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. 2016 Jan 7;9(1):32.
doi: 10.3390/ma9010032.

Buckling Behavior of Substrate Supported Graphene Sheets

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Free PMC article

Buckling Behavior of Substrate Supported Graphene Sheets

Kuijian Yang et al. Materials (Basel). .
Free PMC article

Abstract

The buckling of graphene sheets on substrates can significantly degrade their performance in materials and devices. Therefore, a systematic investigation on the buckling behavior of monolayer graphene sheet/substrate systems is carried out in this paper by both molecular mechanics simulations and theoretical analysis. From 70 simulation cases of simple-supported graphene sheets with different sizes under uniaxial compression, two different buckling modes are investigated and revealed to be dominated by the graphene size. Especially, for graphene sheets with length larger than 3 nm and width larger than 1.1 nm, the buckling mode depends only on the length/width ratio. Besides, it is revealed that the existence of graphene substrate can increase the critical buckling stress and strain to 4.39 N/m and 1.58%, respectively, which are about 10 times those for free-standing graphene sheets. Moreover, for graphene sheets with common size (longer than 20 nm), both theoretical and simulation results show that the critical buckling stress and strain are dominated only by the adhesive interactions with substrate and independent of the graphene size. Results in this work provide valuable insight and guidelines for the design and application of graphene-derived materials and nano-electromechanical systems.

Keywords: buckling; energy method; graphene; molecular mechanics; nano-electromechanical system.

Conflict of interest statement

Kuijian Yang, Shengtao Wang and Qijun Liu conducted all of the simulations and prepared the figures; Fei Pan and Yong Ma developed the theoretical model to explain the results; Yuli Chen supervised the study and wrote the manuscript. All authors reviewed the manuscript.

Figures

Figure 1
Figure 1
Sketch of a graphene sheet subjected to the compressive force F on an infinite large graphene substrate: (a) top view; and (b) side view.
Figure 1
Figure 1
Sketch of a graphene sheet subjected to the compressive force F on an infinite large graphene substrate: (a) top view; and (b) side view.
Figure 2
Figure 2
The compressive stress versus normalized displacement of the monolayer graphene sheet supported by a graphene substrate.
Figure 3
Figure 3
Configurations of the graphene sheet at points A–F of the curve in Figure 2. (a) Δux/l = 1.37%; (b) Δux/l = 2.00%; (c) Δux/l = 3.71%; (d) Δux/l = 24.09%; (e) Δux/l = 50.89%; (f) Δux/l = 50.93%.
Figure 4
Figure 4
The compressive stress versus normalized displacement of the narrow monolayer graphene sheet supported by a graphene substrate.
Figure 5
Figure 5
Configurations of the graphene sheet at points A–E of the curve in Figure 4. (a) Δux/l = 1.85%; (b) Δux/l = 2.59%; (c) Δux/l = 23.72%; (d) Δux/l = 44.00%; (e) Δux/l = 44.11%.
Figure 6
Figure 6
The buckling modes of monolayer graphene sheets with different sizes under uniaxial compression.
Figure 7
Figure 7
The critical buckling stress versus length of the monolayer graphene sheets with different sizes on a graphene substrate.
Figure 8
Figure 8
The critical buckling strain versus width of the monolayer graphene sheets with different sizes on a graphene substrate.
Figure 9
Figure 9
The effect of substrate adhesion on the critical buckling strain. The typical substrate materials are marked by stars.

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