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Research Papers

Mechanics of a Graphene Flake Driven by the Stiffness Jump on a Graphene Substrate

[+] Author and Article Information
Hong Gao

Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: ghgygs@126.com

Hongwei Zhang

State Key Laboratory of Ocean Engineering,
School of Naval Architecture, Ocean and
Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hwzhang@sjtu.edu.cn

Zhengrong Guo

Shanghai Key Laboratory of Mechanics
in Energy Engineering,
Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: zrguo@shu.edu.cn

Tienchong Chang

Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: tchang@staff.shu.edu.cn

Li-Qun Chen

Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai University,
Shanghai 200072, China
e-mail: lqchen@staff.shu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 10, 2017; final manuscript received May 28, 2017; published online June 15, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(8), 081007 (Jun 15, 2017) (6 pages) Paper No: JAM-17-1194; doi: 10.1115/1.4036938 History: Received April 10, 2017; Revised May 28, 2017

Intrinsic driving mechanism is of particular significance to nanoscale mass delivery and device design. Stiffness gradient-driven directional motion, i.e., nanodurotaxis, provides an intrinsic driving mechanism, but an in-depth understanding of the driving force is still required. Based on molecular dynamics (MD) simulations, here we investigate the motion behavior of a graphene flake on a graphene substrate with a stiffness jump. The effects of the temperature and the stiffness configuration on the driving force are discussed in detail. We show that the driving force is almost totally contributed by the unbalanced edge force and increases with the temperature and the stiffness difference but decreases with the stiffness level. We demonstrate in particular that the shuttle behavior of the flake between two stiffness jumps on the substrate can be controlled by the working temperature and stiffness configuration of the system, and the shuttle frequency can be well predicted by an analytical model. These findings may have general implications for the design of nanodevices driven by stiffness jumps.

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References

Figures

Grahic Jump Location
Fig. 1

A graphene flake on the substrate with a stiffness jump. (a) Configuration of a 9.869 nm long (z-direction) and 6.319 nm wide (x-direction) graphene flake on a graphene substrate with a length of 29.883 nm and a width of 6.319 nm. (b) Atoms of the substrate are anchored on two different types of springs, forming a stiffness difference in the middle of the substrate.

Grahic Jump Location
Fig. 2

Displacements (solid lines) and velocities (dotted lines) of the flake on the substrate with a stiffness jump of 0.160|3.204 N/m

Grahic Jump Location
Fig. 3

Shuttling behavior of the graphene flake on the substrate with alternate softer and harder (0.160|3.204 N/m) regions at different temperatures. The displacement of the flake is measured from the center of the hard region of the substrate.

Grahic Jump Location
Fig. 4

Distribution of the interlayer shear force (in the z-direction) on each ring of the flake. The rings 1–4 and 44–47 are the edge rings used to calculate edge forces. The rings 1–4 are in contact with the soft region, while the rings 44–47 are in contact with the hard region of the substrate.

Grahic Jump Location
Fig. 5

Effect of the system temperature on the interlayer forces. The magnitudes of all forces (the driving force Fd, the unbalanced edge force Fue, the edge force from the soft side of the substrate Fes, and the edge force from the hard side of the substrate Feh) increase linearly with temperature.

Grahic Jump Location
Fig. 6

Effect of the substrate stiffness on the interlayer forces: (a) the stiffness of the harder region is 3.204 N/m, (b) the hard-to-soft stiffness ratio is chosen as 10, and (c) the stiffness difference between the soft and hard regions is kept 1.602 N/m

Grahic Jump Location
Fig. 7

Shuttling behavior of the graphene flake at 300 K: (a) the stiffness of the harder region is 3.204 N/m, (b) the hard-to-soft stiffness ratio is chosen as 10, and (c) the stiffness difference between the soft and hard regions is kept 1.602 N/m. The displacement of the flake is measured from the center of the hard region of the substrate.

Grahic Jump Location
Fig. 8

Shuttle frequency of the graphene flake. (a) Temperature effect. The stiffness jump is set as 0.160|3.204 N/m. (b) Stiffness effect. Triangles: the stiffness of the harder region is 3.204 N/m; circles: the hard-to-soft stiffness ratio is chosen as 10; and squares: the stiffness difference between the soft and hard regions is kept 1.602 N/m.

Grahic Jump Location
Fig. 9

Theoretical predictions for the shuttling frequency of the flake, corresponding to the simulation cases shown in Fig. 8

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