micromachines
Article
Interface Friction of Double-Walled Carbon
Nanotubes Investigated Using Molecular Dynamics †
Cheng-Da Wu 1 , Te-Hua Fang 2, * and Fu-Yung Tung 2
1
2
*
†
Department of Mechanical Engineering, Chung Yuan Christian University, 200, Chung Pei Rd.,
Chung Li District, Taoyuan 32023, Taiwan; [email protected]
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences,
Kaohsiung 807, Taiwan; [email protected]
Correspondence: [email protected]; Tel.: +886-7-381-4526 (ext. 5336)
This paper is an extended version of our paper presented in the IEEE 2016 International Conference on
Applied System Innovation (ICASI 2016), Okinawa, Japan, 26–30 May 2016.
Academic Editors: Teen-Hang Meen, Shoou-Jinn Chang, Stephen D. Prior and Artde Donald Kin-Tak Lam
Received: 17 February 2017; Accepted: 7 March 2017; Published: 9 March 2017
Abstract: The interface friction characteristics of double-walled carbon nanotubes (DWCNTs) are
studied using molecular dynamics simulations based on the Tersoff potential. The effects of the
DWCNT type, outer shell diameter, and temperature are evaluated. The simulation results show that
when an inner shell is being pulled out from a DWCNT, the friction force and normal force between
shells increase with increasing the outer shell diameter. The noise of the friction force significantly
increases with the increasing temperature. Zigzag@zigzag and armchair@armchair DWCNTs exhibit
larger friction forces and smaller normal forces compared to those of chiral@chiral DWCNTs.
Keywords: double-walled carbon nanotube; interface friction; friction coefficient; molecular dynamics
1. Introduction
Carbon nanotubes (CNTs) are an important class of carbon-based materials due to their excellent
physical properties, such as high mechanical strength, thermal conductivity, and electrical conductivity,
low density, and large specific area [1]. Due to these remarkable properties, CNTs have many
potential applications in micro-electromechanical systems (MEMS) [2], nano-electromechanical systems
(NEMS) [3], and strain sensors [4], and as an adsorbent of flue gases [5]. In addition, the low interaction
between adjacent shells of multiwalled carbon nanotubes (MWCNTs) due to van der Waals interactions
has inspired studies on CNT-based oscillators and resonators.
Due to the difficulty of manipulation at the nano scale, there have been few experimental studies
focusing on MWCNTs. Zhang et al. [6] investigated the interwall friction and sliding behavior of
centimeter-long DWCNTs. They found that the interwall friction had a linear dependence on the
pull-out velocity of an inner wall, and that the axial curvature of DWCNTs caused a significant increase
in the interwall friction. The interwall friction has been found to be independent of the pull-out
length [7]. Cumings et al. [8] and Akita et al. [9] observed that the pull-out force between nested walls
in MWCNTs reaches a maximum, plateaus, and then drops suddenly.
Molecular dynamics (MD) simulation is a powerful tool for studying material interactions.
Atomic simulation avoids experimental noise and turbulence problems, and can reduce cost.
Many nanosystems have been successfully analyzed using MD, such as nanowelding [10,11],
nanoforming [12], nanoextrusion [13], and nanotribology of metallic glasses [14]. Li et al. [15] studied
the sliding behavior between nested walls in MWCNTs using MD simulations. They found that the
pull-out force for MWCNTs is proportional to the diameter of the outer wall, and independent of
nanotube length and chirality. Xia et al. [16] modeled a pull-out process for DWCNTs by applying a
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that the pull-out force for MWCNTs is proportional to the diameter of the outer wall, and
independent of nanotube length and chirality. Xia et al. [16] modeled a pull-out process for
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DWCNTs
by applying a radial normal pressure on their outer wall and found that the pull-out force
for fractured ends was much larger than that for capped ends. Song and Zha [17] studied the effect
of
intertube
spacing
on the
behavior
of MWCNTs.
study revealed
that
a small ends
intertube
radial
normal
pressure
on sliding
their outer
wall and
found thatTheir
the pull-out
force for
fractured
was
spacing
provides
effective
channel
forSong
loadand
transfer
between
tubes,
of tube length
much larger
than an
that
for capped
ends.
Zha [17]
studied
the regardless
effect of intertube
spacingand
on
wall
number.
the sliding behavior of MWCNTs. Their study revealed that a small intertube spacing provides an
At present,
of the interfacial
tribology
of DWCNTs
with
various
geometric
effective
channelthe
for understanding
load transfer between
tubes, regardless
of tube
length and
wall
number.
characteristics
and
various environmental
temperatures
is still
very clear.
into
At present,
theatunderstanding
of the interfacial
tribology
of not
DWCNTs
withInvestigations
various geometric
this
are
required
for
the
development
of
nanoscale
resonators
and
oscillators,
particularly
based
on
characteristics and at various environmental temperatures is still not very clear. Investigations into this
CNTs
and
potentially
multilayer
graphene.
In
this
work,
MD
simulations
of
an
inner
shell
being
are required for the development of nanoscale resonators and oscillators, particularly based on CNTs
pulled
out from multilayer
a DWCNTgraphene.
are performed
towork,
analyze
the
interfacial of
friction
between
DWCNT
shells.
and potentially
In this
MD
simulations
an inner
shell being
pulled
out
The
effects
of
the
DWCNT
type,
outer
shell
diameter,
and
temperature
are
studied
in
terms
of
atomic
from a DWCNT are performed to analyze the interfacial friction between DWCNT shells. The effects
trajectories,
friction
normal
force.
of the DWCNT
type,force,
outerand
shell
diameter,
and temperature are studied in terms of atomic trajectories,
friction force, and normal force.
2. Methodology
2. Methodology
Figure 1 shows an MD physical model of a DWCNT. The model consists of an inner shell and
an outer
shell,
whoseanlengths
are both
30 nm.
layersThe
of atoms
the leftofend
of theshell
outer
shell
Figure
1 shows
MD physical
model
of aTwo
DWCNT.
modelon
consists
an inner
and
an
were
as whose
fixed layers
toare
support
the
whole
other
layers
atoms
toshell
the fixed
outer set
shell,
lengths
both 30
nm.
Two system.
layers ofTwo
atoms
on the
left of
end
of thenext
outer
were
layers
werelayers
set astoisothermal
atoms,
were
tolayers
ensureofthat
thenext
heattogenerated
duringwere
the
set as fixed
support the
wholewhich
system.
Twoused
other
atoms
the fixed layers
pull-out
process
is
dispersed
outside
the
analytical
region
(layers
of
Newtonian
atoms),
keeping
the
set as isothermal atoms, which were used to ensure that the heat generated during the pull-out process
temperature
in the layers
constant.region
The rest
of the
material was
set askeeping
layers the
of Newtonian
is dispersed outside
the analytical
(layers
of Newtonian
atoms),
temperatureatoms.
in the
Newtonian
atoms
here
whose
is described
by Newton’s
second lawatoms
of motion
layers constant.
The
restmean
of theatoms
material
was motion
set as layers
of Newtonian
atoms. Newtonian
here
without
velocity
scaling.
For
the
inner
shell,
the
order
of
layers
was
reversed
(layers
of
fixed,
mean atoms whose motion is described by Newton’s second law of motion without velocity scaling.
isothermal,
Newtonian
atoms
were
from its
rightofend).
order to analyze
the interfacial
For the innerand
shell,
the order of
layers
wasset
reversed
(layers
fixed,Inisothermal,
and Newtonian
atoms
friction
inner
and
of DWCNTs
duringfriction
a relative
motionthe
process,
the inner
were setbetween
from itsthe
right
end).
Inouter
ordershells
to analyze
the interfacial
between
inner and
outer
shell
moved byduring
its fixed
layers with
a constant
velocity
of 40
m/swas
along
the Y-direction.
total
shellswas
of DWCNTs
a relative
motion
process,
the inner
shell
moved
by its fixedAlayers
displacement
27.5 nmofwas
applied.
boundary
were
used
inwas
the applied.
model.
with a constantofvelocity
40 m/s
alongNo
the periodic
Y-direction.
A total conditions
displacement
of 27.5
nm
The
simulations
are performed
under
a constant
number
of The
atoms,
temperature,
and volume
(NTVa
No periodic
boundary
conditions
were
used in the
model.
simulations
are performed
under
ensemble).
constant number of atoms, temperature, and volume (NTV ensemble).
The
The Tersoff-Brenner many-body
many-body potential
potential function
function [18]
[18] was
was used to model the carbon-carbon
carbon-carbon
atom
interactions.
This
potential
takes
into
account
the
coordination
and
angular
dependence
atom interactions. This potential takes into account the coordination and angular dependence of
of the
the
atoms
atoms and
and is well-suited
well-suited to describing the intrashell covalent bonds. The
The long-range
long-range interactions
interactions of
of
carbon
were characterized
characterizedusing
usingthe
theLennard-Jones
Lennard-Jones
(12-6)
potential
cut-off
radius,
carbon were
(12-6)
potential
[19].[19].
TheThe
cut-off
radius,
time time
step,
step,
and temperature
the simulation
1.01nm,
1 fs,300
andK,300
K, respectively.
and temperature
in theinsimulation
were were
set at set
1.0at
nm,
fs, and
respectively.
Figure
Moleculardynamics
dynamics(MD)
(MD)
model
of double-walled
carbon
nanotubes
(DWCNTs).
The
Figure 1. Molecular
model
of double-walled
carbon
nanotubes
(DWCNTs).
The model
model
of anshell
inner
shell
and an
outer
shell,lengths
whose are
lengths
bothThe
30 nm.
The diameters
of
consistsconsists
of an inner
and
an outer
shell,
whose
both are
30 nm.
diameters
of the outer
the
inner
are2.4
2.73nm,
andrespectively.
2.4 nm, respectively.
andouter
innerand
shells
are shells
2.73 and
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3. Results
and
Discussion
3. Results
and
Discussion
Effect
of DWCNT
Type
3.1.3.1.
Effect
of DWCNT
Type
study
effectof ofthetheDWCNT
DWCNTtype,
type, zigzag@zigzag
zigzag@zigzag (31,0)@(22,0),
(31,0)@(22,0), zigzag@armchair
To To
study
thetheeffect
zigzag@armchair
(31,0)@(12,12),
armchair@armchair
(18,18)@(12,12),
and
chiral@chiral
were
(31,0)@(12,12), armchair@armchair (18,18)@(12,12), and chiral@chiral(20,15)@(14,10)
(20,15)@(14,10)DWCNTs
DWCNTs
were
used.
These
four
types
of DWCNT
have
approximate
outer
and
inner
shell
diameters
and
used.
These
four
types
of DWCNT
have
approximate
outer
and
inner
shell
diameters
ofof
2.42.4
and
1.71.7
nm,
nm,
respectively.
The
space
between
the
shells
is
about
0.35
nm.
Figure
2
shows
the
variation
of
the
respectively. The space between the shells is about 0.35 nm. Figure 2 shows the variation of the friction
friction
forcethe
between
shells
with
four of
types
of DWCNTs.
average
friction
force
force
between
shellsthe
with
time
fortime
the for
fourthe
types
DWCNTs.
The The
average
friction
force
and
and normal force were evaluated by summing the lateral forces and normal forces that the inner
normal force were evaluated by summing the lateral forces and normal forces that the inner shell atoms
shell atoms exerted on the outer shell atoms during the pull-out process, respectively. Both forces
exerted on the outer shell atoms during the pull-out process, respectively. Both forces were averaged
were averaged over a distance of 0.1 nm. The oscillation of the friction force curve decreased with
over a distance of 0.1 nm. The oscillation of the friction force curve decreased with the increasing time
the increasing time due to a decrease in the number of interacting atoms. The friction force curve
due to a decrease in the number of interacting atoms. The friction force curve oscillated with time due
oscillated with time due to a periodic stick-slip process [20]. The average friction forces were −2.3,
to a−1.7,
periodic
process
The zigzag@zigzag,
average friction zigzag@armchair,
forces were −2.3, −armchair@armchair,
1.7, −1.8, and −1.9 nN
−1.8,stick-slip
and −1.9
nN [20].
for the
andfor
thechiral@chiral
zigzag@zigzag,
zigzag@armchair,
armchair@armchair,
and
chiral@chiral
DWCNTs,
respectively;
DWCNTs, respectively; the average normal forces were 0.032, 0.023, 0.019, and 0.058
thenN,
average
normal
forces
were 0.032,and
0.023,
0.019, and 0.058 DWCNTs,
nN, respectively.
zigzag@zigzag
respectively. For
zigzag@zigzag
armchair@armchair
the innerFor
and
outer shells
andmeet
armchair@armchair
DWCNTs,
the
inner
and
outer
shells
meet
the
lattice
matching
the lattice matching requirement, i.e., there is commensurate contact between tworequirement,
graphene
i.e.,sheets
there is[7,21];
commensurate
between
two graphene
sheetsand
[7,21];
therefore,
they forces.
exhibit larger
therefore, contact
they exhibit
larger
friction forces
smaller
normal
The
friction
forces and smaller
normal
The zigzag@armchair
DWCNTs
have the smallestcontact.
average
zigzag@armchair
DWCNTs
have forces.
the smallest
average friction forces
due to incommensurate
friction
forces
due tothe
incommensurate
contact.
In other words,
the twoposition
surfaceswith
haverespect
no energetically
In other
words,
two surfaces have
no energetically
preferred
to one
another,position
and so they
slidetorelative
to eachand
other
low energy
[22].
Thean
preferred
with can
respect
one another,
sowith
theyan
canextremely
slide relative
to eachcost
other
with
chiral@chiral
DWCNTs
the largest normal
forces
due
to incommensurate
contact.
extremely
low energy
cost thus
[22]. have
The chiral@chiral
DWCNTs
thus
have
the largest normal
forcesWith
due to
increasing the pull-out
the friction
curves
in Figure
gradually
converge
fixed 2
incommensurate
contact.distance,
With increasing
the force
pull-out
distance,
the2friction
force
curves to
in aFigure
value
of
−1.6
nN.
This
is
due
to
the
effect
of
the
chirality
of
CNTs
on
the
friction
force
gradually
gradually converge to a fixed value of −1.6 nN. This is due to the effect of the chirality of CNTs on the
decreasing
with increasing
the pull-out
distance. the pull-out distance.
friction
force gradually
decreasing
with increasing
Figure
Variationofoffriction
frictionforce
forcebetween
between shells
shells with time
Figure
2. 2.
Variation
time for
for four
fourDWCNT
DWCNTtypes.
types.
Effect
of Outer
Shell
Diameter
3.2.3.2.
Effect
of Outer
Shell
Diameter
To study the effect of the outer shell diameter (D), three types of chiral@chiral DWCNTs,
To study the effect of the outer shell diameter (D), three types of chiral@chiral DWCNTs, namely
namely (22,18)@(14,10), (24,19)@(14,10), and (26,22)@(14,10), were used, corresponding to D values
(22,18)@(14,10), (24,19)@(14,10), and (26,22)@(14,10), were used, corresponding to D values of 2.73,
of 2.73, 2.93, and 3.26 nm, respectively. Figures 3 and 4 show the variations of the friction force and
2.93, and 3.26 nm, respectively. Figures 3 and 4 show the variations of the friction force and normal
normal force between the shells with time for the three D values. The average friction forces were
force between the shells with time for the three D values. The average friction forces were −2.29,
−2.29, −2.49, and −2.84 nN for D values of 2.73, 2.93, and 3.26 nm, respectively. The friction force and
−2.49,
andforce
−2.84
nN forwith
D values
of 2.73, 2.93,
anddue
3.26
respectively.
The friction
force and
normal
increased
the increasing
D value
to nm,
an increase
in the number
of interacting
normal
force
with reached
the increasing
D valueatdue
an increase
in then
the number
of interacting
atoms.
Theincreased
normal force
its maximum
thetobeginning
and
decreased
with the
atoms.
The
normal
force
reached
its
maximum
at
the
beginning
and
then
decreased
with
thewith
increasing
increasing time. Figure 5 shows the variation of the interaction energy between the shells
time
time.
Figure
5
shows
the
variation
of
the
interaction
energy
between
the
shells
with
time
for
the three
for the three D values. The interaction energy increased with the decreasing D value.
D values. The interaction energy increased with the decreasing D value.
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Figure
3.
Variation
of friction
friction force
force between
between shells with
with time for
for three outer
outer shell diameters.
diameters.
Figure 3.
3. Variation
Variation of
of
Figure
friction force
between shells
shells with time
time for three
three outer shell
shell diameters.
Figure 3. Variation of friction force between shells with time for three outer shell diameters.
Figure 4. Variation of normal force between shells with time for three outer shell diameters.
Figure
4.
of
force
between
shells
with
time
forthree
threeouter
outer
shell
diameters.
Figure
4. Variation
Variation
of normal
normal
force
between
for
three
outer
shell
diameters.
Figure
4. Variation
of normal
force
betweenshells
shellswith
with time
time for
shell
diameters.
Figure
5. Variation
of interaction
energywith
withtime
time for three
Figure
5. Variation
of interaction
energy
threeouter
outershell
shelldiameters.
diameters.
Figure 5. Variation of interaction energy with time for three outer shell diameters.
Figure 5. Variation of interaction energy with time for three outer shell diameters.
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3.3.
EffectofofTemperature
Temperature
3.3.
Effect
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studythe
theeffect
effectof
oftemperature,
temperature, three
300,
and
500500
K, K,
were
used.
ToTo
study
three temperatures,
temperatures,namely
namely150,
150,
300,
and
were
used.
3.3. Effect of Temperature
A
zigzag@zigzag
(31,0)@(22,0)
DWCNT
with
inner
and
outer
shell
diameters
of
1.75
and
2.47
nm,nm,
A zigzag@zigzag (31,0)@(22,0) DWCNT with inner and outer shell diameters of 1.75 and 2.47
respectively,
wasused
used
the
simulation. With
increasing
temperature,
the
shell
To study
the
effect
of simulation.
temperature,
three the
temperatures,
150, 300,
and
500surfaces
K,
werebecame
used.
respectively,
was
ininthe
With
the
increasingnamely
temperature,
the
shell
surfaces
became
more
corrugated due
to an increase
in the
kinetic
energy
of the
atoms.
The of
corrugation
height
A
zigzag@zigzag
(31,0)@(22,0)
DWCNT
with
inner
and
outer
shell
diameters
1.75
and
2.47
nm, is is
more corrugated due to an increase in the kinetic energy of the atoms. The corrugation height
defined
as the difference
in the
diameter ofWith
a given
CNT. The temperature,
corrugation height
varied
in the
range
respectively,
was used
thediameter
simulation.
theCNT.
increasing
the shell
surfaces
became
defined
as the difference
ininthe
of a given
The corrugation height
varied
in the
range of
of 0.24–0.27
nm for the
surface
when
the energy
temperature
increased
from 150height
to 500isK,
more corrugated
dueouter
to an shell
increase
in the
kinetic
of the was
atoms.
The corrugation
0.24–0.27 nm for the outer shell surface when the temperature was increased from 150 to 500 K, and
anddefined
that forasthe
shellinwas
in the range
of 0.1–0.16
nm.corrugation
Figure 6 shows
variation
of the
the inner
difference
the diameter
of a given
CNT. The
height the
varied
in the range
that for the inner shell was in the range of 0.1–0.16 nm. Figure 6 shows the variation of the friction
friction
force
with
time
for
the
three
temperatures.
The
noise
of
the
friction
force
significantly
of 0.24–0.27 nm for the outer shell surface when the temperature was increased from 150 to 500 K,
force
withthat
time
three
temperatures.
The
thenm.
friction
significantly
increased
and
forfor
thethe
inner
shell
was in the range
of
Figure
6 shows
the variation
of these
the with
increased
with
the
increasing
temperature
duenoise
to 0.1–0.16
anof
increase
in
theforce
thermal
fluctuation.
For
thetested
increasing
temperature
due
an
increase
inwas
the about
thermal
fluctuation.
For
these
tested
friction
force
withthe
time
for to
the
three
temperatures.
The
noise
the independence
friction
force
significantly
temperatures,
average
friction
force
−2.42
nN.ofThis
of temperatures,
friction on
thetemperature
average
friction
force
was
about
−
2.42
nN.
This
independence
of
friction
on
temperature
disagrees
increased disagrees
with the increasing
temperature
due
an increaseetinal.,
thewhich
thermal
fluctuation.
Forfriction
these
with a previous
report
bytoSzlufarska
showed
that the
with
a previous
report
by average
Szlufarska
et al.,
showed
the independence
friction
force
tested
temperatures,
the
friction
forcewhich
was about
−2.42 that
nN.
This
ofdecreases
friction
onwith
force
decreases
with increasing
temperature
[23,24]
because
thermal
excitations
help
overcome
temperature
disagrees
with
astick-slip
previous
reportmagnitude.
by Szlufarska
et could
al., which
showed
that
theextremely
friction
increasing
temperature
[23,24]
thermal
excitations
help
overcome
energy barriers
and reduce
energy
barriers
and
reduce
thebecause
jump
This
be concluded
as an
force
decreases
with shells.
increasing
temperature
[23,24] because
thermal
helpbetween
overcome
the
stick-slip
jump
magnitude.
This
could be
as
an extremely
low friction
shells.
low
friction
between
However,
theconcluded
average
normal
force excitations
increases
with
increasing
energy
barriers
and
reduce
the
stick-slip
jump
magnitude.
This
could
be
concluded
as
an
extremely
However,
the average
normal
force
temperature,
as shown
in Figure
7. increases with increasing temperature, as shown in Figure 7.
low friction between shells. However, the average normal force increases with increasing
temperature, as shown in Figure 7.
Figure 6. Variation of friction force between shells with time for temperatures of 150, 300, and 500 K.
Figure
6. Variation
of friction
force
between
timefor
fortemperatures
temperatures
150,
500 K.
Figure
6. Variation
of friction
force
betweenshells
shells with
with time
of of
150,
300,300,
andand
500 K.
Figure 7. Variation
of normal force
betweenshells
shells with
with time
for
temperatures
of of
150,
300,300,
andand
500 K.
Figure
timefor
fortemperatures
temperatures
150,
Figure7.7.Variation
Variationof
ofnormal
normal force
force between
between shells
with time
of 150,
300, and
500500
K. K.
Micromachines 2017, 8, 84
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4. Conclusions
MD simulations were used to investigate the effects of the DWCNT type, outer shell diameter,
and temperature on the interfacial friction of DWCNTs. It was found that the friction force and
normal force between shells increase with an increasing outer shell diameter and that the noise
of the friction force between shells increases with an increasing temperature. Zigzag@zigzag and
armchair@armchair DWCNTs exhibited larger friction forces and smaller normal forces than those of
chiral@chiral DWCNTs.
Acknowledgments: This work was supported by the Ministry of Science and Technology of Taiwan under grants
MOST 104-2221-E-033-062-MY2 and MOST 104-2622-E-033-006-CC3.
Author Contributions: Te-Hua Fang and Fu-Yung Tung conceived and designed the simulations; Fu-Yung Tung
performed the simulation; Te-Hua Fang and Fu-Yung Tung analyzed the data; Cheng-Da Wu wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
O’Connell, M.J. Carbon Nanotubes: Properties and Applications; CRC Press: Bocaraton, FL, USA, 2006.
Servantie, J.; Gaspard, P. Rotational dynamics and friction in double-walled carbon nanotubes. Phys. Rev. Lett.
2006, 97, 186106. [CrossRef] [PubMed]
Qin, Z.; Qin, Q.H.; Feng, X.Q. Mechanical property of carbon nanotubes with intramolecular junctions:
Molecular dynamics simulations. Phys. Lett. A 2008, 372, 6661–6666. [CrossRef]
Qiu, W.; Kang, Y.L.; Lei, Z.K.; Qin, Q.H.; Li, Q. A new theoretical model of a carbon nanotube strain sensor.
Chin. Phys. Lett. 2009, 26, 080701.
Rahimi, M.; Babu, D.J.; Singh, J.K.; Yang, Y.B.; Schneider, J.J.; Plathe, F.M. Double-walled carbon nanotube
array for CO2 and SO2 adsorption. J. Chem. Phys. 2015, 143, 124701. [CrossRef] [PubMed]
Zhang, R.; Ning, Z.; Xu, Z.; Zhang, Y.; Xie, H.; Ding, F.; Chen, Q.; Zhang, Q.; Qian, W.; Cui, Y.; et al.
Interwall friction and sliding behavior of centimeters long double-walled carbon nanotubes. Nano Lett. 2016,
16, 1367–1374. [CrossRef] [PubMed]
Zhang, R.; Ning, Z.; Zhang, Y.; Zheng, Q.; Chen, Q.; Xie, H.; Zhang, Q.; Qian, W.; Wei, F. Superlubricity
in centimetres-long double-walled carbon nanotubes under ambient conditions. Nat. Nanotechnol. 2013, 8,
912–916. [CrossRef] [PubMed]
Cumings, J.; Zettl, A. Low friction nanoscale linear bearing realized from multiwall carbon nanotubes.
Science 2000, 289, 602–604. [CrossRef] [PubMed]
Akita, S.; Nakayama, Y. Extraction of inner shell from multiwall carbon nanotubes for scanning probe
microscope tip. Jpn. J. Appl. Phys. 2003, 42, 3933–3936. [CrossRef]
Wu, C.D.; Fang, T.H.; Wei, H.J. Analysis of welding Au nanowires into T junctions. Mol. Simul. 2016, 42,
1029–1034. [CrossRef]
Wu, C.D.; Fang, T.H.; Wu, C.C. Size effect on cold-welding of gold nanowires investigated using molecular
dynamics simulations. Appl. Phys. A 2016, 122, 218. [CrossRef]
Wu, C.D. Atomistic simulation of nanoformed metallic glass. Appl. Surf. Sci. 2015, 343, 153–159. [CrossRef]
Liu, B.H.; Hsu, Q.C.; Wu, C.D. Nanoextruded NbTi superconductor nanowires investigated using molecular
dynamics simulations. Appl. Phys. A 2016, 122, 465. [CrossRef]
Wu, C.D. Molecular dynamics simulation of nanotribology properties of CuZr metallic glasses. Appl. Phys. A
2016, 122, 486. [CrossRef]
Li, Y.; Hu, N.; Yamamoto, G.; Wang, Z.; Hashida, T.; Asanuma, H.; Dong, C.; Okabe, T.; Arai, M.;
Fukunaga, H. Molecular mechanics simulation of the sliding behavior between nested walls in a multi-walled
carbon nanotube. Carbon 2010, 48, 2934–2940. [CrossRef]
Xia, Z.; Curtin, W.A. Pullout forces and friction in multiwall carbon nanotubes. Phys. Rev. B 2004, 69, 233408.
[CrossRef]
Song, H.Y.; Zha, X.W. Molecular dynamics study of effects of intertube spacing on sliding behaviors of
multi-walled carbon nanotube. Comput. Mater. Sci. 2011, 50, 971–974. [CrossRef]
Tersoff, J. New empirical model for the structural properties of silicon. Phys. Rev. Lett. 1986, 56, 632–635.
[CrossRef] [PubMed]
Micromachines 2017, 8, 84
19.
20.
21.
22.
23.
24.
7 of 7
Tsai, P.C.; Fang, T.H. A molecular dynamics study of the nucleation, thermal stability and nanomechanics
ofcarbon nanocones. Nanotechnology 2007, 18, 105702. [CrossRef]
Li, Q.Y.; Kim, K.S. Micromechanics of friction: Effects of nanometre-scale roughness. Proc. R. Soc. A 2008,
464, 1319–1343. [CrossRef]
Liu, Z.; Yang, J.; Grey, F.; Liu, J.Z.; Liu, Y.; Wang, Y.; Yang, Y.; Cheng, Y.; Zheng, Q. Observation of microscale
superlubricity in graphite. Phys. Rev. Lett. 2012, 108, 205503. [CrossRef] [PubMed]
Erdemir, A.; Martin, J.M. Superlubricity; Elsevier: Amsterdam, The Netherlands, 2007.
Szlufarska, I.; Chandross, M.; Carpick, R.W. Recent advances in single-asperity nanotribology. J. Phys. D
2008, 41, 123001. [CrossRef]
Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Modeling friction: From nano to meso scales.
Rev. Mod. Phys. 2013, 85, 529. [CrossRef]
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