Adsorptive separation of ethylene/ethane mixtures using carbon nanotubes: a molecular dynamics study

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Adsorptive separation of ethylene/ethane mixtures using carbon nanotubes: a molecular

dynamics study

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2013 J. Phys. D: Appl. Phys. 46 395302

(http://iopscience.iop.org/0022-3727/46/39/395302)

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 46 (2013) 395302 (10pp) doi:10.1088/0022-3727/46/39/395302

Adsorptive separation of ethylene/ethanemixtures using carbon nanotubes:a molecular dynamics studyXingling Tian1, Zhigang Wang2, Zaixing Yang3, Peng Xiu3,4

and Bo Zhou1,4

1 Bio-X Lab, Department of Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China2 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012,People’s Republic of China3 Department of Engineering Mechanics, and Soft Matter Research Center, Zhejiang University,Hangzhou 310027, People’s Republic of China

E-mail: [email protected] and [email protected]

Received 16 May 2013, in final form 11 August 2013Published 10 September 2013Online at stacks.iop.org/JPhysD/46/395302

AbstractEthylene/ethane separation is a very important process in the chemical industry. Traditionally,this process is achieved by cryodistillation, which is extremely energy-intensive. Theadsorptive separation is an energy-saving and environmentally benign alternative. In thisstudy, we employ molecular dynamics simulations to study the competitive adsorption of anequimolar mixture of gaseous ethane and ethylene inside single-walled carbon nanotubes(SWNTs) of different diameters at room temperature. We find that for narrow SWNTs, i.e. the(6, 6) and (7, 7) SWNTs, the selectivities towards ethane, fselec, can reach values of 3.1 and3.7, respectively. Such high selectivities are contrary to the opinion of many researchers thatthe adsorptive separation of an ethylene/ethane mixture by means of dispersion interaction isdifficult due to the same carbon number of ethane and ethylene. The key for our observation isthat the role of dispersion interaction of ethane’s additional two hydrogen atoms with theSWNT becomes significant under extreme confinement. Interestingly, the (8, 8) SWNTprefers ethylene to ethane with fselec = 0.6. For wider SWNTs, fselec converges to ∼1. Themechanisms behind these observations, as well as the kinetics of single-file nanopore fillingand kinetics of confined gas molecules are discussed. Our findings suggest that efficientethane/ethylene separation can be achieved by using bundles/membranes of SWNTs withappropriate diameters.

(Some figures may appear in colour only in the online journal)

S Online supplementary data available from stacks.iop.org/JPhysD/46/395302/mmedia

1. Introductions

Ethylene is a very important feedstock in the chemical industryfor the production of rubbers, plastics, fuel componentsand other valuable chemical products. Ethylene is usuallyproduced by steam cracking or thermal decomposition ofethane, resulting in a process gas that is a mixture ofethylene and ethane. The two gases have the same

4 Authors to whom any correspondence should be addressed.

number of carbon atoms and therefore, separating them isan intrinsically difficult problem because of their similarphysicochemical properties, e.g., the very close boiling points[1]. Traditionally, separating ethylene from ethane requiresa cryogenic distillation step, which is very energy-intensive[1, 2]. Hence, the ethylene/ethane separation is one of themost energy-intensive separation processes carried out inthe petrochemical industry [3, 4]. Alternatively, adsorptiveseparation is an energy-saving and environmentally benignprocedure. So far, there are several adsorbents proposed to

0022-3727/13/395302+10$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA

J. Phys. D: Appl. Phys. 46 (2013) 395302 X Tian et al

be usable for ethylene/ethane separation, including variouszeolites [5] (such as ZIF-7 [3] and ZIF-8 [6]), π -complexationsorbents [7] and the microporous carbon adsorbents (activedcarbon [8] and carbon slit pore [1]).

On the other hand, the single-walled carbon nanotubes(SWNTs) possess well-defined hollow structures and thusserve as desirable materials for molecules [9–18], includingethane and ethylene [19–22], adsorbing into their interiors.However, generally speaking, it is difficult to effectivelyseparate the ethylene and ethane by using SWNTs, due totheir very close molecular sizes and the same number ofcarbon atoms. There are only a few theoretical studiesregarding the competitive adsorption of ethane/ethylene insideSWNTs [23, 24]. The simulation by Cruz et al [23] suggestedthat SWNT geometry plays a minor role on the adsorptionproperties of ethane and ethylene. While the Monte Carlosimulation by Albesa et al [24] explored the effects of thetemperature and nanotube diameter on the separation abilityof SWNT bundles; they found that at the same pressureand temperature, more ethane than ethylene adsorbed on thebundles over the entire range of pressures and temperaturesexplored. Despite the above progresses, the diameter effectof SWNTs on the ethylene/ethane separation has not beenfully explored; the mechanistic insights into the competitiveadsorption of ethane and ethylene inside SWNTs are stilllacking.

In this study, using molecular dynamics (MD) simulations(at 298 K, ∼80 bar), we simulate the competitive adsorption ofan equimolar mixture of gaseous ethane and ethylene insideSWNTs of different diameters (in the range of 8.1 Å � D �21.7 Å) and explore the underlying physical mechanisms.For narrow SWNTs, i.e. the (6, 6) and (7, 7) SWNTs, theselectivities towards ethane, fselec (the ratio of an averagenumber of ethane to that of ethylene inside the SWNT),can reach values of 3.1 and 3.7, respectively. Such highselectivities are due to the fact that the role of dispersioninteraction of ethane’s additional two hydrogens with theSWNT wall becomes significant when the molecule is underextreme confinement. More interestingly, the (8, 8) SWNTwith a diameter of 10.8 Å has a preference for ethyleneover ethane (fselec = 0.6). For wider SWNTs, thereis no clear binding preference for the two gases. Themechanisms behind these observations, as well as the kineticsof single-file nanopore filling and the kinetics of confined gasmolecules are discussed. The current study demonstrates thatwhen the SWNT diameter is less than ∼11 Å, the effect ofnanopore size on the adsorption behaviour of the inner ethyleneand ethane is remarkable, which suggests that the effectiveethylene/ethane separation could be achieved by using SWNTswith appropriate diameters.

2. Model and methods

In this study, we constructed various uncapped armchair (n, n)

SWNTs, where n are the integers ranging from 6 to 13 andn = 16. All SWNTs used here are 3.32 nm in length, withdiameters listed in table 1. The SWNTs were placed along thez-axis and positioned at the central region of the cubic boxes

Table 1. Initial setups of the simulated systemsa.

SWNTs D (Å) Nethane Nethylene

(6, 6) 8.14 389 389(7, 7) 9.49 388 388(8, 8) 10.85 388 388(9, 9) 12.20 387 387(10, 10) 13.56 384 384(11, 11) 14.92 382 382(12, 12) 16.27 378 378(13, 13) 17.63 374 374(16, 16) 21.70 371 371

a In this table, D denotes the diameterof SWNT; Nethane and Nethylene denotethe number of ethane and ethylenemolecules, respectively, in thesimulation box.

Figure 1. Snap view of initial simulation system with the (7, 7)SWNT case for demonstration. The SWNT is represented by greybonds; gas molecules are displayed in ball and stick representationswith ethane and ethylene coloured in red and green, respectively.

with side lengths of 5.8 nm. Initially, the simulation boxeswere filled with an equimolar mixture of ethane and ethylenegases; the concentrations for both gases are ∼6.8 mol L−1,corresponding to an initial pressure of 78.8 bar. We notehere that this pressure falls in the high pressure region wherethe ethane/ethylene molecules can fully spread over the innersurface of SWNT [23], which it is easily accessible forindustrial applications [25]. Then the SWNTs were insertedinto the equilibrated binary mixture (see figure 1), with gasmolecules removed if the distance between any carbon atom ofethane/ethylene and any carbon atom of SWNT was less than2.4 Å. After this insertion procedure, the concentrations ofethane/ethylene and pressures of the systems are close to theirinitial setups, with the resulting number of ethane/ethylenelisted in table 1.

Ethane and ethylene were modelled with the OPLSAAforce field [26] (detailed parameters are listed in table 2), whichis commonly used to model hydrocarbon molecules, includingalkanes and alkenes [22, 23, 27]. The carbon atoms of SWNTswere modelled as an uncharged Lennard-Jones particle with across-section of σcc = 3.4 Å and a depth of the potential wellof εcc = 0.086 kcal mol−1 [11–14, 28]. It has been suggested

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Table 2. Partial charges and Lennard-Jones parameters for atoms onethane and ethylene in the OPLSAA force field.

Atom types qi (e) ε (kcal mol−1) σ (Å)

C (C2H4) −0.230 0.076 3.55H (C2H4) 0.115 0.030 2.42C (C2H6) −0.180 0.066 3.50H (C2H6) 0.060 0.030 2.50

Table 3. Average number of inner ethane (〈Nethane〉) and ethylene(〈Nethylene〉) molecules in equilibrium, as well as the selectivity of theSWNT towards ethane, fselec (fselec = 〈Nethane〉/〈Nethylene〉), fordifferent systems. Standard deviations of average numbers andselectivities are obtained from multiple independent simulationsa.

SWNTs 〈Nethane〉 〈Nethylene〉 fselec

(6, 6) 5.3 ± 0.1 1.7 ± 0.1 3.08 ± 0.19(7, 7) 6.7 ± 0.1 1.8 ± 0.1 3.69 ± 0.14(8, 8) 5.6 ± 0.1 9.2 ± 0.1 0.61 ± 0.02(9, 9) 10.1 ± 0.1 11.0 ± 0.1 0.92 ± 0.01(10, 10) 14.1 ± 0.0 12.4 ± 0.0 1.14 ± 0.00(11, 11) 17.3 ± 0.1 15.7 ± 0.1 1.10 ± 0.02(12, 12) 22.5 ± 0.3 20.1 ± 0.3 1.12 ± 0.03(13, 13) 28.8 ± 0.3 23.9 ± 0.3 1.21 ± 0.02(16, 16) 44.6 ± 0.1 38.8 ± 0.1 1.15 ± 0.01

a The results for the (6, 6), (7, 7) and (8, 8) SWNTssystems are averaged from eight independent 80 nssimulations; the results for other SWNTs systems areaveraged from three independent 80 ns simulations.

that at the room temperature being studied here, the neglectof any quadrupole-surface interactions seems adequate [29].The carbon-carbon bond length of 1.42 Å and bond angleof 120

◦were maintained by harmonic potentials with spring

constants of 93 800 kcal mol−1 nm−2 and 126 kcal mol−1 rad−2

[11–14]. The positions of the carbon atoms at the inlet andoutlet of SWNTs were constrained using the position restraint,while other carbon atoms could vibrate freely. In addition, aweak dihedral angle potential was applied to bonded carbonatoms [11].

All MD simulations were performed using Gromcas 4.0.7[30] in an NVT ensemble at 298 K with periodic boundaryconditions applied in all directions. The constant temperaturewas maintained using the v-rescale thermostat [31] (with acoupling coefficient of τT = 0.5 ps). The particle-mesh Ewaldmethod with a real space cutoff of 1 nm was used to treat long-range electrostatic interactions, whereas the vdW interactionswere treated with a cutoff distance of 1.2 nm. LINCS wasapplied to constrain all bonds. For the (6, 6), (7, 7) and(8, 8) SWNTs systems, eight independent simulations for eachsystem were performed to obtain the statistically accurate fselec

(see table 3); for other SWNTs systems, three independentsimulations for each system were performed. The lengths ofall simulations were 80 ns. A time step of 2.0 fs was used anddata were collected every 1 ps.

3. Results and discussion

We have simulated nine types of systems with differentarmchair (n, n) SWNTs, where n = 6–13 and 16. We observe

that both ethane and ethylene can penetrate all SWNTs used,including the narrowest SWNT, the (6, 6) SWNT (8.1 Å indiameter), which is in contrast to a previous simulation [23]where ethane and ethylene were found to be almost incapableof accessing the interior of SWNTs 8.9 Å in diameter. Figure 2displays the number of inner ethane and ethylene with respectto the simulation time, which reflects the dynamical processesof competitive adsorptions of ethane and ethylene insidedifferent SWNTs. Here, a molecule is defined as beinginside the SWNT once its centre of mass enters the SWNT.Remarkably, the (6, 6) and (7, 7) SWNTs prefer ethane toethylene; whereas the (8, 8) SWNT favours ethylene. Whenthe diameter of SWNTs increase further [only the cases for (9,9), (10, 10) and (16, 16) SWNTs are shown for illustrations],it appears that the binding affinities of the two gases to theSWNTs are very close.

We have calculated the average number of inner ethaneand ethylene in equilibrium, together with their standarddeviations obtained from multiple independent simulations,as summarized in table 3. The results are consistent withthe dynamically adsorptive processes shown in figure 2, andthe very small (almost equal to zero) standard deviationsdemonstrate the robustness of our observation. To quantify theselectivity of the SWNT to different types of gases, we havecalculated the ‘selectivity’ of a SWNT towards ethane, fselec,defined as the ratio of the average number of ethane to ethyleneinside the SWNT, i.e. fselec = 〈Nethane〉/〈Nethylene〉. A largerfselec means a higher selectivity towards ethane. The computedfselec are presented in table 3 and the relationship betweenfselec and the diameter of the SWNT is plotted in figure 3.Remarkably, fselec are high for the (6, 6) and (7, 7) SWNTs(3.1 and 3.7 for the two SWNTs, respectively), with the (7, 7)SWNT possessing the maximal fselec. Such high selectivitiesare somewhat unexpected, because the conventional viewsuggests that adsorptive separation of ethane/ethylene mixtureis very difficult owing to the same carbon number of ethaneand ethylene and their very close molecular sizes. Moreinterestingly, in the case of the (8, 8) SWNT, the bindingpreferences of ethane and ethylene to the SWNT becomeopposite (fselec = 0.6); that is, the SWNT prefers ethyleneto ethane. As the diameter increases further, fselec fluctuatearound ∼1, indicating that the inner ethane and ethylene haveclose binding affinities to these SWNTs.

Given that the SWNTs in our simulations have beenpre-loaded with some ethane and ethylene molecules,some researchers may wonder that whether the data intable 3 really correspond to thermodynamic equilibriumor to some kinetically trapped state. To verify thatour observations for SWNTs of small diameters ((6, 6),(7, 7) and (8, 8) SWNTs) are real and not due to somekinetic effect, we have performed additional MD simulationsstarting with empty SWNTs and with SWNTs filled witha single component (pure ethane or ethylene). The resultsare nearly the same as those presented in table 3 (seetable S1 in the online supplementary material for details(stacks.iop.org/JPhysD/46/395302/mmedia)), demonstratingthe robustness of our observations.

In addition to the number of adsorbed molecules, wealso investigate the kinetics of confined fluids, as displayed

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Figure 2. Number of ethane and ethylene molecules (shown in red and black, respectively) within different armchair SWNTs as a functionof the simulation time.

in figure 4. Clearly, ethane prefers to reside inside a nanotubelonger than ethylene in the cases of the (6, 6) and (7, 7) SWNTs,whereas it is shorter than ethylene in the case of (8, 8) SWNT[and (9, 9) SWNT]; when the diameter of SWNTs becomeseven larger, the residence times for ethane and ethylene arenearly identical. These results are consistent with the adsorbeddata in table 3 and figure 3.

Apart from the adsorption properties, the dynamicalprocess of single-file nanopore filling is of scientific interest[32]. We have investigated the kinetics of pore fillingwith ethane/ethylene for narrow SWNTs [(6, 6) and (7, 7)SWNTs], wherein the gas molecules arranged in single-file,by performing the simulations starting with empty SWNTs.We observe that, for the (6, 6) SWNT system, in six out ofeight simulations, ethylene enters the SWNT ahead of ethane;

for the (7, 7) SWNT system, in five out of eight simulations,ethylene enters the SWNT first. These seem to be contraryto the equilibrium simulations wherein ethane shows a clearlyhigher affinity than ethylene to narrow SWNTs. The possiblereason is that ethylene has a smaller molecular size (becauseit possesses a planar geometry due to the presence of the rigidπ bond), so it can enter SWNT relatively easier than ethane atthe beginning of pore filling.

Figure 5 displays the dynamical process of single-filenanopore filling and the subsequent equilibrated process from arepresentative trajectory for the (6, 6) SWNT system. Ethyleneenters the SWNT ahead of ethane; at the time t ≈ 45 ps,the nanopore is completely filled with gas molecules, withethylene predominated (see figure 5(a)); when t ≈ 500 ps,the SWNT is predominately occupied by ethane and the

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Figure 3. Influence of the SWNT diameter, D, on the selectivity ofthe SWNT towards ethane, fselec (black circles). The lines merelyprovide a guide to the eye. Only the error bars for the (6, 6) and(7, 7) SWNTs are shown; for other SWNTs, error bars are not showndue to their very small values (almost equal to zero; see table 3).

system seems to reach equilibrium (see figure 5(b)). Wehave calculated the tfilling and tequ, which are the times neededto accomplish nanopore filling (defined as the time that thetotal number of inner molecules starts to reach the maximalvalue) and to reach equilibrium (defined as the time that thenumber of inner ethane starts to reach its averaged value inequilibrium; according to the data in table 3, here we used6 and 7 as the ‘equilibrium numbers’ for (6, 6) and (7, 7)SWNTs, respectively). We obtain that tfilling = 48 ± 10 psand tequ = 483 ± 266 ps in the (6, 6) SWNT case, andtfilling = 29 ± 9 ps and tequ = 205 ± 79 ps in the (7, 7) SWNTcase. Roughly speaking, the tequ is one order of magnitudelarger than tfilling; tfilling and tequ for the (7, 7) SWNT is twotimes smaller than those for the (6, 6) SWNT.

To understand the interesting findings in figure 3 froman energetic perspective [13, 33, 34], we have calculated theaverage nonbonded interactions, including both vdW andelectrostatic interactions, for an ethane/ethylene moleculeinside the SWNT and in bulk (defined as 1.2 nm away from anyatoms of SWNT for any carbon atoms of the ethane/ethylenemolecule) with the rest of the system and calculated the vdWinteractions of a gas molecule with the SWNT. Table 4(a)summarizes these interaction energies and their differencesbetween ethane and ethylene. It has been shown that when abulk ethane/ethylene moves into a SWNT, it gains considerableinteraction energy, mainly coming from its strong dispersioninteraction with the nanotube; meanwhile, ethane gains moreinteraction energy than ethylene, due to the stronger dispersioninteraction of ethane than ethylene with the nanotube. For(6, 6) and (7, 7) SWNTs, the nanopores are very narrow, sothe role of dispersion interaction of ethane’s additional twohydrogens with the SWNT wall becomes significant under theextreme confinement. Remember that in table 2 the depth ofthe potential well of the carbon atom on ethane is smaller thanthat on ethylene and therefore, the more dispersion interactionenergy gained by the inner ethane derives from the additional

two hydrogens of ethane relative to ethylene. This can befurther verified by decoupling the solid-fluid interaction intoseparate components coming from the carbon and hydrogenatoms (see table 4(b)). As a consequence, the differencesin total interaction energies (��Etotal) between ethane andethylene are profound, resulting in the unexpected highselectivities towards ethane inside (6, 6) and (7, 7) SWNTs.As the diameter increases, the absolute value of ��Etotal

becomes smaller; this explains why fselec converges to ∼1for wider SWNTs [(9, 9) SWNT and more wide SWNTs].However, note that ethane inside (8, 8) SWNT is moreenergetically favourable than ethylene, but the correspondingfselec is noticeably less than 1 (fselec = 0.6); in addition, theabsolute value of ��Etotal for (6, 6) SWNT is larger than thatfor (7, 7) SWNT, but fselec for the former one is smaller thanthat for the latter one. These seeming contradictions suggestthat besides the energetic data presented in table 4, there areother factors that govern the adsorption behaviours of ethaneand ethylene inside SWNTs.

As discussed above, the energetic calculations in table 4are necessary but may not be enough to explain the interestingtrend of fselec versus the SWNT diameter shown in figure 3.In the following, we further explore the mechanisms be-hind the competitive adsorption of the gas mixture insideSWNTs in terms of the steric effect and entropy, based onthe structural information of confined fluids. The structuralproperties of confined fluids include the radial gas densityprofiles (see figure S1 in the online supplementary material(stacks.iop.org/JPhysD/46/395302/mmedia)), orientation dis-tributions of inner gases (see figure 6(b)), as well as thesnapshots to show the equilibrium structures of inner gasesfrom the side view (see figure 6(a)) and the top view (seefigure S2 in the online supplementary material). In the (6,6) SWNT case, since ethane possesses a larger molecularsize, it loses more translational entropy than ethylene underthis ‘tight’ confinement. On the other hand, figures 6(a) and(b) show that ethane tends to ‘lie’ inside the (6, 6) SWNTand that ethane’s orientation distribution is more sharp thanethylene, indicating that ethane loses more rotational entropythan ethylene. Nevertheless, the penalty in ethane’s entropycan be (over)compensated by the gains in enthalpy, so ethaneis still more favourable than ethylene for the SWNT. In the(7, 7) SWNT case, ethane prefers to ‘stand’ instead of lie,which makes ethane not only effectively interact with theSWNT wall via the dispersion interaction, but also gain ex-cess rotational entropy as compared to that inside the (6,6) SWNT—although the orientations of confined fluids aresharply distributed around 90

◦, the confined molecules retain

considerable entropy, since they can rotate freely around theSWNT axis (note that the molecular configurations that corre-spond to θ ≈ 90◦ is much more than those that correspondto θ ≈ 0◦). Thus, the penalty in ethane’s rotational entropybecomes less significant. Accordingly, although the absolutevalue of ��Etotal in the (7, 7) SWNT case is smaller than thatin the (6, 6) SWNT case, the absolute value of ��G (the dif-ference in the overall free energy between ethane and ethylene)in the (7, 7) SWNT case can be larger than that in the (6, 6)SWNT case. This explains why fselec for the (7, 7) SWNT

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Figure 4. Cumulative distributions Plife(t < τ) of the lifetime τ of ethane (red) and ethylene (black) molecules inside different SWNTs.The data for (11, 11), (12, 12) and (13, 13) SWNTs systems are not shown because they are nearly same as the (16, 16) SWNT systems.

Figure 5. Dynamical process of single-file nanopore filling (a) and the subsequent equilibrated process (b) from a representative trajectoryfor the (6, 6) SWNT system.

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Table 4. Energetic analysis (in kcal mol−1). (a) Interaction energies for an ethylene/ethane molecule and their differences between the twogases, averaged from the entire simulationsa . (b) Decoupling the solid-fluid interaction into separate components coming from the carbonand hydrogen atomsb.

(a)SWNTs �Eetha

total EethaSWNT �E

ethytotal E

ethySWNT ��Etotal �ESWNT

(6, 6) −13.30 −13.99 −11.13 −11.74 −2.17 −2.26(7, 7) −10.33 −10.71 −8.70 −9.12 −1.64 −1.59(8, 8) −8.56 −8.31 −7.73 −7.50 −0.83 −0.81(9, 9) −8.17 −7.16 −7.28 −6.45 −0.89 −0.71(10, 10) −7.31 −6.26 −6.54 −5.67 −0.78 −0.59(11, 11) −6.69 −5.65 −5.99 −5.07 −0.70 −0.58(12, 12) −6.54 −5.03 −5.83 −4.51 −0.71 −0.52(13, 13) −6.44 −4.66 −5.73 −4.19 −0.71 −0.48(16,16) −5.83 −3.85 −5.13 −3.37 −0.70 −0.49

(b)SWNTs Eetha

SWNT Eetha-CSWNT Eetha-H

SWNT EethySWNT E

ethy-CSWNT E

ethy-HSWNT �ESWNT �EC

SWNT �EHSWNT

(6, 6) −13.99 −7.31 −6.68 −11.74 −7.60 −4.13 −2.26 0.29 −2.55(7, 7) −10.71 −5.31 −5.40 −9.12 −5.75 −3.37 −1.59 0.44 −2.03(8, 8) −8.31 −4.41 −3.90 −7.50 −4.61 −2.89 −0.81 0.20 −1.01(9, 9) −7.16 −3.77 −3.39 −6.45 −4.04 −2.41 −0.71 0.27 −0.98(10,10) −6.26 −3.28 −2.98 −5.67 −3.58 −2.09 −0.59 0.30 −0.89(11,11) −5.65 −2.96 −2.69 −5.07 −3.21 −1.86 −0.58 0.25 −0.83(12,12) −5.03 −2.64 −2.39 −4.51 −2.87 −1.64 −0.52 0.23 −0.75(13,13) −4.66 −2.43 −2.23 −4.19 −2.66 −1.52 −0.48 0.23 −0.71(16,16) −3.85 −2.01 −1.84 −3.37 −2.14 −1.22 −0.49 0.13 −0.62

a �E?total denotes the difference in total interaction energies for an ethane/ethylene molecule in SWNT vs. in bulk,

and E?SWNT denotes the vdW interaction energies of a gas molecule with the SWNT, where the superscript? is etha

for ethane and ethy for ethylene. ��Etotal is the difference between �Eethatotal and �E

ethytotal; �ESWNT is the difference

between EethaSWNT and E

ethySWNT.

b E?-CSWNT and E?-H

SWNT denote the contributions of carbon and hydrogen atoms, respectively, to the fluid-SWNTinteraction (E?

SWNT), where the superscript? is etha for ethane and ethy for ethylene. �ECSWNT is the difference

between Eetha-CSWNT and E

ethy-CSWNT ; �EH

SWNT is the difference between Eetha-HSWNT and E

ethy-HSWNT .

is larger than that for the (6, 6) SWNT. As to the interestingphenomenon that the (8, 8) SWNT prefers ethylene to ethane,we propose a possible explanation as follows. As displayed infigure 6(a), the confined space of the (8, 8) SWNT just allowsthe inner gas molecules to arrange in a nearly parallel double-strands manner (this can also be seen from the correspondingsubfigures in figures S1 and S2 in the online supplementarymaterial (stacks.iop.org/JPhysD/46/395302/mmedia)). Thisconfined space might be too ‘tight’ for the ethane moleculesin the double-strands molecular wires (ethane has a largermolecular size than ethylene), somewhat similar to the (6, 6)SWNT case where the inner single-file ethane molecules aretightly confined. Therefore, in case of the (8, 8) SWNT, thepenalty in (translational) entropy of the inner ethane is largerthan that of ethylene, thus counteracting the more gains in in-teraction energies of ethane than ethylene inside the SWNT. Incase of the (9, 9) SWNT, the inner molecules seem to becomeunstructured (see the snapshots in figures 6(a) and S2 in theonline supplementary material) and the orientations becomemore broadly distributed.

4. Conclusions

Using MD simulations, we investigate the selective adsorptionof an equimolar mixture of gaseous ethane and ethylene insideSWNTs of different diameters at room temperature. It has

been observed that ethane and ethylene can enter all types ofSWNTs, including the narrowest (6, 6) SWNT. Remarkably,for narrow SWNTs, i.e. the (6, 6) and (7, 7) SWNTs, theselectivities towards ethane, fselec, reach high values (3.1 and3.7, respectively), which is contrary to the opinion of manyresearchers that it is difficult to separate ethane and ethylenevia dispersion interaction (i.e. adsorption onto the nanotubewall) due to the same carbon number of ethane and ethylene.The physical mechanism behind these unexpected selectivitiesis that ethane has two more hydrogens than ethylene; whenthe molecule is under extreme confinement, the dispersioninteraction of its hydrogen atoms with the nanotube cannotbe ignored. More interestingly, in case of the (8, 8) SWNT(10.8 Å in diameter), the adsorptive preference is opposite,that is, this SWNT favours ethylene with an fselec of 0.6.This interesting phenomenon is presumably due to the entropiceffect, which is also an important factor governing the selectiveadsorption of ethane/ethylene inside SWNTs. For widerSWNTs, fselec converges to ∼1, indicating that there is no clearbinding preference between the two gases. For future studies,adsorption isotherms are required to validate whether theinteresting relationship between fselec and the SWNT diameterwe found can be qualitatively replicable to other pressures (thepressure used here is ∼80 bar), at least in the high pressureregion (p � 10 bar according to the calculations by Cruz et al ;in this pressure region, the ethane/ethylene molecules can fully

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Figure 6. Snapshots in side view to show the representative equilibrium structures of the ethane-ethylene mixtures within different armchairSWNTs (a), together with the corresponding orientation distributions of confined gas molecules (b). In subfigure (a), ethane and ethyleneare displayed in ball and stick representations, with SWNTs represented by grey lines. In subfigure (b), we use θ to characterize theorientation of inner gases, which is defined as the angle between C1–C2 (carbon-carbon) bond of ethane/ethylene and the axis of SWNT.

spread over the inner surface of SWNT [23]). Taken together,we demonstrate that when the SWNT diameter is less than∼11 Å, the pore size has a profound influence on the selectiveadsorption of ethane and ethylene and that the adsorptionpreference can be switched by varying the SWNT diameter.Our observations also suggest that the most appropriate SWNTfor ethane/ethylene separation is the SWNT with a diameterof ∼9.5 Å, such as the (7, 7) SWNT, with an fselec of 3.7.Some researchers may question that an fselec of 3.7 cannotbe qualified as ‘high selectivity’. However, consideringthat the traditional approach for ethane/ethylene separation isextremely energy-expensive and that the adsorptive separationis an energy-saving procedure, an fselec of 3.7 might beviewed as ‘high’ for industrial applications. In practice,SWNT bundles or membranes can be used to realize theethane/ethylene separation.

Our findings seem to be in contrast to a previous simulation[23] which showed 1 < fselec < 2 when T = 300 K and

p > 10 bar; it suggested that the SWNT geometry plays aminor role on the adsorption properties of ethane and ethylene.Our findings are also in contrast to another Monte Carlosimulation [24], which indicated that at the same pressure andtemperature more ethane than ethylene adsorbed on the SWNTbundles of various diameters over a broad range of pressuresand temperatures explored; it indicated that the maximumselectivity fselec ≈ 4 occurred only at low temperatures(153 K) with large-diameter SWNTs (at 273 K, the maximumselectivity fselec ≈ 2). One possible reason for the abovedifferences is the different simulated systems. The SWNTsused in [24] is the SWNTs bundles (except for the interior,gas molecules can also bind to the outer surfaces and groovesof SWNTs), rather than single SWNT. The selectivity on theouter surface of SWNTs is relatively small (see the radialgas density profiles in the supplementary material), so theoverall selectivity is small. In addition, they did not simulatea homogeneous (8, 8) SWNTs bundle even though they

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simulated the heterogeneous SWNTs bundle consisting of a (8,8) SWNT, so the reversal binding trend had not been observed.While [23] did not systematically vary the SWNT diameters inthe simulation (see [23] that focused on (9, 9), (16, 0) and (12,6) SWNTs, which share similar diameters), so the interestingdiameter effect of SWNTs on gas separation had not beenobserved. Another possible reason for the differences betweenour findings and previous simulations [23, 24] is the differentmodels used for gas molecules. We used the OPLSAA forcefield, which is an all-atom model, while [23, 24] used the2CLJQ and TraPPE force fields, respectively, both of whichare coarse-grained (united-atom) models. (In [23], althoughthe OPLSAA model was also used to study the diffusioninto pore and surface coverage for pure fluids, the adsorptiveseparation of the binary mixture was simulated with the coarse-grained 2CLJQ model.) As discussed previously in this study,the dispersive force of hydrogens with narrow SWNTs andmolecular configurations (associated with steric and entropiceffects) of gas molecules under extreme confinement arekeys for the observation of adsorptive separation, so it isnecessary to explicitly simulate the hydrogen of gas moleculesin studying gas adsorption inside SWNTs, especially fornarrow SWNTs. It is reasonable to speculate that the coarse-grained models (which were employed in [23, 24]) mightunderestimate the selectivity and the diameter effect of SWNTson gas adsorption. So far, only experimental reports onthe single-component gas adsorption of ethane or ethyleneon SWNTs bundles performed at cryogenic temperaturesare available in the literature [35, 36]. Experiments on theseparation of the binary mixture are highly needed to test ifour interesting findings from MD simulations are real and totest if the bundles/membranes of SWNTs under appropriate(p, T ) conditions can be used as efficient ‘selectors’ forethane/ethylene separation.

Acknowledgments

We thank Professors Xiaowei Tang and Yusong Tu fortheir insightful suggestions. This work is supported by theNational Natural Science Foundation of China (Grant Nos11204269 and 11004076), National Magnetic ConfinementFusion Science Program of China (No 2010GB104003),Zhejiang Provincial Natural Science Foundation of China(Grant No LY12A04007), the Fundamental Research Fundsfor the Central Universities and KYLIN-I Supercomputerin Institute for Fusion Theory and Simulation, ZhejiangUniversity.

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