Selective Adsorption-Based Separation of Flue Gas and Natural Gas in Zirconium Metal-Organic Frameworks Nanocrystals

Carbon capture from flue gas and natural gas offers a green path to construct a net-zero emissions economic system. Selective adsorption-based gas separation by employing metal-organic frameworks (MOFs) is regarded as a promising technology due to the advantages of simple processing, easy regeneration and high efficiency. We synthesized two Zirconium MOFs (UiO-66 and UiO-66-NH2) nanocrystals for selective capture and further removal of CO2 from flue gas and natural gas. In particular, UiO-66-NH2 nanocrystals have a smaller grain size, a large amount of defects, and pending –NH2 groups inside their pores which display effective CO2 selective adsorption abilities over CH4 and N2 with the theoretical separation factors of 20 and 7. This breakthrough experiment further verified the selective adsorption-based separation process of natural gas and flue gas. In one further step, we used the Monte Carlo simulation to investigate the optimized adsorption sites and energy of CO2, N2 and CH4 molecules in the gas mixture. The significantly large adsorption energy of CO2 (0.32 eV) over N2 (0.19 eV) and N2 (0.2 eV) may help us to reveal the selective adsorption mechanism.


Introduction
Carbon dioxide (CO 2 ) is regarded as the primary anthropogenic culprit for global warming and climate change, which is produced by fossil fuel [1]. The atmospheric CO 2 concentration has increased approximately 300-400 ppm over the last 50 years (1960−2016) [2], and is speculated to reach more than 500 ppm by 2050 [3]. The main emission source of CO 2 is the combustion of fossil fuels such as coal, oil, and natural gas. Carbon capture is broadly identified as possessing the great potential to play a critical role in meeting climate change targets [4]. Effective carbon capture is regarded as one key node of the net-zero emission energy system [1]. The major demand for carbon capture comes from the treatment of CO 2 mixture gas including power-plant flue gas, raw natural gas, coal-bed gas, and biogas in which CO 2 is in wide concentration range and is mixed with different gases. For example, about 5%-15% of CO 2 is majorly mixed with N 2 in power-plant flue gas, and a wide range of CO 2 is regarded as an impurity of methane (CH 4 ) for the raw natural gas (CH 4 : >90%, CO 2 : 0.5-1%) and coal-bed (CH 4 : >50%, N 2 :~40%, CO 2 :~1%) [5] gas as well as biogas (CH 4 :~50%, CO 2 :~50%) [6]. Therefore, how to selectively capture CO 2 in a wide range of gas components is a big challenge and is considered as one of seven major challenges in the field of separation processes within chemical engineering [7].
Various CO 2 capture technologies, including absorption, adsorption, cryogenics, and membranes, have been developed [8,9]. Currently, the benchmark industrially demonstrated process for

Synthesis and Characterization
UiO-66 and UiO-66-NH 2 were synthesized in a convenient process, in which the nanocrystals were prepared in a short time (total 2.5 h) under ambient pressure without using pressure autoclave. Typically, Zirconium tetrachloride (ZrCl 4 ), hydrochloric acid (HCl, 37 wt%), terephthalic acid, and N,N-Dimethylformamide (DMF) were placed in a glass vial (100 mL) and vigorously stirred for 30 min at 80 • C. After centrifugation, washing, and drying, UiO-66 and UiO-66-NH 2 particles were then obtained.
The morphologies of UiO-66 and UiO-66-NH 2 crystals were firstly characterized through scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Figure 1a shows the morphology of UiO-66, where the typical particle size in the range of 100-200 nm was found. Synthesized UiO-66-NH 2 possessed a smaller particle size with the typical size less than 100 nm ( Figure 1b). Furthermore, the TEM images also showed that the UiO-66 ( Figure 1c) and UiO-66-NH 2 (Figure 1d) particles possess an irregular shape with the mean particle size around 200 nm (UiO-66) and approximate 100 nm (UiO-66-NH 2 ), respectively, and this was mutually verified by SEM results. The energy-dispersive X-ray spectroscopy (EDS) mapping was employed to investigate the elements' distribution. As indicated in Figure 1e,f, the elements Zr and O uniformly spread over the particles, while the element N was also founded from UiO-66-NH 2 which is derived from the -NH 2 group of the ligand (2-aminoterephtalic acid). The energy-dispersive X-ray spectroscopy (EDS) mapping was employed to investigate the elements' distribution. As indicated in Figure 1e,f, the elements Zr and O uniformly spread over the particles, while the element N was also founded from UiO-66-NH2 which is derived from the -NH2 group of the ligand (2-aminoterephtalic acid). The crystal phase was then examined by X-ray powder diffraction (XRD). Figure 2a shows the major diffraction patterns of UiO-66 and UiO-66-NH2, where the peaks were well consistent with the simulated pattern of UiO-66 reported previously [20]. However, the as-synthesized UiO-66 and UiO-66-NH2 particles exhibited broad peaks with low intensity, suggesting that some disorder and therefore large number of defects would exist in UiO-66 and UiO-66-NH2 [30,31]. Recent studies have shown that defects in MOFs provide a positive influence on catalysis, adsorption, and proton conductivity [32]. Fourier-transform infrared spectroscopy (FTIR) spectra in Figure 2b shows the chemical information of UiO-66 and UiO-66-NH2. They have similar vibrational peaks in the FTIR spectra. The characteristic peak around 3403 cm −1 was ascribed to the vibrational mode of the O-H group, which was related to the adsorbed water from the surface of the samples. A lot of intense peaks in the range of 1700-1200 cm −1 were derived from asymmetrical and symmetrical stretching vibrations of the carboxylate groups. The peaks at 800-600 cm −1 might be ascribed to a Zr-O bond. Especially, the peaks of 1390 and 1264 cm −1 were attributed to the vibrational mode of the C-N band in FTIR spectra of UiO-66-NH2, which originate from the -NH2 group of ligands of UiO-66-NH2. We use acid-base titration to further determine the existence and quantity of defects in UiO-66 and UiO-66-NH2. The titration curves for UiO-66 and UiO-66-NH2 are shown in Figure 2c. There is a slow break in the curve between the pH of five and seven. To better visualize the various equivalence points, the first derivative of the titration curve is further plotted. The results show the distinct equivalence points corresponding to the pKa values in Table 1. These defects can be assigned to bridging-OH, acetic acid, and Zr-OH2, respectively [31]. The thermal stability was also investigated by thermal gravimetric analysis (TGA) (Figure 2d), the weight loss before 100 °C was due to the removal of adsorbed small molecules from air, ca. CO2 and H2O. No obvious decomposition was found before 500 o C for UiO-66 and 300 o C for UiO-66-NH2 indicating their superior stability [20]. The crystal phase was then examined by X-ray powder diffraction (XRD). Figure 2a shows the major diffraction patterns of UiO-66 and UiO-66-NH 2 , where the peaks were well consistent with the simulated pattern of UiO-66 reported previously [20]. However, the as-synthesized UiO-66 and UiO-66-NH 2 particles exhibited broad peaks with low intensity, suggesting that some disorder and therefore large number of defects would exist in UiO-66 and UiO-66-NH 2 [30,31]. Recent studies have shown that defects in MOFs provide a positive influence on catalysis, adsorption, and proton conductivity [32]. Fourier-transform infrared spectroscopy (FTIR) spectra in Figure 2b shows the chemical information of UiO-66 and UiO-66-NH 2. They have similar vibrational peaks in the FTIR spectra. The characteristic peak around 3403 cm −1 was ascribed to the vibrational mode of the O-H group, which was related to the adsorbed water from the surface of the samples. A lot of intense peaks in the range of 1700-1200 cm −1 were derived from asymmetrical and symmetrical stretching vibrations of the carboxylate groups. The peaks at 800-600 cm −1 might be ascribed to a Zr-O bond. Especially, the peaks of 1390 and 1264 cm −1 were attributed to the vibrational mode of the C-N band in FTIR spectra of UiO-66-NH 2, which originate from the -NH 2 group of ligands of UiO-66-NH 2 . We use acid-base titration to further determine the existence and quantity of defects in UiO-66 and UiO-66-NH 2 . The titration curves for UiO-66 and UiO-66-NH 2 are shown in Figure 2c. There is a slow break in the curve between the pH of five and seven. To better visualize the various equivalence points, the first derivative of the titration curve is further plotted. The results show the distinct equivalence points corresponding to the pKa values in Table 1. These defects can be assigned to bridging-OH, acetic acid, and Zr-OH 2 , respectively [31]. The thermal stability was also investigated by thermal gravimetric analysis (TGA) (Figure 2d), the weight loss before 100 • C was due to the removal of adsorbed small molecules from air, ca. CO 2 and H 2 O. No obvious decomposition was found before 500 o C for UiO-66 and 300 o C for UiO-66-NH 2 indicating their superior stability [20].

Pore Structure and Gas Selective Adsorption
The textural characteristics (surface areas, pore size and pore volume) of UiO-66 and UiO-66-NH2 nanocrystals are evaluated by N2 adsorption and desorption analysis at 77 K. The nitrogen adsorption-desorption isotherms and the pore size distribution of UiO-66 and UiO-66-NH2 are shown in Figure 3. The characteristic of isotherms was in accord with type-II adsorption isotherms where the primary adsorption occurred at low relative pressures <0.1 indicated the formation of a highly microporous material with the possibility of a narrow pore size distribution of UiO-66 and UiO-66-NH2. The adsorption curve climbed rapidly at P/P0 values greater than 0.95 indicating the capillary condensation derived from the aggregation of nanoparticles or defects. The results showed that UiO-66 and UiO-66-NH2 had a large Brunauer-Emmett-Teller (BET) surface area of 1308 and 1104 m 2 g −1 , respectively, and it was in good agreement with previously reported UiO-66 structures that contain defects [31,33]. The pore distributions of UiO-66 and UiO-66-NH2 were further investigated through the Nonlocal Density Functional Theory (NLDFT) method based on the adsorption data. The bimodal pore distributions of ultramicropores (<0.7 nm) and supermicropores (0.7-2 nm) were probed as displayed in Figure 3b. Moreover, the pore volume was 0.533 (UiO-66) and 0.462 (UiO-66-NH2) cm 3 g −1 , respectively. These results demonstrated that the prepared UiO-66 and UiO-66-NH2 possess a high surface area in the micropore range and thus enabled a desirable adsorption capability.

Pore Structure and Gas Selective Adsorption
The textural characteristics (surface areas, pore size and pore volume) of UiO-66 and UiO-66-NH 2 nanocrystals are evaluated by N 2 adsorption and desorption analysis at 77 K. The nitrogen adsorption-desorption isotherms and the pore size distribution of UiO-66 and UiO-66-NH 2 are shown in Figure 3. The characteristic of isotherms was in accord with type-II adsorption isotherms where the primary adsorption occurred at low relative pressures <0.1 indicated the formation of a highly microporous material with the possibility of a narrow pore size distribution of UiO-66 and UiO-66-NH 2 . The adsorption curve climbed rapidly at P/P 0 values greater than 0.95 indicating the capillary condensation derived from the aggregation of nanoparticles or defects. The results showed that UiO-66 and UiO-66-NH 2 had a large Brunauer-Emmett-Teller (BET) surface area of 1308 and 1104 m 2 g −1 , respectively, and it was in good agreement with previously reported UiO-66 structures that contain defects [31,33]. The pore distributions of UiO-66 and UiO-66-NH 2 were further investigated through the Nonlocal Density Functional Theory (NLDFT) method based on the adsorption data. The bimodal pore distributions of ultramicropores (<0.7 nm) and supermicropores (0.7-2 nm) were probed as displayed in Figure 3b. Moreover, the pore volume was 0.533 (UiO-66) and 0.462 (UiO-66-NH 2 ) cm 3 g −1 , respectively. These results demonstrated that the prepared UiO-66 and UiO-66-NH 2 possess a high surface area in the micropore range and thus enabled a desirable adsorption capability. Molecules 2019, 24, x FOR PEER REVIEW 5 of 12 With their combination of nanosized, abundant defects and a large number of micropores, UiO-66 and UiO-66-NH2 demonstrated that they have great potential in the field of gas adsorption and separation. The CO2, CH4 and N2 adsorption-desorption curves are given in Figure 4, where the isotherms are recorded under the two temperatures of 273K and 298K, respectively. UiO-66 and UiO-66-NH2 exhibited excellent adsorption performance for CO2 at different temperatures. As shown in Figure 4, the CO2, CH4 and N2 equilibrium adsorption capacities of UiO-66 were 61 cm 3 g −1 , 13.6 cm 3 g −1, and 2.7 cm 3 g −1 at 273 K and 100 kPa, respectively. For 298 K and 100 kPa, the uptake capacities of CO2, CH4, and N2 were 33.4 cm 3 g −1 , 8.1 cm 3 g −1 , and 3.1 cm 3 g −1 , respectively. The enhancement gas adsorption abilities were found from UiO-66-NH2. The CO2, CH4, and N2 equilibrium adsorption capacity of UiO-66-NH2 were 68 cm 3 g −1 , 13.9 cm 3 g −1 , and 2.8 cm 3 g −1 at 273 K and 100 kPa, respectively. And they were 37.   With their combination of nanosized, abundant defects and a large number of micropores, UiO-66 and UiO-66-NH 2 demonstrated that they have great potential in the field of gas adsorption and separation. The CO 2 , CH 4 and N 2 adsorption-desorption curves are given in Figure 4, where the isotherms are recorded under the two temperatures of 273K and 298K, respectively. UiO-66 and UiO-66-NH 2 exhibited excellent adsorption performance for CO 2 at different temperatures. As shown in Figure 4, the CO 2 , CH 4 and N 2 equilibrium adsorption capacities of UiO-66 were 61 cm 3 g −1 , 13.6 cm 3 g −1, and 2.7 cm 3 g −1 at 273 K and 100 kPa, respectively. For 298 K and 100 kPa, the uptake capacities of CO 2 , CH 4 , and N 2 were 33.4 cm 3 g −1 , 8.1 cm 3 g −1 , and 3.1 cm 3 g −1 , respectively. The enhancement gas adsorption abilities were found from UiO-66-NH 2 . The CO 2 , CH 4 , and N 2 equilibrium adsorption capacity of UiO-66-NH 2 were 68 cm 3 g −1 , 13.9 cm 3 g −1 , and 2.8 cm 3 g −1 at 273 K and 100 kPa, respectively. And they were 37.  With their combination of nanosized, abundant defects and a large number of micropores, UiO-66 and UiO-66-NH2 demonstrated that they have great potential in the field of gas adsorption and separation. The CO2, CH4 and N2 adsorption-desorption curves are given in Figure 4, where the isotherms are recorded under the two temperatures of 273K and 298K, respectively. UiO-66 and UiO-66-NH2 exhibited excellent adsorption performance for CO2 at different temperatures. As shown in Figure 4, the CO2, CH4 and N2 equilibrium adsorption capacities of UiO-66 were 61 cm 3 g −1 , 13.6 cm 3 g −1, and 2.7 cm 3 g −1 at 273 K and 100 kPa, respectively. For 298 K and 100 kPa, the uptake capacities of CO2, CH4, and N2 were 33.4 cm 3 g −1 , 8.1 cm 3 g −1 , and 3.1 cm 3 g −1 , respectively. The enhancement gas adsorption abilities were found from UiO-66-NH2. The CO2, CH4, and N2 equilibrium adsorption capacity of UiO-66-NH2 were 68 cm 3 g −1 , 13.9 cm 3 g −1 , and 2.8 cm 3 g −1 at 273 K and 100 kPa, respectively. And they were 37.    The CO 2 capacity was further normalized to the pore volume to recover the affection of chemical components of UiO-66 and UiO-66-NH 2 . As indicated in Figure 5, UiO-66-NH 2 has obvious larger normalized CO 2 adsorption values than UiO-66. This phenomenon showed that the -NH 2 group of ligands in UiO-66-NH 2 may contribute more to the CO 2 molecule adsorption sites, and this conclusion coincides with Ethiraj's conclusion [37]. More importantly, UiO-66 and UiO-66-NH 2 display apparent higher CO 2 adsorption capacity than CH 4 and N 2 under the same temperatures and pressures, meaning that it has potential to remove CO 2 from CH 4 and N 2 by selective adsorption.
Molecules 2019, 24, x FOR PEER REVIEW 6 of 12 The CO2 capacity was further normalized to the pore volume to recover the affection of chemical components of UiO-66 and UiO-66-NH2. As indicated in Figure 5, UiO-66-NH2 has obvious larger normalized CO2 adsorption values than UiO-66. This phenomenon showed that the -NH2 group of ligands in UiO-66-NH2 may contribute more to the CO2 molecule adsorption sites, and this conclusion coincides with Ethiraj's conclusion [37]. More importantly, UiO-66 and UiO-66-NH2 display apparent higher CO2 adsorption capacity than CH4 and N2 under the same temperatures and pressures, meaning that it has potential to remove CO2 from CH4 and N2 by selective adsorption.
To evaluate the potential for real separation of the gas mixture of CO 2 /N 2 and CO 2 /CH 4 of UiO-66-NH 2 , the breakthrough experiments were carried out with binary mixtures of CO 2 /N 2 (15:85, v/v) and CO 2 /CH 4 (10:90, v/v) on a home-made column breakthrough setup (supporting information) which is the typical composition of flue gas and nature gas. As shown in Figure 6b, the results suggest the high-efficiency separation of N 2 from 15:85 CO 2 /N 2 by flowing the mixture gas over a packed column of UiO-66-NH 2 . It could be clearly observed that the N 2 first breakthrough was at 7 s, while the CO 2 could not be detected before its breakthrough point at 49 s. The separation factor was calculated to be seven following the calculation procedure provided in the supporting information. As shown in Figure 6d, the dynamic separation experiment of CO 2 /CH 4 mixed gas (10/90 in volume ration; flow speed of 2 mL min −1 ) was also examined under room temperature (298 K). The breakthrough curves can be divided into three segments based on their adsorption characteristics. The net breakthrough times (with the dead time deducted) of CO 2 and CH 4 were 114 and 226 s, respectively, giving a To evaluate the potential for real separation of the gas mixture of CO2/N2 and CO2/CH4 of UiO-66-NH2, the breakthrough experiments were carried out with binary mixtures of CO2/N2 (15:85, v/v) and CO2/CH4 (10:90, v/v) on a home-made column breakthrough setup (supporting information) which is the typical composition of flue gas and nature gas. As shown in Figure 6b, the results suggest the high-efficiency separation of N2 from 15:85 CO2/N2 by flowing the mixture gas over a packed column of UiO-66-NH2. It could be clearly observed that the N2 first breakthrough was at 7 s, while the CO2 could not be detected before its breakthrough point at 49 s. The separation factor was calculated to be seven following the calculation procedure provided in the supporting information. As shown in Figure 6d, the dynamic separation experiment of CO2/CH4 mixed gas (10/90 in volume ration; flow speed of 2 mL min −1 ) was also examined under room temperature (298 K). The breakthrough curves can be divided into three segments based on their adsorption characteristics. The net breakthrough times (with the dead time deducted) of CO2 and CH4 were 114 and 226 s, respectively, giving a CO2/CH4 (10/90) separation factor of about two. Therefore, the ability of selective adsorption and further remove CO2 from flue gas and natural gas of UiO-66-NH2 has been demonstrated.

Monte Carlo Simulation of Gas Selective Adsorption
A simple MC simulation was further carried out to analyze the distribution position and adsorption energy of CO2, N2 and CH4 in UiO-66-NH2. The simulation results showed that CO2, N2, and CH4 molecules were mainly distributed in the cage surrounded by three ligands of UiO-66-NH2

Monte Carlo Simulation of Gas Selective Adsorption
A simple MC simulation was further carried out to analyze the distribution position and adsorption energy of CO 2 , N 2 and CH 4 in UiO-66-NH 2 . The simulation results showed that CO 2 , N 2 , and CH 4 molecules were mainly distributed in the cage surrounded by three ligands of UiO-66-NH 2 (Figure 7a). At the initial state, one CO 2 molecule and seven N 2 or CH 4 molecules were placed in the cage to follow the chemical components of flue gas and raw natural gas, respectively. The optimized structures for CO 2 and N 2 or CO 2 and CH 4 are shown in Figure 7b,c, respectively. Small molecules were found to be located in the middle of the triangle area which implies that the weak interactions may rest between small molecules and UiO-66-NH 2 . To prove these weak intermolecular interactions, an Independent Gradient Model [41] was carried out for those two structures in Figure 7b,c. The scatter plots for the δ function versus the sign(λ 2 )ρ including intermolecular (red area) and intramolecular (black area) interactions were shown in Figure 7d,e, where the sign(λ 2 )ρ is the sign of the second largest eigenvalue λ 2 of the electron-density Hessian matrix multiplied by the electron density. It could be seen that the electron density of intermolecular interaction is not very large, but not very close to zero either. Based on this we can speculate that the intermolecular interactions in those two systems are weak interactions. The adsorption energy for CO 2 , N 2 , and CH 4 are estimated to be 0.32, 0.19, and 0.20 eV, respectively. It can be speculated that the CO 2 and CH 4 or CO 2 and N 2 mixed gases can be effectively separated by this MOF material, which is consistent with the experimental results.
density. It could be seen that the electron density of intermolecular interaction is not very large, but not very close to zero either. Based on this we can speculate that the intermolecular interactions in those two systems are weak interactions. The adsorption energy for CO2, N2, and CH4 are estimated to be 0.32, 0.19, and 0.20 eV, respectively. It can be speculated that the CO2 and CH4 or CO2 and N2 mixed gases can be effectively separated by this MOF material, which is consistent with the experimental results.

Synthesis of UiO-66 and UiO-66-NH2
A total of 0.625 g of ZrCl4 and 5 mL of 37% HCl aqueous solution were mixed and dissolved in 10 mL of DMF. After 30 min of ultrasonication, 0.615 g of terephthalic acid dissolved in 50 mL of DMF was added to the former solution of ZrCl4 and HCl, and the whole solution was further sonicated by using a batch sonication (Kunshan Ultrasonic Instruments Co., Ltd., KQ-100, Kunshan, China) with Figure 7. Optimized structures and intermolecular interactions between CO 2 , N 2 and CH 4 . Stable porous cage structure of UiO-66-NH 2 (a), stable adsorption structure for CO 2 and N 2 adsorption in UiO-66-NH 2 (b), stable adsorption structure for CO 2 and CH 4 adsorption in UiO-66-NH 2 (c), scatter plot for δ function versus sign(λ 2 )ρ of CO 2 and N 2 (d) and CO 2 and CH 4 (e) adsorption in UiO-66-NH 2 .

Synthesis of UiO-66 and UiO-66-NH 2
A total of 0.625 g of ZrCl 4 and 5 mL of 37% HCl aqueous solution were mixed and dissolved in 10 mL of DMF. After 30 min of ultrasonication, 0.615 g of terephthalic acid dissolved in 50 mL of DMF was added to the former solution of ZrCl 4 and HCl, and the whole solution was further sonicated by using a batch sonication (Kunshan Ultrasonic Instruments Co., Ltd., KQ-100, Kunshan, Jiangsu, China) with the output power of 100 W and the frequency of 40 kHz for the next 30 min. The solution was then kept in a 100 mL glass vial at 80 • C statically without stirring or ultrasonicating at 80 • C for 2 h. UiO-66-NH 2 was prepared following the same process except that 2-aminoterephtalic acid was used to replace the terephthalic acid.

Acid-Base Titrations
A total of 40 mg of sample (activated for 12 h at 150 • C) was added to a 100 mL beaker. An equivalent volume of a 0.01 M NaNO 3 solution was added and allowed to equilibrate for 18 h.
Preceding each titration, a stir bar was added to the beaker and the pH was adjusted to a value of 3.00 with 0.1 M HCl. Following this, the solution was titrated with 0.1 M NaOH of solution (adding 0.04 mL NaOH solution at a time and stirring evenly) with a pH value of 8.

Gas Adsorption Measurement
The N 2 sorption isotherms at 77 K and the gas adsorption isotherms of CO 2 , CH 4, and N 2 at two different temperatures (273 and 298 K) were measured by using a Autosorb-iq3 surface area and porosimeter analyzer (Quantachrome, Boynton Beach, FL, USA). The temperatures (273 and 298 K) were controlled by means of a circulating bath. The samples were degassed at 473 K for 10 h under a vacuum of 10 −5 mmHg before the measurements. The pore size distributions and micropore surface areas were determined using the nonlocal density function theory (NLDFT) method. Gases with a high purity of over 99.995% were used.

Breakthrough Experiments
The breakthrough experiments of flue gas and natural gas separation were conducted in a home-made apparatus as illustrated in our previous reports [42,43].
The absolute adsorbed amount of gas i (q i ) was calculated from the breakthrough curve by the equation: where F i = influent flow rate of the specific gas (cm 3 min −1 ); t 0 = adsorption time (min); V dead = dead volume of the system (cm 3 ); F e = effluent flow rate of the specific gas (cm 3 min −1 ); m = mass of the sorbent (g).
The selectivity of the breakthrough experiment is defined as α = (q 1 /y 1 )/(q 2 /y 2 ), where y i is the mole fraction of gas i in the gas mixture.

DFT Calculations
Monte Carlo (MC) simulations are carried out with the adsorption locator module with the universal force field [44]. All the geometric optimization calculations were performed using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional [45] as implemented in the all-electron DMol 3 code [46,47]. The double numerical plus polarization (DNP) basis set was used throughout the calculations. The convergence criteria were set to be 2 × 10 −5 Ha, 0.004 Ha Å −1 , and 0.005 Å for the energy, the force, and the displacement convergences, respectively. A self-consistent field (SCF) density convergence with a threshold value of 1 × 10 −5 Ha was specified. Independent Gradient Model analysis were carried out using Multiwfn software [48]. A complete MOF channel structure was cut-off from the single-crystal structure of UiO-66. All dangling bonds in the MOF structure (Zr atoms) were saturated by hydroxy groups.

Conclusions
In summary, we synthesized crystals of UiO-66 and UiO-66-NH 2 in nano-size with a high surface area and abundant defects. UiO-66 and UiO-66-NH 2 have selective gas adsorption ability of CO 2 over CH 4 and N 2 . The pure N 2 and CH 4 can be obtained from the simulated flue gas (CO 2 /N 2 , 15/85) and from raw natural gas (CO 2 /CH 4 , 10/90) by a breakthrough operation, respectively. Especially, the separation factors of seven (CO 2 /N 2 ) and two (CO 2 /CH 4 ) were calculated from UiO-66-NH 2 indicating the potential applications for green separation. The results of MC simulation showed that CO 2 displayed preferential adsorption energy over N 2 or CH 4 in the gas mixture through UiO-66-NH 2 . This dynamic study from theoretical and experimental aspects may provide an insight into the selective adsorption and separation of the gases.
Author Contributions: Y.Z. and Y.C. conceived and designed the experiments; P.L. fabricated the materials; P.L. and D.W. analyzed the data; Y.S. performed the theoretical calculation; Y.Z. and Y.C. wrote the manuscript.