APPLIED PHYSICS LETTERS 103, 233106 (2013)
Conduction of water molecules through graphene bilayer
Yu Qiao,1,2,a) Xiang Xu,1,3 and Hui Li3
1
Department of Structural Engineering, University of California San Diego, La Jolla,
California 92093-0085, USA
2
Program of Materials Science and Engineering, University of California San Diego, La Jolla,
California 92093, USA
3
Center of Structural Monitoring & Control, School of Civil Engineering, Harbin Institute of Technology,
Harbin 150090, China
(Received 31 August 2013; accepted 15 November 2013; published online 4 December 2013)
Water conduction across a two-dimensional (2D) graphene bilayer was investigated through
molecular dynamic simulations. Different from one-dimensional (1D) nanofluidics in carbon
nanotubes (CNTs) where CNT chirality has only a secondary effect, when the bilayer structure is
changed from the turbostratic state to the commensurate state, the water infiltration pressure decreases
considerably, as energy valleys are formed. Compared with the 1D nanofludics in a CNT, the
infiltration pressure of 2D nanofluidics in a graphene bilayer tends to be much lower, primarily
C 2013 AIP Publishing LLC.
because of the additional degree of freedom of water molecular motion. V
[http://dx.doi.org/10.1063/1.4839255]
Nanofluidics was investigated extensively in recent
years.1 They have unique properties that are not observable in
conventional, microscopic or macroscopic fluidic systems,
such as the chain-like flow pattern2 and the enhanced conduction rate.3 A variety of nanofluidic devices have been developed for biosensing, microchips, advanced filtration, among
others.4–10 For instance, in a molecular-sized nanotube, only
the axial movement of confined liquid molecules is allowed.
Liquid transportation may follow a “superconduction” procedure if the nanotube/nanopore is lyophilic;11 while in a lyophobic nanoenvironment, liquid molecules have to overcome
the liquid-liquid hydrogen bond and the liquid-solid van der
Waals energy barriers to move forward.12,13 As a result, the
system free energy of the latter is higher,14 which can be
described by the concept of “column resistance.”15
While the previous investigations on nanofluidics
explored many interesting phenomena, most of them were
focused on one-dimensional (1D) systems, i.e., nanotubes,
nanopores, and nanochannels.16,17 It is envisioned that, if an
additional degree of freedom of liquid molecular motion can
be provided, e.g., in a two dimensional (2D) graphene
bilayer, the behaviors of confined liquid may be different,
which will be the focus of the current study.
In order to analyze 2D nanofludic behaviors, the
pressurized infiltration process of water molecules through a
hydrophobic graphene bilayer was examined in an isothermalisovolumetric (NVT) ensemble by Large-Scale Atomic/
Molecular Massively Parallel Simulator (LAMMPS).18 Two
rigid graphene sheets, with the dimension about 28 Å 30 Å,
were laminated to form a 2D bilayer. The interlayer distance
(d-spacing) was set to 7.5 Å.19 Periodic boundary condition
was imposed along the y and z directions (Fig. 1(a)). Two 90 Å
30 Å 14 Å water reservoirs were connected to the bilayer
from both ends, respectively. Initially, 1100 Transferable
Intermolecular Potential 3P (TIP3P) water molecules were
a)
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placed in the left reservoir with the density of 1.0 g/cm3. By
moving a rigid plane (piston), the water molecules were compressed and, as the internal pressure was sufficiently high,
would eventually enter and pass through the bilayer, reaching
the reservoir on the right.
The influence of the rotation angle between the upper
and the lower graphene layers, h, was examined (Fig. 1(b)).
When the two graphene layers were fully aligned, they were
in the commensurate state (h ¼ 0); when the rotation angle
was in the range from 0 to 60 , the two graphene layers
were turbostratic; when h ¼ 60 , the commensurate state was
reached again. In the current study, the bottom graphene
layer was fixed and the orientation of the upper layer was
varied.
The CHARMM force field20 was employed and the
carbon-oxygen LJ 12-6 parameters were, respectively, set as
eCO ¼ 0:392 kJ=mol and rCO ¼ 0:319 nm.21 The particleparticle particle-mesh (PPPM) technique with a root mean
square accuracy of 104 was used to handle the long range
Coulomb interactions among the oxygen and hydrogen
atoms. Stepwise and quasi-static loading condition was
employed. Before loading, the water molecules in the left
FIG. 1. The 2D nanofluidic system: (a) The MD simulation setup; (b) the
top view of the graphene bilayer, showing the upper and the lower graphene
layers of different rotation angles, h.
103, 233106-1
C 2013 AIP Publishing LLC
V
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233106-2
Qiao, Xu, and Li
FIG. 2. Infiltration isotherm curves of the 2D nanofluidic systems.
reservoir were equilibrated under NVT ensemble (300K) for
50 ns. Then, the left rigid wall (piston) was moved toward
right at the velocity of 105 Å/fs and after each 0.1 Å, the
piston was temporarily stopped and the system was equilibrated for 10 ns. Pressure was evaluated from the average
density of the water inside the reservoir by using the
pressure-density state equation of water.22
Figure 2 shows the infiltration isotherm curves. A typical process of pressurized transportation of water molecules
consists of three stages: In stage I, the interaction between
water and graphene is dominated by the van der Waals C-O
attraction. While a few water molecules near the opening
can enter the bilayer via surface diffusion, bulk infiltration
cannot take place as the pressure is insufficient to overcome
the energy barriers.2 In stage II, as the water pressure reaches
the first threshold, water starts to enter the bilayer from the
near end. Finally, in stage III, as the water pressure reaches
the second threshold, water molecules “flow” out of the
Appl. Phys. Lett. 103, 233106 (2013)
bilayer from the far end, and the system behavior reaches the
steady state. An interesting phenomenon is that, in stages II
and III, the turbostratic bilayer, especially when h ¼ 30 , has
a higher infiltration pressure compared with the commensurate state (h ¼ 0 or 60 ).
The interactive potential distribution between water and
graphene layers is explored by calculating the system potential energy as a water molecule moves across the bilayer.
Ten paths, parallel to the x direction and 3 Å away from each
other along the y direction, were analyzed. For each path,
one water molecule was forced to move along the x direction
at the velocity of 105 Å/fs and after each 0.5 Å, the system
potential energy was calculated. Figure 3 shows the potential
energy distributions. There are no obvious fluctuations of the
potential energies in the commensurate bilayer. Energy
peaks (higher than 3.0 kcal/mole) distribute homogeneously
and no energy valleys (lower than 1.5 kcal/mole) are found.
According to Figures 3(b) and 3(f), evident energy valleys
are formed near the two ends of the graphene bilayer when
h ¼ 10 and 50 . More energy valleys and low energy paths
can be observed when h ¼ 30 (Figure 3(d)). As h ¼ 20 and
40 , even though the turbostratic structure induced energy
valleys are relatively low, the energy peak areas are also
reduced. Clearly, compared to the commensurate state, due
to the formation of the energy valleys, the van der Waals
interactive effect in the turbostratic bilayer is considerably
weakened.
For self-comparison purpose, the average infiltration
pressure in stages II and III is used as a measure of the system free energy associated with the water conduction
(Fig. 4). Due to the homogeneously distributed energy peak
areas in the commensurate bilayer, water molecules can
overcome the energy barrier to enter the bilayer quite easily
with the aid of the relatively strong van der Waals attractive
effect, which leads to a low infiltration pressures about
91 MPa. When the upper graphene sheet is rotated by 10 or
50 , energy valleys are built up and the van der Waals
FIG. 3. Interactive potential energy
distributions in graphene bilayers: (a)
h ¼ 0 and 60 ; (b) h ¼ 10 ; (c)
h ¼ 20 ; (d) h ¼ 30 ; (e) h ¼ 40 ; and
(f) h ¼ 50 .
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233106-3
Qiao, Xu, and Li
Appl. Phys. Lett. 103, 233106 (2013)
analyzed. The lowest infiltration pressure was achieved in
the commensurate state; the highest value was achieved
when the rotation angle was 30 , which may be related to the
formation of energy valleys as the two graphene layers are
misaligned. In the 2D nanoenvironment of a graphene
bilayer, the water conduction tends to be easier than in a 1D
nanoenvironment, e.g., a CNT, as it has one more degree of
freedom to lower the system free energy.
One of the authors (Qiao) gratefully acknowledges the
support from The National Science Foundation under Grant
No. ECCS-1028010. The rest two authors (Xu and Li) gratefully acknowledge the support from The Ministry of Science
and Technology (China) under Grant No. 2011BAK02B02
and The Ministry of Transportation (China) under Grant No.
2011318494180.
FIG. 4. The mean infiltration pressure as a function of the rotation angle.
1
attractive effect is reduced. Water molecules need a higher
activation energy to lose hydrogen bonds to enter the bilayer.
As a result, the mean infiltration pressure rises to about
108 MPa. When the rotation angle is 20 or 40 , as both the
energy valleys and peaks are reduced, the van der Waals
attractive effect is lowered slightly, so is the infiltration pressure. Once the upper graphene layer is rotated by 30 , the
effects of interactive potential valleys are most pronounced,
resulting in the maximum infiltration pressure close to
122 MPa. That is, the rotation angle of bilayer is a vital factor dominating the properties of the 2D nanofluidics, which
is quite different from 1D nanofludics in carbon nanotubes
(CNTs) where the effect of CNT chirality is only
secondary.23
Moreover, the effective infiltration pressures in all the
graphene bilayers under investigation tend to be much lower
than that in a CNT, when the CNT diameter (d) is the same
as the bilayer d-spacing (dS). For instance, the infiltration
pressures of a commensurate bilayer with dS 10 nm and
20 nm are about 60 MPa and 34 MPa, respectively; while the
infiltration pressures of a CNT with d 10 nm and 20 nm are
much higher, around 170 MPa and 90 MPa, respectively.24
The only major difference between the two situations is the
configurations of CNT and bilayer; the potential function
and the parameters are all the same, suggesting that, compared with 1D nanofluidics, the resistance to 2D “nanoflow”
in a bilayer is intrinsically reduced, as the additional degree
of freedom allows the confined water molecules to reach a
lower system free energy.
In summary, water conduction in 2D graphene bilayer
was investigated via molecular dynamic (MD) simulations.
Both commensurate and turbostratic structures were
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