Network completeness enables angstrom-scale transport pathways in polymer membranes

Abstract

Achieving high molecular selectivity without compromising mechanical robustness remains a central challenge in separation science. Here we report polymer networks containing covalently embedded diffusion channels that integrate porous frameworks within the polymer matrix. By systematically tuning crosslinking motifs, we introduced network completeness as a quantitative design descriptor that connects bridge connectivity to separation performance. Our density-probe approach provided experimental evidence of sub-3 Å pores, a feature previously only speculated or simulated. The hydrogen-selective ms-oDMB-DB50 membrane surpasses state-of-art polymer performance thresholds while maintaining stable operation over extended periods. This design rule combines engineering practicality with effective diffusion channels arising from a reticular-style network architecture and density-probe readouts. Our results establish a framework for reticular-style design in polymers and identify structural attributes that enable dual-domain functionality for advanced molecular separations.

It is challenging to balance molecular selectivity without compromising mechanical properties. Here, the authors introduce network completeness as a key descriptor to guide the design of subnanometer diffusion channels in hyper-crosslinked polymer membranes. By linking bridge connectivity to separation performance, the authors present an optimized balance of molecular selectivity and mechanical robustness.

Introduction

The key to unlocking the full potential of porous membranes lies in engineering efficient transport channels^1–3. Uniform and well-defined pore structures are essential for achieving selective molecular separation, yet remain challenging to realize in practice^4,5. Reticular synthesis of framework-based porous materials, such as metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) has enabled significant advances in the formation of periodic pores^6–8. Nevertheless, achieving complete node connectivity or defect-free membrane fabrication remains challenging, often requiring the use of binders or matrices^9–12. Modulated approaches, such as electronically induced deprotonation, were introduced to enhance node connectivity¹³. However, even with improved node connectivity and sub-4 Å pore sizes, these membranes have been primarily demonstrated in light hydrocarbon separations.

Polymer membranes, on the other hand, offer complementary engineering advantages, including solution-processability and mechanical robustness¹⁴. Recent studies on high-performing synthetic polymers have focused on varying building units to disrupt chain packing and incorporate more Langmuir-type static pores¹⁵. Nevertheless, the porosity in such polymers is considerably smaller than that of conventional porous materials, and the inherently probabilistic nature of transient pores often leads to underestimation in adsorption-based characterization^16,17. Alternative strategies relating to crosslinked high free volume polymers have been investigated to explore molecular sieving¹⁸. More recently, electron beam irradiation-assisted polymerization has been introduced to modify the microstructure of polymer membranes¹⁹. Hyper-crosslinked polymers, which follow a semi-modular strategy similar to COFs and MOFs, can introduce permanent porosity into membranes²⁰. The post-synthetic nature of the reaction allows structural variation. However, practical membrane fabrication has largely relied on dimethoxymethane crosslinkers due to synthetic challenges and incomplete understanding of this class of materials^21–24. Moreover, its pore-forming process remains insufficiently controlled, preventing rational tuning of polymer porosity and limiting its potential for high-precision separations^25,26.

Together, these limitations drive the need for a design principle that combines the structural precision of frameworks with the processability of polymers. Here, we report a modular network design using electron-rich bridging units that expands access to previously unexplored architectures. We introduce the concept of network completeness, a quantitative metric that decouples crosslinking conversion from bridge connectivity to directly link molecular architecture to pore formation. By applying complementary probes of different kinetic diameters, we elucidate the dual nature of hyper-crosslinked polymer membranes as both porous frameworks and polymeric networks and show how this duality governs molecular transport. This design principle establishes a generalizable paradigm for rationally engineering network polymers and extends the membrane design space beyond the limits of existing polymer systems.

Results

Network architecture and structural transformation

To systematically control the network structure, we designed a modular framework by covalently bonding brominated polyphenylene oxide (DB50) main chain with dimethoxybenzene (DMB) isomers (Fig. 1a). In fact, DMB readily undergoes electrophilic substitution and self-polycondensation into hyper-crosslinked polymers when exposed to electrophiles²⁷. Due to their electron-rich aromatic structures, these units are highly prone to uncontrolled polycondensation, a reactivity that has been exploited for designing hyper-crosslinked polymers as porous frameworks²⁸. As a result, this complicates their incorporation as bridging units and requires delicate control to avoid unwanted polycondensation. We therefore adopted a temperature-dependent approach that suppresses carbocation activity by chilling the crosslinker solution to −1 °C, enabling efficient crosslinking during synthesis. At higher temperatures, the loss of regulation over the crosslinking process was observed, which correlated with a decrease in membrane selectivity (Supplementary Fig. 1).

Fig. 1. Network architecture and physical appearance of hyper-crosslinked polymer membranes.

a Schematic illustration of network polymer membrane structure and representative chemical structures describing network completeness. b Modular design of the final network structure, using DB50 backbones and bridging units: o-DMB, p-DMB, and DMM. c Physical appearance of representative hyper-crosslinked DB50 membrane (ms-oDMB-DB50); the photograph was taken with backlighting to show its transparency. Scanning electron microscopy (SEM) scale bars are 500 nm (top right, surface and cross-section image of ms-oDMB-DB50) and 20 µm (bottom row, cross-section image of DB50 and ms-oDMB-DB50). d Fourier-transform infrared (FTIR) spectra of DB50, pDMB-DB50, oDMB-DB50, and ms-oDMB-DB50.

We fabricated three different network polymer membranes by crosslinking o-DMB, p-DMB, and DMM externally to attain oDMB-DB50, pDMB-DB50, and DMM-DB50, respectively (Fig. 1b). For oDMB-DB50, an additional sample was prepared with twofold higher concentrations of both the crosslinker and catalyst to achieve a more extensively crosslinked network structure (hereafter ms-oDMB-DB50). None of the network polymer membranes showed visible macropores, and all remained transparent, suggesting that the dense internal structures were well-preserved (Fig. 1c, Supplementary Figs. 2-3). The macroscopic preservation led us to investigate molecular-level architecture.

We then shifted our focus to a molecular-level investigation of the crosslinked architecture to understand how different crosslinkers shape the network’s structural features. FTIR spectroscopy screened the chemical signatures of oDMB-DB50, pDMB-DB50 and DB50. Representative peaks of DB50 were preserved in oDMB-DB50 and pDMB-DB50, indicating that DB50 units were incorporated into their structural backbone (Fig. 1d). Building on this observation, two characteristic bonding environments were identified. A split peak at 1500-1530 cm⁻¹, originating from the direct linkages between aromatic rings, confirmed network formation. Meanwhile, signals at 1050–1100 cm⁻¹, arising from the ether bond in methoxyphenyl groups, suggested that some bridges remained incomplete. Nuclear magnetic resonance (NMR) further confirmed that the intended network structures were achieved (Supplementary Figs. 4, 5). For DMM-DB50, the synthesis and structural characterization were already well established in previous studies^21–24, and the design specifically targeted a level of crosslinking optimized to maximize membrane performance.

Impact of network completeness on physical properties

We first quantified the structural transformation from linear to network polymers using conventional descriptors, namely crosslinking degree (CD) and effective crosslinking degree (ECD)²⁹. CD represents the fraction of consumed crosslinkable sites, whereas ECD accounts for crosslinks that can potentially contribute to network connectivity, including partially connected linkages. Both CD and ECD were estimated from deconvoluted NMR peak area (Supplementary Tables 1-4). DMB-derived hyper-crosslinked DB50s exhibited CD and ECD that were greater than DMM-DB50, even under the latter’s extreme reaction conditions (Fig. 2a, Supplementary Table 5). This suggests that DMB, bearing an aromatic ring, is less affected by the steric hindrance from the polymer backbone compared with the short external crosslinker, such as DMM during the crosslinking. Furthermore, both CD and ECD showed only marginal variation across the samples, except for DMM-DB50. Although ECD helps assess structural durability and quantifies crosslinks, it remains insufficient to determine whether the introduced crosslinkers form complete bridge structures that generate static pores.

Fig. 2. Structural transformations with network formation and completion.

a Crosslinking level indicators crosslinking degree, effective crosslinking degree, and bridge connectivity of hyper-crosslinked DB50. Individual data points are plotted as dots without edges (n = 2). Mean values are represented with edges, and error bars represent the standard deviation. b Suppression of long-range order upon network formation after network formation (left) and with increasing crosslinking level (right). The shaded areas correspond to the crystalline contributions. c Structural changes associated with enhanced thermal stability, as evidenced by derivative thermogravimetry (DTG) curves.

To capture the impact of network completeness-induced reticular structure, we defined the bridge connectivity degree (BCD), which was also obtained from NMR peak deconvolution. BCD effectively quantifies the fraction of crosslinks that form complete bridges by connecting both ends. These completed bridges, distinct from partially connected linkages, contribute to the formation of network pores. For two cases employing DMB crosslinkers, comparable BCD values were obtained for pDMB-DB50 (57%) and oDMB-DB50 (55%). In contrast, DMM-DB50, prepared with a shorter crosslinker, exhibited a slightly lower BCD (51%). Although the variation is smaller than that observed for CD and ECD, it still suggests that BCD is not entirely independent of geometric factors. Importantly, BCD increased from oDMB-DB50 (55%) to ms-oDMB-DB50 (73%), showing that higher crosslinker concentration improves network completeness, resulting in effective transport pathways. The increased fraction of completed bridges also renders ms-oDMB-DB50 more compact, reducing its thickness relative to oDMB-DB50 (Fig. 1c, Supplementary Table 6). The introduced BCD thus quantitatively defines the concept of network completeness and provides a framework applicable to diverse polymer networks in which pores serve as a key factor.

We next examined physical properties reflecting structural transformation induced by changes in network connectivity. For networks formed with DB50, crystallinity decreased relative to the precursor polymer membrane, reflecting disruption of long-range order by bridge formation (Fig. 2b)³⁰. Crystallinity, initially 24% in the precursor, disappeared in DMM-DB50 and pDMB-DB50 but persisted at 14% in oDMB-DB50. Although DMM-DB50, pDMB-DB50, and oDMB-DB50 exhibited a similar BCD, only oDMB-DB50 retained partial crystallinity, suggesting the effective role of the bridging unit in reticular design. To better understand the structural transformation, we focused on the oDMB-DB50 series and examined how it affected thermal stability. During the transition from DB50 to oDMB-DB50, DTG peaks coalesced from two to one with a slight temperature shift, whereas ms-oDMB-DB50 exhibited a more pronounced shift of the main peak (Fig. 2c). These progressive changes mirror the transition to more complete network formation, supporting the observed thermal stability.

Two domains of the network polymer membranes

Unlike crystalline porous frameworks, such as COFs or MOFs, which are defined solely by their lattice pores, hyper-crosslinked polymer films exhibit a dual identity as both porous frameworks and polymeric networks (Fig. 3a). This duality arises because rigid bridges coexist with flexible chain segments, generating transient voids and static pores that together enhance gas transport by increasing the probability of gas hopping between pores³¹.

Fig. 3. Coexisting porous and network domains across o-DMB-derived hyper-crosslinked DB50.

a Schematic illustration of dual identity as porous frameworks and polymer matrix. b Porous domain analyzed by bulk density measurement based on Archimedes principles. Individual data points without edges are jittered horizontally to avoid overlap (n = 3). Mean values are shown with edges, and error bars indicate standard deviations. c Porous domain analyzed using CO₂ adsorption at 273 K; pore size distributions of the film samples with increased crosslinking level. Distribution starts at 3.30 Å, corresponding to the kinetic diameter of CO₂. d Skeletal density changes induced by sample preparation, revealing detectable pores originating from both domains. Individual data points without edges are jittered horizontally (n = 1 − 3). Mean values are shown with edges, and for n > 1, error bars indicate standard deviations. e Pore size distribution of the sample prepared in the powdered form.

To examine the interplay between two domains, we compared oDMB-DB50 with ms-oDMB-DB50, both derived from DB50. We first examined the porous framework domain by comparing pore accessibility at different probe sizes within the same sample form factor. Bulk density was measured using ethanol as the liquid probe. It decreased from 1.35 g cm^-3 in DB50 to 1.32 g cm^-3 and 1.33 g cm^-3 in oDMB-DB50 and ms-oDMB-DB50 with more network pores introduced (Fig. 3b). The apparent densities decreased after network formation, suggesting that some gases remained trapped. By changing the probe phase to gas, CO₂ sorption (kinetic diameter 3.30 Å) revealed sub-nanometer pores in both oDMB-DB50 and ms-oDMB-DB50, with a major peak centered at 6 Å (Fig. 3c). ms-oDMB-DB50 displayed sharper resolution and an additional small fraction of pores smaller than 4 Å, consistent with the higher network completeness. Moving to a smaller probe, He (kinetic diameter 2.60 Å) detected narrower pores relevant to H₂ transport that was depicted by increase in estimated skeletal density. It increased from 1.35 g cm^-3 in DB50 to 1.45 g cm^-3 in oDMB-DB50 and 1.48 g cm^-3 in ms-oDMB-DB50, indicating the presence of static pores inaccessible to CO₂ (Fig. 3d). All three densities increased with increasing crosslinking level, and the difference became more pronounced for smaller probes, highlighting the importance of selecting an appropriate probe to reliably capture the porous framework domain.

We then turned to the polymeric network domain, interpreted by sampling-dependent density measurements. CO₂ sorption alone showed little change, and pore size distributions were essentially identical between films and powders (Fig. 3e). In contrast, skeletal density measured with He detected narrower pores relevant to H₂ (kinetic diameter 2.89 Å) transport, and showed clear form factor dependence, indicating increased sub 3 Å-pore accessibility. Powdered ms-oDMB-DB50 density reached 2.01 g cm^-3, substantially higher than the oDMB-DB50 film (1.48 g cm^-3), as greater surface exposure enabled better pore accessibility (Fig. 3d). These observations bridge pore-level analysis with the network-level transformation, allowing a dual-probe framework to disentangle porous and polymeric domains. This sensitivity to sampling method also reflects the function of polymeric network domain as a matrix which embeds pores.

This dual-probe approach overcomes the long-standing limitations of conventional sorption analysis by integrating probe-size and sampling effects. It clarifies how pores act as structural motifs that couple network architecture to transport and outlines a general principle that can be extended to engineering polymer networks beyond hydrogen separation application.

Molecular transport and durability of network polymer membranes

Precisely controlled molecular transport through the well-defined pores of hyper-crosslinked DB50 membranes underpins their high-throughput and selective molecular separation performance. In this work, we demonstrate their effectiveness in H₂ separation. Covalently bonded network pores accessible to H₂, as confirmed by skeletal densities, enable rapid yet discriminative H₂ transport, revealing the molecular sieving nature of the hyper-crosslinked DB50. To elucidate this mechanism, H₂ was paired with N₂, a non-condensable gas, to minimize solubility contributions and better resolve molecular sieving effects.

The separation performance of oDMB-DB50 was compared with pDMB-DB50, DMM-DB50 and ms-oDMB-DB50. Among oDMB-DB50, pDMB-DB50, and DMM-DB50, oDMB-DB50 showed the highest separation performance, with H₂ permeability of 6020 Barrer and H₂/N₂ permselectivity of 16 (Supplementary Table 7). While all three membranes showed marginal differences in BCD, indicating a similar level of static porosity, their separation performances varied (Fig. 4a). pDMB-DB50 exhibited the lowest separation performance, likely due to its bridge structure that induces the largest interchain spacing. This was also reflected in the kinetic diameter cut-off (KDCO), where relatively high permeabilities were observed for all gases (Fig. 4b). In contrast, DMM-DB50 and oDMB-DB50 displayed similar sharpness in KDCO. Given their comparable BCD values, both membranes possess pore structures suitable for N₂ exclusion. However, oDMB-DB50 appears to have more favorable microstructures for H₂ transport, resulting in better H₂/N₂ separation performance.

Fig. 4. Structure-performance relationships in hyper-crosslinked DB50 membranes.

a H₂ and N₂ separation performance depending on the external crosslinker measured with single gas. b Molecular sieving behavior derived from the single gas permeabilities of H₂, CO₂, O₂, N₂, and CH₄. c Evolution of H₂/N₂ mixed gas separation during structural transformation from DB50 to ms-oDMB-DB50. Individual data points are plotted without edges (n = 3 – 4). Mean values (with edges), and error bars represent standard deviations. d Schematic illustration of structural evolution from DB50 to ms-oDMB-DB50. e Selectivity of oDMB-DB50 and ms-oDMB-DB50 primarily arises from diffusion rather than solubility. f Stability of ms-oDMB-DB50 performance during 100 h of continuous operation. g Flexibility of ms-oDMB-DB50. h Separation performance of ms-oDMB-DB50 under compaction.

Within the same structural motif, both single gas separation and H₂/N₂ mixed gas separation performance improved markedly with increasing crosslinking level (Figs. 2a, 4a, c). Although H₂ diffusivities were increased to a similar order of magnitude in oDMB-DB50 and ms-oDMB-DB50, the transition from oDMB-DB50 to ms-oDMB-DB50 led to a noticeable enhancement in the H₂/N₂ separation factor (Supplementary Table 8). This improvement was unattainable by varying the bridging unit type alone, as the BCD changed only marginally, indicating that the exceptional increase in separation performance in ms-oDMB-DB50 originates from improved bridge connectivity (Fig. 4d). In oDMB-DB50, incomplete bridges left dangling crosslinkers, enhancing H₂ permeability but at the same time producing non-selective pathways that reduced H₂/N₂ separation factor below DB50. On the other hand, ms-oDMB-DB50, by narrowing the interchain spacing and completing bridges, improved pore definition and directly uplifted both H₂ permeability and H₂/N₂ separation factor.

The enhanced H₂/N₂ separation performance can be attributed to the coexistence of additional static pores arising from network pores alongside free volume. This interpretation is supported by the increase in diffusivity selectivity with BCD, while solubility selectivity remains nearly unchanged (Fig. 4e). Such behavior is consistent with a diffusion-driven molecular sieving mechanism. Although sorption analysis displayed a major peak near 6 Å (Fig. 3c), density measurements revealed the presence of narrower pores accessible to He but not CO₂ (Fig. 3d), which is consistent with the higher H₂/N₂ separation performance of ms-oDMB-DB50 (5895 Barrer, 71). Accordingly, despite the relatively high solubility of CO₂, CO₂ permeability of ms-oDMB-DB50 remained low. This further supports that diffusivity, rather than solubility, governs transport due to restriction by the ultra-microporous network pores (Supplementary Fig. S6). These results demonstrate that quantified network completeness provides a predictive link between molecular architecture and macroscopic transport behavior.

Notably, ms-oDMB-DB50 positioned well above the upper bound redefined by synthetic polymer membranes in 2015 (Fig. 4c)³². Exceeding the upper bound with scalable network films indicates that this design principle highlights the practical potential to advance separation performance beyond conventional polymer membranes and synthetic polymer membranes. Furthermore, H₂/N₂ separation performance of ms-oDMB-DB50 remained stable over 100 h as a freestanding membrane (Fig. 4f), with only 8% decrease in H₂ permeability and 6% increase in H₂/N₂ selectivity. Together with scalability, mechanical robustness and flexibility of ms-oDMB-DB50 manifested the potential of hyper-crosslinked polymer membranes as durable engineering materials (Fig. 4g, Supplementary Table 9). The ultimate tensile strength of ms-oDMB-DB50 was 39.2 MPa, which was around twice that of known best-performing hyper-crosslinked polymer membrane, and its modulus was 0.97 GPa, typical of glassy polymers²⁴. At higher pressures, ms-oDMB-DB50 underwent compaction, exhibiting marginal change in permeability and a reduced separation factor (Supplementary Fig. 7). However, even with this compaction effect, the separation performance remained above the 2015 upper bound (Fig. 4h). These engineering attributes point to practical viability in industrial separation modules, where long-term robustness is critical as separation stability.

Discussion

In conclusion, we establish network completeness, captured by effective CD and bridge connectivity degree, as a quantitative design principle governing the performance of network polymer membranes. These metrics link molecular architecture to transport, as highlighted by the contrasting separation performance of oDMB-DB50 and ms-oDMB-DB50. The coexistence of two domains was clarified using probes with different kinetic diameters, beyond the reach of conventional sorption analyses. Our approach to incorporating DMB, a challenging bridging element, readily diversified the design space and can extend from hydrogen to broader molecular separations. This study not only demonstrates rational design of polymer networks with tailored porosity but also opens the possibility of implementing reticular design in scalable film formats, offering benefits for robust membrane technologies across gas separation membrane to organic solvent separation membrane and redox flow battery separator. Furthermore, by embedding bridge connectivity into quantitative metrics, network completeness aligns polymer networks with the broader concept of reticular design³³ and establishes a quantitative route to systematically tailor porosity beyond conventional polymer systems.

Methods

Membrane fabrication

o-DMB (0.5 mol eq. relative to iron(III) chloride) was added to iron chloride solution (300 mM in nitrobenzene) at -1 °C. DB50 (0.22 mol eq. relative to o-DMB, based on the repeating unit of DB50) coupon was put into the solution and heated under reflux at 80 °C for 12 hours. After the reaction, oDMB-DB50 was washed thoroughly with methanol three times and stored in methanol. pDMB-DB50 was fabricated by hyper crosslinking DB50 in a solution prepared by adding p-DMB solution (0.5 mol eq. relative to iron chloride, 1.5 M in nitrobenzene) to iron chloride solution (333 mM in nitrobenzene). Crosslinking reaction protocols were identical to those described above, while maintaining the molar ratio between pDMB and DB50. For ms-oDMB-DB50, the concentrations of iron chloride and o-DMB provided to DB50 coupon were doubled, while all other conditions remained unchanged.

NMR spectroscopy

Solid-state ¹³C NMR spectroscopy was performed using 400 MHz Avance III HD (Bruker, 400 MHz, WB). Spectrum for each sample type was recorded twice under high-power proton decoupling conditions to obtain sharp resonance peaks. Hyper-crosslinked polymer membranes were swollen in acetone before grinding, and powdered samples were sieved through a 100-mesh stainless-steel screen. Powdered membranes were dried over a hot plate at 60 °C overnight.

Crosslinking level

The crosslinking level was evaluated by the CD, effective CD and bridge connectivity degree, which were calculated from deconvoluted ¹³C NMR spectra. The spectra were deconvoluted using a nonlinear least-squares fitting routine implemented in Python (SciPy). A pseudo-Voigt function, which combines Gaussian and Lorentzian line shapes, was employed to accurately describe the experimental peaks. The baseline was modeled as a linear function (y = c₀ + c₁x) and optimized concurrently with the peak parameters. Initial peak positions were assigned based on the theoretical chemical shifts, and all parameters (amplitude, center, width, and mixing factor) were iteratively refined until the coefficient of determination (COD) exceed or at least approach 0.99. The CD, ECD and BCD were calculated as follows:

$$\text{CD}=\frac{2{\mathrm{A}}_{\text{bridge}}+{\mathrm{A}}_{\text{dangling}}}{2{\mathrm{A}}_{\text{bridge}}+{\mathrm{A}}_{\text{dangling}}+{\mathrm{A}}_{\text{remaining}}}\times 100$$ 1

$$\text{ECD}=\frac{{\mathrm{A}}_{\text{bridge}}}{2{\mathrm{A}}_{\text{bridge}}+{\mathrm{A}}_{\text{dangling}}+{\mathrm{A}}_{\text{remaining}}}\times 100$$ 2

$$\text{BCD}=\frac{{\mathrm{A}}_{\text{bridge}}}{{\mathrm{A}}_{\text{bridge}}+{\mathrm{A}}_{\text{dangling}}}\times 100$$ 3

where A_bridge, A_dangling, and A_remaining represent the integrated peak areas corresponding to bridging unit, dangling end, and remaining reaction site on phenyl ring, respectively (detailed peak assignments are summarized in Supplementary Tables 1-3).

Density measurements

The apparent density was determined by the Archimedes method using ethanol as the immersion medium, and measurements were taken after all air bubbles had detached from the sample surface. All samples were degassed at ambient temperature (100 Torr) for at least overnight prior to measurement. The skeletal density was calculated from the solid volume measured using an ASAP2020 analyzer (Micromeritics). The samples were dried at ambient temperature (100 mTorr) and degassed at 150 °C under high vacuum. To minimize the chain-packing effects caused by annealing, DB50 was degassed at the same temperature used for drying the corresponding polymer after synthesis, and the degassing time was extended to two days. Powder samples were loosely packed into the sample tube without external compression to minimize densification artifacts. All density measurements were performed under identical isothermal (295 K) and ambient pressure conditions using the same measurement protocol. Due to the flexible nature of the DB50 film, the sample was powdered using a blender instead of a mortar. The kinetic diameters of the gases were referenced from the literature: He (2.60 Å), H₂ (2.89 Å), and CO₂ (3.30 Å)³⁴.

Gas permeation tests

The freestanding membrane was kept in methanol before testing and dried under ambient conditions prior to measurement. The membrane was then placed in the permeation cell and sealed with a Viton O-ring. The effective membrane area was 2.54 cm². All permeation tests were performed at 295 K under an upstream pressure of 1.25 atm using a constant-pressure variable-volume permeation system. The inlet gases were supplied through a mass flow controller (MFC), the permeate flow rate was measured using a bubble flow meter, and the permeate composition was analyzed with a gas chromatograph (GC, YL6500).

The purity of each single gas (He, Ar, H₂, CO₂, O₂, N₂, and CH₄) and 50:50 H₂/N₂ gas mixture used as the feed gas was 99.999%. He was used as the carrier gas for single gas permeation tests, except for H₂, for which Ar was used instead. To verify measurement accuracy, N₂ permeability was measured for both carrier gases and the results were compared. Membrane selectivity in single gas permeation was defined as permselectivity, calculated from:

$$\text{Permselectivity}=\frac{{\mathrm{P}}_{\text{H}2}}{{\mathrm{P}}_{\text{N}2}}$$ 4

where P_H2 and P_N2 are the single gas permeabilities of H₂ and N₂, respectively.

For the mixed gas permeation tests, Ar was used as the carrier gas, and the stage cut was maintained at approximately 1%. Steady-state permeation was determined when consistent separation performance was maintained for at least 1 h. Membrane selectivity was expressed as the separation factor, calculated from:

$$\text{Separation factor}=\frac{{\mathrm{y}}_{\text{H}2}/{\mathrm{y}}_{\text{N}2}}{{\mathrm{x}}_{\text{H}2}/{\mathrm{x}}_{\text{N}2}}$$ 5

where x_i and y_i represent the concentration of component i in the feed and permeate streams, respectively. In addition, a 100 h stability test was conducted using the freestanding membrane under the same conditions as the mixed-gas permeation tests.

Author contributions

H.L. wrote the manuscript, conceived the research and materials design, devised the characterization strategies for proving duality and performed BCD calculations, performed polymer synthesis, fabricated membranes, conducted characterizations, and carried out gas permeation tests of hyper-crosslinked polymer membranes. S.C. performed mechanical stability tests, and assisted with gas permeation test and H₂, N₂ sorption tests of DB50. T.H.B. administrated the project and acquired funding, and provided general supervision.

Peer review

Peer review information

Nature Communications thanks Zhongde Dai, Wanqin Jin, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

T. H. B. discloses support for the research of this work from the National Research Foundation of Korea (NRF) grants funded by the Korean government (MSIT) [grant numbers: RS-2025-00559826 and RS-2025-02218827].

Data availability

The source data for Figs. 1–4 and Supplementary Figs. 1, 4–8 are provided with this paper as a Source Data file. The images and other data supporting the findings of this study are available within the article or its Supplementary Information file. All the data are available from the corresponding author on request. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73860-0.