For synthesizing ROFs, benzene-1,3,5–tricarbaldehyde— 2,2′-(Ethylenedioxy)bis(ethylamine) or 4,7,10-trioxa-1,13-tridecanediamine—acetonitrile (MeCN), and N-methyl-2-pyrrolidone (NMP) were used. All reagents were purchased from Sigma-Aldrich and used without further purification (purity ≥98%).

Four polymeric materials (P1–P4) were synthesized and used to fabricate the corresponding membranes (M1–M4). Each polymer was obtained via an imine-condensation reaction between benzen-1,3,5-tricarbaldehyde core centers and one of 2,2′-(Ethylenedioxy)bis(ethylamine) or 4,7,10-trioxa-1,13-tridecanediamine segments. Polymers P1 and P2 were prepared using the former, while P3 and P4 were synthesized using the latter with an aldehyde-to-diamine molar ratio of 1:1.5. MeCN was used as the solvent for P1 and P3, while NMP was used for P2 and P4. The resulting polymer solutions were transferred into 100-mL round-bottom flasks and refluxed at 70 °C with continuous stirring overnight. The chemical structures of the reaction units used to synthesize the four polymers are presented in Supplementary Figure S1.

After polymerization, membranes M1–M4 were obtained by casting the corresponding polymer solutions (P1–P4) onto Teflon plates, followed by slow solvent evaporation and drying under vacuum at 80 °C overnight. The choice of MeCN and NMP as solvents for ROF synthesis was based on their polar aprotic nature, which supports reversible imine bond formation and ensures good solubility of all monomers. Moreover, their distinct boiling points and polarity profiles influence membrane morphology: MeCN promotes faster evaporation and denser structures, while NMP allows more reaction time, probably leading to an open network formation due to slower solvent removal. These differences impact the microstructure and, ultimately, the gas separation performance of the resulting membranes.

The physicochemical properties of fabricated ROF membranes were characterized before gas permeability testing. The chemical structures were confirmed by ¹H NMR (BRUKER NMR AVANCE 300 MHz) and FTIR spectroscopy (Nicolet 710). Thermal stability was assessed via thermogravimetric analysis (TGA, Hi-Res TGA 2950, TA Instruments) and differential scanning calorimetry (DSC, Modulated DSC 2920, TA Instruments). The thickness and quality of the cast membranes were examined using scanning electron microscopy (SEM, Hitachi S-4800 field emission microscope). A digital micrometer was used to manually measure the membrane thickness at five different points. The average value and standard deviation were calculated to ensure accuracy and account for variability. The contact angle was measured using ImageJ software to provide insights into the membrane surface properties, particularly hydrophobicity.

Single gas permeability measurements for CO₂ and CH₄ gases with purity (99.99%) were carried out at 30 °C using the experimental setup shown in Figure 1. The setup was composed of two identical compartments (feed and permeate) made of stainless steel, which were separated by the membrane to be tested with an effective surface area of 9.62 cm². The desired pure gas was pressurized through both compartments (feed and permeate) and a pressure difference (∼0.7 bar) was imposed after opening the permeate outlet. Two pressure transducers (Druck, PDCR 910 models 99166 and 991675, England) were used to monitor the pressure profiles in each compartment. An Elcometer^® 124 Thickness Gauge (United Kingdom) instrument was used to estimate the membrane thickness.

The ¹H-NMR spectra for the synthesized polymers were recorded in deuterated chloroform (CDCl₃) at 300 MHz (Figures 2a,b). The spectra in Figure 2 indicate the presence of signals at 8.5–8 ppm, which are associated with the formed imine bond formation (PEO–NCH) within the polymer matrix. The signals around 8.0–7.5 ppm correspond to the aromatic benzene rings, while those at the aliphatic region (4.0–1.0 ppm) correspond to the methylene (–CH₂–) protons of PEGs groups (Vöge et al., 2014b; Abdelrahim et al., 2016).

Figure 3 shows the FTIR spectra of the synthesized ROF membranes, confirming the formation of imine bonds. The peaks at 1,661.3 cm^-1 correspond to C=N stretching mode for imine groups within the polymer structure, while the peak of aldehyde groups observed at 1700 cm^-1 disappear (Abdelrahim et al., 2016; Ioannidi et al., 2021). The peaks at 2,926.4 cm^-1 and 874.5 are respectively associated with C–H stretching and bending modes for aliphatic PEO (Luo et al., 2016; Vollas et al., 2018). The peaks at 2,871.6 cm^-1 and 1,097.0 cm^-1 are respectively attributed to C–H (aliphatic) stretching and bending modes (Abdelrahim et al., 2016; Ioannidi et al., 2021). The peaks at 1,447.3 cm^-1 and 1,254.5 cm^-1 are respectively linked to the C=C stretching mode of aromatic ring and C–O ether bonds (Vöge et al., 2014a; Luo et al., 2016; Ioannidi et al., 2021).

Figure 4a shows the TGA measurements for the fabricated membranes. The polymeric samples were preheated at 100 °C for 30 min under nitrogen flow (10 °C/min) to remove the adsorbed water within the polymer matrix. The degradation curves were recorded in a nitrogen flow (10 °C/min) to a maximum heating temperature (700 °C). It was observed that there are two stages of thermal degradation for all membranes. The first degradation stage had a mass loss of ∼10 wt% for M1 and M2 at 100 °C–175 °C and a mass loss of ∼5 wt% for M3 and M4 at 100 °C–250 °C.

This first degradation stage is attributed to the evaporation of moisture and residual solvent present within the polymer’s backbone. The second degradation stage shows a mass loss of ∼95 wt% for M1 and M2 occurring between 175 °C and 450 °C, while for M3 and M4, a similar mass loss of ∼95 wt% occurred between 250 °C and 700 °C. This degradation stage should be ascribed to the thermal decomposition and loss of polyethylene oxide (PEO) chains within the membrane structure (Fares et al., 1994; Theodosopoulos et al., 2017; Ioannidi et al., 2021). The main decomposition products were non-cyclic ethers (i.e., ethoxy-ethane and methoxy-methane), ethylene oxide, CO₂, CO, and water (Fares et al., 1994; Theodosopoulos et al., 2017; Ioannidi et al., 2021).

The two stages in the figure demonstrate that higher temperatures are required for thermal degradation in membranes with longer PEO chains (M3 and M4) than those with shorter PEO chains (M1 and M2). This indicates that the thermal stability of M3 and M4 is higher than that of M1 and M2 owing to the presence of longer PEO chains. These enhance the degree of crystallinity within the membrane structures, as previously observed in other PEO-based membranes, where crystallinity increased with the length of the PEO backbone (Theodosopoulos et al., 2017; Ioannidi et al., 2021; Sandru et al., 2024).

Figure 4b shows the differential scanning calorimetry (DSC) measurements for the fabricated membranes. The measurements were performed under nitrogen flow (10 °C/min) up to a maximum heating temperature of 150 °C. As shown in the figure, the recorded glass transition temperatures (Tg) are approximately −45, −20, 5, and 50 °C for M1, M2, M3, and M4, respectively. This means that membranes M3 and M4 with longer PEO chains exhibit higher Tg values than M1 and M2, which have shorter PEO chains. As mentioned before, this might be related to the crystallization behavior of longer PEO chains within the polymer matrix, which enhances the potential for higher crosslinking through the membrane’s backbone. Furthermore, higher Tg values indicate restricted segmental motion and a more rigid ROF network, which tends to reduce chain packing defects and enhance size-sieving. This results in improved selectivity, especially for gas pairs with small differences in kinetic diameter, such as CO₂ and CH₄ with kinetic diameters of approximately 3.3 Å and 3.8 Å, respectively (Robeson, 2008; Robeson et al., 2009). Therefore, ROF membranes with higher PEO content are expected to achieve slightly increased Tg and corresponding improvements in CO₂/CH₄ selectivity, consistent with this mechanism.

Figure 5 and Supplementary Figure S2 represent the contact angle values obtained for the fabricated ROF membranes. The measurements were recorded using the ImageJ contact angle plugin, a widely used image analysis tool for quantifying the wettability of surfaces by measuring the contact angle formed between a liquid droplet and a solid substrate. The analysis provides an accurate and reproducible estimation of surface hydrophilicity or hydrophobicity. In this study, water droplets were placed on the membrane surface, images were captured with a calibrated camera, and three measurements per sample were averaged to ensure reliability and minimize error due to surface heterogeneity (Giovambattista et al., 2007).

As shown in Figure 5 and Supplementary Figure S2, the reported contact angle values represent the average of the observed left- and right-angle measurements, which were nearly identical. The relatively high contact angles suggest that the fabricated membranes possess high hydrophobicity and a symmetrical surface morphology. Moreover, Figure 5 shows that the recorded contact angles for membranes with longer PEO chains (M3 and M4) are slightly higher than those for membranes with shorter PEO chains (M1 and M2). This means that M3 and M4 exhibited higher hydrophobic surface properties than M1 and M2, owing to the higher crosslinking degree within the M3 and M4 membrane backbones.

Furthermore, the figure showed that the synthesized membranes demonstrate this trend consistently. This is a surprising observation, showing the solvent effect on the polymerization and crosslinking properties of the fabricated polymeric membranes, as it results in variations in the chemical, crosslinking, and hydrophobic properties of the developed membranes. In addition, the contact angle measurements obtained agree with the data from the thermal analysis measurements: membranes synthesized in NMP solvent (M2 and M4) exhibited slightly higher thermal degradation stability and glass transition temperatures than those synthesized in MeCN solvent (M1 and M3, respectively) under similar polymerization conditions.

The organic solvent enhances the mobility of the building units, increasing the likelihood of the reactive groups approaching each other to initiate polymer bond formation (HC = N). Additionally, the NMP solvent interacts more strongly with the PEO segments, removing water from interactions with the PEO chains and therefore controlling the structural organization of the ROF materials; this affects their pore distribution and fractional pore volume within the membrane backbones. Therefore, the utilization of organic solvents with different polarities in the polymerization reaction affects the chemical structure of the fabricated ROF membranes, as previously observed in molecular simulation studies (Dupuis et al., 2022).

Figures 6, 7 present the SEM images of the fabricated polymeric membranes, displaying both surface and cross-section views, respectively. The SEM images reveal that the membranes exhibit a dense and nonporous structure. The thickness of the membranes was consistently approximately 300 ± 25 μm, indicating uniformity in membrane fabrication. Additionally, no visible pores or defects were observed on the membrane surface, confirming its compact nature. The recorded thicknesses agree with our previous findings (Abdelrahim et al., 2016; Sandru et al., 2024), and were chosen based on our prior experience with ROF membranes to balance mechanical stability, ease of handling, and reproducible casting. A uniform thickness is critical for minimizing defect formation during solvent evaporation. While permeance is inversely proportional to membrane thickness, selectivity remains largely unaffected as it depends on the ratio of gas permeabilities. This behavior is consistent with the solution–diffusion transport mechanism typical for dense and hybrid polymer membranes. Furthermore, Figure 7 shows that M1 and M2 display homogeneous monolithic profiles, whereas M3 and M4 reveal faint lamellar features near the edges, attributable to PEO-induced phase separation. These minor differences in surface texture and layer uniformity align with variations in solvent evaporation rates and polymer PEO segment mobility, which are critical for tailoring membrane properties.

The flexibility and manual mechanical test for the fabricated ROF membranes was performed by us previously (Sandru et al., 2024). As shown in Supplementary Figure S3, the ROF membrane exhibited good flexibility and mechanical integrity upon manual bending and folding. No visible cracks, delamination or structural damage were observed, indicating that the ROF membrane possesses sufficient mechanical robustness for handling and potential gas separation applications.

The pure gas permeabilities through the fabricated membranes (M1–M4) and the ideal selectivities for the pure gases CO₂ and CH₄ were determined at 30 °C under a pressure difference of 0.7 bar (Supplementary Table S1). The results show that, for all membranes, CO₂ permeability is higher than CH₄ permeability. This behavior is attributed to specific parameters such as the dipolar interactions of CO₂ molecules with the imine (–HC = N) and PEO functional groups within the ROF membranes, as well as the higher polarity and quadrupole moment of CO₂ in comparison with the nonpolar CH₄ gas. Moreover, the kinetic diameter of CO₂ is smaller than that of CH₄, which facilitates its diffusion. These factors collectively influence CO₂ adsorption affinity and diffusion through the fabricated membranes (Bao et al., 2011; Basu et al., 2011; Herm et al., 2011; Nordin et al., 2015; Yahia et al., 2024; Yahia et al., 2025). Furthermore, CO₂ permeability through the M3 and M4 membranes was higher than that of M1 and M2, indicating the influence of membrane composition on gas transport properties. This might be related to the higher hydrophobic surface and higher glass transition properties of M3 and M4 compared to M1 and M2 owing to the differences in the PEO chains within the membrane’s backbones. As mentioned previously, M3 and M4 possess longer PEO chains, and this might cause an increase in the fractional free volume (FFV) and enhance CO₂ diffusion through the membrane chains. Furthermore, the membranes synthesized in NMP solvent showed higher permeability values and selectivity than those synthesized in the MeCN solvent. This behavior could be attributed to the solvent’s effect on the membrane’s chemical structure and crosslinking degree, as mentioned in Sections 3.3 and 3.4.

Figure 8 shows the relationship between the permeability (PCO₂) and ideal selectivity (CO₂/CH₄) for the fabricated membranes. Results show that the ideal selectivity for membranes fabricated with shorter PEO chains is higher than for membranes fabricated with longer PEO chains. This indicates that the presence of longer PEO chains within the membrane structure slightly increases both CO₂ permeability and ideal selectivity. It is worth noting that both CO₂ permeability and ideal selectivity increase simultaneously, which is uncommon (Robeson, 1991; Freeman, 1999; Robeson, 2008; Robeson et al., 2009; Swaidan et al., 2015; Comesaña-Gándara et al., 2019; Corrado and Guo, 2020). This indicates that replacing short-chain functional groups with longer-chain groups within the membrane structure improves membrane performance. Therefore, the incorporation of longer polyethylene oxide (PEO) chains and NMP solvent into the membrane matrix was expected to enhance CO₂ permeability over CH₄. This effect is attributed to structural changes in the membrane and enhanced affinity toward CO₂ (Dupuis et al., 2022; Sandru et al., 2024).

Furthermore, the kinetic diameters of CO₂ and CH₄ are approximately 3.3 Å and 3.8 Å, respectively (Robeson, 2008; Robeson et al., 2009). This difference plays a critical role in their transport through the membrane. In polymeric and hybrid membranes such as ROF-based MMMs, gas separation occurs predominantly via the solution–diffusion mechanism, where permeability is a function of both diffusivity and solubility. The smaller size of CO₂ allows it to diffuse more easily through the membrane matrix, while its higher condensability and quadrupole moment enable stronger interactions with polar groups such as ether oxygens in PEO and imine functionalities (–HC = N) within the ROF framework (Fares et al., 1994; Giovambattista et al., 2007; Basu et al., 2011; Nordin et al., 2015). These interactions enhance CO₂ solubility via dipole-quadrupole and Lewis acid–base interactions, resulting in significantly higher CO₂ permeability and selectivity over CH₄. On the other hand, CH₄, being non-polar and less condensable, lacks such specific interactions and exhibits lower diffusivity due to its larger kinetic diameter. Therefore, the combination of size-exclusion effects, specific CO₂–polymer interactions, and the flexible as well as microporous nature of ROFs synergistically contribute to the observed superior CO₂/CH₄ separation performance.

Nevertheless, the most significant goal in gas membrane development is the combination of high permeability and acceptable selectivity, which is limited by the trade-off between permeability and selectivity. Furthermore, Figures 9a, b illustrate the CO₂/CH₄ separation performance of the fabricated ROF membranes (M1–M4) compared to previously reported PEO-based membranes (Supplementary Table S2—Rahman et al., 2013; Tena et al., 2013; Ghadimi et al., 2014; Qiu et al., 2016; Bengtson et al., 2017; Chen et al., 2017; Nebipasagil et al., 2017; Bandehali et al., 2020) plotted against the 1991, 2008, and 2015 Robeson upper-bound correlations (Robeson, 1991; Robeson, 2008). The CO₂/CH₄ selectivity is shown as a function of CO₂ permeability.

The reference lines represent the Robeson upper bounds, which indicate the classical trade-off between permeability and selectivity observed in most polymeric membranes. Typically, as permeability increases, selectivity decreases. In contrast to this trend, the fabricated membranes in this study (M1–M4) show a clear and steady increase in both CO₂ permeability and CO₂/CH₄ selectivity as we move from M1 to M4. Specifically, M1 and M2 lie below the 1991 Robeson upper bound, M3 lies directly on this upper bound, and M4 surpasses the 1991 limit and approaches the 2008 Robeson upper bound, thus demonstrating significant overall improvement in separation performance.

This remarkable behavior can be attributed to the tailored design of the ROF membranes through the incorporation of different PEO segment lengths and the use of organic solvents with varied polarity during the synthesis process. This strategy enhances polymer packing, dynamic mobility, and gas sorption affinity. Specifically, the increased CO₂ affinity of the ROF membranes (via PEO and imine groups), combined with the smaller kinetic diameter of CO₂ relative to CH₄, improves CO₂ transport without negatively impacting CH₄ transport, thus permitting performance beyond the 1991 Robeson limit and potentially enabling future designs to surpass both the 2008 (Robeson, 2008) and 2015 (Swaidan et al., 2015) upper bound limits. Hence, our findings strongly support the hypothesis that the strategic tuning of polymer architecture and processing conditions can overcome the conventional permeability–selectivity trade-off and unlock new performance frontiers for CO₂/CH₄ separation. This validates the promise of ROF membranes as a competitive platform for advanced gas separation applications. Furthermore, to evaluate the stability of the fabricated ROF membranes, preliminary aging tests were conducted by storing the membranes under ambient conditions for 1 month. The results showed no significant changes in gas permeability or selectivity, indicating good structural stability and resistance to physical aging over time.

As shown in Supplementary Table S3, the developed ROF membranes (M1–M4) demonstrate CO₂ permeability (155.54–179.76 barrer) superior to conventional polymeric membranes such as cellulose acetate (CA) (1.26–52.6 barrer) (Moghadassi et al., 2014; Sanaeepur et al., 2016; Mubashir et al., 2018; Mubashir et al., 2019; Jia et al., 2020) and Matrimid^® (12–20 barrer) (Dorosti et al., 2014; Kertik et al., 2017). While some CA-based membranes achieve higher CO₂/CH₄ selectivity (up to 53.98—Moghadassi et al., 2014), this is typically accompanied by low CO₂ permeability (≤5 barrer), highlighting the permeability–selectivity trade-off common in polymeric membranes. In contrast, the synthesized membranes (M1–M4) exhibit a balanced performance, with selectivity values (15.45–31.4) comparable to or exceeding those of commercial membranes, such as CA: 4.44–53.98 (Moghadassi et al., 2014; Sanaeepur et al., 2016; Mubashir et al., 2018; Mubashir et al., 2019; Jia et al., 2020) and polyimide (P84): 67–93 (Guo et al., 2018; Sheng et al., 2020), while maintaining significantly higher gas permeation rates. Furthermore, the solvent choice (NMP or MeCN) appears to influence membrane performance, with NMP-processed membranes (M2, M4) showing marginally higher permeability and selectivity than their MeCN counterparts (M1, M3). This trend aligns with studies on conventional polymers, where solvent selection impacts membrane morphology and gas transport properties (Moghadassi et al., 2014; Sanaeepur et al., 2016; Mubashir et al., 2018; Mubashir et al., 2019; Jia et al., 2020). Notably, the performance of M3 and M4 approaches the upper bound for polymeric membranes, suggesting their potential for industrial CO₂/CH₄ separation applications where both high permeability and selectivity are critical.

Although single-gas permeation tests were conducted in the current study due to the limitations of our manual setup (operating up to 3 bar), these tests remain widely accepted for preliminary screening of membrane materials, offering valuable insights into intrinsic permeability and selectivity (Baker and Low, 2014). The applied conditions (30 °C, up to 3 bar with pressure difference ∼0.7 bar) are also relevant to practical applications such as biogas upgrading (Sridhar et al., 2007). To complement these results, our group recently investigated structurally related ROF-based membranes under mixed-gas and elevated-pressure conditions (3–10 bar) using an advanced gas permeation setup. The results of that research (Sandru et al., 2024) revealed stable CO₂/CH₄ selectivity trends under realistic conditions and confirmed the robustness of ROF membranes up to 10 bar. These findings reinforce the current results and support the suitability of ROF membranes for applications such as biogas and landfill gas upgrading. Future research will focus on evaluating the long-term and high-pressure performance of the present ROF membranes under industrially relevant mixed-gas conditions.