CH4 Separation Performance in Negatively Charged

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Improved CO2/CH4 Separation Performance in Negatively Charged Nanoporous Graphene Membranes Chengzhen Sun, and Bofeng Bai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00181 • Publication Date (Web): 05 Mar 2018 Downloaded from http://pubs.acs.org on March 6, 2018

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The Journal of Physical Chemistry

Improved CO2/CH4 Separation Performance in Negatively Charged Nanoporous Graphene Membranes Chengzhen SUN, Bofeng BAI* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University

*Corresponding author, email: [email protected]

Abstract We propose a negatively charged nanoporous graphene (NPG) membrane which presents an improved separation performance of CO2/CH4 gas mixtures. The CO2 permeance and the selectivity of CO2 molecules over CH4 molecules both increase after adding negative partial charges on each carbon atom. The CO2 permeance can increase from 6.81×105 GPU for the neutral NPG membrane up to 5.65×106 GPU for a partial charge of -0.125 e, and the selectivity increases correspondingly from 10.4 to 42.8. The improved separation performance can be attributed to the relatively enhanced adsorption of CO2 molecules and weakened adsorption of CH4 molecules on the graphene surface at high partial charges. The enhanced adsorption of CO2 molecules can enhance their permeation abilities by improving the surface contributions, especially on the molecular deliverability from surface to pore area for permeation. The weakened adsorption of CH4 molecules can weaken the permeation abilities of themselves due to the limited surface contributions and simultaneously improve the CO2 permeance by abating their blocking effects for the permeation of CO2 molecules. Meanwhile, the enhanced adsorption layer on graphene surface can further enhance the net CO2 permeance by preventing the permeated molecules moving back to the feed side.

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1. Introduction

In the past few years, it was demonstrated that the graphene sheet with nanometer-sized pores (nanoporous graphene, NPG) was a very promising gas separation membrane 1-6, owing to its atomic thickness 7-8, good chemical stability 9-10 and high mechanical strength

11-12

. Because of the one-atomic thickness and the

sub-nanometer pore size, the permeability and selectivity of NPG membranes can exceed those of conventional polymer gas separation membranes by several orders of magnitude. Encouraged by the great potential of NPG membranes, more and more researchers devote themselves into the related studies and the NPG-based gas separation membranes are becoming a reality under the efforts of scientists.

Since showing the possibility of NPG membranes for gas separation by Jiang et al. 2, the great potential of these conceptual membranes was further confirmed by several theoretical works 1, 13-14. Afterward, people tried to fabricate the NPG membranes and experimentally demonstrate their potential. The first experimental measurement was performed by Koenig et al.

15

, who demonstrated the selective gas transport through

NPGs with a variety of gas species. Then, Celebi et al. 16 reported a high gas transport rate through double-layer NPGs with a large area up to square millimeters. Since then, it was shown that the industrial-scale NPG-based membranes can be really fabricated to realize efficient gas separation

17-18

. Currently, the NPG membranes for gas

separation are widely investigated both from the experimental and theoretical insights 17-21

. With the accumulation of these cutting-edge research works, the mechanisms of


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molecular permeation through NPG membranes are well understood and the fabrication route of NPG-based membranes is basically established.

In order to make the NPG membranes more efficiently, several methods are detected to enhance their permeability and selectivity

22-26

. For example, Lu et al.

24

showed

that the hydrogen purification efficiency of NPG membranes can be significantly improved by doping of B or N atoms on the pore rim. Huang et al.

25

demonstrated

that the inter-layer-connected NPGs exhibited higher permeance and selectivity for separating H2/CH4 mixtures. Tian et al.

26

enabled the nonselective large pores with

sizes of 1 nm to be selective by coating a monolayer of ionic liquid on NPG membranes. Lei et al.

27

showed that the charges on the pore rim can reduce the

potential energy of H2S around the pore and improve the selectivity of H2S molecules relative to CH4 molecules. However, this work only discussed the effects of pore-rim charges on the separation performance of NPG membranes. In summary, people are still searching ways to make the NPG membranes applicable and overcome the challenges faced currently. For the water purification based on NPG membranes, people found that the charged NPG membranes presented a significantly improved purification efficiency and ion selectivity

28-31

. The electrical interactions between

ions and graphene membranes played a profound role on the selective translocation of diverse ions.

Inspired by the charged NPG membranes for water purification, here we propose a negatively charged NPG membrane with improved separation performance for the



gaseous CO2/CH4 mixtures. This charged membrane can simultaneously enhance the permeance of CO2 molecules and the selectivity of CO2 molecules over CH4 molecules. By adding negative partial charges on the graphene carbon atoms, we show from molecular dynamics (MD) insights that the CO2 permeance increases with increasing the values of partial charges and the CH4 molecules are always non-permeating. We attribute this interesting phenomenon to the relatively enhanced adsorption of CO2 molecules and weakened adsorption of CH4 molecules on the graphene surface. The permeation ability of CO2 molecules is improved along with the enhanced adsorption intensities of themselves; furthermore, the weakened adsorption of CH4 molecules can not only improve the CO2 permeance but also reduce the CH4 permeance. We believe that this study can provide a promising direction of optimizing the NPG membranes for efficient gas separation.

2. Simulation system and model

To show the separation performance of negatively charged NPG membranes, we investigate the separation processes through a set of MD simulations. The MD simulations are performed in a non-equilibrium system, where the NPG membrane of area 4×4 nm2 (see Figure 1(a)) divides the simulation box into two chambers with equal volume and the gas mixture (CH4 and CO2 molecules) is originally arranged in one chamber (feed side). At the beginning of simulations, the 500 CH4 molecules and 500 CO2 molecules are arranged alternatively and uniformly in the feed side of simulation box. With the passage of simulation time, the permeating molecules in the


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feed side can migrate to the other side (permeate side) by permeating through the nanopore in NPG membranes. Periodic boundary conditions are applied in the directions parallel to the graphene surface, while reflective wall boundary conditions are applied in the direction perpendicular to the graphene surface. To model the negatively charged NPG membranes, we add a negative partial charge (ranging from 0.0 e to -0.125 e) to each graphene carbon atom. In this study, the NPG membranes with a pore functionalized by N and H atoms are employed to effectively separate CO2 molecules from CH4 molecules. The nanopores are created based on the 12-graphene-ring-units pore (pore diameter is 0.61 nm

32

), by passivating 5

unsaturated C atoms with H atoms and dopping the remaining 4 C atoms with N atoms. The pore configuration is shown in Figure 1(b). We design the configuration of this graphene nanopore mainly to obtain a good sieving effect for the CH4 and CO2 molecules. The doped N atoms in the left and right sides enlarge the size of pore and make the pore presenting an elliptical shape, such that the linear CO2 molecules can easily permeate through, while the spherical CH4 molecules hardly permeate through. Meanwhile, the N functionalization can enhance the molecular adsorption intensities of CO2 molecules owing to the ‘Lewis acid-base’ interactions 33-34 to further improve their permeation abilities. The size of the N/H modified nanopore is definitely much smaller than 0.61 nm for the passivation of H atoms, and is slightly larger than the diameter of CH4 molecules 0.38 nm molecules 0.33 nm

36

35

and much larger than the diameter of CO2

, because few CH4 crossings and plenty of CO2 crossings are

observed (see next section). Owing to the periodic boundaries, the number density of



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the pores in our simulated NPG membranes is 6.25×1012 cm2, which is comparable to the pore densities of the fabricated NPG membranes in experimental studies 17, 37-39. The height of the simulation box is 140 nm, thus the initial pressure of feed side is estimated as 21.1 bar based on the ideal gas equation (pV = NkBT).

The simulations are run for 1.0×108 timesteps with a time step of 0.2 fs in a NVT ensemble. The system temperature is equilibrated at 350 K using a Nosé-Hoover thermostat. For the temperature of interest here, firstly it approaches to the actual temperature in the membrane separation processing

40-41

, secondly the quantum

effects are expected to be small at this temperature 42-44 such that MD simulations can accurately predict the molecular transport phenomena. During the simulations, if the carbon atoms are not fixed, a vertical displacement of graphene membrane will appear owing to the collisions with gas molecules. However, the carbon atoms cannot be entirely fixed in the simulations, because the vibration of graphene membrane caused by the collisions with gas molecules should be properly considered for a more accurate description of the graphene sheet at experimentally relevant temperatures. Thus, one corner carbon atom in graphene is fixed, which can not only prevent the vertical displacement of graphene membrane, but also allow the slight vibration of the other carbon atoms in response to collisions with gas molecules. However, the vibration cannot make sure the graphene atoms and the corresponding molecular adsorption layers symmetrically locate at the center of the simulation box (see the discussion of molecular adsorption on NPG membranes in below). To check a


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possible molecular crossing event, the molecular coordinates are periodically analyzed with a very short time period of 4.0 ps.

In this study, the all-atom classical MD simulations are performed and thus the interacting potentials are considered from atomic levels. The pair interactions among carbon atoms in graphene and carbon and hydrogen atoms in CH4 molecules are all modeled by the popular AIREBO potential

45

; while the pair interactions in CO2

molecules are modeled by the three-site model with three partial charges 36. In these models, the Van der Waals and electrostatic interactions are both considered. Meanwhile, the long-rang Coulombic interactions are considered by using the Particle-Particle Particle-Mesh method. For the atomic pairs/chains, the bond and angle interactions are particularly modeled. For CH4 molecules and carbon atoms in graphene, the bond and angle interactions are included in the AIREBO potential model; while for CO2 molecules and the functionalized atoms on the pore rim, the bond and angle interactions are all modeled by the harmonic type potential. The details of these potential models and the potential parameters for all the atoms involved in these simulations can be found in our early works 46-48.

3. Results and discussion 3.1 Improved separation performance

To investigate the separation performance of the charged NPG membranes, we obtain the molecular permeance through the time-variation of the number of permeated



molecules. By detecting the molecular number in permeate side (Nnet), the time-varying molecular crossing number can be obtained, as shown in Figure 2. As firstly seen from this figure, the CH4 and CO2 molecules present the distinctive permeation abilities, demonstrating that this kind of NPG membranes can effectively separate the CO2/CH4 mixtures with a considerable selectivity. After negatively charging the NPG membranes, the permeation abilities of CO2 molecules are enhanced obviously; namely, the molecular number in permeate side increases more sharply over time. Moreover, the permeation abilities of CO2 molecules increase significantly with increasing the partial charges on NPG membranes. For example, for q = -0.125 e (q is the value of partial charges on the carbon atoms in charged NPG membranes), more than 200 CO2 molecules permeate through the NPG membrane in 100 million timesteps. However, the permeation abilities of CH4 molecules are still very weak even for the charged NPG membranes. The highest number of permeated CH4 molecules through charged NPG membranes in 100 million timesteps is only 16. This phenomenon clearly indicates that the selectivity of CO2 molecules over CH4 molecules also increases in the charged NPG membranes, and further that the separation performance of CO2/CH4 mixtures in charged NPG membranes is significantly improved.

To quantify the molecular permeation abilities, we obtain the molecular permeance by fitting the time-varying curves of molecular crossing number. Based on the relation between permeation flux and molecular permeance, an expression of molecular crossing number Nnet as a function of time t can be deduced 46, as follows:


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10

N net = (250 − N al 2) × (1 − e −8.24×10

Pτ

)

(1)

where Nal is the average number of adsorbed molecules on both sides of NPG membrane, P is the molecular permeance in unit of mol/sm2Pa. Thus, by fitting the time-varying curves of molecular crossing number in the form of Eq. (1), the molecular permeance of CO2 and CH4 molecules can be obtained from the exponent in the time decay, as shown in Figure 3(a). After obtaining the permeance P of each gas species, the selectivity of CO2 molecules over CH4 molecules can be easily obtained as S = PCO2/PCH4. For the neutral NPG membranes, the CO2 permeance is up to 6.81×105 GPU (1 GPU = 3.35×10-10 mol/m2sPa), and the CH4 permeance is only 6.52×104 GPU; the selectivity of CO2 molecules over CH4 molecules is 10.4. It is believed that the calculation of molecular permeance in the non-equilibrium system is accurate, because the results obtained in the equilibrium and non-equilibrium systems presented a very good agreement with each other, as illustrated in our early work 32.

Subsequently, the molecular permeance and selectivity of the charged NPG membranes at various partial charge values are obtained, as shown in Figure 3(b). It can be seen that the permeance of CO2 molecules increases obviously with increasing the partial charges on the carbon atoms. However, the selectivity of NPG membranes presents a disordered dependence on the partial charge; but, in overall the selectivity of negatively charged NPG membranes are higher than that of the neutral NPG membrane. This disordered dependence is related to the rough calculation of CH4 permeance; namely, the number of permeated CH4 molecules is very small and the



uncertainty in the calculation of CH4 permeance is very high. Thus, the CH4 permeance does not present a regular dependence on the partial charge (see Figure 2(b)), and accordingly the dependence of selectivity on the partial charge presents an obvious disorder. Anyway, the separation performance of negatively charged NPG membranes is significantly improved both in terms of CO2 permeance and selectivity.

3.2 Underlying mechanisms

In this section, we dedicate to reveal the underlying mechanisms why the CO2/CH4 separation performance of NPG membranes can be improved by negatively charging the carbon atoms. Because the molecular permeation ability is directly related to the molecular adsorption on NPG membranes, we firstly analyze the molecular adsorption characteristics on NPG membranes at different partial charges on carbon atoms. Figure 4(a) gives a number density distribution of CO2 molecules along the z-direction averaged over the entire simulation period. As seen from this figure, the number density presents a non-symmetrical distribution; namely, the number of adsorbed molecules on feed side is higher than that on permeate side. In our simulation period, the permeated molecules are less than the molecules in feed side; thus, less molecules are adsorbed on the permeate side. The number density distribution is also higher at a higher partial charge on carbon atoms; this indicates that the adsorption intensity of CO2 molecules enhances with increasing the partial charge. Meanwhile, it is found that the width of adsorption layer is wider for the higher partial charges. The width of adsorption layer is defined based on the following


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criterion: beyond the adsorption layer, the molecular number density decays to the gas-phase value. Take the neutral graphene membrane for example, by observing that the gas density typically decays to its gas-phase value for (approximately) |z| > 0.6 nm, we define the width of adsorption layer on one side as 0.6 nm. While at q = -0.125 e, the width of adsorption layer increases up to 9.5 Å. For the wide adsorption layer, more than one layer of molecules can adsorb onto the graphene surface. It should be noted that the adsorption layers are not symmetrically located at the center of simulation box and a few molecules still exist in the graphene zone. These phenomena are caused by the vibration of graphene sheet during simulations (as mentioned above); owing to the gas collision-induced vibration, a few gas molecules can enter into the graphene zone and the adsorption layers also swing with the graphene sheet.

With increasing the partial charge, the number of adsorbed CO2 molecules on two sides of graphene increases while that of CH4 molecules decreases, as seen from Figure 4(b). For the CO2 molecules, the negative charges on carbon atoms can enhance the attractive electrostatic interactions between CO2 molecules and graphene, because the C atoms in CO2 molecules feature a very high positive partial charge of 0.6512 e. Therefore, the adsorption of CO2 molecules gets stronger with increasing the negative partial charge on carbon atoms. However, the adsorption of CH4 molecules weakens with increasing the partial charges due to the competitive mechanism with CO2 molecules; when the adsorption of CO2 molecules gets stronger, more adsorption sites on graphene surface are occupied and less CH4 molecules can



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adsorb onto the graphene surface. For the negatively charged NPG membranes, the interactions between CH4 molecules and graphene may get more repulsive due to the negative C atoms in CH4 molecules, which can also contribute to the weakened adsorption of CH4 molecules. At higher partial charges on carbon atoms, more CO2 molecules adsorb on the graphene surface, which promotes the molecular permeation of themselves through the nanopore by improving the surface contributions. For the strongly adsorbed molecules, the molecular permeance is high owing to the enhanced surface flux where the molecules interact with the graphene surface during permeation process, as systematically illustrated by Sun et al.

32

Therefore, the

permeance of CO2 molecules increases with increasing the partial charge on carbon atoms, which is the main reason for the improvement in the CO2/CH4 separation performance of negatively charged NPG membranes.

Meanwhile, the weakened adsorption of CH4 molecules also has a positive contribution on the improved CO2/CH4 separation performance. Firstly, the weakened adsorption of CH4 molecules weakens the permeation abilities of themselves owing to the restricted surface contributions. Secondly, the weakened adsorption of CH4 molecules can abate their blocking effects for the permeation of CO2 molecules. A detailed illustration on the blocking effects of non-permeating components can be found in the work by Wen et al.

49

Thus, the weakened adsorption of CH4 molecules

improves the CO2/CH4 separation performance both by decreasing the CH4 permeance and increasing the CO2 permeance.


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The enhanced contributions of surface adsorption and diffusion on molecular permeation at high partial charges can be confirmed from the number density distributions on graphene surface. Figure 5 gives the relative number density (Nd/Ndmax) distributions of CO2 molecules in the adsorption layer of feed side, where Nd is the adsorbed molecular number on the unit graphene surface with an area of 1.74 Å2, Ndmax is the maximum value of Nd. It can be seen that the density distributions are obviously non-uniform, especially in the center of graphene surface (pore area). In the pore center, the number density is particularly high for the congestion effect

50

,

because the molecules are in line waiting for permeating through. The strong adsorption of CO2 molecules in the pore center is also partly related to the ‘Lewis acid-base’ interactions between the doped N atoms and the CO2 molecules, where the doped N atoms can act as Lewis-bases while the C atoms in CO2 molecules can act as Lewis-acids owing to the charge separation effect in the gas molecules 33-34. A special attention should be paid to the density distributions around the pore, which are directly related to the molecular permeation abilities through the pore. For a more clear display, the curves of the density distributions along the central line are also inserted in the figures. It can be found that the curve configurations are different at various partial charges. At lower partial charges, a low pit appears around the pore center; while at higher partial charges, the low pit disappears and the number densities distribute uniformly around the pore. The low pit is caused by the molecular permeation through the pore and is related to the molecular diffusion rate along the surface to the pore area. The appearance of low pit indicates that the molecular



deliverability from the surface to the pore is not fast enough; while the disappearance of low pit means that the molecules can be sufficiently supplied from the surface to ensure a high molecular permeability. Therefore, the partial charges on carbon atoms attract CO2 molecules adsorbing onto the graphene surface and improve the molecular deliverability from surface to pore area for further permeation; finally, the CO2 permeance is enhanced at high partial charges on carbon atoms. It is noted from this figure that the thickness of adsorption layer increases with increasing the partial charges; namely, at higher partial charges more molecules are adsorbed on the graphene surface and the absolute number densities are higher.

The adsorption layer on graphene surface may have another positive contribution on the molecular permeance by inhibiting the molecular crossing-back motions from permeate side to feed side. This inhibition effect can be well analyzed from the aspect of molecular trajectories during permeation. We obtain the molecular crossing number NF-P and NP-F, respectively; NF-P is the molecular crossing number from feed side to permeate side, while NP-F is the molecular crossing number from permeate side to feed side. Figure 6(a) shows the time-variations of NF-P, NP-F and Nnet for CO2 molecules at q = 0. Over time, the three numbers all necessarily increase gradually with the permeation of molecules. It is very important to give a further analysis on the three numbers at the end of simulations for various partial charges, as shown in Figure 6(b). It can be clearly seen that the three numbers all increase with increasing the partial charge. At high partial charges, the densely adsorbed molecules can promote both the molecular crossings in the two directions. It should be noted that the


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net molecular number in permeate side (Nnet) is not exactly equal to the difference between NF-P and NP-F (NF-P - NP-F), because part of the permeated molecules are adsorbed on the graphene surface and do not always stay in permeate side. Here, we define a number Be to reflect the inhibition effect of adsorption layer on the molecular crossing-back motions, as follows:

Be =

(500 − N al − 2 N net ) N P − F 500 N F −P

(2)

where NP-F/NF-P is the percentage of the molecular crossing-back motions to the molecular crossings from feed side to permeate side, (500-Nal-2Nnet)/500 is a coefficient to eliminate the negative effect of pressure difference between feed side and permeate side on the molecular crossing-back motions. The higher the Be number, the weaker the inhibition effect of adsorption layer on the graphene surface. Generally, the Be number decreases with increasing the partial charges on carbon atoms, as shown in Figure 6(b). It clearly demonstrates that at higher partial charges the adsorption layer can prevent more permeated molecules moving back to the feed side. The enhanced inhibition effect at high partial charges can enhance the CO2 permeance by decreasing the molecular crossing-back motions (NP-F). This is definitely another mechanism which promotes the net permeation rates of CO2 molecules by preventing the molecules in permeate side moving back to feed side.

4. Conclusions and suggestion



We demonstrate from MD insights that the negatively charged NPG membranes present an improved separation performance of CO2/CH4 mixtures. The CO2 permeance and the selectivity of CO2 molecules over CH4 molecules both increase with increasing the partial charges on carbon atoms. The CO2 permeance can increase from 6.81×105 GPU for the neutral NPG membranes up to 5.65×106 GPU at q = -0.125 e, and the selectivity increases from 10.4 to 42.8. The improved separation performance can be attributed to the relatively enhanced adsorption of CO2 molecules and weakened adsorption of CH4 molecules on the graphene surfaces. The enhanced adsorption of CO2 molecules can enhance their permeation abilities by improving the surface contributions on the molecular permeance, especially on the molecular deliverability from surface to pore area for permeation. The weakened adsorption of CH4 molecules can weaken the permeation abilities of themselves due to the limited surface contributions and further improve the CO2 permeance by abating their blocking effects for the permeation of CO2 molecules. Meanwhile, the enhanced adsorption layer on graphene surface can enhance the CO2 permeance by preventing the molecules in permeate side moving back to feed side and increasing the net molecular number in permeate side.

In the practical applications, the negatively charged NPG membranes can be both realized by applying an electric field and applying a negatively-charged porous substrate. For applying an electric field, the graphene membrane can directly connect to a negative electrode of the power source. While the porous substrate with negative charges can be realized by coating a polymerized composition comprising unsaturated


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monomers

with

an

anionic

N-(alkoxymethyl)-acrylamide

group,

e.g.

N-(hydroxymethyl)-

and

51

. For both two methods, the partial charges on

graphene membranes can be easily adjusted. In the case of applying an electric field, the charge value is directly related to the output voltage of electric power source; in the case of applying a negatively-charged porous substrate, the partial charges can be varied by adjusting the concentrations and types of unsaturated monomers with anionic group on the coating layer. In the real applications, the system for applying an electric field is a little complex because an external power source should be necessarily supplied and connected with the membrane module. While for the method of applying a porous substrate with negative charges, the partial charges are added during the preparation of membranes and no additional components are required in the system. Thus, the method of applying a porous substrate with negative charges seems to be more promising both from the aspects of adjustable charge value and simplified system composition. We expect that this study can point toward a promising direction of optimizing the NPG membranes for efficient gas separation with high permeance and considerable selectivity.

Acknowledgement We acknowledge the financial supports from the National Natural Science Foundation of China for project No. 51506166 and Distinguished Young Scientists No. 51425603.



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Figure Captions:

Figure 1 Schematic illustration of the simulation system and the configuration of the N/H modified nanopore. (a) Simulation box and boundary conditions; (b) Pore structure; (c) Negatively charged NPG membrane.

Figure 2 Time-varying molecular crossing number at different partial charges on graphene carbon atoms. (a) CO2; (b) CH4.

Figure 3 Variation of permeance and selectivity with the partial charges on carbon atoms. (a) Calculation of the molecular permeance for the neutral NPG membranes; (b) CO2 permeance and selectivity of the charged NPG membranes.

Figure 4 Molecular adsorption on NPG membranes at different partial charges on carbon atoms. (a) Number density distributions of CO2 molecules along the z-direction; (b) Number of adsorbed CH4 and CO2 molecules.

Figure 5 Relative number density (Nd/Ndmax) distributions of CO2 molecules in the adsorption layer of feed side. Nd is the adsorbed molecular number on the unit graphene surface with an area of 1.74 Å2, Ndmax is the maximum value of Nd. The inserted curves represent the number density distributions along the central line (red dash line) of the graphene. The inserted figure in the bottom-right corner gives the thickness of the adsorption layer on feed side.



Figure 6 Molecular trajectories during permeation through the NPG membranes. (a) Time-variations of the number of the molecular crossings in two directions and the number of molecules in permeate side; (b) Molecular number during permeation at the end of simulations and the Be number at different partial charges.


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TOC Graphic



(a)

(b)

Reflective boundary Periodic boundary

C

(c) Graphene Reflective boundary

z 4 nm

4 nm

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x

y

Figure 1


4 nm

N

H

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(a)


(b)

Figure 2



(a)

(b)

Figure 3


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(a)

(b)

Figure 4



q = 0.0 e

q = -0.0125 e

q = -0.025 e

q = -0.0375 e

q = -0.05 e

q = -0.075 e

q = -0.1 e

q = -0.125 e

Figure 5


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(a)


Feed side

Membrane

NF-P

Permeate side

(b)

Nnet

NP-F

Adsorption layer

Figure 6


CH4 Separation Performance in Negatively Charged

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