Int. J. Nanosci. Nanotechnol., Vol. 7, No. 4, Dec. 2011, pp. 173-182
Transport of a Liquid Water-Methanol Mixture in a Single
Wall Carbon Nanotube
N. Farhadian
Chemical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad,
Mashhad, I. R. Iran
(*) Corresponding author: [email protected]
(Received: 17 Sep. 2011 and Accepted: 05 Nov. 2011)
Abstract:
In this work, a molecular dynamics simulation of the transport of water - methanol mixture through the
single wall carbon nanotube (SWCNT) is reported. Methanol and water are selected as fluid molecules since
water represents a strongly polar molecule while methanol is as an intermediate between polar and strongly
polar molecules. Some physical properties of the methanol-water mixture such as radial and axial density,
hydrogen bonding, number of contacts and minimum distance between mixture and SWCNT molecules and
also diffusivity of the mixture as a transport property were calculated during the simulation. Results showed
that mixture of the selected molecules inside SWCNT have different properties during transport along the
SWCNT in comparison with pure fluids inside SWCNT. Also methanol molecules diffuse faster than water
molecules inside nanotube due to a weaker hydrogen bonding network. These differences among physical
properties of the fluids inside SWCNT can be a key parameter for designing the new separation equipments
and sensors using SWCNT.
Keywords: Molecular Dynamics Simulation, Diffusion, Hydrogen bond, minimum distance.
1. INTRODUCTION
Carbon nanotubes (CNTs) are one of the most
active areas in new technologies. The extraordinary
physical, chemical, and mechanical properties
of carbon nanotubes have made them attractive
materials for numerous applications [1,2].The
unique mechanical and electrical properties of
carbon nanotubes [3] have prompted an interest
for technical application in a number of fields
including membranes, biosensors [4], atomic force
microscopy [5]. A key aspect of these applications
is the interaction of the surrounding fluid with the
carbon nanotube. In macroscopic scale the NavierStokes equation can provide a reasonable description
of fluids hydrodynamics only at very small Knudsen
numbers [6]. When the system length scale reduces
to the nanometer, however, the behavior of the flow
is mainly affected by the movements of the discrete
particles that compose the system at the atomic level
[7]. At this scale, molecular modeling becomes
the effective methods. Among them molecular
dynamics (MD) simulation is the most effective
way to describe the details of the flow and to study
many fundamental nanofluid problems, which
can be extremely difficult to investigate by other
means. Molecular dynamics simulation is a form of
investigation where the motion and the interaction
of a certain number of “virtual” atoms or molecules
are studied. Molecular simulation is a very powerful
toolbox in modern molecular modeling, and enables
us to follow and understand structure and dynamics
173
i. and mixture
Molecular
Dynamics
SimulationOur
Methodology
the present study, we examine the properties of both pure
liquids
in the SWCNT.
study
ii.
Calculation
the
properties
of
water
in
the SWCNT
can be divided to these sections:
iii.
Calculation the properties of methanol in the SWCN
Molecular Dynamics Simulation Methodology
iv.
Calculation
theproperties
properties of
of acomponents
mixture ofwater-methanol(50%mo
with extreme detail
on the
scales
where
to the
investigate
the physical
ii. – literally
Calculation
properties
of water in
SWCNT
i.
motion of individual
can be tracked.
in in
thetheSWCNT.
iii. atoms
Calculation
the properties of methanol
SWCN Molecular dynamics simulation
In the specific field of fluids confined in nanotubes,
involves
integration
of Newton’s
equation of motion
2- Models
and Simulation
Methodology
iv.
Calculation the properties of a mixture
ofwater-methanol(50%mol)intheSWCNT
early works were focused on the behavior of a pure
for each atom in an ensemble in order to generate
2.1
Simulation
and simple fluids like methane [8, 9] ethane[8]
information
onMethodology
the variation in the position, velocity,
Molecular
dynamics
methodaswas
used to investigate
the physical prop
ethylene[8] 2argon[10,
11]
helium,
[11]
neon,[10]
and
acceleration
ofsimulation
each particle
a function
of
Models and Simulation Methodology
and hydrogen [12,13] or water confined in simpler
time.
The equations
solved
are [24]:
the
SWCNT.
Molecular
dynamics
simulation involves integration of Newton’s
2.1 Simulation Methodology
nanopores [14,15-16]. The first article, to our
antheensemble
order to generate
information
on the variation in the
Molecular dynamics
methodwas
was usedeach
to
physicalinproperties
of components
in
f i investigate
=atom
mi ain
knowledge, dedicated
to MD ofsimulation
water in CNTs
(1)
i acceleration
as a equation
function oftime.Theequationssolvedare[24]:
the SWCNT.
simulation involves
integration
Newton’s
of motion for
written by Gordillo
and Molecular
Martı [17]dynamics
and followed
∂U of eachofparticle
f
=
−
i
by many others
[18-23].
In
all
previous
studies,
the
(2)
f i  mi a∂i on
each atom in an ensemble in order to generate information
ri the variation in the position, velocity, and
movement of a pure component was investigated in
acceleration of each particle as a function oftime.Theequationssolvedare[24]:
U
th
the SWCNT while in many industrial applications
Where
f i   fi is the force exerted on the i atom, mi is its
ri a is its acceleration. The force acting(1)
m
it is necessaryf i to
know
the properties of a mixture
mass, and
on
i ai
i
in the CNT’s. In the present study, we examine the
each atom
is obtained
from
potential
U, and a is its accelerati
force exerted
onathe
ith atom,function
mi is its mass,
Where
fi is the
i
U
(2)


properties of fboth
pure
and
mixture
liquids
in
the
such
as
that
depicted
below
[24]:
i
each atom is obtained from a potential function U,suchasthatdepictedbelow[24
ri be divided to these sections:
SWCNT. Our study can

b
• Molecular
Dynamics
force exertedMethodology
on the ith atom, mi is its mass,kand
ai is its
acceleration.
The force acting on
Where
fi is theSimulation
k ijk
ij
eq 2
U   (rij  rij )  
( ijk   ijkeq ) 2   k  1  cos(n(   eq ))  
• Calculation
the
properties
of
water
in
the
each atom is obtained from a potential function U,suchasthatdepictedbelow[24]:
i j
bond 2
angle 2
(3)
SWCNT

 Aij Bij
k ijb
k ijk
qi q j 
• Calculation the properties
of methanol
in the
( ijk   ijkeq ) 2   k  1  cos(n(   eq ))    12  6 
U   (rij  rijeq ) 2  

SWCN
4 0 rij 
rij
i j 
bond 2
angle 2
 rij
• Calculation the properties of a mixture of waterwhere the first three terms reflect intramolecular
interactions between covalently
(3)
methanol (50 %mol) in the SWCNT
where the first three terms reflect intramolecular
interactions between covalently bonded atoms and
last termbetween
describes
the non-bonded
interactions
where
the first
three terms reflect intramolecular the
interactions
covalently
bonded atoms
and the
2. MODELS
AND
SIMULATION
(van der Waals and electrostatic). The constants2 kb,
METHODOLOGY
kθ, and kφ are force constants for the covalent bonds,
bond
angles, and dihedrals, respectively, rij are the
2
2.1. Simulation Methodology
distances between atoms i and j, Aij and Bij are the
Molecular dynamics simulation method was used
Lenard Jones parameters, and q is a partial charge



Figure 1: A hexagonal graphite sheet to create a zig-zag or armchair nanotube by rolling up along x or y axis
174
Farhadian

describe the geometry and phonon structure of graphite and fullerene crysta
last term describes the non-bonded interactions (van der Waals and electrostatic). The constants kb, kθ, and
A binary mixture of water and methanol is examined in this study. The sim
kφ are force constants for the covalent bonds, bond angles, and dihedrals, respectively, rij are the distances
to describe
water-water interactions. Th
liquid
heat of vaporization
and diffusion
[24]. Simulations
were
performed
using Gromacs
ribes the non-bonded interactions
(van der
Waals
electrostatic).
The constantsofBerendsenet.al[28]wasused
kb, kθ,density,
and
between atoms
i and
j, Aand
ij and Bij are the Lenard Jones parameters, and q is a partial charge [24].
constant asand
compared
with experimental
software [25] and visualization was done by VMD
structural
thermodynamics
properties, data
such[28].
as liquid density, heat
onstants for the covalentSimulations
bonds, bond angles,
and dihedrals, Gromacs
respectively,
rij are [25]
the distances
software
and
visualization
was
done
by
VMD
V.3.1
This
model
is
described
by
intra-molecular
harmonic
V.3.1 packagewere
[26].performedb using
constantascomparedwithexperimentaldata[28].Thismodelisdescribe
ns (van
TheJones
constants
k , kθ, andand q is a partial charge
Bijelectrostatic).
are the Lenard
parameters,
[24].
ms
i andder
j, Waals
Aij andand
stretching
and bending between the hydrogen and
package[26].
stretching
and bending
between the hydrogen and oxygen atoms as equation
bond
angles,
and
dihedrals,
respectively,
r
are
the
distances
oxygen
atoms
2.2.
Model
Systems
ij
were performed using Gromacs software [25] and visualization was done by VMD V.3.1 as equation 6:
1
1
Lenard Jones parameters,
and qSystems
is acarbon
partialnanotube
charge [24].
A
can be viewed as
2.2single-walled
Model
U (rij , ijk )  KWr (rij  rW ) 2  KW ( ijk  W ) 2 (6)
a graphite sheet
that isby
rolled
up V.3.1
into a cylinder. As
2
2
software [25] and visualization
was done
VMD
A
single-walled
carbon
nanotube
can
be
viewed
as
a
graphite
sheet
that
is
rolled
up
into
a cylinder. As (6)
shown in Figure 1, either the zig-zag (n,0) nanotube
stems
along
or the
armchair
(n,n) nanotube
along along
y
shownxinaxis
Fig.1,
either
the zig-zag
(n,0) nanotube
x axis or the armchair (n,n) nanotube along y axis
axis
can
be
formed,
where
the
index
(n,m)
indicates
and KWθ are the parameters of the
Where KAs
ed carbon nanotube cancan
be be
viewed
as awhere
graphite
is rolled
up into
cylinder.
wr and
3
Where
KWr
of the
rW and W are
formed,
the sheet
indexthat
(n,m)
indicates
the ahelical
structure
of K
a nanotube.
In this study,
wepotential;
 are the parameters
r
the helical structure of a nanotube. In this study, we
potential; W and θW
W are the reference bond length
1, either the zig-zag (n,0) nanotube along x axis or the armchair (n,n) nanotube along y axis
construct the armchair (n,n) nanotube.
and
angle,
respectively.
angle,
respectively.
wed
as a graphite
that
is rolled
uphelical
into
a cylinder.
As
d, where
the indexsheet
(n,m)
indicates
the
structure
of a nanotube.
In this
study,
we
The
applied
carbon
nanotube
is modeled
by termsFig.
Non-bonded
interactionsofofwater
water
molecules
1 Non-bonded interactions
molecules
are are
comprised of a Lennar
morse
bond, along
harmonic
comprised of a Lennard-Jones (LJ) term between
ube along(n,n)
x axis
or thedescribing
armchair (n,n)
nanotube
y axiscosine of the
armchair
nanotube.
The applied
carbon
modeled
by termsasdescribing
morse
bond,
cosine
of
the bending
oxygen
atoms,
andharmonic
aand
Coulomb
potential:
bending
angle,
andnanotube
a 2-foldistorsion
potential
the
oxygen
atoms,
a Coulomb
potential:
cates the helical structure of a nanotube.
In
this
study,
we
Fig. 1 torsion potential as equation 4:
equation
angle, and4:a 2-fold
1 qi q j
U
r

(
)
(7)
(7)
ij
arbon nanotube is modeled by terms describing morse bond, harmonic cosine of the bending
1
1 0 rij
2
2 4
1 potential asUequation
( rij , ijk ,4:
ijkl )  K Cr ( ij  1)  K C (cos  ijk  cos  C )  K C (1  cos 2ijkl ) (4)
-fold Fig.
torsion
ε
the permittivity
permittivityinina avacuum,
vacuum,and
andq q, i,q are the partial cha
where
2
where  00 isis2the
i
j
erms describing morse bond, harmonic cosine of the bending
q
are
the
partial
charges[29].
Table
2
shows
some
1
1
j
2
2
 K Cr ( ij  1)  where
K C (cos  ijk  cos  C )  K C (1  cos 2ijkl ) (4)parameters
parameters of
ofthe
theSPC
SPCwater
watermodel.
model.
kl ) 4:
on
2
2
(4)
  ( rij  rC )
Table 1
1 ij  e
(5)
Table 1: Parameters for the carbon interaction
cos  ijk  cos  C ) 2  K C (1  cos 2ijkl ) (4)
Table 1.
Table 2
potentials
[27]
2
Table 1.
j  rC )
angles,
and
r
all
the
distances
and  ijk and ijkl represent all the possible bending and torsion
ij represents
1

2
ForK Cr
methanol
molecules,
of simple
418AA models have been pre
(5)
 478
478..99kJmol
kJmol 1 A
A2 a number
rrCC  11..418
K Cr 
where
proposed
by Jorgensen
wi
1et al.[30]andbyHaughneyetal.[27]havebeen
between bonded atoms. KC, K C , and K C are the force
the 1stretch,
bend,
torsion
 Cand
120
0000
K Cconstants
 562
562..22of
kJmol
− γ ( rij and
− rC )torsion angles, and rij represents all the distances
 
represent
all
the
possible
bending

 120
..00
K
kJmol
kl
C
C

(5)
Both models give results for a range of properties that are in good
ξij = e
1
b
1
reference
parameters
for
potentials, respectively, and rC ,  C , and C the corresponding
b  25
  22..1867
1867
A1methanol
geometry
1
K Ctorsion
.12
12
kJmolIn
 
experimental
values.
our
simulations,
each
molecule is

A
K
25
.
kJmol
ded atoms. KC, K C , andθK C are the force constants of the stretch, bend, and
C
φijkl represent
nding and torsion angles,
rij represents
all thealldistances
the possible bending
and and
ijk and
graphite. The Morse stretch and angle bending parameters
werepotentials
first given
Guo simulations
et al.[27] and
optimized
forbyliquid
(OPLS) proposed by Jo
and torsion angles, and rij represents all the
reference geometry parameters for
spectively, and rC ,  C , and C the corresponding
subsequently
used by
Tuzun
et
al [11].
parameters,
listed
Table
were
derived
to
of thebetween
stretch,
bend,
and
torsion
distances
bonded
atoms.
KC , These
K Cθ , and
Jorgensen’s
model 1,can
both
gas-phase
Table
2: in
Parameters
forreproduce
theoriginally
SPC water
model
and dimmer properties
 are the force constants
K
are
the
force
constants
of
the
stretch,
bend,
Morse stretch and angle
bending
parameters
were
first
given
by
Guo
et
al.[27]
and
the
carbon-water
potentials
[30]
Cφ
describe
the geometry and phonon structure of graphite and
fullerene crystals.
Table
2.the OPLS model, three interaction sites ar
temperature
and pressure.
In2.
Table
rC , θ C , and φC
C the corresponding and
reference
geometryrespectively,
parameters
torsion potentials,
andfor
used by Tuzun et al [11]. These parameters, listed in Table 1, were originallynuclei,
derivedhydroxyl
to
1 2
proton
(CH3) group centered o
1 A2(H), and united
KWr 
 4637
4637kJmol
kJmol
the corresponding reference geometry parameters
rrWW  11..methyl
00AA
K
A
Wr
nding
parameters
were
first
given
by
Guo
et
al.[27]
and
eometry and phonon structure
of mixture
graphite
and
fullerene
crystals.
for
graphite.
The Morse
stretch
and angleis bending
Table3showsLJparametersandpartialcharges
for methanol, water and
A binary
of
water
and methanol
examined in this
study. The simple
point charge (SPC) model
K W 
 383
383kJmol
kJmol 11rad
rad 22
109..47
4700
K
WW  109
se parameters, listed inparameters
Table 1, were
were originally
first givenderived
by Guotoet al.[27] and
W
ofBerendsenet.al[28]wasused to describe water-water interactions. The SPC model gives reasonableTable 3
subsequently
used by Tuzun et al [11]. These
= -- 0.82
0.82
= 0.41
0.41
fure
graphite
and
fullerene
crystals.
qqHH=
qqO=
of water and methanol
is examined
in
study.
The
simple point
(SPC)
modelPreparation
2.3O density,
System
structural
and
thermodynamics
properties,
suchcharge
as liquid
heat of vaporization and diffusion
parameters,
listed
in this
Table
1, were
originally
derived
describe
the geometry
and phonon
of gives Here,
et.al[28]wasused toto
describe
water-water
interactions.
The structure
SPC model
reasonable
a detailed comparison among physical
properties of the molecules
constantascomparedwithexperimentaldata[28].Thismodelisdescribedbyintra-molecular
harmonic
Table3.
graphite
andpoint
fullerene
crystals.
For
methanol
molecules,
a
number
of
simple
xamined
in
this
study.
The
simple
charge
(SPC)
model
Table3.
thermodynamics properties,
such
liquid between
density, the
heat
of vaporization
andalong
diffusion
SWCNT
has been
performed by using three
simulation systems defi
stretching
andasbending
hydrogen
and oxygen
atoms
as
equation
6:
A
binary mixture
of water and methanol
is examined
models
have been
previously proposed.
Site
(nm)
(kJ/mol) The qq(e)
(e)
Site
σσ (nm)
εε (kJ/mol)
e
water-water
interactions.
The
SPC
model
gives
reasonable
omparedwithexperimentaldata[28].Thismodelisdescribedbyintra-molecular
harmonic
in this study. The
simple
point
charge
(SPC)
model
models
proposed
by
Jorgensen
et
al.[30]
and
by
1
1
2
H
O
Uheat
(rij ,ofijkand
)vaporization
oxygen
KWr
(rijwas
 ras
)equation
to describe
KW6:H
(22O
 W ) 2 (6)Haughneyet
such
as liquid
density,
and
diffusion
of
Berendsen
et. al
[28]
used
wateral.[27] have
beenSWCNT
widely used for
W
ijk
2.3.1 Water Transport
through
bending
between
the hydrogen
atoms
2 The SPC model gives
2 reasonable
O
0.31656
0.1554
-0.82
water
interactions.
O
0.31656
0.1554
liquid
simulations.
Both
models
give
results for -0.82
a[28].Thismodelisdescribedbyintra-molecular harmonic
The system consists of 216 molecules of water and a single wall carbon
1
1
structural and thermodynamics
properties, such as
aH
Hrange of properties
0.0 that are in good
0.0 agreement 0.41
0.41
0.0
0.0
KWr
(rij  atoms
rW ) 2 as equation
KW ( ijk6: W ) 2 (6)
and
oxygen
nm
and
the
length
of
4
nm.
CNT
type
is armchair. The box size is 4nm
2
2
k
CH
CH3OH
OH
3
3 performed
for 2 ns at the NVT ensemble. The Berendsen
algorithm was us
175 0.265
International Journal of Nanoscience
CH3 and Nanotechnology
0.3775
0.8661
 W ) (6)
2
CH3
0.3775
0.8661
0.265
the system. The boundary condition was selected as periodic type.
O
0.3070
0.7113
-0.7
O
0.3070
0.7113
-0.7
3
3
Nanotube
H
0.0
0.0
0.0
2.3.2 Methanol Transport through SWCNT
0.435
0.435
The system consists of 216 molecules of methanol and a single wall carbo
0.2328
0.0
C
0.34
0.2328
0.0
2 nm and the 4 nm length. CNT type is armchair. The box size is 4nm
KW  383kJmol 1rad 2
W  109.47 0
qO= - 0.82
qH= 0.41
Table 3: Lenard-Jonzes parameters and partial
charges for water, Methanol and nanotube.
Table3.
Site
σ (nm)
ε (kJ/mol)
q (e)
O
0.31656
0.1554
-0.82
H
0.0
0.0
0.41
CH3
0.3775
0.8661
0.265
O
0.3070
0.7113
-0.7
H
0.0
0.0
0.435
C
0.34
0.2328
0.0
H2O
CH3OH
Nanotube
with the available experimental values. In our
simulations, each methanol molecule is described
with the model for optimized potentials for liquid
simulations (OPLS) proposed by Jorgensen et al.
[30], because Jorgensen’s model can reproduce both
gas-phase dimmer properties and liquid density at
ambient temperature and pressure. In the OPLS
model, three interaction sites are positioned on
the oxygen (O) nuclei, hydroxyl proton (H), and
united methyl (CH3) group centered on the carbon
(C), respectively. Table 3 shows LJ parameters and
partial charges for methanol, water and nanotube.
2.3. System Preparation
Here, a detailed comparison among physical
properties of the molecules in the pure and mixture
fluids along SWCNT has been performed by using
three simulation systems defined as below:
2.3.1. Water Transport through SWCNT
The system consists of 216 molecules of water and
a single wall carbon nanotube with the diameter of
2 nm and the length of 4 nm. CNT type is armchair.
The box size is 4nm × 4nm × 4nm. Simulation
was performed for 2 ns at the NVT ensemble.
The Berendsen algorithm was used to control the
temperature of the system. The boundary condition
was selected as periodic type.
2.3.2. Methanol Transport through SWCNT
176
The system consists of 216 molecules of methanol
and a single wall carbon nanotube with the diameter
of 2 nm and the 4 nm length. CNT type is armchair.
The box size is 4nm × 4nm × 4nm. Simulation
was performed for 2 ns at the NVT ensemble.
The Berendsen algorithm was used to control the
temperature of the system. The boundary condition
was selected as periodic type.
2.3.3. Methanol-Water Mixture Transport
through SWCNT
216 molecules of water and 216 molecules of
methanol were selected to examine transport
properties of the mixture (50 % mol) in the CNT
22
according above specification at 300 K for 2 ns. The
selected CNT and simulated systems are shown in
Figure 2.
3. RESULTS AND DISCUSSION
For the different systems as defined in the previous
sections, MD calculations were performed. Results
are shown in the following sections:
3.1. Density
At the first step, the radial and axial densities of
the molecules were calculated inside SWCNT. As
Figures 3 and 4 show for both systems (WaterCNT, Methanol-CNT), radial densities have the
Farhadian
(b)
12
(C)
14
14
Figure 2: (a) CNT configuration and size, (b)
Water-CNT simulated system, (c) methanol-CNT
Fig. 2system.
simulated
maximum peak near the CNT’s wall and after that
density reaches to the constant value equal to the
bulk density while axial density at the entrance and
exit point of the carbon nanotube
is higher than that
13
of bulk density. Howevr, upon molecules entrance
14
Figure 3: (a) Radial density of water in waterCNT system, (b) Axial density of water in waterCNT system, (c ) Radial density of methanol
in methanol-CNT system,
Fig. 3 (d) Axial density of
methanol in methanol-CNT system.
International Journal of Nanoscience and Nanotechnology
177
1000
1000
1000
Density (kg/nm^3)
750
Mixture
Mixture
Pure
Pure
500
500
250
0
(C)
750
750
Mixture
Pure
500
(a)
Density (kg/nm^3)
Density (Kg/nm^3)
(a)
250
250
0
0.5
1
1.5
00
2
r (nm)
00
0.5
1
21
z (nm)
r (nm)
1.5
3
42
1200
Density (Kg/nm^3)
(d)
800
Mixture
Pure
16
400
0
0
1
2
3
4
z (nm)
Mixture
Purearound
down
to the500nanotube, it is coming up and
the constant value. The fluctuation of this property
in the250Water-CNT system is more than that of the
Methanol-CNT system. In the mixture, above
0
observation
can be seen for methanol molecules
0
1
2
3
4
but there is no peak for radial
z (nm) density of water
molecules and the absolute value of the curves for
both components is less than that of the pure state.
3.2. Hydrogen Bonding
The averaged number of H-bonds per molecules
for different systems is shown
in Figure 5 and table
16
4. The hydrogen bond numbering between water
molecules at Water-CNT system is about 3.5, while
this value is about 1.2 for methanol molecules
at Methanol-CNT system. The hydrogen bond
numbering for mixture inside the CNT decreases
for both components ranges from 0.5-1.2. In the
mixture, new hydrogen bonding between methanol
and water molecules was created which decreases
178
Density (Kg/nm^3)
Density (Kg/nm^3)
Figure
4: (a) Radial density of methanol in water-methanol-CNT system, (b) Radial density of water in
1000
1000
(C)of methanol in water-methanol-CNT
water-methanol-CNT system, (c ) Axial density
system, (d) Axial density
(C)
of
water
in
water-methanol-CNT
system.
750
750
Mixture
Fig. 4 between pure molecules.
Pure
the hydrogen
bonding
500
Totally, the summation of the hydrogen bonding
at any 250
time is less than those of pure fluids inside
SWCNT.
0
0
3.3. Diffusion
3.3
2 Diffusion
3
1
z (nm)
4
To calculate
the diffusion coefficient of the
To calculate the diffusion coefficient
of the molecules
inside SWCNT by MD calculation,
it is the
necessary
to calculate
mean square displacement (
to calculate the mean square displacement (MSD)
water and methanol molecules inside SWC
of the molecules, at first. Figure 6 shows the MSD
SWCNT.
AllSWCNT
systems the MSD curves ha
of water and methanol molecules
inside
and Figure 7 shows the MSDbehavior
of the mixture
of the inside
fluids inside SWCNT. To c
16
SWCNT. All systems the MSD curves have the
insidenanotubeEinsteinequationcanbeuse
linear trend versus time which
shows the diffusive
N
behavior of the fluids inside SWCNT. 1To calculate
s
lim
(ri (t )  ri (0)) 2
the self diffusion coefficient ( D )of the molecules
t


2dNbe
1
 used i as
inside nanotube Einstein equation can
follows:
Where N is the number of molecules of com

α
mass of molecule i of
ri is the center of(6)
α
coefficient of water molecules inside CNT in
Farhadian
17
while for methanol molecules this value inc
mixture, the self diffusion coefficient of me
dynamics movement of methanol inside CNT
between methanol molecules rather than wa
and methanol molecules inside CNT rather th
SWCNT. All systems the MSD curves have the linear trend versu
behavior of the fluids inside SWCNT. To calculate the self diffusion
insidenanotubeEinsteinequationcanbeusedas follows:
# Hydrogen Bond
4
Dss 
(a)
3
2
1
0
0
500
1000
1500
2000
time (ps)
# Hydrogen Bond
1.5
(b)
1
0.5
0
0
500
1000
1500
2000
time (ps)
1
lim
2dN tt
N
N



 (r (t )  r (0))
ii11
ii
ii
22
Where Nα is the number of molecules of component
is the number
ofsystem,
molecules
of component
Where
Nααdimension
α,
d is the
of the
t is the
time, and α, d is the dimens
α
of molecule
i of icomponent
is the
ar
thecenter
centerofofmass
mass
of molecule
of component α. Results are
riiα is
α. Results are shown in table 5. The diffusion
coefficient of water molecules inside CNT in the mixture decreases rat
coefficient of water molecules inside CNT in the
while fordecreases
methanolrather
molecules
increases
mixture
than this
purevalue
water
inside during mixture tra
SWCNT
while
methanol
moleculesofthis
value is more than water
mixture, the
selffordiffusion
coefficient
methanol
increases during mixture transport along SWCNT.
dynamics
of self
methanol
inside
CNT, This
Also
in themovement
mixture, the
diffusion
coefficient
of maybe because of
methanol
is more than
water molecules
which
shows
table5,thedeviati
between methanol
molecules
rather than
water.
In table5,thedeviatio
the faster dynamics movement of methanol inside
and methanol molecules inside CNT rather than pure components (bulk
CNT, This maybe because of the weaker hydrogen
bond network between methanol molecules ratherFig. 6
than water. In table 5, the deviation of diffusion
Fig. 7
coefficient of water and methanol molecules inside
Table 5
CNT rather than pure components (bulk) was
reported.
3.4Minimum Distance
Finally, the minimum distance and the number of contacts of wate
wat
3.4. Minimum Distance
t
mixture the
withminimum
the SWCNT
wall were
calculated.
8a shows that th
Finally,
distance
and the
number Figure
of
contacts
in the with the water mo
moleculesof iswater
moreand
thanmethanol
two-foldmolecules
in comparison
mixture
with
the
SWCNT
wall
were
calculated.
maximum and minimum points at some special times. Figure 8b sho
Figure 8a shows that the number of contacts for
nearly constant
distance
SWCNT
wall during
the simulation
methanol
molecules
is with
morethethan
two-fold
in
comparison
water
curve
this distancewith
has the
some
moremolecules.
vibration This
because
of the more and unc
has the local maximum and minimum points at some
methanol
molecules.
special
times.
Figure 8b shows that water molecules
have the nearly constant distance with the SWCNT Fig. 8
wall during the simulation time while for methanol
molecules this distance has some more vibration
4. Conclusions
because
of the more and unconstant number of
contacts
of
theMD
methanol
molecules.
In this work,
simulations
were performed to study the physical pro
the mixture of water-methanol (50 mol %) through a single wall c
4.
CONCLUSIONS
showed
that radial densities of the molecules inside the SWCNT have
Figure 5: (a) Number of
hydrogen
bonding among
Fig.
5
water molecules in the water-CNT system, (b)
Number of hydrogen bonding among methanol
molecules in the methanol-CNT system, (c) Number
18 water, methanol and
of hydrogen bonding among
water-methanol molecules in the water-methanolCNT system.
In this work, MD simulations were performed to study
the physical properties of the pure components and 6
the mixture of water-methanol (50 mol %) through
a single wall carbon nanotube. Density analysis
showed that radial densities of the molecules inside
the SWCNT have a maximum peak near the CNT’s
wall and after that become constant equal to the bulk
International Journal of Nanoscience and Nanotechnology
179
Table 4.
H-bondTable
Numbering
H-bond
4. AveragedH-bond
number Table
of hydrogen
bonds per molecule.H-bond
4.
SystemH-bond Numbering
Water
- Water
H-bond
Methanol
- Methanol
H-bond
Water-Methanol
H-bond
Experiment
System
Water - Water
Methanol - Methanol
Water-Methanol
PureMethanol
Experiment
-
1-3[30]
-
PureWater
PureMethanol
3-4[30]
-
-
1-3[30]
-
Methanol-Water
PureWater
-
3-4[30]
-
1[31]
-
Methanol-Water
Modeling
-
-
1[31]
Modeling
Water-CNT
3.50
-
-
Water-CNT
Methanol-CNT
3.50
-
-
1.20
-
-
Methanol-CNT
Water-Methanol-CNT
0.93
1.20
0.46
1.20
0.93
0.46
1.20
Water-Methanol-CNT
Table 5. Calculated diffusion coefficients
inside SWCNT at the different systems
Table5.
System
System
Pure water
Pure water
Pure methanol
Pure methanol
Water inside CNT
Water inside CNT
Methanol inside CNT
Methanol inside CNT
Methanol-Water inside
Methanol-Water inside
CNT
CNT
Table5.
Diffusion Coef. (cm2/s)
Diffusion Coef. (cm2/s)
D_water
D_water
5.100×10-5[30]
5.100×10-5[30]
3.100×10-5
3.100×10-5
2.802 × 10-5
2.802 × 10-5
D_methanol
D_methanol
2.2×10-5[30]
2.2×10-5[30]
3.310×10-5
3.310×10-5
3.930×10-5
3.930×10-5
Percent Deviation
Percent
from
pureDeviation
component
from pure component
Water
Methanol
Water
Methanol
-39.22
-39.22
+50.45
-45.05
-45.05
+50.45
+78.63
+78.63
density, but axial density in the box is fluctuating
number of contacts of the molecules inside SWCNT.
around a constant value. These calculations provide a
All results showed that methanol molecules have
picture of how water and methanol molecules arrange
faster dynamics behavior rather than water molecules
themselves inside a SWCNT and produce a certain
in the mixture of water-methanol-CNT system.
value of density across the diameter and axial axes.
Understanding the different physical and transport
Total calculated number of hydrogen bond for the
properties of the mixture along SWCNT can be useful
mixture inside SWCNT was between those values for
for designing the new nano-scale systems.
two pure systems. This shows the new hydrogen bond
formation between water and methanol molecules
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