■ INTRODUCTION

The reduction of carbon dioxide (CO 2 ) emissions is one of the grand challenges of the 21st century because the fast-increasing concentration of CO 2 (one of the main greenhouse gases) in the atmosphere has led to several significant environmental issues, such as the melting of the polar ice caps, rising sea levels, and climate change. Recently, the 13th World Meteorological Organization (WMO) Global Atmosphere Watch (GAW) annual Greenhouse Gas (GHG) bulletin reported that the CO 2 concentration reached new highs in 2016 (403.3 ± 0.1 ppm), and the record increase was larger than the average growth rate over the past decade. 1 Although several technologies and processes for CO 2 capture, storage, and utilization have been developed, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] more efforts are still needed to halt the growing CO 2 concentration in the atmosphere.

The fast increase in CO 2 concentration is primarily due to the enormous consumption of fossil fuels, e.g., coal, oil, and natural gas. Therefore, one of the possible solutions is to use renewable H 2 as an alternative energy source. However, to date, more than 95% of H 2 used in industry is produced through steam-methane reformation and a subsequent water-gas shift reaction. The effluent gas typically consists of 71-75% H 2 , 15-20% CO 2 , 4-7% CH 4 , 1-4% CO, and other gases such as H 2 O. 21 Thus, CO 2 capture and separation from the mixed CO 2 and H 2 gases is required at the least to prevent the release of the CO 2 produced from steam-methane reformation into the atmosphere.

Recently, porous material membranes such as metal-organic frameworks (MOFs) and covalent-organic frameworks (COFs) have demonstrated effective gas-separation capabilities and thus have been recognized as promising media for practical gas adsorption and separation, particularly for CO 2 capture. [22][23][24][25] Also, carbon nanomaterials, such as porous graphene and carbon nanotubes (CNTs), have been proposed as promising candidates for gas separation, particularly for H 2 purification. [26][27][28][29][30][31][32][33] However, membrane-based gas separation has to compromise between high permeability and high selectivity.

Hydrate-based technology has been considered to be another promising technology for gas capture and separation besides the conventional technologies (e.g., absorption, adsorption, and membranes) because of its relatively low cost and simple operation. 34 Clathrate hydrates are well-known crystalline inclusion compounds formed by the enclathration of guest species into cages of host-ice frameworks under certain temperature and pressure conditions. 35 The selective capture of guest molecules in the clathrate hydrates offers the possibility of effective gas separation because the conditions for the formation of the clathrate hydrates are strongly affected by the guest species to be encaged. 34,[36][37][38][39][40][41][42][43][44] However, the development of hydrate-based CO 2 separation technology is still hampered by the slow growth rate and low selectivity during the hydrate formation process. Numerous investigations suggest that the use of additives can enhance the hydrate formation kinetics and selectivity. [45][46][47][48][49][50][51] Gas hydrate formations in porous media are widespread phenomena in nature. Previous investigations showed that microscale confinement and surface features have both promotion and inhibition effects on the gas hydrate nucleation and growth. [52][53][54][55][56][57][58][59][60][61] For example, microscale confinement and the hydrophilic surface of graphene oxide inhibit the hydrate phase, 58 while Casco et al. found that the confinement and hydrophobic surface of carbon cavities can increase the methane hydrate formation rate and lower the hydrate nucleation pressures (below 4 MPa). 59 When the pore size is reduced to subnanometer levels, the hydrogen-bonding network in water is disrupted by the highly confined environment, thereby affecting the kinetics of crystallization. [62][63][64][65][66][67][68][69][70] Our previous studies showed that thousands of atmospheric pressures are needed to form monolayer or bilayer gas clathrates within 2D nanoslits, [68][69][70][71] whereas quasi-one-dimensional (Q1D) core-sheath polygonal hydrogen and CO hydrates can be formed spontaneously within single-walled carbon nanotubes (SW-CNTs) under ambient pressure. 72,73 More interestingly, the highly preferential adsorption of CO over H 2 is observed in Q1D hydrates within SW-CNTs. 73 Can the Q1D CO 2 hydrates be formed spontaneously in SW-CNTs under ambient pressure, and can the selective adsorption of CO 2 over H 2 (for the mixture dissolved in water) occur within the Q1D hydrates? In this work, we have performed systematic studies to address both questions. The studies can also improve our understanding of different gas clathrates inside a nanoconfined space. By means of molecular dynamics (MD) simulations, we find that the Q1D heptagonal, octagonal, and nonagonal CO 2 hydrates can be formed spontaneously within SW-CNTs under ambient pressure. More interestingly, highly preferential adsorption of CO 2 over H 2 is also observed within the polygonal hydrates near ambient conditions.

■ MODEL AND COMPUTATIONAL METHODS

The classical MD simulations are carried out by using the Gromacs 4.5 software 74 package to study the formation of Q1D clathrate hydrates within SW-CNTs, where the SW-CNTs with two open ends are immersed in the dilute CO 2 (or CO 2 /H 2 ) aqueous solution. Three zigzag SW-CNTs with indexes (17, 0), (18, 0), and (19, 0) (whose diameters are 1.33, 1.41, and 1.49 nm, respectively) are considered as our previous studies showed that under ambient pressure the guest-free clathrates can be formed in SW-CNTs with smaller diameters (only a few gas molecules occupy the nanochannels of ice nanotubes), while no clathrates were observed in SW-CNTs with larger diameters. 73 Also, the (10, 10) and (12, 9) SW-CNTs with diameters of 1.356 and 1.429 nm are considered to study the effect of chirality on SW-CNTs. The parameters of SW-CNTs, H 2 O, and H 2 molecules are also similar to those used in our previous study, 73 while the CO 2 molecule is treated using the EPM2 model. 75 All MD simulations are carried out with the NPT ensemble for 10-500 ns, depending on temperature T and the hydrate formation process. (A detailed simulation description is given in the Supporting Information).

■ RESULTS AND DISCUSSION First, the system with the SW-CNTs immersed in a dilute aqueous CO 2 solution is initially equilibrated at 300 K and 1 bar, followed by stepwise cooling in temperature steps of 10 K at ambient pressure. We observed the spontaneous formation of Q1D heptagonal and octagonal CO 2 hydrates in (17, 0) and (18, 0) SW-CNTs, respectively, at 260 K and the formation of a nonagonal CO 2 hydrate in (19, 0) SW-CNT at 240 K. As shown in Figure 1A-C, CO 2 molecules are entrapped within the interior space of the polygonal ice nanotubes and form a single-file wire, akin to the formation of polygonal CO hydrates in the same SW-CNTs. 73 Importantly, as shown in Figure 1D, a heptagonal ice nanotube allows, on average, ∼6.8 CO 2 molecules per supercell to form the heptagonal CO 2 hydrate in (17, 0) SW-CNT. Hence, many more CO 2 molecules are trapped in the heptagonal nanochannel of the ice nanotube than CO (∼1.8) or H 2 (∼3.0) molecules. 73 There are ∼7.1 CO 2 , ∼7.8 CO, or ∼7.6 H 2 molecules 73 trapped in the filled octagonal CO 2 , CO, or H 2 hydrate within (18, 0) SW-CNT, respectively, and there are ∼10.5 CO 2 , ∼9.08 CO, or ∼10.2 H 2 molecules, 73 respectively, contained in the filled nonagonal CO 2 , CO, or H 2 hydrates in (19, 0) SW-CNT. In other words, equal numbers of CO 2 , CO, or H 2 molecules can be enclosed within the octagonal (and nonagonal) hydrates. The calculated CO 2 weight storage efficiencies for heptagonal, octagonal, and nonagonal hydrates within (17, 0), (18, 0), and (19, 0) SW-CNTs are about 2.43, 2.36, and 3.23%, respectively.

To understand the capturing capability of Q1D polygonal hydrates in SW-CNTs, we first examined the trajectory of CO 2 molecules in hydrates (Figures 2 andS1). Figures 2 andS1 show the motions z(t) of all of the individual CO 2 molecules along the nanotube axis. All of the CO 2 molecules in the Q1D hydrate formed a single-file chain so that they moved coherently. Most CO 2 molecules oscillate near their equilibrium positions along the z axis. Also, the denser curves indicate more of the CO 2 molecules in the hydrate. Thus, the axial CO 2 density increases with increasing nanotube diameter. Also, we noted that the highest and lowest curves (i.e., at the ends of the CNT) are discontinuous. The discontinuity of the curves indicates that CO 2 molecules exit or enter the hydrate in SW-CNTs. Hence, the CO 2 exchange at the open ends of nanotubes can be observed.

To gain more insight into the polygonal hydrates, we computed the CO 2 molecular orientation and axial density profiles within the hydrates (Figure 3A,B). Here, we define θ as the angle between the CO 2 molecular axis and the positive direction of the z axis (tube axis). As shown in Figure 3A, this orientation is mainly located at 9°, indicating that the CO 2 molecules in a heptagonal hydrate are likely to stay along the hydrate axis, consistent with the single-file structure of CO 2 molecules within the heptagonal hydrate. With the increase in the nanotube diameter (i.e., Q1D hydrate channel diameter), the CO 2 molecular axis deviates from the z axis (Q1D hydrate axis). The deviation can also be observed from the site-site axial distribution functions (ADF) of the CO 2 molecules (Figure 3B). In the heptagonal hydrate (Figure 3B), the first peak of the carbon (C)-carbon (C) ADF (the center atom of CO 2 molecules) is located at ∼0.55 nm, indicating a CO 2 molecule every 0.55 nm length along the z axis. The first and second peaks of the carbon (C)-oxygen (O) ADF are located at ∼0.44 and ∼0.67 nm, suggesting that the CO 2 molecule stays along the tube axis due to the nearly equal distance of the CO 2 oxygen atoms along the z axis in the hydrate (∼0.23 nm) and the length of a free CO 2 (about 0.23 nm). Note that the second peak of C-C ADF is located at ∼0.84 nm, and this peak value is much lower than those of the first and third peaks. This is not an indication of the next-nearest neighbor but of the nearest neighbor with a large distance (i.e., vacancy). The results are consistent with the snapshot of the heptagonal hydrate (Figure 1A). With increasing nanotube diameter (i.e., Q1D hydrate channel diameter), the distance of the nearest neighbor of the CO 2 molecule becomes smaller (about 0.52 nm for the octagonal hydrate and 0.40 nm for the nonagonal hydrate), suggesting that the axial CO 2 density increases. Also, rapidly decaying peaks and the shrinking distance of the first and

The Journal of Physical Chemistry C

Article second peaks of C-O ADFs for octagonal and nonagonal hydrates indicate that the CO 2 molecular axis deviates from the z axis, consistent with the snapshots of the hydrates (Figure 1B,C) and the CO 2 molecular orientation (Figure 3A).

Next, we studied the systems with the SW-CNTs immersed in a dilute CO 2 /H 2 aqueous solution at ambient pressure. Similar to the dilute CO 2 aqueous solution, Q1D heptagonal and octagonal hydrates are formed spontaneously in (17, 0) and (18, 0) SW-CNTs at 260 K, while the formation of the nonagonal hydrate is observed in a (19, 0) SW-CNT at 240 K. Note that many CO 2 molecules and few H 2 molecules are trapped in the Q1D polygonal hydrates (Movies S1 and S2 and Figure 4). Also, importantly, the heptagonal hydrate in (17,0) SW-CNT contains, on average, about 6.4 CO 2 and 1.1 H 2 molecules, respectively (Figure 5A). Thus, the ratio of CO 2 /H 2 trapped within the heptagonal hydrate is about 5.8. The number of CO 2 molecules in the hydrate fluctuates between 5 and 9 in the course of the MD simulation, while for most of the time, the number of H 2 molecules fluctuates between 0 and 2. It appears that the Q1D heptagonal hydrate can entail high efficiency to separate the CO 2 and H 2 molecules in dilute CO 2 / H 2 aqueous solution, contrary to the dilute CO/H 2 aqueous solution. 73 For the octagonal hydrate in (18, 0) SW-CNT, the average number of CO 2 molecules is about 7.7, while that of the H 2 molecules is only 0.7 (Figure 5B). As a result, the ratio of CO 2 /H 2 for the octagonal hydrate is about 11. Therefore, the Q1D octagonal hydrate can entail higher efficiency to separate the CO 2 and H 2 molecules in a dilute CO 2 /H 2 aqueous solution as well. In (19, 0) SW-CNT, the mean number of CO 2 molecules within the nonagonal nanochannel is about 12.3, whereas that of the H 2 molecules is only 0.8 (Figure 5C). The ratio of CO 2 /H 2 for the nonagonal hydrate is about 15. Hence, the nonagonal hydrate may entail much higher efficiency to separate the CO 2 and H 2 molecules in a dilute CO 2 /H 2 aqueous solution.

To understand the high selective adsorption of CO 2 over H 2 in Q1D hydrates, we computed the potential of mean force (PMF), that is, the free-energy profile, for a gas molecule moving from the bulk solution into the polygonal ice nanotube. (Detailed simulation description is given in the Supporting Information.) As shown in Figure 6, the PMF profiles for the heptagonal hydrate in the (17, 0) SW-CNT show that the energy barriers for CO 2 and H 2 molecules are about -13.9 and -4.5 kJ/mol, respectively. The PMF profiles for the octagonal hydrate in the (18, 0) SW-CNT show that the PMF difference for a CO 2 molecule is about -14.8 kJ/mol and that of a H 2 molecule is ∼-7.5 kJ/mol. For the nonagonal hydrate in the (19, 0) SW-CNT, the energy barrier for a CO 2 molecule is about -11.5 kJ/mol, and that of a H 2 molecule is ∼-5.2 kJ/ mol. The negative values of the PMF barriers for CO 2 and H 2 molecules indicate that both molecules would prefer to enter the nanochannels of the Q1D polygonal hydrates within SW-CNTs. More importantly, the much more negative value of the PMF difference for a CO 2 molecule indicates that a CO 2 molecule is more preferred over a H 2 molecule to be adsorbed in the hydrate.

To study the effect of the CNTs' chirality on hydrate formation and the high selectivity of CO 2 over H 2 , we carried out additional MD simulations with (10, 10) and (12, 9) SW-CNTs immersed in the dilute CO 2 (or CO 2 /H 2 ) aqueous solution. By decreasing the temperature, the helical and octagonal hydrates are formed spontaneously within (10, 10) and (12, 9) SW-CNTs, respectively. Also, importantly, the highly selective adsorption of CO 2 over H 2 in the hydrates was observed (Figure 7). The formation of 1D gas hydrates within CNTs and the high selectivity of CO 2 over H 2 are dependent on the SW-CNTs' diameter rather than their chirality, as in the case of the formation of the Q1D polygonal ice nanotube in SW-CNTs. 64 We also carried out additional MD simulations to demonstrate that the solubility of CNTs in water does not affect the formation of 1D gas hydrates within CNTs and the high selectivity of CO 2 over H 2 . Here, the SW-CNT membrane composed of (18, 0) SW-CNTs combined with two opposing graphene sheets is used to separate the gas aqueous solution. The spontaneous formation of the octagonal hydrate in the CNT membrane and the high selectivity of CO 2 over H 2 in the hydrate were observed as well (Figure 8 and Movie S4).

We performed the latest MD simulations to study the stability of the Q1D hydrates under a gas atmosphere. In the simulation system, many water molecules are removed, and a few of the water molecules are adsorbed near the ends of

■ CONCLUSIONS

We have presented simulation evidence of the spontaneous formation of Q1D polygonal (7-, 8-, and 9-gonal) CO 2 hydrates within SW-CNTs under ambient pressure for SW-CNTs immersed in a dilute CO 2 aqueous solution. The polygonal CO 2 hydrates are very similar to the polygonal H 2 and CO hydrates previously reported. 73 More interestingly, the highly selective adsorption of a CO 2 over a H 2 molecule is observed within the Q1D polygonal hydrates due to the much lower value of the PMF difference for a CO 2 molecule compared to that of a H 2 molecule to be trapped in the hydrates. Also, our results show that the formation of 1D gas hydrates within CNTs and the high selectivity of CO 2 over H 2 are dependent on the SW-CNTs' diameter rather than their chirality, as in the case of the formation of the Q1D polygonal ice nanotube in SW-CNTs. 64 Note that our previous study also showed the high preferential adsorption of a CO over a H 2 molecule in the Q1D polygonal hydrates. 73 Hence, the formation of Q1D hydrates may be a useful approach for the capture of CO 2 and for the removal of CO 2 and CO from H 2 , particularly for hydrogen purification from the syngas in fuel-cell devices.