, requiring a force of ~10 nN to break a single atomic chain. Carbyne has a fairly large room-temperature persistence length of about 14 nm. Surprisingly, the torsional stiffness of carbyne can be zero but can be 'switched on' by appropriate functional groups at the ends. Further, under appropriate termination, carbyne can be switched into a magnetic-semiconductor state by mechanical twisting. We reconstruct the equivalent continuum-elasticity representation, providing the full set of elastic moduli for carbyne, showing its extreme mechanical performance (e.g. a nominal Young's modulus of 32.7 TPa with an effective mechanical thickness of 0.772 A). We also find an interesting coupling between strain and band gap of carbyne, which is strongly increased under tension, from 3.2 to 4.4 eV under a 10% strain. Finally, we study the performance of carbyne as a nanoscale electrical cable, and estimate its chemical stability against self-aggregation, finding an activation barrier of 0.6 eV for the carbyne-carbyne cross-linking reaction and an equilibrium cross-link density for two parallel carbyne chains of 1 cross-link per 17 C atoms (2.2 nm).
306 citations
TL;DR: Progress in the development of nanoporous graphene and graphene oxide (GO) membranes, the mechanism of graphene molecular sieve action, structural design, hydrophilic nature, mechanical strength and antifouling properties and the principal challenges associated with nanopore generation are discussed in detail.
Abstract: Owing to their atomically thin structure, large surface area and mechanical strength, 2D nanoporous materials are considered to be suitable alternatives for existing desalination and water purification membrane materials. Recent progress in the development of nanoporous graphene based materials has generated enormous potential for water purification technologies. Progress in the development of nanoporous graphene and graphene oxide (GO) membranes, the mechanism of graphene molecular sieve action, structural design, hydrophilic nature, mechanical strength and antifouling properties and the principal challenges associated with nanopore generation are discussed in detail. Subsequently, the recent applications and performance of newly developed 2D materials such as 2D boron nitride (BN) nanosheets, graphyne, molybdenum disulfide (MoS2), tungsten chalcogenides (WS2) and titanium carbide (Ti3C2Tx) are highlighted. In addition, the challenges affecting 2D nanostructures for water purification are highlighted and their applications in the water purification industry are discussed. Though only a few 2D materials have been explored so far for water treatment applications, this emerging field of research is set to attract a great deal of attention in the near future.
305 citations
TL;DR: This work finds that the planar hypercoordinate two-dimensional monolayer system is quite stable during short annealing simulations up to 900 K, and predicts that it is a nonmagnetic metal.
Abstract: Two-dimensional (2D) materials with planar hypercoordinate motifs are extremely rare due to the difficulty in stabilizing the planar hypercoordinate configurations in extended systems. Furthermore, such exotic motifs are often unstable. We predict a novel Cu2Si 2D monolayer featuring planar hexacoordinate copper and planar hexacoordinate silicon. This is a global minimum in 2D space which displays reduced dimensionality and rule-breaking chemical bonding. This system has been studied with density functional theory, including molecular dynamics simulations and electronic structure calculations. Bond order analysis and partitioning reveals 4c–2e σ bonds that stabilize the two-dimensional structure. We find that the system is quite stable during short annealing simulations up to 900 K, and predict that it is a nonmagnetic metal. This work opens up a new branch of hypercoordinate two-dimensional materials for study.
304 citations
TL;DR: In this article, a useful ammonia (NH3) gas sensor based on reduced graphene oxide (RGO) and polyaniline (PANI) hybrid was presented, where PANI nanoparticles were successfully anchored on the surface of RGO sheets by using RGO-MnO2 hybrids as both of the templates and oxidants for aniline monomer during the process of polymerization.
Abstract: Here we present a useful ammonia (NH3) gas sensor based on reduced graphene oxide (RGO)–polyaniline (PANI) hybrids. PANI nanoparticles were successfully anchored on the surface of RGO sheets by using RGO–MnO2 hybrids as both of the templates and oxidants for aniline monomer during the process of polymerization. The resultant RGO–PANI hybrids were characterized by transmittance electron microscopy, infrared spectroscopy, Raman spectroscopy, UV-Vis spectroscopy, and scanning electron microscopy. The NH3 gas sensing performance of the hybrids was also investigated and compared with those of the sensors based on bare PANI nanofibers and bare RGO sheets. It was revealed that the synergetic behavior between both of the candidates allowed excellent sensitivity and selectivity to NH3 gas. The RGO–PANI hybrid device exhibited much better (3.4 and 10.4 times, respectively, with the concentration of NH3 gas at 50 ppm) response to NH3 gas than those of the bare PANI nanofiber sensor and bare graphene device. The combination of the RGO sheets and PANI nanoparticles facilitated the enhancement of the sensing properties of the final hybrids, and pave a new avenue for the application of RGO–PANI hybrids in the gas sensing field.
304 citations
TL;DR: A novel approach to identifying emerging topics in science and technology using two large scale models of the scientific literature based on direct citation and co-citation to nominate emerging topics using a difference function that rewards clusters that are new and growing rapidly.
304 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