3.1. Effect of Pore Size on the Adsorption of CO2/N2 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.
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,
, 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
deff = dCNT−
σO−C = 0.49 nm, where
nm is determined according to (
σo + σC)/2, using the LJ size parameters of carbon atoms (
) of the CNT and oxygen atom (
) 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.
3.2. Effect of Single Impurity on the Adsorption of CO2/N2 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
2O, 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 CO
2, an inhibition coefficient is defined as
where
and
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
2O 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
2O 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).
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.
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,
, which comprehensively evaluates the effect of the CO
2 adsorption and the CO
2/N
2 selectivity on the separation performance, by following
where
and
denote the adsorption of CO
2 and the CO
2/N
2 selectivity for the CNT of interest at the target pressure, respectively, while
and
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.
and
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
2O and O
2, the changes in performance coefficient are generally negligible, except for the results of CO
2/N
2/H
2O 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
2O > 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.
3.3. 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 interesting to explore the cooperative impact on the adsorption of CO2 in this part. Due to the hydrophobicity of carbon nanotubes, the adsorption of water molecules is weak, and a small amount of H2O barely affects the adsorption and separation of CO2/N2. In order to further explore the effect of H2O on CO2/N2 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.
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
2O–SO
2 indicate in the small-diameter (6, 6) and (7, 7) CNTs, SO
2 is subject to stronger H
2O–SO
2 interaction than CO
2–H
2O, thereby enhancing the adsorption of SO
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, so the presence of water can also promote the CO2/N2 selectivity. The selectivity of CO2/N2 in the small diameter is increased by the combination of the two impure gases. In particular, at 1 bar, the CO2/N2 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 CO2 is also very limited due to the competitive adsorption of H2O and SO2. For (7, 7) CNT array, the adsorption space is promoted, so the adsorption capacity of CO2 in (7, 7) CNT array becomes higher than that in (6, 6) CNTs. As the inhibition of CO2 in (7, 7) CNTs is weaker than that in (6, 6) CNT array, the selectivity of CO2/N2 is higher. To sum up, the adsorption of H2O molecules mainly occurs between tubes, thereby inhibiting the adsorption of CO2 between tubes, while SO2 molecules compete with CO2 molecules in tubes to induce the inhibition effect. The competition between the two effects determines the adsorption distribution of CO2 inside and outside the tube. In addition, the interaction of H2O and SO2 improves the selectivity of CO2/N2, and the (7, 7) CNT array maintains the best CO2/N2 adsorption and separation performance except the results at low pressure of 0.1 bar.