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Stretch-induced softening of bending rigidity in graphene
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10.1063/1.4716024
/content/aip/journal/apl/100/19/10.1063/1.4716024
http://aip.metastore.ingenta.com/content/aip/journal/apl/100/19/10.1063/1.4716024
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Deformation in a unit cell of graphene. (a) The four-atom unit cell used in stress-strain calculations. Three parameters, , , and , are used to describe the deformation. Variations of the parameters as the unit cell is (b) stretched equibiaxially, or uniaxially in the (c) armchair or (d) zigzag directions.

Image of FIG. 2.
FIG. 2.

Schematic of stretching and rolling of graphene sheets: (a) stretching in the armchair direction and rolling about the armchair and zigzag directions; (b) stretching in the zigzag direction and rolling about the armchair and zigzag directions; and (c) equibiaxial stretching and rolling about the armchair and zigzag directions.

Image of FIG. 3.
FIG. 3.

Stretch induced softening of bending resistance in graphene. (a) Strain energy density profiles for nanotubes made of pre-stretched graphene sheets against the inverse square of the tube radius. The solid and open squares are DFT results for and when , while the solid and open triangles are DFT results for and when . The corresponding lines are linear fittings whose slope is equal to half of the bending stiffness. (b) The bending stiffnesses of graphene and as a function of the tube radius when (c-e) The bending stiffness of graphene as a function of the stretching strain. For , the stiffness-strain relation can be approximated by a linear function , where  nN · nm,  nN · nm,  nN · nm,  nN · nm,  nN · nm, and  nN · nm. (f) Comparison between the bending stiffness of graphene obtained from DFT (red) calculations and that from bond orbital theory with (black) and (blue) scaling laws.

Image of FIG. 4.
FIG. 4.

The equilibrium structures of (a) zigzag and (b) armchair CNS subjected to axial stretching at strain levels of . The blue atoms are carbon and yellow ones are hydrogen. (c) Mean surface energy of armchair and zigzag CNSs as a function of the corresponding axial stretching strain. Inset shows a schematic of stacking between two graphene layers where atom C in the upper layer projects onto position C’ within the lower layer. (d) Variation ofthe dimensionless parameter with strain as graphene is stretched in the armchair (red) and zigzag (black) directions.

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/content/aip/journal/apl/100/19/10.1063/1.4716024
2012-05-10
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stretch-induced softening of bending rigidity in graphene
http://aip.metastore.ingenta.com/content/aip/journal/apl/100/19/10.1063/1.4716024
10.1063/1.4716024
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