Customizing Pore System in a Microporous Metal–Organic Framework for Efficient C₂H₂ Separation from CO₂ and C₂H₄

Abstract

Selective-adsorption separation is an energy-efficient technology for the capture of acetylene (C₂H₂) from carbon dioxide (CO₂) and ethylene (C₂H₄). However, it remains a critical challenge to effectively recognize C₂H₂ among CO₂ and C₂H₄, owing to their analogous molecule sizes and physical properties. Herein, we report a new microporous metal–organic framework (NUM-14) possessing a carefully tailored pore system containing moderate pore size and nitro-functionalized channel surface for efficient separation of C₂H₂ from CO₂ and C₂H₄. The activated NUM-14 (namely NUM-14a) exhibits sufficient pore space to acquire excellent C₂H₂ loading capacity (4.44 mmol g⁻¹) under ambient conditions. In addition, it possesses dense nitro groups, acting as hydrogen bond acceptors, to selectively identify C₂H₂ molecules rather than CO₂ and C₂H₄. The breakthrough experiments demonstrate the good actual separation ability of NUM-14a for C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures. Furthermore, Grand Canonical Monte Carlo simulations indicate that the pore surface of the NUM-14a has a stronger affinity to preferentially bind C₂H₂ over CO₂ and C₂H₄ via stronger C-H···O hydrogen bond interactions. This article provides some insights into customizing pore systems with desirable pore sizes and modifying groups in terms of MOF materials toward the capture of C₂H₂ from CO₂ and C₂H₄ to promote the development of more MOF materials with excellent properties for gas adsorption and separation.

1. Introduction

Accompanied by worldwide economic advances, energy demand and supply have appeared cumulatively prominent; the thirst for high-purity raw materials, conveniently feasible technological streams, and desired final products has turned into even more unprecedented impendency. Industrial chemical separations occupy a large proportion of the quotient of global energy consumption, which has achieved a spectacular 10–15%, amounting to half of the usage amount of industrial energy in the United States [1]. Among the multitudinous commodity chemicals involving industrial interest, acetylene (C₂H₂) and ethylene (C₂H₄) are the two kinds of the most critical feedstocks for the electronic industry and polymerization manufacturing. Mature C₂H₂ fabrication methods in the petrochemical industry mainly rely on thermal cracking of hydrocarbons or partial oxidation of natural gas, and then obtained C₂H₂ production can be employed to cut/weld metals or manufacture diversiform high-value chemicals, such as vinyl chloride, acetaldehyde, acrylic acid derivatives, and synthetic fiber/rubber [2]. However, carbon dioxide (CO₂) as an unwished impurity is inevitably mingled in the obtained C₂H₂ production during the aforementioned preparation processes, which will ultimately injure the quality of the downstream chemical products [3]. Therefore, the separation of C₂H₂/CO₂ mixtures became of great importance in the petrochemical industry. In addition, C₂H₄, as an indispensable building block in the chemical synthesis industry with global annual production about 201 Mt by 2020, is generally used to manufacture polyethylene, vinyl chloride, ethylene oxide, etc. [4]. C₂H₄ is usually obtained by the catalytic cracking of hydrocarbons and steam cracking of naphtha; nevertheless, trace amounts of C₂H₂ as contaminants often inevitably coexist in C₂H₄ production. These C₂H₂ impurities about 1000–5000 ppm not only would significantly affect the quality of the resulting polyethylene but also can further form solid metal acetylide to block the fluid stream-triggering explosion [5]. Under this background, capturing trace C₂H₂ from C₂H₂/C₂H₄ mixture to purify C₂H₄ also became an imperative task. The similar geometric characteristics, including molecular size and shape, and alike physical properties mainly referring to the boiling point between C₂H₂ and CO₂ or C₂H₄ molecules, render the separations of C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures as high-challenge scientific problems [6,7,8]. Researchers in the petrochemical industry have devoted massive efforts to pursuing solutions for overcoming these separation difficulties. The current commercial pathway principally depends on cryogenic distillation, which has a high energy penalty and expensive economic cost. Porous materials utilizing selective physisorption with high energy efficiency, low investment cost, and environmentally friendly peculiarity might provide a promising alternative to separate these troublesome mixtures.

Metal–organic frameworks (MOFs) with large surface area, high porosity, fascinating modularity, and abundant functionality, as new-style crystalline porous materials, are constructed with metal ions/clusters and organic linkers. Because of their unique characteristics, MOFs have received wide attention in numerous application fields, such as gas storage and separation, heterogeneous catalysis, proton conduction, and fluorescence detection [9,10,11,12]. The most remarkable advantage of MOF materials over other traditional porous materials (such as zeolite, silica gel, and porous carbon) lies in the tunability of the pore system, predominantly referring to pore size/shape and pore surface chemistry. Plentiful adsorption-based MOFs were explored to address C₂H₂ separations challenges, which have obtained certain achievements [13,14]. Although a large number of research results indicated that incorporating strong binding sites (such as Lewis basic sites and open metal sites) into large-pore MOFs can effectively promote high C₂H₂ uptake capacities, most of them exhibited low separation selectivity and even terrible actual dynamic breakthrough properties due to their large pore size [15,16]. On the other side, the introduction of fluorinated anions (such as SiF₆²⁻, NbOF₅²⁻, and TiF₆²⁻) as hydrogen-bonding acceptors (HBAs) into ultra-microporous pillared hybrid MOFs can preferentially bind C₂H₂ molecules to dramatically enhance the separation selectivity [17,18]. However, the majority of ultra-microporous MOFs with excellent separation performance exhibited relatively low C₂H₂ loading capacity owing to their limited pore space. Recently, through the structure–performance relationship screening of 62 reported top-performing C₂H₂ adsorbents, Zhai et al. found that tuning the aperture of MOFs within the range of moderate pore size (5.0–7.5 Å), combined with accessible HBAs, is an effective route to break through the trade-off barrier between C₂H₂ storage and C₂H₂/CO₂ separation [19]. Many studies have shown that embedding functional groups (such as -F, -NO₂, -NH₂, -OH) into MOF channels can also improve the separation selectivity of C₂H₂/C₂H₄ without a slight sacrifice in intrinsic moderate pore volumes or surface areas to adsorb a large amount of the objective gas molecules [20,21]. Therefore, if a porous MOF contains a suitable pore system that is simultaneously provided with both moderate pore size and high-density accessible functional groups like HBAs, it may synchronously possess satisfactory separation performance for C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures. Although multiple design strategies, such as the isoreticular chemistry principle [22], pore–space partition strategy [23], and forming structural interpenetration [24], have been developed to guide the synthesis of desired MOF materials, difficult challenges still remain in customizing MOF materials with desirable pore systems. This is because even subtle effects can lead to undesirable results in the uncontrollable and complex self-assembly process of the MOFs.

Herein, we designed and synthesized a novel Ni-MOF {[Ni(TPT)(NPC)(H₂O)]·solvent}_n (NUM-14, TPT = 2,4,6-tri(4-pyridinyl)-1,3,5-triazine, H₂NPC = 3-nitrophthalic acid), featuring a desired pore size of 5.8 Å and functionalized pore environment decorated by abundant nitro groups serving as hydrogen bond receptors, which can preferentially capture C₂H₂ for achieving efficient separation of C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures. The single-component adsorption isotherms indicate that NUM-14a (activated NUM-14) has a good adsorption capacity for C₂H₂ with 4.44 mmol g⁻¹, exceeding some cutting-edge MOF materials. The predicted IAST selectivities and practical breakthrough experiments for C₂H₂/C₂H₄ and C₂H₂/CO₂ mixtures demonstrated that NUM-14a has favourable separation potential for these two kinds of mixed gases. Moreover, the values of Q_st calculation quantitatively vindicated that NUM-14a owns the strongest interaction with C₂H_2, stronger than with CO₂ and C₂H₄, which is also proved from another side by Grand Canonical Monte Carlo (GCMC) calculations. Both experimental and theoretical results show that NUM-14a can realize the efficient separation of C₂H₂ from CO₂ and C₂H₄, and that this fine performance mainly comes from its suitable pore system.

2. Results and Discussion

2.1. Single Crystal X-ray Diffraction Structure

The solvothermal reaction of TPT, H₂NPC, and Ni(NO₃)₂ in a DMF/H₂O mixed solvent system at 100 °C for 72 h harvested jade-green blocky crystals of as-synthesized NUM-14. The crystallographic structure analysis manifested that NUM-14 crystallizes in the trigonal P3₁21 space group. The asymmetric unit of NUM-14 contains one Ni²⁺ atom, half of deprotonated NPC²⁻ ligand, and a half of TPT ligand. Each Ni²⁺ atom has a six-coordinate mode to form slightly distorted octahedral geometry with three N atoms from three different TPT ligands and two carboxylate O atoms from two different NPC²⁻ linkers, as well as one terminal water molecule. Each NPC²⁻ ligand connected two Ni²⁺ atoms to form a 1D infinite helix chain spiraling counterclockwise along the c axis. Each TPT ligand also coordinate with two Ni²⁺ atoms to generate two kinds of infinite 1D helix chains along the c axis, in which one of them rotates clockwise and another inversely rotates counterclockwise (Figure S1). Then three types of spiral chains make up one channel column. The remaining end of TPT ligands as pore wall on each channel column is connected to the adjacent channel column to form two kinds of one-dimensional channel structures along the c axis, one of which is the triangular channel with an aperture of about 6 Å while the another is similar to the former except that the nitro groups on the NPC²⁻ linkers toward its interior (Figure 1b–d). The coordinate mononuclear Ni²⁺ octahedron and TPT ligand can be simplified as 5- and 3-connected nodes, respectively (Figure 1a). Therefore, NUM-14 can be simplified as a 2-nodal 3,5-connected topology network with the point symbol of (4·7²)(4³·6²·7⁴·8) (Figure 1b) [25]. Calculation by PLATON revealed that the solvent-accessible volume in fully desolvated NUM-14 is 59.4%. The accessible channel surface in NUM-14a is mainly composed of the pyridine/triazine rings and abundant nitro groups in ligands, getting a very polar and rich hydrogen bond receptor pore environment.

2.2. Purity and Stabilities of NUM-14

The experimental and activated PXRD patterns are strongly consistent with the simulated model based on the single-crystal data confirming the high-phase purity and skeleton stability after the degassing of NUM-14 (Figure S2). The thermostability was demonstrated by TGA. As shown in Figure S3, it can be seen that the skeleton of NUM-14 remains stable up to 300 °C. As shown in Figure S4, through testing PXRD of NUM-14 samples soaked in various common solvents for 1 week, we found that NUM-14 acquits itself well in solvent stability under different conditions.

2.3. Gas Adsorption Properties of NUM-14a

The activated sample of NUM-14a was prepared by heating the CH₂Cl₂-exchanged sample under preset high vacuum conditions at 40 °C for the duration of 10 h. Then, the N₂ sorption isotherm was recorded at 77 K to characterize and evaluate the permanent porosity of NUM-14a. As indicated in Figure 2a, it shows a reversible type-I adsorption curve with the saturated loading of 289.9 cm³ g⁻¹ and is akin to multitudinous typical microporous MOF materials [26,27]. According to the N₂ adsorption isotherm, the BET (Brunauer–Emmett–Teller) and Langmuir surface areas were calculated, which reached 1075.5 and 1194.2 m² g⁻¹, respectively. The Horvath–Kawazoe method was applied to calculate the pore size distribution and the result exhibited the main aperture concentrates upon 5.8 Å, which allows small gas molecules to pass through easily.

Combining with appropriate pore size and functionalized polar surface, NUM-14a is promising for evaluating C₂H₂ adsorption and separation performance from CO₂ and C₂H₄. As shown in Figure 2b,c, single-component sorption isotherms of NUM-14a for C₂H₂, CO₂, and C₂H₄ were measured at 273 and 298 K. Under 1 bar, these pure-component gas adsorption isotherms revealed that the C₂H₂ adsorption capacities of NUM-14a are 143.1 and 99.5 cm³ g⁻¹ at 273 and 298 K, respectively, which is markedly higher than that of CO₂ (102 and 50.2 cm³ g⁻¹) and C₂H₄ (115.8 and 82.7 cm³ g⁻¹), implying the distinctly stronger adsorption ability of NUM-14a for C₂H₂ than CO₂ and C₂H₄. Noteworthily, the adsorption capacity of C₂H₂ (4.44 mmol g⁻¹) at 298 K and 1 bar in NUM-14a is superior to most top-performing MOFs, like Zn-FBA (1.03 mmol g⁻¹) [28], IPM-101 (2.55 mmol g⁻¹) [29], ZNU-1 (3.41 mmol g⁻¹) [30], ZNU-4 (3.58 mmol g⁻¹) [31], and ZJU-74a (3.83 mmol g⁻¹) [32], which is attributed to its high porosity. Moreover, the C₂H₂/CO₂ uptake ratio at 298 K and 1 bar for NUM-14a reaches 1.98, while the uptake ratio of C₂H₂/C₂H₄ is only 1.20. Inspired by the distinctive uptake capacity and preferential binding of C₂H₂ for NUM-14a, we then calculated the isosteric enthalpies of adsorption (Q_st), a crucial metric that quantifies the interaction strength between gas molecules and pores in MOFs, by the Virial-type equation to quantitatively estimate the binding affinity between gas molecules and host framework (Figures S5–S7). The calculated Q_st at near-zero coverage for C₂H₂ (31.57 kJ mol⁻¹) is higher than CO₂ (22.89 kJ mol⁻¹) and C₂H₄ (23.67 kJ mol⁻¹), demonstrating the relatively stronger host–guest affinity for NUM-14a toward C₂H₂ in contrast to CO₂ and C₂H₄ (Figure 2d). These results of Q_st are adequately consistent with the gas adsorption behaviors as depicted in single-component isotherms and prove the feasibility of the C₂H₂ preferential adsorption in the framework of NUM-14a.

2.4. Gas Separation Performances of NUM-14a

Given the preferential capture and stronger affinity of C₂H₂ than CO₂ and C₂H₄ in NUM-14a, IAST was further adopted to evaluate the separation performances of NUM-14a for C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures. Single-component adsorption isotherms of C₂H₂ and C₂H₄ obtained from experimental determinations were fitted by the dual-site Langmuir–Freundlich model, while the isotherms of CO₂ were fitted by the single-site Langmuir–Freundlich equation for pursuing the more accurate consistency between experimental data and theoretical model (Figures S8–S13). The fitting results were then used to predictably calculate adsorptive selectivities for equimolar C₂H₂/CO₂ and C₂H₂/C₂H₄ with two different ratios of 50/50 or 1/99 at 273 and 298 K (Figure 3a,b). As revealed in Figure 3b, the calculated selectivity of NUM-14a for equimolar C₂H₂/CO₂ (50:50, v/v) is 3.37 at 298 K and 100 kPa, which is lower than some famous MOF materials under the same conditions, such as CuI@UiO-66-(COOH)₂ (185.00) [33], ATC-Cu (53.60) [34], and MOF-OH (25.00) [35], and slightly lower than that of FJU-118a (7.80) [36], BUT-85 (6.10) [37], but higher than many other well-known materials, such as [Ca(dtztp)_0.5] (1.70) [38], [Ni(tzba)_0.5(F)(bpy)] (2.20) [39], CAU-10H (2.50) [40] and SNNU-5-Sc (2.66) [41]. Due to the similar C₂H₂ and C₂H₄ adsorption behavior, although NUM-14a exhibits relatively low selectivities for C₂H₂/C₂H₄ mixtures with volume ratios of 1:99 (1.63) and 50:50 (1.61) at 298 K and 100 kPa, the result for C₂H₂/C₂H₄ (1:99, v/v) is still comparable to many consequences of reported MOFs, such as 1.13 for NUM-12a [42], 1.61 for Zn(ad)(int) [4], 1.59 for ZJNU-14 [43], 1.77 for ZJNU-7 [44], and 2.1 for UiO-67-(NH₂)₂ (Table S2) [45].

To further evaluate the separation performance of NUM-14a for C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures, we performed dynamic breakthrough experiments in a packed tube using NUM-14a as physical adsorbent at 298 K under a total inlet gas flow rate of 2 mL min⁻¹. As shown in Figure 4a, the breakthrough curve clearly proves that NUM-14a can effectively separate the C₂H₂/CO₂ mixture. When the equimolar C₂H₂/CO₂ gas mixture passes through the adsorption column, the CO₂ gas first elutes due to its deficient uptake capacity. Then, C₂H₂ breaks through the packed column with a penetration time of 19 min g⁻¹ and the adsorbent slowly tends to saturate soon afterward. Ultimately, the outlet gas flow reaches adsorption equilibrium with the same components as the imported stream at 55 min g⁻¹. Similarly, the separation performance of NUM-14a for the equimolar C₂H₂/C₂H₄ mixture is described in Figure 4b. The experiment result displays that C₂H₂ gas can be more preferably adsorbed in the separation unit than C₂H₄, so the pure C₂H₄ can be obtained with a time interval of 5 min g⁻¹, which is shorter than the breakthrough time of the C₂H₂/CO₂ mixture because of the stronger adsorption capacity of C₂H₄ relative to CO₂. These breakthrough tests undoubtedly testify to the ability of NUM-14a for separating C₂H₄ from mixtures containing CO₂ or C₂H₄.

2.5. Adsorption Mechanism

To profoundly investigate the interesting gas adsorption behaviors between the preferential sites and adsorbed gas molecules within NUM-14a, GCMC calculations were conducted to probe the interaction between the gas molecules and the host framework at 298 K and 1 bar. As shown in Figure 5a, for adsorbed C₂H₂ in pores, three strong binding sites of hydrogen bonds were found, where two distances of C-H···O between C₂H₂ and two nitro oxygen atoms are 2.378 Å and 3.608 Å, and the distance of C-H···O between terminal hydrogen atom of C₂H₂ and one carbonyl oxygen atom is 2.611 Å. The CO₂ molecule only interacts with the framework of NUM-14a through one weak C-H···O (3.562 Å) hydrogen bond interaction between acidic hydrogen atom on the pyridine ring and the basic oxygen atom at the end of CO₂ molecule (Figure 5b). For the C₂H₄ molecule which has weaker acidic than C₂H₂ and therefore has a weaker affinity to basic sites, two hydrogen bond interactions between C₂H₄ with two nitroxides were sought with long C-H···O distances (2.487 and 3.074 Å) (Figure 5c). By comparing GCMC calculation results, we can find that the pore surface of NUM-14a shows a stronger recognition effect on C₂H₂ molecules than CO₂ and C₂H₄, explaining the reason for outstanding capture and separation performance of C₂H₂ in NUM-14a observed in experiments.

According to the adsorption data, we can find that NUM-14a has a good adsorption capacity for C₂H₂, which is mainly attributed to its medium pore size and large porosity. Moreover, the combination of separation experiments and the simulation calculations shows that NUM-14a has stronger binding forces for C₂H₂ compared with CO₂ and C₂H₄, which is possibly ascribed to the stronger synergistic hydrogen bond interactions between C₂H₂ and nitro group and the exposed oxygen atom. All of these prove that the customized fabrication of a pore system with moderate pore size and modified surface with HBAs in MOFs is beneficial to separate C₂H₂/CO₂ and C₂H₂/C₂H₄ mixtures.

3. Materials and Methods

3.1. Materials and Characterization

All chemicals and reagents were purchased from commercial suppliers and used without further purification. Powder X-ray diffraction (PXRD) was measured on a Rigaku Miniflex 600 with Cu Kα radiation (λ = 1.5425 Å) under air conditions. Thermogravimetric analysis (TGA) was recorded on a Rigaku standard thermogravimetry-differential thermal analysis (TG-DTA) analyzer, utilizing an empty and clean Al₂O₃ crucible as reference (heating rate = 10 °C min⁻¹ in Ar atmosphere).

3.2. Gas Sorption Measurements

Before the sorption measurement, the sample of NUM-14 was soaked in dichloromethane for 3 days to exchange solvent molecules in the channels. The degas procedure for the solvent-exchanged NUM-14 was conducted at 40 °C under a high vacuum (less than 10⁻⁵ Torr) for 10 h and led to the formation of activated sample NUM-14a. The N₂ sorption isotherm measurement was carried out using a Micrometrics ASAP 2460 volumetric gas adsorption analyzer at 77 K in a liquid nitrogen bath. The C₂H₂, C₂H₄, and CO₂ sorption isotherm measurements were carried out at 273 and 298 K respectively using a Micrometrics ASAP 2020M volumetric gas adsorption analyzer.

3.3. X-ray Crystallography

Single-crystal X-ray diffraction data of NUM-14 were collected on the Rigaku XtaLAB PRO MM007 DW diffractometer with Cu Kα radiation (λ = 1.54184 Å) at T = 99.99 (1) K. The structure was solved with the SHELXT program and refined by full-matrix least-squares against F² using the SHELXL program [46,47]. Anisotropic thermal parameters were implemented to all non-hydrogen atoms, and all hydrogen atoms were placed in the calculated positions and refined with isotropic thermal parameters. The Solvent Mask in Olex2 software was employed to remove scattering contributions of the disordered solvent molecules and the generated solvent-free data of direction intensities were further refined [48]. Details of the crystal parameters, data collection, and refinement of NUM-14 are listed in Table S1.

3.4. Synthesis of NUM-14

A solvothermal reaction of Ni(NO₃)₂·6H₂O (29.0 mg, 0.1 mmol), TPT (18.7 mg, 0.06 mmol), and H₂NPC (21.1 mg, 0.1 mmol) in 2.5 mL of a mixed solvent of DMF/H₂O (4:1, v/v) was kept at 100 °C for 3 days, and blocky crystals of NUM-14 were first time synthesized in 83% yield based on the TPT ligand. When the reaction temperature slowly cooled to room temperature, a fresh sample was collected by filtration and washed with fresh DMF several times.

3.5. Isosteric Enthalpy of Adsorption Calculations

The experimental adsorption data of C₂H₂, CO₂, and C₂H₄ at 273 and 298 K in NUM-14a were fitted using a virial model (Equation (1)):

$$\mathit{ln}\mathit{P}=\mathit{ln}\mathit{N}+\frac{\mathbf{1}}{\mathit{T}}{\displaystyle \mathbf{\sum }}_{\mathit{i}=\mathbf{0}}^{\mathit{m}}{\mathit{a}}_{\mathit{i}}{\mathit{N}}^{\mathit{i}}+{\displaystyle \mathbf{\sum }}_{\mathit{j}=\mathbf{0}}^{\mathit{n}}{\mathit{b}}_{\mathit{j}}{\mathit{N}}^{\mathit{j}}$$

(1)

where P is the pressure in Torr, N is the adsorbed amount in mmol g⁻¹, T is the temperature in K, and a_i and b_j are virial coefficients.

The isosteric enthalpies of adsorption (Q_st) were calculated based on the fitted virial coefficients using the following equation (Equation (2)):

$${\mathit{Q}}_{\mathit{s}\mathit{t}}=-\mathit{R}{\displaystyle \mathbf{\sum }}_{\mathit{i}=\mathbf{0}}^{\mathit{m}}{\mathit{a}}_{\mathit{i}}{\mathit{N}}^{\mathit{i}}$$

(2)

Q_st is the coverage-dependent isosteric heat of adsorption and R is the universal gas constant.

3.6. Adsorption Selectivity Calculations

Ideal adsorbed solution theory (IAST) was utilized to predict gas adsorption selectivity of binary mixtures from the experimental single-component isotherms of C₂H₂, CO₂, and C₂H₄ [49]. The experimental pure-component adsorption isotherms of C₂H₂ and C₂H₄ were initially fitted by the dual-site Langmuir–Freundlich model (Equation (3)), while CO₂ was fitted by the single-site Langmuir–Freundlich model. That is, only the first half of Equation (3) is used to fit the experimental data to obtain a perfect fitting degree:

$$\mathit{q}=\frac{{\mathit{q}}_{\mathit{A},\mathit{s}\mathit{a}\mathit{t}}{\mathit{b}}_{\mathit{A}}{\mathit{p}}^{\mathbf{1}/{\mathit{n}}_{\mathbf{1}}}}{\mathbf{1}+{\mathit{b}}_{\mathit{A}}{\mathit{p}}^{\mathbf{1}/{\mathit{n}}_{\mathbf{1}}}} +\frac{{\mathit{q}}_{\mathit{B},\mathit{s}\mathit{a}\mathit{t}}{\mathit{b}}_{\mathit{A}}{\mathit{p}}^{\mathbf{1}/{\mathit{n}}_{\mathbf{2}}}}{\mathbf{1}+{\mathit{b}}_{\mathit{B}}{\mathit{p}}^{\mathbf{1}/{\mathit{n}}_{\mathbf{2}}}}$$

(3)

where p is the pressure in kPa, q is the adsorbed amount in mmol g⁻¹, and q_A,sat and q_B,sat are the saturation capacities of two distinct adsorption sites A and B in mmol g⁻¹. b_A and b_B are the affinity coefficients in kPa⁻¹, and n₁ and n₂ represent the deviations from an ideal homogeneous surface.

Then the fitted parameters were used to calculate the selectivity (Equation (4)):

$${\mathit{S}}_{\mathit{A}/\mathit{B}}=\frac{{\mathit{X}}_{\mathit{A}}/{\mathit{X}}_{\mathit{B}}}{{\mathit{Y}}_{\mathit{A}}/{\mathit{Y}}_{\mathit{B}}}$$

(4)

In which, X_i and Y_i represent the mole fractions of component i in the adsorbed and bulk phases, respectively.

3.7. Breakthrough Experiments

The breakthrough experiments for C₂H₂/CO₂ (50:50, v/v) and C₂H₂/C₂H₄ (50:50, v/v) mixtures were completed on the Multi-component Adsorption Breakthrough Curve Analyzer from Beishide Instrument Technology Co., Ltd. (Beijing, China). An activated crystalline powder sample (1.30 g) was packed into a breakthrough column (6 mm diameter and 4 mL volume) with a 3 cm length of the sample loading, which was purged with He flow (50 mL min⁻¹), sustaining 120 min at 40 °C before each breakthrough experiment. Subsequently, the mixed gas flows of C₂H₂/CO₂ and C₂H₂/C₂H₄ with a flow rate of 2 mL min⁻¹ were respectively introduced into the adsorber at 298 K. At the same time, the compositions of effluents from the packed column were monitored and analyzed in real-time by online mass spectrometry.

3.8. Grand Canonical Monte Carlo Simulations

The GCMC simulations were performed for the adsorption of C₂H₂, CO₂, and C₂H₄ in NUM-14a with the Material Studio 8.0. The optimal adsorption sites were simulated under 298 K with a pressure of 1.0 bar. We used 1.0 × 10⁷ cycles for equilibration, and the production steps were set to 1.0 × 10⁶. The framework of NUM-14a and adsorbate molecules were treated as a rigid structure. A standard Lennard–Jones and Coulomb model was used and the Lennard–Jones parameters for the framework atoms as well as adsorbate molecules were adopted from the universal force field (UFF). Ewald summation was used to calculate electrostatic interactions for both adsorbent–adsorbate and adsorbateadsorbate interactions.

4. Conclusions

In summary, we constructed a new Ni-based MOF NUM-14, which has a fascinating pore system featuring an appropriate pore size and pleasant pore environment, to separate C₂H₂ well from CO₂ and C₂H₄. By a feat of its pore characteristic, NUM-14a can adsorb more C₂H₂ than CO₂ and C₂H₄. With the advantages of a nitro-functionalized pore wall framework, NUM-14a expresses greater affinity to C₂H₂ through hydrogen bond interactions. Furthermore, the strong pure-component gas adsorption behavior and favorable C₂H₂/CO₂, and C₂H₂/C₂H₄ separation performance are achieved by NUM-14a. In addition, the underlying selective adsorption mechanism and separation reason are revealed by GCMC simulations at the molecular level. This work can guide the designed synthesis of desirable MOFs with a tailor-made pore system and practical application of them for high-challenge gas separation problems.