Conduction of water molecules through graphene bilayer

Yu Qiao,1,2,a) Xiang Xu,1,3 and Hui Li31Department of Structural Engineering, University of California San Diego, La Jolla,California 92093-0085, USA2Program of Materials Science and Engineering, University of California San Diego, La Jolla,California 92093, USA3Center 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

because of the additional degree of freedom of water molecular motion. VC 2013 AIP Publishing LLC.

[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 conduc-

tion rate.3 A variety of nanofluidic devices have been devel-

oped 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” proce-

dure if the nanotube/nanopore is lyophilic;11 while in a lyo-

phobic 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 isothermal-

isovolumetric (NVT) ensemble by Large-Scale Atomic/

Molecular Massively Parallel Simulator (LAMMPS).18 Two

rigid graphene sheets, with the dimension about 28 A� 30 A,

were laminated to form a 2D bilayer. The interlayer distance

(d-spacing) was set to 7.5 A.19 Periodic boundary condition

was imposed along the y and z directions (Fig. 1(a)). Two 90 A

� 30 A� 14 A water reservoirs were connected to the bilayer

from both ends, respectively. Initially, 1100 Transferable

Intermolecular Potential 3P (TIP3P) water molecules were

placed in the left reservoir with the density of 1.0 g/cm3. By

moving a rigid plane (piston), the water molecules were com-

pressed 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 (h¼ 0); when the rotation angle

was in the range from 0� to 60�, the two graphene layers

were turbostratic; when h¼ 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 particle-

particle particle-mesh (PPPM) technique with a root mean

square accuracy of 10�4 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.

a)Author to whom correspondence should be addressed. Electronic mail:

yqiao@ucsd.edu. Tel.: þ1-858-534-3388. Fax: þ1-656-534-1310

0003-6951/2013/103(23)/233106/3/$30.00 VC 2013 AIP Publishing LLC103, 233106-1

APPLIED PHYSICS LETTERS 103, 233106 (2013)

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reservoir were equilibrated under NVT ensemble (300K) for

50 ns. Then, the left rigid wall (piston) was moved toward

right at the velocity of 10�5 A/fs and after each 0.1 A, the

piston was temporarily stopped and the system was equili-

brated 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 typi-

cal 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

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 h¼ 30�, has

a higher infiltration pressure compared with the commensu-

rate state (h¼ 0� or 60�).The interactive potential distribution between water and

graphene layers is explored by calculating the system poten-

tial energy as a water molecule moves across the bilayer.

Ten paths, parallel to the x direction and 3 A 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 10�5 A/fs and after each 0.5 A, 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

h¼ 10� and 50�. More energy valleys and low energy paths

can be observed when h¼ 30� (Figure 3(d)). As h¼ 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 sys-

tem 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. 2. Infiltration isotherm curves of the 2D nanofluidic systems.

FIG. 3. Interactive potential energy

distributions in graphene bilayers: (a)

h¼ 0� and 60�; (b) h¼ 10�; (c)

h¼ 20�; (d) h¼ 30�; (e) h¼ 40�; and

(f) h¼ 50�.

233106-2 Qiao, Xu, and Li Appl. Phys. Lett. 103, 233106 (2013)

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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 pres-

sure. 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 fac-

tor 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, com-

pared 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

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) grate-

fully 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.

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FIG. 4. The mean infiltration pressure as a function of the rotation angle.

233106-3 Qiao, Xu, and Li Appl. Phys. Lett. 103, 233106 (2013)

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