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Mechanical properties of Graphene
Graphene-two dimensional carbon based material is under a lot of research these days due to its extraordinary mechanical, electronical, and thermal properites. Understanding the mechanical properties such as tensile, shear, compression, and bending properites are very important because it has the crucial role for the potential applications of graphene. Recently, graphen is showed the strongest material under tension test, even stronger than the diamond and carbon nanotube. It is also important to investigate graphene is still the strongest under shear, compression or bending. In this letter, I will describe the anomalous thermal expansion coeffcient which affects the mechanical properties and other mechanical properties available online. In addition, to investige the various properties, such as size, temperature or chirality effect, several different results using different potentials, methods are compared to give researchers better references to compare those each other.
Thermal Expansion Coefficient
There are several studies about the anomalous thermal properties of graphene using several methods, which is the negative thermal expansion coefficient (TEC). DFT simulation shows graphene has the negative TEC in the temperature range of 0~2500K, and Monte carlo (MC) based LCBOPII potential shows that graphene has the negative TEC before 900K and it becomes positive after that. There is also experiment result available using scanning electron microscope (SEM) showing the similar behavior of TEC. It is very important to understand the effect of TEC for the mechanical properties, because it would be the key factor to determine the mechanical properties under the certain temperature range. Comparions with different published data is given in the below figure.
| TEC [K^-1] | Method/Condition |
|---|---|
| -4.8 * 10^-6 in the range of 0~300K | Monte Carlo simulation [24] |
| around -7*10^-6~3*10^-6 | Experiment, SEM [25] |
| around -4*10^-6 ~ -1*10^-6 | Density Functional Theory [26] |
Uniaxial Tension Properties
| Young's Modulus [TPa] | Fracture Stress [GPa] | Method/Condition/Materials |
|---|---|---|
| 0.5 | Experiment [1] graphene sheet<5 layers | |
| 1.02±0.03 | Experiment [3]static test of bulk graphite | |
| 0.25±0.15 | Experiment [2] tip-induced deformation test of graphene | |
| 1.0±0.1 | 130±10 | Experiment [4] monolayer graphene |
| 1.06 | ab inito [5] graphene | |
| 1.11 | all-electron ab inito method [8] graphene | |
| 0.89 | h got from electron-density contour-plot value | |
| 1.24±0.01 | DFT-LDA, DFT-GGA method [6] | |
| 1.05 | 110/121 | DFT-LDA [9] 0K |
| 118-121 | ab initio [7] | |
| 1.026 | MD simulattion with REBO potential [10] graphite 300 | |
| 0.720/0.710 | 83/93 | MD simulation with REBO potential [14]graphene |
| 0.997 | Brenner potential [11] graphene | |
| 0.972 | Tersoff [12] | |
| 0.945 | Molecular Mechanics finite element method [15] graphene | |
| 1.06 | Molecular Mechanics theory [16] graphite |
Since graphene approved to be the strongest material in the world under tension test, it is very important to know and understand the young's modulus and fracture stress variation under diverse conditions such as different temperatures, sizes, and methods. Furthermore, it is also very important to investigate the mechanical properties under various conditions when considering the applications of graphene. Since the experiment has the limitation under diverse conditions, there are several simulation method depending on the accuracy, cost and conditions. Most reliable result would be ab initio method but it is the most expensive method, people prefer using other classical molecular dynamics (MD) or empirical potential based Tight binding (TB) to study further. There are always issues for the simulation for the different conditions on the properties, it is crucial to understand the simulation method and use it properly for the specific conditions.
Shear Test properties
| Shear Modulus [TPa] | Method/Condition |
|---|---|
| 0.321(Zigzag) 0.228(Armchair) | Molecular Mechanics Methods [17] |
| 0.208~0.213 | AMBER/Morse model based truss-type analytical modesl [18] |
| 0.408 | Density functional theory [19] |
| 0.358 | Molecular Dynamics w/ AMBER force field [20] |
| 0.49 at 900K | Monte Carlo simulation [21] |
There are several results for the shear modulus for the graphene. The values are ranging between 0.208 and 0.49 under various simulations. Further research through experiments should be done for the comparions and accuracies. In addition, it is also important to know the fracture values under shear or torsion. —Preceding unsigned comment added by 98.212.158.245 (talk) 05:29, 20 November 2009 (UTC)
In the tension test case, we have available experiment data to compare it to the simulation and verify the results. However, for the shear properties case, we do not have the experiment result yet, so it is important to have other similar materials such as graphite and single walled carbon nanotube (SWNT). The table is in the below for the comparisons.
| Shear Modulus [TPa] | Fracture Stress [GPa] | Method/Condition/Materials |
|---|---|---|
| 0.44±0.3 | Graphite, Experiment [27] | |
| ~0.5 | CNT, Structural mechanics analysis [28] | |
| 0.45 | CNT, Empirical lattice dynamics model [29] | |
| 0.41 | CNT, Experiment using SEM [30] | |
| 0.34 | 25 | CNT, MD with Brenner's 2nd generation [31] |
Other mechanical properties
1. Compression test
Since the single layer of graphene is very thin film like mateirlal, it is very weak-easily buckled under compression force. It is shown that [22] the critical compression load for graphene is 3.75 nN for zigzag, and 2.8nN for armchair using molecular dynamics simulation. There are not many published data availble due to its weakness under compression.
2. Bending test
There are two results available for the temperature dependent bending rigidity of graphene. Using molecular dynamics simulation[23], it is proved that bending rigidity decreases as temperature increases due to the effect of the thermal fluctuation. However, using atomistic Monte Carlo simulation[24], the result is opposite - increasing bending rigidity with increasing temperature. The further study should be done to resolve this issue.
References
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[2] Cristina Gomez-Navarro, Marko Burghard, and Klaus Kern, “Elastic Properties of Chemically Derived Single Graphene Sheets”, Nano letters 8(7) 2045-2049 (2008).
[3] O. L. Blakslee, D. G. Proctor, E. J. Seldin, G. B. Spence, and T. Weng, “Elastic Constants of Compression-Annealed Pyrolytic Graphite “, Journal of Applied Physics 41(8) 3373-3382 (1970).
[4] Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, and James Hone, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene”, Science 321 (18) 385-388 (2008).
[5] Daniel Snchez-Portal, Emilio Artacho, and Jos M. Soler, “Ab initio structural, elastic, and vibrational properties of carbon nanotubes”, Physical Review B 59(19) 12678-12688 (1999).
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[7] Roopam Khare, Steven L. Mielke, Jeffrey T. Paci, Sulin Zhang, Roberto Ballarini, George C. Schatz,and Ted Belytschko, “ Coupled quantum Mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets”, Physical Review B 75 075412 (2007).
[8] Gregory Van Lier, Christian Van Alsenoy, Vic Van Doren, and Paul Geerlings, “As initio study of the elastic properties of single-walled carbon nanotubes and graphene”, Chemical Physics Letters 326 181-185 (2000).
[9] Fang Liu, Pingbing Ming, and Ju Li, “Ab initio calculation of ideal strength and phonon instability of graphene under tension”, Physical Review B 76 064120 (2007).
[10] WenXing Bao, ChangChun Zhu, and WanZhao Cui, “Simulation of Young’s modulus of single-walled carbon nanotubes by molecular dynamics”, Physica B 352 156-163 (2004).
[11] H. Jiang, Y. Huang, and K. C. Hwang, “A Finite-Temperature Continuum Theory Based on Interatomic Potentials”, Journal of Engineering Materials and Technology 127 408-416 (2005).
[12] Nachiket R. Raravikar, Pawel Keblinski, Apparao M. Rao, Mildred S. Dresselhaus, Linda S. Schadler, and Pulickel M. Ajayan, “Temperature dependence of radial breathing mode Raman frequency of single-walled carbon nanotubes”,Physical Review B 66, 235424 (2002)
[13] J. Tersoff, “Empirical interatomic potential for silicon with improved elastic properties”, Physical Review B 38, 9902 (1988).
[14] ZhiPing Xu, “Graphene nano-ribbon under tension”, http://arxiv.org/abs/0709.0992,arXiv [1] (United States), (2007).
[15] Michele Meo, Marco Rossi, “Prediction of Young’s modulus of single wall carbon nanotubes by molecular-mechanics basesd finite element modelling”, Journal of Composites Science and Technology 66 1597-1605 (2006).
[16] Tienchong Chang, Huajian Gao, “Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model”, Journal of the Mechanics and Physics of Solids 51(6) 1059-1074 (2003).
[17] Sakhaee-Pour, A, ""Elastic properties of single-layered graphene sheet"", Solid State Communications, v. 149, iss. 1-2, p. 91-95 (2009)
[18] F Scarpa et al, "Effective elastic mechanical properties of single layer graphene sheets", 2009 Nanotechnology 20 065709 (11pp)
[19] Ricardo Faccio et al, "Mechanical properties of graphene nanoribbons", 2009 J. Phys.: Condens. Matter 21 285304 (7pp)
[20] Jia-Lin Tsai et al, "Characterizing mechanical properties of graphite using molecular dynamics simulation", Materials and Design 31 (2009) 194?199
[21] K. V. Zakharchenko et al, "Finite temperature lattice properties of graphene beyond the quasiharmonic approximation", Phys. Rev. Lett. 102, 046808 (2009)
[22] Yuanwen GAo, Peng Hao, "Mechanical properties of monolayer graphene under tensile and compressive loading", Physica E 41 (2009) 1561–1566
[23] P. Liu et al, "Temperature dependent bending rigidity of graphene", APL 94, 2331912(2009)
[24] A. Fasolino, J. H. Los & M. I. Katsnelson, "Intrinsic ripples in graphene", Nature Materials 6, 858 - 861 (2007)