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Molecular sieving through a graphene
nanopore: non-equilibrium molecular
dynamics simulation
Article · March 2017
DOI: 10.1016/j.scib.2017.03.004
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Science Bulletin 62 (2017) 554–562
Contents lists available at ScienceDirect
Science Bulletin
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Article
Molecular sieving through a graphene nanopore: non-equilibrium
molecular dynamics simulation
Chengzhen Sun, Bofeng Bai ⇑
State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history:
Received 11 January 2017
Received in revised form 22 February 2017
Accepted 28 February 2017
Available online 7 March 2017
Keywords:
Graphene nanopore
Molecular sieve
Molecular dynamics
Gas separation membrane
a b s t r a c t
Two-dimensional graphene nanopores have shown great promise as ultra-permeable molecular sieves
based on their size-sieving effects. We design a nitrogen/hydrogen modified graphene nanopore and conduct a transient non-equilibrium molecular dynamics simulation on its molecular sieving effects. The distinct time-varying molecular crossing numbers show that this special nanopore can efficiently sieve CO2
and H2S molecules from CH4 molecules with high selectivity. By analyzing the molecular structure and
pore functionalization-related molecular orientation and permeable zone in the nanopore, density distribution in the molecular adsorption layer on the graphene surface, as well as other features, the molecular
sieving mechanisms of graphene nanopores are revealed. Finally, several implications on the design of
highly-efficient graphene nanopores, especially for determining the porosity and chemical functionalization, as gas separation membranes are summarized based on the identified phenomena and mechanisms.
Ó 2017 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.
1. Introduction
Graphene and its derivatives [1–4] are reasonably thought to be
very promising candidates for separation membrane materials
owing to their atomic thickness. With the efforts of scientists,
graphene-based membranes are indeed in development. A pristine
sheet of graphene is fully impermeable to any molecule due to the
unfavorable energy barriers of its tightly-packed carbon atoms,
even helium and hydrogen molecules. However, aqueous protons
that are smaller than atoms exhibit high conductance through graphene [5,6]. Consequently, graphene can be directly adopted as a
proton transport/exchange membrane, while it can only be
employed as molecular and ionic separation membranes after the
artificial introduction of nanometer-sized pores (called as nanoporous graphene (NPG)) [7–11]. Graphene oxide, a derivative of
graphene, is a good substitute of the NPG membrane for molecular
and ionic separation [12–15]. The separation mechanism of NPG
membranes is basically the molecular and ionic sieving effects
(Fig. 1) and the mechanism of proton transport/exchange graphene
membranes is purely that graphene is a good conductor of protons
(Fig. 1). By contrast, the separation mechanisms of graphene oxide
membranes are relatively complicated, such as selective molecular
and ionic transport through the interconnected nanochannels
between the graphene oxide sheets, the wrinkles and holes in gra⇑ Corresponding author.
E-mail address: bfbai@mail.xjtu.edu.cn (B. Bai).
phene oxide sheets, among others (Fig. 1). Graphene-based membranes seem simple in theory; however, in practice, many efforts
should be devoted to developing these state-of-the-art membranes. For molecular sieving, NPG membranes and graphene
oxide membranes are both effective. Currently, laminated graphene oxide membranes seem more promising for molecular and
ionic separations due to their ease of synthesis and scale up. However, atomically-thick NPG is the limit of membranes and its corresponding extremely high permeance will be very beneficial in
many applications. Advanced methods (e.g., plasma etching and
chemical oxidation etching [7,16,17]) are being rapidly developed
to fabricate NPGs with highly controllable pores, in place of the traditional robust methods, such as electron beam irradiation [18]
and ion beam bombardment [19].
Graphene pore-based NPGs have shown potential in gas separation [20], water desalination [21], isotope separation [22], and
DNA sequencing [23]. Recently, several experimental studies
[7–9,14,24–27] successfully demonstrated that NPG membranes
are becoming a reality and that isolated graphene nanopores can
be created. Since NPG was first proposed as a gas separation membrane by Jiang et al. [20], it has received attention from a variety of
research communities [7,28–30]. Until now, most of the relevant
studies have been conducted based on theoretical calculations
due to their practicability and low economic cost, especially in
regard to molecular dynamics (MD) and density functional theory
methods. The effects of surface adsorption [31–33], nonpermeating component [34], chemical modifications [35,36] and
http://dx.doi.org/10.1016/j.scib.2017.03.004
2095-9273/Ó 2017 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.
C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
Fig. 1. Mechanisms of graphene-based membranes. The mechanism of NPG
membranes is mainly the molecular and ionic size-sieving effects, and that of
graphene oxide membranes is selective molecular and ionic permeation through
interconnected nanochannels, wrinkles and holes in the graphene oxide, and so on.
For graphene proton transport/exchange membranes, the aqueous proton can
directly transport through the electron clouds of carbon atoms.
others on molecular permeation were elucidated. Lei et al. [37]
tested the sieving effect of a pristine graphene nanopore for the
separation of H2S/CH4 and revealed the effects of atomic charges
by adding charges on the pore-rim carbon atoms. Hauser and Schwerdtfeger [38] showed that structure relaxation can significantly
reduce the permeation barriers of gas molecules through two flexible nanopores (all-H and N/H modified pore) and discussed, in
detail, the interactions between functionalized pore rims and gas
molecules. The mechanisms of molecular permeation through graphene nanopores have basically been revealed. In our early work
[39], we identified two regimes from which molecules permeate
through nanopores; the molecules permeate through nanopores
directly from the bulk phase without interacting with the graphene
surface or they permeate by diffusion through the graphene surface. Owing to their excellent performance in gas separation,
NPG membranes and other graphene-related materials were
demonstrated to have great application prospects in other gasrelated technologies, such as hydrogen storage, carbon capture
and gas sensors [28,40–44].
Development of industrial NPG gas separation membranes is in
progress, and several corresponding experimental studies have
been performed. Initially, a micrometer-sized NPG membrane
was fabricated by Koenig et al. [7] and fast mass transport through
graphene nanopores was demonstrated by their measurements of
the permeation fluxes of several gases. Then, a double-layer NPG
and few-layer NPG sheet were fabricated by Celebi et al. [8] and
Kim et al. [14], respectively. The areas of these membranes were
up to the industrial scale, and selective gas permeation was identified. Boutilier et al. [27] conducted a systematic experimental
study to quantify the effects of tears and intrinsic defects on the
performance of NPG membranes. To realize NPG-based membrane
separation technology, great developments in large-area graphene
fabrication and high-quality pore generation and modification are
expected.
Permeability and selectivity are two competing factors for separation membranes. It is expected that membranes maintain high
selectivity of a permeating gas over a non-permeating gas with a
high permeability of the permeating gas, to achieve excellent performance and overcome the Robeson upper bound [45]. The high
permeability of NPG membranes can be spontaneously assured
by their intrinsic atomic thickness, but the high selectivity must
555
be deliberately pursued with optimal nanopores. The size-sieving
effects would be down if the graphene nanopores are designed
inappropriately, resulting in a poor separation performance of
NPG membranes. In this paper, we design a graphene nanopore
functionalized by N and H atoms and conduct a systematical and
thorough MD study on the size-sieving effect. The MD simulation
is performed in a non-equilibrium system, where the feed side is
initially filled with a mixture of gases, while the permeate side is
kept in a vacuum. We show that the graphene nanopore can efficiently sieve H2S and CO2 molecules from CH4 molecules with
higher permeance (on the order of 105 GPU; 1 GPU = 3.35 1010 mol/(m2 s Pa)) and selectivity (on the order of 20). We also reveal
the molecular sieving mechanisms of graphene nanopores from
the aspects of pore configurations, molecular size and structure,
graphene-molecule interactions, among others. Meanwhile, based
on the identified phenomena and mechanisms, several implications on the design of high-efficient graphene nanopore-based
gas separation membranes are summarized, such as on the porosity, pore functionalization, and so on. Coupled with the super corrosion resistance of graphene [46,47], these results additionally
demonstrate the potential of NPG membranes to remove acid gases
(i.e., H2S and CO2) from natural gas, exhibiting exceptional significances in energy savings and environmental protection.
2. Simulation model
2.1. Pore structure
We design a graphene nanopore based on a pore consisting of
12 graphene-rings, as shown in Fig. 2. Then, we modify the pore
with 4 N atoms and 5 H atoms; namely, 5 unsaturated C atoms
(3 top C atoms and 2 bottom C atoms) are passivated with H atoms,
while the remaining 4 C atoms are doped with N atoms. The pore
size and configuration are determined to make sure that CH4 has a
few crossings, while H2S and CO2 can easily permeate the nanopore. The N functionalization not only enlarges the size of the pore
to achieve high permeation of CO2 and H2S molecules, but also
enhances the adsorption intensities of CO2 and H2S molecules,
which further improves the permeability. Notably, the 12
graphene-ring pore without chemical modification is nonselective and the CH4 molecules can easily permeate it. Additionally, the all-hydrogen-passivated nanopore is impermeable to
CH4 molecules and weakly permeable to CO2 and H2S molecules.
Therefore, the N/H modified nanopore exhibits a better sieving
effect than the all-H modified nanopore.
Fig. 2. Graphene nanopore modified by N and H atoms. Gray spheres denote C
atoms in graphene, pink spheres denote N atoms, and green spheres denote H
atoms.
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C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
For NPG membranes with such nanopores, the spacing distance
among the nanopores is assigned 4 nm (Fig. 2). In this case, the
number density of the pores is 6.25 1012 cm2, which is comparable to the pore densities (exceeding 1012 cm2) in the fabricated
NPG membranes in the laboratory of O’Hern et al. [24]. The contribution of the graphene surface on the molecular permeation is very
pronounced, because the vast majority of molecules permeate
through the nanopore after being adsorbed onto the graphene surface. The contribution of the graphene surface is more significant
as the pore number density decreases. Detailed investigations on
the adsorption of CO2 and H2S molecules on graphene (or with
N/H modifications) can be found in prior studies [42,43,48].
Ebond ¼ K bond ðr r0 Þ2 ;
ð2Þ
where Kbond is the bond stretch coefficient and r0 is the equilibrium
bond distance (bond length). The harmonic angle deformation
potential is given by:
Eangle ¼ K angle ðh h0 Þ2 ;
ð3Þ
where Kangle is the angle deformation coefficient and h0 is the equilibrium value of the angle. The related parameters in the harmonic
potentials are listed in Table S3 (online).
3. Results and discussion
2.2. Simulation system and method
3.1. Molecular adsorption
To examine the sieving effect of this graphene nanopore, we
perform MD simulations for the separation of H2S/CH4 and CO2/
CH4 mixtures in a non-equilibrium system. In the system, there
are 1,000 mixed gas molecules, namely 500 for the permeating
component (i.e., H2S or CO2) and 500 for the non-permeating component (i.e., CH4). Initially, the molecules are arranged alternatively and uniformly in the feed side of graphene, while the
permeate side is kept in a vacuum, as seen in Fig. S1a (online). Graphene is located at the center of the simulation box with a height
of 140 nm. In graphene, one corner carbon atom is fixed to prevent
vertical displacement, while the other carbon atoms slightly
vibrate in response to collisions with gas molecules. Periodic
boundary conditions are applied in the x- and y-directions (parallel
to the graphene surface), while the reflective wall condition is
applied in the z-direction (perpendicular to the graphene surface).
On account of the periodic boundary conditions, we use graphene
with an area of (4 4) nm2 based on the spacing distance among
nanopores and place the nanopore in the center of graphene (see
the yellow frame in Fig. 2). The simulation is run in a NVT ensemble with a temperature of 350 K. A simulation period of
1.26 108 timesteps (time step is 0.3 fs) is chosen such that the
permeating gases transport through the nanopore at a relatively
fast rate, ensuring high accuracy in the calculation of permeance
(see below). We periodically analyze the molecular coordinates
with a short period (4.5 ps) to check whether a possible molecular
crossing event occurs. Based on the ideal gas equation (pV ¼ NkB T),
the initial pressure of the feed side is estimated as 21.1 bar.
For carbon and hydrogen atoms in the graphene sheet and CH4
molecules, the atomic interactions are modeled by the AIREBO
potential model; while for H2S and CO2 molecules, they are modeled by a three-site model. In this model, the Lennard-Jones potential and Coulombic potential are coupled together, as follows:
For permeable graphene nanopores, molecules originally
located at the feed side can migrate to the permeate side. Therefore, the number of molecules in the feed side decreases gradually,
while that in the permeate side increases. As seen from
Fig. 3a and b, the molecular number density distribution along
the z-direction, averaged over the entire simulation period, shows
a discrepancy between the feed side and permeate side; namely,
the average number of molecules in the feed side is higher than
that in the permeate side. Meanwhile, it can be observed that the
molecules in the feed and permeate sides do not distribute uniformly; instead, they partially adsorb onto the graphene surface.
On the graphene surface, there is a zone (0.17 nm < |z| < 0.6 nm,
called adsorption layer) that presents a high density of molecules;
away from this zone (|z| > 0.6 nm), the molecules distribute uniformly. A higher molecular number density in the adsorption layer
indicates a stronger adsorption intensity on the graphene surface,
which is determined by the interactions between gas molecules
and graphene atoms. It can be seen from the figures that the order
of the molecular adsorption intensity is H2S > CO2 > CH4, which is
related to the distinct atomic Van der Waals and coulombic interactions. Due to the molecular permeation, the number of molecules in the adsorption layer varies with the simulation time;
namely, the corresponding molecular number in the feed side
decreases over time, while that in permeate side increases over
time (Fig. 3c and d). The time-variation of the molecular number
in the adsorption layer for H2S is more obvious than that for CO2
because more H2S molecules can permeate through the nanopore
(see below). However, we note that the total number of molecules
in the adsorption layer of both sides equilibrates at a constant
value. Although molecular migrations between the feed side and
permeate side frequently occur, the total number of molecules in
the two sides remains constant such that the effective pressure
in the system is basically stable. Therefore, the molecular adsorption on both sides of the graphene surface is in a quasiequilibrium state. It is noted that, in the simulations, the separations of CO2 and H2S molecules from CH4 molecules are conducted
separately; in the event that the CO2 and H2S molecules are mixed
together and simultaneously separated from CH4 molecules, the
adsorption of one component would be decreased due to the competitive mechanism, which can induce a reduction in the permeation rate of this component, as illustrated by Wen et al. [34].
In the adsorption layer of the feed side, a non-uniform molecular density distribution is presented owing to the surface-guided
molecular permeation. Based on the distinct distribution characteristics, we recognize three different zones in the adsorption layer,
i.e., the peripheral zone, Fick zone and accumulation zone (Fig. 4).
In the peripheral zone, owing to the uniformly located graphene
carbon atoms that are far from the nanopore, gas molecules also
distribute uniformly because of homogeneous atomic interactions.
In the Fick zone, the molecules diffuse along the graphene surface
to the nanopore and some permeate through; accordingly, the
/ðr ij Þ ¼
8 12 6 Cq q
< 4e r
þ i j
r
:
r ij
0
r ij
vrij
ðr ij < r cut Þ
;
ð1Þ
ðr ij P r cut Þ
where r is the length scale, e is the energy scale, qi and qj are the
atomic charges, C is an energy-conversion constant, and v is the
dielectric constant. In our simulations, the relative dielectric constants are all adopted as 1. The parameters of the three-site model
are listed in Tables S1 and S2 (online). To save on computation cost,
we only consider the charges on the graphene atoms near the pore
(as shown in Fig. S1b online) because the charges on the remaining
graphene carbon atoms are negligible.
In the simulations, the bond stretch and angle deformation are
properly considered. For CH4 molecules and the CAH bond in graphene, they are included in the AIREBO potential model; while for
H2S and CO2 molecules as well as other functionalized groups, they
are modeled by the harmonic potential. The harmonic bond stretch
potential is given by:
C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
557
Fig. 3. Adsorption characteristics of molecules on the graphene surface. (a,b) Molecular number density distribution along the z-direction for the separation of CO2/CH4 and
H2S/CH4, respectively. (c,d) Time-variation of the adsorbed molecular number in the feed and permeate sides for the separation of CO2/CH4 and H2S/CH4, respectively.
Fig. 4. Molecular number density distributions in the adsorption layer of the feed side for (a) CO2 and (b) H2S. Three different zones are identified, including the peripheral
zone, Fick zone and accumulation zone. Nd is the adsorbed molecular number on the unit graphene surface with an area of 1.74 Å2.
molecules have a lower number density distribution than the
peripheral zone. In this zone, molecular diffusion is driven by the
concentration gradient along the radial direction and dominated
by Fick’s first law; therefore, this zone is denoted as Fick zone.
The accumulation zone is located at the center of the nanopore,
where the permeating molecules are ‘‘in line” to wait to permeate
through the nanopore due to the restriction of the pore size. Therefore, in the accumulation zone, the molecules aggregate and the
corresponding molecular number density is particularly high. It is
noted that the low molecular number density in the Fick zone is
also partially related to the absence of graphene atoms (in nanopore) for attracting gas molecules.
3.2. Molecular permeation
Owing to the size-sieving effect of the N/H modified graphene
nanopore, the permeation abilities of the permeating molecules
with smaller sizes (CO2 and H2S) and non-permeating molecules
with a larger size (CH4) are different. As seen from Fig. 5a and b,
the molecular number N in the permeate side (zi < 0.6 nm) of permeating molecules sharply increases with the passage of time,
while that of non-permeating molecules increases very slowly
and only a few CH4 molecules appear in the permeate side. These
results demonstrate that the graphene nanopore has a high selectivity of CO2 and H2S molecules over CH4 molecules. We also
observed that the number of permeated H2S molecules is higher
than that of CO2 molecules owing to the distinct molecular kinetic
parameters and adsorption intensity on the graphene surface.
Compared with CO2 molecules, H2S molecules are larger (kinetic
diameter: H2S 0.36 nm [37] versus CO2 0.33 nm [49]), yet lighter
(relative molecular mass: H2S 34 versus CO2 44), resulting in a
comparable permeation ability from the viewpoint of molecular
kinetic parameters. However, the stronger adsorption intensity of
H2S molecules helps them improve the permeation ability by
molecular diffusion on the graphene surface [39].
The number of permeated molecules N is a function of time s,
the form of which can be derived based on the relationship
between flux J in unit of mol/s and permeance S in unit of mol/
(m2 s Pa),
J¼
dN 1
¼ SDPAg ;
ds N A
ð4Þ
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C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
Fig. 5. Molecular permeation through the graphene nanopore. (a,b) Time-variation of the permeated molecular number for the separation of CO2/CH4 and H2S/CH4,
respectively. (c,d) Probability distribution of the permeating molecules in the nanopore for CO2 and H2S, respectively.
where Ag is the area of the graphene sheet (Ag = 16 1018 m2), NA
is the Avogadro constant, and DP is the pressure difference between
the feed and permeate sides. As the driving force for molecular permeation, the pressure difference between the feed and permeate
sides decreases with the permeation of molecules. For a system
with an initial pressure of 21.1 bar in the feed side, the pressure difference is:
DP ¼
500 Nal 2N
21:1bar;
500
ð5Þ
where Nal is the average number of molecules that are adsorbed on
both sides of graphene surface, which can be obtained from the MD
simulations. Thus,
dN
¼ 4:12 1010 Sð500 Nal 2NÞ:
ds
ð6Þ
After integrating the above equation, we obtain
10
N ¼ ð250 Nal =2Þ ð1 e8:2410 Ss Þ:
ð7Þ
It is noted that exponent b in the time decay is given by:
b ¼ 8:24 1010 S:
ð8Þ
Based on the form of Eq. (7), we can fit the time-varying molecular permeation number N as a function of time s based on the
simulation results. With the fitted exponent b, the permeance S
can be easily obtained from Eq. (8). As seen from Fig. 5a and b,
the permeance of CO2 and H2S is much higher than that of CH4,
and the permeance of H2S (S = 1.18 106 GPU) is higher than that
of CO2 (S = 5.96 105 GPU). The probability distributions of
permeating molecules in the nanopore are presented in
Fig. 5c and d; it is found that the molecular permeable zone is rect-
angular due to the limitation of the nanopore, and the permeable
area of CO2 is larger than that of H2S because of its smaller molecular size. For CO2 molecules with a ‘‘line structure”, there are two
high-probability zones along the lateral direction where the CO2
molecules prefer to permeate through the nanopore. This phenomenon is related to the strong attracting interactions between
the CO2 molecules and 4 doped N atoms in the graphene nanopore.
For the H2S molecules with a ‘‘triangle structure”, molecules generally prefer to permeate from the center of the nanopore.
The distinct molecular permeation ability can be explained by
the interaction energy profile between molecules and graphene.
The interaction energy is acquired using first principle calculations
with the DMol3 code embed in Materials Studio software. To
acquire the profiles, we place the molecules on the axis perpendicular to the graphene surface and passing through the center of
nanopore, and discontinuously change the distance (adsorption
height) between the molecules and pore center at an interval of
0.05 nm. For CH4, CO2 and H2S molecules, the interactions are basically attractive as the adsorption height varies from 0.0 to 0.6 nm
(except the interactions of CH4 molecules from 0.5 to 0.6 nm), as
seen from Fig. 6. For the attractive interaction, the higher the
energy barrier (maximum value of the profile), the faster the molecule permeates through the nanopore. Based on the energy barriers
(CO2: 0.380 eV and H2S: 3.115 eV), it can be concluded that the
permeation rates of H2S molecules are faster than those of CO2
molecules, which is consistent with the results obtained from the
MD simulations. Meanwhile, the attractive well for H2S molecules
is very deep, indicating that the molecules can easily diffuse to the
pore center. Additionally, the different energy barriers can explain
the diversity in the molecular adsorption intensity on the graphene
surface. It is noted that the Lewis-acid-base interaction significantly contributes to the attractions between the graphene
C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
Fig. 6. Interaction energy between gas molecules and graphene as a function of the
adsorption height.
nanopore and CO2 or H2S molecules, because the doped N atoms
act as Lewis-bases while the C in CO2 molecules or S in H2S molecules act as Lewis-acids owing to the charge separation effect in
the gas molecules. Previous investigations for the Lewis-acidbase interactions between organic heterocycles and CO2 molecules
can be found in the work by Vogiatzis et al. [48] and work by Hauser and Schwerdtfeger [38] for NPG membranes.
Due to the limitation of the pore size, frequent collisions with
pore-rim atoms occur in the permeation process of molecules.
We try to reflect the collision strength by the variations in the
angles between the five CAH bonds and graphene surface. As seen
from Fig. 7a and b, the alternately varying angles have both positive (bond directs toward feed side) and negative (bond directs
toward permeate side) values, meaning that the molecules can permeate through the nanopore in either direction, although the net
permeation is toward the permeate side. It is noted that the fluctuation ranges in the CAH bonds in different locations are different,
namely, the three top CAH bonds have wide-range fluctuations,
while the two bottom CAH bonds have small-range fluctuations.
In the top zone of the nanopore, the molecules hardly permeate
owing to the small area and as a result many ineffective collisions
occur; while in the bottom zone, the molecules can easily permeate with a few collisions. For the CO2 and H2S molecules, the variations in the angles are similar because the collision momentum
determined by the molecular mass is comparable.
Owing to the difference in the structures of CO2 and H2S molecules, the molecular orientations during the permeation process
are different. We define an angle a between the molecular interconnect line and graphene surface. The detailed illustrations of
the angle are depicted in Fig. 8a for CO2 molecules and Fig. 8c for
H2S molecules. For a given molecule, there should be an optimal
angle to permeate through the nanopore, indicating that the molecule must adjust its orientation before entering the nanopore. As
shown in Fig. 8b, after being adsorbed on the graphene surface,
the angle a of a CO2 molecule varies over a wide range. While, as
the molecule enters the nanopore with a decrease in its zposition (indicated by the purple zone in the figure), the angle a
increases up to nearly 90°. This means that the molecule prefers
to permeate the nanopore with a perpendicular orientation with
respect to the graphene surface. The inserted map in Fig. 8a clearly
shows three snapshots during the permeation process of the CO2
molecule. Unlike CO2 molecules, the orientations of H2S molecules
are not specified during the permeation process, as shown in
Fig. 8d. In the nanopore (purple zone), angle a does not vary with
the same trend but present a fluctuation mode, indicating that the
559
H2S molecule can permeate the nanopore without a particular orientation (the snapshots in Fig. 8c). It is noted that the bond angles h
of the CO2 and H2S molecules fluctuate within a narrow range
around their equilibrium values (the inserted maps in Fig. 8b for
CO2 molecules and Fig. 8d for H2S molecules). The same trend of
molecular orientations during the permeation process is observed
in other molecular crossing events.
To permeate the nanopore, the vast majority of molecules first
adsorbs onto the graphene surface and then diffuses to the pore
region for possible permeation events. Therefore, the experience
times during the permeation process for CO2 and H2S molecules,
with distinct adsorption abilities on the graphene surface, may
have different probability distributions. We define the experience
time as the period that a molecule stays in the adsorption layers
on both sides of the graphene and in the pore during the permeation process, i.e., the time interval after adsorbing on one side of
graphene and before desorbing from the other side. Based on the
probability distributions of the permeating CO2 and H2S molecules
(Fig. 9), it is shown that most of the molecules, including CO2 and
H2S molecules, can permeate the nanopore in a relatively short
time period. However, the range of experience time for H2S molecules is wider than that of CO2 molecules, and the longest experience time of H2S molecules reaches up to 756 ps. This discrepancy
is induced by the distinct adsorption intensities on the graphene
surface. The strongly adsorbed molecules encounter massive collisions with the other molecules in the adsorption layer, delaying
the molecular diffusion on the graphene surface toward the pore
region. Therefore, H2S molecules exhibit a wide range of experience times during the permeation process.
3.3. Performance evaluation
As a novel molecular sieve, graphene nanopores hold great promise for gas separations. Here, we compare the performance of the
N/H modified graphene nanopore with those of traditional polymer gas separation membranes. For the purpose of an effective
comparison, we adopt data on polymer membranes from the literature by Robeson [45]. It is noted that the comparison for the separation of H2S/CH4 mixtures is missing owing to the absence of the
Robeson upper bond of H2S/CH4 mixtures in the literature. As seen
from Fig. 10, the separation performance of the graphene nanopore
for the separation of CO2/CH4 is far better than that of polymer
membranes, namely, the graphene nanopore can maintain a high
selectivity (8.57) with a high permeance of the permeating molecules (5.96 105 GPU). Furthermore, the performance of the graphene nanopore exceeds the Robeson upper bond for the
separation of CO2/CH4, demonstrating the great potential of graphene nanopores as high-efficiency molecular sieves. It is believed
that this nanopore also maintains a good performance for separating H2S/CH4 mixtures, where the permeance of H2S is up to
1.18 106 GPU and the selectivity reaches 20.57.
4. Implications
Based on the phenomena and mechanisms identified above,
four implications on the design of high-efficiency graphene nanopores for NPG gas separation membranes are summarized regarding porosity, pore functionalization, and so on, as follows:
(1) The graphene surface has a positive contribution to the
molecular permeation through graphene nanopores by
attracting molecules for adsorption. To fabricate NPG membranes, scientists cannot blindly pursue high porosity, which
would result in a large permeable area with a small graphene surface area. An optimal porosity should be detected
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C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
Fig. 7. Time-variations of the angles of CAH bonds with respect to the graphene surface for the separation of CO2/CH4 (a) and H2S/CH4 (b). The positive angle indicates that
the bond directs toward the feed side, while the negative angle is toward the permeate side. The three top CAH bonds are marked as ①, ② and ③, respectively; and the two
bottom CAH bonds are marked as ④ and ⑤, respectively.
Fig. 8. Molecular orientations during the permeation process. (a,b) Variation of the molecular angle a with respect to the graphene surface during the permeation process of a
CO2 molecule. (c,d) Variation of the molecular angle a with respect to the graphene surface during the permeation process of a H2S molecule. The inserted maps show the
variations in the bond angle h of the CO2 and H2S molecules, respectively.
C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
Fig. 9. Probability distributions of the experience time during the permeation
process for CO2 (a) and H2S (b) molecules.
561
tionalization for given gas molecules. Therefore, the pore
interactions should be the main consideration when choosing chemical elements for pore functionalization.
(3) In the determination of functionalized atoms on the nanopore, scientists should also consider the bond length and
atomic mass. The bond between passivated atoms and carbon atoms can fluctuate because of collisions with gas molecules. The fluctuation ranges for the passivated atoms with
smaller masses are larger than those with bigger masses
owing to the constant collision momentum from the given
gas molecules. A shorter bond length and larger fluctuation
range can induce a larger permeable area of the nanopore.
Therefore, atoms with a short bond length and small mass
have priority for functionalization on the pore rim, on the
premise that the graphene nanopore can effectively prevent
the non-permeating molecules.
(4) The combination of the size-sieving effects with the other
sieving effects (such as polarity-sieving effects, chargesieving effects, etc.) is beneficial for improving the selectivity
of the graphene nanopore. Therefore, the comprehensive
graphene nanopores, which can also have other sieving
effects with the application of chemical functionalization,
external electric fields, and so on, are preferable.
5. Conclusions and perspective
Fig. 10. Comparison between the separation performance of graphene nanopore
and those of polymer membranes. The upper bound of polymer membranes for the
separation of CO2/CH4 mixtures is adopted from Robeson [45], where the thickness
of the polymer membranes is assumed as 0.1 lm (see the study by Li et al. [13]) for
the unit conversion between the permeance (GPU) and permeability (barrer).
to obtain a balance in the contributions of pore area and surface area. In addition, some measures can be applied to
enhance the contribution of the surface area, such as chemical functionalization on the graphene surface and charging
of the graphene atoms.
(2) To achieve a high selectivity for gas separation, the design of
the configurations of graphene nanopores should consider
the pore size and pore shape as well as the pore interactions
with gas molecules. The pore interactions can affect the permeable area of the nanopore and improve or inhibit the permeability of gas molecules. The pore size and shape are
related to the sizes and structures of the sieving molecules,
while the pore interactions can be adjusted by the pore func-
With transient non-equilibrium MD simulations, we demonstrate that the N/H modified graphene nanopore can efficiently
separate gaseous CO2 and H2S molecules from CH4 molecules and
that it has a better comprehensive performance than traditional
polymer membranes. The sieving mechanisms of graphene nanopores for mixture gas molecules are revealed with consideration
for the distinct pore configurations, molecular structure and size
as well as graphene-molecule interactions, among others. The distinct molecular permeation abilities can be explained by both the
molecular kinetic parameters and adsorption intensities on the
graphene surface as well as the interaction energy profiles between
the gas molecules and graphene. A non-uniform molecular density
distribution is presented on the graphene surface because of
surface-guided molecular permeation, namely, three different
zones (i.e., the peripheral zone, Fick zone and accumulation zone)
are identified. The molecular sizes and functionalized atoms
greatly affect the rectangular permeable zone in the nanopore. In
the easily-permeable zone, the molecules can permeate through
accompanying by a few collisions with the passivated hydrogen
atoms. Owing to the distinct molecular structures (linear CO2
molecule versus triangular H2S molecule), CO2 molecules prefer
to permeate with an orientation that is perpendicular to the graphene surface, while H2S molecules can permeate without a particular orientation. For molecules with a stronger adsorption
intensity, the experience time during the permeation process is
longer. Finally, the significant implications of these results in
designing high-efficiency graphene pore-based gas separation
membranes are summarized, in terms of the porosity, pore functionalization, among others.
Although NPG membranes seem to have great promise, there
are many challenges with making such membranes available to
industries. The precise control of high-density graphene nanopores
is definitely the greatest challenge. Other obvious challenges
include the fabrication of large-area, defect-free graphene;
mechanical stability at high pressures; scale-up and supporting
of the thin membranes; and common issues, such as fouling, blocking, and concentration polarization. For precise control of graphene
nanopores, the top-down method is currently more promising, in
which advanced pore generation methods (e.g., plasma etching
and chemical oxidation) should be applied instead of electron
562
C. Sun, B. Bai / Science Bulletin 62 (2017) 554–562
beam irradiation, ion beam bombardment and other robust methods. The chemical vapor deposition method can be used to cover
the inherent defects and external damages. Substantial efforts are
urgently needed to solve these issues and make the NPG membranes practical for use in industry. Furthermore, the studies on
the graphene-based membranes may not only make the atomically
thick separation membranes a reality in the near future, they may
unintentionally inspire many new research directions due to their
great application prospects in the fields of energy conversion and
storage, biological science, and so on.
Conflict of interest
The authors declare that they have no conflict of interest.
Acknowledgments
This work was supported by the National Science Funds for
Distinguished Young Scholars (51425603), the National Natural
Science Foundation of China (51506166) and the National Science
Foundation for Post-doctoral Scientists of China (2016T90915).
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.scib.2017.03.004.
Reference
[1] Allen MJ, Tung VC, Kaner RB. Honeycomb carbon: a review of graphene. Chem
Rev 2010;110:132–45.
[2] Li F, Qu Y, Zhao M. Efficient helium separation of graphitic carbon nitride
membrane. Carbon 2015;95:51–7.
[3] Dasgupta T, Punnathanam SN, Ayappa KG. Effect of functional groups on
separating carbon dioxide from CO2/N2 gas mixtures using edge functionalized
graphene nanoribbons. Chem Eng Sci 2015;121:279–91.
[4] Kwon HT, Jeong HK. Improving propylene/propane separation performance of
zeolitic-imidazolate framework ZIF-8 membranes. Chem Eng Sci
2015;124:20–6.
[5] Hu S, Lozada-Hidalgo M, Wang FC, et al. Proton transport through one-atomthick crystals. Nature 2014;516:227–30.
[6] Achtyl JL, Unocic RR, Xu L, et al. Aqueous proton transfer across single-layer
graphene. Nat Commun 2015;6:6539.
[7] Koenig SP, Wang LD, Pellegrino J, et al. Selective molecular sieving through
porous graphene. Nat Nanotechnol 2012;7:728–32.
[8] Celebi K, Buchheim J, Wyss RM, et al. Ultimate permeation across atomically
thin porous graphene. Science 2014;344:289–92.
[9] Surwade SP, Smirnov SN, Vlassiouk IV, et al. Water desalination using
nanoporous single-layer graphene. Nat Nanotechnol 2015;10:459–64.
[10] Sun C, Wen B, Bai B. Recent advances in nanoporous graphene membrane for
gas separation and water purification. Sci Bull 2015;60:1807–23.
[11] Xu P, Yang J, Wang K, et al. Porous graphene: properties, preparation, and
potential applications. Chin Sci Bull 2012;57:2948–55.
[12] Joshi RK, Carbone P, Wang FC, et al. Precise and ultrafast molecular sieving
through graphene oxide membranes. Science 2014;343:752–4.
[13] Li H, Song Z, Zhang X, et al. Ultrathin, molecular-sieving graphene oxide
membranes for selective hydrogen separation. Science 2013;342:95–8.
[14] Kim HW, Yoon HW, Yoon SM, et al. Selective gas transport through fewlayered graphene and graphene oxide membranes. Science 2013;342:91–5.
[15] Shin Y, Liu W, Schwenzer B, et al. Graphene oxide membranes with high
permeability and selectivity for dehumidification of air. Carbon
2016;106:164–70.
[16] Huh S, Park J, Kim YS, et al. UV/Ozone-oxidized large-scale graphene platform
with large chemical enhancement in surface-enhanced raman scattering. ACS
Nano 2011;5:9799–806.
[17] Liu L, Ryu SM, Tomasik MR, et al. Graphene oxidation: thickness-dependent
etching and strong chemical doping. Nano Lett 2008;8:1965–70.
View publication stats
[18] Fischbein MD, Drndić M. Electron beam nanosculpting of suspended graphene
sheets. Appl Phys Lett 2008;93:113107.
[19] Russo CJ, Golovchenko JA. Atom-by-atom nucleation and growth of graphene
nanopores. Proc Natl Acad Sci USA 2012;109:5953–7.
[20] Jiang DE, Cooper VR, Dai S. Porous graphene as the ultimate membrane for gas
separation. Nano Lett 2009;9:4019–24.
[21] Cohen-Tanugi D, Grossman JC. Water desalination across nanoporous
graphene. Nano Lett 2012;12:3602–8.
[22] Hauser AW, Schwerdtfeger P. Nanoporous graphene membranes for efficient
3
He/4He separation. J Phys Chem Lett 2011;3:209–13.
[23] Postma HWC. Rapid sequencing of individual DNA molecules in graphene
nanogaps. Nano Lett 2010;10:420–5.
[24] O’Hern SC, Boutilier MSH, Idrobo JC, et al. Selective ionic transport through
tunable subnanometer pores in single-layer graphene membranes. Nano Lett
2014;14:1234–41.
[25] O’Hern SC, Jang D, Bose S, et al. Nanofiltration across defect-sealed nanoporous
monolayer graphene. Nano Lett 2015;15:3254–60.
[26] Jain T, Rasera BC, Guerrero RJS, et al. Heterogeneous sub-continuum ionic
transport in statistically isolated graphene nanopores. Nat Nanotechnol
2015;10:1053–7.
[27] Boutilier MSH, Sun C, O’Hern SC, et al. Implications of permeation through
intrinsic defects in graphene on the design of defect-tolerant membranes for
gas separation. ACS Nano 2014;8:841–9.
[28] Schrier J. Carbon dioxide separation with a two-dimensional polymer
membrane. ACS Appl Mater Interfaces 2012;4:3745–52.
[29] Liu H, Dai S, Jiang D. Permeance of H2 through porous graphene from
molecular dynamics. Solid State Commun 2013;175–176:101–5.
[30] Lu R, Rao D, Lu Z, et al. Prominently improved hydrogen purification and
dispersive metal binding for hydrogen storage by substitutional doping in
porous graphene. J Phys Chem C 2012;116:21291–6.
[31] Dai J, Yuan J, Giannozzi P. Gas adsorption on graphene doped with B, N, Al, and
S: A theoretical study. Appl Phys Lett 2009;95:232105.
[32] Drahushuk LW, Strano MS. Mechanisms of gas permeation through single
layer graphene membranes. Langmuir 2012;28:16671–8.
[33] Sun C, Bai B. Fast mass transport across two-dimensional graphene nanopores:
nonlinear pressure-dependent gas permeation flux. Chem Eng Sci
2017;165:186–91.
[34] Wen B, Sun C, Bai B. Inhibition effect of a non-permeating component on gas
permeability of nanoporous graphene membrane. Phys Chem Chem Phys
2015;17:23619–26.
[35] Shan M, Xue Q, Jing N, et al. Influence of chemical functionalization on the CO2/
N2 separation performance of porous graphene membranes. Nanoscale
2012;4:5477–82.
[36] Wu T, Xue Q, Ling C, et al. Fluorine-modified porous graphene as membrane
for CO2/N2 separation: molecular dynamic and first-principles simulations. J
Phys Chem C 2014;118:7369–76.
[37] Lei G, Liu C, Xie H, et al. Separation of the hydrogen sulfide and methane
mixture by the porous graphene membrane: effect of the charges. Chem Phys
Lett 2014;599:127–32.
[38] Hauser AW, Schwerdtfeger P. Methane-selective nanoporous graphene
membranes for gas purification. Phys Chem Chem Phys 2012;14:13292–8.
[39] Sun C, Boutilier MSH, Au H, et al. Mechanisms of molecular permeation
through nanoporous graphene membranes. Langmuir 2014;30:675–82.
[40] Du AJ, Zhu ZH, Smith SC. Multifunctional porous graphene for nanoelectronics
and hydrogen storage: new properties revealed by first principle calculations. J
Am Chem Soc 2010;132:2876–7.
[41] Sun C, Bai B. Gas diffusion on graphene surfaces. Phys Chem Chem Phys
2017;19:3894–902.
[42] Reshak AH, Auluck S. Adsorbing H2S onto a single graphene sheet: a possible
gas sensor. J Appl Phys 2014;116:103702.
[43] Ganji MD, Sharifi N, Ardjmand M, et al. Pt-decorated graphene as superior
media for H2S adsorption: a first-principles study. Appl Surface Sci
2012;261:697–704.
[44] Sun C, Bai B. Diffusion of gas molecules on multilayer graphene surfaces:
dependence on the number of graphene layers. Appl Therm Eng
2017;116:724–30.
[45] Robeson LM. The upper bound revisited. J Membrane Sci 2008;320:390–400.
[46] Prasai D, Tuberquia JC, Harl RR, et al. Graphene: corrosion-inhibiting coating.
ACS Nano 2012;6:1102–8.
[47] Raman RS, Banerjee PC, Lobo DE, et al. Protecting copper from electrochemical
degradation by graphene coating. Carbon 2012;50:4040–5.
[48] Vogiatzis KD, Mavrandonakis A, Klopper W, et al. Ab initio study of the
Interactions between CO2 and N-containing organic heterocycles.
ChemPhysChem 2009;10:374–83.
[49] Liu H, Dai S, Jiang D. Insights into CO2/N2 separation through nanoporous
graphene from molecular dynamics. Nanoscale 2013;5:9984–7.