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Carbon nanoscrolls
Fabrication of Carbon Nanoscrolls from Monolayer Graphene
Dan Xia, Qingzhong Xue,* Jie Xie, Huijuan Chen, Cheng Lv, Flemming Besenbacher, and Mingdong Dong*A simple way of synthesizing carbon nanotube (CNT)/graphene (GN) nanoscroll core/shell nanostructures is demonstrated using molecular dynamics (MD) simulations. The simulations show that GN sheets can fully self-scroll onto CNTs when the CNT radius is larger than a threshold of about 10 Å, forming a stable core/shell structure. Increasing the length of the GN sheet results in multilayered carbon nanoscroll (CNS) shells that exhibit a tubular structure similar to that of multiwall CNTs. The distances between the CNT and the GN wall or adjacent GN walls are about 3.4 Å. It is found that the van der Waals force plays an important role in the formation of the CNT/GN nanoscroll core/shell-composite nanostructures. However, the chirality of the CNT and the GN sheet does not affect the self-scrolling process, which thus provides a simple way of controlling the chirality and physical properties of the resulting core/shell structure. It is expected that this preparation method of CNT/GN nanoscroll core/shell composites will lead to further development of a broad new class of carbon/carbon core/shell composites with enhanced properties and even introduce new functionalities to composite materials.
1. Introduction
Carbon nanotubes (CNTs) and graphene (GN) are
two of the most promising nanomaterials in the carbon
family due to their ideal 1- and 2D structures. Since their
discovery in 1991 [ 1 ] and 2004, [ 2 ] respectively, they have
© 2010 Wiley-VCH Vewileyonlinelibrary.com
DOI: 10.1002/smll.201000646
D. Xia , Prof. Q. Z. Xue , J. Xie , H. J. Chen , C. Lv College of Physics Science and TechnologyChina University of PetroleumDongying, Shandong 257061, P. R. China E-mail: [email protected]
F. Besenbacher , M. Dong Interdisciplinary Nanoscience Center (iNANO) and Department of Physics and AstronomyUniversity of AarhusDK-8000 Aarhus C, DenmarkE-mail: [email protected]. dk
attracted tremendous interest because of their unique prop-
erties [ 3–10 ] and promising applications. [ 11–18 ] The properties
of CNTs have been investigated in great detail during the
past few years and research into GN is rapidly catching up
with that of CNTs. Recently, folding and curling GN sheets
have been intensively researched and have been proposed
for the generation of novel nanostructures. [ 19–21 ] As a result,
another interesting carbon nanomaterial, called a carbon
nanoscroll (CNS), has arisen. The CNS structure has been
studied by rolling up a single GN sheet with varying diam-
eter and chirality, depending on the sheet size and roll direc-
tion. [ 22 , 23 ] CNSs are remarkable structures that share some
of the rich mechanical and electronic properties exhibited
by CNTs and GN but are also expected to exhibit novel
features. Some theoretical studies have predicted unusual
electronic [ 23 ] and optical properties [ 24 ] of CNSs because
of their unique topology. Unlike CNTs, the CNS diameter
can be easily varied because it is not a closed topological
structure. These properties can be exploited for a variety
rlag GmbH & Co. KGaA, Weinheim small 2010, 6, No.18, 2010–2019
Carbon Nanoscrolls from Graphene
Figure 1 . Snapshots of a GN sheet with a length of 53.379 Å self-scrolling onto a (8,8) CNT core at time intervals from 0 to 500 ps.
0 ps 1 ps 100 ps
150 ps 175 ps 500 ps
of technological applications, such as chemical doping, [ 22 ]
hydrogen storage, [ 25 ] and nanoactuators in nanomechanical
devices. [ 22 , 26 ]
There are several methods for fabricating CNSs, including
arc discharge, [ 27 ] high-energy ball milling of GN, [ 28 ] and the
chemical route. [ 29–31 ] However, these methods are not able
to produce high-purity, high-quality CNSs. Recently, Xu et al.
reported a simple and effi cient method for the in situ fabrica-
tion of high-quality CNSs and their direct incorporation into
devices. [ 32 ] Current routes for the synthesis of CNS structures
depend on the self-assembly of exfoliated graphite sheets
and lack suffi cient control over CNS diameter and chirality,
thus requiring a postsynthesis sorting processes. Therefore,
the development of new and alternative methods for synthe-
sizing CNSs with well defi ned diameter and chirality repre-
sents a great challenge in today’s nanotechnology.
By using molecular dynamics (MD) simulations, we inves-
tigate a simple method of synthesizing novel CNT/CNS core/
shell-composite nanostructures by the rolling up of single
GN sheets induced by CNTs. There are several reports of
core/shell structures with excellent properties [ 33–36 ] that make
them promising candidates for applications such as nanoelec-
tronic devices [ 35 ] or integrated circuits. [ 36 ] In this work, the
surface-adsorption stress of the CNTs, which results from the
van der Waals (vdW) force, is used to bend GN sheets to roll
up and cover the CNT surface. The process consists of two
basic steps: 1) placing GN sheets in close proximity to CNTs
and 2) the bending and rolling up of GN sheets into CNSs by
the CNTs’ surface stress. For a given CNT, the CNT size and
GN chirality determine the CNS diameter and chirality. Com-
pared with the stochastic growth process, this method con-
trols the diameter and chirality of the CNSs in a deterministic
manner. The CNT/CNS core/shell structures formed by these
two novel carbon materials have excellent properties, such as
high carrier mobility and high mechanical strength, and could
be used as microcircuit interconnects, nanoelectronic devices,
or nanosensors.
2. Results and Discussion
The self-scrolling of CNT/GN core/shell nanostructures
was simulated using MD. Figure 1 shows snapshots of the
interaction between an (8,8) CNT and a GN sheet with a
length of 53.379 Å. When the GN is placed beside the (8,8)
CNT, the CNT and the GN approach each other because of
attractive forces. During the approach, the GN atoms, which
are closer to the CNT than the other atoms, move faster
towards it and fi nally attach onto the CNT surface, as shown
in Figure 1 at t = 1 ps, because the vdW force acting on the
carbon atoms of the GN is stronger the closer they are to the
CNT surface. After the attachment of the nearest GN carbon
atoms onto the CNT, the GN begins to roll and gradually
wraps around the whole CNT (see Videos S1 and S2 in the
Supporting Information). At t = 175 ps, the wrapping is com-
plete and a tubular CNS is formed. After t = 175 ps, the CNT
and GN remain in a relatively stable state so the confi gura-
tions of the composite structure at t = 175 ps and t = 500 ps
appear more or less identical.
© 2010 Wiley-VCH Verlag GmbHsmall 2010, 6, No.18, 2010–2019
The interaction energy, refl ecting the adhesion between
the CNT and the GN, is defi ned as [ 33 ]
Einteraction � Etotal − (EGN + ECNT) ,
(1)
where Etotal is the energy of the system including the GN and
the CNT, EGN is the energy of the single GN sheet without the
CNT, and ECNT is the energy of the single CNT without the
GN. The deformation energy is defi ned as the difference
between the carbon structure’s initial energy and its energy
determined after a certain simulation step. In order to study
the self-scrolling in detail, we calculate the interaction energy
and deformation energy between the GN and CNT, as shown
in Figure 2 . From Figure 2 a, we can observe that the interac-
tion energy between the GN and the CNT shows a rapid ini-
tial increase, which is considerably slowed down at t ≈ 20 ps.
Finally, at t ≈ 175 ps, the interaction energy saturates. This indi-
cates that the system reaches a stable state after the GN has
completely wrapped onto the CNT. As shown in Figure 2 b,
the deformation energy of the GN shows a similar time
dependence as the interaction energy between the GN and
the CNT. In the case of the CNT, however, the deformation
2011 & Co. KGaA, Weinheim www.small-journal.com
D. Xia et al.
2012
full papers
Figure 2 . Change of the interaction energy and deformation energies with simulation time: a) the interaction energy between GN and CNT; b) the deformation energies of GN and CNT.
0 100 200 300 400 500
0
-200
-400
-600
-800
Inte
ract
ion
Ene
rgy
(Kca
l/mol
)
Simulation Time (ps)
(a) Interaction energy
0 100 200 300 400 500
550
600
650
700
750
Def
orm
atio
n E
ner
gy (
Kca
l/mol
)
Simulation Time (ps)
GN CNT (8,8)
(b) Deformation energy
energy saturates directly after the fi rst rapid increase and
only exhibits some minor fl uctuations for the rest of the simu-
lation. This indicates that the CNT reaches a relatively stable
state already at t ≈ 20 ps.
The process of self-scrolling a GN sheet onto a CNT
depends on the diameter of the CNT. When the diameter of
the CNT is < 10 Å, the CNT cannot induce the GN to wrap
it completely. As a result, we chose the (8,8) CNT for our
simulations, which is the least armchair-shaped CNT that can
induce a GN sheet even with a very long length to completely
wrap onto the CNT.
It is known that the chirality of CNTs and GN sheets
has a signifi cant effect on the properties of the CNTs and
the GN. A CNT is of metallic type when it exhibits armchair
chirality, whereas the CNT can be semiconducting type or
semimetallic type when its chirality is zigzag or armchair-
like. [ 37 ] Also, the chirality of a GN sheet can change its type
from metallic to semiconducting. [ 38 ] To investigate the effect
www.small-journal.com © 2010 Wiley-VCH Verlag Gm
Figure 3 . Schematics of the fi ve different chiral nanotubes with similar pin the MD simulations.
(8, 8) (9, 7) (10, 6) (12, 3)
of chirality on the mechanical properties of the composite
system, we simulated an armchair GN sheet interacting with
CNTs of different chiralities, as well as an (8,8) armchair
CNT interacting with GN sheets with different chiralities.
Five types of CNTs with different chiral angles, θ , ranging
from 0 to 30 ° were generated, as shown in Figure 3 . The cor-
responding chiral angle θ and diameter D n of the CNTs with
( n , m ) indices could be determined by using the rolling GN
model: [ 39 ]
2 � arctan
( √3m
2n + m
);
Dn �√
3
Bb√
(n2 + m2 + nm) (0 ≤ m ≤ n),
(2)
bH & Co. KGaA, Weinh
arameters utilized
(14, 0)
where b is the length of the C–C bond
(0.142 nm). The total number of atoms,
diameter, and length of each chiral nano-
tube are given in Table 1 . Figure 4 shows
the GN sheets with different chiralities
and the CNT/CNS core/shell-composite
nano structures formed after the MD sim-
ulations. The GNs are fi nite-size sheets
having special orthotropic behaviour and
positive Poisson ratios. [ 40 , 41 ] From Figure 4 ,
we can observe that different CNSs are
formed by rolling up GN sheets of different
chiralities and the CNSs formed exhibit the
single-wall CNT (SWCNT) structure with
different chiralities. To clarify the infl uence
of the chirality on the adhesion of this
CNT/CNS core/shell-composite structure,
we determine the saturation interaction
energies between the armchair GN and
the CNTs with different chiralities as well
as the saturation interaction energies per
unit surface between the (8,8) armchair
CNT and the GN sheets with different chi-
ralities, as shown in Figure 5 . From Figure 5 a,
eim small 2010, 6, No.18, 2010–2019
Carbon Nanoscrolls from Graphene
© 2010 Wiley-VCH Verlag GmbHsmall 2010, 6, No.18, 2010–2019
Table 1. Total number of atoms, diameter, and length of each chiral nanotube utilized in MD simulations.
Type of SWNTs
H atoms C atoms CNT diameter [Å]
CNT length [Å]
Chiral angle θ [deg]
(8,8) SWNT
armchair
32 672 10.85 51.65 30.00
(9,7) SWNT 32 672 10.88 51.54 25.87
(10,6) SWNT 32 672 10.96 51.12 21.79
(12,3) SWNT 30 672 10.76 52.06 10.89
(14,0) SWNT
zigzag
28 672 10.96 51.12 0.00
Figure 4 . Snapshots of GN sheets with different chiralities and the core/shCNT (the red highlighted structures represent the formed CNSs with differe
Figure 5 . a) Saturation interaction energies between the armchair GN shinteraction energies between the (8,8) CNTs and the different chiral GN sh
(8,8) (9,7) (10,6) (12,3) (14,0)0
-100
-200
-700
-800
-900
Inte
ract
ion
Ene
rgy
(Kca
l/mol
)
Chirality
(a)
we can observe that the CNT chirality has a negligible infl u-
ence on the adhesion. Similarly, the chirality of the GN sheets
affects the adhesion between the GN and the CNTs only
slightly, as shown in Figure 5 b.
The information on the interfacial region of the fi nal
structure can be characterized by the concentration profi le
of the combination consisting of the CNT core and the GN
shell. The concentration profi le is calculated for 3D peri-
odic structures by computing the atom-density profi le within
evenly spaced slices parallel to the bc , ca , and ab planes. In
practice, this is equivalent to taking the a , b , and c compo-
nents of the fractional coordinates of each atom and inde-
pendently generating a plot for each component. Figure 6 a,b
2013 & Co. KGaA, Weinheim www.small-journal.com
ell-composite nanostructures formed by the vdW force between GN and nt chiralities).
eets with a length of 53.379 Å and different chiral CNTs. b) Saturation eets.
0 5 10 15 20 25 30-0.38
-0.40
-0.42
-0.44
Inte
ract
ion
En
rgy
per
Un
it S
urfa
ce (
Kca
l/mol
•Å²)
Chiral Angle (°)
(b)
D. Xia et al.
2014 www.small-journal.com © 2010 Wiley-VCH Verlag Gm
full papers
Table 2 . Distances d1 to d4 between the CNT and the GN sheet and the a
Different chiral CNTs and the armchair GNs
d1 d2 d3 d4 da
(8,8)
armchair
3.993 4.054 3.525 3.044 3.521
(9,7) 2.972 3.544 2.986 3.484 3.147
(10,6) 3.016 3.505 3.509 3.509 3.345
(12,3) 3.016 2.521 3.525 3.474 3.338
(14,0) 3.525 3.001 3.503 3.002 3.343
Figure 6 . Concentration profi le of the fi nal structure including the (14,0) CNT and armchair GN in a) the X direction and b) the Y direction. c) Snapshot of the composite structure.
62 64 66 68 70 72 74 76 78 80 820
5
10
15
20
25
30C
(X
)
X (Å)
GN CNT (14,0)
d1 d2
(a)
64 66 68 70 72 74 76 78 80 82 840
5
10
15
20
25
C (
Y)
Y (Å)
GN CNT (14,0)
d3 d4
(b)
(c)
shows the concentration profi le of the fi nal structure of the
(14,0) zigzag CNT and the armchair GN sheet in the X and
Y directions, respectively. Here, we defi ned four distances, d1
to d4 , as shown in Figure 6 c. As marked in Figure 6 a,b, d1 is
3.525 Å, d2 is 3.001 Å, d3 is 3.503 Å, and d4 is 3.002 Å. All
of these distances are about or less than 3.4 Å, which is the
shortest distance of the graphite layer, and have thus almost
entered the strong-adhesive-binding region of the chemical
bond. The interaction energy between the armchair GN sheet
and the (14,0) zigzag CNT reaches ≈ − 777 Kcal mol − 1 . These
distances and the interaction energy indicate that the adhe-
sion between the GN sheet and the CNT is so strong that
they can hardly be separated again.
The distances d1 – d4 are determined from the concentra-
tion profi les for both the interaction between the armchair
GN sheet and the CNTs with different chiralities and the
interaction between the (8,8) armchair CNT and the GN
sheets with different chiralities. The results are shown in
Table 2 , which also gives the average distance, da , between
the CNT core and the GN shell. Because of the irregular
shape of the formed CNS in the X direction, the distance d2
has been omitted in the averaging. The average value, da , is
found to vary from 2.960 to 3.521 Å. Most of these values are
less than the shortest distance of the graphite layer, 3.4 Å.
This indicates that the above conclusion is valid for all cases
investigated in this study and that GN wrapping onto CNTs
results in stable core/shell structures with only little infl uence
of the chirality of both the GN sheet and the CNT.
Because the physical properties of the GN sheets and
the CNTs can be controlled by varying their chirality, it is
important to form different kinds of CNT/CNS core/shell
composites with different chiralities. Through this simple
self-scrolling, we can produce different types of heterojuc-
tion materials, including the semiconductor/semiconductor,
semiconductor/metal, and metal/metal types of CNT/CNS
core/shell composites, which are promising candidates for
various applications including nanomechanical devices or
nanocircuits.
In addition, we simulated GN sheets with different
lengths scrolling onto a CNT to investigate the size effect on
the adhesion. We chose six GN sheets with different lengths
of 30.340, 53.379, 74.394, 122.806, 202.664, and 255.127 Å,
respectively. It can be seen from Figure 7 that all the GN
sheets can completely self-scroll onto the CNT, forming
bH & Co. KGaA, Weinheim small 2010, 6, No.18, 2010–2019
verage distance, da .
Different chiral GNs and the (8,8) armchair CNTs
d1 d2 d3 d4 da
Zigzag 3.509 4.034 3.503 3.503 3.505
5 ° 3.509 3.509 3.498 3.503 3.504
10 ° 3.826 3.930 2.516 2.984 3.109
15 ° 3.878 3.509 2.501 2.501 2.960
20 ° 2.984 2.516 3.525 2.997 3.169
25 ° 2.984 2.989 3.529 3.484 3.332
Carbon Nanoscrolls from Graphene
Figure 7 . Size effect of the interaction between an (8,8) CNT and GN sheet with a width of 33.393 Å and different lengths.
30.340 Å 53.379 Å 493.47 Å
122.806 Å 202.664 Å 721.552 Å
a multilayered shell structure around the single-wall core
for sheet lengths > 54 Å. The saturated interaction energies
between the CNT and the GN sheets of various lengths, as
well as their saturated deformation energies are plotted in
Figure 8 . From Figure 8 a, we can observe that the interaction
energy between the CNT and the GN sheets increases rap-
idly until the GN length reaches 53.379 Å, which corresponds
to the length of a GN sheet that completely wraps the CNT
in one turn. A further increase of the GN length leads only
to a slight increase of the interaction energy. For very large
values of the GN length, a slight decrease of the interaction
energy is observed. This can be explained by the increasing
distance between the overlapped GN sheet and the CNT,
leading to a reduced interaction between the overlapped GN
sheet and the CNT. In addition, with the further increase of
the scrolled layer, the π – π interaction of the overlapped parts
decreases the total free energy of the GN sheet, [ 22 ] which also
leads to a somewhat-reduced interaction energy. In Figure 8 b,
© 2010 Wiley-VCH Verlag GmbHsmall 2010, 6, No.18, 2010–2019
Figure 8 . a) Interaction energies between an (8,8) CNT and GN sheets wsheets.
0 50 100 150 200 250-400
-500
-600
-700
-800
-900
Inte
ract
ion
Ene
rgy
(Kca
l/m
ol)
Lengthes of GNs (Å)
(a) Interaction energy
the deformation energy of the CNT remains almost constant,
indicating that the deformation of the CNT is independent
of the length of the GN. The deformation energy of the GN
sheet, however, increases rapidly with the GN length until
the CNT is completely wrapped. For large GN lengths, the
interaction energy decreases again dramatically. Again, this is
caused by the π – π interaction of the overlapped parts, which
decreases the total free energy of the GN.
To clarify the interaction between the long GN sheet (length
of 255.127 Å) and the CNT, we investigated this structure fur-
ther. The molecular model of the CNT/CNS core/shell-com-
posite structure formed by scrolling a GN sheet of 255.127-Å
length onto a (8,8) armchair CNT is shown in Figure 9 a,b in
side and top view, respectively. The concentration profi le of the
structure in the X direction is plotted in Figure 9 c. In a similar
manner to that described above, seven distances, d5 to d11 , are
defi ned that measure the distances between the different layers
of the core/shell structure (see Figure 9 b) and can be obtained
2015 & Co. KGaA, Weinheim www.small-journal.com
ith various lengths. b) Deformation energies of the CNT and the GN
0 50 100 150 200 250
400
500
600
700
800
Def
orm
atio
n E
ner
gy (
Kca
l/mol
)
Lengthes of GNs (Å)
CNT GN
(b) Deformation energy
D. Xia et al.
2016
full papers
Figure 9 . Molecular model of the CNT/CNS core/shell-composite structure formed by scrolling a GN sheet with a length of 255.127 Å onto an (8,8) armchair CNT in a) side view and b) top view. (c) Concentration profi le of the composite structure.
(a)(b)
130 135 140 145 150 155 160 1650
10
20
30
40
50
d11d10d9
d8d7d6
C (
X)
X (Å)
(8,8) CNT GN-255.127 Å
d5
(c)
from the separation distances between two adjacent peaks in
the concentration profi le given in Figure 9 c. From the concen-
tration-profi le analysis, we can obtain the values of the seven
distances as 3.283, 3.363, 3.363, 3.283, 3.371, 3.283, and 3.442
Å, respectively. Again, all these distances are about or even
less than the shortest distance of the graphite layer, 3.4 Å,
and have thus almost entered the strong-adhesive-binding
region of the chemical bond. Therefore, we can conclude that,
even for the multilayered GN shell, the core/shell structure is
stable. The CNS formed by the scrolled long GN sheet resem-
bles the multiwall CNT and the radius and the chirality of this
kind of “multiwall CNT” can be controlled by modulating
the radius of the CNT and chirality of the GN. This is a huge
improvement compared with stochastic growth, which cannot
control the diameter and chirality of the CNS in a determin-
istic way.
www.small-journal.com © 2010 Wiley-VCH Verlag Gm
Figure 10 . Size effect of the interaction between a GN sheet of size 33.39
(8, 8) (9, 9) (10, 10)
The chirality of the CNS can be controlled by using dif-
ferent chiral GN sheets to wrap around the CNTs as dis-
cussed above. Furthermore, the diameter of the CNS can also
be controlled since it depends on the CNT diameter. Six types
of armchair CNTs with different diameters were chosen to
study the wrapping of a long GN sheet around the CNTs. The
armchair CNTs under investigation were (8,8), (9,9), (10,10),
(11,11), (12,12), and (13,13) with diameters of 10.85, 12.20,
13.56, 14.92, 16.27, and 17.63 Å, respectively. The MD simula-
tions show that the length of the GN sheet that can wrap these
CNTs in a single turn is 53.379, 57.582, 61.785, 65.988, 70.191,
and 74.394 Å, respectively. From the size-effect study and the
geometry-confi guration analysis, we can obtain the size rela-
tionship between the GN sheet and the CNT roughly as
L � B (D + 2d); D > 10o
A,
(3)
bH & Co. KGaA, Weinheim small 2010, 6, No.18, 2010–2019
3 Å × 74.394 Å and armchair CNTs with different diameters.
(11, 11) (12, 12) (13, 13)
Carbon Nanoscrolls from Graphene
Figure 11 . a) Snapshot of the CNT put in close proximity to GN (33.393 Å × 53.379 Å) at places i and ii. b) The formed core/shell nanostructure; c) Snapshot of the CNT put in close proximity to GN (33.393 Å × 122.806 Å) at places I, II, and III, d) The core/shell nanostructure formed by the interaction between the CNT put at places I, II, and the GN. e) The core/shell nanostructure formed by the interaction between the CNT put at place III and the GN.
(a)
(b)
(d)(e)
(c)
where L is the length of the GN sheet, D is the diameter of
the CNT, and d is the average distance between the CNT
and the self-scrolled GN sheet. D > 10 Å accounts for the
minimum CNT diameter needed to induce the self-scolling
of the GN sheet (see above). When Equation 3 is satisfi ed, a
core/shell structure with single-layered shell can be produced.
When L > π ( D + 2 d ), there is an overlap of the GN shell, that
is, a multilayered shell is formed.
The interactions between a GN sheet of 74.394 Å in length
and CNTs with different diameters are shown in Figure 10 .
We can observe that the GN sheets can self-scroll onto all the
CNTs. Single-turn wrapping of the GN sheet is obtained for
the (13,13) armchair CNT, whereas smaller CNT diameters
lead to overlapping of the GN sheet.
Moreover, the location of the CNT placed in close prox-
imity to the GN has a great effect on the scrolling process. When
the GN length and CNT diameter size satisfy Equation 3 ,
the CNT can induce the self-scrolling of the GN wherever the
CNT is placed in close proximity to the GN. Figure 11 a shows
the (8,8) CNT induce the self-scrolling of GN (33.393 Å ×
53.379 Å) whether the CNT is put at position i or ii and the
fi nal confi guration formed is shown in Figure 11 b. When L >
π ( D + 2 d ), the GN can self-scroll onto the CNT and only
the perpendicular distance between the CNT and one
end of the GN is shorter than the value L = π ( D + 2 d ).
Figure 11 c shows a snapshot of the (8,8) CNT put in close
proximity to the GN (33.393 Å × 122.806 Å) at places I,
II, and III. The CNT at places I and II can induce the self-
scrolling of GN (as shown in Figure 11 d) but the CNT at
© 2010 Wiley-VCH Verlag Gmbsmall 2010, 6, No.18, 2010–2019
place III cannot induce the self-scrolling of GN like the mul-
tiwall CNT (as shown in Figure 11 e).
3. Conclusions
In summary, we have used MD simulations to study the
self-scrolling process of GN sheets onto CNTs. When the
diameter of the CNT exceeds a threshold of ≈ 10 Å, the CNT
can induce the GN sheet to scroll onto the CNT surface
by vdW interactions, thus forming a stable CNT/CNS core/
shell nanostructure. The simulations show that, by increasing
the length of the GN sheet, multilayered CNS shells can be
obtained that exhibit a tubular structure similar to that of
multiwall CNTs. The diameter and the chirality of the CNS
can be controlled through the dimensions and chirality of the
CNTs and the GN sheets. The chirality of both the CNT and
the GN sheet is found to have no strong infl uence on the self-
scrolling process, which thus enables the fabrication of a core/
shell structure that combines metal/semiconductor, metal/
metal, or semiconductor/semiconductor junctions. Since the
diameter of the CNS can be easily expanded by charge injec-
tion or intercalation, [ 22 ] it can be used as a nanoactuator. In
addition, this CNT/CNS core/shell-composite nanostruc-
ture can be used as nanocircuit interconnect since the cur-
rent density of the CNS can reach values as high as 5 × 10 7
A cm − 2 . [ 32 ] Thus, the results presented here may stimulate
further research to explore both the physical properties and
additional applications of CNT/CNS core/shell nanostruc-
tures and the further development of a broad new class of
materials with enhanced properties.
4. Experimental Section
MD simulations : MD simulations were implemented using the DISCOVER code in Materials Studio. The interatomic interactions are described by the force fi eld of the condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS). [ 42 ] This is the fi rst ab initio force fi eld that has been parametrized and validated using condensed-phase properties in addition to various ab initio and empirical data and it has been shown to be appli-cable in describing the mechanical properties of CNTs. [ 43 , 44 ] The Andersen method [ 45 ] was employed in the thermostat to control the thermodynamic temperature and generate the correct statis-tical ensemble. As a temperature control, the thermodynamic tem-perature was kept constant by allowing the simulated system to exchange energy with a “heat bath”. [ 45 ] The force fi eld is expressed as a sum of valence (or bonding), cross-terms, and nonbonding interactions:
E total = E valence + E cross- term + E nonbonded (4)
E valence = ∑b
[K 2 (b − b0)2 + K 3 (b − b0)3 + K 4 (b − b0)4]
+∑2
[H2 (2−20)2 + H3 (2−20)3 + H4 (2− 20)4]
+∑N
[V1[1− cos(N−N 01)] + V2[1− cos(2N −N0
2)]
+ V3[1− cos(3N −N03)]]
+∑x
K xP 2 + E U B (5)
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E cross-term � ∑b
∑b′
F bb′ (b − b0) b′ − b′0
+ ∑2
∑2′
F22 ′ (2 − 20) 2 ′− 2 ′0
+ ∑b
∑2
F b2 (b − b0) (2 − 20)
+∑b
∑N
F bN (b − b0) × [V1 cos(N) + V2 cos(2N) + V3 cos(3N)
]+ ∑
b′
∑N
F b′N b′ − b′0 b
′ − b′0
)× [
F 1 cos(N) + F 2 cos(2N) + F 3 cos(3N)]
+ ∑2
∑N
F2N (2 − 20) × [V1 cos(N) + V2 cos(2N) + V3 cos(3N)
]+∑
N
∑2
∑2 ′
K N22′ cos(N) (2 − 20) × 2 ′ − 2 ′0
)
(
( )
)
E non-bond �
∑i> j
[Ai j
r 9i j
− Bi j
r 6i j
]+
∑i> j
qi qj
gri j+ E H-bond
(7)
The valence energy, E valence , is generally accounted for by terms including bond stretching, valence-angle bending, dihedral -angle torsion, and inversion. The cross-term interaction energy, E cross-term , accounts for factors such as bond or angle distortions caused by nearby atoms to accurately reproduce the dynamic properties of molecules. The nonbonding interaction term, E non-bond , accounts for the interactions between nonbonded atoms and results mainly from vdW interactions. In Equation 1– 4 , q is the atomic charge, ε is the dielectric constant, and r ij is the i – j atomic separation dis-tance. b and b′ are the lengths of two adjacent bonds, θ is the two-bond angle, φ is the dihedral-torsion angle, and χ is the out-of-plane angle. b 0 , ki (i = 2–4), θ 0 , Hi ( i = 2–4), φ i
0 (i = 1–3), V i ( i = 1–3), F bb ′ , b 0 ′, F θ θ ′ , θ ′0 , F b θ , F b φ , F b ′ θ , F i ( i = 1–3), F θ φ , K φ θ θ ′ , A ij , and B ij were fi tted from quantum-mechanical calculations and imple-mented in the Discover module of Materials Studio.
MD simulations were performed in periodic boundary condi-tions in the range of 150 × 150 × 54.2205 Å 3 at 300 K. When the GN length was longer than 150 Å, the range of the periodic boundary condition was increased correspondingly. In this work, we considered different CNTs and GN sheets. As initial confi gura-tions, a series of GN sheets with the same width of 33.393 Å were aligned parallel to the CNTs with a separation of ≈ 5 Å. The models were put into an constant-volume/constant-temperature dynamics ( NVT ) ensemble simulation at 300 K. A time step of 1 fs was used and data was collected at intervals of 1 ps. The full-precision tra-jectory was then recorded and the results were analyzed.
Supporting Information
Supporting Information is available from the Wiley Online Library or from the author. It contains videos: Video S1: MD simulation showing a GN sheet with a length of 53.379 Å deforming and self-scrolling onto an (8,8) armchair CNT in cross-section; view Video S2: MD simulation showing a GN sheet with a length of 53.379 Å deforming and self-scrolling onto an (8,8) armchair CNT in side view.
(6)
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Acknowledgements
This work is supported by the Cultivation Fund of the Key Scientifi c and Technical Innovation Project, Ministry of Education of China (708061), Natural Science Foundation of China (10974258), Pro-gram for New Century Excellent Talents in University (NCET-08-0844) and Postgraduate Innovation Fund of China University of Petroleum (SZ10-39).
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Received: April 17, 2010 Revised: June 14, 2010 Published online: August 16, 2010
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