Impact of Impure Gas on CO2 Capture from Flue Gas Using Carbon Nanotubes: A Molecular Simulation Study

We used a grand canonical Monte Carlo simulation to study the influence of impurities including water vapor, SO2, and O2 in the flue gas on the adsorption of CO2/N2 mixture in carbon nanotubes (CNTs) and carboxyl doped CNT arrays. In the presence of single impure gas, SO2 yielded the most inhibitions on CO2 adsorption, while the influence of water only occurred at low pressure limit (0.1 bar), where a one-dimensional chain of hydrogen-bonded molecules was formed. Further, O2 was found to hardly affect the adsorption and separation of CO2. With three impurities in flue gas, SO2 still played a major role to suppress the adsorption of CO2 by reducing the adsorption amount significantly. This was mainly because SO2 had a stronger interaction with carbon walls in comparison with CO2. The presence of three impurities in flue gas enhanced the adsorption complexity due to the interactions between different species. Modified by hydrophilic carboxyl groups, a large amount of H2O occupied the adsorption space outside the tube in the carbon nanotube arrays, and SO2 produced competitive adsorption for CO2 in the tube. Both of the two effects inhibited the adsorption of CO2, but improved the selectivity of CO2/N2, and the competition between the two determined the adsorption distribution of CO2 inside and outside the tube. In addition, it was found that (7, 7) CNT always maintained the best CO2/N2 adsorption and separation performance in the presence of impurity gas, for both the cases of single CNT and CNT array.

In our previous study, grand canonical Monte Carlo (GCMC) simulations were conducted to investigate the adsorption of CO 2 in the internal space of individual single CNTs in the presence of pre-adsorbed water [3].It was found that the pre-loaded water provided additional H 2 O-CO 2 interactions to facilitate the adsorption of CO 2 , by taking up the adsorption site available for CO 2 .Similarly, as reported by Yu et al. [1], the presence of SO 2 in the gas phase exerted a negative effect on the adsorption of CO 2 for CO 2 /N 2 /SO 2 mixture in HKUST-1 at ambient temperature.By comparison, the presence of O 2 exerted little effect on the adsorption of CO 2 in HKUST-1.The main components of flue gases generated by coal-fired power plants include N 2 (about 73-77%), CO 2 (15-16%), H 2 O (5-7%), O 2 (about 3-4%) [12], and trace amounts of SO 2 , etc. [25,26].Therefore, the impurity gases, such as H 2 O, O 2 , and SO 2 are expected to impose a significant influence on the adsorption and separation of CO 2 from flue gas using CNTs [1,3,[27][28][29][30].
In practice, oxidation defects often occurred during the acidic/oxidative purification of carbon nanotubes [31], where oxygen-containing functional groups (mainly carbonyl and carboxyl) could be grafted to the defect sites [32].The oxygen-containing functional groups, such as carboxyl and hydroxyl groups, are hydrophilic, so it could significantly enhance the adsorption of water vapor contained in flue gas, which thus imposes strong influence on the adsorption in CNTs for the rest components in flue gas [33,34].Further, instead of single carbon nanotube, carbon nanotube bundles were generally obtained during the synthesis procedure.Therefore, to explore the influence of impurity gases on the adsorption and separation of CO 2 from flue gas in a practical manner, the adsorption of gas mixtures (CO 2 /N 2 /X, X denotes the impurity gases, H 2 O, SO 2 , and O 2 ) in the functionalized CNT bundles are required.To the best of our knowledge, the adsorption behavior of impurity gases in the functionalized CNT bundles is still unknown.Hence, the effects of three impurity gases on the separation of CO 2 in CNT also have not been systematically studied.Different from binary mixture, there are more complex interactions between three impurity gases, the cooperative impact on CO 2 adsorption has hardly been studied.In addition, little is known about how the cooperative effects between adsorbate-CNT interaction and interaction between impurity and adsorbate affect CO 2 /N 2 selectivity.Discussions related to these and other related issues will be obtained in detail in this work.Furthermore, the influence on the optimum diameter of CNTs for separating CO 2 /N 2 is not reported yet.
In this work, GCMC and density functional theory (DFT) simulations were conducted to investigate the adsorption separation of CO 2 from flue gases using carbon nanotubes in the presence of impurity species (H 2 O, O 2 and SO 2 ), in order to fundamentally reveal the impacts of impurity gases on the adsorption behaviors and separation performance of CO 2 .DFT calculations were specifically conducted to add the carboxyl groups to the vacant oxidation defects of CNTs.Both the adsorption of gas mixtures in single carbon nanotubes and carbon nanotube bundles with functional groups were systematically considered.The separation of SO 2 /N 2 mixtures also was investigated in CNTs.As both adsorption capacity and selectivity determine the performance of the adsorbents, the performance coefficient of functionalized CNT bundles was used to comprehensively evaluate the CO 2 separation potential using CNTs.

Simulation Details 2.1. Molecular Models
In our simulations, CO 2 was modeled by EMP2 model of Harris and Yung [35].N 2 and O 2 were treated as a rigid three-site model with two LJ sites carrying negative charges to represent the N/O atoms, associated with a dummy particle located at center of mass (COM) being used to carry the positive charges to maintain the electrostatic neutralization of molecule [36].H 2 O was represented by the SPC/E model, which treated H 2 O as a rigid molecule with a positive charges on H atoms and negative partial charges on the O atom [37].SO 2 is modeled as a three-site model as well, with a charged LJ particle being assigned for each atom [38].In addition, the Steele parameters were used to represent the carbon atoms in CNTs.All of the configurational parameters [13], LJ parameters, and partial charges of these guest molecules and the CNTs are summarized in Table 1.The adsorption configuration of gas molecules in four CNTs, the optimized structure of CNT unit cell with defects, and the constructed CNT array can be seen in Figure 1a,b.
The interactions of adsorbate-adsorbent and adsorbate-adsorbate are described by the dispersion and electrostatic terms, given by u (α,β) where r (α,β) ij is the distance between the atom i and j of molecules α and β.The LJ size parameter σ ij and well depth parameter ε ij for the interactions between different species were estimated using Lorentz-Berthelot mixing rules [39], and the Dot Line Method was used to modify the long range electrostatic interactions in CNTs [40,41].
where ( ) , ij r  is the distance between the atom i and j of molecules  and  .The LJ size parameter  ij and well depth parameter  ij for the interactions between different species were estimated using Lorentz-Berthelot mixing rules [39], and the Dot Line Method was used to modify the long range electrostatic interactions in CNTs [40,41].

Grand Canonical Monte Carlo Simulations
To gain insights of the effect of impure gases on the adsorptive separation of CO 2 from flue gas using CNTs, three impurity gases, SO 2 , H 2 O, and O 2 , were used to conduct simulations for the adsorption in four different CNTs ((6, 6), (7,7), (10,10) and (12,12)), having the diameters of 0.81 to 1.63 nm, were considered.Initially, the adsorption of binary mixture CO 2 /N 2 in different CNTs was examined to find out the optimized pore size of the CNT for CO 2 separation.Afterwards, ternary mixtures, including CO 2 /N 2 /SO 2 , CO 2 /N 2 /O 2 , and CO 2 /N 2 /H 2 O were used to determine the effects of individual single impurity on the separation performance of CNTs.Eventually, the simulations for the adsorption of quinary mixture, CO 2 /N 2 /SO 2 /H 2 O/O 2 was conducted to reveal the effect of the co-existing impure gases on the CO 2 separation, and the optimal CNT pore size for CO 2 separation in practice.In all the simulations, the molar ratio of CO 2 /N 2 mixture was fixed at 16/84 in the bulk phase, while the partial pressure of H 2 O in the ternary mixtures being set as at its saturation pressure of 3.537 kPa, at 300 K.In addition, the mole fraction of SO 2 and O 2 in the ternary mixture was set as 0.08% and 4%, respectively.However, for the quinary mixture, the mole fractions of each gas species were defined as: 16 CO 2 : 4 O 2 : 3.16 H 2 O: 0.08 SO 2 [17], which were chosen to mimic the practical composition of flue gases.
GCMC simulations were conducted to measure the adsorption and separation of CO 2 from flue gas in consideration of the effects of impurities, the adsorbate chemical potential µ, system volume V, and temperature T were maintained constant during simulations.Three Monte Carlo trial moves including the displacement, insertion, and deletion with corresponding probabilities of 0.4, 0.3, and 0.3 were implemented.The fugacities of the components in the bulk phases were calculated using the Peng-Robinson equation of state [42] (PR EOS) for mixtures.For the binary mixture, 1 × 10 7 configurations were used to equilibrate the system, which was supplemented by another 5 × 10 7 configurations for statistical analysis.For the ternary mixtures, the configurations used for equilibration and statistics become 1 × 10 8 and 2 × 10 8 , respectively.For the quinary mixture, 3 × 10 8 and 6 × 10 8 configurations were used for equilibration and measuring the isotherm measurement.The equilibrium selectivity, S ij , was calculated according to where, x i and y i were the molar fractions of component i in the adsorbed and bulk phases, respectively.Four kinds of CNTs with different diameters were doped with carboxyl groups to form CNT bundles.Firstly, the original unit cell of carbon nanotube model was established.Carbon atoms were randomly deleted to produce a vacant defect, where each vacant defect contained three sp3 hybrid carbon atoms.The carboxyl group was randomly grafted to one of the SP 3 hybrid carbon atoms, and hydrogen atoms were added to the other two carbon atoms to saturate the free valence.After the three vacancy defects were modified, the cell was randomly rotated and spliced three times to form a supercell, to derive the original structure of functionalized CNTs.Then, the density functional theory (DFT) was used to optimize the structure to derive the best geometry.The DFT calculation was conducted in Vienna ab initio simulation package (VASP) software package, where Perdew Burke ernzerhof (PBE) [43] was used as the exchange correlation function and a plane-wave cutoff energy was set to be 550 eV.The optimized structure was used to construct 2 × 2 carbon nanotube arrays, where the inter-tube distance was maintained at 0.6 nm.The simulation box containing CNT bundles has dimensions of 38 × 38 × 50 Å, and the periodic boundary conditions were applied in the x and y directions.

Effect of Pore Size on the Adsorption of CO 2 /N 2 Mixture in CNTs
The adsorption of CO 2 /N 2 mixture (with a mole ratio of 16/84 in the gas phase) in the CNTs at 300 K is conducted to derive the optimal diameter for CO 2 capture, where the pore diameters varies from 0.81 to 1.63 nm. Figure 2 depicts the adsorption isotherms of CO 2 /N 2 and the corresponding CO 2 /N 2 selectivity at 300 K.As suggested, within the diameter range, all the adsorption isotherms of CO 2 and N 2 could be represented by type I according to the IUPAC classification.It is seen that the adsorption of CO 2 and the CO 2 /N 2 selectivity in the (6,6) CNT with a diameter of 0.81 nm achieves their maxima below 1.0 bar.However, for the pressure range from 1.0 to 5.0 bar, the (7, 7) CNT with a diameter of 0.95 nm exhibits superior performance on separation CO 2 /N 2 in comparison with the performance in the rest, in which both the adsorption of CO 2 and the CO 2 /N 2 selectivity are the highest.In the larger (10,10) and (12,12) CNTs, although the adsorption amount of CO 2 monotonically increases with pressure, which is consistently higher than the result in the small CNT, the CO 2 /N 2 selectivity is dramatically reduced compared with the value in the (6, 6) and (7, 7) CNTs.Consequently, the enlarged CNT diameter promotes the adsorption capacity of CO 2 and N 2 simultaneously, while reducing the CO 2 /N 2 selectivity for the weak adsorbate-adsorbent interactions.Considering the superior adsorption amount of CO 2 and significantly higher CO 2 /N 2 selectivity, the (6,6) and (7,7) CNTs can provide great potential on CO 2 separation from flue gas.

Effect of Pore Size on the Adsorption of CO2/N2 Mixture in CNTs
The adsorption of CO2/N2 mixture (with a mole ratio of 16/84 in the gas phase) in the CNTs at 300 K is conducted to derive the optimal diameter for CO2 capture, where the pore diameters varies from 0.81 to 1.63 nm. Figure 2 depicts the adsorption isotherms of CO2/N2 and the corresponding CO2/N2 selectivity at 300 K.As suggested, within the diameter range, all the adsorption isotherms of CO2 and N2 could be represented by type I according to the IUPAC classification.It is seen that the adsorption of CO2 and the CO2/N2 selectivity in the (6,6) CNT with a diameter of 0.81 nm achieves their maxima below 1.0 bar.However, for the pressure range from 1.0 to 5.0 bar, the (7, 7) CNT with a diameter of 0.95 nm exhibits superior performance on separation CO2/N2 in comparison with the performance in the rest, in which both the adsorption of CO2 and the CO2/N2 selectivity are the highest.In the larger (10,10) and (12,12) CNTs, although the adsorption amount of CO2 monotonically increases with pressure, which is consistently higher than the result in the small CNT, the CO2/N2 selectivity is dramatically reduced compared with the value in the (6, 6) and (7, 7) CNTs.Consequently, the enlarged CNT diameter promotes the adsorption capacity of CO2 and N2 simultaneously, while reducing the CO2/N2 selectivity for the weak adsorbate-adsorbent interactions.Considering the superior adsorption amount of CO2 and significantly higher CO2/N2 selectivity, the (6,6)   It is understood that the adsorption of CO2/N2 mixture in the CNTs is determined by the competition effect between the adsorbate-adsorbent interactions and the entropic ef- It is understood that the adsorption of CO 2 /N 2 mixture in the CNTs is determined by the competition effect between the adsorbate-adsorbent interactions and the entropic effect.Figure 3 illustrates the variation of CO 2 -CNT and N 2 -CNT interactions with pressures in the CNTs with different pore sizes, where the detailed calculating procedure was provided in our previous study [3].Although both the CO 2 -CNT and N 2 -CNT interactions decrease with the pore size of CNTs, the dependency of interactions on the pore size is stronger for CO 2 .Accordingly, the preferential adsorption of CO 2 over N 2 is suppressed in the larger CNTs, leading to the reduced CO 2 /N 2 selectivity.In consideration of the nominal diameter, d CNT , of the (6, 6) CNT is 0.81 nm, the effective diameter for CO 2 molecules rotating inside the (6,6) CNT can be approximately measured as d eff = d CNT −σ O−C = 0.49 nm, where σ O−C = 0.32 nm is determined according to (σ o + σ C )/2, using the LJ size parameters of carbon atoms (σ C ) of the CNT and oxygen atom (σ O ) of the CO 2 molecule.As the molecule size of CO 2 molecule (0.5331 nm) in the axial direction is larger and that for N 2 molecule (0.441 nm), CO 2 molecules in our simulations are found to distribute almost in parallel to the axis of the (6, 6) CNT, showing strong rotational restrictions.However, the rotational freedom of N 2 is negligibly affected.In addition, random distributions of CO 2 molecules are observed in the (7, 7) CNT with a diameter of 0.95 nm, suggesting that the dramatically enhanced entropic effect is responsible for the reduced CO 2 /N 2 selectivity in the (6, 6) CNT, compared to the (7, 7) CNT.
Molecules 2022, 27, x FOR PEER REVIEW 6 fect.Figure 3 illustrates the variation of CO2-CNT and N2-CNT interactions with p sures in the CNTs with different pore sizes, where the detailed calculating procedure provided in our previous study [3].Although both the CO2-CNT and N2-CNT int tions decrease with the pore size of CNTs, the dependency of interactions on the pore is stronger for CO2.Accordingly, the preferential adsorption of CO2 over N2 is suppre in the larger CNTs, leading to the reduced CO2/N2 selectivity.In consideration of the n inal diameter, CNT d , of the (6, 6) CNT is 0.81 nm, the effective diameter for CO2 molec rotating inside the (6,6)

Effect of Single Impurity on the Adsorption of CO2/N2 Mixtures in CNTs
The adsorption of ternary mixtures, CO2/N2/X in CNTs at 300 K, with X denoti specific impure gas including H2O, SO2, and O2, is further investigated.It is found insignificant impact of impurities on the separation of CO2 is found in the (10, 10) and 12) CNTs in all the cases, so all the simulation results for the (10,10) and (12,12) CNT provided in Figure S1 in the Supporting Information, and the results for the (6, 6) an 7) CNTs are explored.The results for the adsorption of CO2 and CO2/N2 selectivity in t two CNTs are plotted in Figure 4.The adsorption curves of three impurities are show Figure S2.

Effect of Single Impurity on the Adsorption of CO 2 /N 2 Mixtures in CNTs
The adsorption of ternary mixtures, CO 2 /N 2 /X in CNTs at 300 K, with X denoting a specific impure gas including H 2 O, SO 2 , and O 2 , is further investigated.It is found that insignificant impact of impurities on the separation of CO 2 is found in the (10, 10) and (12,12) CNTs in all the cases, so all the simulation results for the (10,10) and (12,12) CNTs are provided in Figure S1 in the Supporting Information, and the results for the (6, 6) and (7, 7) CNTs are explored.The results for the adsorption of CO 2 and CO 2 /N 2 selectivity in these two CNTs are plotted in Figure 4.The adsorption curves of three impurities are shown in Figure S2.To quantify the inhibition effect of impurity gas on the adsorption of CO2, an inhibition coefficient is defined as Where b a and im a represents the adsorbed amounts of CO2 for the binary CO2/N2 mix- ture and for the ternary CO2/N2/X mixture, respectively.As suggested, for the impure gas SO2, the inhibition coefficient in the (6, 6) CNT reaches up to 50.5%, 59.6%, and 61.9%, under the pressure of 0.1, 1.0, and 12.5 bar, respectively.Similarly, the inhibition coeffi- To quantify the inhibition effect of impurity gas on the adsorption of CO 2 , an inhibition coefficient is defined as where a b and a im represents the adsorbed amounts of CO 2 for the binary CO 2 /N 2 mixture and for the ternary CO 2 /N 2 /X mixture, respectively.As suggested, for the impure gas SO 2 , the inhibition coefficient in the (6,6) CNT reaches up to 50.5%, 59.6%, and 61.9%, under the pressure of 0.1, 1.0, and 12.5 bar, respectively.Similarly, the inhibition coefficients in the (7, 7) CNT corresponds to 12.9%, 31.2%, and 28.1% under the same condition.However, as seen in Figure 4c, the impact of H 2 O on the adsorption of CO 2 is significant at low pressure (0.1 bar), which yields an inhibition coefficient of 64.5%.When the pressure is increased to above 0.1 bar, the inhibition coefficient of H 2 O sharply reduces to be negligible.It is interesting to find that both the adsorption of CO 2 and the CO 2 /N 2 selectivity is barely affected by the presence of O 2 in the gas phase.Figure 5a-c depicts the interactions of CO 2 -CNT and of impurity gas X-CNT in the (6, 6) and (7, 7) CNTs.As given in Figure 5, it is evident that SO 2 has much stronger adsorption affinity with the nanotube wall than CO 2 , so strong adsorptive competition between SO 2 and CO 2 occurs, associated with the adsorption space being favorably occupied by SO 2 molecules.Meanwhile, the interactions between CO 2 molecules and the nanotube wall becomes weaker due to the introduction of SO 2 , so it is safe to conclude that the competitive adsorption and the weakened CO 2 -CNT interactions are responsible for negative impacts on the adsorption of CO 2 .Similar to the decreased adsorption of CO 2 , the adsorption of N 2 also becomes smaller in the presence of SO 2 (see Figure S3 in Supplementary Materials).However, as seen in Figure 4c, the impact of H2O on the adsorption of CO2 is significant at low pressure (0.1 bar), which yields an inhibition coefficient of 64.5%.When the pressure is increased to above 0.1 bar, the inhibition coefficient of H2O sharply reduces to be negligible.It is interesting to find that both the adsorption of CO2 and the CO2/N2 selectivity is barely affected by the presence of O2 in the gas phase.Figure 5a-c depicts the interactions of CO2-CNT and of impurity gas X-CNT in the (6, 6) and (7, 7) CNTs.As given in Figure 5, it is evident that SO2 has much stronger adsorption affinity with the nanotube wall than CO2, so strong adsorptive competition between SO2 and CO2 occurs, associated with the adsorption space being favorably occupied by SO2 molecules.Meanwhile, the interactions between CO2 molecules and the nanotube wall becomes weaker due to the introduction of SO2, so it is safe to conclude that the competitive adsorption and the weakened CO2-CNT interactions are responsible for negative impacts on the adsorption of CO2.Similar to the decreased adsorption of CO2, the adsorption of N2 also becomes smaller in the presence of SO2 (see Figure S3 in Supplementary Materials).In addition, although both the adsorption amounts of CO2 and N2 are decreased by the presence of SO2 in the (6, 6) and (7, 7) CNTs, only a slight decrease in the CO2/N2 selectivity is found for (6, 6) CNT and the CO2/N2 selectivity is even enhanced in the (7, 7) CNT.To explain this phenomenon, the adsorbate-adsorbate interaction energies are esti- In addition, although both the adsorption amounts of CO 2 and N 2 are decreased by the presence of SO 2 in the (6, 6) and (7, 7) CNTs, only a slight decrease in the CO 2 /N 2 selectivity is found for (6, 6) CNT and the CO 2 /N 2 selectivity is even enhanced in the (7, 7) CNT.To explain this phenomenon, the adsorbate-adsorbate interaction energies are estimated as a function of pressure for SO 2 -CO 2 and SO 2 -N 2 in Figure 5d.It is seen that CO 2 molecules are strongly attracted by the adsorbed SO 2 molecules in the (6, 6) and (7, 7) CNTs, whereas N 2 molecules suffer the strong repulsions from SO 2 molecules.As the additional CO 2 -SO 2 interactions actually facilitate the selective adsorption of CO 2 over N 2 , the CO 2 /N 2 selectivity is enhanced by SO 2 in the (7, 7) CNT.However, the adsorbed SO 2 also enhances the entropic effect for CO 2 adsorbing in the (6, 6) CNT, further restricting the rotation freedom of CO 2 molecules, but this entropic effect exerts insignificant effect on the rotation of N 2 molecules.Although the adsorption of CO 2 is energetically favorable in the (6,6) CNT in the presence of SO 2 , the strengthened entropic effect has completely dominated over the energetic effect, thereby leading to the dramatically reduced CO 2 adsorption.The adsorption reduction arising from the dominant entropic effect is more significant for N 2 due to its unfavorable energetic field exerted by SO 2 .Therefore, the CO 2 /N 2 selectivity is reduced in the presence of SO 2 in the (6, 6) CNT.
Figure 4c indicates that, at the rather low pressure <0.1 bar (water vapor is at its saturation pressure, under a mole fraction of ~35.64%), noticeable adsorption of water vapor is found in the (6, 6) CNT, where considerable adsorption space is occupied.As depicted in Figure 6, the adsorption of water vapor decreases rapidly as a consequence of the competitive adsorption of CO 2 and N 2 , where the corresponding partial pressures are enhanced at higher pressures.The inset of Figure 6 depicts the molecular configuration of water adsorbed in the (6, 6) CNT.As reported in the previous study, negligible adsorption of water was observed in the CNTs until the partial pressure of water vapor reached a critical pressure, where water molecules filled the CNT immediately and completely once the partial pressure was above the critical pressure [12,44].It is shown that the critical pressure for the (6,6) CNT is around the saturation pressure of water at 300 K, which is increased to 1.75 times of the saturation pressure in the (7, 7) CNT.Based on this reason, negligible adsorption of water is observed in the (7, 7) CNT within the pressure range investigated, while the effect of water vapor is only significant at rather low pressure in the (6, 6) CNT.CNTs, whereas N2 molecules suffer the strong repulsions from SO2 molecules.As the ad ditional CO2-SO2 interactions actually facilitate the selective adsorption of CO2 over N2 the CO2/N2 selectivity is enhanced by SO2 in the (7, 7) CNT.However, the adsorbed SO also enhances the entropic effect for CO2 adsorbing in the (6, 6) CNT, further restricting the rotation freedom of CO2 molecules, but this entropic effect exerts insignificant effec on the rotation of N2 molecules.Although the adsorption of CO2 is energetically favorable in the (6,6) CNT in the presence of SO2, the strengthened entropic effect has completely dominated over the energetic effect, thereby leading to the dramatically reduced CO2 ad sorption.The adsorption reduction arising from the dominant entropic effect is more sig nificant for N2 due to its unfavorable energetic field exerted by SO2.Therefore, the CO2/N selectivity is reduced in the presence of SO2 in the (6, 6) CNT. Figure 4c indicates that, at the rather low pressure <0.1 bar (water vapor is at its sat uration pressure, under a mole fraction of ~35.64%), noticeable adsorption of water vapor is found in the (6, 6) CNT, where considerable adsorption space is occupied.As depicted in Figure 6, the adsorption of water vapor decreases rapidly as a consequence of the com petitive adsorption of CO2 and N2, where the corresponding partial pressures are enhanced at higher pressures.The inset of Figure 6 depicts the molecular configuration of water adsorbed in the (6, 6) CNT.As reported in the previous study, negligible adsorption of water was observed in the CNTs until the partial pressure of water vapor reached a critical pressure, where water molecules filled the CNT immediately and completely once the partial pressure was above the critical pressure [12,44].It is shown that the critica pressure for the (6,6) CNT is around the saturation pressure of water at 300 K, which is increased to 1.75 times of the saturation pressure in the (7, 7) CNT.Based on this reason negligible adsorption of water is observed in the (7, 7) CNT within the pressure range investigated, while the effect of water vapor is only significant at rather low pressure in the (6, 6) CNT. Figure 3e-f depicts the adsorption isotherms for CO2 and CO2/N2 selectivity in the presence of O2 in the (6, 6) and (7, 7) CNTs, where both the adsorbed amounts and the CO2/N2 selectivity are hardly affected.This result can be explained by the analysis of the Figure 4e,f depicts the adsorption isotherms for CO 2 and CO 2 /N 2 selectivity in the presence of O 2 in the (6, 6) and (7, 7) CNTs, where both the adsorbed amounts and the CO 2 /N 2 selectivity are hardly affected.This result can be explained by the analysis of the interaction energy between guest molecules and CNTs.As given in Figure 5c, the interactions of O 2 -CNT are much stronger than the counterparts of N 2 -CNT, so the competitive adsorption occurs between O 2 and N 2 , leading to an enhanced CO 2 /N 2 selectivity.However, the concentration of O 2 in the gas phase is only 4%, far below the mole concentration of N 2 , 84% of N 2 .Therefore, no significant decreases in adsorption of N 2 occurred, which is also applicable to the result for CO 2 .A similar result is found in ZIF-68: the presence of O 2 has a negligible effect on CO 2 adsorption [12].
Apparently, the presence of impurity gas generally imposes a negative effect on the adsorption of CO 2 , particularly in the rather small CNTs.However, the CO 2 /N 2 selectivity demonstrates a complex dependency on the impure gases, which can be enhanced, reduced, or nearly unaffected.Meanwhile, both the adsorption of CO 2 and the CO 2 /N 2 selectivity remain almost unaffected in the larger (10, 10) and (12,12) CNTs, making it difficult to predict the optimal CNT with the highest separation performance.Therefore, it is necessary to introduce the performance coefficient, λ e , which comprehensively evaluates the effect of the CO 2 adsorption and the CO 2 /N 2 selectivity on the separation performance, by following where M t and S t denote the adsorption of CO 2 and the CO 2 /N 2 selectivity for the CNT of interest at the target pressure, respectively, while M p and S p represent the adsorption of CO 2 and the CO 2 /N 2 selectivity for the standard case, respectively, which are chosen as the adsorption of CO 2 and the CO 2 /N 2 selectivity of the (7, 7) CNT at 300 K and 1.0 bar.α 1 and α 2 are the weight factor s, which are set as 1.0 in this work.Figure 7 illustrates the variation of the performance coefficient versus pressure in the (6, 6) CNT and (7, 7) CNT.As suggested, the performance coefficient is slightly increased in the (7, 7) CNT, while it becomes significantly decreased in the (6, 6) CNT.It is seen that SO 2 exhibits the most influential impact on the adsorption of CO 2 among the three impure gases considered.More specifically, the presence of SO 2 dramatically reduces the performance coefficient in the (6, 6) CNT, which is 180% lower than the results for CO 2 /N 2 mixture.This is caused by the strong competitive adsorption between SO 2 and CO 2 .For the impurities of H 2 O and O 2 , the changes in performance coefficient are generally negligible, except for the results of CO 2 /N 2 /H 2 O mixture at 1 bar.Based on the above results, it is readily derived that the influence of impurities on the CO 2 adsorption in CNTs followed the pattern: SO 2 > H 2 O > O 2 .Figure 7 indicates that, in the presence of impurities, the (6, 6) CNT still provides better performances for CO 2 capture than other CNTs when the pressures are below 0.5 bar, while the (7, 7) CNT exhibits the superior performance at higher pressures.
Additionally, we explored the adsorptive separation performance of CNTs for capturing SO 2 from the CO 2 /N 2 /SO 2 mixture by measuring the isotherm curve of SO 2 and the SO 2 /N 2 selectivity, which are depicted in Figure 8.It should be pointed out that the (6, 6) CNT with a diameter of 0.81 nm exhibits outstanding performance for separation of SO 2 /N 2 , in which the maximum adsorbed amounts of SO 2 and the highest selectivity are achieved among the CNTs considered.More specifically, the SO 2 /N 2 selectivities are unprecedentedly high, reaching 16,796, 13,965 and 7892 at the pressures of 0.1, 1.0 and 12.5 bar at 300 K, in the (6, 6) CNT.
except for the results of CO2/N2/H2O mixture at 1 bar.Based on the above results, it is readily derived that the influence of impurities on the CO2 adsorption in CNTs followed the pattern: SO2 > H2O > O2. Figure 7 indicates that, in the presence of impurities, the (6,6) CNT still provides better performances for CO2 capture than other CNTs when the pressures are below 0.5 bar, while the (7, 7) CNT exhibits the superior performance at higher pressures.Additionally, we explored the adsorptive separation performance of CNTs for capturing SO2 from the CO2/N2/SO2 mixture by measuring the isotherm curve of SO2 and the SO2/N2 selectivity, which are depicted in Figure 8.It should be pointed out that the (6,6) CNT with a diameter of 0.81 nm exhibits outstanding performance for separation of SO2/N2, in which the maximum adsorbed amounts of SO2 and the highest selectivity are achieved among the CNTs considered.More specifically, the SO2/N2 selectivities are unprecedentedly high, reaching 16,796, 13,965 and 7892 at the pressures of 0.1, 1.0 and 12.5 bar at 300 K, in the (6, 6) CNT.

Impacts of Impurities on CO2 Capture in Functionalized CNT Arrays
From the previous simulation results, it is evident that SO2, as a polar molecule, yielded the strongest interaction with CNT, exerting the greatest impact on CO2/N2 adsorption and separation.As there are more complex interactions between impurities, it is

Impacts of Impurities on CO 2 Capture in Functionalized CNT Arrays
From the previous simulation results, it is evident that SO 2 , as a polar molecule, yielded the strongest interaction with CNT, exerting the greatest impact on CO 2 /N 2 adsorption and separation.As there are more complex interactions between impurities, it is interesting to explore the cooperative impact on the adsorption of CO 2 in this part.Due to the hydrophobicity of carbon nanotubes, the adsorption of water molecules is weak, and a small amount of H 2 O barely affects the adsorption and separation of CO 2 /N 2 .In order to further explore the effect of H 2 O on CO 2 /N 2 adsorption, the hydrophilic carboxyl modified CNT is studied.In order to keep the same number of carboxyl groups distributed on the unit cell of CNT with different diameters, the mass fraction of carboxyl group doping is about 5.01-9.64%.After structure optimization by DFT, a 2 × 2 carbon nanotube array is constructed.When the tube spacing is set at 0.6 nm, GCMC is used to simulate the gas adsorption in carbon nanotube arrays with different diameters, using a fixed temperature and gas composition.After simulation, the adsorption configurations inside and outside the carbon nanotubes are calculated, respectively.
Figure 9 depicts the adsorption curves of CO 2 and N 2 and CO 2 /N 2 selectivity mixed with impurity gases in four kinds of carbon nanotube arrays with tube spacing of 0.6 nm and temperature of 300 K.For CO 2 /N 2 mixture, the optimal diameter of CNT bundle for adsorption separation of CO 2 is found in the (6, 6) CNT, which is different from the result based on single CNT.This is because (6,6) CNT not only has the strongest adsorbate CNT interaction, but also can provide additional adsorption space between tubes, so the adsorption capacity becomes enhanced.Under the combined effect of the two factors, (6,6) CNT array has the best adsorption capacity and CO 2 /N 2 selectivity under 10 bar.At higher pressure, due to the limited adsorption space, the adsorption capacity becomes lower than that for the (7, 7) CNT array.Compared with the binary mixture, the adsorption capacity of CO 2 and N 2 in quinary mixture is severely inhibited, especially in the small diameter (6,6) CNT array, but the adsorption capacity of CO 2 and N 2 in the (7, 7) CNT array is the highest below 1 bar.In the (10,10) and (12,12) CNT arrays with large diameters, the adsorption capacity of CO 2 increases almost linearly with the pressure, which becomes dominant when the pressure is greater than 1 bar.In addition, the CO 2 /N 2 selectivity of the quinary mixture is increased.In particular, for (7, 7) CNT arrays, the adsorption capacity of CO 2 and N 2 decreased by 2.28 times and 4.45 times at 1 bar, respectively, but the selectivity increased by 1.95 times.This is because the inhibition effect is stronger for N 2 (nonpolar molecule), in comparison with CO 2 .In addition, the selectivity of CO 2 /N 2 in the quinary mixture is increased.By calculating the performance coefficient, as shown in Figure 10, it is found that (7, 7) CNT array always maintains the best adsorption separation performance, except some results at a very low pressure of 0.1 bar.
In order to explore the inhibition mechanism in the CNT array with a small diameter, the adsorption ratio inside and outside the CNT (amount adsorbed inside the CNT/adsorption amount outside the CNT) is calculated.According to Figure 11 plotted the ratio of internal and external adsorption capacity for binary and quinary mixtures.As suggested, in the binary mixture, CO 2 and N 2 tend to be trapped by the outside of the tube in the small diameter, except some measurements at the pressure below 1 bar.This is due to the strong interaction between adsorbate and CNT in the small diameter below 1 bar.With increase in sorbate loading, the adsorption space in the tube is limited, so a large amount of adsorbate is captured by the outside of the tube.However, the interaction between adsorbate and CNT is weak in CNT with large diameter, so CO 2 molecules tend to be adsorbed outside the tube.In the quinary mixture, the adsorption distribution of CO 2 molecules is more complex.In the (12,12) CNT array, CO 2 molecules begin to be adsorbed mainly in the tube, which is distributed uniformly outside the tube with pressure.With the increase in the pressure, the pressure in the tube becomes dominant.
of CO2 and N2 decreased by 2.28 times and 4.45 times at 1 bar, respectively, but the selectivity increased by 1.95 times.This is because the inhibition effect is stronger for N2 (nonpolar molecule), in comparison with CO2.In addition, the selectivity of CO2/N2 in the quinary mixture is increased.By calculating the performance coefficient, as shown in Figure 10, it is found that (7, 7) CNT array always maintains the best adsorption separation performance, except some results at a very low pressure of 0.1 bar.In order to explore the inhibition mechanism in the CNT array with a small diameter, the adsorption ratio inside and outside the CNT (amount adsorbed inside the CNT/adsorption amount outside the CNT) is calculated.According to Figure 11 plotted the ratio of internal and external adsorption capacity for binary and quinary mixtures.As suggested, in the binary mixture, CO2 and N2 tend to be trapped by the outside of the tube in the small diameter, except some measurements at the pressure below 1 bar.This is due to the strong interaction between adsorbate and CNT in the small diameter below 1 bar.With increase in sorbate loading, the adsorption space in the tube is limited, so a large amount of adsorbate is captured by the outside of the tube.However, the interaction between adsorbate and CNT is weak in CNT with large diameter, so CO2 molecules tend to be adsorbed outside the tube.In the quinary mixture, the adsorption distribution of CO2 molecules is more complex.In the (12,12) CNT array, CO2 molecules begin to be adsorbed    The isothermal curves of water molecules and SO2 in the modified CNTs are plotted in Figure 12, where the adsorption capacity of water molecules after carboxyl modification is greatly improved.The adsorption is mainly distributed between tubes, while the adsorption capacity inside tubes is almost zero.According to the molecular snapshot of water molecules adsorbed in (7, 7) CNT array in Figure 13, a large number of water molecules are adsorbed and aggregated between tubes to form chain structures, but the adsorption of water molecules in tubes is hardly observed.At the same time, the adsorption capacity of water molecules decreases with the increase in tube diameter.By calculating the mass fraction of doping carboxyl, it is found that the carboxyl content is an important factor to affect the adsorption capacity of water molecules.As the diameter of the tube increased, the mass fraction of carboxyl group decreases, leading to the decrease in the adsorption capacity of water molecules.The presence of water molecules promotes the adsorption of SO2 in the small-diameter nanotube arrays.In Figure 14, the results for interaction energy of H2O-SO2 indicate in the small-diameter (6,6) and (7, 7) CNTs, SO2 is subject to stronger H2O-SO2 interaction than CO2-H2O, thereby enhancing the adsorption of SO2.The isothermal curves of water molecules and SO 2 in the modified CNTs are plotted in Figure 12, where the adsorption capacity of water molecules after carboxyl modification is greatly improved.The adsorption is mainly distributed between tubes, while the adsorption capacity inside tubes is almost zero.According to the molecular snapshot of water molecules adsorbed in (7, 7) CNT array in Figure 13, a large number of water molecules are adsorbed and aggregated between tubes to form chain structures, but the adsorption of water molecules in tubes is hardly observed.At the same time, the adsorption capacity of water molecules decreases with the increase in tube diameter.By calculating the mass fraction of doping carboxyl, it is found that the carboxyl content is an important factor to affect the adsorption capacity of water molecules.As the diameter of the tube increased, the mass fraction of carboxyl group decreases, leading to the decrease in the adsorption capacity of water molecules.The presence of water molecules promotes the adsorption of SO 2 in the small-diameter nanotube arrays.In Figure 14, the results for interaction energy of H 2 O-SO 2 indicate in the small-diameter (6,6)         In the modified CNTs, carboxyl group has little effect on the adsorption of adsorbate molecules.By simulating the adsorption of quinary mixture in a single carboxyl modified CNT, the results show that the adsorption capacity of various adsorbents is reduced, in comparison with the simulation results for unmodified CNTs.This is due to the introduction of defect groups (or the lack of carbon atoms) which weaken the interaction between the adsorbate molecules and the wall of small-diameter CNTs, so the adsorption capacity is reduced.The introduction of carboxyl group barely promotes the adsorption and separation coefficient of adsorbate molecules in the carbon tubes, suggesting that H 2 O plays an important role in the adsorption capacity and distribution of CO 2 .In the modified CNTs, carboxyl group has little effect on the adsorption of adsorbate molecules.By simulating the adsorption of quinary mixture in a single carboxyl modified CNT, the results show that the adsorption capacity of various adsorbents is reduced, in comparison with the simulation results for unmodified CNTs.This is due to the introduction of defect groups (or the lack of carbon atoms) which weaken the interaction between the adsorbate molecules and the wall of small-diameter CNTs, so the adsorption capacity is reduced.The introduction of carboxyl group barely promotes the adsorption and separation coefficient of adsorbate molecules in the carbon tubes, suggesting that H2O plays an important role in the adsorption capacity and distribution of CO2.
The adsorption of CO2 and N2 in the quinary mixture outside the tube is seriously inhibited, but the inhibition or promotion for adsorption inside the tube varies with nanotubes with different diameters.As the carboxyl functional group hardly exerts a positive effect on the adsorption of CO2 molecules in the tube, the adsorption of CO2 molecules in the tube is mainly affected by the interaction with other adsorbate molecules.Due to the large amount of adsorbed water molecules between the small nanotubes, the adsorption of CO2 molecules mainly occurs in the tube.However, at low pressures, the adsorption of SO2 in the tube is enhanced due to the presence of H2O.Meanwhile, the adsorption of CO2 in the tube is strongly inhibited by the intensive competitive adsorption, so CO2 adsorption mainly occurs outside the tube at low pressures.According to the previous simulation results of CO2/N2/SO2 mixture in a single CNT, SO2 has little effect on the adsorption of CO2 in a large diameter tube, so CO2 is mainly adsorbed in the tube at low pressure.With the increase in pressure, the adsorption amount of H2O outside the tube decreases, where the inhibition effect weakens, so CO2 molecules begin to adsorb outside the tube, and are finally evenly distributed inside and outside the tube.In addition, the adsorption enthalpy of CO2 is increased by the attraction of H2O-CO2 in the tube, where the adsorption space is abundant in the large diameter tube, so the adsorption of CO2 increases.
As derived from the previous analysis, SO2 can enhance the selectivity of CO2/N2 in the small diameter.In addition, CO2 is subject to stronger interaction from H2O than N2, The adsorption of CO 2 and N 2 in the quinary mixture outside the tube is seriously inhibited, but the inhibition or promotion for adsorption inside the tube varies with nanotubes with different diameters.As the carboxyl functional group hardly exerts a positive effect on the adsorption of CO 2 molecules in the tube, the adsorption of CO 2 molecules in the tube is mainly affected by the interaction with other adsorbate molecules.Due to the large amount of adsorbed water molecules between the small nanotubes, the adsorption of CO 2 molecules mainly occurs in the tube.However, at low pressures, the adsorption of SO 2 in the tube is enhanced due to the presence of H 2 O.Meanwhile, the adsorption of CO 2 in the tube is strongly inhibited by the intensive competitive adsorption, so CO 2 adsorption mainly occurs outside the tube at low pressures.According to the previous simulation results of CO 2 /N 2 /SO 2 mixture in a single CNT, SO 2 has little effect on the adsorption of CO 2 in a large diameter tube, so CO 2 is mainly adsorbed in the tube at low pressure.With the increase in pressure, the adsorption amount of H 2 O outside the tube decreases, where the inhibition effect weakens, so CO 2 molecules begin to adsorb outside the tube, and are finally evenly distributed inside and outside the tube.In addition, the adsorption enthalpy of CO 2 is increased by the attraction of H 2 O-CO 2 in the tube, where the adsorption space is abundant in the large diameter tube, so the adsorption of CO 2 increases.
As derived from the previous analysis, SO 2 can enhance the selectivity of CO 2 /N 2 in the small diameter.In addition, CO 2 is subject to stronger interaction from H 2 O than N 2 , so the presence of water can also promote the CO 2 /N 2 selectivity.The selectivity of CO 2 /N 2 in the small diameter is increased by the combination of the two impure gases.In particular, at 1 bar, the CO 2 /N 2 selectivity of (6, 6) CNT array increases from 30.4 to 53.8, while an increase from 30.7 to 59.9 are found for (7, 7) CNT array.The growth ratio corresponds to 1.77 and 1.95 times, respectively.As the adsorption space in (6, 6) CNT array is very small, the derived adsorption capacity of CO 2 is also very limited due to the competitive adsorption of H 2 O and SO 2 .For (7, 7) CNT array, the adsorption space is promoted, so the adsorption capacity of CO 2 in (7, 7) CNT array becomes higher than that in (6,6) CNTs.As the inhibition of CO 2 in (7, 7) CNTs is weaker than that in (6,6) CNT array, the selectivity of CO 2 /N 2 is higher.To sum up, the adsorption of H 2 O molecules mainly occurs between tubes, thereby inhibiting the adsorption of CO 2 between tubes, while SO 2 molecules compete with CO 2 molecules in tubes to induce the inhibition effect.The competition between the two effects determines the adsorption distribution of CO 2 inside and outside the tube.In addition, the interaction of H 2 O and SO 2 improves the selectivity of CO 2 /N 2 , and the (7, 7) CNT array maintains the best CO 2 /N 2 adsorption and separation performance except the results at low pressure of 0.1 bar.

Conclusions
In this work, a grand canonical Monte Carlo simulation is used to investigate the influence of impurity gases, including water, SO 2 , and O 2 , on the adsorption of CO 2 in singe CNTs and functionalized CNT bundles.Initially, the effect of pore size of CNT on the adsorption of CO 2 /N 2 mixture is examined, and it is revealed that the adsorption capacity had a strong dependence on the CNT diameter.Further, the influence of single impure gas on the adsorption of CO 2 in CNTs is explored.By calculating inhibition coefficient to evaluate the influence on the adsorption of CO 2 , results indicate that SO 2 is the most influential impure to affect the adsorption of CO 2 /N 2 .By introducing SO 2 , the interaction of CO 2 -CNT became weaker.Meanwhile, SO 2 could compete with CO 2 for the adsorption site, which exerts a negative effect on the adsorption of CO 2 , so the adsorption amount of CO 2 has a significant decrease.Furthermore, the (6, 6) CNT exhibits superior performance for adsorption separation of SO 2 /N 2 .As for H 2 O, due to the partial pressure decreases sharply with pressure, decrease on the adsorption of CO 2 only occurs noticeably bellow 0.1 bar.The existence of O 2 hardly changes the adsorption amounts andthe CO 2 /N 2 selectivity.Moreover, the performance coefficient is calculated to evaluate the adsorptive separation of CO 2 comprehensively.It is shown that SO 2 was the most influential impure gas to affect the adsorptive separation of CO 2 from flue mixture.Eventually, the coexisting influence of three impure gases is also investigated.The performance coefficient is also calculated for the complex correlation with the diameter; however, it is hardly affected by the complex interaction among adsorbates.Among our simulations, the (7, 7) CNT yields the superior performance for CO 2 adsorption and separation, where both the maximum uptakes and the highest selectivity occurs to the ambient temperature and pressure.

Supplementary Materials:
The following supporting information can be downloaded online.Institutional Review Board Statement: Not applicable.

Figure 1 .
Figure 1.Snapshots of the adsorption of CO2/N2 mixture in four CNTs in the presence of impurities, at 1.0 bar and 300 K, where the blue and cyan spheres used for N2 molecules, while the red and cyan spheres were for CO2 molecules, and O2 molecules were marked as the red and yellow spheres (e.g., Red = oxygen, yellow = sulfur, cyan = carbon, blue = nitrogen) (a).The optimized structure of CNT unit cell with defects, and the constructed 2 × 2 CNT array (b).

Figure 1 .
Figure 1.Snapshots of the adsorption of CO 2 /N 2 mixture in four CNTs in the presence of impurities, at 1.0 bar and 300 K, where the blue and cyan spheres used for N 2 molecules, while the red and cyan spheres were for CO 2 molecules, and O 2 molecules were marked as the red and yellow spheres (e.g., Red = oxygen, yellow = sulfur, cyan = carbon, blue = nitrogen) (a).The optimized structure of CNT unit cell with defects, and the constructed 2 × 2 CNT array (b).

Figure 2 .
Figure 2. Adsorption isotherms of (a) CO2 and (b) N2, and (c) the variation of the corresponding CO2/N2 selectivity with pressure in different CNTs, at 300 K.

2 Figure 2 .
Figure 2. Adsorption isotherms of (a) CO 2 and (b) N 2 , and (c) the variation of the corresponding CO 2 /N 2 selectivity with pressure in different CNTs, at 300 K.

Figure 3 .
Figure 3. Variation of the interaction energies of (a) CO2-CNT and (b) N2-CNT with pressure, a K.

Figure 3 .
Figure 3. Variation of the interaction energies of (a) CO 2 -CNT and (b) N 2 -CNT with pressure, at 300 K.

Figure 6 .
Figure 6.Variation of the H2O mole ratio with total pressure of CO2/N2/H2O mixture, with the partia pressure of H2O fixed at the saturation vapor pressure.The inset depicted a snapshot of the distri bution of water in(6,6) CNT at 0.1 bar and 300 K, in which a one-dimensional chain was evidently obtained.

Figure 6 .
Figure 6.Variation of the H 2 O mole ratio with total pressure of CO 2 /N 2 /H 2 O mixture, with the partial pressure of H 2 O fixed at the saturation vapor pressure.The inset depicted a snapshot of the distribution of water in (6, 6) CNT at 0.1 bar and 300 K, in which a one-dimensional chain was evidently obtained.

Figure 7 .
Figure 7. Variation of the performance coefficients of different CNTs in the presence of SO 2 (a), H 2 O (b), and O 2 (c), relative to the adsorption of binary CO 2 /N 2 mixture (CO 2 /N 2 is 16/84) in the (7, 7) CNT at 1.0 bar and 300 K.

Figure 8 .
Figure 8. Adsorption of (a) SO 2 and (b) SO 2 /N 2 selectivity for the CO 2 /N 2 /SO 2 in CNTs with diameter varied from 0.807 to 1.626 nm at 300 K.

Figure 10 .
Figure 10.Performance coefficients of CO2/N2 adsorption and separation of quinary mixtures in modified CNTs with different diameters.

Figure 10 .
Figure 10.Performance coefficients of CO 2 /N 2 adsorption and separation of quinary mixtures in modified CNTs with different diameters.

Figure 11 .
Figure 11.The ratio of adsorption capacity of (a,b) CO2 and (c,d) N2 in binary and quinary mixtures inside and outside the CNT arrays, with four different diameters.

Figure 11 .
Figure 11.The ratio of adsorption capacity of (a,b) CO 2 and (c,d) N 2 in binary and quinary mixtures inside and outside the CNT arrays, with four different diameters.

Figure 12 .
Figure 12.Isothermal adsorption curves of water molecules (a) and SO2 (b) inside and outside the tube in unmodified and modified CNT array.

Figure 12 .
Figure 12.Isothermal adsorption curves of water molecules (a) and SO 2 (b) inside and outside the tube in unmodified and modified CNT array.

Figure 12 .
Figure 12.Isothermal adsorption curves of water molecules (a) and SO2 (b) inside and outside the tube in unmodified and modified CNT array.
CNT can be approximately measured as deff = dCNT-σO-C = 0.49 where 0.32 ) of the CO2 molecule.A molecule size of CO2 molecule (0.5331 nm) in the axial direction is larger and that fo molecule (0.441 nm), CO2 molecules in our simulations are found to distribute almo parallel to the axis of the (6, 6) CNT, showing strong rotational restrictions.However rotational freedom of N2 is negligibly affected.In addition, random distributions of OC − = nm is determined according to (σo + σC)/2, using the LJ size param of carbon atoms ( C  ) of the CNT and oxygen atom ( O  molecules are observed in the (7, 7) CNT with a diameter of 0.95 nm, suggesting tha dramatically enhanced entropic effect is responsible for the reduced CO2/N2 selectivi the (6, 6) CNT, compared to the (7, 7) CNT.
and (7, 7) CNTs, SO 2 is subject to stronger H 2 O-SO 2 interaction than CO 2 -H 2 O, thereby enhancing the adsorption of SO 2 .