Exploiting equilibrium-kinetic synergetic effect for separation of ethylene and ethane in a microporous metal-organic framework

A phosphate-anion pillared metal-organic framework can separate ethylene and ethane through synergism of equilibrium and kinetics.

Abstract

Physisorption is a promising technology to cut cost for separating ethylene (C₂H₄) from ethane (C₂H₆), the most energy-intensive separation process in the petrochemical industry. However, traditional thermodynamically selective adsorbents exhibit limited C₂H₄/C₂H₆ selectivity due to their similar physiochemical properties, and the performance enhancement is typically at the expense of elevated adsorption heat. Here, we report highly-efficient C₂H₄/C₂H₆ adsorption separation in a phosphate-anion pillared metal-organic framework ZnAtzPO₄ exploiting the equilibrium-kinetic synergetic effect. The periodically expanded and contracted aperture decorated with electronegative groups within ZnAtzPO₄ enables effective trapping of C₂H₄ and impedes the diffusion of C₂H₆, offering an extraordinary equilibrium-kinetic combined selectivity of 32.4. The adsorption heat of C₂H₄ on ZnAtzPO₄ (17.3 to 30.0 kJ mol⁻¹) is substantially lower than many thermodynamically selective adsorbents because its separation capability only partially relies on thermodynamics. The separation mechanism was explored by computational simulations, and breakthrough experiments confirmed the excellent C₂H₄/C₂H₆ separation performance of ZnAtzPO₄.

INTRODUCTION

As an important feedstock in petrochemical industries, ethylene (C₂H₄) is one of the highest-yield chemicals in the world with a global production capacity of more than 170 million tons in 2016 (1). C₂H₄ is usually manufactured by steam cracking and thermal decomposition of naphtha or ethane (C₂H₆), and the product inevitably contains a certain amount of C₂H₆ impurity. To obtain polymer-grade C₂H₄ as the raw material for downstream high value-added products, it is necessary to remove the residual C₂H₆, which is a challenging task due to the very close molecular size of C₂H₆ (3.81 Å × 4.08 Å × 4.82 Å) and C₂H₄ (3.28 Å × 4.18 Å × 4.84 Å) and their similar physical properties (2, 3). Industrial separation of C₂H₄ and C₂H₆ is generally realized by energy-intensive cryogenic distillation that requires very harsh operation conditions (4), typically at temperature as low as −90° to −15°C and pressure up to 23 bar under a high reflux ratio in distillation towers installed with more than 150 trays (5). The energy used for C₂H₄/C₂H₆ and C₃H₆/C₃H₈ separation accounts for more than 0.3% of the global energy consumption; therefore, developing energy-efficient methods for C₂H₄/C₂H₆ separation is highly demanded and is recognized as one of the most important industrial tasks to change the world’s energy footprint (6).

Adsorption separation enabling efficient gas purification under mild conditions is an energy-saving alternative technology to cryogenic distillation (7–13), and the key lies in developing advanced porous materials (14–16). With regard to C₂H₄/C₂H₆ separation, introducing transition-metal ions and unsaturated metal sites into the adsorbents has been widely accepted as a feasible approach (5, 17–21), because they can selectively interact with π-electrons of C₂H₄ molecules. However, the π-complexation–related materials generally present limited stability, especially in the presence of moisture and sulfides (22), and demand high energy cost for the adsorbents’ regeneration because of their strong affinity to C₂H₄ (23). Porous materials that are amenable to achieve complete molecular sieving are ideal for C₂H₄/C₂H₆ separation (24). However, to precisely control aperture size to a critical range necessary to exclude C₂H₆ is very challenging, and pores with such limited size typically lead to low diffusion rate and gas uptake. Considering that a practical separation process is simultaneously controlled by effects that arise from thermodynamics and kinetics, adsorbents that can exploit both equilibrium and kinetic selectivity are appealing for gas capture and purification (25, 26) but intractable to design and prepare. Previously, most porous materials reported for C₂H₄/C₂H₆ separation are principally based on their discrepant thermodynamic affinity for the guests (27–30). Only a few of zeolites and coordination polymer have been described as suitable substances for kinetic separation (31–33), largely because the analogous dimensions of C₂H₄ and C₂H₆ bring critical difficulty to fabricate pores with appropriate sizes that permit the passing of C₂H₄ while limiting the diffusion of slightly bulkier C₂H₆ molecules. Moreover, the ultimate efficiencies of reported kinetically selective adsorbents are basically confined by disadvantageous thermodynamic effects, in which case the capacity of C₂H₆ at the equilibrium state is quite close to or even exceeds that of C₂H₄ under a wide pressure range. These observations suggest that there is still a broad space to further enhance the separation of C₂H₄ and C₂H₆ by developing porous materials with optimal adsorption thermodynamics and kinetics.

Here, we reveal the high-efficient separation of C₂H₄ and C₂H₆ in a phosphate-anion (PO₄³⁻) pillared metal-organic framework (MOF) {Zn₃(Atz)₃(PO₄)}_∞ (ZnAtzPO₄; Atz = 3-amino-1,2,4-triazole) by exploiting synergetic effect of equilibrium and kinetics. The material features periodically expanded and contracted pore decorated by electronegative groups, which provides sufficient binding sites for C₂H₄ and effectively impedes the diffusion of C₂H₆, inducing an outstanding recognition ability to C₂H₄ over C₂H₆. The equilibrium-kinetic combined selectivity (32.4), as well as C₂H₄ capacity of ZnAtzPO₄, outperforms those of the state-of-the-art materials. The extraordinary performance was achieved along with ultralow adsorption heat (17.3 kJ mol⁻¹ for C₂H₄ at zero loading), and gas molecules adsorbed on the material can be easily removed at ambient temperature, indicating the promising prospect of the material for industrial application. DFT-D (dispersion-corrected density functional theory) calculations and molecular dynamics (MD) simulations were used to give insights into the unique separation mechanism, and breakthrough experiments for the C₂H₄/C₂H₆ (50:50, v/v) mixture were carried out to confirm the excellent performance of ZnAtzPO₄.

RESULTS

Pore structure and C₂H₄/C₂H₆ adsorption property

ZnAtzPO₄ was prepared by hydrothermal reaction of phosphoric acid, zinc carbonate basic, and Atz in a mixture of water, methanol, and aqueous ammonia under 180°C for 2 days (34). The structure of ZnAtzPO₄ contains two-dimensional cationic layers (fig. S1), which are fabricated by Zn²⁺ cations and deprotonated Atz ligands in both tridentate and bidentate coordination modes. The organic ligands only connect to Zn²⁺ cations via nitrogen atoms contained in the triazole rings, and the amino groups are all free of coordination. The layers are further pillared by PO₄³⁻ anions, resulting in the final porous framework of ZnAtzPO₄. As shown in Fig. 1A and fig. S1, the channel of ZnAtzPO₄ is decorated by intruding amino groups from bidentate-coordinated Atz ligands (highlighted by rose), which are arranged in an antiparallel manner along a, and abundant electronegative oxygen atoms from PO₄³⁻ anion pillars alongside the channel. The pillars adopt a staggered fashion, periodically contracting and expanding the cross section of the channel (Fig. 1B); therefore, the channel can be vividly described as iterant pocket-like space interconnected by narrow bottleneck structure. The pocket-like space each contains two symmetric passages (Fig. 1C) with the same size of 4.94 Å, which is enough to accommodate both C₂H₄ and C₂H₆ guests. In contrast, the neck is much narrower (3.82 Å, distance between N…N; Fig. 1D), which is quite close to the minimum dimension of C₂H₆ (3.81 Å) but apparently larger than that of C₂H₄ (3.28 Å). We anticipated that this delicate pocket-like structure would facilitate C₂H₄ trapping, but the narrow bottleneck would probably set a barrier for C₂H₆ to diffuse in the channel of ZnAtzPO₄.

Fig. 1. Schematic illustration of the structure of ZnAtzPO₄.

(A) Three-dimensional structure of ZnAtzPO₄ viewed from a. (B) Connolly surface indicating periodically expanded and contracted cross-section area of ZnAtzPO₄. (C) Schematic representation of the pocket-like space containing two symmetric passages. (D) Local environment and aperture size of the narrow bottleneck structure. [Color mode: C, gray (40%); H, gray (25%); N, light blue; Zn, sky blue; P, yellow; O, red. Bidentate-coordinated Atz ligands are highlighted by rose.]

Inspired by the eligible structure of ZnAtzPO₄, we further analyzed its thermodynamic and kinetic adsorption characteristics for C₂H₄ and C₂H₆ by measuring single-component adsorption isotherms and time-dependent gas uptake profiles. From the adsorption isotherms shown in Fig. 2A, ZnAtzPO₄ has a C₂H₄ uptake of 1.92 mmol g⁻¹ at 298 K and 1 bar, equivalent to 3.04 mmol cm⁻³ (table S1). The adsorption capacity of C₂H₄ is higher than C₂H₆ in the whole pressure range, indicative of its preferable thermodynamic affinity for C₂H₄. The C₂H₄/C₂H₆ uptake ratio reached 1.85 at 1 bar, exceeding that of some excellently performing equilibrium-based porous materials for C₂H₄/C₂H₆ separation, such as HKUST-1 (1.19) (35), zeolite 5A (1.42) (36), and PAF-1-SO₃Ag (1.82) (5). As the temperature reduced to 273 K, the gas uptake ratio further increased to 2.04, and the amount of C₂H₄ captured attained 2.41 mmol g⁻¹. Meanwhile, kinetic studies suggested that the material exhibited much faster adsorption rate for C₂H₄ than C₂H₆. As shown in Fig. 2B, the adsorption of C₂H₄ reached equilibrium within about 40 min at 298 K and about 45 min at 273 K, with the capacities consistent to those taken from adsorption isotherms. After a continuous recording for 150 min, the amount of C₂H₆ adsorbed on the sample still has not reached that under the equilibrium state and persists climbing up gradually. Fitting the data with micropore diffusion model gave a kinetic selectivity of 36.6 at 298 K and up to 140.7 at 273 K (table S1), highlighting the potential of ZnAtzPO₄ to separate the C₂H₄/C₂H₆ mixture through a unique equilibrium-kinetic synergetic effect, which has rarely been observed in MOFs (37). To objectively compare the separation performance of ZnAtzPO₄ with other adsorbents ever reported for C₂H₄/C₂H₆ separation, we further calculated the equilibrium-kinetic combined selectivity (38) based on their diffusivities and Henry’s constants for C₂H₄ and C₂H₆ gases. As shown in Fig. 2C and table S1, ZnAtzPO₄ displays a dramatic combined selectivity reaching up to 32.4 at 273 K. At ambient temperature, the selectivity is calculated as 12.4, higher than those of other kinetically selective adsorbents measured under similar conditions, like ITQ-29 (~1.31), Si-CHA (~1.31), and ITQ-55 (~6.4) (31, 32).

Fig. 2. Single-component gas adsorption properties.

(A) Single-component adsorption isotherms of C₂H₄ and C₂H₆ on ZnAtzPO₄ under 298 and 273 K. (B) Time-dependent gas uptake profiles of C₂H₄ and C₂H₆ at 0.4 bar and different temperatures. (C) Equilibrium-kinetic combined selectivity (C₂H₄/C₂H₆) and C₂H₄ uptake of ZnAtzPO₄, ITQ-29, Si-CHA, and ITQ-55. Data for ITQ-55 were collected at 303 K, and those for ITQ-29 and Si-CHA were collected at 301 K. (D) Highest value of Q_st calculated for C₂H₄ on ZnAtzPO₄, UTSA-280, zeolite 5A, Mg-MOF-74, Co-gallate, Fe-MOF-74, PAF-1-SO₃Ag, and (Cr)-MIL-101-SO₃Ag.

To evaluate the strength of interactions between ZnAtzPO₄ and C₂H₄/C₂H₆ gases, the isosteric heat of adsorption (Q_st) was calculated for C₂H₄ and C₂H₆ based on their adsorption isotherms under three different temperatures using the Clausius-Clapeyron equation (fig. S2). The material exhibits moderate Q_st for C₂H₄, with the value varying from 17.31 to 29.98 kJ mol⁻¹. It is worth mentioning that the maximum value of Q_st for C₂H₄ is remarkably lower than those of UTSA-280 (35.0 kJ mol⁻¹) (24), zeolite 5A (37 kJ mol⁻¹) (36), Co-gallate (44 kJ mol⁻¹) (3), and many other adsorbents containing transition-metal ions and unsaturated metal sites, such as Mg-MOF-74 (42.6 kJ mol⁻¹) (39), Fe-MOF-74 (47.5 kJ mol⁻¹) (20), PAF-1-SO₃Ag (106 kJ mol⁻¹) (5), and (Cr)-MIL-101-SO₃Ag (120 kJ mol⁻¹) (21) (Fig. 2D). The moderate heat of adsorption reveals the possibility to regenerate this material under mild conditions; thereby, oligomerization of C₂H₄ that may happen under the catalysis of open metal sites could be avoided. For equilibrium-based adsorbents, the effective adsorption separation of C₂H₄ and C₂H₆ principally relies on the discrepancy between the affinities of the gases to the adsorbent; here, usually high isosteric heat is required for the preferentially adsorbed guest to achieve desirable selectivity. In the case of ZnAtzPO₄, the excellent selectivity achieved under the modest Q_st largely owns its way to exploit the synergetic effect of equilibrium and kinetics, which means that the separation capability of ZnAtzPO₄ is only partially reliant on thermodynamics. The kinetic characteristics of ZnAtzPO₄ also contribute to maximize the purification performance, without affecting the adsorption heat.

Besides, ZnAtzPO₄ presents great stability to air and moisture. After the sample was exposed to humid atmosphere (298 K, 70% humidity) for 4 weeks, no obvious change in its powder x-ray diffractometry (PXRD) pattern could be observed as compared to the as-synthesized sample (fig. S3). C₂H₄/C₂H₆ adsorption isotherms and time-dependent gas uptakes measured on the sample revealed that, after such treatment, their sorption properties still remained almost unchanged (fig. S3). Furthermore, thermal gravimetric analysis (TGA) indicates that this material exhibits excellent thermal stability, with the decomposition temperature approaching 420°C (fig. S4). These results qualify ZnAtzPO₄ as a promising candidate for industrial separation of C₂H₄ and C₂H₆.

Exploring separation mechanism by computational method

To gain insights into the unusual equilibrium-kinetic synergetic effect of ZnAtzPO₄ to effectively adsorb C₂H₄, first-principles DFT-D calculations were conducted to explore the preferential binding sites. The computational results demonstrate that ZnAtzPO₄ provides two distinct binding sites for C₂H₄ (Fig. 3, A and B). The capacious pocket-like space each contains two symmetric apertures (Fig. 1C), and they offer identical binding site (site I) to the olefin and can be reckoned as molecule traps. In this site, C₂H₄ molecule interacts with the channel mainly through weak hydrogen bonding interactions (Fig. 3A). It locates close to the pillaring PO₄³⁻ anions and bonds to the surrounding oxygen atoms from three different pillars via C─H…O hydrogen bonds. The shortest C─H…O bond has a length of 2.65 Å, while the others are longer and range from 2.90 to 3.16 Å. In addition, the C₂H₄ guest also strengthens its interaction with ZnAtzPO₄ by forming C─H…N hydrogen bonds with nitrogen atom coming from both amino group and triazole ring of the Atz ligands, with lengths of 2.54 to 3.16 Å. The second binding site (site II, Fig. 3B) for C₂H₄ is near the center of the bottleneck structure, which joins two adjacent pockets. The mechanism for C₂H₄ to interact with the adsorbent in this site is quite different from that in site I (Fig. 3A), where the molecular interactions are mainly dominated by hydrogen bonds. In site II, there is only one quite weak C─H…O bond formed between C₂H₄ and the PO₄³⁻ pillar, with the length being 3.05 Å. Because of the specific chemical environment, the adsorbate is mainly stabilized by supermolecular N─H…C interactions with hydrogen atoms of the intruding amino groups from the bidentate-coordinated Atz ligands, and their lengths are in the range of 2.94 to 3.18 Å. The fact that there is a lack of strong hydrogen bond (C─H…O/N < 2.3 Å) (2) in sites I and II proves that the adsorbate merely interacts with the pore through weak intermolecular interactions, consistent to the quite modest value of Q_st as has been calculated. Furthermore, the DFT-D study on C₂H₆ reveals that unlike C₂H₄, the C₂H₆ molecule can only approach the binding site in the capacious pocket-like space (fig. S5). The molecular dimension of C₂H₆ is comparable to the size of the bottleneck structure, and it induces a steric hindrance to prevent the bottleneck to expose the second binding site to C₂H₆. The distinct modes between C₂H₄ and C₂H₆ to interact with the pore may be the reason that endows ZnAtzPO₄ with the excellent thermodynamic selectivity.

Fig. 3. DFT-D–calculated preferable binding sites for C₂H₄ in ZnAtzPO₄ and distribution of the aperture size of the bottleneck calculated from MD simulations.

(A) Site I. (B) Site II. [Color mode: C, gray (40%); H, gray (25%); N, light blue; Zn, sky blue; P, yellow; O, red. Bidentate-coordinated Atz ligands are highlighted by rose. Broken lines refer to C─H…N/O hydrogen bonds and supermolecular N─H…C interactions. All interatomic distances are in angstroms.] (C) Distribution of the aperture size of the bottleneck for empty structure of ZnAtzPO₄ (orange), ZnAtzPO₄ with C₂H₄ molecules (violet), and ZnAtzPO₄ with C₂H₆ molecules (gray) at 298 K.

The diffusion behaviors of C₂H₄ and C₂H₆ in the pore of ZnAtzPO₄ were further investigated by performing MD simulations to reveal the kinetic characteristics. The simulations demonstrate that, when each cell of ZnAtzPO₄ contains two gas molecules, the diffusivities of single-component C₂H₄ and C₂H₆ are 2.07 × 10⁻¹⁰ m² s⁻¹ and 7.17 × 10⁻¹² m² s⁻¹ under 298 K. The ideal kinetic selectivity is calculated as 29 and agrees well with the experimental measurement (~36). For the equimolar C₂H₄/C₂H₆ gas mixture, the diffusivities of C₂H₄ and C₂H₆ are 1.12 × 10⁻¹⁰ m² s⁻¹ and 7.47 × 10⁻¹² m² s⁻¹, respectively. Although the adsorption kinetics of C₂H₄ in the mixture declines as compared to its single component maybe due to the steric effect of slow-diffusing C₂H₆, the material still exhibits a prominent kinetic selectivity of 15. The results also indicate that after introducing C₂H₆ molecules to the channel of ZnAtzPO₄, the bottleneck exhibits obvious transient structural transformations to adapt to the sluggish passing of C₂H₆, and the aperture size prominently increases to 4.1 Å, about 0.3 Å larger than that without gas molecules (Fig. 3C). Snapshots (fig. S6) show that the expansion of the bottleneck-like window is mainly facilitated by slight rotation of the bidentate-coordinated Atz ligands that intrude amino groups to the channel. On the contrary, study on the diffusion of C₂H₄ reveals that after inserting the gas molecule to the channel, no obvious change in the aperture size of the bottleneck was observed, and its probability distribution is quite consistent to that of an empty host (Fig. 3C). These results suggest that the diffusion of C₂H₆ in the channel strongly relies on the flexibility of ZnAtzPO₄, considering that the size of the bottleneck (3.82 Å) at the ground state is so close to the extreme size (3.81 Å) to allow the passing of C₂H₆, setting a barrier for its penetration. The much smaller dimension of C₂H₄ (3.28 Å) allows it to travel along the pore more freely, without the necessity to expand the narrow windows, which thereby induces the marked kinetic selectivity of ZnAtzPO₄.

Breakthrough experiments

It is worth emphasizing that removal of C₂H₆ from C₂H₄ is yet a technical challenge in industry. To further probe the validity of the equilibrium-kinetic synergetic effect for C₂H₄/C₂H₆ separation, breakthrough experiments for a C₂H₄/C₂H₆ (50:50, v/v) gas mixture were performed on a stainless column packed with the ZnAtzPO₄ material at 273 K and 1 bar. As shown in Fig. 4A, the component of C₂H₆ broke through the column quickly after 26 min, whereas C₂H₄ was retained in the adsorption bed for nearly 70 min. The retention time for C₂H₄ is two times more than that of C₂H₆. Moreover, the elution of C₂H₄ was accompanied by a remarkable roll-up phenomenon of C₂H₆, meaning that the C₂H₆ molecules that have already been adsorbed can be largely displaced by the olefin, indicative of the excellent competition ability of C₂H₄ over C₂H₆ on the binding sites of ZnAtzPO₄. After the concentration of eluting gas remained unchanged, the amount of C₂H₄ adsorbed into the column reached 1.80 mmol g⁻¹, equivalent to 6.7 times that of C₂H₆ (0.27 mmol g⁻¹) (fig. S7), highlighting the great efficiency of ZnAtzPO₄ for actual C₂H₄/C₂H₆ adsorption separation. Besides, recycling measurements reveal that ZnAtzPO₄ can retain its separation capability, with the breakthrough time being almost unchanged within five cycles (Fig. 4B and fig. S7). After simple desorption procedure manipulated by purging the material with inert gas (He) at ambient temperature, the column was well regenerated and reserved similar breakthrough curve (fig. S7), benefitting from the very modest adsorption heat as has been calculated. This further presents ZnAtzPO₄ as a brilliant microporous material for industrial separation of C₂H₄ and C₂H₆. By exploiting the equilibrium-kinetic synergetic effect, we successfully achieved the high-efficient C₂H₄/C₂H₆ adsorption separation with ZnAtzPO₄. With the solid empirical evidence, we believe that it would bring a new train of thoughts and tactics for the splitting of close-boiling light hydrocarbons.

Fig. 4. Breakthrough curve and recycling tests for C₂H₄/C₂H₆ gas mixture on ZnAtzPO₄.

(A) Breakthrough curve of ZnAtzPO₄ for C₂H₄/C₂H₆ gas mixture (50:50, v/v) at 273 K and 1 bar with a flow rate of 0.75 ml/min. (B) Recycling breakthrough tests for C₂H₄/C₂H₆ (50:50, v/v) separation with ZnAtzPO₄.

DISCUSSION

In summary, we reported the separation of C₂H₄/C₂H₆ in a phosphate-anion pillared microporous MOF, which exhibits a unique equilibrium-kinetic combined selectivity to the olefin and is attractive for practical separation. The equilibrium-kinetic synergetic effect of ZnAtzPO₄ mainly originates from its delicate pore structure, featuring periodically expanded and contracted cross section. Its minimum aperture size approaches the limit for C₂H₆ to pass through, and the diffusion of C₂H₆ depends on transient structural transformations of the neck-like structure, which seriously slows down the diffusion rate of the paraffin. On the other hand, the pore of ZnAtzPO₄ is decorated with abundant electronegative functional groups that are amenable to construct stable interaction network with C₂H₄ and trap the olefin efficiently. Computational methods were applied to explore the binding sites of the guest molecules and further verify the faster adsorption kinetics of C₂H₄. Moreover, recycling breakthrough experiment for the C₂H₄/C₂H₆ gas mixture (50:50, v/v) was carried out, and it confirmed the outstanding capability of ZnAtzPO₄ for C₂H₄/C₂H₆ separation.

As most porous materials ever reported for C₂H₄/C₂H₆ separation are typically based on single mechanism (either thermodynamic or kinetic), examples to explore synergetic effect of equilibrium and kinetics in this regard are rare. The unprecedented selectivity achieved on ZnAtzPO₄ proves that the strategy conveyed by this work is feasible and practical and highlights a broad space to further boost the adsorption separation of C₂H₄ and C₂H₆ in a newfangled way. Taking advantage of such synergetic effect allows highly efficient selective adsorption of C₂H₄ under modest Q_st, because the separation process only partially relies on thermodynamics. As a glaring merit, the material can be regenerated under mild conditions with less energy consumption. In brief, this work not only provides a porous material with impressive C₂H₄ purification performance but also brings a new strategy for developing the next-generation materials for energy-efficient gas separation.

MATERIALS AND METHODS

Experimental design

Chemicals

All the chemicals were obtained from commercial resources and used as received without any further purification. Methanol (anhydrous, 99%) was purchased from Sigma-Aldrich. Phosphoric acid [85 weight % (wt %)], ammonium hydroxide (30 wt %), and 3-amino-1,2,4-triazole (96%) were purchased from Macklin. 3Zn(OH)₂·2ZnCO₃ was purchased from Strem Chemicals.

Synthesis of {Zn₃(Atz)₃(PO₄)}_∞ (ZnAtzPO₄)

Samples of ZnAtzPO₄ were synthesized according to the literature report (34) with minor modifications. A mixture containing 0.035 g of phosphoric acid, 0.1 g of 3Zn(OH)₂·2ZnCO₃, 0.4 g of 3-amino-1,2,4-triazole, 2 ml of H₂O, and 2 ml of methanol was added to a Teflon tube, then sealed and placed in an oven with a temperature of 180°C for 48 hours, and cooled to room temperature naturally. The colorless precipitation was collected by filtration, then washed with methanol, and dried in air. Last, the product was heated at 60°C under high vacuum for 2 hours and then at 100°C for another 12 hours to obtain the activated sample of ZnAtzPO₄.

Characterization methods

PXRD data were collected on a SHIMADZU XRD-600 diffractometer (Cu K_αλ = 1.540598 Å) with an operating power of 40 kV, 30 mA, and a scan speed of 4.0°/min. The range of 2θ was from 5° to 50°. TGA data for activated sample of ZnAtzPO₄ were recorded on an apparatus of TGA Q500 V20.13 Build 39, from room temperature to 800°C, with a ramp of 10°/min under N₂ atmosphere.

Kinetic adsorption measurement

The time-dependent adsorption profiles of C₂H₄ and C₂H₆ were measured on Intelligent Gravimetric Analyzer (IGA-100, HIDEN). About 100 mg of ZnAtzPO₄ was first loaded to the sample chamber and activated at 100°C under high vacuum for 4 hours. After being cooled to specific temperature, the chamber was backfilled with He, until the pressure reached 0.4 bar. Upon the analysis started, a single-component gas of C₂H₄ or C₂H₆ was introduced into the chamber at a rate of 35 ml/min. The mass of the sample loaded with gas molecules was continuously recorded for 150 min.

Statistical analysis

The equilibrium-kinetic combined selectivity (S_ij) is defined as (38)

$$S_{\mathit{ij}}={\mathrm{\alpha }}_{\mathit{ij}}\times {{\mathrm{\beta }}_{\mathit{ij}}}^{0.5}$$ (1)

In Eq. 1, α_ij represents the separation selectivity based on thermodynamic equilibrium alone and can be calculated from the ratio of Henry’s constants (Eq. 2). β_ij represents the kinetic selectivity based on diffusion rates of the gas molecules and can be obtained from the ratio of diffusion time constants (Eq. 3)

$${\mathrm{\alpha }}_{\mathit{ij}}=H_i/H_j$$ (2)

$${\mathrm{\beta }}_{\mathit{ij}}={D\text{'}}_i/{D\text{'}}_j$$ (3)

In Eq. 3, D′ (D_c/r_c²) can be further derived from the following micropore diffusion model (Eq. 4), where m_t is the gas uptake at time t, m_∞ is the gas uptake at equilibrium, D_c is the intracrystalline diffusivity of gas molecules in porous media, and r_c is the radius of the equivalent spherical particle. D′ can be obtained from the square of the slope ($\frac{m_t}{m_{\infty }}$ plotted against $\sqrt{t}$) multiplied by π/36

$$\frac{m_t}{m_{\infty }}\approx \frac{6}{r_c}\sqrt{\frac{D_{C}t}{\mathrm{\pi }}}(m_t/m_{\infty } <0.3)$$ (4)

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/15/eaaz4322/DC1