Guest Solvent-Directed Isomeric Metal–Organic Frameworks for the Kinetically Favorable Separation of Carbon Dioxide and Methane

Abstract

The adsorptive separation of CH₄ from CO₂ is a promising process for upgrading natural gas. However, thermodynamically selective adsorbents exhibit a strong affinity for CO₂ and thus require a high energy compensation for regeneration. Instead, kinetic separation is preferred for a pressure swing adsorption process, although precise control of the aperture size to achieve a tremendous discrepancy in diffusion rates remains challenging. Here, we report a guest solvent-directed strategy for fine-tuning the pore size at a sub-angstrom precision to realize highly efficient kinetic separation. A series of metal–organic frameworks (MOFs) with isomeric pore surface chemistry were constructed from 4,4′-(hexafluoroisopropylidene)-bis(benzoic acid) and dicopper paddlewheel notes. The resultant CuFMOF·CH₃OH (CuFMOF-c) exhibits an excellent kinetic separation performance thanks to a periodically expanding and contracting aperture with the ideal bottleneck size, which enables the effective trapping of CO₂ and impedes the diffusion of CH₄, offering an ultrahigh kinetic selectivity (273.5) and equilibrium-kinetic combined selectivity (64.2). Molecular dynamics calculations elucidate the separation mechanism, and breakthrough experiments validate the separation performance.

Content

《1. Introduction 》

1. Introduction

Natural gas, which primarily consists of methane (CH₄), will grow to account for a quarter of the global energy demand in the coming decades [1–3]. Nevertheless, the abundant low-quality natural gas, which has a medium concentration of CH₄ mixed with basically equivalent amounts of carbon dioxide (CO₂), cannot meet the demand for industrial applications [4–6]. Consequently, the CO₂ must be removed to improve the combustion efficiency and prevent equipment and pipeline corrosion during transportation [7–13]. At present, the mature industrial technology of CO₂ removal involves amine scrubbing, which is costly due to the huge energy input required for absorbent regeneration and is susceptible to oxidative and thermal degradation [14–17].

Adsorbent-based separation processes have been proposed as an alternative technology with a lower regeneration energy, higher efficiency, and easier operation [18–30]. However, porous adsorbents such as zeolites and amine-functionalized silicas still show high adsorption enthalpies for CO₂, despite demonstrating remarkable thermodynamic selectivity [31–34]. Instead, kinetic separation based on a difference in diffusion rate is preferred if the adsorbents are hydrophobic and show significant kinetic selectivity. For example, carbon molecular sieves (CMSs) can purify natural gas based on kinetic separation, with an adsorption heat of CO₂ as low as 10.9 kJ∙mol^–1 [35,36]. Nonetheless, it remains challenging to precisely control the micropores of carbon adsorbents by means of carbonization in order to manipulate the kinetic selectivity of CO₂/CH₄ [37–39].

Versatile metal–organic frameworks (MOFs) could serve as an ideal platform to meet the strict prerequisites for kinetic separation due to their structural diversity and pore size fine-tunability [40–54]. For example, Lee et al. [55] demonstrated the efficient kinetic separation of propylene/propane in isostructural zincpillared-paddlewheel MOFs by controlling the pore apertures and the rectangular-plate morphology of the crystals. Similarly, Lyndon et al. [56] proposed a mixed-linker strategy for fine-tuning structurally flexible apertures (~3 Å, 1 Å = 10^–10 m), which facilitates the selective diffusion of ethylene over ethane. Recently, Gu et al. [57] presented a copper (Cu)-based MOF in which flip-flop molecular motions within the framework structure provide kinetic gate functions that enable the efficient separations of oxygen/ argon and ethylene/ethane. Nevertheless, few efforts have been devoted to construct MOFs for the kinetic separation of CO₂/CH₄, partially due to the difficulty of fabricating an appropriate aperture with sub-angstrom precision, and partially because of the close kinetic diameters of CO₂ (3.3 Å) and CH₄ (3.8 Å).

Herein, we report a guest solvent-directed isomeric microporetuning strategy within a ultra-microporous Cu(hfipbb)- (H₂hfipbb)_0.5 (where H₂hfipbb is 4,4' -(hexafluoroisopropylidene)- bis(benzoic acid)), termed CuFMOF-a, for the kinetic separation of CO₂/CH₄. As the parent, CuFMOF-a exhibits a periodically expanding and contracting aperture with a bottleneck size of 3.2 Å × 3.5 Å that hinders the diffusion of CH₄. Its offspring, CuFMOF·CH₃OH (termed CuFMOF-c), which has a similar pore surface and an aperture size increased by 0.2 Å, facilitates the diffusion of CO₂ but prevents the diffusion of CH₄, with an unprecedented kinetic selectivity. CuFMOF·DMF (termed CuFMOF-b; DMF is short for N,N-dimethylformamide), which has an aperture size that is further increased by 0.2 Å, promotes the diffusion of both CO₂ and CH₄, which diminishes the kinetic separation of CO₂/CH₄. Moreover, CuFMOF-c shows a moderate thermodynamic selectivity of CO₂ over CH₄; thus, the synergetic equilibrium-kinetic effect boosts the efficient breakthrough separation of a CO₂/CH₄ gas mixture. Grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations further demonstrate the critical role of pore-size tuning for kinetic separation.

《2. Experimental section 》

2. Experimental section

《2.1. Materials》

2.1. Materials

The organic ligand H₂hfipbb (98%) was obtained from TCI (China). Copper chloride dihydrate (CuCl₂·2H₂O, 99.99%) and copper nitrate trihydrate (CuNO₃·3H₂O, 99%) were purchased from Aladdin (China) and Macklin (China), respectively. Carbon dioxide (99.999%), methane (99.999%), helium (99.999%), and mixed gases CH₄/CO₂ (50/50, v/v) were customized from Jingong Co., Ltd. (China). All chemicals were obtained from commercial sources and were used as received without further purification.

《2.2. Synthesis of CuFMOF-a》

2.2. Synthesis of CuFMOF-a

The synthesis of CuFMOF-a followed the previously reported procedure by Pan et al. [58]. Excess H₂hfipbb (729 mg, 1.86 mmol) with Cu(NO₃)₂·3H₂O (145 mg, 0.6 mmol) and 30 mL deionized water were heated at 150 °C for 12 h to obtain blue columnar crystals. After cooling to room temperature, the product was washed with DMF to remove excess H₂fipbb; it was then washed with deionized water and finally dried in air.

《2.3. Synthesis of CuFMOF-b》

2.3. Synthesis of CuFMOF-b

The organic linker H₂hfipbb (235.4 mg, 0.6 mmol) and Cu (NO₃)₂·3H₂O (145 mg, 0.6 mmol) were dissolved in a mixture of DMF (36 mL) and deionized water (12 mL). The solution was heated in an autoclave at 65 °C for 48 h to obtain blue crystals. The product was washed with DMF (30 mL) three times and then with methanol (30 mL) three times, and was finally dried at room temperature.

《2.4. Synthesis of CuFMOF-c》

2.4. Synthesis of CuFMOF-c

The organic linker H₂hfipbb (117.7 mg, 0.3 mmol) and CuCl₂·2H₂O (51.2 mg, 0.3 mmol) were dissolved in a mixture of DMF (14 mL) and methanol (14 mL) and acidified with 0.1 mol∙L^–1 HCl (0.7 mL) to yield the product. The solution was heated in an autoclave at 80 °C for 24 h to obtain blue petal-like crystals. The product was washed with DMF (30 mL) three times and then with methanol (30 mL) three times. Finally, it was dried at room temperature.

《2.5. Gas adsorption measurements》

2.5. Gas adsorption measurements

To remove all the guest solvent in the framework, the CuFMOFc sample (~300 mg) was degassed at 120 °C for 24 h prior to measurements. CO₂ and CH₄ adsorption isotherms were measured on a Micromeritics ASAP 2460 (Micromeritics Instrument Corp., USA). The Brunauer–Emmett–Teller (BET) surface areas of CuFMOF-c and CuFMOF were characterized by CO₂ adsorption–desorption isotherms at 195 K.

《2.6. Adsorption kinetics measurements》

2.6. Adsorption kinetics measurements

The kinetic adsorption profiles were measured on an Intelligent Gravimetric Analyzer (IGA001, Hiden, UK), which uses a gravimetric technique to accurately measure the transient gas uptake as a function of time under various operating conditions. For each test, about 120 mg of MOF sample was loaded into the sample basket; then, the system was outgassed at 393 K for 8 h prior to the dynamic gas sorption measurements. The adsorption kinetics were obtained by measuring the mass change at a given temperature at 100 mbar (1 mbar = 10^–3 bar = 100 Pa), and the pressure was boosted up by introducing the target gas into sample chamber from 0 to 100 mbar at 200 mbar∙min^–1 . The adsorption kinetics were collected at various temperatures from 278 to 318 K. After each test, the chamber was backfilled with the target gas to 1000 mbar, and the sample was replaced by the new sample for the next test. All the gases used (CH₄, CO₂, and He) were of ultrahigh purity (99.999%).

《2.7. Dynamic breakthrough experiments and desorption experiments》

2.7. Dynamic breakthrough experiments and desorption experiments

The breakthrough experiments for the CO₂/CH₄(50/50, v/v) mixtures were carried out at a flow rate of about 2.5 mL∙min^–1 (298 K, 1.01 bar). Activated MOF particles (CuFMOF-a, 1.317 g; CuFMOF-b, 1.053 g; CuFMOF-c, 1.172 g) were packed into a Φ4.6 mm × 100 mm stainless steel column under a nitrogen (N₂) atmosphere. After each breakthrough experiment, the adsorption bed was regenerated by helium flow with a rate of 20 mL∙min^–1 at 298 K for 30 min. Based on the mass balance, the gas adsorption capacities can be determined as follows:

where q_i is the equilibrium adsorption capacity of gas i (mmol∙g^–1 ), C_iis the feed gas concentration, V is the volumetric feed flow rate (mL∙min^–1 ), t is the adsorption time (min), F₀ and F are the inlet and outlet gas molar flow rates, respectively, and m is the mass of the adsorbent (g).

《2.8. Density functional theory calculations》

2.8. Density functional theory calculations

First-principles density functional theory (DFT) calculations were performed using the Materials Studio’s CASTEP code.47. Vanderbilt-type ultrasoft pseudopotentials and the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange correlation were used for all structure geometry optimization calculations. A cutoff energy of 544 eV and a 3 × 3 × 2 k-point mesh were found to be sufficient for the total energy to converge within 0.05 MeV per atom. The optimized structures were consistent with the experimentally determined crystal structure of the coordination networks.

《2.9. GCMC and MD simulation》

2.9. GCMC and MD simulation

We performed adsorption and diffusion simulations of CO₂and CH₄ in CuFMOF-a, CuFMOF-b, and CuFMOF-c using GCMC [59] and MD, respectively. All simulations were performed at room temperature using a rigid MOF structure with atomic positions obtained from experimental data. A simulation volume of 2 × 2 × 2 crystallographic unit cells was used for all simulations. Assuming that the MOF is rigid greatly reduces the complexity of defining interatomic potentials for these simulations, as well as their computational efficiency. CH₄ was modeled as a spherical Lennard–Jones (LJ) particle [60], while CO₂ was modeled as a rigid three-site molecule using the elementary physical model-2 (EPM2) [61] and as an all-atom model with LJ potentials and atomic charges to approximate the quadrupole moment of CO₂. A comparison of the experimental adsorption isotherms (Fig. S1 in Appendix A) with the simulated adsorption isotherms (Fig. S2 in Appendix A) revealed that the simulated adsorption data is slightly higher than that of the experimental adsorption. However, under ideal circumstances, it will be slightly higher than the actual data, due to the existence of cell defects and other problems. Thus, the parameters work well for CO₂ and CH₄, indicating that the parameters used are reasonable.

The Lorentz–Berthelot mixing rules were employed to calculate the adsorbate–MOF LJ cross-interaction parameters by using the universal force field (UFF) [62] for the framework atoms. The charges on an atom in the MOF were determined by means of dispersion-corrected density functional theory (DFT-D) calculations with Accelrys DMol³ in the Materials Studio package. DFT calculations were conducted under the GGA with a PBE and double numerical plus polarization (DNP) basis set. A semi-empirical dispersion correction was included in the calculation to account for van der Waals interactions. The space cut-off radius (4.0 Å) and a 2 × 2 × 2 k-point mesh were used for geometry optimization, and a convergence tolerance with a fine quality was employed in the calculations. We used MD to compute the self-diffusion coefficient of CO₂. MD was performed in the canonical ensemble with a Nose–Hoover thermostat [63] for a time of 20 ns for each loading and/or composition we considered. Initial states were created using GCMC. The self-diffusion calculation is based on the Einstein equation:

where c is the concentration of the adsorbate molecules, d is the dimension of system space, N_m is the number of molecules in the system, and r_j(t) is the displacement of the labeled particle j at time t.

《3. Results and discussion 》

3. Results and discussion

《3.1. Synthesis and characterization of MOFs》

3.1. Synthesis and characterization of MOFs

CuFMOF was successfully synthesized according to a previously reported method [58]. As demonstrated by single-crystal X-ray diffraction analysis, CuFMOF-a was further expanded into a three-dimensional (3D) framework structure by connecting the carboxylic acid hfipbb^2– ligand at the apical position of six connected nodes (Fig. 1(a)). Each bent shape of the hfipbb^2– ligand of these materials adopts a spiral extension to link the upper and lower layers, which constructs a structure that periodically outspreads and contracts the cross-section of the channel (Fig. 1(b)). Consequently, the channel can be described as a narrow bottleneck structure interconnected by an iterant cage space.

The pore size was measured to be 3.5 Å, which is slightly larger than the kinetic diameter of CO₂ (3.3 Å) and smaller than that of CH₄ (3.8 Å). Given that the solubility of the organic ligand of CuFMOF-a in water is quite low, DMF was added to dissolve the ligand. Surprisingly, a new form of crystal MOF, denoted as CuFMOF-b, was obtained. Unlike the structure of the parent, CuFMOF-a, the paddlewheel copper atoms in CuFMOF-b act as a four-connected node that connects the four bent shapes of the ligands located in the equatorial plane, while the apical positions of the nodes connect to the DMF, forming a single-layer network in the ac-plane (Fig. 1(c), Table S1 in Appendix A).

Interestingly, the chiral pores of CuFMOF-b are formed by entangled left-handed spiral double strands, while those of CuFMOF-a are formed by entangled right-handed spiral double strands. Notably, the bending angles of the V-shaped hfipbb^2– within CuFMOF-a (72.8°) are slightly larger than those of CuFMOF-b (71.8°) due to the different coordination structure of the top linker of the copper square pyramidal shape (Figs. 1(b) and (d)), thus giving CuFMOF-b a subtly larger channel bottleneck with a pore size of 3.9 Å. Similarly, another MOF with an isomeric pore surface, denoted as CuFMOF-c, was fabricated for the first time by replacing water with methanol as the guest solvent (Fig. 1(e), Table S1). As evidenced by single-crystal analysis, the as-synthesized CuFMOF-c is crystallized in the Pccn space group and features an isomeric chiral pore structure formed by entangled left-handed spiral double strands, like those of CuFMOF-b, although the bending angle is smaller and the bottleneck of the channel is reduced to 3.7 Å (Fig. 1(f)). This alteration may originate from the different coordinated solvent molecules associated with the axial position of the copper atoms; thus, it influences the supramolecular arrangement of the MOF layers. To further demonstrate the role of the coordinated solvent molecules in tuning the isomeric pore structure, single-crystal X-ray diffraction tests were performed of the activated MOFs. It was found that the solvent molecules were still firmly coordinated with the copper atoms after activation in a vacuum at 120 °C for 24 h (Table S2 in Appendix A).

《Fig. 1》

Fig. 1. Schematic representation of the synthesis of CuFMOF-a, CuFMOF-b, CuFMOF-c, and their corresponding structures. The crystal structure of the as-synthesized (a) CuFMOF-a, (c) CuFMOF-b, and (e) CuFMOF-c along the b-axis showing the one-dimensional (1D) channels. The dihedral angle of the bent-shape hfipbb^2– ligand and the Connolly surface indicate the periodic expansion and contraction of the cross-section of the channel in (b) CuFMOF-a, (d) CuFMOF-b, and (f) CuFMOF-c. The nets are highlighted in dark green for clarity. Color code: Cu (green), F (yellow), C (gray), O (red), N (blue); H atoms are omitted for clarity.

The ultra-microporous structure of these MOFs was verified by CO₂ adsorption tests at 195 K, which revealed the typical characteristics of micropores, as seen from the steep increase of the isotherms within the relative pressure range of 0.01 (Fig. S3 in Appendix A). It is worth noting that the steep increase of the isotherms at a relative pressure from 0.7 to 0.8 on CuFMOF-b and CuFMOF-c may be caused by the agglomeration of MOFs. The BET specific surface areas were calculated to be 56.4, 126.4, and 82.6 m² ∙g^–1 for CuFMOF-a, CuFMOF-b, and CuFMOF-c, respectively.

《3.2. Static adsorption tests and kinetic adsorption experiments》

3.2. Static adsorption tests and kinetic adsorption experiments

Inspired by the appropriate pore size and well-developed porosity, adsorption isotherms of CO₂and CH₄ were collected (Fig. 2(a) and Fig. S1). As shown in Fig. 2(a), CuFMOF-c displays the highest CO₂ uptake of 0.93 mmol∙g^–1 at 298 K and 100 kPa, surpassing those of CuFMOF-a (0.64 mmol∙g^–1 ) and CuFMOF-b (0.80 mmol∙g^–1 ), which is consistent with the order of the BET specific surface areas. In addition, the CH₄ uptake decreases from 0.58 to 0.31 mmol∙g^–1 when going in order from CuFMOF-c to CuFMOF-a, which is lower than that of CO₂, demonstrating the weaker affinity between CH₄ molecules and the MOF structure. The Henry’s selectivities of CO₂/CH₄ were calculated to be 5.0, 3.2, and 2.9 for CuFMOF-a, CuFMOF-b, and CuFMOF-c, respectively, which are slightly lower than that of 5A (Sinopec) zeolite (7.8) [64] and Bergbau–Forschung (BF)-CMS (5.2) [35]. The isosteric heat of adsorption (Q_st) was calculated based on single-component isotherms collected at 278, 298, and 318 K, by using the Clausius– Clapeyron equation and Langmuir–Freundlich model (Fig. S2 and Tables S3–S5 in Appendix A). The optimal CuFMOF-c exhibits a moderate Q_st for CO₂ and CH₄ with respective values of 21.97 and 17.66 kJ∙mol^–1 at zero coverage, indicating its easy generation and great potential in practical energy-saving applications.

The delicate structure of these MOFs inspired us to evaluate their CO₂/CH₄ kinetic separation performance. Time-dependent kinetic adsorption isotherms of CO₂ and CH₄ were measured at various temperatures ranging from 278 to 318 K (Figs. 2(b) and (c), Fig. S4 in Appendix A). As expected, all MOFs showed a considerably faster diffusion rate for CO₂ than for CH₄ over the whole temperature range. The adsorption of CO₂in CuFMOF-b and CuFMOF-c reached equilibrium within 5 min at 298 K and 100 mbar (Fig. 2(b)). In contrast, CuFMOF-a exhibited the lowest diffusion rate of CO₂ because it has the narrowest pore size, and did not reach equilibrium until 30 min under identical conditions. As for CH₄ diffusion, the fastest diffusion rate was observed for CuFMOF-b due to its further increased pore size at the bottleneck. The quantity of CH₄ adsorption for CuFMOF-a and CuFMOF-c still did not reach an equilibrium state after 60 min and kept climbing up gradually. Therefore, the difference in the diffusion behavior of CO₂ and CH₄ was the greatest for CuFMOF-c.

《Fig. 2》

Fig. 2. (a) Single-component adsorption isotherms of CO₂ and CH₄ for CuFMOF-a (blue), CuFMOF-b (green), and CuFMOF-c (red) at 298 K; the solid lines represent the fitting curves via the Langmuir equation, and the solid dots and circles represent experimental data. (b, c) Time-dependent gas uptake profiles of CO₂ and CH₄ for CuFMOF-a (blue), CuFMOF-b (green), and CuFMOF-c (red) at 298 K and 100 mbar at different time scales. (d) Performance comparison of various adsorbents on CO₂/CH₄. (e) Experimental column breakthrough curves for a binary mixture of CO₂/CH₄ (50/50, v/v) at 298 K and 1 bar with a flow of 2.5 mL∙min^–1 . The ordered mesoporous carbon obtained after the removal of silica was referred as sOMC. C is the outlet gas concentration, and C₀ is the outlet gas concentration at equilibrium.

To achieve a better quantitative comparison of the diffusion rate, we adopted the classic micropore diffusion mode [65] to quantify the kinetic selectivity. The diffusion time constants (D_c/ r_c² , where D_c is the intracrystalline diffusivity, and r_c is the radius of the equivalent spherical particle) for CO₂ and CH₄ were calculated, from which the kinetic selectivity could be obtained (Tables S6 and S7 in Appendix A). CuFMOF-a, which has the smallest pore size, exhibited an inconspicuous difference in the adsorption kinetics of CO₂ and CH₄. CuFMOF-a showed diffusion time constants of 1.950 × 10^–4and 1.215 × 10^–5 s^–1 for CO₂ and CH₄ at 298 K, respectively, giving a CO₂/CH₄ kinetic selectivity of merely 16.1, because not only is the diffusion of CH₄ restricted when it diffuses from one center cage through the bottleneck to another adjacent center cage, but the diffusion of CO₂ is also restricted due to the too-narrow pore size. Nevertheless, CuFMOF-b, which features the largest pore size, presents a kinetic selectivity of CO₂/CH₄(36.1), with the diffusion time constant of CH₄ dramatically increasing to 7.31 × 10^–5 s^–1 and that of CO₂ slightly increasing to 2.64 × 10^–3s^–1 at 298 K. Notably, the diffusion time constants of CO₂and CH₄at 298 K on CuFMOF-c were calculated to be 1.803 × 10^–3 and 1.795 × 10^–5 s^–1 , offering a dramatic CO₂/CH₄ kinetic selectivity of up to 100.5. These observations can be elucidated qualitatively by the size of the narrow bottleneck, which naturally facilitates the diffusion of the smaller CO₂ molecules while setting a barrier that prevents the larger CH₄ molecules from diffusing in the channel. Compared with CuFMOF-a and CuFMOF-b, the pore size in CuFMOF-c (3.7 Å) is an optimal aperture for the kinetic separation of CO₂ and CH₄, as it is large enough for CO₂ to diffuse into but smaller than the kinetic diameter of CH₄, resulting in a high kinetic selectivity of CO₂/CH₄. These results indicate that structural pore size tuning via solvent substitution is a promising strategy for kinetic separation.

It is worth noting that the diffusion rate steadily decreases with decreasing temperature, with the diffusion rate of CH₄ being more significantly affected by temperature than that of CO₂. When the temperature was further decreased to 278 K, a remarkably high kinetic selectivity of CO₂/CH₄ (273.5) was obtained on CuFMOF-c, which is significantly higher than that of other reported kinetically selective adsorbents such as CMS-3K (1.1) [66], CMS-T3A (91.7) [67], BF-CMS (180) [35], and 5A zeolite (3.6) [64], and comes second only to CMS-3A (537.3) [35] (Table S7). The diffusion activation energy of CO₂ and CH₄ were calculated using the Arrhenius equation (see Appendix A). The significantly higher diffusion activation energy of CH₄ in comparison with that of CO₂ further demonstrates the high selectivity of CO₂ over CH₄on these MOFs (Table S8 in Appendix A). The equilibrium-kinetic combined selectivity [68], which is an important parameter to evaluate the performance of adsorbents, was also calculated and compared. As displayed in Fig. 2(d) and Table S7, a dramatically high combined selectivity (64.2) was achieved on CuFMOF-c, outperforming that of most reported adsorbents and even being comparable to those of commercial CMSs such as CMS-3A (64.9) [35] and BF-CMS (69.8) [35]. This finding indicates the great potential of CuFMOFc for CO₂/CH₄ separation.

《3.3. Breakthrough experiments and the MOFs’ stability》

3.3. Breakthrough experiments and the MOFs’ stability

To investigate the potential of these MOFs for CO₂/CH₄in an actual separation process, real-time dynamic breakthrough experiments were conducted. CH₄ was first eluted within 2 min∙g^–1 , whereas CO₂ was retained on CuFMOF-c until 10 min∙g^–1 . This was followed by a retention time on CuFMOF-b of 7 min∙g^–1 and on CuFMOF-a of 5 min∙g^–1 . The dynamic uptake of CO₂ was calculated to be 0.50, 0.58, and 0.76 mmol∙g^–1 , respectively, for CuFMOF-a, CuFMOF-b, and CuFMOF-c, which is consistent with the results of the aforementioned static adsorption tests (Fig. 2(e)). Moreover, high-purity CH₄ (> 99%) was obtained with a calculated productivity of 0.22, 0.18, and 0.24 mmol∙g^–1 for CuFMOF-a, CuFMOF-b, and CuFMOF-c, respectively.

Multiple breakthrough experiments were performed, and it was observed that there was no obvious decay in the dynamic adsorption uptake of CO₂ after 5 cycles (Figs. S5(a)–(c) in Appendix A), which demonstrates the excellent recyclability of these MOFs for CO₂/CH₄ separation. The desorption curves obtained by using helium to purge the column after the breakthrough experiments were also collected (Figs. S5(d)–(f) in Appendix A), and indicated the easy generation of adsorbents under mild ambient conditions.

Concerns about the stability of the adsorbents were also raised. The thermal stability of these MOFs was examined by means of thermogravimetric analysis (TGA; Fig. S6 in Appendix A). It was found that CuFMOF-a, CuFMOF-b, and CuFMOF-c are highly thermally stable up to 563, 548, and 488 K, respectively. Powder X-ray diffraction (PXRD) patterns of these MOFs under different conditions were also collected (Fig. S7 in Appendix A). After soaking the MOFs in water for 24 h and exposing them to air for a month, no loss of crystallinity was observed, showing the robust chemical stability of these MOFs due to the hydrophobic characteristics of the fluorine-containing ligand.

《3.4. GCMC and MD simulations》

3.4. GCMC and MD simulations

To structurally elucidate how CO₂ and CH₄ diffuse in the onedimensional (1D) channel, GCMC and MD simulations were carried out. The GCMC simulation of the adsorption isotherms (Fig. S8 in Appendix A) matches well with the experimental results. As shown in Figs. 3(a)–(c), when each cell contains two gas molecules, the self-diffusion coefficients of the single-component CO₂ are calculated to be 1.2 × 10^–6 , 1.19 × 10^–5 , and 1.51 × 10^–5 cm² ∙s^–1 for CuFMOF-a, CuFMOF-c, and CuFMOF-b, respectively, following the order of the diffusion rate of CO₂ obtained from the kinetic adsorption tests. It is noteworthy that the self-diffusivity of CO₂decreases with increased loading. However, CH₄ cannot pass through the narrow bottleneck between adjacent capacious cage space on the nanosecond timescales available using MD, which is consistent with the results reported by Watanabe et al. [69].

The difference in the minimum potential energy of CO₂and CH₄ (Figs. 3(d)–(f)), which is obtained by calculating the energy when a molecule is moved along a 1D channel of MOFs at each point, is the intrinsic reason for the disparity in the diffusion rates. The minimum energy occurs at the center of the capacious cage space, where CH₄ and CO₂ molecules are mainly accommodated (Fig. S9 in Appendix A). The diffusion energy barriers of CH₄ and CO₂ in CuFMOF-a were measured to be 69.8 and 22.4 kJ∙mol^–1 (Fig. 3(d)), respectively, reflecting CuFMOF-a’s slowest diffusion rate. As the pore size increases, the diffusion energy barriers of CH₄ and CO₂ decrease to 55.6 and 15.4 kJ∙mol^–1 , respectively, in CuFMOF-c (Fig. 3(f)). As for CuFMOF-b, which has the largest pore size, the diffusion energy barriers of CH₄ and CO₂ were estimated to be 38.4 and 16.7 kJ∙mol^–1 (Fig. 3(e)), respectively, indicating that these molecules can pass through the channel more easily. However, the insignificant difference between the movement of CH₄ and CO₂ in CuFMOF-b results in a lower kinetic selectivity for CO₂/CH₄separation. Therefore, CuFMOF-c is shown to have the most suitable pore size for the kinetic separation of CO₂ and CH₄.

《Fig. 3》

Fig. 3. (a–c) Self-diffusivity (D_s) of CO₂ in (a) CuFMOF-a, (b) CuFMOF-b, and (c) CuFMOF-c at 298 K. (d–e) Minimum potential energy of CH₄ (red) and CO₂ (blue) as a function of position along the 1D channel pore axis in (d) CuFMOF-a, (e) CuFMOF-b, and (f) CuFMOF-c. uc: unit cell.

《3.5. DFT-D calculations》

3.5. DFT-D calculations

To provide further insight into the interactions between the gas molecules and MOFs, we analyzed the interactions of CO₂ and CH₄with the framework at the maximum and minimum energy positions when a rigid molecule is moved along a 1D channel (Fig. 4; Figs. S10 and S11 in Appendix A). In the center of the capacious cage space of CuFMOF-c, the interactions between the CO₂ molecules and the MOF mainly occur through weak O^δ–H^δ+ dipole– dipole interactions (C–H…O) with a distance of 3.067–3.082 Å from the hydrogen atom on the aromatic ring (Fig. 4(c)). In addition, the CH₄ molecules form C–H···π bonds with a distance of 3.305 Å from the side of the aromatic ring that is rich in π-electrons (Fig. 4(e)). However, a large energy barrier exists when moving CH₄ and CO₂ through the narrow bottleneck connecting two cages along the b-axis direction. In this cramped site, CO₂ was restrained by stronger C–H···O bonds ranging from 2.453 to 3.083 Å (Fig. 4(d)). In contrast, CH₄ was firmly trapped via stronger C–H···π interactions of 3.113–3.218 Å from four surrounding symmetric aromatic rings (Fig. 4(f)), which formed a formidable steric hindrance to prevent the diffusion of CH₄, due to the molecular dimension of CH₄ being comparable to the pore size of the bottleneck structure. A similar phenomenon happened on CuFMOF-a and CuFMOF-b, as depicted in Figs. S10 and S11. These results are consistent with those of the diffusion energy barriers, further demonstrating the importance of pore size tuning for diffusion.

《Fig. 4》

Fig. 4. Scheme of (a) CO₂ and (b) CH₄ molecules moving through the 1D channel. MD was used to calculate the minimum energy binding sites of (c, d) CO₂ and (e, f) CH₄ in the center of the capacious cage space and the smallest bottleneck of the CuFMOF-c structure, which corresponds to the lowest points and the highest points in minimum potential energy diagrams, respectively. The different nets are highlighted in dark green and gray for clarity. Color code: Cu (green), F (yellow), C (gray), O (red).

《4. Conclusions》

4. Conclusions

In summary, we demonstrated the fine-tuning of a geometric structure through a guest solvent-directed strategy in a hydrothermal synthesis that created a subtle discrepancy in the 1D pore aperture of the structure. The highly selective kinetic separation of carbon dioxide and methane over a wide temperature range was realized due to the delicate aperture structure, which periodically outspread and contracted the cross-section of the channel, thereby allowing the entrance of CO₂ but severely hindering the diffusion of CH₄. Ultrahigh kinetic selectivity and equilibriumkinetic combined selectivity were achieved on CuFMOF-c, surpassing most top-performing adsorbents. This work not only offers a strategy for fine-tuning the host structure but also indicates that an appropriate pore size is a critical step for efficient kinetic separation, providing important clues for the kinetic separation of other gas mixtures with close size and structural similarity.

《Acknowledgments》

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China (21722609 and 21878260) and the Zhejiang Provincial Natural Science Foundation of China (LR170B060001).

《Compliance with ethics guidelines》

Compliance with ethics guidelines

Dan Lai, Fuqiang Chen, Lidong Guo, Lihang Chen, Jie Chen, Qiwei Yang, Zhiguo Zhang, Yiwen Yang, Qilong Ren, and Zongbi Bao declare that they have no conflict of interest or financial conflicts to disclose.

《Data availability statement》

Data availability statement

All crystallographic data are available free of charge from the Cambridge Crystallographic Data Centre. The data shown in the plots and those that support the findings of this study are available from the corresponding author on reasonable request.

CIF data for CuFMOF-a (CCDC number: 232689).

CIF data for CuFMOF-b (CCDC number: 1872560).

CIF data for CuFMOF-c (CCDC number: 2004270).

《Appendix A. Supplementary material》

Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2022.03.022.

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