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.

References

1.
Serey
,
X.
,
Mandal
,
S.
,
Chen
,
Y.
, and
Erickson
,
D.
,
2012
, “
DNA Transport and Delivery in Thermal Gradients Near Optofluidic Resonators
,”
Phys. Rev. Lett.
,
108
(
4
), p.
048102
.
2.
Barreiro
,
A.
,
Rurali
,
R.
,
Hernandez
,
E.
,
Moser
,
J.
,
Pichler
,
T.
,
Forro
,
L.
, and
Bachtold
,
A.
,
2008
, “
Subnanometer Motion of Cargoes Driven by Thermal Gradients Along Carbon Nanotubes
,”
Science
,
320
(
5877
), pp.
775
778
.
3.
Huang
,
Y.
,
Zhu
,
S.
, and
Li
,
T.
,
2014
, “
Directional Transport of Molecular Mass on Graphene by Straining
,”
Extreme Mech. Lett.
,
1
, pp.
83
89
.
4.
Burdick
,
J.
,
Laocharoensuk
,
R.
,
Wheat
,
P.
,
Posner
,
J.
, and
Wang
,
J.
,
2008
, “
Synthetic Nanomotors in Microchannel Networks: Directional Microchip Motion and Controlled Manipulation of Cargo
,”
J. Am. Chem. Soc.
,
130
(
26
), pp.
8164
8165
.
5.
Huck
,
W.
,
2008
, “
Responsive Polymers for Nanoscale Actuation
,”
Mater. Today
,
11
(
7–8
), pp.
24
32
.
6.
Ebbens
,
S.
, and
Howse
,
J.
,
2010
, “
In Pursuit of Propulsion at the Nanoscale
,”
Soft Matter
,
6
(
4
), pp.
726
738
.
7.
Chang
,
T.
,
Zhang
,
H.
,
Guo
,
Z.
,
Guo
,
X.
, and
Gao
,
H.
,
2015
, “
Nanoscale Directional Motion Towards Regions of Stiffness
,”
Phys. Rev. Lett.
,
114
(
1
), p.
015504
.
8.
Wang
,
J.
, and
Manesh
,
K.
,
2010
, “
Motion Control at the Nanoscale
,”
Small
,
6
(
3
), pp.
338
345
.
9.
Browne
,
W.
, and
Feringa
,
B.
,
2006
, “
Making Molecular Machines Work
,”
Nat. Nanotechnol.
,
1
(
1
), pp.
25
35
.
10.
Pop
,
E.
,
2010
, “
Energy Dissipation and Transport in Nanoscale Devices
,”
Nano Res.
,
3
(
3
), pp.
147
169
.
11.
Leng
,
J.
,
Guo
,
Z.
,
Zhang
,
H.
,
Chang
,
T.
,
Guo
,
X.
, and
Gao
,
H.
,
2016
, “
Negative Thermophoresis in Concentric Carbon Nanotube Nanodevices
,”
Nano Lett.
,
16
(
10
), pp.
6396
6402
.
12.
Kudernac
,
T.
,
Ruangsupapichat
,
N.
,
Parschau
,
M.
,
Macia
,
B.
,
Katsonis
,
N.
,
Harutyunyan
,
S.
,
Ernst
,
K.
, and
Feringa
,
B.
,
2011
, “
Electrically Driven Directional Motion of A Four-Wheeled Molecule on a Metal Surface
,”
Nature
,
479
(
7372
), pp.
208
211
.
13.
Ouakad
,
H.
, and
Younis
,
M.
,
2009
, “
Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators
,”
ASME J. Comput. Nonlinear Dyn.
,
5
(
1
), p.
011009
.
14.
Huang
,
T.
,
Flood
,
A.
,
Brough
,
B.
,
Liu
,
Y.
,
Bonvallet
,
P.
,
Kang
,
S.
,
Chu
,
C.
,
Guo
,
T.
,
Lu
,
W.
,
Yang
,
Y.
,
Stoddart
,
J.
, and
Ho
,
C.
,
2006
, “
Understanding and Harnessing Biomimetic Molecular Machines for NEMS Actuation Materials
,”
IEEE Trans. Autom. Sci. Eng.
,
3
(
3
), pp.
254
259
.
15.
David
,
R.
,
Jensen
,
B.
,
Black
,
J.
,
Burnett
,
S.
, and
Howell
,
L.
,
2010
, “
Modeling and Experimental Validation of DNA Motion in Uniform and Nonuniform DC Electric Fields
,”
ASME J. Nanotechnol. Eng. Med.
,
1
(
4
), p.
041007
.
16.
Fischer
,
P.
, and
Ghosh
,
A.
,
2011
, “
Magnetically Actuated Propulsion at Low Reynolds Numbers: Towards Nanoscale Control
,”
Nanoscale
,
3
(
2
), pp.
557
563
.
17.
Shaw
,
S.
, and
Murthy
,
P.
,
2010
, “
Magnetic Drug Targeting in the Permeable Blood Vessel—The Effect of Blood Rheology
,”
ASME J. Nanotechnol. Eng. Med.
,
1
(
2
), p.
021001
.
18.
Hernandez
,
S.
,
Bennett
,
C.
,
Junkermeier
,
C.
,
Tsoi
,
S.
,
Bezares
,
F.
,
Stine
,
R.
,
Robinson
,
J.
,
Lock
,
E.
,
Boris
,
D.
,
Pate
,
B.
,
Caldwell
,
J.
,
Reinecke
,
T.
,
Sheehan
,
P.
, and
Walton
,
S.
,
2013
, “
Chemical Gradients on Graphene to Drive Droplet Motion
,”
ACS Nano
,
7
(
6
), pp.
4746
4755
.
19.
Wang
,
W.
,
Duan
,
W.
,
Ahmed
,
S.
,
Mallouk
,
T.
, and
Sen
,
A.
,
2013
, “
Small Power: Autonomous Nano- and Micromotors Propelled by Self-Generated Gradients
,”
Nano Today
,
8
(
5
), pp.
531
554
.
20.
Guo
,
Z.
,
Chang
,
T.
,
Guo
,
X.
, and
Gao
,
H.
,
2012
, “
Mechanics of Thermophoretic and Thermally Induced Edge Forces in Carbon Nanotube Nanodevices
,”
J. Mech. Phys. Solids
,
60
(
9
), pp.
1676
1687
.
21.
Coluci
,
V.
,
Timoteo
,
V.
, and
Galvao
,
D.
,
2009
, “
Thermophoretically Driven Carbon Nanotube Oscillators
,”
Appl. Phys. Lett.
,
95
(
25
), p.
253103
.
22.
Becton
,
M.
, and
Wang
,
X.
,
2014
, “
Thermal Gradients on Graphene to Drive Nanoflake Motion
,”
J. Chem. Theory Comput.
,
10
(
2
), pp.
722
730
.
23.
Hou
,
Q.
,
Cao
,
B.
, and
Guo
,
Z.
,
2009
, “
Thermal Gradient Induced Actuation in Double-Walled Carbon Nanotubes
,”
Nanotechnology
,
20
(
49
), p.
495503
.
24.
Piazza
,
R.
,
2008
, “
Thermophoresis: Moving Particles With Thermal Gradients
,”
Soft Matter
,
4
(
9
), pp.
1740
1744
.
25.
Barnard
,
A.
,
2015
, “
Materials Science: Nanoscale Location Without Fuel
,”
Nature
,
519
(
7541
), pp.
37
38
.
26.
Lv
,
C.
,
Chen
,
C.
,
Chuang
,
Y.
,
Tseng
,
F.
,
Yin
,
Y.
,
Grey
,
F.
, and
Zheng
,
Q.
,
2014
, “
Substrate Curvature Gradient Drives Rapid Droplet Motion
,”
Phys. Rev. Lett.
,
113
(
2
), p.
026101
.
27.
Yin
,
Y.
,
Chen
,
C.
,
Lu
,
C.
, and
Zheng
,
Q.
,
2011
, “
Shape Gradient and Classical Gradient of Curvatures: Driving Forces on Micro/Nano Curved Surfaces
,”
Appl. Math. Mech.
,
32
(
5
), pp.
533
550
.
28.
Yang
,
J.
,
Yang
,
Z.
,
Chen
,
C.
, and
Yao
,
D.
,
2008
, “
Conversion of Surface Energy and Manipulation of a Single Droplet
,”
Langmuir
,
24
(
17
), pp.
9889
9897
.
29.
Dai
,
C.
,
Guo
,
Z.
,
Zhang
,
H.
, and
Chang
,
T.
,
2016
, “
Nanoscale Linear-to-Linear Motion Converter of Graphene
,”
Nanoscale
,
8
(
30
), pp.
14406
14410
.
30.
Ansari
,
R.
,
Gholami
,
R.
,
Shojaei
,
M.
,
Mohammadi
,
V.
, and
Sahmani
,
S.
,
2013
, “
Surface Stress Effect on the Vibrational Response of Circular Nanoplates With Various Edge Supports
,”
ASME J. Appl. Mech.
,
80
(
2
), p.
021021
.
31.
Becton
,
M.
, and
Wang
,
X.
,
2016
, “
Controlling Nanoflake Motion Using Stiffness Gradients on Hexagonal Boron Nitride
,”
RSC Adv.
,
6
(
56
), pp.
51205
51210
.
32.
Wang
,
C.
, and
Chen
,
S.
,
2015
, “
Motion Driven by Strain Gradient Fields
,”
Sci. Rep.
,
5
(
1
), p.
13675
.
33.
Guo
,
Y.
,
Guo
,
W.
, and
Chen
,
C.
,
2007
, “
Modifying Atomic-Scale Friction Between Two Graphene Sheets: A Molecular-Force-Field Study
,”
Phys. Rev. B
,
76
(
15
), p.
155429
.
34.
Zhang
,
H.
,
Guo
,
Z.
,
Gao
,
H.
, and
Chang
,
T.
,
2015
, “
Stiffness-Dependent Interlayer Friction of Graphene
,”
Carbon
,
94
, pp.
60
66
.
35.
Zheng
,
Q.
, and
Liu
,
Z.
,
2014
, “
Experimental Advances in Superlubricity
,”
Friction
,
2
(
2
), pp.
182
192
.
36.
Feng
,
X.
,
Kwon
,
S.
,
Park
,
J.
, and
Salmeron
,
M.
,
2013
, “
Superlubric Sliding of Graphene Nanoflakes on Graphene
,”
ACS Nano
,
7
(
2
), pp.
1718
1724
.
37.
Brenner
,
D.
,
Shenderova
,
O.
,
Harrison
,
J.
,
Stuart
,
S.
,
Ni
,
B.
, and
Sinnott
,
S.
,
2002
, “
A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbons
,”
J. Phys. Condens. Matter
,
14
(
4
), pp.
783
802
.
38.
Girifalco
,
L.
,
Hodak
,
M.
, and
Lee
,
R.
,
2000
, “
Carbon Nanotubes, Buckyballs, Ropes, and a Universal Graphitic Potential
,”
Phys. Rev. B
,
62
(
9
), pp.
13104
13110
.
39.
Guo
,
Z.
,
Chang
,
T.
,
Guo
,
X.
, and
Gao
,
H.
,
2011
, “
Thermal-Induced Edge Barriers and Forces in Interlayer Interaction of Concentric Carbon Nanotubes
,”
Phys. Rev. Lett.
,
107
(
10
), p.
105502
.
40.
Shi
,
M.
,
Kan
,
Q.
,
Sha
,
Z.
, and
Kang
,
G.
,
2015
, “
The Edge-Related Mechanical Properties of Fluorographene Nanoribbons
,”
ASME J. Appl. Mech.
,
82
(
4
), p.
041007
.
41.
Li
,
J.
,
Zhang
,
H.
,
Guo
,
Z.
,
Chang
,
T.
, and
Gao
,
H.
,
2015
, “
Edge Forces in Contacting Graphene Layers
,”
ASME J. Appl. Mech.
,
82
(
10
), p.
101011
.
42.
Zheng
,
Q.
, and
Jiang
,
Q.
,
2002
, “
Multiwalled Carbon Nanotubes as Gigahertz Oscillators
,”
Phys. Rev. Lett.
,
88
(
4
), p.
045503
.
43.
Luo
,
M.
,
Zhang
,
Z.
, and
Yakobson
,
B.
,
2013
, “
Tunable Gigahertz Oscillators of Gliding Incommensurate Bilayer Graphene Sheets
,”
ASME J. Appl. Mech.
,
80
(
4
), p.
040906
.
44.
Ansari
,
R.
, and
Sadeghi
,
F.
,
2012
, “
On the Oscillation Frequency of Ellipsoidal Fullerene–Carbon Nanotube Oscillators
,”
ASME J. Nanotechnol. Eng. Med.
,
3
(
1
), p.
011001
.
45.
Fang
,
H.
, and
Xu
,
J.
,
2013
, “
Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization
,”
ASME J. Appl. Mech.
,
81
(
5
), p.
051001
.
You do not currently have access to this content.