A Facilitated Gas Transport Strategy: 3D Porous Hyper-crosslinked Polymers Incorporating 6FDA-based Polyimide Matrix for the Design and Fabrication of Mixed Matrix Membranes with High Permeability

Economic membrane technologies are a perennial hot topic in the eld of natural gas purication and O 2 enrichment. In this work, novel hyper cross-linked polymers (HCPs) incorporating 6-FDA based polyimide (PI) MMMs were prepared via a casting method for enhancing different gas transport (CO 2 , CH 4 , O 2 , and N 2 ). The gas permeation experiments showed that compared with pure PI lms, adding HCPs effectively promotes gas transport, increases gas permeability, and maintains ideal selectivity. The permeability of HCPs/PI MMMs toward CO 2 and O 2 was as high as 105.85 barrer and 24.03 barrer, respectively, and the ideal selectivity of CO 2 /CH 4 and O 2 /N 2 was 15.67 and 3.00, respectively. Molecular dynamic simulations further veried that adding HCPs was benecial to gas transport thanks to large FFV of MMMs. Thus, HCPs have potential utility in the fabrication of MMMs for facilitating gas transport in the eld of natural gas purication and O 2 enrichment. and selectivity.


Introduction
Gas separation is an essential separation process in natural gas puri cation, ue gas separation, and O 2 enrichment [1−6] . Membrane technologies are usually used for gas separation thanks to its environmentally friendly process and low energy consumption [7][8][9]. Unfortunately, the permeation has always been a problem restricting gas separation performance in membrane technology [10]. In general, gas separation membranes are divided into homogeneous and heterogeneous structures. Dense membranes with homogeneous structures have poor permeation and thus are restricted in industrial applications.
Mixed matrix membranes (MMMs) with heterogeneous structures are excellent candidates for gas separation because they facilitate gas transport of llers, including plenty of porous structures and functional groups [11]. Porous structures promote gas transport and functional groups and are bene cial to gas dissolution-diffusion, which break through low permeation and realize highly effective gas separation [12][13][14].
MMMs consist of llers with porous structures in a polymeric matrix, including rubber polymers and glassy polymers. Normally, glassy polymers such as polysulfone [15,16], cellulose [17,18], and polyimide [19][20][21] can nicely separate well gas. Of these, polyimide (PI) with highly thermal stability, good chemical stability, and strong mechanical stability has been extensively used as gas separation membrane [22,23]. More signi cantly, the largely fractional free volume (FFV) of aromatically uorinated PI is bene cial to gas transport [24,25]. However, a polymer matrix with a large FFV will result in gas selectivity reduction that falls into conventional trade-off effects. Thus, preparing PI MMMs with high permeability and suitable selectivity is still an important challenge.
In recent years, researchers have focused on the utility of llers with tailored porous structure and functional groups for improving gas transport and overcoming trade-off effect. For example, Koros and coworkers synthesized zeolite-like MOF (ZMOF) ller for the preparation of ZMOF/PI MMMs. Gas permeation experiments show that ZMOF/PI MMMs enhanced CO 2 permeability due to the incorporation of ZMOF ller with an a nity CO 2 framework that enhanced CO 2 sorption and facilitated gas diffusivity [26]. Yeong and coworkers prepared zeolite T as inorganic ller for the fabrication of Zeolite T/PI MMMs in CO 2 /CH 4 separation. Zeolite T could effectively improve CO 2 and CH 4 transport properties.
Compared to pure PI lms, the permeability of Zeolite T/PI MMMs toward CO 2 increased 80%.
Additionally, Zeolite T/PI MMMs also improved in CO 2 plasticization resistant [27]. Chung and coworkers fabricated zeolitic imidazolate framework (ZIF)-71 inorganic llers with a diameter of less than 100 nm, and the llers were compatibly incorporated in PI membranes. ZIF-71 in the PI membranes enhanced gas permeation, and the permeability of ZIF-71/PI MMMs toward pure CO 2 was three-fold higher than pure PI membrane [28]. In short, developing a perfect ller in MMMs is an effective approach to promote gas transport and break through the trade-off effect.
The permeability and selectivity of MMMs are greatly improved after incorporating the llers. However, the incompatible interfaces between llers and polymer matrix have always been a problem due to the effect of defects caused by weak compatibility on gas transport and selectivity [37]. Recently, hypercrosslinking polymers (HCPs) with porous organic frameworks have become a hot issue. HCPs usually exhibit a free-defect interface in the course of fabrication of MMMs thanks to good compatibility between the llers and polymer matrix. More importantly, HCPs are a kind of novel ller with ne prospect in MMMs due to their good ability to capture gas [38]. Some reports indicated that the use of HCPs for the preparation of MMMs can break through the trade-off effect and greatly facilitate gas transport [39].
However, there are limited reports on the use of HCPs for the preparation of HCPs/PI MMMs, and there are few studies on the gas transport of HCPs/PI MMMs. Clearly explaining the gas transport in HCPs/PI MMMs has an important impact on the structural design and manufacturing process of PI MMMs.
In this work, we rst prepared 6FDA-based PI MMMs using novel HCPs as the organic ller. We then used 2-phenylimidazole and α, α-dichloro-p-xylene as reaction monomers, and the HCPs were synthesized by direct polymerization. Poly(2-phenylimidazole-co-α, α-dichloro-p-xylene) is simultaneously a weak acid and a weak basic due to its special chemical structure. HCPs and 6FDA-based PI were blended to prepare the HCPs/PI MMMs by a solution casting process. The gas separation properties and molecular dynamic simulations of the HCPs/PI MMMs are researched by separation of CO 2 /CH 4 and O 2 /N 2 .

Preparation of PI MMMs
Synthesis of hyper-crosslinked polymers (HCPs) The synthetic route of HCPs refers to the literature [40,41]. The process is as follows: 5 mmol of 2phenylimidazole and 5 mmol of α, α´-dichloro-p-xylene were fully dissolved in 10.00 ml of 1,2dichloroethane, and then 10 mmol of FeCl 3 was added into the above solution. The system was polymerized at 80°C for 24 h under a nitrogen atmosphere. The resulting brown product was stirred in methanol for 24 h to remove unreacted monomers and anhydrous FeCl 3 . After the product was ltered and washed with ultrapure water, the product was dried in a vacuum oven at 60°C for 12 h. The nal product was called HCPs. The synthetic process is shown in Scheme 1. HCP characterization is shown in Figure S1. Figure S1 shows that HCPs are amorphous with a diameter of about 102 nm.

Preparation of PI MMMs
The HCPs were added to 5.0 ml of DMAc solution and stirred for 2 h (the mass ratio of HCPs and PI is 0.02, 0.04, 0.06, and 0.08). We then continued dispersing for another 1 h by ultrasonic treatment after 0.500 g of PI was added into the above system and stirred for 12 h to totally dissolve. This process was according to Freeman [42], and the synthesis process of 6FDA-based PI is shown in Scheme S1. The casting solution was evenly coated on an ultra-at watch glass, and DMAc was evaporated at 60°C.
Finally, the formed membrane was laid on a common watch glass to heat treatment at 60°C for 2 h, 120°C for 4 h, 180°C for 4 h, and 220°C for 12 h. The PI MMMs were obtained and labeled as HCPs-0.02/PI, HCPs-0.04/PI, HCPs-0.06/PI, and HCPs-0.08/PI. (A blank experiment with pure PI lm was prepared via the steps aforementioned except for adding HCPs.)

Characterization
The crystalline phase of HCPs and HCPs/PI MMMs was determined by an X-ray diffractometer (XRD, Bruker D8 Discover, German). After grinding the powders with an agate mortar, the powders were put on a glass slide and tested at 10°/min sweep speed with a Cu target. The tube voltage, the current, and the scan range were 40 kV, 200 mA, and 5°-50°, respectively. The chemical structures of HCPs and HCPs/PI MMMs were characterized by Fourier transform infrared spectroscopy (FT-IR, Bruker Vertex 70, German).
The test range of HCPs is 4000-600 cm -1 , which was tested by a KBr tablet method. The test range of MMMs is 4000-600 cm -1 via re ection mode test. The morphology of HCPs and HCPs/PI MMM adhered to the carbon conductive adhesive and was sprayed with gold and detected by a scanning electron microscope (SEM, Hitachi S4800, Japan). N 2 adsorption was used to measure the speci c surface area and pore size distribution of HCPs (BET and BJH, micromeritics ASAP2460, USA). The mechanical strength of the HCPs/PI MMMs was tested using a universal stretching machine (XD-121A, Shanghai Xinda Instrument Co., Ltd., China). The tested membranes were cut into 6 cm × 1 cm strips to test their tensile strength and elongation at breaking.

Evaluation of gas separation performance
Single gas permeation performances of pure PI lm and HCPs/PI MMMs were measured by the variablevolume method. After these membranes were placed into the porous supporter, the system was sealed in a speci c membrane chamber. The feed gas pressure was conveniently adjusted by a back-pressure gauge. The gas permeability was determined in the sequence of CH 4 , N 2 , O 2 , and CO 2 at 308.15 K under 0.1 MPa with an effective membrane area of approximately π cm 2 . The frame cell was degassed for 1 h to remove the residual air. The pressure on the lower side of membrane chamber was controlled at -0.1 MPa. The experimental data were recorded when the system was kept at a stable state.
Permeability (P, barrer) was the averaged value from three times experimental results. According to the growing rate of downstream pressure with time under steady state, P was calculated by Eq. (1) as below: Here, V is the gas volume under the membrane, A is the effective membrane area (cm 2 ), T is the experimental temperature (K), l is the thickness of membrane (cm), and p 2 is the upper pressure of membrane.
The ideal selectivity for two gases is calculated via Eq. (2): Eq. (2) Here, P A is the gas permeability of pure gas A, and P B is the gas permeability of pure gas B.

Molecular dynamic simulations
The FFV of PI lm and HCPs/PI MMMs was calculated by molecular dynamic (MD) simulation. Gromacs 2018.4 package was used to perform all molecular models for MD simulation. In detail, twenty-three molecular chains composed of dianhydride and diamine with 30 repeating units (including a big HCPs unit in MMMs) for each were placed in a cubic simulation cell and make the best use of the balance between cell dimension and calculation time. Energy minimization processes over 800 iterations to obtain stable structures were used to perform all of the molecular models. Then, the MD calculations were carried out under an NVT ensemble for duration of 100 ps at 300 K. The Newton second law of motion was applied to estimate the dynamic behaviors of polymer molecules. The theoretical calculations adopted the COMPASS force eld. The FFV of PI lm and HCPs/PI MMMs can be calculated by the following Eq. (3): Here, V 0 , V 1 and V 2 are the speci c volume, occupied volume and the van der Waals volume of 6FDA based polyimide, respectively.

SEM images of PI membranes
Whether HCPs can be uniformly dispersed in MMMs is an important indicator for evaluating the quality of MMMs. Gas separation performance will greatly reduce once the HCPs get together and form agglomeration. Fig. 1a and 1b show the overlooking SEM image and the cross-sectional SEM image of pure PI lm, respectively. A pure PI lm with a homogenous structure is relatively smooth and dense. Fig.  1c

FT-IR spectra of PI membranes
FT-IR spectra can assess the degree of amidization of the polymer. The FT-IR spectra of pure PI lm and different HCPs/PI MMMs are shown in Fig. 2. The wavenumber at 1785 cm -1 and 1725 cm -1 is the symmetric and asymmetric stretching vibration peaks of C=O in the imides groups, while the wavenumber at 1370 cm -1 and 718 cm -1 is the stretching and bending vibration peaks of C-N [43,44]. The characteristic peak at about 3300-3500 cm -1 is the stretching vibration of N-H in poly(amic acid), which is not detected. The result shows that the polymers achieved amidation. In addition, the assigned peaks at 1250 cm -1 and 1140 cm -1 are the stretching vibration of C-F in PI, demonstrating that the uorinated polyimides have been successfully obtained [45]. The characteristic peaks of different HCPs/PI MMMs are the same as those of pure PI lm, indicating that no new chemical bond was formed between HCPs and PI.

Mechanical strength of PI membranes
The MMMs need to withstand a certain pressure during gas separation. Therefore, the MMMs should have su cient mechanical strength. The mechanical strength of HCPs/PI MMMs is necessarily assessed. Elongation at breaking and the tensile strength of pure PI lm and different PI/HCPs MMMs are displayed in Fig. 3. As shown in Fig. 3 [46,47]. The tensile strength of HCPs/PI MMMs will reduce because of excessive HCPs that may be related to the interfacial effect forming agglomeration of HCPs.

Gas separation performance
Gas separation performance is an important and ultimate index to evaluate the quality of MMMs. Fig. 4a shows gas separation performance of pure PI lm and HCPs/PI MMMs for CO 2 /CH 4 at 35°C and 0. To better assess gas transport properties of MMMs, the CO 2 and CH 4 permeability and ideal selectivity data are displayed in Fig. 4b in a Robeson's diagram for the corresponding CO 2 and CH 4 pair. The ideal selectivity obviously decreases as Robeson de nes the linear relationship as "upper bound" accompanied by an improvement of gas permeability in MMMs. Here, the CO 2 and CH 4 are below the upper-bound line and represent the perfect combination of permeability and ideal selectivity for the xed gas pair. However, they show a favorable tendency to increase the gas permeability, while the ideal selectivity basically remains unchanged after adding HCPs, which is different from the typical trade-off phenomenon of polymer membranes. In this respect, the HCPs are used to prepare MMMs in an effective approach to successfully improve gas transport and break the trade-off effect. Obviously, as shown in Fig. 4a and Fig. 5a, HCPs/PI MMMs have relatively weaker transport abilities to CH 4 , O 2 , and N 2 than CO 2 . HCPs with imidazole-type poly-ionic liquid structures have certain catalytic properties for the cyclization of CO 2 to carbonate. These can be used as a CO 2 capture and conversion material [49][50][51][52]. This makes CO 2 easy to be adsorbed in HCPs. When HCPs are used as the ller of PI MMMs, the solubility coe cient of PI MMMs to CO 2 can be enhanced, and it may increase the gas permeability and accelerate the CO 2 gas transport.
The results on permeability and ideal selectivity in the Robeson's diagram for the corresponding O 2 and N 2 pair (Fig. 5b) are analogous to the corresponding CO 2 and CH 4 pair; however, the permeability and ideal selectivity of HCPs/PI MMMs to O 2 /N 2 are obviously lower than those of CO 2 /CH 4 . This also demonstrates that the interaction between HCPs and CO 2 leads to better permeability and selectivity than that of HCPs and O 2 .

Analysis of gas separation process
The gas separation performance of MMMs strongly depends on MMM structures. To gain an insight into the relation between the permeability and selectivity of MMMs and microstructure, the average interspacing distance (d-spacing) stands for the distance between polymer chain segments that re ects the permeability coe cient of MMMs. The d-spacing value of MMMs can be calculated by Bragg's equation [28]. XRD patterns of the PI lm and HCPs/PI MMMs are shown in Fig. 6 Fig. 7 shows that the free volume of HCPs/PI MMMs is signi cantly larger than that of pure PI lms. According to the literature, the large free volume provides a fast channel for gas transport, thereby enhancing gas permeability [27,45]. The other simulation results of MMMs containing different HCP amounts are shown in supporting information Fig. S2; the speci c values obtained by simulation are shown in supporting information Table S1.
The density of HCPs/PI mixed polymers in stable state varied from 1.5358 to 1.3553 g/cm 3 , which is higher than 6FDA-based polyimides, and the FFV of MMMs (0.1892-0.2498) is also higher than most of 6FDA-based polyimide [54]. Combining supporting information Fig. S2 with Table S1, we see that the FFV of MMMs containing different HCP amounts is larger than that of pure PI lms. As the amount of HCPs increases, the FFV of PI MMMs rst increases and then slightly decreases. Therefore, although the permeation ux of HCPs/PI MMMs to different gases is higher than that of pure PI lms, the gas transport of HCPs/PI MMMs does not always increase with more HCPs. When the amount of HCPs added is 0.04%, the FFV of HCPs/PI MMMs reaches a maximum (0.2498). Therefore, the permeability of different gases is the largest. The permeability gradually reduces as even more is added. This also proves that the gas permeability not only is related to the d-space of the membranes but also has a greater relationship with the FFV of the membrane. In contrast, the ideal selectivity of different gas pairs reduces according to the large FFV; this result agrees with Fig. 4 and Fig. 5.

Conclusion
In this work, HCPs/PI MMMs were successfully obtained by HCPs containing 2-phenylimidazole structure as a ller and 6-FDA-based PI as a polymer matrix. The as-prepared MMMs were characterized by XRD, FT-IR, SEM, and a universal tensile testing machine. The results show that the as-prepared HCPs/PI MMMs were amorphous with no chemical bonding between HCPs and PI. The HCPs could be easily dispersed in the PI matrix. Even at 0.08 wt.% HCP, the MMMs still did not cause defects at the interface between HCPs and PI due to their perfect compatibility other than slight agglomeration.
The MMMs had good mechanical properties due to the structure of PI itself and the presence of HCPs. When the HCPs were 0.04 wt.%, the tensile strength at break of MMMs was as high as 44.2 MPa, which is much greater than the 24.0 MPa of pure PI lm. Gas permeation experiments showed that MMMs had better gas transport capabilities than pure PI lms, especially for CO 2 ; the permeability was improved, and the ideal selectivity is maintained without drastically decreasing. The permeability of CO 2 and O 2 was 69.6% and 73.5% higher than that of pure PI lm, and the permeability of CH 4 and N 2 was 124.0% and 91.6% higher than that of pure PI lm. However, the ideal selectivity of MMMs for CO 2 /CH 4