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Journal of Advanced PhysicsVol. 5, pp. 1–8, 2016(www.aspbs.com/jap)

Selective Nanopores in Graphene Sheet forSeparation I-129 Isotope from AirSeyyed Mahmood Fatemi1,2,∗, Hamid Sepehrian2, and Masoud Arabieh1

1Department of Nano Chemistry, College of Science, University of Tehran, Tehran, Iran2Nuclear Science and Technology Research Institute, AEOI, P.O. Box 11365/8486, Tehran, Iran

Molecular dynamic simulation was used to investigate the ability of nanoporous graphene membrane in gasseparation process. Three di-atomic gases (I2, N2 and O2) were considered, in which different pore sizes weremodeled on graphene. The structure contains an impermeable movable wall (piston) to push the mixture gasestoward the nanoporous graphene membrane. Two different simulations were carried out, with two differentpiston velocities. Two key factors in gases separation process are the pore size of graphene and the velocityof movable wall. The results revealed that I-129 separation was improved by using proper size of pore and bydecreasing the velocity of movable wall. It was also found that the I-129 gas radionuclides could be completelyseparated from nitrogen and oxygen molecules in the pore-12 graphene configuration. It was also found thatnitrogen was more strongly adsorbed onto the membrane than oxygen, while I-129 was not adsorbed.

KEYWORDS: Molecular Dynamic (MD) Simulation, Nanoporous Graphene Membrane, Separation, Mean-SquaredDisplacement (MSD), Diffusion Coefficients.

1. INTRODUCTIONIodine-129 (129I) is one of the 7 long-lived fission productsthat are produced in significant amounts, this radioactivegas released into the environment by nuclear explosions,nuclear power plants, nuclear weapons and also naturally.I-129 decays with a half-life of 15.7 million years, withlow-energy beta and gamma emissions, to xenon-129.1

This radioactive, have similar physical properties with sta-ble iodine, however this radioactive decomposed over time.Iodine, is a non-metallic element, purple black color anda solid crystalline and have unusual sublimation charac-terized; this means without becoming a liquid, directlyturn from solid to vapor, at room temperature. This vaporcauses irritation of eyes, nose and throat. Because I-129 islong-lived and relatively mobile in the environment, it is ofparticular importance in long-term management of spentnuclear fuel. I-129 is likely to be the radionuclide of mostpotential impact at long times. I-129 is not deliberatelyproduced for any practical purposes. However, its longhalf-life and its relative mobility in the environment havemade it useful for a variety of dating applications. Theseinclude identifying very old waters based on the amountof natural I-129 or its Xe-129 decay product. The sepa-ration of such an important gas is an interesting subject

∗Author to whom correspondence should be addressed.Emails: m.fatemi@khayam.ut.ac.ir, mfatemi@aeoi.gov.irReceived: 27 November 2015Accepted: 1 May 2016

of scientific investigations. On the other hand, Membrane-based technology is gaining larger acceptance comparedwith other traditionally utilized separation technologiesused for gas separation. This is because membrane-basedtechnology offers several benefits such as low investmentcost, facile operation, large size, small footprint, and easymaintenance.2�3 Membrane materials, such as polymerfilms,4�5 zeolite,6 carbon micropores,7 carbon nanotubes,8

and organic framework9�10 have been widely used for gaspurification. However, these traditional membrane materi-als are limited in their overall selectivity/permeability foreconomically viable gas separation, because these mem-brane materials have drawbacks of an inherent trade-offbetween selectivity and permeability.11 Recently, graphene,a single atomic layer carbon material with particular struc-tural and fantastic properties, is expected as a promisingmembrane material for gas purification.12 Pristine per-fect graphene sheet is impermeable to gases as smallas He.13 In order to achieve the gas separation, generationof pores is necessary.14–16 However, several studies haveinvestigated the influence of chemical functionalizationon graphene membrane.17–19 Graphene with sub-nanometersized pores has been shown to be potent as a filter for sep-aration of different molecules20–22 with considerable effi-ciency gains compared to traditional technologies. Thesenanoparticle membranes are expected to yield high selec-tivity through molecular size exclusion effects,23�24 whileachieving high permeability due to the very small thick-ness of graphene layer.15 A separation mechanism based

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on molecular size works well as long as the differencesbetween the kinetic diameters of the gas molecules aresufficiently large, but becomes less effective the smallerthe differences get. According to the mechanism of sepa-ration behaviors in many cases, the control of the pore sizeis an indispensable characteristic of a good membrane.25

The good separation membrane should have controllablepore size, stable structure, and efficient permeability. Weanalyze the suggested strategy of pore size enlargement,a combination of ring removal, for a larger set of differentpore models, calculate bound states of gas atoms in thesepores, and discuss the more realistic case of a pore sizedistribution for the most effective pore type. If pore sizebecome sufficiently small, molecular sieving can be usedto separate molecules that differ kinetic diameter. Onlysmaller gas molecules can be permeate through the mem-brane. In the other word, separation on molecular siev-ing operates on molecular size exclusion principle.26 Forexample, Du et al.27 reported that the shape and size ofthe graphene pores had a significant effect on the sepa-ration properties of H2/N2, and a smaller pore can effec-tively prevent N2 from permeating. When the pore size isbig enough, the numbers of nitrogen molecules penetrat-ing exceeds that of hydrogen molecules due to the stronginteraction between N2 and graphene membrane. Koeniget al.28 experimentally measured the permeation rates anddetermined the separation factors of a few of gases (H2,CO2, Ar, N2, CH4, SF6� through the pores, and found thatthe pore size had an important influence on the transportperformance of the gases.Although the preparation, properties and applications of

porous graphene have been discussed in detail,20�21 forexample Jiao et al.3 analyzed the mechanism for gas andisotope separation. In this study, we use an impermeablemovable wall (piston) to push the mixture gases towardthe nanoporous graphene membrane and investigated theeffect of the velocity of piston.

2. COMPUTATIONAL PROCEDUREThe molecular permeation of three different diatomicgases, namely I2, O2 and N2 through porous graphenemembranes which different pore sizes was investigated.We considered the Iodine-129 isotopes in the gas mix-ture system. For simplicity, throughout the text the I-129is shown by general I2 symbol. All MD simulationswere performed using the LAMMPS package (Large-scale Atomic/Molecular Massively Parallel Simulator)package29 and structures were visualized using the VMDpackage.30 The simulation was performed in an NVTensemble for 5000 ps. The Nosé-Hoover barostat andthermostat31 were applied to maintain the pressure andtemperature at 1 atm and 300 K, with damping coeffi-cients 1 ps−1 and 0.1 ps−1, respectively (solid iodine canindeed sublime in this temperature). Time step of 1 fs wasused during the simulation and non-bonded van-der-Waals

interactions were modeled in terms of 12–6 Lennard-Jonesfamous potentials32 with a cut-off distance of 1.2 nm,that is:

ULJ�rij �=∑j>i

4�ij

[(�ij

rij

)12

−(�ij

rij

)6](1)

Wherein �ij is the well depth, �ij is the collision diameter,and rij is the distance between the two interacting atomsi and j . The harmonic approximation was considered forC–C bonds of graphene whereas the oxygen, nitrogen andiodine molecules were treated by using Morse potential:

U�r�=De�1− e1−��r−re��2 (2)

Wherein De is the depth of the energy from the bottom ofthe well to the bond dissociation, re is the bond length ina given bound state, and � control the width of the well.The parameters used for bond and nonbond interactionsare given in Tables I and II, respectively.A simulation box with the dimension of 30 Å×30 Å×

100 Å was constructed.This system contains a nanoporous graphene membrane

in the middle of the box in Cartesian coordinate origin(0, 0, 0) as the separator and dividing the simulation boxwith the height of 10 nm into two equal volume chambers(right and left chambers) and two impermeable wall withequal distances on both sides of the nanoporous graphenelocating at Cartesian coordinates (0, 0, 50) and (0, 0, −50)of the simulation box, which are in the case of movable(piston) and stationary, respectively (see Fig. 1). Initially,an equal number of 30 molecules of I2, O2 and N2 wereloaded into the right chamber (see Fig. 1), while the otherside was vacuum.The structure contains an impermeable movable wall

(piston) to push the mixture gases toward the nanoporousgraphene membrane. In order to study the effect of thevelocity of movable wall in the efficiency of I2 separa-tion process, two different piston velocities that located atthe Cartesian coordinate (0, 0 and +50) of the simulationbox, were considered for each pore size. Every simulationruns 5 ns to equilibrate the system, which the rigid pis-ton velocity was kept at V = 0, and 10 ns subsequentlyto collect the statistical data. During equilibrium, the totalenergy of the system was monitored whether the systemhad reached the equilibrium state or not. Following theequilibrium phase, two different simulations were carried

Table I. Parameters used for nonbonding interactions. a[Ref. 33],b[Ref. 34], c[Ref. 35].

Atom �i (kcal/mol) �i (Å) q (e) m (au)

Nitrogena 01819 3680 0 14006Oxygena 02246 3430 0 15999Iodineb 03390 4009 0 129000Carbonc 00700 3550 0 12011

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LETable II. Morse Parameters used for bonding interactions. Data givenfrom a[Ref. 33], b[Ref. 34].

Molecule re (Å) De (kcal/mol) � (Å−1�

Nitrogena 1207 11795 2680Oxygena 1098 22507 2642Iodineb 266 35606 1867

out for each of above case, with two different piston veloc-ities; V1 = 5 and V2 = 25 nm/ns. When an impermeablemovable wall was moved with the velocity of V , it pushedthe mixture of gases toward the nanoporous graphene andcaused to flow the gas through the graphene along theZ direction. Like the case of conventional steered molecu-lar dynamics (SMD) simulations, in which only an imper-meable movable wall is pulled. Furthermore, one does notneed to know or assume the mechanism of gas passage toset up the simulations, and the system will determine byitself which gas molecules crossing through the graphene.Thus one can observe at the atomic level a permeationevent that is similar to what happens in reality.

To construct the nanoporous membrane, a pore wasregarded on the center of graphene sheet, as can be seenin Figure 2.

Reflective boundary conditions were applied in thez-direction of the simulation box (normal to the grapheneplane) while periodic boundary conditions were consid-ered in the other two directions.36 To avoid vertical dis-placement of the entire nanoporous graphene membrane,the position of nanoporous graphene membrane was fixed.Nanopores were created by selectively removing atomsfrom the graphene sheet. Various sizes of pores were con-sidered and the number of graphene ring units removedso that the carbon atoms at the pore rim kept saturated,which would not lead immediately to chemical reactionswith the gas molecules. Six, nine, ten, thirteen, four-teen and fifteen carbon atoms were removed to build thePore-7 (P-7), P-10, P-11, P- 12, P-13 and P-14, respec-tively. (see Fig. 3). As shown in Figure 3, some carbon

Fig. 1. Initially snapshots of the gas molecules loaded into the right chamber, Colors assigned to each molecules are Red (O2�, Blue (N2�, Yellow (I2�and Green (graphene sheets).

Fig. 2. A pore were regarded on the center of graphene sheet.

atoms of the single layer graphene arbitrarily removedto generate axially symmetric shape of nanopores. TheP-7 and P-10 were fabricated by removing carbon atomswhose coordinates fulfilled the condition, circle equation,where r is the diameter of the pore. The other poreswere constructed by removing carbon atoms to build thenoted pore, without any specific equation. All nanoporesfabricating procedure was conducted with HyperChempackage.37

3. RESULTS AND DISCUSSIONIn this section, we analyze the plots of mean-squared dis-placement (MSD) for various pores, in the following, dif-fusion coefficients, the number of crossed gas moleculesthrough graphene membrane, the effect of geometry dis-tortions on the transient gas molecules, flow of gases andVan der Waals interaction were investigated.

3.1. MSDResults obtained from calculating MSD of gas moleculesin P-7 and P-12 which are displayed in Figures 4 and 5

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Fig. 3. Structures of the nanopores employed in the simulation. Thepores are named by the number of the graphene ring units removed i.e.,(a) P-7, (b) P-10, (c) P-11, (d) P-12, (e) P-13, (f) P-14.

respectively. Figure 4 showed MSD versus time for I2, N2

and O2 in the P-7 of porous graphene membrane.As seen, none of the molecule of gases could cross

through the nanoporous graphene membrane since the sizeof pore is smaller than kinetic diameter of all molecule ofgases.Figure 5 shows MSDs versus time in the pore-12 of

nanoporous graphene membrane. In P-12, restriction of thesize and shape for oxygen and nitrogen gas molecules forpermeation begins to vanish and molecules cross throughgraphene membrane in P-12. As regards size of p-12 isbigger for oxygen and nitrogen gas molecules, nitrogenmolecules fewer passes respect to oxygen molecules. Cor-responding simulation snapshots of molecular sieving ofI2 molecules are show in Figure 6.

3.2. Diffusion CoefficientsUsing MD trajectories, the diffusion coefficients of I2 andair in the various ring of porous graphene membrane werecalculated. The diffusion coefficients were evaluated fromthe limiting slope of the MSD curve against time using theEinstein relation.38 This equation relates the long-time (t)

Fig. 4. Calculated MSD versus time for I2 and air in the pore-7 ofporous graphene membrane.

Fig. 5. Calculated MSD versus time for I2, N2 and O2 in the pore-12of nanoporous graphene membrane.

limit of MSD of the particles to the diffusivity, D,through

D = 1

6limt→�

��r�t+t�− r�t��2�t

(3)

The diffusion coefficients (Å2/ps) for titled molecules canbe calculated from the MSD versus time graphs. Thesequantities are summarized in Table III.The results show that:

(I) no molecule passes throw the nanoporous graphenemembrane in the P-7, which is in contrast to the pore-14case,(II) The P-12 is more favored for I2 separation.

Accordingly, the results of current simulations candidatethe P-12 of nanoporous graphene membrane for separationof I2 from other air.

3.3. The Number of Crossed Gas Molecules ThroughGraphene Membrane

To finding the effect of the pore size in passing gasmolecules through graphene membrane, the numbers ofgas molecules passed the membrane were calculated.Figure 7 shows total number of crossed gas moleculesthrough graphene membrane versus time for I2� N2 and

Fig. 6. Snapshot of the gas molecules passing through pore-12.

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LETable III. The calculated diffusion coefficients of I2, N2 & O2 at vari-ous pore size.

Molecule Pore-7 Pore-12 Pore-14

Diffusion coefficients (Å2/ps) O2 00000 02578 04155N2 00000 00910 03442I2 00000 00000 03327

O2 in the pore-7 porous graphene membrane in 10 nssimulation.

These graphs confirm that, none of gas molecules couldcross through P-7 graphene membrane. When the pore sizeis increased to P-12, still I2 could not pass the membrane.Figure 8 shows total number of crossed gas moleculesthrough graphene membrane versus time for I2, N2 andO2 in the pore-12 of porous graphene membrane. Figure 9shows the typical trajectory of gases separation whichfinally molecular sieving of I2 occurs on the P-12 of porousgraphene, during the 10000 ps of the simulation time.

Figure 10 shows total number of crossed gases throughgraphene membrane versus time for I2, N2 and O2 in theP-14 of porous graphene membrane. At P-14 pore size,all of the gases could cross through graphene member. Inpore-10 only allowed the O2 molecules to permeate thegraphene sheet. In the case of I2 and N2, the restriction ofthe molecular orientation largely prohibits the permeation.When nitrogen and oxygen molecules are not blocked bythe pores (e.g., pore-12), there are more oxygen moleculesthat could permeate through the porous graphene mem-brane than nitrogen molecules which may related to theless potential barrier of permeation for Oxygen molecules.We calculated the permeation events in Table IV. The poresize of the models is defined as the average of the short-est and largest distances between the opposite atoms ofthe pore rim17 and the pores were designed similar to theexperiment.27

As shown in Table IV, there is no molecule observed topermeate through P-7, 8 and 9 during a 10 ns simulation,

Fig. 7. Total number of crossed gas molecules through graphene mem-brane versus time for I2, N2 and O2 in the pore-7 of porous graphenemembrane with (a) fix and (b) motion conditions of pristine graphenesheet, respectively.

Fig. 8. Total number of crossed gas molecules through graphene mem-brane versus time for I2, N2 and O2 in the pore-12 of porous graphenemembrane with (a) fix and (b) motion conditions of pristine graphenesheet, respectively.

the size of P-7, 8 and 9 are too small for nitrogen andoxygen to get through. In this way, when the pore sizeincreases to P-10, there are twelve O2 molecules that per-meate through the pore during a 10 ns simulation, andthe corresponding number of nitrogen molecules are zero.When the pore size further increases to P-12, nitrogen andoxygen molecules permeate through the porous graphene.There are still less nitrogen and oxygen molecules that per-meate through the porous graphene in P-12. The restrictionof the molecular orientation largely prohibits the perme-ation of I2 molecules. I2 molecules can be completely sepa-rated from nitrogen and oxygen molecules by model P-12.When nitrogen and oxygen molecules are not blocked bythe pores (e.g., pore-12), there are more oxygen moleculesthat permeate through the porous graphene membrane thannitrogen molecules. In this way, the number of permeat-ing oxygen molecules through P-12 increases and is morethan that of the nitrogen molecules. When the pore sizefurther increases, there are still more oxygen moleculesthat permeate through the nanopores than nitrogen. Thepermeation ratio, defined as the ratio of the numbers of

Fig. 9. Typical trajectory of gases separation which finally molecularsieving of I2 occurs on the P-12 of porous graphene, during the 5000 psof the simulation time.

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Fig. 10. Total number of crossed gas molecules through graphene mem-brane versus time for I2, N2 and O2 in the pore-14 of porous graphenemembrane with fix condition.

permeation events of the two types of gas molecules, couldbe used to describe the selectivity of the membrane. Thepermeation ratio is presented in two ways, permeation ratioO2/I2 and permeation ratio N2/I2. The higher permeationratio means better selectivity of the membrane. If the per-meation ratio is equal to one, there is no selectivity. Themaximum O2/I2 and N2/I2 permeation ratio is observedin P-12.

3.4. Effect of the Velocity of Movable WallWhen an impermeable movable wall was moved with thevelocity of V , it pushed the mixture of gases toward thenanoporous graphene and caused to flow the gas throughthe graphene along the Z direction. In order to study theeffect of the velocity of movable wall in the efficiencyof I2 separation process, number of crossing molecules ofgases through nanoporous graphene membrane were calcu-lated in two different velocities. Figure 11 shows the totalnumber of crossing gases through nanoporous graphenemembrane versus time for O2, in P-12 porous graphenemembrane in velocities of V1 = 5 and V2 = 25 nm/ns.During the simulation, it was found that, for P-12 case,

by increasing the piston velocity the separation capabilitywas decreased. It was due to that by increasing the pis-ton velocity, the average of the kinetic energy of all ofgases was increased and therefore, the probability of I2gases entering to the vicinity of graphene are more than

Table IV. Pore size, pore area, and the number of passing gas moleculesthrough nanoporous graphene membrane.

Nanoporous P-7 P-8 P-9 P-10 P-11 P-12 P-13 P-14

Size (Å) 651 708 722 774 850 859 897 986Area (Å2� 3279 3747 4215 4684 5152 5620 6090 6552I2-passage 0 0 0 0 0 0 0 10O2-passage 0 0 0 12 2 22 4 22N2-passage 0 0 0 0 0 6 2 14SOz/Iz

0 0 0 � Low � Low 22SNz/I2

0 0 0 0 0 � Low 14

Fig. 11. Total number of crossing gases through nanoporous graphenemembrane versus time for O2, in pore-12 porous graphene membrane invelocities of V1 = 5 and V2 = 25 nm/ns.

N2 and O2, cause of strongly adsorbed of I2 gases ontographene. Results show that I2 separation was improvedby decreasing the velocity of movable wall.

3.5. The Effect of Geometry Distortions on theTransient Gas Molecules

Geometry distortions could also affect the transition of gasmolecules through the nanopores membrane. The crossingof gas molecules through P-10 and P-11 (with the porearea of 0.468 nm2, 0.515 nm2, respectively) were consid-ered for the propose of comparison. Considering the poresizes, it is expected that the P-11 is preferred to P-10 forgas permeation, but the results showed a contrary expecta-tion. In other words, MD simulation predicted less numberof gas molecules could cross through membrane in P-11which may be related to the distorted geometry of P-11. Sothe mean numbers of gas atoms in P-10 and P-11 through-out of simulation were calculated. Figure 12 show totalnumber of crossed gas molecules through graphene mem-brane versus time for oxygen in the P-10 and P-11 ofporous graphene membrane.

Fig. 12. Total number of crossed gas molecules through graphene mem-brane versus time for O2 in the pore-10 and pore-11 of porous graphenemembrane.

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Fig. 13. Total number of crossed gas molecules through graphene mem-brane versus time for oxygen and nitrogen, in the pore-12 and pore-13of porous graphene membrane.

Similarly, this phenomenon occurs for P-12 and P-13.Figure 13 show total number of crossed gas moleculesthrough graphene membrane versus time for oxygenand nitrogen in the P-12 and P-13 of porous graphenemembrane.

3.6. Calculated the Flow of GasesThe flow is used to characterize the membrane permeabil-ity quantitatively, which is defined as:

F = N (mol)S�m2�T �s�

(4)

Where N is the moles of gas molecules that permeatedthrough the membrane, S refers to the area of membranein total, and T is the time duration. We calculated the flowof I2, O2 and N2 in various membrane models in the fixcondition, as shown in Figure 14.

There is a prodigious increase of the flow of O2

molecules at of the P-12 area, where the restriction of thesize and shape to the N2 permeation begins to vanish. Afterthat, the flow of O2 and N2 molecules became reduced. Inthe case of the nitrogen and oxygen molecules, the flow of

Fig. 14. Flow of gas molecules passing through the porous graphenemembranes at different pore areas.

Fig. 15. VDW energy between the gas molecule and the edge atoms ofpore-7 at graphene membrane.

nitrogen and oxygen molecules reduced at pore-13, whichis due to the different shape of P-12 and P-13. After that,the nitrogen and oxygen flow increases as the pore areaincreases.

3.7. Van der Waals InteractionThe van der Waals interactions between gas molecules andthe edge atoms of pore at graphene membrane are alsocalculated in the fix condition.As shown in Figure 15, the average of VDW energy

between the O2 and N2 molecules and the edge atoms ofP-12 at graphene membrane is more negative than I2 cause,transit O2 and N2 molecules through porous graphenemembrane. This results in more permeation events of O2

and N2 molecules through porous graphene than that of I2.

4. CONCLUSIONWe found that the nanoporous graphene membrane couldbe used to separate Iodine-129 gas radionuclides from air.In the pore-12, nitrogen and oxygen molecules permeatethrough the nanoporous graphene. The restriction of themolecular orientation largely prohibits the permeation of I2molecules. Two key factors in gases separation process arethe pore size of graphene and the velocity of movable wall.The results revealed that I-129 separation was improved byusing proper size of pore and by decreasing the velocityof movable wall. It was also found that geometry distor-tions were effective parameter in transient gas moleculesthrough the membrane. However, in the pore-12, the bestselectivity of I2 from air is achieved with the pore sizebarely bigger than the nitrogen and oxygen molecule andsmaller than the I2 molecules.

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