Vol.2, No.8, 902-910 (2010) Natural Science
http://dx.doi.org/10.4236/ns.2010.28111
Copyright © 2010 SciRes. OPEN ACCESS
Molecular dynamics simulations of the interaction of
carbon nanotube and a carbon disulfide solvent
Kholmirzo Kholmurodov1,2*, Guzel Aru1, Kenji Yasuoka3
1Laboratory of Radiation Biology, Joint Institute for Nuclear Research, Dubna, Russia; *Corresponding Author: mirzo@jinr.ru
2International University “Dubna”, Dubna, Russia
3Department of Mechanical Engineering, Keio University, Yokohama, Japan
Received 4 February 2010; revised 18 March 2010; accepted 24 March 2010.
ABSTRACT
An analysis of the molecular dynamics (МD) of
the interaction between a carbon nanotube
(CNT) and a carbon disulfide active solvent (CS2)
has been carried out. The aim of the present
work is to estimate the dynamical and structural
behavior of the CNT-CS2 system at different
relative atomic concentrations and under tem-
perature changes. The structural radial distri-
bution functions and the dynamical configura-
tions have been built for a CNT interacting with
a CS2 solvent. A nontrivial observation for the
CNT-CS2 system is that the solvent carbon
disulfide atoms make up a patterned (layered)
formation around the carbon nanotube.
Keywords: Molecular Dynamics; Carbon Nanotube;
Carbon Disulfide Solvent
1. INTRODUCTION
Among the organic materials, carbon Nanotubes (CNTs)
are unique for their electrical and chemical properties.
They are very interesting in terms of material research
and electronic applications. Depending on their chemical
structure, carbon nanotubes (CNTs) can be used as an
alternative to organic or inorganic semiconductors as
well as conductors. The chemical bonding of nanotubes
is composed entirely of sp2 bonds, similar to those of
graphite. This bonding structure, which is stronger than
the sp3 bonds found in diamonds, provides the molecules
with their unique strength. Nanotubes naturally align
themselves into "ropes" held together by van der Waals
forces. The nature of the bonding of a nanotube is
described by quantum chemistryspecifically, orbital
hybridization. Solvents in which the CNTs can be solub-
ilized include chlorobenzene, chloroform, methylene
chloride, carbon disulfide, benzene, etc. The solubilities
of the carbon nanotubes in these solvents range from
about 0.01 to 5.0 mg/ml [1-4].
The aim of the present paper is to simulate the
dynamical and structural properties of a CNT interacting
with a carbon disulfide (CS2) solvent taking into account
the Van der Waals forces only. For the CNT-CS2 system,
we simulate different relative CNT solvent concentra-
tions and temperature scales. In the description of the
physical properties of the CNT, we employ the Tersoff
potential [5]. It is a special case of a density-dependent
potential, which reproduces the properties of the cova-
lent bonding in systems containing carbon, silicon, ger-
manium, etc, and alloys of these elements. A special
feature of the potential is that it allows bond breaking
and associated changes in bond hybridization. The ener-
gy is modelled as a sum of pair-like interactions where,
however, the coefficient of the attractive term in the pair-
like potential (which plays the role of the bond order)
depends on the local environment giving a many-body
potential.
The Tersoff potential has 11 atomic and 2 bi-atomic
parameters (see, formulas 1-9):
()[ ()()]
ijCijRijij Aij
Ufrfrfr
, (1)
where the potential parameters have the following
forms:
( )exp()
R
ijijij ij
f
rA ar
, (2)
()exp( )
Aij ijijij
f
rB br
, (3)
()
Cij
fr
11
cos[( )/( )]
22 ij ijij ij
rR rR
,ij ijij
RrS
,
(4)
In (1) ()
ij
f
rand ()
Aij
f
r mean repulsive and attrac-
tive, ()
Cij
f
rpotential cutoff functions (()
Cij
fr
()
Cij
fr
1 for ij ij
rR
and ()
Cij
fr0 for ij ij
rS).
It is worth noting that the main feasure of the Tersoff
potential is that the coefficients in (1) reflect many-body
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
Copyright © 2010 SciRes. OPEN ACCESS
903
nature of the interactions. The basic means of the coeffi-
cients is that the strenth of each bond depends on the
local environment and is lowered when the number of
neighboors is relatively high. This dependence can ac-
centuate or diminish the attractive force relative to the
repulsive force, according to the environment, such that:
1/2
(1 )
iii
ijiji ij
L

 
 , (5)
,
()( )
ijC ikikijk
kij
Lfrg
, (6)
222 22
()1//[(cos)]
ijki iiiiijk
gcdcdh

 , (7)
()/2
ijij
aaa , ()/2
iji j
bbb , (8)
1/2
()
iji j
AAA, 1/2
()
iji j
BBB, 1/2
()
iji j
AAA,
1/2
()
iji j
RRR, 1/2
().
iji j
SSS (9)
We have accepted the following values: 1
ii
,
ij ji

, 1
ii
, ij ji
.
The carbon disulfide (CS2) solvent has a com-
paratively high solubility (~7.9 mg/ml). Several earlier
papers considered interaction between the CS2 solvent
and a fullerene (C60) solution [6-12]. The C60-CS2
system belongs to a class of solutions where a peak in
the temperature dependence of solubility is observed
(Tmax~280 K). The structural features of the fullerene in
a solution, as well as the fullerenesolvent (C60–CS2)
interaction mechanism have been investigated in detail
in [6-12] by different methods (small-angle neutron
scattering (SANS) and others). As was noted in [12], the
characteristic size of the CS2 molecule (~0.3 nm) is
comparable to that of the C60 fullerene (~ 1 nm); so, any
interface organization of the CS2 molecules different
from that in bulk must result in a significant difference
between the interface and bulk molecular density of the
solvent, and, hence, affect the visible size of the
fullerene.
2. MATERIALS AND METHODS
We performed the molecular dynamics (MD) simulation
of several CNT-CS2 model systems. The MD simulation
was based on the DL_POLY general-purpose code
[13-15]. The MD cell is orthorhombic and square in the
XY plane (30.7 × 30.7 × 41.7). The integration algorithm
is an NPT Berendsen ‘ensemble’.
The CNT (carbon nanotube) consists of 800 carbon
atoms in a nanotube of 41.7 angstrom in length (see
Figure 1). For the CNT, we used the Tersoff potential
parameters of the DL_POLY software database
[13-14]:
A
= 1393.6, a= 3.4879, B = 346.74, b= 2.2119,
R = 1.8, S = 2.1,
= 1.5724 × 10-7,
= 0.72751, c= 38049, d=
4.3484, h = –0.57058.
The CS2 molecules were treated as rigid with the bond
length of 1.55 angstrom between carbon and sulfide
atoms (Figure 2). Throughout the computation, only the
Lennard-Jones (LJ) interactions were taken into account.
The number of the CS2 solvent molecules was varied, so
we simulated CNT-solvent model systems of different
relative atomic concentrations: x = 0.2, 0.4, …, 1.0
(Figure 3). The LJ potential was also used for the CNT
solvent interactions; the potential and parameteres are
shown in Table 1, where C denotes the CNT carbon
Figure 1. Structural presentations of the carbon
nanotube (CNT) (top and bottom).
Table 1. Potential parameters of the CNT-CS2 model.
Atomic pair Potential Functional form Parameters ε, eV σ, Å
C-C S Lj
12 6
() 4Ur rr

 

 
 
ε, σ 0.0044 3.35
C-S Lj ε, σ 0.0082 3.44
S-S Lj ε, σ 0.0153 3.52
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
Copyright © 2010 SciRes. OPEN ACCESS
904
Figure 2. Structural presentations of the CS2 solvent
(top and bottom).
Figure 3. Structural presentations of the CNT-
CS2 system (top and bottom).
atoms and Csthe carbon atoms of the CS2 solvent.
3. RESULTS AND DISCUSSIONS
The dynamics of the interaction between the CNT
(carbon nanotube) and the CS2 solvent has been studied
at different ratios of the CNT-solvent atomic concen-
trations:
S
CNT
N
xN
where Ns is the number of the solvent atoms and NCNT is
the number of the CNT atoms. We have simulated five
CNT-CS2 systems with x = 0.2, 0.4, 0.6, 0.8 and 1. We
call the systems with x = 0.2 and x = 1 low- and
high-density systems, respectively. The CNT consists of
800 carbon (C) atoms. Further, we denote the carbon
atoms of the CS2 solvent as Cs.
3.1. Structural RDFs for the CNT-Solvent
Atomic Pairs
In Figure 4, we present the behavior of the radial
0246810121416
0,5
1,0
1,5
2,0
2,5
g(r), [C-CS]
r, Ao
1: x=0.2
2: x
3: x
4: x
5: x
1
2
3
4
5
0246810121416
0,5
1,0
1,5
2,0
2,5
g(r), [C-S]
r
,
A
0
1: x=0.2
2: x=0.4
3: x=0.6
4: x0. 8
5: x=1.0
1
2
3
4
5
Figure 4. Structural RDFs for the atomic pairs
C-Cs and C-S at different ratios of the CNT–
solvent atomic concentration x.
S C S
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
Copyright © 2010 SciRes. OPEN ACCESS
905
distribution function (RDF) for the CNT-solvent atomic
pairs C-Cs and C-S at different values of x. It can be seen
that the RDF of the CNT-CS2 system at x > 0.4 obeys a
similar law. For all values of x, we have clearly observed
two peaks in the RDF graphs. However, for x > 0.4,
Figure 4 shows an additional small RDF peak between
the first two ones. This behavior of the RDF points to a
structural rearrangement of the CNT-CS2 system, which
is going from the low density phase (x = 0.2) into the
high density phase (x = 1). The additional (third) peak in
the RDF curve has also been observed on the
temperature dependence (part III below).
3.2. Structural RDFs for the Solvent-Solvent
Atomic Pairs
In Figures 5 and 6, the radial distribution functions
(RDFs) are presented for the solvent-solvent atomic
pairs (Cs-Cs, Cs-S, and S-S) at different values of x. It is
seen that the RDFs of the solvent atoms differ from each
other by their first peaks only; the secondary peaks for
all solvent-solvent atomic pairs (CS2-CS2) are similar.
The RDF for the S-S atoms has a comparably large first
0 2 4 6 810121416
0,5
1,0
1,5
2,0
2,5
g(r), [Cs-Cs]
r, A0
1: x=0.2
2: x=0.4
3: x=0.6
4: x=0.8
5: x=1.0
1
2
3
45
0246810121416
0,5
1,0
1,5
2,0
2,5
g(r), [Cs-S]
r, Ao
1:x=0.2
2: x=0.4
3: x=0.6
4: x=0.8
5: x=1.0
1
2
3
45
Figure 5. Structural RDF for the atomic pairs
Cs-Cs and Cs-S at different ratios of the CNT
solvent atomic concentration x.
0246810121416
0,5
1,0
1,5
2,0
2,5
g(r), [S-S]
r, Ao
1: x=0.2
2: x=0.4
3: x=0.6
4: x=0.8
5: x=1.0
1
2
3
45
Figure 6. Structural RDF for the atomic pair S-S at dif
ferent ratios of the CNT–solvent atomic concentration x.
peak (Figure 6). This indicates that in the solvent media,
the atomic pair S-S has a relatively high ordering in
comparison with the Cs-Cs one. The RDF first peak for
the Cs-S atomic pair (Figure 5, below) is low as com-
pared with S-S ones. We attribute such behavior to an
influence of CNT’s carbon (C) atoms on the CNT
solvent interaction process and ordering.
3.3. MD-Simulated Structural CNT-CS2
Configurations
We have compared the MD structural configurations of
the CNT-CS2 system for the low-density (x = 0.2) and
high-density (x = 1) phases. In Figure 7, MD-simulated
snapshots are presented for x = 0.2. Figure 7 shows the
side and top views (left and righr, respectively) of the
CNT-CS2 system; the snapshots correspond to the
moments of t = 0 (top), 10 ps (middle), and 80 ps
(bottom). It is seen that starting from arbitrarily
distributed positions at the initial (t = 0) state, the solvent
(CS2) atoms become more structured in the later states of
the dynamics around and inside the CNT.
The CS2 structuring behavior around the CNT has also
been observed during temperature variation in the
CNT-CS2 system. In Figure 8, the RDF curves are
displayed for the low density phase (x = 0.2) depending
on temperature: T = 200 K (1), T = 250 K (2), and T =
300 K (3). Figure 8 shows the RDF results for
CNT-solvent atomic pairs C-Cs (left) and C-S (right).
The RDFs in Figure 8 show some RDF changes (only
for the first peaks).
Figure 9 shows RDF curves for the solvent-solvent
atomic pairs Cs-Cs (left) and Cs-S (right). A visible
change in the RDF graph is seen for the atomic pair Cs-S.
During the temperature variation, we observe changes
for Cs-S both in the first and secondary peaks.
A is seen in the RDF graph in Figure 10, the atomic
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
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906
(a) Low-density phase (x = 0.2)
Figure 7. Snapshots of the CNTsolvent configurations at a low density (relative atomic concen-
tration x = 0.2).
t = 0 t=0
t = 10 ps t = 10 ps
t = 80 ps
t = 80 ps
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
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907
34567891011121314151
6
1,0
1,5
2,0
2,5
1: T=200K
2: T=250K
3: T=300K
g(r), [C-CS]
r, Ao
1
2
3
345678910111213141516
1,0
1,5
2,0
2,5
1: T=200K
2: T=250K
3: T=300K
g(r), [C-S]
r, Ao
1
2
3
Figure 8. Structural RDFs for the atomic pairs C-Cs and C-S at x = 0.2 with temperature.
345678910111213141516
1,0
1,5
2,0
2,5
1: T=200K
2: T=250K
3: T=300K
g(r), [CS-CS]
r, Ao
1
2
3
34567891011121314151
6
1,0
1,5
2,0
2,5
1: T=200K
2: T=250K
3: T=300K
g(r), [CS-S]
r, Ao
1
3
2
Figure 9. Structural RDF for the atomic pairs Cs-Cs and Cs-S at x = 0.2 with temperature.
345678910 11 12 13 14 15 16
1,0
1,5
2,0
2,5 1: T=200K
2: T=250K
3: T=300K
g(r), [S-S]
r, Ao
1
2
3
Figure 10. The structural RDF for the atomic pair S-S at x
= 0.2 with temperature.
pair S-S has a relatively high ordering in the solvent
media. Also, the RDF for the S-S pair shows a strong
temperature dependence. We see that the amplitude of
the first peak decreases twice as the temperature in-
creases from T = 200 K to 300 K.
In Figure 11, the MD snapshots are presented for the
high density phase (x = 1).
Comparing these results with those of the low density
phase (x = 0.2, Figure 7), we observe a similar structural
formation of the CS2 solvent atoms around the CNT.
However, the RDFs of the high-density phase are
strongly specific against the low-density phase RDFs. A
comparison of Figures 12-14 with Figures 8-10 is
straightforward.
3.4. Patterned Structure Formation in the
CNT-CS2 System
One of the nontrivial observations for the CNT-CS2
system is that the solvent carbon disulfide atoms make
up a patterned (layered) formation around the carbon
nanotube. In Figure 15, we present a CNT-CS2 resultant
structure where the atomic distributions are compared in
three regions (marked by the circles 1, 2, and 3). It is
seen that in regions 1 and 2, the solvent CS2 atoms have
to be configured similarly to CNT’s shape. The solvent
atoms inside and outside the CNT are regularly
distributed within the spheres of the same radii off the
CNT. In contrast, for region 3 we observe an
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
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908
(b) High density phase (x = 1)
Figure 11. Snapshots of the CNTsolvent configurations at a high density (relative atomic concen-
tration x = 1).
t = 10 ps t = 10 ps
t = 0 t = 0
t = 80 ps t = 80 ps
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
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909
345678910111213141516
0,9
1,0
1,1
1,2
1,3
1: T=200K
2: T=250K
3: T=300K
g(r), [C-CS]
r, Ao
1
23
345678910111213141516
0,9
1,0
1,1
1,2
1,3
1: T=200K
2: T=250K
3: T=300K
g(r), [C-S]
r, Ao
1
2
3
Figure 12. Structural RDFs for the atomic pairs C-Cs and C-S at x = 1 with temperature.
345678910111213141516
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1: T=200K
2: T=250K
3: T=300K
g(r), [CS-CS]
r, Ao
2
3
1
2
34567891011 12 1314 15 16
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1: T=200K
2: T=250K
3: T=300K
g(r), [CS-S]
r, Ao
1
2
3
Figure 13. Structural RDFs for the atomic pairs Cs-Cs and Cs-S at x = 1 with temperature.
3 45 6 7 8910111213141516
1,0
1,5
2,0
2,5
g(r), [S-S]
r, Ao
1: T=200K
2: T=250K
3: T=300K
1
2
3
Figure 14. Structural RDF for the atomic pair S-S at x = 1
with temperature.
irregular structure of the same atoms that results from
solvent-solvent ineraction. It should be noted that Figure
15 shows an important example of a graphene-
Figure 15. The CNT-CS2 atomic distributions for three
regions shown as circles 1, 2, and 3.
K. Kholmurodov et al. / Natural Science 2 (2010) 902-910
Copyright © 2010 SciRes. OPEN ACCESS
910
like (patterned, layered) behavior. Such formations are
of great importance for the applications and tech-
nological uses of the CNT-CS2 systems [1-12].
4. ACKNOWLEDGEMENTS
This work has been fulfilled under joint collaboration agreements
Daresbury Laboratory, UK - Keio University, Japan - JINR, Russia.
This work was supported in part by Grant in Aid for the Global Center
of Excellence Program for “Center for Education and Research of
Symbiotic, Safe and Secure System Design” from the Ministry of
Education, Culture, Sport, and Technology in Japan. We thanks Prof.
William Smith (Daresbury Laboratory, UK) for the software support.
We would like to thank Prof. Mikhail V. Altaisky (the Joint Institute for
Nuclear Research, Dubna) for helpful discussions.
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