# Nanosheets of a Layered Metal–Organic Framework for Separation of CO2/CH4 using Mixed Matrix Membranes

Meng He, Yinlin Chen, Wanpeng Lu, Lixia Guo, Kui Hu, Xue Han, Inigo Vitorica-Yrezabal, Catherine Dejoie, Andrew N. Fitch, Martin Schröder, et al.

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Meng He, Yinlin Chen, Wanpeng Lu, Lixia Guo, Kui Hu, et al. Nanosheets of a Layered Metal–Organic Framework for Separation of CO2/CH4 using Mixed Matrix Membranes. ACS Applied Materials & Interfaces, 2024, 16 (25), pp.32524–32532. 10.1021/acsami.4c05611. hal-05098733

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# Nanosheets of a Layered Metal–Organic Framework for Separation of CO₂/CH₄ using Mixed Matrix Membranes

Meng He, Yinlin Chen, Wanpeng Lu, Lixia Guo, Kui Hu, Xue Han, Inigo Vitorica-Yrezabal, Catherine Dejoie, Andrew N. Fitch, Martin Schröder,* and Sihai Yang*

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Cite This: ACS Appl. Mater. Interfaces 2024, 16, 32524–32532

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**ABSTRACT:** Mixed matrix membranes represent an important technology for gas separations. Nanosheets of metal–organic framework (MOF) materials of high aspect ratio and size-selective gas transport properties have the potential to promote the efficient mixing of components to form membranes for gas separation. Herein, we report a bottom-up synthesis of extended sheets of kagomé (kgm) topology, $kgm^{t-Bu}$, via the linkage of [Cu₂(O₂CR)₄] paddlewheels with 5-tert-butylisophthalic acid. The growth of the layered structure can be controlled by the choice of solvent and modulator. Nanosheets of $kgm^{t-Bu}$ of average thickness of 20 nm and aspect ratio of 40 to 50 can be obtained, and the sieving effect of the channels in $kgm^{t-Bu}$ boost the efficient separation of CO₂ over CH₄. A mixed matrix membrane comprising $kgm^{t-Bu}$ nanosheets with Matrimid shows a 32% enhancement in CO₂/CH₄ selectivity compared with the membrane incorporating the MOF in the particulate form.

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**KEYWORDS:** metal–organic framework, nanosheet, powder diffraction, mixed-matrix membranes, gas separation

## 1. INTRODUCTION

Membrane-based gas separation is considered advantageous over energy-intensive separation techniques such as distillation.¹,² However, conventional polymeric gas separation membranes are limited by the intrinsic trade-off between the gas permeability and selectivity often described by the gas-pair dependent upper bounds.³,⁴ Porous materials such as zeolites and metal–organic framework (MOF) materials demonstrate enhanced gas separation performance well beyond the upper bounds of membranes.⁵ However, preparations of stand-alone membranes of these porous materials are nontrivial due to their crystalline nature.⁶ As an alternative, mixed matrix membranes (MMMs) afford a practical strategy in utilizing porous materials for high-performance gas separation membranes by distributing particles of porous material within a continuous polymer matrix.⁷

MOFs have been investigated as efficient solid physisorbents due to their selective adsorption and transport properties, and this has attracted interest in transferring these properties into MMMs for membrane-based gas separations.⁸⁻¹⁰ However, inadequate mixing between the polymer matrix and MOF can lead to the formation of heterogeneous phases and performance-deteriorating defects.¹¹ More efficient mixing within membranes may be achieved by functionalization and shaping of MOF particles.¹²,¹³ Recently, MOFs with nanosheet morphology have received much attention in the preparation of MOF/polymer MMMs.¹⁴⁻¹⁶ These nanosheets are characterized by a high aspect ratio of lateral dimensions with respect to thickness, as well as aligned pores along a

specific crystallographic direction due to the preferred orientation. Nanosheets of MOFs can be prepared top-down via exfoliation of its bulk material using sonication,¹⁷ ball milling,¹⁸ or intercalation.¹⁹ Alternatively, they can be synthesized bottom-up from their respective building blocks by exploiting synthetic methodologies in a controllable manner to form nanosheets of desired size and shape.¹⁴,¹⁵,²⁰⁻²³ Nanosheets derived from both 2D layered and nonlayered MOFs have been prepared by methods including diffusion-modulated growth,¹⁴ surfactant-assisted synthesis,¹⁵ and crystal growth control.²² Unlike the top-down approach that relies on preordered layered MOF structures, the bottom-up approach allows facile manipulation of the exposed facet and channel alignment along with controllable size and shape of the resultant material. For example, [001]-oriented nanosheets of the pillar-layered AlFFIVE-1-Ni can be prepared by controlling the concentration of the pillaring component and temperature.²² Nanosheets of (001)-AlFFIVE-1-Ni have been incorporated and aligned in-plane within polyimide matrices, where the 1D channels of the MOF structure lie in the [001] direction. As a result, the nanosheet effectively provides a short gas diffusion pathway with molecular sieving effects leading to

Received: April 6, 2024

Revised: May 19, 2024

Accepted: May 20, 2024

Published: June 13, 2024

<figure><img src="image_9.png" /></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 1.** Views the structure of kgm**t-Bu**. Views of (a) the structure of the linker and [Cu₂(OOCR)₄] paddlewheel, (b) the monolayer showing the two types of channels, (c) the triangular motif, and (d) the hexagonal motif consisting of [Cu₂(OOCR)₄] paddlewheel and linkers. View of (e) the projection of the layered structure along the *c* axis and (f) the AA stacking of layers along *c*-axis (viewed in the *ab* plane). Color: carbon, gray; oxygen, red; copper, cyan. Hydrogen and oxygen atoms of axial coordinated water on [Cu₂(OOCR)₄] paddlewheels have been omitted for clarity.</figcaption></figure>

MMMs with outstanding CO₂/CH₄ and H₂S/CH₄ separation performance at up to 60 wt % MOF loading.²²

Herein, we report the synthesis of a layered MOF, named **kgm**<sup>t-Bu</sup> (**kgm** = kagomé), constructed by reaction of Cu(II) salts with 5-tert-butylisophthalic acid (5-*t*-Bu-H₂ip). The structure comprises undulating metal–ligand monolayers of **kgm** topology, and these stack in an AA fashion to form two distinct 1D channels with a narrowest opening of 3.2 Å. Inspired by the solvent-induced interlayer separation effect of dimethylformamide (DMF) on isostructural MOFs,²⁴ nano-sheets of **kgm**<sup>t-Bu</sup> (*ns*-kg **m**<sup>t-Bu</sup>) were obtained by using 1:1 DMF/MeOH as a solvent to slow down the packing of layers. In addition, acetic acid was added to modulate the crystal growth via linker exchange, and this led to the formation of *ns*-**kgm**<sup>t-Bu</sup> with a thickness of ca. 20 nm and aspect ratios of 40–50. Notable differences in morphology, surface area, and gas adsorption properties were observed between the bulk particles of **kgm**<sup>t-Bu</sup> (*bp*-**kgm**<sup>t-Bu</sup>) and *ns*-kg **m**<sup>t-Bu</sup>. MMMs prepared with *ns*-**kgm**<sup>t-Bu</sup> and Matrimid exhibit superior CO₂/CH₄ selectivity over both the bare polyimide membrane and the membranes prepared from *bp*-kg **m**<sup>t-Bu</sup> and Matrimid. Molecular dynamics simulations of the diffusivities of CO₂ and CH₄ within **kgm**<sup>t-Bu</sup> unveiled a size-screening effect originating from the distinct channels formed by the nanosheets of **kgm**<sup>t-Bu</sup>.

## 2. EXPERIMENTAL METHODS

**2.1. Chemical and Materials.** Cu(NO₃)₂·3H₂O, 5-tert-butylisophthalic acid (5-*t*-Bu-H₂ip), benzimidazole, pyridine, and chloroform (CHCl₃) were purchased from Sigma-Aldrich, Cu(CH₃COO)₂·H₂O from Alfa Aesar, and N,N-dimethylformamide (DMF), acetic acid (AcOH), ethanol (EtOH), and methanol (MeOH) from Fisher

Scientific. All chemicals were used as received without any further treatment. Polyamide (PI) Matrimid 5218 was purchased from Huntsman Advanced Materials and activated under dynamic vacuum at 453 K overnight to remove adsorbed moisture prior to the preparation of membranes.

**2.2. Synthesis of Single Crystals of kgm**<sup>t-Bu</sup>. Single crystals of **kgm**<sup>t-Bu</sup> (*sc*-**kgm**<sup>t-Bu</sup>) were prepared via slow diffusion according to a modified procedure.²⁵ A solution of DMF and EtOH (1:1, 3 mL) containing 5-*t*-Bu-H₂ip (11 mg, 0.05 mmol) and benzimidazole (3.0 mg, 0.025 mmol) was placed at the bottom of an 8 mL Wheaton vial. An aqueous solution (1.5 mL) of Cu(NO₃)₂·3H₂O (12 mg, 0.05 mmol) was layered onto the ligand. The vial was sealed and left upright at room temperature for over a week to give light blue hexagonal crystalline plates.

**2.3. Synthesis of Bulk bp-kgm**<sup>t-Bu</sup>. Bulk powder of **kgm**<sup>t-Bu</sup> (*bp*-**kgm**<sup>t-Bu</sup>) was prepared by mixing and stirring a solution of DMF/MeOH (1:1, 20 mL) containing Cu(NO₃)₂·3H₂O (240 mg, 1 mmol) and 5-*t*-Bu-H₂ip (222 mg, 1 mmol) with pyridine (81.7 µL, 1 mmol) for 24 h at room temperature. A blue precipitate was obtained via centrifugation and washed 3 times with DMF to remove unreacted ligands and metal salts. Residual DMF and pyridine were removed by solvent exchange multiple times with acetone. Light blue *bp*-**kgm**<sup>t-Bu</sup> (28 mg) was obtained as a powder after drying in the air. Element analysis was performed for [Cu(5-*t*-Bu-ip)(H₂O)]·0.5CH₃OH or C₁₂.₅H₁₆O₅.₅Cu. Calcd (%), C: 47.23, H: 5.03, Cu: 20.01. Found (%), C: 47.35, H: 4.92, Cu: 19.08.

**2.4. Synthesis of Nanosheet ns-kgm**<sup>t-Bu</sup>. Cu(CH₃COO)₂·H₂O (50 mg, 0.25 mmol) and 5-*t*-Bu-H₂ip (55 mg, 0.25 mmol) were each dissolved in DMF/MeOH (1:1, 20 mL). Acetic acid (143 µL; 10 mol equiv) was added as modulator to the solution of 5-*t*-Bu-H₂ip, and the solution of metal salt was added dropwise into it over 30 min from a dropping funnel under stirring. The solution became cloudy after about 1 h and was left stirring for 24h. The precipitate was collected and washed following the same procedure as for the bulk sample
above. The blue powder product (11.3 mg) was obtained after drying in air and then dispersed and stored under CHCl₃ for further use. For the preparation of membranes, the nanosheets were activated by heating at 453 K to remove residual solvent and moisture.

### 3. RESULTS AND DISCUSSION

#### 3.1. Synthesis and Structure of Single Crystals and Bulk Powder of kg m⁻¹-Bu.
Single crystals of kgm⁻¹-Bu (sc-kgm⁻¹-Bu) were prepared by layering an aqueous solution of Cu(NO₃)₂ over a layer of DMF/EtOH (v/v = 1/1) containing the linker 5-t-Bu-H₂ip (Figure 1a) and benzimidazole as a modulator. Slow diffusion and mixing of Cu(II) ions and the linker results in light blue hexagonal single crystals after 3 days. The single-crystal X-ray structure of [Cu₂(C₁₂H₁₅O₄)₂(H₂O)₂] confirms the formation of a layered structure of kgm topology, isostructural with other reported kgm materials (Figure 1b).²⁴,²⁶ Within the monolayer, three [Cu₂(OOCR)₄] paddlewheels are linked by three linkers to form a triangular frustum-shaped motif. A secondary pseudohexagonal motif is formed by six surrounding triangular motifs to create a pocket space with a 4.8 Å maximum diameter (Figure 1c). The triangular motifs in the monolayer point alternatively in opposite directions, and this results in an undulated structure (Figure 1e) with neighboring layers stacked upon each other to form two types of channels. Channel I is formed via the stacking of the triangular motifs, featuring a polar surface decorated with O-centers from carboxylates and the coordinated water molecule on the [Cu₂(OOCR)₄] paddlewheel. Channel II is formed via stacking of the pseudohexagonal motifs, possessing a nonpolar internal surface due to surrounding tert-butyl groups from the linker. Both channels adopt irregular interior shapes as an array of stacking cones. The aperture of both channels is constrained by the hydrogen atoms of the linker, with the narrowest opening in both channels measuring approximately 3.2 Å in diameter based upon the crystallographic structure (Figure S6).

Bulk bp-kgm⁻¹-Bu was obtained by mixing equimolar quantities of Cu(NO₃)₂·3H₂O and 5-t-Bu-H₂ip in the presence of 1 equiv of pyridine in DMF/MeOH (v/v = 1/1). Powder X-ray diffraction (PXRD) patterns of bp-kgm⁻¹-Bu show that peaks at 7.3° and 9.5° are missing compared to the simulated pattern from the single crystal structure (Figure 2). Le Bail refinement²⁷ of the PXRD pattern using the trigonal space group P-3m1 (No. 164) yielded a set of unit cell parameters [a

<figure><img src="image_11.png" /><figcaption>**Figure 2.** PXRD patterns of ns-kgm⁻¹-Bu and bp-kgm⁻¹-Bu and the oriented pattern of nanosheets with the simulated pattern based upon the structural model obtained from refinement of the structure of sc-kgm⁻¹-Bu.</figcaption></figure>

= 18.7298(12), c = 7.0647(6) Å], which differ from those of the single crystal structure [a = 18.5264(3), c = 12.1041(2) Å]. The shorter c axis suggests that the metal-ligand layers pack more tightly in the powder structure than in the single crystal structure, and this was confirmed by the crystal structure of bp-kgm⁻¹-Bu obtained by the Rietveld refinement of synchrotron PXRD data. Unlike sc-kgm⁻¹-Bu where the adjacent monolayers interact through weak van der Waals forces, the monolayers in bp-kgm⁻¹-Bu interact strongly via hydrogen bonds formed between the axial water on the [Cu₂(OOCR)₄] paddlewheel units with an O···O distance of 3.17(6) Å. As inspired by previous studies on solvent-induced interlayer separation,²⁴ the effect of solvent on the layered structure was investigated. Two new PXRD peaks at 6.9° and 8.8° appeared on immersing bp-kgm⁻¹-Bu in DMF, indicating an expansion of unit cell parameters to a = 18.74(3), c = 12.89(2) Å], close to the lattice parameters derived from the single crystal X-ray structure (Figure 3a). Similar features were reproduced when

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Interlayer expansion of the structure of kgm⁻¹-Bu. Effects of (a) DMF and (b) THF on the PXRD patterns of bp-kgm⁻¹-Bu and (c) schematic illustration of the solvent-induced interlayer expansion.</figcaption></figure>

immersing bp-kgm⁻¹-Bu in THF. Interestingly, the interlayer expansion can be reversed on drying the THF-immersed sample in air (Figure 3b). This suggests that close packing of monolayers in the presence of polar solvent such as DMF and THF and that interlayer separation can thus be controlled by the choice of solvent mix.
**3.2. Synthesis and Structure of ns-kgm**<sup>t-Bu</sup>. A bottom-up synthesis method was adopted to form nanosheets of the layered MOF. Previously reported **kgm** MOFs have used MeOH and pyridine as the solvent and modulator, respectively, in their synthesis.<sup>24,26</sup> However, direct mixing of these components leads to rapid precipitation of bulk **bp-kgm**<sup>t-Bu</sup>, so a methodology to control the crystal growth was required in order to generate nanosheets of ns-kgm<sup>t-Bu</sup>. [Cu(OAc)<sub>2</sub>] incorporating a preformed [Cu<sub>2</sub>(OOCR)<sub>4</sub>] paddlewheel structure was therefore used with acetic acid as a modulator to control carboxylate linker-exchange rate between the carboxylates in [Cu(OAc)<sub>2</sub>] and 5-*t*-BuH<sub>2</sub>ip.<sup>12,28,29</sup> Based on the above observations on the solvent effects on the observed layered structures, a 1:1 mixture of DMF and MeOH was used as the solvent to control the packing of monolayers in favor of nanosheet formation.

The PXRD pattern for ns-*kgm*<sup>t-Bu</sup> showed peak positions matching those of *bp-kgm*<sup>t-Bu</sup> (Figure 2). An oriented PXRD sample of ns-*kgm*<sup>t-Bu</sup> was prepared by placing drops of nanosheet suspension onto zero background plates to investigate the preferred orientation of the nanosheets. The out-of-plane pattern of the oriented ns-*kgm*<sup>t-Bu</sup> sample showed 3 main peaks at 12.1°, 24.6°, and 37.4° corresponding to the (001), (002), and (003) planes, respectively, suggesting that the monolayers in ns-*kgm*<sup>t-Bu</sup> stack preferentially along the *c*-axis aligned with the channel openings.

The effects of reaction time and concentration of modulator on the preparation of ns-*kgm*<sup>t-Bu</sup> were investigated and optimized by monitoring the dimensions of the product using atomic force microscopy (AFM). For ns-*kgm*<sup>t-Bu</sup>, by increasing the reaction time from 4 to 8 h at a fixed concentration of acetic acid at 10 equiv, the obtained nanosheets increase in thickness from an average of 15.7 to 19.3 nm (Figure 4a,b). However, prolonging the reaction time to 24 h resulted in a negligible change in the observed thickness (Figure S3a) nor lateral dimensions of the nanosheets (Figure S3c). The concentration of the acetic acid modulator shows notable impacts on both the thickness and lateral dimensions of the nanosheets (defined by the length of the hexagonal edge). Using 5 equiv of acetic acid in the synthesis afforded sheets of an average thickness of 8.5 nm and lateral dimensions of less than 500 nm. Increasing to 10 equiv of acetic acid led to an increase in thickness to 19.3 nm with lateral dimensions extended to 870 nm. At 20 equiv of acetic acid the dimensions were only slightly increased to 19.9 nm in thickness with lateral dimensions of 939 nm, within the error of nanosheets prepared with 10 equiv of modulator (Figure S3b). These results confirm that acetic acid functions as a structure-directing agent, promoting the growth of monolayers along the *ab*-plane. This modulator, in combination with the mixed solvents, effectively regulate the packing of monolayers and facilitate the formation of nanosheets with aspect ratios of 40–50. Using 10 equiv of acetic acid and a reaction time of 24 h resulted in a reproducible synthesis of ns-*kgm*<sup>t-Bu</sup> with stable morphology and low thickness, and this form was thus chosen in the preparation of MMMs.

**3.3. Characterization of ns-kgm**<sup>t-Bu</sup> and *bp-kgm**<sup>t-Bu</sup>. The SEM/TEM images of ns-*kgm*<sup>t-Bu</sup> and *bp-kgm*<sup>t-Bu</sup> show clear differences in morphology: *bp-kgm*<sup>t-Bu</sup> exhibits thick plates in random shapes with a thickness of over 100 nm as measured by AFM (Figure 5c,d). In comparison, ns-*kgm*<sup>t-Bu</sup> shows hexagonal features (Figure 4) with a much lower thickness of an average 20 nm and high aspect ratio of 40–50

<figure><img src="image_13.png" /><figcaption>**Figure 4.** Effect of reaction time and acetic acid modulator on the thickness of ns-*kgm*<sup>t-Bu</sup>. AFM height images of nanosheets prepared with reaction times of (a) 4 h, (b) 8 h, and (c) 24 h in the presence of 10 equiv of acetic acid. Views of nanosheets prepared with (d) 5 equiv, (e) 10 equiv, and (f) 20 equiv of acetic acid at the same reaction time of 8 h.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 5.** SEM images of (a) ns-*kgm*<sup>t-Bu</sup> and (c) *bp-kgm*<sup>t-Bu</sup>. AFM height images of (b) ns-*kgm*<sup>t-Bu</sup> and (d) *bp-kgm*<sup>t-Bu</sup> with insets of height profiles along marked lines.</figcaption></figure>

(Figure 5a,b, S4). The N<sub>2</sub> adsorption isotherms for ns-*kgm*<sup>t-Bu</sup> and *bp-kgm*<sup>t-Bu</sup> at 77K were measured after activation at 333 K, and the Brunauer–Emmett–Teller (BET) surface areas (S<sub>BET</sub>) extracted from these isotherms were determined as 368 and 232 m<sup>2</sup> g<sup>-1</sup>, respectively (Figure 6a). Activation of the materials at 453 K removed the coordinated water molecules on the [Cu<sub>2</sub>(OOCR)<sub>4</sub>] paddlewheel, and S<sub>BET</sub> further increased to 468 and 386 m<sup>2</sup> g<sup>-1</sup> for ns-*kgm*<sup>t-Bu</sup> and *bp-kgm*<sup>t-Bu</sup>, respectively (Figure 6b). The T-plot analysis of the N<sub>2</sub>
<figure><img src="image_15.png" /><figcaption>**Figure 6.** Adsorption isotherms measured at 77 K for N₂ in ns-*kgm*⁻t-Bu and bp-*kgm*⁻t-Bu activated at (a) 333 K and (b) 453 K. Adsorption isotherms of (c) CO₂ and (d) CH₄ in ns-*kgm*⁻t-Bu and bp-*kgm*⁻t-Bu at 298 K.</figcaption></figure>

isotherms at 77 K afford the external surface area and pore volume for the samples activated at 453 K. The material ns-*kgm*⁻t-Bu displays an external surface area of 179 m² g⁻¹ compared with bp-*kgm*⁻t-Bu at 91.3 m² g⁻¹, while the micropore volume are similar between the two samples (0.1189 vs 0.1196 cm³ g⁻¹, respectively). Thus, the high aspect ratio of ns-*kgm*⁻t-Bu contributes significantly to the higher N₂ adsorption. An H1-type hysteresis was observed for ns-*kgm*⁻t-Bu at high relative pressure (P/P₀ > 0.7) and assigned to interparticle porosity formed by the stacking of the nanosheets. Pore size distributions measured using the Horvath–Kawazoe method were obtained for the 333 K activated sample (Figure S5). For both samples, the peaks centered around 4 Å reflect the smaller pore of channel I with the larger pore contributing from the pseudohexagonal motif.

The different morphologies observed in this work impact the gas adsorption performance for CO₂ and CH₄ uptake and selectivity. Gravimetric adsorption isotherms confirm that bp-*kgm*⁻t-Bu shows uptakes for CO₂ and CH₄ of 1.36 and 0.32 mmol g⁻¹, respectively, at 1 bar and 298 K with uptakes for ns-*kgm*⁻t-Bu of 0.80 and 0.37 mmol g⁻¹, respectively, Figure 6c,d. Ideal adsorption solution theory (IAST) analysis for an equimolar mixture CO₂/CH₄ at 1 bar shows a selectivity of 18.5 (using the dual-site Langmuir Freundlich model) for ns-*kgm*⁻t-Bu, which is much lower than the 108.4 (derived from dual-site Langmuir Freundlich model) and 50.1 (derived the single-site Langmuir Freundlich model) for bp-*kgm*⁻t-Bu (Figure S7). Given the identical chemical compositions, these differences closely relate to the morphologies of the isolated materials. The layered structure of *kgm*⁻t-Bu is constructed of monolayers stacked along the c axis in an AA mode. Thus, the thickness of the particle is directly related to the number of stacking monolayers, which determines the channel length and

ultimately the available pore volume for gas adsorption. For CO₂, the bulk powder has slightly higher pore volume and smaller external surface area, leading to a higher CO₂ uptake. For CH₄, both channels of the layered structure have limiting pore diameters lower than the kinetic diameters of CH₄, suggesting that the adsorption of CH₄ is primarily on the external surface. As ns-*kgm*⁻t-Bu possesses higher external surface area, the CH₄ uptake is slightly increased compared to that of bp-*kgm*⁻t-Bu, resulting in a lower CO₂/CH₄ adsorption selectivity.

Thermogravimetric analysis (TGA) was carried out for both ns-*kgm*⁻t-Bu and bp-*kgm*⁻t-Bu. Upon increasing temperature in air, both samples lose adsorbed solvent/moisture (ca. 10 wt %) below 200 °C (Figure S8) with decomposition at around 300 °C to give a black powder at 600 °C. The molar ratio of linker to metal (L/M) calculated from the TGA curve (ca. 1.08) is consistent with a theoretical ideal value of 1.0 based upon the crystal structure.

**3.4. MMMs for CO₂/CH₄ Separation.** CO₂ is commonly found in natural gas as an impurity that is not combustible and leads to acid formation. Thus, separation and removal of CO₂ from CH₄, the main component of natural gas, enhance the energy density of the gas and prevent pipeline corrosion. Improving the efficiency of separation membranes can also significantly reduce the cost of purification of natural gas. The potential of the layered *kgm*⁻t-Bu in membrane-based CO₂/CH₄ separation was evaluated by preparing MMMs using fillers of nanosheet and bulk powder morphologies. Nanoparticles of ns- or bp-*kgm*⁻t-Bu were dispersed in CHCl₃ and mixed with a commercial polyimide matrix (Matrimid 5218) at mass loadings of 2–10 wt %. Membranes were cast via solvent evaporation.
<figure><img src="image_16.png" /><figcaption>**Figure 7.** Cross-sectional SEM images of (a) and (b) ns-*kgm*<sup>t-Bu</sup> Matrimid membranes, and of (c) and (d) 8 wt % *bp-kgm*<sup>t-Bu</sup> Matrimid membranes.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 8.** CO₂/CH₄ separation as a function of mass loading ratio of (a) ns-*kgm*<sup>t-Bu</sup> Matrimid and (b) ns-*kgm*<sup>t-Bu</sup> Matrimid MMMs. Long-term performance of (c) 8 wt % ns-*kgm*<sup>t-Bu</sup> Matrimid and (d) 8 wt % bp-*kgm*<sup>t-Bu</sup> Matrimid membranes.</figcaption></figure>

The filler-polymer mixing efficiency in the MMMs was examined by using cross-sectional SEM images. Agglomerated particles were observed in the cross section of the membrane prepared from 8 wt % bp-*kgm*<sup>t-Bu</sup> Matrimid but were absent for the ns-*kgm*<sup>t-Bu</sup>/polymer membrane (Figure 7). Gas permeabilities were obtained from a single gas permeation test through the membranes at a working pressure of 3 bar and effective surface area for the membrane of 19.6 cm². The ideal separation selectivity was calculated from the ratio of individual gas permeabilities (P<sub>CO₂</sub>/P<sub>CH₄</sub>), and the effect of mass loading on separation was studied. At low mass loadings, the CO₂ permeability steadily increased from 7.29 Barrer for the bare

Matrimid membrane to 7.80 Barrer for the 4 wt % ns-*kgm*<sup>t-Bu</sup> loaded Matrimid membrane. At higher loadings of ns-*kgm*<sup>t-Bu</sup>, the CO₂ permeability decreased to 7.53 Barrer at 8 wt % loading and 7.05 Barrer at 10 wt % loading (Figure 8a). In comparison, the MMMs with bp-*kgm*<sup>t-Bu</sup> displayed a monotonic decrease with lower CO₂ permeabilities of 6.52 and 6.01 Barrer at 8 and 10 wt % loading, respectively (Figure 8b). The MMMs with the ns-*kgm*<sup>t-Bu</sup> filler thus displayed overall higher CO₂ permeabilities than MMMs with bp-*kgm*<sup>t-Bu</sup>. On the other hand, the CH₄ permeability of ns-*kgm*<sup>t-Bu</sup> Matrimid membrane decreased from 0.132 to 0.097 Barrer when increasing the loading from 2 wt % to 10 wt %
(Figure 8a). Membranes with bp-kgm**t-Bu** filler showed slightly higher CH₄ permeability of 0.137 and 0.102 Barrer at 2 and 10 wt % loading, respectively (Figure 8b). In contrast, the bare Matrimid membrane exhibited a CH₄ permeability of 0.140 Barrer. Consequently, the ns-kgm**t-Bu** Matrimid membrane showed a CO₂/CH₄ selectivity of 70.5 at 10 wt % loading, which is notably higher than both the 10 wt % bp-kgm**t-Bu** Matrimid membrane (59.1) and the bare Matrimid membrane (52.2). The separation performance of the 10 wt % ns-kgm**t-Bu** Matrimid membrane (α<sub>CO₂/CH₄</sub> = 70.5, P<sub>CO₂</sub> = 6.7) is among the best-performing MOF nanosheet Matrimid MMMs and is comparable to membranes prepared with nanosheets of CuBDC¹⁶¹⁴ and NH₂-MIL-53(Al)¹⁵ with Matrimid (Table 1, Tables S5 and S6).

<table><caption>**Table 1.** Comparison of Performance of CO₂/CH₄ Separation of Reported MOF Nanosheets Matrimid MMMs</caption><thead><tr><th>MOFs</th><th>loading/wt %</th><th>P<sub>CO2</sub>/Barrer</th><th>α<sub>CO2/CH4</sub></th><th>ref.</th></tr></thead><tbody><tr><td>CuBDC</td><td>8.2</td><td>4.1</td><td>78.7</td><td>14</td></tr><tr><td>CuBDC</td><td>12</td><td>6.3</td><td>38.0</td><td>16</td></tr><tr><td>NH₂-MIL-53(Al)</td><td>8</td><td>13.3</td><td>31.1</td><td>15</td></tr><tr><td>NH₂-MIL-53(Al)</td><td>16</td><td>13.5</td><td>34.4</td><td></td></tr><tr><td>ns-kgm<sup>t-Bu</sup></td><td>0</td><td>7.1</td><td>53.5</td><td>this work</td></tr><tr><td></td><td>8</td><td>7.3</td><td>65.2</td><td></td></tr><tr><td></td><td>10</td><td>6.7</td><td>70.5</td><td></td></tr><tr><td>bp-kgm<sup>t-Bu</sup></td><td>8</td><td>6.5</td><td>57.4</td><td></td></tr><tr><td></td><td>10</td><td>6.0</td><td>59.1</td><td></td></tr></tbody></table>

The superior CO₂/CH₄ separation selectivity of ns-kgm**t-Bu** Matrimid MMMs was attributed to both the morphology of the nanosheet and the layered structure of the MOF. The nanosheet morphology shortens the pathway for molecular diffusion through the membrane, while the width of the smallest channel (3.2 Å) enables sieving of gas molecules. The kinetic diameter of CO₂ (3.3 Å³⁰) is very close to that of this narrowest channel, and the linear molecular geometry thus enables its diffusion through the channels, while transport of nonlinear CH₄ molecules (3.8 Å³⁰) is more limited. To compare the solution-diffusion process for different gases, Henry coefficients (K<sub>H</sub>) were calculated using a grand canonical Monte Carlo (GCMC) simulation to evaluate the affinity of the gases in kgm**t-Bu**. The layered MOF shows significantly higher affinity for CO₂ (K<sub>H,CO₂</sub> = 5.3 × 10⁻⁴ mol kg⁻¹ Pa⁻¹) than CH₄ (K<sub>H,CH₄</sub> = 3.2 × 10⁻⁵ mol kg⁻¹ Pa⁻¹), and molecular dynamic simulations on the self-diffusivity of CO₂ and CH₄ in kgm**t-Bu** were also conducted (Figure S9). The mean squared displacement (MSD) of CH₄ molecules in the framework reached a plateau only after a few picoseconds (ps), leading to a negligible CH₄ diffusion coefficient (D<sub>CH₄</sub>). In contrast, CO₂ molecules diffuses freely with diffusion coefficients correlated with the number of CO₂ molecule per unit cell. The value of D<sub>CO₂</sub> increased from 3.58 × 10⁻¹² m² s⁻¹ (1 CO₂ per cell) to 4.9 × 10⁻¹¹ m² s⁻¹ (3 CO₂ per cell) (Table S4), thus confirming the preferred sorption and diffusion of CO₂ over CH₄ within the layered MOF. It should be noted that D<sub>CO₂</sub> for Matrimid is between 10⁻¹³ – 10⁻¹² m² s⁻¹.³¹ Thus, D<sub>CO₂</sub> in kgm**t-Bu** was only slightly higher than that of the polymer matrix, which explains the limited improvement in permeability observed for these in MMMs.

The gas permeation performance after 24 h was tested for 8 wt % ns-kgm**t-Bu** or bp-kgm**t-Bu** loaded MMMs (Figure 8c,d). Both membranes initially displayed a transition stage during

which the permeability of CO₂ increased gradually and the CO₂/CH₄ selectivity dropped. This reflects the time required for equilibration due to the dense nature of the polymer membrane. This transition stage was more obvious in the MMMs with bp-kgm**t-Bu** due to the lower CO₂ permeability. The 8 wt % ns-kgm**t-Bu** Matrimid membrane reached its highest CO₂ permeability (ca. 6.7 Barrer) after around 5 h and this was maintained throughout the rest of measurements (Figure 8c). The membrane with bp-kgm**t-Bu** at the same loading reached a slightly lower CO₂ permeability of ca. 6.2 Barrer after 24 h. However, the ns-kgm**t-Bu** MMM maintained a higher CO₂/CH₄ selectivity of 66.2, whereas the 8 wt % bp-kgm**t-Bu** Matrimid membrane showed a lower selectivity of 51.8 after the extended run (Figure 8d). Thus, the ns-kgm**t-Bu** Matrimid membrane showed a more consistent CO₂/CH₄ separation performance in comparison with that of the bp-kgm**t-Bu** Matrimid membrane.

## 4. CONCLUSIONS

We have described the bottom-up synthesis of nanosheets of the layered MOF kgm**t-Bu**. The use of a polar solvents (DMF or THF) along with a modulator successfully controls crystal growth in favor of forming nanosheets with high aspect ratios. The downsizing of the layered structure into nanosheets significantly alters the adsorption performance and surface areas in comparison with its bulk counterpart. The channels in kgm**t-Bu** function as size-selective molecular sieves with CO₂ flowing more readily than CH₄, as supported by simulation analysis. This affords enhanced CO₂ permeability and higher CO₂/CH₄ selectivity in the ns-kgm**t-Bu** Matrimid membranes compared with both the pure Matrimid membrane and bp-kgm**t-Bu** Matrimid MMMs. Furthermore, the ns-kgm**t-Bu** Matrimid membranes maintained their high selectivity and permeability in extended gas permeation tests.

### ■ ASSOCIATED CONTENT

**● Supporting Information**

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsami.4c05611.

Characterization methods including diffraction, AFM, TGA, TEM; membrane preparation and gas permeation test methods; structure and refinement and analysis of nanosheets; adsorption isotherms and IAST fittings; DFT and GCMC calculation methods and molecular dynamic simulations; single crystal structure of kgm**t-Bu** (CCDC 2204427) and crystal structure of bulk powder of kgm**t-Bu** (CCDC 2204003) are available free of charge from the Cambridge Crystallographic Data Centre (https://www.ccdc.cam.ac.uk/) (PDF)

### ■ AUTHOR INFORMATION

**Corresponding Authors**

Martin Schröder – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.; ● orcid.org/0000-0001-6992-0700; Email: M.Schroder@manchester.ac.uk

Sihai Yang – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.; College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences, Peking University, Beijing 100871, China; ● orcid.org/0000-0002-1111-9272; Email: Sihai.Yang@manchester.ac.uk
## Authors

**Meng He** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.; orcid.org/0000-0001-7373-9779

**Yinlin Chen** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.

**Wanpeng Lu** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.

**Lixia Guo** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.; College of Chemistry and Molecular Engineering, Beijing National Laboratory for Molecular Sciences, Peking University, Beijing 100871, China

**Kui Hu** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.

**Xue Han** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.; College of Chemistry, Beijing Normal University, Beijing 100875, China

**Inigo Vitorica-Yrezabal** – Department of Chemistry, University of Manchester, Manchester M13 9PL, U.K.

**Catherine Dejoie** – The European Synchrotron Radiation Facility, Grenoble 38043, France; orcid.org/0000-0003-3313-3515

**Andrew N. Fitch** – The European Synchrotron Radiation Facility, Grenoble 38043, France

Complete contact information is available at:
https://pubs.acs.org/10.1021/acsami.4c05611

## Author Contributions

M.H. performed materials synthesis, experimental investigations on membranes, data analysis, and preparation of drafts manuscript. Y.C. and M.H. performed the membrane test and crystal structure analysis. Gas adsorption experiments were performed by W.L., L.G., and X.H. SEM and TEM images were obtained by K.H. The single crystal diffraction experiments were conducted by I.V.–Y. and high-resolution PXRD at ESRF by C.D. and A.N.F. M.S., S.Y., and X.H. originated, designed and supervised the project. They reviewed and edited the manuscript with M.H. and all authors.

## Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

We thank EPSRC (EP/1011870) and University of Manchester for funding. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 742401, NANOCHEM and PoC665632). We are grateful to the European Synchrotron Radiation Facility (ESRF) for access to beamline ID22. Computational work was conducted using the Computational Shared Facility (CSF) at The University of Manchester. M.H., L.G., and K.H. are supported by the China Scholarship Council (CSC).

## REFERENCES

(1) Ulbricht, M. Advanced Functional Polymer Membranes. *Polymer (Guildf.)* **2006**, *47*, 2217–2262.

(2) Ismail, A. F.; Chandra Khulbe, K.; Matsuura, T. *Gas Separation Membranes: Polymeric and Inorganic*; Springer International Publishing: Cham, 2015.

(3) Robeson, L. M. Correlation of Separation Factor versus Permeability for Polymeric Membranes. *J. Membr. Sci.* **1991**, *62*, 165–185.

(4) Robeson, L. M. The Upper Bound Revisited. *J. Membr. Sci.* **2008**, *320*, 390–400.

(5) Dechnik, J.; Gascon, J.; Doonan, C. J.; Janiak, C.; Sumby, C. J. Mixed-matrix Membranes. *Angew. Chem., Int. Ed. Engl.* **2017**, *56*, 9292–9310.

(6) Denny, M. S.; Moreton, J. C.; Benz, L.; Cohen, S. M. Metal–Organic Frameworks for Membrane-Based Separations. *Nat. Rev. Mater.* **2016**, *1*, 16078.

(7) Chung, T.-S.; Jiang, L. Y.; Li, Y.; Kulprathipanja, S. Mixed Matrix Membranes (MMMs) Comprising Organic Polymers with Dispersed Inorganic Fillers for Gas Separation. *Prog. Polym. Sci.* **2007**, *32*, 483–507.

(8) Car, A.; Stropnik, C.; Peinemann, K.-V. Hybrid Membrane Materials with Different Metal–Organic Frameworks (MOFs) for Gas Separation. *Desalination* **2006**, *200*, 424–426.

(9) Ordoñez, M. J. C.; Balkus, K. J., Jr; Ferraris, J. P.; Musselman, I. H. Molecular Sieving Realized with ZIF-8/Matrimid® Mixed-Matrix Membranes. *J. Membr. Sci.* **2010**, *361*, 28–37.

(10) Cheng, Y.; Ying, Y.; Japip, S.; Jiang, S.-D.; Chung, T.-S.; Zhang, S.; Zhao, D. Advanced Porous Materials in Mixed Matrix Membranes. *Adv. Mater.* **2018**, *30*, 201802401.

(11) Katayama, Y.; Bentz, K. C.; Cohen, S. M. Defect-Free MOF-Based Mixed-Matrix Membranes Obtained by Corona Cross-Linking. *ACS Appl. Mater. Interfaces* **2019**, *11*, 13029–13037.

(12) Stock, N.; Biswas, S. Synthesis of Metal–Organic Frameworks (MOFs): Routes to Various MOF Topologies, Morphologies, and Composites. *Chem. Rev.* **2012**, *112*, 933–969.

(13) Cohen, S. M. Postsynthetic Methods for the Functionalization of Metal–Organic Frameworks. *Chem. Rev.* **2012**, *112*, 970–1000.

(14) Rodenas, T.; Luz, I.; Prieto, G.; Seoane, B.; Miro, H.; Corma, A.; Kapteijn, F.; Llabrés i Xamena, F. X.; Gascon, J. Metal–Organic Framework Nanosheets in Polymer Composite Materials for Gas Separation. *Nat. Mater.* **2015**, *14*, 48–55.

(15) Pustovarenko, A.; Goesten, M. G.; Sachdeva, S.; Shan, M.; Amghouz, Z.; Belmabkhout, Y.; Dikhtiarenko, A.; Rodenas, T.; Keskin, D.; Voets, I. K.; Weckhuysen, B. M.; Eddaoudi, M.; de Smet, L. C. P. M.; Sudhölter, E. J. R.; Kapteijn, F.; Seoane, B.; Gascon, J. Nanosheets of Nonlayered Aluminum Metal–Organic Frameworks through a Surfactant-assisted Method. *Adv. Mater.* **2018**, *30*, 201707234.

(16) Shete, M.; Kumar, P.; Bachman, J. E.; Ma, X.; Smith, Z. P.; Xu, W.; Mkhoyan, K. A.; Long, J. R.; Tsapatsis, M. On the Direct Synthesis of Cu(BDC) MOF Nanosheets and Their Performance in Mixed Matrix Membranes. *J. Membr. Sci.* **2018**, *549*, 312–320.

(17) Foster, J. A.; Henke, S.; Schneemann, A.; Fischer, R. A.; Cheetham, A. K. Liquid Exfoliation of Alkyl-Ether Functionalised Layered Metal–Organic Frameworks to Nanosheets. *Chem. Commun.* (Camb.) **2016**, *52*, 10474–10477.

(18) Peng, Y.; Li, Y.; Ban, Y.; Jin, H.; Jiao, W.; Liu, X.; Yang, W. Metal–Organic Framework Nanosheets as Building Blocks for Molecular Sieving Membranes. *Science* **2014**, *346*, 1356–1359.

(19) Arslan, H. K.; Shekhah, O.; Wieland, D. C. F.; Paulus, M.; Sternemann, C.; Schroer, M. A.; Tiemeyer, S.; Tolan, M.; Fischer, R. A.; Wöll, C. Intercalation in Layered Metal–Organic Frameworks: Reversible Inclusion of an Extended $\pi$-System. *J. Am. Chem. Soc.* **2011**, *133*, 8158–8161.

(20) Junggeburth, S. C.; Diehl, L.; Werner, S.; Duppel, V.; Sigle, W.; Lotsch, B. V. Ultrathin 2D Coordination Polymer Nanosheets by Surfactant-Mediated Synthesis. *J. Am. Chem. Soc.* **2013**, *135*, 6157–6164.

(21) Kang, Z.; Peng, Y.; Hu, Z.; Qian, Y.; Chi, C.; Yeo, L. Y.; Tee, L.; Zhao, D. Mixed Matrix Membranes Composed of Two-Dimensional Metal–Organic Framework Nanosheets for Pre-Combustion $CO_2$ Capture: A Relationship Study of Filler Morphology versus Membrane Performance. *J. Mater. Chem. A Mater. Energy Sustain.* **2015**, *3*, 20801–20810.
(22) Datta, S. J.; Mayoral, A.; Murthy Srivatsa Bettahalli, N.; Bhatt, P. M.; Karunakaran, M.; Carja, I. D.; Fan, D.; Graziane M. Mileo, P.; Semino, R.; Maurin, G.; Terasaki, O.; Eddaoudi, M. Rational Design of Mixed-Matrix Metal-Organic Framework Membranes for Molecular Separations. *Science* **2022**, *376*, 1080–1087.

(23) Cheng, Y.; Wang, X.; Jia, C.; Wang, Y.; Zhai, L.; Wang, Q.; Zhao, D. Ultrathin Mixed Matrix Membranes Containing Two-Dimensional Metal-Organic Framework Nanosheets for Efficient CO₂/CH₄ Separation. *J. Membr. Sci.* **2017**, *539*, 213–223.

(24) Au, V. K.-M.; Nakayashiki, K.; Huang, H.; Suginome, S.; Sato, H.; Aida, T. Stepwise Expansion of Layered Metal–Organic Frameworks for Nonstochastic Exfoliation into Porous Nanosheets. *J. Am. Chem. Soc.* **2019**, *141*, 53–57.

(25) Xue, D.-X.; Lin, Y.-Y.; Cheng, X.-N.; Chen, X.-M. Chen, X-M, A Tetracarboxylate Dicopper(II) Paddle-Wheel-Based 2-D Porous Coordination Polymer with Gas Adsorption Properties. *CrystEngComm* **2007**, *7*, 1332–1336.

(26) Bonneau, M.; Sugimoto, K.; Otake, K.-i.; Tsuji, Y.; Shimanaka, N.; Lavenn, C.; Kitagawa, S. Guest-selective Gate-opening by Pore Engineering of Two-dimensional Kagomè Lattice Porous Coordination Polymers. *Nat. Sci.* **2021**, *1*, No. e10020.

(27) Rodriguez-Carvajal, J. Fullprof: A Program for Rietveld Refinement and Pattern Matching Analysis. In *Abstract of the Satellite Meeting on Powder Diffraction of the XV Congress of the IUCr*; Toulouse, France, 1990; p 127.

(28) Flügel, E. A.; Ranft, A.; Haase, F.; Lotsch, B. V. Synthetic Routes toward MOF Nanomorphologies. *J. Mater. Chem.* **2012**, *22*, 10119.

(29) Sakata, Y.; Furukawa, S.; Kondo, M.; Hirai, K.; Horike, N.; Takashima, Y.; Uehara, H.; Louvain, N.; Meilikhov, M.; Tsuruoka, T.; Isoda, S.; Kosaka, W.; Sakata, O.; Kitagawa, S. Shape-Memory Nanopores Induced in Coordination Frameworks by Crystal Downsizing. *Science* **2013**, *339*, 193–196.

(30) Li, J.-R.; Kuppler, R. J.; Zhou, H.-C. Selective Gas Adsorption and Separation in Metal–Organic Frameworks. *Chem. Soc. Rev.* **2009**, *38*, 1477–1504.

(31) Checchetto, R.; Scarpa, M.; De Angelis, M. G.; Minelli, M. Mixed Gas Diffusion and Permeation of Ternary and Quaternary CO₂/CO/N₂/O₂ Gas Mixtures in Matrimid®, Polyetherimide and Poly(Lactic Acid) Membranes for CO₂/CO Separation. *J. Membr. Sci.* **2022**, *659*, No. 120768.