Molecular Dynamics Study on Mechanical Responses of Circular Graphene Nanoflake under Nanoindentation
Graphene, a single-atom sheet, has been considered as
the most promising material for making future nanoelectromechanical
systems as well as purely electrical switching with graphene
transistors. Graphene-based devices have advantages in scaled-up
device fabrication due to the recent progress in large area graphene
growth and lithographic patterning of graphene nanostructures. Here
we investigated its mechanical responses of circular graphene
nanoflake under the nanoindentation using classical molecular
dynamics simulations. A correlation between the load and the
indentation depth was constructed. The nanoindented force in this
work was applied to the center point of the circular graphene nanoflake
and then, the resonance frequency could be tuned by a nanoindented
depth. We found the hardening or the softening of the graphene
nanoflake during its nanoindented-deflections, and such properties
were recognized by the shift of the resonance frequency. The
calculated mechanical parameters in the force-vs-deflection plot were
in good agreement with previous experimental and theoretical works.
This proposed schematics can detect the pressure via the deflection
change or/and the resonance frequency shift, and also have great
potential for versatile applications in nanoelectromechanical systems.
[1] G. I. Giannopoulos, I. A. Liosatos, and A. K. Moukanidis,” Parametric
study of elastic mechanical properties of graphene nanoribbons by a new
structural mechanics approach,” Physica E, vol. 44, pp. 124–134, Oct.
2011.
[2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson,
I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas
of massless Dirac fermions in graphene,” Nature, vol. 438, pp. 197–200,
Nov.2005.
[3] I. W. Frank, D. M. Tanenbaum, A. M. van der Zande, P. L. McEuen,
“Mechanical properties of suspended graphene sheets,” Journal of
Vacuum Science Technology B, vol. 25, pp. 2558–2561, Nov./Dec.2007.
[4] V. Sazonova, Y. Yaish, H. Üstünel, D. Roundy, T. A. Arias, and P. L.
McEuen, “A tunable carbon nanotube electromechanical oscillator,”
Nature, vol. 431, pp. 284–287, Sep. 2004.
[5] J. S. Bunch, A. M. van der Zande, S. S. Verbridge, I. W. Frank, D. M.
Tanenbaum, J. M. Parpia, H. G. Craighead, and P. L. McEuen,
“Electromechanical resonators from graphene sheets,” Science, vol. 315,
pp. 490–493, Jan. 2007.
[6] O. K. Kwon, J. H. Lee, K.-S. Kim, and J. W. Kang, “Developing
ultrasensitive pressure sensor based on graphene nanoribbon: Molecular
dynamics simulation” Physica E, vol. 47, pp. 6–11, Jan. 2013.
[7] F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I.
Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules
adsorbed on graphene,” Nature Mater., vol. 6, pp. 652–655, July 2007.
[8] C. Y. Wang, K. Mylvaganam, and L. C. Zhang, “Wrinkling of monolayer
graphene: A study by molecular dynamics and continuum plate theory,”
Phys. Rev. B, vol. 80, pp. 155445, Oct. 2009.
[9] S. Jun, T. Taxhi, and H. S. Park, “Size-Dependence of the Nonlinear
Elastic Softening of Nanoscale Graphene Monolayers Under Plane-Strain
Bulge Tests,” J. Nanomater., vol. 2001, pp. 380286, 2011.
[10] V. Sorkin and Y. W. Zhang, “Graphene-based pressure nano-sensors,” J.
Mol. Mater., vol. 17, pp. 2825–2830, 2011.
[11] M. Poot and H. S. J. van der Zant, “Nanomechanical properties of
few-layer graphene membranes,” Appl. Phys. Lett., vol. 92, pp. 063111,
Feb. 2008.
[12] C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L.
Stormer, T. F. Heinz, and J. Hone, “Performance of Monolayer Graphene
Nanomechanical Resonators with Electrical Readout,” Nature
Nanotechnol., vol. 4, pp. 861–867, Sep. 2009.
[13] K. M. Milaninia, M. A. Baldo, A. Reina, and J. Kong, “All graphene
electromechanical switch fabricated by chemical vapor deposition,” Appl.
Phys. Lett., vol. 95, pp. 183105, Nov. 2009.
[14] J. Tersoff, Phys. Rev. B, “Modeling solid-state chemistry: Interatomic
potentials for multicomponent systems,” vol. 39, pp. 5566–5568, March
1989.
[15] D. W. Brenner, “Empirical potential for hydrocarbons for use in
simulating the chemical vapor deposition of diamond films,” Phys. Rev. B,
vol. 42, pp. 9458–9471, Nov. 1990.
[16] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic
properties and intrinsic strength of monolayer graphene,” Science, vol.
321, pp. 385–388, (2008).
[17] K. T. Wan, S. Guo, and D. A. Dillard, “A theoretical and numerical study
of a thin clamped circular film under an external load in the presence of a
tensile residual stress,” Thin Solid Films, vol. 425, pp. 150–162, Feb.
2003.
[18] U. Komaragiri and M. R. Begley, “The Mechanical Response of
Freestanding Circular Elastic Films Under Point and Pressure Loads,” J.
Appl. Mech., vol. 72, pp. 203–212, Mar. 2005.
[19] E. Cadelano, P. L. Palla, S. Giordano, and L. Colombo, “Nonlinear
elasticity of monolayer graphene,” Phys. Rev. Lett., vol. 102, pp. 235502,
June 2009.
[20] J. Zhou and R. Huang, “Internal lattice relaxation of single-layer graphene
under in-plane deformation,” J. Mech. Phys. Solids, vol. 56, pp.
1609-1623, Apr. 2008.
[21] M. Arroyo and T. Belytschko, “Finite crystal elasticity of carbon
nanotubes based on the exponential Cauchy-Born rule,” Phys. Rev. B, vol.
69, pp. 115415, Mar. 2004.
[22] N. M. Bhatia and W. Nachbar, “Finite indentation of an elastic membrane
by a spherical indenter,” Int. J. Non-Linear Mech., vol. 3, pp. 307–324,
Sep. 1968.
[23] O. K. Kwon, G.-Y. Lee, H. J. Hwang, and J. W. Kang, “Molecular
dynamics modeling and simulations to understand gate-tunable
graphene-nanoribbon-resonator,” Physica E, vol. 45, pp. 194–200, Aug.
2012.
[24] O. K. Kwon, J. H. Lee, J. Park, K.-S. Kim, and J. W. Kang, “Molecular
dynamics simulation study on graphene-nanoribbon-resonators tuned by
adjusting axial strain,” Curr. Appl. Phys., vol. 13, pp. 360–365, Mar.
2013.
[25] A. Isacsson, “Nanomechanical displacement detection using coherent
transport in graphene nanoribbon resonators,” Phys. Rev. B, vol. 84, pp.
125452, Sep. 2011.
[26] S. K. Georgantzinos, G. I. Giannopoulos, D. E. Katsareas, P. A. Kakavas,
and N. K. Anifantis, “Size-dependent non-linear mechanical properties of
graphene nanoribbons,” Computat. Mater. Sci., vol. 50, pp. 2057–2062,
May 2011.
[27] S. K. Georgantzinos, D. E. Katsareas, and N. K. Anifantis, “Graphene
characterization: A fully non-linear spring-based finite element
prediction,” Physica E, vol. 43, pp. 1833–1839, Aug. 2011.
[28] H. Bu, Y. Chen, M. Zou, H. Yia, K. Bi, and Z. Ni, “Atomistic simulations
of mechanical properties of graphene nanoribbons,” Phys. Lett. A, vol.
373, pp. 3359–3362, Sep. 2009.
[29] H. Zhao, K. Min, and N. R. Aluru, “Size and Chirality Dependent Elastic
Properties of Graphene Nanoribbons under Uniaxial Tension” Nano Lett.,
vol. 9, pp. 3012–3015, Aug. 2009.
[30] J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M.
Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable Atomic
Membranes from Graphene Sheets” Nano Lett., vol. 8, pp. 2458–2462,
Aug. 2008.
[31] W. H. Duan and C. M. Wang, “Nonlinear bending and stretching of a
circular graphene sheet under a central point load,” Nanotechnology, vol.
20, pp. 075702, Feb. 2009.
[32] S. Shivaraman, R. A. Barton, X. Yu, J. Alden, L. Herman, M. V. S.
Chandrashekhar, J. Park, P. L. McEuen, J. M. Par-pia, H. G. Craighead,
and M. G. Spencer, “Free-Standing Epitaxial Graphene,” Nano Lett., vol.
9, pp. 3100–3105, Sep. 2009.
[33] F. Traversi, F. J. Gúzman-Vázquez, L. G. Rizzi, V. Russo, C. S. Casari, C.
Gómez-Navarro, and R. Sordan, “Elastic properties of graphene
suspended on a polymer substrate by e-beam exposure,” New J. Phys., vol.
12, pp. 023034, Feb. 2010.
[34] J. Atalaya, A. Isacsson, and J. M. Kinaret, “Continuum Elastic Modeling
of Graphene Resonators,” Nano Letters, vol. 8, pp. 4196–4200, Oct.
2008.
[1] G. I. Giannopoulos, I. A. Liosatos, and A. K. Moukanidis,” Parametric
study of elastic mechanical properties of graphene nanoribbons by a new
structural mechanics approach,” Physica E, vol. 44, pp. 124–134, Oct.
2011.
[2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson,
I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas
of massless Dirac fermions in graphene,” Nature, vol. 438, pp. 197–200,
Nov.2005.
[3] I. W. Frank, D. M. Tanenbaum, A. M. van der Zande, P. L. McEuen,
“Mechanical properties of suspended graphene sheets,” Journal of
Vacuum Science Technology B, vol. 25, pp. 2558–2561, Nov./Dec.2007.
[4] V. Sazonova, Y. Yaish, H. Üstünel, D. Roundy, T. A. Arias, and P. L.
McEuen, “A tunable carbon nanotube electromechanical oscillator,”
Nature, vol. 431, pp. 284–287, Sep. 2004.
[5] J. S. Bunch, A. M. van der Zande, S. S. Verbridge, I. W. Frank, D. M.
Tanenbaum, J. M. Parpia, H. G. Craighead, and P. L. McEuen,
“Electromechanical resonators from graphene sheets,” Science, vol. 315,
pp. 490–493, Jan. 2007.
[6] O. K. Kwon, J. H. Lee, K.-S. Kim, and J. W. Kang, “Developing
ultrasensitive pressure sensor based on graphene nanoribbon: Molecular
dynamics simulation” Physica E, vol. 47, pp. 6–11, Jan. 2013.
[7] F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I.
Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules
adsorbed on graphene,” Nature Mater., vol. 6, pp. 652–655, July 2007.
[8] C. Y. Wang, K. Mylvaganam, and L. C. Zhang, “Wrinkling of monolayer
graphene: A study by molecular dynamics and continuum plate theory,”
Phys. Rev. B, vol. 80, pp. 155445, Oct. 2009.
[9] S. Jun, T. Taxhi, and H. S. Park, “Size-Dependence of the Nonlinear
Elastic Softening of Nanoscale Graphene Monolayers Under Plane-Strain
Bulge Tests,” J. Nanomater., vol. 2001, pp. 380286, 2011.
[10] V. Sorkin and Y. W. Zhang, “Graphene-based pressure nano-sensors,” J.
Mol. Mater., vol. 17, pp. 2825–2830, 2011.
[11] M. Poot and H. S. J. van der Zant, “Nanomechanical properties of
few-layer graphene membranes,” Appl. Phys. Lett., vol. 92, pp. 063111,
Feb. 2008.
[12] C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L.
Stormer, T. F. Heinz, and J. Hone, “Performance of Monolayer Graphene
Nanomechanical Resonators with Electrical Readout,” Nature
Nanotechnol., vol. 4, pp. 861–867, Sep. 2009.
[13] K. M. Milaninia, M. A. Baldo, A. Reina, and J. Kong, “All graphene
electromechanical switch fabricated by chemical vapor deposition,” Appl.
Phys. Lett., vol. 95, pp. 183105, Nov. 2009.
[14] J. Tersoff, Phys. Rev. B, “Modeling solid-state chemistry: Interatomic
potentials for multicomponent systems,” vol. 39, pp. 5566–5568, March
1989.
[15] D. W. Brenner, “Empirical potential for hydrocarbons for use in
simulating the chemical vapor deposition of diamond films,” Phys. Rev. B,
vol. 42, pp. 9458–9471, Nov. 1990.
[16] C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic
properties and intrinsic strength of monolayer graphene,” Science, vol.
321, pp. 385–388, (2008).
[17] K. T. Wan, S. Guo, and D. A. Dillard, “A theoretical and numerical study
of a thin clamped circular film under an external load in the presence of a
tensile residual stress,” Thin Solid Films, vol. 425, pp. 150–162, Feb.
2003.
[18] U. Komaragiri and M. R. Begley, “The Mechanical Response of
Freestanding Circular Elastic Films Under Point and Pressure Loads,” J.
Appl. Mech., vol. 72, pp. 203–212, Mar. 2005.
[19] E. Cadelano, P. L. Palla, S. Giordano, and L. Colombo, “Nonlinear
elasticity of monolayer graphene,” Phys. Rev. Lett., vol. 102, pp. 235502,
June 2009.
[20] J. Zhou and R. Huang, “Internal lattice relaxation of single-layer graphene
under in-plane deformation,” J. Mech. Phys. Solids, vol. 56, pp.
1609-1623, Apr. 2008.
[21] M. Arroyo and T. Belytschko, “Finite crystal elasticity of carbon
nanotubes based on the exponential Cauchy-Born rule,” Phys. Rev. B, vol.
69, pp. 115415, Mar. 2004.
[22] N. M. Bhatia and W. Nachbar, “Finite indentation of an elastic membrane
by a spherical indenter,” Int. J. Non-Linear Mech., vol. 3, pp. 307–324,
Sep. 1968.
[23] O. K. Kwon, G.-Y. Lee, H. J. Hwang, and J. W. Kang, “Molecular
dynamics modeling and simulations to understand gate-tunable
graphene-nanoribbon-resonator,” Physica E, vol. 45, pp. 194–200, Aug.
2012.
[24] O. K. Kwon, J. H. Lee, J. Park, K.-S. Kim, and J. W. Kang, “Molecular
dynamics simulation study on graphene-nanoribbon-resonators tuned by
adjusting axial strain,” Curr. Appl. Phys., vol. 13, pp. 360–365, Mar.
2013.
[25] A. Isacsson, “Nanomechanical displacement detection using coherent
transport in graphene nanoribbon resonators,” Phys. Rev. B, vol. 84, pp.
125452, Sep. 2011.
[26] S. K. Georgantzinos, G. I. Giannopoulos, D. E. Katsareas, P. A. Kakavas,
and N. K. Anifantis, “Size-dependent non-linear mechanical properties of
graphene nanoribbons,” Computat. Mater. Sci., vol. 50, pp. 2057–2062,
May 2011.
[27] S. K. Georgantzinos, D. E. Katsareas, and N. K. Anifantis, “Graphene
characterization: A fully non-linear spring-based finite element
prediction,” Physica E, vol. 43, pp. 1833–1839, Aug. 2011.
[28] H. Bu, Y. Chen, M. Zou, H. Yia, K. Bi, and Z. Ni, “Atomistic simulations
of mechanical properties of graphene nanoribbons,” Phys. Lett. A, vol.
373, pp. 3359–3362, Sep. 2009.
[29] H. Zhao, K. Min, and N. R. Aluru, “Size and Chirality Dependent Elastic
Properties of Graphene Nanoribbons under Uniaxial Tension” Nano Lett.,
vol. 9, pp. 3012–3015, Aug. 2009.
[30] J. S. Bunch, S. S. Verbridge, J. S. Alden, A. M. van der Zande, J. M.
Parpia, H. G. Craighead, and P. L. McEuen, “Impermeable Atomic
Membranes from Graphene Sheets” Nano Lett., vol. 8, pp. 2458–2462,
Aug. 2008.
[31] W. H. Duan and C. M. Wang, “Nonlinear bending and stretching of a
circular graphene sheet under a central point load,” Nanotechnology, vol.
20, pp. 075702, Feb. 2009.
[32] S. Shivaraman, R. A. Barton, X. Yu, J. Alden, L. Herman, M. V. S.
Chandrashekhar, J. Park, P. L. McEuen, J. M. Par-pia, H. G. Craighead,
and M. G. Spencer, “Free-Standing Epitaxial Graphene,” Nano Lett., vol.
9, pp. 3100–3105, Sep. 2009.
[33] F. Traversi, F. J. Gúzman-Vázquez, L. G. Rizzi, V. Russo, C. S. Casari, C.
Gómez-Navarro, and R. Sordan, “Elastic properties of graphene
suspended on a polymer substrate by e-beam exposure,” New J. Phys., vol.
12, pp. 023034, Feb. 2010.
[34] J. Atalaya, A. Isacsson, and J. M. Kinaret, “Continuum Elastic Modeling
of Graphene Resonators,” Nano Letters, vol. 8, pp. 4196–4200, Oct.
2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:71300", author = "Jeong-Won Kang", title = "Molecular Dynamics Study on Mechanical Responses of Circular Graphene Nanoflake under Nanoindentation", abstract = "Graphene, a single-atom sheet, has been considered as
the most promising material for making future nanoelectromechanical
systems as well as purely electrical switching with graphene
transistors. Graphene-based devices have advantages in scaled-up
device fabrication due to the recent progress in large area graphene
growth and lithographic patterning of graphene nanostructures. Here
we investigated its mechanical responses of circular graphene
nanoflake under the nanoindentation using classical molecular
dynamics simulations. A correlation between the load and the
indentation depth was constructed. The nanoindented force in this
work was applied to the center point of the circular graphene nanoflake
and then, the resonance frequency could be tuned by a nanoindented
depth. We found the hardening or the softening of the graphene
nanoflake during its nanoindented-deflections, and such properties
were recognized by the shift of the resonance frequency. The
calculated mechanical parameters in the force-vs-deflection plot were
in good agreement with previous experimental and theoretical works.
This proposed schematics can detect the pressure via the deflection
change or/and the resonance frequency shift, and also have great
potential for versatile applications in nanoelectromechanical systems.", keywords = "Graphene, pressure sensor, circular graphene
nanoflake, molecular dynamics.", volume = "9", number = "9", pages = "561-5", }