Mechanical characterization of nanoindented graphene via molecular dynamics simulations
© Fang et al; licensee Springer. 2011
Received: 16 January 2011
Accepted: 3 August 2011
Published: 3 August 2011
The mechanical behavior of graphene under various indentation depths, velocities, and temperatures is studied using molecular dynamics analysis. The results show that the load, elastic and plastic energies, and relaxation force increased with increasing indentation depth and velocity. Nanoindentation induced pile ups and corrugations of the graphene. Resistance to deformation decreased at higher temperature. Strong adhesion caused topological defects and vacancies during the unloading process.
Graphene has received a lot of attention due to its good mechanical and electromagnetic properties [1–3], including a zero electron bandgap, a high electron emission rate, and elastic scattering [4–6]. Atomic-scale graphene can be fabricated using micro-mechanical chop crack , thermal expansion , and extension growth  techniques. Studies [10–13] have found that the band-field effect of a 10-nm-thick graphene sheet is similar to that of a small (less than 1.2 nm in diameter) nanographite particle.
Novoselov and Geim  used graphene to fabricate a small crystal tube. Monolayer graphene is considered a suitable material for investigating two-dimensional quantization phenomena, such as temperature-trigger plasma , quantization absorption spectrum , and the fractional quantum Hall effect . In addition, the hexagonal symmetric structure of graphene makes it a candidate material for nano devices.
Many studies [17–25] have focused on the chemical functionalization of graphene, especially on the effect of absorbed atoms on the electronic and chemical properties of graphene. However, the mechanical properties of graphene under indentation, which are important for developing sensors, resonators, and impermeable membranes, have yet to be investigated.
In this study, the effects of nanoindentation depth and velocity on the mechanical properties and contact behavior of graphene at various temperatures are investigated using molecular dynamics (MD) simulations. Adhesion, relaxation, defects, and deformation are discussed.
The Lennard-Jones potential function is employed to describe the interaction between the diamond tip and the graphene atoms. The Tersoff empirical potential energy function  is generally used to simulate the interaction between graphene carbon atoms.
Results and discussion
The tip then indented the graphene. The absorptive force gradually turns into a repulsive force. As the indentation depth increased, the stress wave spread out farther from the center, inducing ripples and corrugations. Figure 2b shows the tip at its maximum indentation depth. During the subsequent packing stage, the substrate releases the indentation-induced energy, as shown in Figure 2c. Finally, the tip moves up at a constant velocity (the same as that used for the indentation). Some substrate atoms beneath the tip move up during the unloading process to create a peak, as shown in Figure 2d.
The affected area, load, elastic and plastic energies, and relaxation force increased with increasing indentation depth.
Nanoindentation-induced pile ups and corrugations of graphene were observed. Strong adhesion causes topological defects and vacancies.
The average contact stiffnesses of the graphene at temperatures of 0, 200, 300, and 400 K are 58.7, 58.1, 49.48, and 36.6 N/m, respectively.
At higher temperature, the kinetic energy among atoms increases, which weakens covalent bonds and thus decreases resistance to deformation. The load, elastic and plastic energies, and relaxation force decrease with increasing temperature.
With a fast indentation, the graphene has insufficient time to respond, which leads to a high load, elastic and plastic energies, and relaxation force.
The authors would like to thank the National Science Council of Taiwan for financially supporting this research under grant NSC 96-2628-E-151-004-MY3.
- Lijima S: Helical microtubules of graphitic carbon. Nature 1991, 354: 56. 10.1038/354056a0View ArticleGoogle Scholar
- Kong J, Chapline MG, Dai H: Functionalized carbon nanotubes for molecular hydrogen sensors. Adv Mater 2001, 13: 1384. 10.1002/1521-4095(200109)13:18<1384::AID-ADMA1384>3.0.CO;2-8View ArticleGoogle Scholar
- Wu J, Pisula W, Müllen K: Graphenes as potential material for electronics. Chem Rev 2007, 107: 718. 10.1021/cr068010rView ArticleGoogle Scholar
- Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, Dubonos SV, Firsov AA: Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438: 197. 10.1038/nature04233View ArticleGoogle Scholar
- Zhang Y, Tan YW, Stormer HL, Kim P: Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005, 438: 201. 10.1038/nature04235View ArticleGoogle Scholar
- Novoselov KS, Jiang D, Schedin F, Booth TJ, Khotkevich VV, Morozov SV, Geim AK: Two-dimensional atomic crystals. Proc Natl Acad Sci USA 2005, 102: 10451. 10.1073/pnas.0502848102View ArticleGoogle Scholar
- Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Firsov AA: Electric field effect in atomically thin carbon films. Science 2004, 306: 666. 10.1126/science.1102896View ArticleGoogle Scholar
- Schnoepp HC, Li JL, McAllister MJ, Sai M, Herrera-Alonso H, Adamson DH, Prud Homme RK, Car R, Saville DA, Aksay IA: Functionalized single graphene sheets derived from splitting graphite oxide. J Phys Chem B 2007, 110: 8535.View ArticleGoogle Scholar
- Berger C, Song Z, Li T, Li X, Ogbazghi AY, Feng R, Dai Z, Marchenkov AN, Conrad EH, First TN, de Heer WA: Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J Phys Chem B 2004, 108: 19912. 10.1021/jp040650fView ArticleGoogle Scholar
- Tersoff J: Empirical interatomic potential for carbon, with applications to amorphous carbon. Phys Rev Lett 1988, 61: 2879. 10.1103/PhysRevLett.61.2879View ArticleGoogle Scholar
- Hölscher H, Ebeling D, Schwarz UD: Friction at atomic-scale surface steps: experiment and theory. Phys Rev Lett 2008, 101: 246105.View ArticleGoogle Scholar
- Wang X, Ouyang Y, Li X, Wang H, Guo J, Dai H: Room-temperature all-semiconducting sub-10-nm graphene nanoribbon field-effect transistors. Phys Rev Lett 2008, 100: 206803.View ArticleGoogle Scholar
- Ponomarenko LA, Schedin F, Katsnelson MI, Yang R, Hill EW, Novoselov KS, Geim AK: Chaotic dirac billiard in graphene quantum dots. Science 2008, 320: 356. 10.1126/science.1154663View ArticleGoogle Scholar
- Shyu FL, Lin MF: Plasmons and optical properties of semimetal graphite. J Phys Soc Jpn 2000, 69: 3781. 10.1143/JPSJ.69.3781View ArticleGoogle Scholar
- Sadowski ML, Martinez G, Potemski M, Berger C, de Heer WA: Landau level spectroscopy of ultrathin graphite layers. Phys Rev Lett 2006, 97: 266405.View ArticleGoogle Scholar
- Zang Y, Tan YW, Stormer HL, Kim P: Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005, 438: 201. 10.1038/nature04235View ArticleGoogle Scholar
- Boukhvalov DW, Katsnelson MI: Chemical functionalization of grapheme. J Phys Condens Matter 2009, 21: 344250.View ArticleGoogle Scholar
- Boukhvalov DW, Katsnelson MI: Chemical functionalization of graphene with defects. Nano Lett 2008, 8: 4373. 10.1021/nl802234nView ArticleGoogle Scholar
- Ou Yang F, Huang B, Li Z, Xiao J, Wang H, Xu H: Chemical functionalization of graphene nanoribbons by carboxyl groups on Stone-Wales defects. J Phys Chem C 2008, 112: 12003. 10.1021/jp710547xView ArticleGoogle Scholar
- Kudin KN: Zigzag graphene nanoribbons with saturated edges. ACS Nano 2008, 2: 516. 10.1021/nn700229vView ArticleGoogle Scholar
- Li Y, Ding F, Yakobson BI: Hydrogen storage by spillover on graphene as a phase nucleation process. Phys Rev B 2008, 78: 041402.Google Scholar
- Roman T, Dino WA, Nakanishi H, Kasai H, Sugimoto T, Tange K: Hydrogen pairing on graphene. Carbon 2007, 45: 218. 10.1016/j.carbon.2006.09.027View ArticleGoogle Scholar
- Ramanathan T, Abdala AA, Stankovich S, Dikin DA, Herrera-Alonso M, Piner RD, Adamson DH, Schniepp HC, Chen X, Ruoff RS, Nguyen ST, Aksay IA, Prud'homme RK, Brinson LC: Functionalized graphene sheets for polymer nanocomposites. Nature Nanotechnology 2008, 3: 327. 10.1038/nnano.2008.96View ArticleGoogle Scholar
- Duplock EJ, Scheffler M, Lindan PJD: Hallmark of perfect graphene. Phys Rev Lett 2004, 92: 225502.View ArticleGoogle Scholar
- Boukhvalov DW, Katsnelson MI, Lichtenstein AI: Hydrogen on graphene: electronic structure. total energy, structural distortions and magnetism from first-principles calculations. Phys Rev B 2008, 77: 035427.View ArticleGoogle Scholar
- We CD, Fang TH, Chan CY: A molecular dynamics simulation of the mechanical characteristics of a C 60 -filled carbon nanotube under nanoindentation using various carbon nanotube tips. Carbon 2011, 49: 2053. 10.1016/j.carbon.2011.01.034View ArticleGoogle Scholar
- Lee GD, Wang CZ, Yoon E, Hwang NM, Kim DY, Ho KM: Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers. Phys Rev Lett 2005, 95: 205501.View ArticleGoogle Scholar
- Kudin KN, Ozbas B, Schniepp HC, Prud'homme RK, Aksay IA, Car R: Raman spectra of graphite oxide and functionalized graphene sheets. Nano Lett 2008, 8: 36. 10.1021/nl071822yView ArticleGoogle Scholar
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