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Qu C, Shi D, Chen L, Wu Z, Wang J, Shi S, Gao E, Xu Z, Zheng Q. Anisotropic Fracture of Graphene Revealed by Surface Steps on Graphite. PHYSICAL REVIEW LETTERS 2022; 129:026101. [PMID: 35867457 DOI: 10.1103/physrevlett.129.026101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2022] [Revised: 06/06/2022] [Accepted: 06/13/2022] [Indexed: 06/15/2023]
Abstract
The anisotropic fracture toughness G(θ) is an intrinsic feature of graphene and is fundamental for fabrication, functioning, and robustness of graphene-based devices. However, existing results show significant discrepancies on the anisotropic factor, i.e., the ratio between zigzag (ZZ) and armchair (AC) directions, G_{ZZ}/G_{AC}, both qualitatively and quantitatively. Here, we investigate the anisotropic fracture of graphene by atomic steps on cleaved graphite surfaces. Depending on the relation between the peeling direction and local lattice orientation, two categories of steps with different structures and behaviors are observed. In one category are straight steps well aligned with local ZZ directions, while in the other are steps consisting of nanoscale ZZ and AC segments. Combined with an analysis on fracture mechanics, the microscale morphology of steps and statistics of their directions provides a measurement on the anisotropic factor of G_{ZZ}/G_{AC}=0.971, suggesting that the ZZ direction has a slightly lower fracture toughness. The results provide an experimental benchmark for the widely scattered existing results, and offer constraints on future models of graphene fracture.
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Affiliation(s)
- Cangyu Qu
- Institute of Superlubricity Technology, Research Institute of Tsinghua University in Shenzhen, Shenzhen 518057, China
| | - Diwei Shi
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Li Chen
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Zhanghui Wu
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Jin Wang
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Songlin Shi
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Enlai Gao
- Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
| | - Zhiping Xu
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Quanshui Zheng
- Institute of Superlubricity Technology, Research Institute of Tsinghua University in Shenzhen, Shenzhen 518057, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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Kalosakas G, Lathiotakis NN, Papagelis K. Uniaxially Strained Graphene: Structural Characteristics and G-Mode Splitting. MATERIALS (BASEL, SWITZERLAND) 2021; 15:67. [PMID: 35009214 PMCID: PMC8746274 DOI: 10.3390/ma15010067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Revised: 12/16/2021] [Accepted: 12/17/2021] [Indexed: 06/14/2023]
Abstract
The potential use of graphene in various strain engineering applications requires an accurate characterization of its properties when the material is under different mechanical loads. In this work, we present the strain dependence of the geometrical characteristics at the atomic level and the Raman active G-band evolution in a uniaxially strained graphene monolayer, using density functional theory methods as well as molecular dynamics atomistic simulations for strains that extend up to the structural failure. The bond length and bond angle variations with strain, applied either along the zigzag or along the armchair direction, are discussed and analytical relations describing this dependence are provided. The G-mode splitting with strain, as obtained by first principles' methods, is also presented. While for small strains, up to around 1%, the G-band splitting is symmetrical in the two perpendicular directions of tension considered here, this is no longer the case for larger values of strains where the splitting appears to be larger for strains along the zigzag direction. Further, a crossing is observed between the lower frequency split G-mode component and the out-of-plane optical mode at the Γ point for large uniaxial strains (>20%) along the zigzag direction.
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Affiliation(s)
- George Kalosakas
- Department of Materials Science, University of Patras, GR-26504 Rio, Greece
| | - Nektarios N. Lathiotakis
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11634 Athens, Greece;
| | - Konstantinos Papagelis
- Department of Solid State Physics, School of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece;
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Ryu GH, Jung GS, Park H, Chang RJ, Warner JH. Atomistic Mechanics of Torn Back Folded Edges of Triangular Voids in Monolayer WS 2. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2021; 17:e2104238. [PMID: 34708519 DOI: 10.1002/smll.202104238] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Revised: 09/07/2021] [Indexed: 06/13/2023]
Abstract
Triangular nanovoids in 2D materials transition metal dichalcogenides have vertex points that cause stress concentration and lead to sharp crack propagation and failure. Here, the atomistic mechanics of back folding around triangular nanovoids in monolayer WS2 sheets is examined. Combining atomic-resolution images from annular dark-field scanning transmission electron microscopy with reactive molecular modelling, it is revealed that the folding edge formation has statistical preferences under geometric conditions based on the orientation mismatch. It is further investigated how loading directions and strong interlayer friction, interplay with WS2 lattice's crack preference, govern the deformation and fracture pattern around folding edges. These results provide fundamental insights into the combination of fracture and folding in flexible monolayer crystals and the resultant Moiré lattices.
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Affiliation(s)
- Gyeong Hee Ryu
- School of Materials Science and Engineering, Gyeongsang National University, Jinju, 52828, Republic of Korea
| | - Gang Seob Jung
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - Hyoju Park
- Materials Graduate Program, Texas Materials Institute, The University of Texas at Austin, 204 East Dean Keeton Street, Austin, TX, 78712, USA
| | - Ren-Jie Chang
- Department of Materials, University of Oxford, 16 Parks Road, Oxford, OX1 3PH, UK
| | - Jamie H Warner
- Walker Department of Mechanical Engineering, The University of Texas at Austin, 204 East Dean Keeton Street, Austin, TX, 78712, USA
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Kalosakas G, Lathiotakis NN, Papagelis K. Width Dependent Elastic Properties of Graphene Nanoribbons. MATERIALS 2021; 14:ma14175042. [PMID: 34501132 PMCID: PMC8433791 DOI: 10.3390/ma14175042] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 08/27/2021] [Accepted: 08/30/2021] [Indexed: 11/23/2022]
Abstract
The mechanical response of graphene nanoribbons under uniaxial tension, as well as its dependence on the nanoribbon width, is presented by means of numerical simulations. Both armchair and zigzag edged graphene nanoribbons are considered. We discuss results obtained through two different theoretical approaches, viz. density functional methods and molecular dynamics atomistic simulations using empirical force fields especially designed to describe interactions within graphene sheets. Apart from the stress-strain curves, we calculate several elastic parameters, such as the Young’s modulus, the third-order elastic modulus, the intrinsic strength, the fracture strain, and the Poisson’s ratio versus strain, presenting their variation with the width of the nanoribbon.
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Affiliation(s)
- George Kalosakas
- Materials Science Department, University of Patras, GR-26504 Rio, Greece
- Correspondence: ; Tel.: +30-2610-996310
| | - Nektarios N. Lathiotakis
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens, Greece;
| | - Konstantinos Papagelis
- School of Physics, Department of Solid State Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece;
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Graphene Oxides Derivatives Prepared by an Electrochemical Approach: Correlation between Structure and Properties. NANOMATERIALS 2020; 10:nano10122532. [PMID: 33348545 PMCID: PMC7766825 DOI: 10.3390/nano10122532] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Revised: 12/14/2020] [Accepted: 12/15/2020] [Indexed: 01/04/2023]
Abstract
Graphene oxide (GO) can be defined as a single monolayer of graphite with oxygen-containing functionalities such as epoxides, alcohols, and carboxylic acids. It is an interesting alternative to graphene for many applications due to its exceptional properties and feasibility of functionalization. In this study, electrochemically exfoliated graphene oxides (EGOs) with different amounts of surface groups, hence level of oxidation, were prepared by an electrochemical two-stage approach using graphite as raw material. A complete characterization of the EGOs was carried out in order to correlate their surface topography, interlayer spacing, defect content, and specific surface area (SSA) with their electrical, thermal, and mechanical properties. It has been found that the SSA has a direct relationship with the d-spacing. The EGOs electrical resistance decreases with increasing SSA while rises with increasing the D/G band intensity ratio in the Raman spectra, hence the defect content. Their thermal stability under both nitrogen and dry air atmospheres depends on both their oxidation level and defect content. Their macroscopic mechanical properties, namely the Young’s modulus and tensile strength, are influenced by the defect content, while no correlation was found with their SSA or interlayer spacing. Young moduli values as high as 54 GPa have been measured, which corroborates that the developed method preserves the integrity of the graphene flakes. Understanding the structure-property relationships in these materials is useful for the design of modified GOs with controllable morphologies and properties for a wide range of applications in electrical/electronic devices.
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Hillebrand M, Many Manda B, Kalosakas G, Gerlach E, Skokos C. Chaotic dynamics of graphene and graphene nanoribbons. CHAOS (WOODBURY, N.Y.) 2020; 30:063150. [PMID: 32611115 DOI: 10.1063/5.0007761] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Accepted: 06/06/2020] [Indexed: 06/11/2023]
Abstract
We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically calculating the maximum Lyapunov exponent, we quantify the chaoticity for a spectrum of energies in both systems. We find that for all cases, the chaotic strength increases with the energy density and that the onset of chaos in graphene is slow, becoming evident after more than 104 natural oscillations of the system. For the GNRs, we also investigate the impact of the width and chirality (armchair or zigzag edges) on their chaotic behavior. Our results suggest that due to the free edges, the chaoticity of GNRs is stronger than the periodic graphene sheet and decreases by increasing width, tending asymptotically to the bulk value. In addition, the chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same width. Furthermore, we show that the composition of 12C and 13C carbon isotopes in graphene has a minor impact on its chaotic strength.
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Affiliation(s)
- M Hillebrand
- Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa
| | - B Many Manda
- Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa
| | - G Kalosakas
- Department of Materials Science, University of Patras, GR-26504 Rio, Greece
| | - E Gerlach
- Lohrmann Observatory, Technische Universität Dresden, D-01062 Dresden, Germany
| | - Ch Skokos
- Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa
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Naumis GG, Barraza-Lopez S, Oliva-Leyva M, Terrones H. Electronic and optical properties of strained graphene and other strained 2D materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:096501. [PMID: 28540862 DOI: 10.1088/1361-6633/aa74ef] [Citation(s) in RCA: 116] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.
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Affiliation(s)
- Gerardo G Naumis
- Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Mexico City 01000, Mexico
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Xia X, Hao J, Wang Y, Zhong Z, Weng GJ. Theory of electrical conductivity and dielectric permittivity of highly aligned graphene-based nanocomposites. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:205702. [PMID: 28337974 DOI: 10.1088/1361-648x/aa68ec] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Highly aligned graphene-based nanocomposites are of great interest due to their excellent electrical properties along the aligned direction. Graphene fillers in these composites are not necessarily perfectly aligned, but their orientations are highly confined to a certain angle, [Formula: see text] with 90° giving rise to the randomly oriented state and 0° to the perfectly aligned one. Recent experiments have shown that electrical conductivity and dielectric permittivity of highly aligned graphene-polymer nanocomposites are strongly dependent on this distribution angle, but at present no theory seems to exist to address this issue. In this work we present a new effective-medium theory that is derived from the underlying physical process including the effects of graphene orientation, filler loading, aspect ratio, percolation threshold, interfacial tunneling, and Maxwell-Wagner-Sillars polarization, to determine these two properties. The theory is formulated in the context of preferred orientational average. We highlight this new theory with an application to rGO/epoxy nanocomposites, and demonstrate that the calculated in-plane and out-of-plane conductivity and permittivity are in agreement with the experimental data as the range of graphene orientations changes from the randomly oriented to the highly aligned state. We also show that the percolation thresholds of highly aligned graphene nanocomposites are in general different along the planar and the normal directions, but they converge into a single one when the statistical distribution of graphene fillers is spherically symmetric.
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Affiliation(s)
- Xiaodong Xia
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, People's Republic of China. Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903, United States of America
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Oliva-Leyva M, Wang C. Low-energy theory for strained graphene: an approach up to second-order in the strain tensor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:165301. [PMID: 28300043 DOI: 10.1088/1361-648x/aa62c9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
An analytical study of low-energy electronic excited states in uniformly strained graphene is carried out up to second-order in the strain tensor. We report a new effective Dirac Hamiltonian with an anisotropic Fermi velocity tensor, which reveals the graphene trigonal symmetry being absent in first-order low-energy theories. In particular, we demonstrate the dependence of the Dirac-cone elliptical deformation on the stretching direction with respect to graphene lattice orientation. We further analytically calculate the optical conductivity tensor of strained graphene and its transmittance for a linearly polarized light with normal incidence. Finally, the obtained analytical expression of the Dirac point shift allows a better determination and understanding of pseudomagnetic fields induced by nonuniform strains.
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Affiliation(s)
- Maurice Oliva-Leyva
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de Mexico, Apartado Postal 70-360, 04510 Mexico City, Mexico
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Numerical Investigation of the Fracture Mechanism of Defective Graphene Sheets. MATERIALS 2017; 10:ma10020164. [PMID: 28772525 PMCID: PMC5459152 DOI: 10.3390/ma10020164] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 01/26/2017] [Accepted: 02/08/2017] [Indexed: 11/24/2022]
Abstract
Despite the unique occurrences of structural defects in graphene synthesis, the fracture mechanism of a defective graphene sheet has not been fully understood due to the complexities of the defects. In this study, the fracture mechanism of the monolayer graphene with four common types of defects (single vacancy defect, divacancy defect, Stone–Wales defect and line vacancy defect) were investigated systematically for mechanical loading along armchair and zigzag directions, by using the finite element method. The results demonstrated that all four types of defects could cause significant fracture strength loss in graphene sheet compared with the pristine one. In addition, the results revealed that the stress concentration occurred at the carbon–carbon bonds along the same direction as the displacement loading due to the deficiency or twist of carbon–carbon bonds, resulting in the breaking of the initial crack point in the graphene sheet. The fracture of the graphene sheet was developed following the direction of the breaking of carbon–carbon bonds, which was opposite to that of the displacement loading.
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In situfast polymerization of graphene nanosheets-filled poly(methyl methacrylate) nanocomposites. J Appl Polym Sci 2016. [DOI: 10.1002/app.43423] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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