N2 Separation Membranes

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Theoretical Design of Highly-Efficient CO/N Separation Membranes Based on Electric Quadrupole Distinction Yuanyuan Qu, Feng Li, and Mingwen Zhao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b04921 • Publication Date (Web): 28 Jul 2017 Downloaded from http://pubs.acs.org on July 31, 2017

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The Journal of Physical Chemistry

Theoretical Design of Highly-Efficient CO2/N2 Separation Membranes Based on Electric Quadrupole Distinction Yuanyuan Qua,#，Feng Li a,b, #, Mingwen Zhaoa,* a

School of Physics, Shandong University, Jinan, 250100, Shandong, China

b

School of Physics and Technology, University of Jinan, Jinan 250022, Shandong, China

#

These authors contributed equally.

Corresponding Author *To whom correspondence should be addressed. Email: [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Membrane separation of CO2/N2 in fossil fuel gas is promising for the control of greenhouse gas emission, but challenging due to close kinetic diameters. Here, we propose a generalized model for the design of efficient CO2/N2 separation membranes by taking advantage of the large difference between the electric quadrupole moments of the two molecules. The interaction between the molecular electric quadrupole moment and the built-in electric field of the membrane leads to high CO2/N2 selectivity. We validate this model in five nitrogen-rich membranes: g-C3N4, g-C3N3, C2N-h2D, g-C12N8 and p-BN, and demonstrate via molecular dynamics simulations that highly efficient CO2/N2 separation can be achieved in the theoretically predicted g-C12N8 membrane with a permeance of 2.8×105 GPU. This work offers a guidance to improve the separation efficiency of molecules with distinct electric quadrupole moments.


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Introduction Separating CO2 from fossil fuel gas and post-combustion capture of CO2 are effective strategies for CO2 emission reduction. Traditional sorbent-based methods for CO2 capture employ amine-containing molecules frameworks

4,5

and porous carbons

6-8

1

, metal-organic frameworks

2,3

, covalent-organic

, however, face several drawbacks such as low energy

efficiency, equipment corrosion, regeneration of sorbents and toxicity 9. Compared to traditional gas separation methods, the membrane-based technology has attracted considerable attentions due to its low energy cost, small footprint and environmental friendly 10,11

. Graphene is an ideal candidate for gas separation due to its one-atom thickness and

robustness. However, both theoretical and experimental approaches indicate that a perfect graphene sheet is impermeable to any gas molecules

12,13

. Therefore, nanoporous graphene was

theoretically proposed for gas separation, e.g. He, H2, N2, CH4

14-18

. In the past few years,

experiments have demonstrated the potential applications of nanoporous graphene membranes for gas separation utility

19-24

. Inspired by the success of the nanoporous grahpene, the gas

separation performance of other one-atom-thin membranes with intrinsic pores are investigated, such as graphenylene 25, polyphenylene 26,27, graphdiyne 28-32, graphitic carbon nitride 11,27,33,34. In recent years, ultrathin membranes have been proposed theoretically for CO2 separation, such as expanded porphyrins

35

, porous graphene

36,37

, as well as graphenylene

25

. These membranes

with size-specific pores serving as selective channels were employed for CO2 separation through size sieving effect. However, separating CO2 from N2, the main component of fuel gas mixture, is challenging in the size-sieving membranes due to their very close kinetic diameters (3.3-3.9 Å


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for CO2 and 3.64-3.8 Å for N2) 38. Searching for new separation mechanism is therefore highly desirable. It is noteworthy that CO2 and N2 have distinct electric quadrupole moments which are 14.27×10-40 C•m2 (CO2) and -4.65×10-40 C•m2 (N2)

39

. Under a non-uniform electric field, the

contribution of quadrupole moments will significantly affect the separation process. This huge quadropole moment distinction has been demonstrated to enhance the CO2/N2 separation efficiency both by theoretical and experimental studies

6,7,40-44

. Previous works have indicated

that adding Lewis base group (e.g. N, O) or Lewis acid group (e.g. H) to the pores of the membrane can effectively tune the energy barrier for CO2 diffusion and improve the CO2/N2 selectivity

35,36,45

. However, the quadrupole-moment-driven separation mechanism has not been

well understood, which hinders the improvement of CO2/N2 separation efficiency. In this work, we propose a simple model of quadrupole-moment-driven separation process to guide the design of highly efficient CO2/N2 separation membranes. We demonstrate that the interaction between the build-in electric field around the pores and the quadrupole moments of gas molecules plays a prominent role in the penetration process, which leads to efficient separation. We propose a factor (Q) to evaluate the CO2/N2 separation ability of a membrane. This model is validated in five nitrogen-rich membranes: g-C3N4 BN

46

44

, g-C3N3

44

, C2N-h2D

45

, p-

, g-C12N8. By means of molecular dynamics simulations, we demonstrate highly efficient

CO2/N2 separation in the g-C12N8 membrane with a permeance of 2.8×105 GPU. This work also offers a guidance to increase the separation efficiency of gas molecules with distinct electric quadrupole moments.


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Theoretical Details Our first-principles calculations were performed within the density functional theory (DFT) using the plane-wave pseudo potential approach as implemented in the Vienna Ab initio Simulation Package (VASP) 49-51. The generalized gradient approximation (GGA) in the form of the Perdew-Burke-Ernzerhof (PBE) was adopted for the exchange-correlation functional 52. The van der Waals (vdW) interactions were included explicitly by using a corrected PBE functional (DFT-D2) 53. The electron wavefunctions were expanded using the plane-waves with the energy cutoff of 500 eV. Structural optimizations were carried out using a conjugate gradient (CG) method until the remaining force on each atom was less than 0.01 eV/Å. Vacuum space larger than 30 Å was used to avoid the interaction between adjacent images. The Monkhorst-Pack meshes of 5×5×1 were used in sampling the Brillouin zone for the 2×2 supercells of all membranes

54

. For the transition state calculations, we have performed minimum energy path

profiling using the climbing image nudged elastic band method (CNEB) as implemented in the VASP transition state tools

55,56

. The structural convergence criteria were similar to that used in

the above-mentioned structural optimization. In the subsequent calculations of the potential energy profiles for gas molecules penetrating the membrane pores, the nearest-neighbor atoms surrounding the penetrated pores were fully relaxed while the z-coordinates of the other atoms were kept fixed. The molecular dynamics simulations was performed by GROMACS package

57

in the NVT

ensemble with periodic boundary conditions in all directions. The z-coordinates (perpendicular to the membrane) of the membrane are fixed. The van der Waals parameters for the membrane were taken from the CHARMM27 force field (Table S2). Models of three partial charges were adopted for CO2 and N2 molecules

36,58,59

, where the three-charge-site N2 model has two


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Lennard-Jones interaction nitrogen sites and a massless point charge located in the middle of the two nitrogen, accounting for the correct quadrupole moment (Table S3). The atomic charges of the membranes were obtained from the ESP fitting according to the Merz–Kollman scheme by Gaussian 09 at the B3LYP/6-31g(d) level

60

using a fragmental cluster of each membrane (Fig.

S1 & Table S1).

Results and Discussion A theoretical model for gas separation We separate the interaction energy W between the membrane and a gas molecule with electric quadrupole moment into two parts: Van der Waals (vdw) interaction energy Wvdw and electrostatic interaction energy Wei due to the quadrupole moment. The electrostatic interaction t r energy for a quadrupole moment D in an external electric field E is

r 1 t Wei = − D : ∇E 6

(1).

Since the membrane used for gas separation usually has symmetrical atomic arrangement around the pore center in the membrane plane (xy plane), the electrostatic interaction energy at the pore center for a linear molecule (e. g. CO2 and N2) can be simplified to 1 ∂E Wei = − Dzz z 6 ∂z

(2). x = y = z =0

Here we focus on the interaction energy at the pore center mainly due to two facts: 1) the electrostatic interaction energy reaches its maximum at the pore center; 2) the transition state of a gas molecule penetrating the pore of a membrane which corresponds to the energy barrier


6

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usually locates in the pore center. Considering the spatial distribution of the electric quadrupole moment near the pore center, we introduce a parameter α to normalize the electric quadrupole moment Dzz, and (2) becomes Wei = −

α 6

D zz

∂E z ∂z

. The electrical field in the pore center can x= y = z =0

be regarded as the sum of the electrical field of the charged atoms surrounding the pore, therefore, we should have

∂E z ∂z

where k =

1 4πε 0

= k∑ x = y = z =0

i

qi ri3

(3),

, qi represents the atomic charge (positive or negative) for each atom, ri

represents the distance between each atom and the pore center (please see detailed derivation in SI). Here, we define a separation factor of a membrane as Q = ∑ i

qi . A simple illustration of the ri3

model is shown in Fig. 1, where the charged atoms are distributed symmetrically around the pore center. The electrostatic interaction energy at the pore center then can be written as Wei = −

kα Dzz Q . 6

Figure 1. The illustration of the model. The pore is formed by positively or negatively charged atoms.


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Supposing that the two molecules with similar kinetic diameters (e.g. CO2 and N2) experience similar vdw energy profiles when penetrating the pore, the electrostatic interactions arising from the quadrupole moments of gas molecules determine their energy barrier difference. The energy barrier difference at the pore center ∆W can be approximated replaced by their electrostatic energy difference ∆Wei . We have

∆W = −

αk 6

Q∆D

(4),

where ∆D = D1 - D2 is the quadrupole moment difference between these two linear molecules. The selectivity of a membrane to the two molecules can be evaluated by S = e − ∆W / RT , according to Arrhenius equation 61,62, as the pore center corresponds to the transition state. In the following parts, we take the CO2/N2 separation as a model system to validate our model, as well as to determine the parameter α.

Five membranes for CO2/ N2 separation According to the above model, highly-efficient CO2/N2 separation should have a large Q value. Graphene-like carbon nitride materials have natural porous configurations suitable for gas separation 11,27,34. The spiral distribution of the charged N and C atoms around the pores leads to build-in electric field which facilitates CO2/N2 separation. Therefore, four graphene-like carbon nitride membranes, namely g-C3N4, g-C3N3, C2N-h2D, g-C12N8, and a porous boron nitride (pBN) as shown in Fig. 2 are considered, which are expected to have large Q values due to the polar nature. The g-C3N4, g-C3N3, C2N-h2D membranes used for gas separation (He or H2) have been extensively investigated theoretically in previous works

11,34,63-65

. The optimized lattice


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constants are 7.13 Å for g-C3N4 lattice, 7.12 Å for g-C3N3 lattice, 8.33 Å for C2N-h2D lattice, 8.35 Å for g-C12N8 lattice and 6.88 Å for p-BN lattice respectively, consistent with previous literatures 11,34,48,64. The sizes of the pores are indicated by circles in Fig. 2. The atomic charges qi and the distance between atoms and the pore center ri for each membrane can be found in Table S1. The separation factor Q, together with the energy and the energy differences for CO2 and N2 at the pore center of each membrane are summarized in Table 1. The variation of the energy difference ∆W with the separation factor Q are plotted in Fig. 3. A linear fitting of the data give rise a slope of 10.02 VÅ3, corresponding to α=6.95, with a correlation coefficient of 0.96, indicating the feasibility and validity of our model.


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Figure 2. Top view of (2×2) supercell of five membranes. The yellow circles indicate the inscribed circles of the pores. The brown balls indicate C atoms, the blue balls indicate N atoms and the green balls indicate B atoms, respectively. (A) g-C3N4 supercell; (B) p-BN supercell; (C) g-C3N3 supercell; (D) C2N-h2D supercell; (E) g-C12N8 supercell.

It is noteworthy that the built-in electric field in g-C3N3, C2N-h2D and g-C12N8 membranes leads to negative (positive) W value for CO2 (N2) and thus decreases (increases) the energy of CO2 (N2) at pore center, which increase the CO2/N2 selectivity. Although g-C4N3 has the largest ∆W value corresponding to highest CO2/N2 selectivity, the large positive WCO2 decreases the CO2 permeance. In view of this, we focus on C2N-h2D and g-C12N8 membranes with negative WCO2 and high ∆W values as suitable candidates for CO2/N2 separation for further investigation.

Table 1. The energy (eV), the energy differences (eV) for CO2 and N2 at the pore center of each membrane and the separation factor Q (eV/Å3) for each membrane.

g-C3N4

p-BN

g-C3N3

C2N-h2D

g-C12N8

WCO2

1.197

0.433

-0.186

-0.243

-0.513

WN 2

2.327

0.719

0.641

0.570

0.017

∆W

-1.13

-0.286

-0.827

-0.813

-0.530

Q

-0.104

-0.018

-0.076

-0.063

-0.051


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Figure 3. (A) Energy barrier difference ∆W (black squares) varies with separation factor Q. The red line is the linear fitting of ∆W verses Q.

Molecular dynamics simulation In order to estimate the CO2 permeance, we performed all-atom molecular dynamics simulation to investigate the CO2/N2 separation efficiency by the g-C12N8 and C2N-h2D membranes. In the simulation system, two sheets of each membrane were placed in the center of a simulation box of dimension of 4.176 nm×4.176 nm×50 nm (g-C12N8) or 4.165nm×3.6 nm×50 nm (C2N-h2D), with a distance of 16 nm. At the initial state, 140 CO2 and 140 N2 molecules are randomly placed in between the two sheets as shown in Fig. 4A. The simulations were carried out at 500 K which is the temperature in fuel gases.


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Figure 4. (A) The snapshot of the initial configuration where the gas molecules are sandwiched between two g-C12N8 membranes. (B) Pure CO2 permeation through the g-C12N8 membrane at 500 K, where different CO2 curves indicate different trajectories. (C) A snapshot for a CO2 molecule passing through the pore of g-C12N8 membrane.

For the g-C12N8 membrane, a total of 10 ns simulation was performed for each trajectory and the numbers of permeate CO2 and N2 were recorded as shown in Fig. 4B. There is no N2 permeation in all three trajectories (red dashed line in Fig. 4B). There are about 70 CO2


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molecules passing through the g-C12N8 membrane within 10 ns on average of three trajectories, corresponding to a permeance of 2.8×105 GPU (1GPU=3.35×10-10 mol m-2 s-1 Pa-1). Fig. 4C shows a snapshot of a CO2 molecule passing through the g-C12N8 membrane. In contrary to the case of g-C12N8 membrane, none of the gas molecules (both CO2 and N2) was found to pass through the C2N-h2D membrane within 20 ns for three trajectories, suggesting the low CO2 permeance.

To reveal the origins of the permeance difference of these two membranes, we calculated the energy profiles for CO2 and N2 passing through the g-C12N8 and C2N-h2D membranes respectively, as plotted in Fig. 5A&B, using the CNEB method based on first-principles calculations. The interaction between the built-in electric field of membranes and the quadrupole moments of gas molecules leads to attractive states of CO2 molecule at the pore center for both membranes. However, for the C2N-h2D membrane, there is an energy barrier of ~0.25 eV at 4 Å away from the pore center, which greatly reduces the possibility of CO2 penetration through the pores. The lowest energy state of CO2 in the pore center has the molecular axis perpendicular to the membrane. Therefore, CO2 molecules should align perpendicular to the membrane in the collision processes to increase the penetration possibility. Meanwhile, CO2 molecules should have enough energy to overcome this energy barrier via thermal fluctuation. These two requirements lead to low CO2 permeance through the C2N-h2D membrane.


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Figure 5. Energy profiles for CO2 and N2 passing through the C2N-h2D membrane (A) and gC12N8 membrane (B) based on CNEB method. Potential of mean force (PMF) of CO2 and N2 passing through the C2N-h2D membrane (C) and g-C12N8 membrane (D) by umbrella sampling. The position of the membrane corresponds to 0 Å.

To simulate the effects of molecule alignment and thermal fluctuation, we calculated the free energy profiles of CO2 and N2 molecules passing through the pores of these two membranes via potential of mean force (PMF) analysis. The PMF curves obtained by umbrella sampling method are plotted in Fig. 5C&D. Obviously, the PMF profiles differ significantly from the potential


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energy profiles calculated by the CNEB method. Due to the randomness of the molecule alignments in the collision process, the free energy barriers for molecules passing through both membranes are much increased, resulting in energy barriers of ~4.39 kBT ( for g-C12N8) and ~14.95 kBT (for C2N-h2D) at 500 K. It should be noted that an energy barrier of ~ 5 kBT is regarded low enough for a molecule to pass through by thermal fluctuation

66

. Therefore, CO2

can easily pass through the g-C12N8 membrane with high permeance. The C2N-h2D membrane, however, has a high free energy barrier, and thus lower CO2 permeability. Compared with CO2, N2 molecules experience much higher free energy barriers, ~12.75 kBT (for g-C12N8) and ~29.90 kBT (for C2N-h2D), indicating the high CO2/N2 selectivity of the two membranes. According to Arrhenius equation 61,62, the CO2/ N2 selectivity of the g-C12N8 membrane can be estimated to be 4.3×103.

Comparison with previous studies and applications We compared the CO2 separation performance (permeance and selectivity) of g-C12N8 membrane with that in previous works on CO2 separation by a few porous two-dimensional membranes. The results are summarized in Table 2 below. With similar permeance, the selectivity of the g-C12N8 membrane is superior to that of ame-4O, PG-4N4H and PG-ES1 membranes. Although the selectivity of the g-C12N8 membrane is lower than that of ame-2O membrane, the permeance, however, are much higher that that of ame-2O membrane. Moreover, it has been reported that CO2 permeance over 4.0×103 GPU with a CO2/N2 selectivity of 40 would reduce the CO2 capture cost below $15/ton 67. Therefore, the g-C12N8 membrane proposed in this study is a competitive membrane for CO2 separation and holds promising for CO2 capture applications.


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Table 2. Comparison of CO2 permeance (GPU) and CO2/N2 ideal selectivity between difference ultrathin membranes: g-C12N8 (this study), ame-4O (ref. 35), ame-2O (ref. 35), PG-4N4H (ref. 36) and PG-ES1 (ref. 37). g-C12N8

ame-4O

ame-2O

PG-4N4H

PG-ES1

permeance

2.8×105

7.2×104

8.0×103

2.9×105

3×105

selectivity

4.3×103

2.2×102

1.4×106

3×102

6×101

Conclusions To conclude, we propose a generalized model for design of highly-efficient CO2/N2 separation membranes by taking advantage of the large difference of electric quadrupole moments between these two molecules. We define a Q factor which is related to the spatial distribution of charged atoms around the pores in the membranes to predict the separation efficiency. The interaction between the molecular electric quadrupole moment and the built-in electric field leads to high CO2/N2 selectivity. Using this model, we design five two-dimensional nitrogen-rich porous structures as candidates and demonstrate high CO2/N2 separation efficiency in the g-C12N8 membrane through molecular dynamics simulations. This model is not restricted to CO2/N2 separation, but also applicable for other linear gas molecules with distinct quadrupole moments.


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ASSOCIATED CONTENT

Supporting Information. Supporting Information included Supplementary Figures , Supplementary Tables and Supplementary Method.

AUTHOR INFORMATION The authors declare no competing financial interests.

ACKNOWLEDGMENT The following financial support is acknowledged: National Natural Science Foundation of China (No. 21433006, 11504204), the 111 project (No. B13029), the Fundamental Research Funds of Shandong University (Grant No. 2015HW012), the Technological Development Program in Shandong Province Education Department (Grant No. J14LJ03). The calculations were performed at the National Super Computing Centre in Jinan.

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TOC GRAPHIC


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Figure 1. The illustration of the model. The pore is formed by positively or negatively charged atoms. 68x35mm (300 x 300 DPI)


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Figure 2. Top view of (2×2) supercell of five membranes. The yellow circles indicate the inscribed circles of the pores. The brown balls indicate C atoms, the blue balls indicate N atoms and the green balls indicate B atoms, respectively. (A) g-C3N4 supercell; (B) p-BN supercell; (C) g-C3N3 supercell; (D) C2N-h2D supercell; (E) g-C12N8 supercell. 177x184mm (300 x 300 DPI)



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Figure 3. (A) Energy barrier difference ∆W (black squares) varies with separation factor Q. The red line is the linear fitting of ∆W verses Q. 81x64mm (300 x 300 DPI)


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Figure 4. (A) The snapshot of the initial configuration where the gas molecules are sandwiched between two g-C12N8 membranes. (B) Pure CO2 permeation through the g-C12N8 membrane at 500 K, where different CO2 curves indicate different trajectories. (C) A snapshot for a CO2 molecule passing through the pore of g-C12N8 membrane. 177x164mm (300 x 300 DPI)



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Figure 5. Energy profiles for CO2 and N2 passing through the C2N-h2D membrane (A) and g-C12N8 membrane (B) based on CNEB method. Potential of mean force (PMF) of CO2 and N2 passing through the C2N-h2D membrane (C) and g-C12N8 membrane (D) by umbrella sampling. The position of the membrane corresponds to 0 Å. 177x142mm (300 x 300 DPI)


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N2 Separation Membranes

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