## Introduction

Physisorptive separation using porous sorbents has been of interest for some time17,18,19,20. In principle, sorbents can supercede traditional distillation separation methods and offer low energy consumption with easy operation and excellent safety. In the past two decades, metal-organic frameworks (MOFs), also known as porous coordination polymers, have emerged as a promising class of physisorbents for the capture, separation, and purification of light hydrocarbon gas mixtures21,22. Based on the concept of crystal engineering, MOFs can be fine-tuned in terms of pore size and pore chemistry23,24,25,26. in a manner that is infeasible for traditional porous sorbents such as activated carbon and zeolites27,28. The separation of gas mixtures via physisorption depends on several factors, including polarity, size, and shape of gas molecules. In general, the greater the difference in these factors, the easier it is to achieve efficient separation. The physisorptive separation of industrially gas mixtures such as ethylene/ethane29,30,31,32,33, ethylene/acetylene19,34,35,36, acetylene/carbon dioxide37,38,39, propylene/propyne40,41, and propane/propylene20,42,43 exemplify what seemed intractable challenges that have recently been addressed by microporous MOFs with suitable pore size and chemistry to enable selective binding. Propyne/propadiene separation, however, (Fig. 2a) remains unresolved. Whereas thermodynamically driven separation (Fig. 2b) has proven effective for other separations, it is mitigated here by the almost identical polarizability of propyne vs. propadiene (55.5 × 10−25 cm3 vs. 56.9 × 10−25 cm3)44,45,46. These critical requirements cause difficulty for separation propyne/propadiene mixtures47.

Here, we address the challenge of propyne/propadiene separation and report a thermodynamic-kinetic dual-drive separation strategy (Fig. 2d) using microporous MOF adsorbents with dense open metal sites (OMSs) and cage-based molecule traps which would offer the needed performance driven by two factors: (i) The C ≡ C moiety in propyne offers distinct binding to OMSs. (ii) The pore shapes of adsorbents can be adjusted to control gas diffusion to enhance the dynamic screening effect. Our study reveals that microporous MOFs with both a high-density of OMSs and restricted cage-based molecule traps, as exemplified by HKUST-1 and MOF-505, exhibit the best separation performance by comprehensive comparison of a range of candidate sorbent. Importantly, HKUST-1 is one of the few MOFs that has been manufactured at an industrial scale with current production methodology offering a space-time yield of 400,000 kg m−3 day−148.

## Results and discussion

### Structure and basic characterizations

We selected a sorbent library comprising traditional porous materials (activated carbon and zeolites) and three types of MOFs (14 different sorbents) classified as follows: (I) MOFs with OMSs, including HKUST-1, MOF-505, Mg-MOF-74, NKMOF-1-Ni, MIL-100-Cr, MIL-100-Fe and MIL-101-Cr; (II) Hybrid ultramicroporous MOFs with strong binding sites (e.g., SiF62− and NbOF52), including SIFSIX-2-Cu-i, SIFSIX-3-Ni, UTSA-200 (SIFSIX-14-Cu-i) and ZU-62; (III) MOFs without strong binding sites, including UiO-66, UiO-67, and ZIF-8 (Supplementary Table 1 for detailed structural parameters). Screening of this library was conducted by dynamic breakthrough tests to find the best performing candidates for propyne/propadiene separation. In addition, the equilibrium adsorption isotherms, simulated gas sorption studies, and kinetic adsorption behavior of the library were evaluated (Fig. 3). Activated carbon and zeolites were obtained via commercial sources. All MOFs samples in this study were prepared according to the previous procedures reported in the literature or using appropriately modified procedures. Powder X-ray diffraction (PXRD), BET surface area measurement, and scanning electron microscopy (SEM) data (Supplementary Figs. 16) confirmed that all MOFs possessed high crystallinity and the expected sorption parameters.

### Single-component equilibrium adsorption isotherms

Isosteric heat of adsorption (Qst) values reflect the affinity of a sorbent for a sorbate and are an indicator of thermodynamically driven separation. Type-I microporous MOFs with OMSs could be classified into two categories: (i) HKUST-1 and MOF-505 with cage-based molecule trap structure (Supplementary Fig. 11); (ii) Mg-MOF-74 and NKMOF-1-Ni with the regular one-dimensional channel. Their Qst were evaluated by the Clausius–Clapeyron equation through fitting the adsorption isotherm using dual-site Langmuir (DSL) model and dual-site Langmuir–Freundlich (DSLF) model equation (Supplementary Figs. 1215). The initial Qst values for propyne and propadiene for HKUST-1, MOF-505, Mg-MOF-74, and NKMOF-1-Ni were 42 and 40, 78 and 58, 53 and 46, 65 and 54 kJ mol−1, respectively (Supplementary Fig. 16). Qst towards propyne was higher than that of propadiene for all optimized MOFs with OMSs. Massively Parallel MC (MPMC) theoretical calculations also indicated that the binding affinity for propyne was stronger than that for propadiene47.

Ideal adsorbed solution theory (IAST) selectivity can be used to estimate thermodynamic separation performance. The selectivity of microporous MOFs with OMSs was calculated using IAST through fitting gas isotherm at 298 K by the DSL and DSLF equation (Supplementary Figs. 1215). Considering the context of industrial separations, we calculated based on a propyne/propadiene (50/50, ν/ν) mixture at 298 K (Fig. 6a). NKMOF-1-Ni exhibited the highest selectivity of 6.0 with a selectivity > 4.8 across the pressure range. The selectivities of HKUST-1 and Mg-MOF-74 were slightly lower than NKMOF-1-Ni in the low-pressure area (<0.01 bar) and tended to be consistent with each other under the remaining pressure range (0.01–1 bar). These selectivity results indicate that microporous MOFs with OMSs materials should possess good separation performance.

In order to further evaluate separation performance, transient breakthrough simulations were conducted for propyne/propadiene feed mixtures (50/50, ν/ν) at 298 K and 1 bar using the methodology described in earlier publications46. Fig. 3b showed the outlet concentrations of propyne exiting in the fixed bed of HKUST-1, MOF-505, Mg-MOF-74, and NKMOF-1-Ni as a function of the dimensionless time, τ, for propyne/propadiene mixture. Although the IAST selectivity of NKMOF-1-Ni was the highest, the τ break value for NKMOF-1-Ni was not the highest, possibly attributing to its lowest uptake capacity for propyne. The simulated dynamic breakthrough results are related to adsorption selectivity, uptake capacity, and crystal density, etc. The hierarchy of the τ break values in the MOFs with OMSs is HKUST-1 > Mg-MOF-74 > MOF-505 > NKMOF-1-Ni. HKUST-1, MOF-505, Mg-MOF-74, and NKMOF-1-Ni demonstrated efficient and similar separation performance for propyne/propadiene (50/50, ν/ν) mixture.

### Kinetic adsorption study

In summary, our study emphasizes the importance of both kinetics and thermodynamics with respect to the separation performance of propadiene vs. propyne. Dynamic gas mixture breakthrough experiments revealed that MOFs with OMSs and cage-based molecule traps exhibited such synergy to afford benchmark separation performance (propadiene production up to 69.6 cm3/g, purity > 99.5%) whereas traditional porous materials such as activated carbon and zeolites showed no separation effect. Our study offers a design principle for sorbent selection along with a screening protocol that might be broadly applied for sorbent evaluation.

## Methods

### Preparation of MOF materials and characterization

All samples were synthesized according to Supplementary Method 2. PXRD test was conducted using microcrystalline samples on a Rigaku Ultima IV diffractometer (40 kV, 40 mA, Cu Kα1, 2λ = 1.5418 Å). The measured parameter included a scan speed of 2 (°)/min, a step size of 0.02 (°). All MOFs samples were tested by ASAP 2020 PLUS Analyzer (Micromeritics) with Dewar (liquid N2) and a homemade intelligent temperature control system (0–80 °C). The SEM images were obtained on HITACHI SU3500.

### Breakthrough experiment

The breakthrough experiments were performed at a flow rate of 2 mL/min (298 K, 1.01 bar) for the propyne/propadiene (50/50, v/v) mixture. The MOF powder was packed into Φ 4 × 150 mm stainless steel column and activated by blowing pure helium (He). The column stacking density and column voidages of all samples tested were controlled in a similar condition. The breakthrough set-up consisted of two same fixed-bed stainless steel columns. One was used as a test sample and the other as a blank control to stabilize the gas flow. Both columns were housed in a temperature control system. The flow rates of all gases were regulated by mass flow controllers. The composition of the efflux gas of the test sample column was monitored by gas chromatography (Shimadzu, GC 2030, FID-Flame Ionization Detector, detection limit 100 ppb).

The propadiene productivity (q) was calculated by integration of the breakthrough curves f(t). The purity of propadiene is higher or equal to a threshold value during the integration interval from t1 to t2

$$q=\frac{{C}_{i}({{{{{\rm{propadiene}}}}}})}{{C}_{i}\left({{{{{\rm{propyne}}}}}}\right)+{C}_{i}({{{{{\rm{propadiene}}}}}})}\times \left({\int }_{t2}^{t1}f(t){dt}\right)$$

### Kinetic adsorption isotherm test

The kinetic adsorption behavior of HKUST-1, MOF-505, Mg-MOF-74, and NKMOF-1-Ni was performed on thermogravimetric analysis Instruments (Q50). During the test, we controlled the gas flow rate of propyne and propadiene to be 20 cm3/min. The data was collected in the High-Resolution Dynamic mode with a sensitivity of 1.0, a resolution of 4.0, and the weight changes during propyne and propadiene gas adsorption step were monitored under the isothermal condition at 25 °C (298 K).

### Qst, IAST and transient breakthrough simulation calculation

The Qst was determined from the unary isotherm by use of the Clausius–Clapeyron equation. IAST calculations were carried out for the following mixture 50/50 propyne/propadiene mixture at 298 K. Transient breakthrough simulations were carried out for 50/50 propyne/propadiene feed mixture at 298 K and 100 kPa.