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Effect of Intrinsic Ripples on Elasticity of the Graphene Monolayer.

Lee S - Nanoscale Res Lett (2015)

Bottom Line: The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening.This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene.The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical, Robotics and Energy Engineering, Dongguk University-Seoul, Seoul, 100715, Korea. sjunlee@dongguk.edu.

ABSTRACT
The effect of intrinsic ripples on the mechanical response of the graphene monolayer is investigated under uniaxial loading using molecular dynamics (MD) simulations with a focus on nonlinear behavior at a small strain. The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening. For a small strain, entropic contribution is dominant due to intrinsic ripples, leading to elasticity softening. As the ripples flatten at increasing strain, the energetic term due to C-C bonds stretching competes with the entropic contribution, followed by energetic dominant deformation. Elasticity softening is enhanced at increased temperature as the ripple amplitude increases. The study shows that the intrinsic ripple of graphene affects elasticity. This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene. The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.

No MeSH data available.


Related in: MedlinePlus

Variation of intrinsic ripple amplitudes of a monolayer graphene as a function of temperature obtained with the REBO potential (black squares) and with the Tersoff potential (red triangles)
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Fig10: Variation of intrinsic ripple amplitudes of a monolayer graphene as a function of temperature obtained with the REBO potential (black squares) and with the Tersoff potential (red triangles)

Mentions: Figure 9a shows the temperature-dependent elasticity calculated from the 2D and 3D MD simulations. For 3D simulations, the initial and maximum values of the tangent modulus are selectively shown. For 2D simulations, the initial and maximum values are the same since elasticity decreases through the entire strain range. For 2D simulations, the elasticity does not change significantly with varying temperature since there is no rippling effect. The slightly decreasing elasticity in 2D is due to the thermal effect on the C–C bond stretching. The decreasing slope is larger for the Tersoff potential (blue open squares) than for the REBO potential (black squares). In 3D simulations, for the REBO and Tersoff potential, both the maximum and initial elasticity decrease almost linearly as the temperature increases. This reduction follows the tendency of increasing out-of-plane displacements shown in Fig. 10, showing a linear increase depending on temperature. The decreasing slope of the Tersoff potential is larger than that of the REBO potential, suggesting that the Tersoff potential is more sensitive to change in temperature. For the Tersoff potential, at 200 K, the maximum and initial elasticity are the same due to the continuous decrease in the tangent modulus as shown in Fig. 8d. These differences between REBO and Tersoff can be explained by change in ripple amplitudes shown in Fig. 10. For the Tersoff potential, the ripple amplitudes increase more sharply than for the REBO potential. In addition, the ripple amplitudes are lower in the low-temperature ranges, resulting in weaker elasticity softening than the REBO potential.Fig. 9


Effect of Intrinsic Ripples on Elasticity of the Graphene Monolayer.

Lee S - Nanoscale Res Lett (2015)

Variation of intrinsic ripple amplitudes of a monolayer graphene as a function of temperature obtained with the REBO potential (black squares) and with the Tersoff potential (red triangles)
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4621976&req=5

Fig10: Variation of intrinsic ripple amplitudes of a monolayer graphene as a function of temperature obtained with the REBO potential (black squares) and with the Tersoff potential (red triangles)
Mentions: Figure 9a shows the temperature-dependent elasticity calculated from the 2D and 3D MD simulations. For 3D simulations, the initial and maximum values of the tangent modulus are selectively shown. For 2D simulations, the initial and maximum values are the same since elasticity decreases through the entire strain range. For 2D simulations, the elasticity does not change significantly with varying temperature since there is no rippling effect. The slightly decreasing elasticity in 2D is due to the thermal effect on the C–C bond stretching. The decreasing slope is larger for the Tersoff potential (blue open squares) than for the REBO potential (black squares). In 3D simulations, for the REBO and Tersoff potential, both the maximum and initial elasticity decrease almost linearly as the temperature increases. This reduction follows the tendency of increasing out-of-plane displacements shown in Fig. 10, showing a linear increase depending on temperature. The decreasing slope of the Tersoff potential is larger than that of the REBO potential, suggesting that the Tersoff potential is more sensitive to change in temperature. For the Tersoff potential, at 200 K, the maximum and initial elasticity are the same due to the continuous decrease in the tangent modulus as shown in Fig. 8d. These differences between REBO and Tersoff can be explained by change in ripple amplitudes shown in Fig. 10. For the Tersoff potential, the ripple amplitudes increase more sharply than for the REBO potential. In addition, the ripple amplitudes are lower in the low-temperature ranges, resulting in weaker elasticity softening than the REBO potential.Fig. 9

Bottom Line: The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening.This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene.The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical, Robotics and Energy Engineering, Dongguk University-Seoul, Seoul, 100715, Korea. sjunlee@dongguk.edu.

ABSTRACT
The effect of intrinsic ripples on the mechanical response of the graphene monolayer is investigated under uniaxial loading using molecular dynamics (MD) simulations with a focus on nonlinear behavior at a small strain. The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening. For a small strain, entropic contribution is dominant due to intrinsic ripples, leading to elasticity softening. As the ripples flatten at increasing strain, the energetic term due to C-C bonds stretching competes with the entropic contribution, followed by energetic dominant deformation. Elasticity softening is enhanced at increased temperature as the ripple amplitude increases. The study shows that the intrinsic ripple of graphene affects elasticity. This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene. The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.

No MeSH data available.


Related in: MedlinePlus