Developing Mixed Matrix Membranes with Good CO2 Separation Performance Based on PEG-Modified UiO-66 MOF and 6FDA-Durene Polyimide

The use of mixed matrix membranes (MMMs) comprising metal–organic frameworks (MOFs) for the separation of CO2 from flue gas has gained recognition as an effective strategy for enhancing gas separation efficiency. When incorporating porous materials like MOFs into a polymeric matrix to create MMMs, the combined characteristics of each constituent typically manifest. Nevertheless, the inadequate dispersion of an inorganic MOF filler within an organic polymer matrix can compromise the compatibility between the filler and matrix. In this context, the aspiration is to develop an MMM that not only exhibits optimal interfacial compatibility between the polymer and filler but also delivers superior gas separation performance, specifically in the efficient extraction of CO2 from flue gas. In this study, we introduce a modification technique involving the grafting of poly(ethylene glycol) diglycidyl ether (PEGDE) onto a UiO-66-NH2 MOF filler (referred to as PEG-MOF), aimed at enhancing its compatibility with the 6FDA-durene matrix. Moreover, the inherent CO2-philic nature of PEGDE is anticipated to enhance the selectivity of CO2 over N2 and CH4. The resultant MMM, incorporating 10 wt% of PEG-MOF loading, exhibits a CO2 permeability of 1671.00 Barrer and a CO2/CH4 selectivity of 22.40. Notably, these values surpass the upper bound reported by Robeson in 2008.


Introduction
Greenhouse gas emissions, particularly CO 2 emissions, have escalated unprecedentedly primarily due to the continuous utilization of fossil fuel-based energy sources.Consequently, these energy sources are frequently identified as the primary contributors to the elevation of global temperatures and the ensuing changes to the climate.In response to this challenge, substantial efforts have been directed globally toward decreasing the CO 2 concentration of the atmosphere.Among these efforts is the development of carbon capture, utilization, and storage (CCUS) technology.This technology focuses on capturing the CO 2 generated from fossil fuel use and converting it into valuable substances, such as alcohols and bioplastics, thereby transforming CO 2 emissions into a resource rather than a pollutant [1,2].
Presently, CO 2 separation is predominantly accomplished through various methods including chemical absorption, cryogenic distillation, adsorption, and chemical looping.Thus, the introduction of organic oligomers was intended to counteract MOF particle aggregation.
Polymers incorporating ethylene oxide (EO) units, such as polyethylene glycol (PEG), have found extensive applications in the production of gas separation membranes owing to their pronounced CO 2 solubility.Nevertheless, when the EO unit concentration in polymers surpasses a specific threshold, the molecules tend to aggregate due to heightened crystallinity, causing a decline in permeability [32].
We have recently reported the synthesis of PIM-[durene(m)-co-PEG/PPG(n)]-polyimide membranes.These membranes contained a rigid porous polymer unit with intrinsic microporosity (PIM) and a soft PEG/PPG unit that were uniformly mixed due to a unique chain threading effect [33].This uniform chain threading of PEG/PPG units onto the PIM structure resulted in well-mixed PEG/PPG and PIM.However, incorporating the PEG/PPG unit greatly reduced the permeability of CO 2 compared to that of pristine PIM, as the unique chain threading effect disturbed the free volume of the highly porous PIM.
In this work, Zr-based UiO-66-NH 2 , notable for its permeability, was subjected to grafting with PEG, yielding a PEG-grafted MOF.As a filler, the PEG-modified UiO-66-NH 2 (PEG-UIO-66-NH 2 ) was then incorporated in a 4,4 -(Hexafluoroisopropylidene) diphthalic anhydride-durene polyimide (6FDA-durene PI), used as the matrix or support, to prepare a self-standing MMM for high-performance CO 2 separation.The effect of the PEG-modified MOF filler loading levels relative to 6FDA-durene PI on the thermal behavior, morphology, and gas separation behavior was then extensively investigated.
Polyethylene glycol diglycidyl ether (PEGDE)-modified UiO-66-NH 2 (PEG-UIO-66-NH 2 ) has been previously crosslinked with polyvinyl amine (PVAm) and used to coat a polysulfone substrate and prepare a composite membrane [34].The ether oxygen groups derived from PEG-UIO-66-NH 2 , in conjunction with the amino groups of PVAm, showed an enhanced affinity toward carbon dioxide (CO 2 ).Although this work has demonstrated that PEG-modified MOF (PEG-MOF) can enhance CO 2 separation performance, it differs from the current study because PEG-MOF was used as a coating material.The use of PEG-MOF as a filler in MMMs has not previously been reported.

Preparation of PEG-Functionalized UiO-66 MOF
The UiO-66-NH 2 MOF was synthesized following the reported procedure [35].In a 30 mL volume of dimethylformamide (DMF), a mixture containing ZrCl 4 (0.50 g, 2.14 mmol), 2-amino terephthalic acid (0.39 g, 2.14 mmol), and 3.3 mL of acetic acid was dissolved.This solution was then placed in a Teflon-lined autoclave and heated at 120 • C in an oven.After heating, the resulting yellow suspension was centrifuged and subjected to multiple methanol washing steps.Further purification involved re-dispersing in methanol for a week followed by centrifugation.Subsequently, activation was carried out under vacuum at 120 • C for 24 h.
For the synthesis of PEG-UIO-66-NH 2 , a post-synthetic modification of UiO-66-NH 2 was conducted as outlined in Scheme 1.Initially, UiO-66-NH 2 nanoparticles (1.18 g) were dispersed in 1-butanol (74 mL) through sonication.Following dispersion, the solution was transferred to a two-neck round bottom flask, and an excess of PEGDE was dissolved in the suspension and stirred for 30 min.The modification was then carried out under reflux at 80 • C for 24 h under a N 2 atmosphere.To eliminate excess unreacted PEGDE, the resultant PEG-UiO-66-NH 2 underwent a series of steps, including centrifugation, dispersion, and ultrasonication, to exchange the solvent with fresh methanol.The final yellow powder product was dried at 50 • C under vacuum for 24 h, yielding the PEG-UIO-66-NH 2 material.for a week followed by centrifugation.Subsequently, activation was carried out under vacuum at 120 °C for 24 h.For the synthesis of PEG-UIO-66-NH2, a post-synthetic modification of UiO-66-NH2 was conducted as outlined in Scheme 1.Initially, UiO-66-NH2 nanoparticles (1.18 g) were dispersed in 1-butanol (74 mL) through sonication.Following dispersion, the solution was transferred to a two-neck round bottom flask, and an excess of PEGDE was dissolved in the suspension and stirred for 30 min.The modification was then carried out under reflux at 80 °C for 24 h under a N2 atmosphere.To eliminate excess unreacted PEGDE, the resultant PEG-UiO-66-NH2 underwent a series of steps, including centrifugation, dispersion, and ultrasonication, to exchange the solvent with fresh methanol.The final yellow powder product was dried at 50 °C under vacuum for 24 h, yielding the PEG-UIO-66-NH2 material.

Preparation of PEG-MOF-Incorporated 6FDA-Durene-Based Mixed Matrix Membranes
A matrix of 300 mg 6FDA-durene polymer was dissolved in 10 mL of chloroform and stirred for 1 h.For the creation of MMM-3, MMM-5, MMM-10, and MMM-15, PEG-MOF filler was dispersed in 3 mL of chloroform at concentrations of 3 wt%, 5 wt%, 10 wt%, and 15 wt% relative to the 6FDA matrix using ultrasonication and stirring.Subsequently, the dispersed filler solution was introduced to the 6FDA-durene solution and subjected to sonication to ensure uniform distribution of the MOF throughout the matrix.The resultant mixture was then poured into a Petri dish and allowed to air dry for 12 h at room temperature to form a membrane.To thoroughly eliminate the solvent, the prepared membrane was further dried at 80 • C in a vacuum oven.

Characterization and Measurements
The membranes' structures and physical properties were assessed using a 1 H NMR Agilent 400-MR (400 MHz) instrument (Santa Clara, CA, USA), employing deuterated chloroform (CDCl 3 ) and deuterium oxide (D 2 O) as solvents, with tetramethylsilane (TMS) as a reference for the internal deuterium lock.Fourier Transform Infrared (FTIR) spectroscopy was conducted using a PerkinElmer FT-IR Spectrum Two (Shelton, WA, USA).The membrane thickness was measured using a micrometer (Mitutoyo Model 547-201, Sakado, Japan).Thermal characteristics were determined through thermogravimetric analysis (TGA) using a Scinco TGA/N-1000 analyzer (Seoul, Republic of Korea) employing a nitrogen flow at a heating rate of 10 • C min −1 .Morphological evaluation was carried out using wide-angle X-ray diffraction (WAXD) and scanning electron microscopy (SEM).WAXD spectra of the membranes were collected using a Rigaku HR-XRD Smart Lab diffractometer (Tokyo, Japan) at a scanning rate of 0.2 • min −1 within a 2θ range spanning 5 • to 50 • , with a Cu-Kα X-ray source (λ = 1.54 Å).The BET surface area was determined through nitrogen adsorption experiments at 77 K using a Micromeritics ASAP 2020 HD88 instrument (Norcross, GA, USA).Gas separation measurements were conducted using the Time-lag instrument under constant volume-variable pressure conditions, as outlined in our prior study [36].Detailed information regarding the instrumentation and characterization procedures is provided in the Supporting Information.

Synthesis and Characterization of UiO-66-NH 2 and UiO-66-NH 2 (PEG-MOF) Containing PEG
Zirconium chloride was subjected to a reaction with 2-amino terephthalic acid, employing the test procedure outlined in existing literature [35].The objective was to synthesize UiO-66-NH 2 , characterized as an amine-terminated metal-organic framework (MOF) as depicted in Scheme 1.The molecular structure of UiO-66-NH 2 was confirmed using 1 H NMR (Figure S1).The crystalline structure of the resultant UiO-66-NH 2 was investigated using powder X-ray diffraction (PXRD).A thorough cross-reference was conducted by juxtaposing the PXRD findings with the corresponding X-ray diffraction analysis outcomes documented in the literature [23].This comparative analysis unequivocally validated the congruence of the obtained patterns with those detailed in the literature (Figure 1a).
The structural assessment of the synthesized PEG-MOF commenced by subjecting it to digestion using an aqueous solution of NaOD, yielding its 1 H NMR spectra for detailed structural analysis (Figure 1b).The analysis revealed distinctive absorption peaks corresponding to Ar-H at the 6.5-7.5 ppm range, along with proton peaks attributable to the -CH-and -CH 2 functionalities of PEG within the PEG-MOF, discernible at 1.3-3.75ppm.This unequivocally confirmed the successful functionalization of the amine groups present in UiO-66-NH 2 with PEGDE.
Further validation of the structural integrity of both the UiO-66-NH 2 MOF and the PEG-MOF was pursued through FTIR spectroscopy (Figure 1c).The distinctive peaks detected at 3460 cm −1 and 3348 cm −1 within the MOF spectrum were attributed to the asymmetric and symmetric stretching vibrations of the primary amine.Notably, the bands evident at 1658 cm −1 (asymmetric stretching) and 1383 cm −1 (symmetric stretching) were linked to the carboxyl groups originating from the 2-aminoterephthalic acid present in UiO-66-NH 2 .However, discernible distinctions emerged subsequent to the incorporation of PEGDE into the MOF.The broad absorption peaks spanning the 3200 cm −1 to 3600 cm −1 interval were attributed to the hydroxyl and secondary amine groups inherent to PEG-MOF.Furthermore, the methylene group derived from the PEGDE graft in UiO-66-NH 2 exhibited dual peaks at 2914 cm −1 and 2875 cm −1 , corresponding to the asymmetric and symmetric stretching vibrations.Of utmost significance, definitive proof of PEGDE grafting within the PEG-MOF was underscored by the emergence of distinctive peaks at 1088 cm −1 and 950 cm −1 , resonating with the stretching vibration of the ether group (C-O-C) intrinsic to PEGDE [34,37].The structural assessment of the synthesized PEG-MOF commenced by subjecting it to digestion using an aqueous solution of NaOD, yielding its 1 H NMR spectra for detailed structural analysis (Figure 1b).The analysis revealed distinctive absorption peaks corresponding to Ar-H at the 6.5-7.5 ppm range, along with proton peaks attributable to the -CH-and -CH2 functionalities of PEG within the PEG-MOF, discernible at 1.3-3.75ppm.This unequivocally confirmed the successful functionalization of the amine groups present in UiO-66-NH2 with PEGDE.
Further validation of the structural integrity of both the UiO-66-NH2 MOF and the PEG-MOF was pursued through FTIR spectroscopy (Figure 1c).The distinctive peaks detected at 3460 cm −1 and 3348 cm −1 within the MOF spectrum were attributed to the asymmetric and symmetric stretching vibrations of the primary amine.Notably, the bands evident at 1658 cm −1 (asymmetric stretching) and 1383 cm −1 (symmetric stretching) were linked to the carboxyl groups originating from the 2-aminoterephthalic acid present in UiO-66-NH2.However, discernible distinctions emerged subsequent to the incorporation of PEGDE into the MOF.The broad absorption peaks spanning the 3200 cm −1 to 3600 cm −1 interval were attributed to the hydroxyl and secondary amine groups inherent to PEG-MOF.Furthermore, the methylene group derived from the PEGDE graft in UiO-66-NH2 exhibited dual peaks at 2914 cm −1 and 2875 cm −1 , corresponding to the asymmetric and symmetric stretching vibrations.Of utmost significance, definitive proof of PEGDE grafting within the PEG-MOF was underscored by the emergence of distinctive peaks at 1088 Subsequently, an in-depth analysis of the crystalline structure of UiO-66-NH 2 was executed through PXRD and the alterations in structure pre-and post-functionalization were scrutinized (Figure 1a).The diffraction peaks observed in UiO-66-NH 2 exhibited alignment with those documented in the existing literature [38][39][40].Notably, the PXRD spectra of PEG-MOF displayed a near-identical pattern to that of UiO-66-NH 2 .This substantiated that the crystallinity and fundamental framework of the MOF remained conserved, even subsequent to the grafting of PEGDE onto UiO-66-NH 2 .The PXRD spectra of PEG-MOF prominently showcased crystal peaks of high intensity, indicative of the MOF's channel structure being extended over a significant distance, thus rendering it conducive for molecular transportation.
Subsequently, the nitrogen adsorption and desorption characteristics of both UiO-66-NH 2 and PEG-MOF were assessed at 77 K (Figure 1d).The determination encompassed the measurement of BET surface areas, revealing that PEG-MOF exhibited an area of 317.47 m 2 g −1 , which was notably lower in comparison to UiO-66-NH 2 (1041.8m 2 g −1 ).This reduction in the surface area within PEG-MOF was ascribed to the partial occupation of the pores Polymers 2023, 15, 4442 7 of 16 by neighboring PEG chains integrated into the MOF framework.In essence, the PEGDE units effectively utilized the vacant volume on the MOF's surface.This outcome substantiated the successful grafting of PEGDE onto the UiO-66-NH 2 MOF, thereby culminating in the synthesis of PEG-MOF.
The morphologies and particle dimensions of UiO-66-NH 2 and PEG-MOF were additionally subjected to scrutiny through SEM, as depicted in Figure 2. The findings unequivocally revealed that the incorporation of PEGDE did not induce substantial alterations in the morphological characteristics.
of PEG-MOF prominently showcased crystal peaks of high intensity, indicative of the MOF's channel structure being extended over a significant distance, thus rendering it conducive for molecular transportation.
Subsequently, the nitrogen adsorption and desorption characteristics of both UiO-66-NH2 and PEG-MOF were assessed at 77 K (Figure 1d).The determination encompassed the measurement of BET surface areas, revealing that PEG-MOF exhibited an area of 317.47 m 2 g −1 , which was notably lower in comparison to UiO-66-NH2 (1041.8m 2 g −1 ).This reduction in the surface area within PEG-MOF was ascribed to the partial occupation of the pores by neighboring PEG chains integrated into the MOF framework.In essence, the PEGDE units effectively utilized the vacant volume on the MOF's surface.This outcome substantiated the successful grafting of PEGDE onto the UiO-66-NH2 MOF, thereby culminating in the synthesis of PEG-MOF.
The morphologies and particle dimensions of UiO-66-NH2 and PEG-MOF were additionally subjected to scrutiny through SEM, as depicted in Figure 2. The findings unequivocally revealed that the incorporation of PEGDE did not induce substantial alterations in the morphological characteristics.MOF's channel structure being extended over a significant distance, thus rendering it conducive for molecular transportation.

Fabrication and Characterization of MMMs
Subsequently, the nitrogen adsorption and desorption characteristics of both UiO-66-NH2 and PEG-MOF were assessed at 77 K (Figure 1d).The determination encompassed the measurement of BET surface areas, revealing that PEG-MOF exhibited an area of 317.47 m 2 g −1 , which was notably lower in comparison to UiO-66-NH2 (1041.8m 2 g −1 ).This reduction in the surface area within PEG-MOF was ascribed to the partial occupation of the pores by neighboring PEG chains integrated into the MOF framework.In essence, the PEGDE units effectively utilized the vacant volume on the MOF's surface.This outcome substantiated the successful grafting of PEGDE onto the UiO-66-NH2 MOF, thereby culminating in the synthesis of PEG-MOF.
The morphologies and particle dimensions of UiO-66-NH2 and PEG-MOF were additionally subjected to scrutiny through SEM, as depicted in Figure 2. The findings unequivocally revealed that the incorporation of PEGDE did not induce substantial alterations in the morphological characteristics.

Morphological Analysis Using WAXD and SEM
Alterations in the morphological attributes of the MMMs subsequent to the integration of PEG-MOF, a PEGDE-grafted MOF, were scrutinized via wide-angle X-ray diffractometry (WAXD) (Figure 4).In the pristine state of the 6FDA-durene-PI (prior to PEG-MOF incorporation), a broad peak materialized at 13.6 • , aligning with the distinctive amorphous signature of 6FDA-durene.
Across all MMMs incorporating PEG-MOF, the aforementioned broad diffraction peak consistently manifested at an identical position; however, its intensity notably diminished (Figure 4).This attenuation in peak intensity was rationalized by the incorporation of the MOF particles into the polymer support [22].In marked contrast, distinct peaks characteristic of the rigid crystalline configuration of the introduced MOF exhibited an augmented intensity, aligning with an increase in MOF content.This unequivocally underscored the MOF incorporation), a broad peak materialized at 13.6°, aligning with the distinctive amorphous signature of 6FDA-durene.
Across all MMMs incorporating PEG-MOF, the aforementioned broad diffraction peak consistently manifested at an identical position; however, its intensity notably diminished (Figure 4).This attenuation in peak intensity was rationalized by the incorporation of the MOF particles into the polymer support [22].In marked contrast, distinct peaks characteristic of the rigid crystalline configuration of the introduced MOF exhibited an augmented intensity, aligning with an increase in MOF content.This unequivocally underscored the preservation of the innate crystalline structure of the incorporated filler particles within the MMMs.Such a trend finds commonality within the diffraction spectra of various other MMM variants [41][42][43].The microstructural attributes of the acquired MMMs were subjected to further analysis in relation to the content of PEG-MOF, utilizing their SEM cross-sectional imagery as a basis.These findings were then juxtaposed with the microstructural characteristics evident within the unmodified 6FDA-durene-based membrane (Figure 5).When examining the cross-sectional views of both 6FDA-durene and all MMMs, no instances of defects were discernible (Figure 5a).In contrast, the dispersion of MOF particles within the 6FDA-durene polymer matrix exhibited variance contingent on the MOF content (Figure 5b-e).A homogeneous distribution of PEG-MOF in MMMs was observed in the SEM-EDX mapping images (Figure S2).Specifically, the PEG-MOF particles exhibited uniform dispersion within MMM-3 (Figure 5b), MMM-5 (Figure 5c), and MMM-10 (Figure 5d).However, in the case of MMM-15 (Figure 5e), some aggregations of PEG-MOF particles were observable.
Broadly speaking, the even dispersion of MOF particles within a polymer matrix facilitates the rapid diffusion of gas molecules through the MOF structure's pores.This, in turn, engenders heightened efficacy in molecular transport and, consequently, improved gas permeability [19,20,24,26].Conversely, in cases where the membrane structure The microstructural attributes of the acquired MMMs were subjected to further analysis in relation to the content of PEG-MOF, utilizing their SEM cross-sectional imagery as a basis.These findings were then juxtaposed with the microstructural characteristics evident within the unmodified 6FDA-durene-based membrane (Figure 5).When examining the cross-sectional views of both 6FDA-durene and all MMMs, no instances of defects were discernible (Figure 5a).In contrast, the dispersion of MOF particles within the 6FDAdurene polymer matrix exhibited variance contingent on the MOF content (Figure 5b-e).A homogeneous distribution of PEG-MOF in MMMs was observed in the SEM-EDX mapping images (Figure S2).Specifically, the PEG-MOF particles exhibited uniform dispersion within MMM-3 (Figure 5b), MMM-5 (Figure 5c), and MMM-10 (Figure 5d).However, in the case of MMM-15 (Figure 5e), some aggregations of PEG-MOF particles were observable.
Broadly speaking, the even dispersion of MOF particles within a polymer matrix facilitates the rapid diffusion of gas molecules through the MOF structure's pores.This, in turn, engenders heightened efficacy in molecular transport and, consequently, improved gas permeability [19,20,24,26].Conversely, in cases where the membrane structure consists of particle aggregates, the pores encircling the MOF-polymer interface might experience blockage, or the polymer could undergo densification.These effects could potentially culminate in a decrease in gas separation efficiency [11].
Consequently, an assessment of the morphological attributes of the MMMs and the impact incurred by the introduction of PEG-MOF was conducted, relying on the insights drawn from the XRD and SEM analyses.Intriguingly, across all MMMs, no instances of defects were identified, irrespective of the PEG-MOF content.Nonetheless, this exploration enabled the identification of an optimal MOF content, one that fosters a more homogeneous distribution of MOF particles, thereby translating into enhanced gas separation efficacy.Consequently, an assessment of the morphological attributes of the MMMs and the impact incurred by the introduction of PEG-MOF was conducted, relying on the insights drawn from the XRD and SEM analyses.Intriguingly, across all MMMs, no instances of defects were identified, irrespective of the PEG-MOF content.Nonetheless, this exploration enabled the identification of an optimal MOF content, one that fosters a more homogeneous distribution of MOF particles, thereby translating into enhanced gas separation efficacy.

Thermal Properties of the MMMs
Thermogravimetric analysis (TGA) was conducted to investigate the impact of PEG-MOF on the thermal characteristics of the resulting MMMs (Figure S3).In the TGA graph of UiO-66-NH2, a noticeable weight loss transpired due to moisture evaporation from the surface at temperatures below 100 °C.This was followed by an additional weight loss of around 134 °C attributed to the evaporation of absorbed moisture or the solvent (DMF).Beyond 300 °C, a third weight loss, attributed to MOF decomposition, was observed (Figure S3a) [22,23].Comparatively, the initial decomposition temperature of PEG-MOF exceeded that of UiO-66-NH2 due to the grafting of PEG (Figure S3a).
Subsequently, the thermal characteristics of the PEG-MOF-incorporated MMMs were scrutinized and compared against those acquired from the pristine 6FDA-durenebased PI (Figure S3b).The initial weight loss observed in the MMMs proved to be smaller than that exhibited by the pristine 6FDA-durene membrane.Notably, this tendency showed an increase with rising PEG-MOF content.This phenomenon was ascribed to the fact that PEG-MOF decomposition transpired at temperatures lower than those required for the degradation of 6FDA-durene.Across the various MMMs containing distinct proportions of PEG-MOF, the onset of MOF decomposition manifested at 300 °C, a value notably lower than that of 6FDA-durene.In contrast, the weight reduction linked to the primary polymer's decomposition was consistent across all MMMs, manifesting at nearly the same temperature.

Thermal Properties of the MMMs
Thermogravimetric analysis (TGA) was conducted to investigate the impact of PEG-MOF on the thermal characteristics of the resulting MMMs (Figure S3).In the TGA graph of UiO-66-NH 2 , a noticeable weight loss transpired due to moisture evaporation from the surface at temperatures below 100 • C.This was followed by an additional weight loss of around 134 • C attributed to the evaporation of absorbed moisture or the solvent (DMF).Beyond 300 • C, a third weight loss, attributed to MOF decomposition, was observed (Figure S3a) [22,23].Comparatively, the initial decomposition temperature of PEG-MOF exceeded that of UiO-66-NH 2 due to the grafting of PEG (Figure S3a).
Subsequently, the thermal characteristics of the PEG-MOF-incorporated MMMs were scrutinized and compared against those acquired from the pristine 6FDA-durene-based PI (Figure S3b).The initial weight loss observed in the MMMs proved to be smaller than that exhibited by the pristine 6FDA-durene membrane.Notably, this tendency showed an increase with rising PEG-MOF content.This phenomenon was ascribed to the fact that PEG-MOF decomposition transpired at temperatures lower than those required for the degradation of 6FDA-durene.Across the various MMMs containing distinct proportions of PEG-MOF, the onset of MOF decomposition manifested at 300 • C, a value notably lower than that of 6FDA-durene.In contrast, the weight reduction linked to the primary polymer's decomposition was consistent across all MMMs, manifesting at nearly the same temperature.

Gas Separation Performance of MMMs
The gas separation efficiency of the MMMs incorporating the PEG-MOF-a UiO-66-NH2 variant with PEG grafting-was evaluated using constant-volume and variablepressure techniques at a temperature of 30 • C and a pressure of 1 atm (Tables 1 and 2).Subsequent to the assessment, the acquired findings were juxtaposed with the data derived from the 6FDA-durene-PI membrane.The permeability of the MMMs containing PEG-MOF displayed an ascending trend corresponding to the augmented PEG-MOF content (Table 1).This trend suggested that gas molecules traversed the MOF pores and polymer matrix in a sequential manner.Particularly noteworthy was the significantly elevated permeability of CO 2 observed across all membranes in comparison to other gases.This outcome was attributed to the diminutive kinetic diameter of CO 2 , coupled with its potent interaction with PEG.As a consequence, an enhanced solubility-selectivity emerged (Table 2).The gas separation performance of an MMM comprising 10 wt% of unaltered (without PEG) MOF was further compared.In particular, the permeability of all the gases increased for the molecules with smaller kinetic diameters compared to their behavior in the pristine 6FDA-durene PI (Table 1).This increase is attributed to the increased diffusivity of gas molecules through the porous channels in the membrane due to the MOFs (Table 2).Although the permeabilities of the MMMs with PEG-modified MOFs were lower than in UiO-66-NH 2 -MMM, significant improvements in CO 2 /N 2 and CO 2 /CH 4 selectivities compared to their behavior in UiO-66-NH 2 -MMM were observed due to the increased solubility-selectivity obtained from the CO 2 -philic PEG groups after modification of the MOF.
Generally, a gas's permeability in membranes is influenced by its kinetic diameter.The kinetic diameters of the gases used in the measurements are as follows: CH 4 (3.8Å) > N 2 (3.64 Å) > CO 2 (3.3 Å).It was discerned that as the kinetic diameter of a gas diminished, its permeability within a membrane augmented [44].In simpler terms, CO 2 , characterized by a smaller kinetic diameter, displayed heightened diffusivity in comparison to the other gases (Table 2).
The selectivity of each membrane was determined by calculating the ratio of permeabilities for two distinct gases within them.Notably, the CO 2 selectivity of the MMMs in relation to N 2 and CH 4 , both nonpolar gases, exhibited a superior value in comparison to the 6FDA polymer.This enhancement stemmed from the substantial solubility of the PEG functional groups integrated within the MOF, particularly within the CO 2 environment.Out of all the membranes, the MMM featuring a MOF content of 10 wt% demonstrated the most favorable gas separation performance, excelling in both permeability and selectivity (Figure 6a,b).With a higher MOF content (15 wt%), the permeability exhibited an increase, yet both CO 2 /N 2 and CO 2 /CH 4 selectivities experienced a decline.This phenomenon could be attributed to the emergence of non-selective pores brought about by MOF aggregation within this particular MMM, a conclusion substantiated by earlier morphological analysis findings [11,45,46].

Permeability Versus Selectivity of the MMMs
The permeability and selectivity data of the PEG-MOF-containing mixed matrix membranes (MMMs) developed in the present study are presented in Figure 7.These results have been juxtaposed with the 2008 Robeson upper bounds [5,6,46] to assess their It is important to highlight that the augmentation in permeability observed in the MOFincorporated MMMs primarily stems from the enhancement of their diffusion coefficients.
Nevertheless, in the context of this study, the solubility-selectivity traits of the PEG constituents took precedence, shaping the overarching diffusion behavior that consequently bolstered the permeability of the MMMs.This interpretation finds further reinforcement in the preceding BET analysis outcomes.Within the PEG-MOF structure, the pores were partially occupied by CO 2 -philic PEG components, contributing to a decrease in the BET surface area and the overall pore volume.
As per the existing literature, PEG components exhibit remarkable flexibility, enabling them to efficiently interface with the MOF surface and even permeate the MOF pores [47][48][49][50].This phenomenon is particularly accentuated within UiO-66-based MOFs and PEG systems, where the presence of robust hydrogen bonds between the MOF and the oligomers is notable [51][52][53].
Furthermore, the microstructural examination conducted through SEM corroborated the absence of any defects within these MMMs.This observation underscores the nearly flawless interfacial compatibility prevailing between the PEG-MOF and the filler matrix within these membranes.
the 2008 Robeson upper bound, as illustrated in Figure 7b.
Among the array of prepared MMMs, MMM-15 stands out, revealing a CO2 permeability of 1789.50Barrer and a CO2-CH4 selectivity of 18.78.While it falls below the 2008 upper bound, it unquestionably showcased superior performance compared to the reported MMMs.This observation underscores the overall excellence in permeability and selectivity exhibited by all the prepared MMMs, rendering them compelling prospects for industrial membrane applications.S2 in the Supplementary Material contains information on each referenced membrane.

Conclusions
In this study, we started by synthesizing UiO-66-NH2 nanoparticles, then covalently modified them through the grafting of a CO2-philic PEGDE unit.These tailored MOFs,  S2 in the Supplementary Material contains information on each referenced membrane.
Among the array of prepared MMMs, MMM-15 stands out, revealing a CO 2 permeability of 1789.50Barrer and a CO 2 -CH 4 selectivity of 18.78.While it falls below the 2008 upper bound, it unquestionably showcased superior performance compared to the reported MMMs.This observation underscores the overall excellence in permeability and selectivity exhibited by all the prepared MMMs, rendering them compelling prospects for industrial membrane applications.

Conclusions
In this study, we started by synthesizing UiO-66-NH 2 nanoparticles, then covalently modified them through the grafting of a CO 2 -philic PEGDE unit.These tailored MOFs, referred to as PEG-MOFs, were subsequently integrated into a 6FDA-durene matrix at varying weight percentages (3 wt%, 5 wt%, 10 wt%, and 15 wt%) using a solution-casting technique to craft mixed matrix membranes (MMMs).Extensive characterization encompassing XRD, SEM, and TGA analyses was conducted on the fabricated membranes.In contrast to the unmodified MOF, the PEG-MOF exhibited an increased presence of organic segments, promoting superior interfacial compatibility between the polymer matrix and MOFs.Notably, up to a loading of 10 wt% PEG-MOF, the polymer matrix and filler demonstrated a synergistic affinity, yielding a defect-free structure for the MMM, a fact confirmed by SEM outcomes.
The remarkable compatibility between the PEG-grafted MOF and the polymer matrix, combined with the presence of CO 2 -philic PEG units, imparted a noteworthy enhancement in the gas separation performance across all the MMMs developed in this study.With an augmented PEG-MOF content, CO 2 permeability and CO 2 /N 2 as well as CO 2 /CH 4 selectivity exhibited a progressive increase.Particularly notable are the MMMs-specifically, MMM-3, MMM-5, and MMM-10-incorporating 3 wt%, 5 wt%, and 10 wt% PEG-MOF loading, which surpassed the 2008 Robeson upper bound for CO 2 /CH 4 separation.Importantly, when juxtaposed with the unmodified 6FDA-durene polymer membrane (P(CO 2 ) = 973.90Barrer, CO 2 /N 2 = 12.71, and CO 2 /CH 4 = 14.76), the MMM incorporating 10 wt% PEG-MOF (MMM-10) boasted exceptional CO 2 permeability (P(CO 2 ) = 1671.00Barrer) along with superior CO 2 selectivity over N 2 and CH 4 (CO 2 /N 2 = 18.86 and CO 2 /CH 4 = 22.40).Emerging as the top-performing membrane, it not only surpassed the 2008 Robeson upper bound for CO 2 /CH 4 separation but also approached the upper bound for CO 2 /N 2 separation, positioning it as a highly promising candidate for efficient CO 2 extraction from flue gases.
Furthermore, the TGA analysis validated the robust thermal stability of these membranes-a vital prerequisite for the prospective commercialization of gas separation membranes.Based on the findings of this investigation, we envision that through a well-devised interface modification strategy for MOF fillers within MMMs, it is conceivable to obtain commercial-grade membranes exhibiting robust gas separation performance.
innate crystalline structure of the incorporated filler particles within the MMMs.Such a trend finds commonality within the diffraction spectra of various other MMM variants [41-43].

Figure 6 .
Figure 6.(a) Permeability and (b) selectivity of the MMMs with different MOF contents.

Figure 6 .
Figure 6.(a) Permeability and (b) selectivity of the MMMs with different MOF contents.

Figure 7 .
Figure 7.Comparison of separation performances between the PEG-MOF-based MMMs and other polyimides, commercial polymers, and other MMMs concerning the 2008 Robeson upper bounds.(a) CO2/N2 and (b) CO2/CH4.TableS2in the Supplementary Material contains information on each referenced membrane.

Figure 7 .
Figure 7.Comparison of separation performances between the PEG-MOF-based MMMs and other polyimides, commercial polymers, and other MMMs concerning the 2008 Robeson upper bounds.(a) CO 2 /N 2 and (b) CO 2 /CH 4 .TableS2in the Supplementary Material contains information on each referenced membrane.

Table 2 .
Gas diffusion coefficient, solubility coefficient, diffusivity selectivity, and solubility selectivity of each MMM.