# Rubberby organic frameworks (ROFs) toward ultrapermeable CO 2 -selective membranes

Marius Sandru, Marie Prache, Thomas Macron, Lidia Căta, Mehmet Göktuğ Ahunbay, May-Britt Hägg, Guillaume Maurin, Mihail Barboiu

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Marius Sandru, Marie Prache, Thomas Macron, Lidia Căta, Mehmet Göktuğ Ahunbay, et al., Rubberby organic frameworks (ROFs) toward ultrapermeable CO2 -selective membranes. Science Advances, 2024, 10 (46), pp.eadq5024. 10.1126/sciadv.adq5024. hal-04990538

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MATERIALS SCIENCE

Rubbery organic frameworks (ROFs) toward
ultrapermeable CO₂-selective membranes

Marius Sandru<fnref n="1" />,², Marie Prache², Thomas Macron³, Lidia Căta⁴, Mehmet Göktuğ Ahunbay⁵,⁶,
May-Britt Hägg², Guillaume Maurin⁵, Mihail Barboiu³,⁴*

The capture of CO₂ is of high interest in our society representing an essential tool to mitigate man-made climate warming. Membrane technology applied for CO₂ capture offers several advantages in terms of energy savings, simple operation, and easy scale-up. Glassy membranes are associated with low gas permeability that negatively affect on their industrial implementation. Oppositely, rubbery membranes offer high permeability, but their selectivity is low. Here we report rubbery organic frameworks (ROFs) combining the high permeability of soft matrices with the high sieving selectivity of molecular frameworks. The best performing membranes provide a CO₂/N₂ selectivity up to 104 with a CO₂ permeability up to 1000 Barrer, representing relevant performances for industrial implementation. Water vapors have a positive effect on CO₂ permeability, and the CO₂/N₂ selectivity is higher than in dry conditions, as most of CO₂ gas emissions are present in fully humidified gas streams. The synergetic high permeability/selectivity performances are superior to that observed with current state-of-the-art polymeric membranes.

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INTRODUCTION

Global warming and greenhouse gas effects are now topics of high interest. They are related to climate change and its negative effects due to human activities. Carbon dioxide, CO₂, is present in the emissions resulted from power generation by combustion of fossil fuels, steel and cement industries, refineries, and transportation (1). An efficient strategy for the reduction of the greenhouse gases emissions is to develop CO₂ capture technologies adapted to the characteristics of each individual source: CO₂ content, volume of gas to be treated, location, and gas contaminants (2). Among other industrial methods (i.e., absorption in solvents or solid sorbents and cryogenic distillation), the membrane separation technology (2–18) offers advantages such as energy savings, simple operation, and easy scale-up for main gas separations: (i) CO₂ versus N₂ from flue gas (10 to 20% CO₂, 1 atm, 50°C) (2), (ii) CO₂ versus CH₄ from natural gas or natural gas sweetening (3), and (iii) CO₂ versus H₂ for precombustion capture (45% CO₂, 70 bar, 300°C) (4). There are as well several limitations for membrane technology such as (i) the trade-off between CO₂ permeance and selectivity; (ii) low durability and loss of performances when exposed to water or contaminants present in gas (SO₂, H₂S, and hydrocarbons); and (iii) good performance only at high CO₂ concentrations.

De novo design of membranes for molecular scale gas separations has become an area of expanding interest. Achieving high gas permeability while keeping a reasonable selectivity is usually obtained with membranes for which the gas transport is controlled by the gas diffusivity in glassy materials or by gas solubility in rubbery

materials (5). The gas diffusivity can be controlled for low permeable glassy polymers and can be improved by using rubbery polymers and increasing the solubility of CO2. The gas permeability may be increased by using a rubbery polymer with permeable soft segments (Fig. 1A). Fixed site carrier membranes combine the solution-diffusion mechanism, with a reversible chemical reaction with CO2-philic carriers present in the membrane (6–8). Innovative molecular sieving microporous polymers (PIMs) (9–11), metal organic frameworks (MOFs) (12–14), and covalent organic frameworks (COFs) (15) have been identified as promising emerging materials for energy-efficient membrane gas separations. Nonetheless, there are many challenges in translating their excellent molecular separation properties into performant scalable and inexpensive industrial-scale membranes and filtration modules needed for effective gas capture. For zeolitic membranes (16), film formation becomes limited by local defects and intercrystallite inhomogeneities. Nanocomposite membranes (13, 17) can be prepared to regulate the manner in which MOF and COF fillers and the polymeric matrix can synergistically act. Engineered MOF crystals into polymer matrices may successfully translate their excellent molecular sieving properties into macroscopic mixed matrix membranes, but there are still challenges regarding the membrane area upscaling, module sealing, brittleness, and costly production process (18).

Emerging soft and porous crystals (19), liquid MOFs (20), liquid cages (21), and flexible COFs (22) with permanent metastable transient porosity arising from local dynamics of framework components have been proposed as continuous phases with enhanced mechanical and thermal properties for improved CO₂ capture applications (23). We postulate earlier by an advanced computational methodology combining quantum and force field molecular simulations (24) and experimentally demonstrate in these studies (25, 26) that one of the not yet explored strategies for addressing such scale-up challenges and to achieve improved performance, in terms of both permeability and selectivity, is to use the rubbery organic frameworks (ROFs). The ability to connect rubbery connectors and core centers through reversible bonds controlled at molecular level results in the formation of flexible stable membrane films,

<footnote n="1">¹SINTEF Industry, SINTEF AS, NO-7465, Trondheim, Norway. ²Department of Chemical Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway. ³Institut Européen des Membranes, Adaptive Supramolecular, Nanosystems Group, University of Montpellier, ENSCM, CNRS, Place Eugène Bataillon, CC 047, F-34095, Montpellier, France. ⁴Babes-Bolyai University, Supramolecular Organic and Organometallic Chemistry Center (SOOMCC), Cluj-Napoca, 11 Arany Janos str., 400028, Cluj-Napoca, Romania. ⁵Institut Charles Gerhardt Montpellier, Univ. Montpellier, CNRS, ENSCM, Place Eugène Bataillon, CC 047, F-34095, Montpellier, France. ⁶Department of Chemical Engineering, Istanbul Technical University, Maslak, Istanbul 34469, Turkey.</footnote>

<footnote>*Corresponding author. Email: mihail-dumitru.barboiu@umontpellier.fr</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Conceptual and synthetic details of studied ROF membranes. (A) Schematic diagram representing the performances of glassy/crystalline, rubbery polymeric, and ROF membranes. P, Permeability; S, Selectivity. (B) Synthesis and schematic representation of chain packing of **T1** to **T6** ROF membranes, combining linear polyTHFs **1** and **2** (red line), star-type **3** and **4** (green star), and linear (red line) **5** and **6** polyPPOs, connected via imine-carbonyl/amine chemistry to BTA core **1** (blue circle). The addition of CO₂-phylic histamine, H heads (yellow) results in the formation of membranes **T1H** to **T6H**. It generates structural diversity of self-standing ROF membrane films with elastomeric behaviors. The photo represents membrane **T6**.</figcaption></figure>
combining high gas sorption of permeable rubbery polymers with the selective diffusion of mesh-sieving architectures of selective crystalline polymers (Fig. 1A) (27). The key challenge in the construction of such dynamic ROF frameworks is the adaptive formation of gas sieving/taming molecular domains. Elastomeric frameworks can be better processed into membranes compared to Metal Organic Frameworks (MOFs), Zinc Imidazolate Frameworks (ZIFs), or zeolites, preventing the formation of defects. The dynamic connectivity between molecular components results in the formation of homogeneous and robust thin films circumventing the intrinsic poor film formation and brittleness of porous solids. This is achieved by introducing elastomeric domains in a controlled manner while retaining desirable gas-sieving properties of crystalline porous frameworks. We hypothesize that the short distance connectivity in the soft solid state may promote transient intrinsic porosity due to the strong constraints of their three-dimensional (3D) networking at the molecular level, generating adaptive functions for materials. (22)

RESULTS

Synthesis and structural characterization

Linear or cross-linked macromolecular connectors with nanometric dimensions and connection centers have been used to synthesize a library of ROFs and further fabricate dense self-supported membranes for gas separation. Several building blocks are used as the precursors to prepare the ROFs BTA₂·1₃, BTA₂·2₃, BTA·3, BTA·4, BTA₂·5₃, and BTA₂·6₃: benzenetrialdehyde (BTA) bis(3-amino-propyl)polytetrahydro furan and 1) polytetrahydrofuran (polyTHF) [number-average molecular weight (Mn), ~350 g mol⁻¹]; 2) polyTHF (Mn, ~1100 g mol⁻¹); 3) the star-type glycerol-tris[poly(propyleneglycol)-amine-terminated] ether T3000 (Mn, ~3000 g mol⁻¹); 4) T440 (Mn, ~440 g mol⁻¹); 5) linear bis(3-aminopropyl)-polypropylene glycol D400 (Mn, ~400 g mol⁻¹); and 6) D2000 (Mn, ~2000 g mol⁻¹) poly(propylene-oxide) (polyPPOs). Reflux in chloroform overnight followed by evaporation of solvent at 60°C was used to form and cast T1 to T6 membrane films (Fig. 1B). A second series of membranes T1H to T6H were prepared by using the histamine ROFs BTA·1·H, BTA·2·H, BTA·3₀.₆₆·H, BTA·4₀.₆₆·H, BTA·5·H, and BTA·6·H. These ROFs were used to manufacture a comprehensive library of membranes including a large variety of structural features: (i) The hydrophobic linear polyTHF 1 and 2, the hydrophilic star-type 3 and 4, and linear 5 and 6 poly(PPO) have been used to generate the membrane soft phases, allowing a high gas solubility and enhancing the CO₂ permeability; poly(ethylene-oxide) (PEO) polymers have been used to provide a good balance between CO₂ solubility and permeation. However, they crystallize (5), potentially hindering the permeation of gases. Different methods have been used to decrease the crystallinity of PEO, including the use of low temperature or the use of low molar mass PEO monomers (28, 29). (ii) The presence of methyl groups in PPO prevents the chain packing, suppressing PPO crystallization and increasing the free volume and consequently CO₂ permeability (30). (iii) The ROFs contain a combination of both linear and star-type macromonomers, interconnected via reversible imine bonds, resulting in the formation of frameworks with a certain cross-linking degree that control the free volume at nanometric level. (iv) The bulky connectors have a protecting effect against the hydrolysis of the imine bonds. (v) The histamine, H heads are CO₂-phylic functional subunits, which may increase the water content in the membrane and increase the CO₂ selectivity of the respective ROFs (22–26).

The ¹H nuclear magnetic resonance (NMR) analysis of CDCl₃ allows easy identification of peaks corresponding to total conversion to imine-substituted BTA₂·1₃, BTA₂·2₃, BTA·3, BTA·4, BTA₂·5₃, and BTA₂·6₃ or BTA·1·H, BTA·2·H, BTA·3₀.₆₆·H, BTA·4₀.₆₆·H, BTA·5·H, and BTA·6·H ROFs. The reported experimental molar compositions have been obtained by the integration of the aromatic and imine protons of N-substituted BTA, using the solvent peak as reference.

The elastomeric behavior for most of the obtained membranes is confirmed by their low glass transition temperatures Tg ~ -37° to -14°C, with T1 to T6 membranes softer than T1H to T6H ones (table S2). The presence of H-bonding imidazoles from histamine generates crystalline domains in which water clusters can be included. The Tg values are the lowest for T3, T3H, T6, and T6H, indicating an increasing of the free volume of the matrix with the use of poorly packed star-type and longer linear connectors 3 and 6 compared with the compact, well-packed shorter and linear polymer chains of 1, 2, and 5 and the highly cross-linked polymer matrix of 4, leading to glassy T4 and T4H structures. The crystallization temperature Tc, detected for T2 and T2H membranes containing longer polyTHF1100 and high degradation temperatures (320° to 370°C), is probably related to cross-linked frameworks making ROFs suitable for harsh environments or high temperature testing.

The surface morphologies of T1H (linear polyTHF, 250 g mol⁻¹), T3H (star T3000, 3000 g mol⁻¹), and T5 (linear D400, 400 g mol⁻¹) membranes were further investigated by atomic force microscopy (AFM; figs. S1 to S3). The AFM images show that these membranes present on surface bubble shapes of 0.2 µm for shorter linear segments in T1H and T5H and 1 µm for longer cross-linked segments in T3H, indicative of high roughness that can be obtained with increasing the mass of the polymers.

Fourier transform infrared (FTIR) spectra demonstrate the formation of polyimines, with the detection of vibration bands at 1450 and 1600 cm⁻¹, associated with aromatic moieties conjugated with —C≡N— bonds for which stretching vibrations are observed at 1640 to 1690 cm⁻¹ (fig. S4 and tables S3 and S4). The intensity of the C≡N vibration bands strongly depends on the nature of the connectors and is related to the degree of cross-linking of the frameworks. The sharp bands at 1070 and 1150 cm⁻¹ attributed to the —C—O—C— stretching vibration, as well as the —CH₂,as and —CH₂,sym stretches visible in the range of 2750 to 2957 cm⁻¹, are proportional to the number of groups of the PPO chains (tables S3 and S4). Evidence for histamine incorporation was obtained from the vibration band at 1585 cm⁻¹ assigned to the C≡C stretching of the imidazole. A broad band centered around 3400 cm⁻¹ attributed to the O—H stretching vibration of H-bonded water can be observed for some membranes, especially those containing histamine.

Most of the CO₂ sources such as flue gas are fully humidified, and water absorption in membranes can play an important role in CO₂ separation, enhancing performances as in the case of fixed site carrier/facilitated transport membranes or decreasing performances by a competitive sorption in glassy polymers or excessive swelling and plasticization (fig. S5). Consequently, water swelling experiments of ROF membranes were performed using controlled fully humidified atmosphere. As expected, the membranes T1H to T6H containing hydrophilic histamine H requires longer equilibrium time to reach steady state (100 hours) and adsorbs almost three to four times more water than the free histamine membranes T1 to T6 (60 hours) (table S5 and fig. S6). The imidazole of histamine forms strong
H bonds with water, and the membranes T1H to T6H are expected to absorb more water with longer adsorption time to completely swell the membranes. For histamine T1H to T6H series, the glassiest polymers absorb more water (T1H and T5H), and the water uptake decreases with the $T_g$ decreasing of the more rubbery T3H and T6H polymers (table S5). For series T1 to T6 without histamine, hydrophilic T1 (linear PEO) had the highest water absorption, and hydrophobic T6 (linear PPO) had the lowest amount of water. A similar trend is observed, the most rubbery materials T3 and T6 have the lowest $T_g$ absorbing the least amount of water.

## Single and mix gas transport

Single gas $N_2$, $CH_4$, and $CO_2$ permeation experiments have been performed in this order, by using a time lag permeation rig at 5 bar and 25°C (Table 1 and figs. S7 and S8). Mixed gas experiments have also been performed using a gas mixture of 10% $CO_2$ to 90% $N_2$ at 1.2- and 5-bar feed absolute pressure and 25°C, in dry and humidified conditions (Table 2 and fig. S10).

As a general trend, the single gas $CO_2$ permeabilities and, consequently, the corresponding $CO_2/N_2$ selectivity of the softer (lower $T_g$) membranes T1 to T6 (except for T3) are higher by a factor ranging between ×2 and ×16 compared with their equivalent in T1H to T6H membrane series. This is confirmed and correlated with the $CO_2$ sorption data in figs. S12 and S13 and table S7, which implies either a stronger material affinity toward $CO_2$ or the presence of a molecular sieving capacity as observed for glassy rigid polymers, a highly unexpected property of a rubbery polymer. When T1H, T3H, and T5H membranes were tested with increased applied feed pressure from 3 to 10 bar, for T1H and T5H, both $CO_2$ permeability and $CO_2/N_2$ or $CO_2/CH_4$ selectivities increased, due to synergetic increase of $CO_2$ solubility and sieving properties with pressure. The T1H membrane presented a 36% increase and T5H membrane a 24% increase in $CO_2/N_2$ selectivity, where $CO_2/CH_4$ selectivity remained constant for T1H and increased 21% for T5H with pressure (table S6 and fig. S9). It became apparent that, if the length of the polyTHF or polyPPO chains increases (T2, T3, and T6 have longer chains versus T1, T4, and respective T5), then the $CO_2$, $N_2$, and $CH_4$ permeabilities increase for both series, while the single gas $CO_2/N_2$ and $CO_2/CH_4$ selectivities increase for T1H to T6H and decrease

for T1 to T6 (Table 1 and Fig. 2, A to C). As an example, the single gas $CO_2/N_2$ selectivity increased with chain length by 13% between T1H and T2H and decreased between T1 and T2 by 24% with chain length increase. This can imply that the histamine imidazoles provide more rigidity/compact packing via strong H bonding for T1H to T6H membranes leading to an increased sieving capacity and higher $CO_2$ selectivity. The membrane T6 has good performance for both $CO_2/N_2$ and $CO_2/CH_4$ separation and presents the best compromise selectivity/permeability. The use of shorter connectors in T1 and T5 leads to good selectivity $S_{CO_2/N_2} = 41$ to 55 and a reasonable $CO_2$ permeability (~300 Barrer) for both series. The gas permeability increases with pressure and is correlated with the rubbery state of the polymer. T2H, T3H, and T2 show good $CO_2$ permeability, however, with a lower selectivity. There is no particular trend observed regarding the $N_2$ permeability when comparing the two series.

The permeability and selectivity evaluated from the single gas components are ideal, without taking into account the interaction between gasses and competitive transport in a gas mixture as expected in a gas mixture with $CO_2$ concentration below 20% water vapors. Consequently, the performances may change when membranes are tested with mixed gases and in the presence of humidity. The mixed gas permeation experiments performed using 10% $CO_2$ in $N_2$ gas mixture as feed confirmed these suppositions (Table 2). Two gas feed pressures were used for testing: a low pressure of 1.2 bar close to real flue gas pressure in power generation industry and 5 bar as used for single gas permeation experiments. Testing was performed using both dry and fully humidified [100% relative humidity (RH)] gasses as in the flue gas, breathing, and biogas processes (2, 3).

The $CO_2/N_2$ selectivity substantially varies between mixed and single dry gas tests (Fig. 2C), while no important variation is observed for $CO_2$ permeability (except T4 and T5H). All T1H to T6H membranes present $CO_2/N_2$ selectivity under 30 when tested with mixed dry gas, and all the membranes T1 to T6, except T4, have selectivity values higher than 30. Comparing the results at 5 bar, all the T1 to T6 membranes, except T1 and T5, presents higher $CO_2/N_2$ selectivity when tested with mixed gases compared to a single dry gas test, supporting the hypothesis of sieving rubbery membranes.

<table><caption>Table 1. Single gas permeation experiments at 5-bar feed pressure and 25°C.</caption><thead><tr><th rowspan="2">Membrane</th><th colspan="3">Permeability (Barrer)</th><th colspan="2">Selectivity</th></tr><tr><th>CO<sub>2</sub></th><th>N<sub>2</sub></th><th>CH<sub>4</sub></th><th>CO<sub>2</sub>/N<sub>2</sub></th><th>CO<sub>2</sub>/CH<sub>4</sub></th></tr></thead><tbody><tr><td>T1H</td><td>2.34</td><td>0.09</td><td>0.17</td><td>26</td><td>14</td></tr><tr><td>T2H</td><td>196</td><td>7</td><td>22</td><td>30</td><td>9</td></tr><tr><td>T3H</td><td>424</td><td>15</td><td>50</td><td>28</td><td>8.5</td></tr><tr><td>T5H</td><td>34</td><td>13</td><td>15</td><td>2.5</td><td>2.3</td></tr><tr><td>T6H</td><td>517</td><td>108</td><td>194</td><td>4.8</td><td>2.7</td></tr><tr><td>T1</td><td>59</td><td>1</td><td>4</td><td>42.5</td><td>14</td></tr><tr><td>T2</td><td>250</td><td>8</td><td>27</td><td>31</td><td>9</td></tr><tr><td>T3</td><td>711</td><td>43</td><td>126</td><td>17</td><td>6</td></tr><tr><td>T4</td><td>119</td><td>107</td><td>123</td><td>1.1</td><td>1</td></tr><tr><td>T5</td><td>34</td><td>0.81</td><td>2.24</td><td>42</td><td>15</td></tr><tr><td>T6</td><td>895</td><td>27</td><td>104</td><td>33</td><td>9</td></tr></tbody></table>
<table><caption>Table 2. Mixed gas permeation experiments with dry and 100% RH humidified feed gas 10% CO₂ in N₂ at 25°C.</caption><thead><tr><th rowspan="2">Membrane</th><th colspan="4">CO₂ permeability (Barrer)</th><th colspan="4">CO₂/N₂ selectivity</th></tr><tr><th colspan="2">Feed pressure (dry)</th><th colspan="2">Feed pressure (humid)</th><th colspan="2">Feed pressure (dry)</th><th colspan="2">Feed pressure (humid)</th></tr></thead><tbody><tr><td>T1H</td><td>1.2 bar</td><td>5 bar</td><td>1.2 bar</td><td>5 bar</td><td>1.2 bar</td><td>5 bar</td><td>1.2 bar</td><td>5 bar</td></tr><tr><td>T2H</td><td>159</td><td>174</td><td>115</td><td>125</td><td>1</td><td>5</td><td>9</td><td>24</td></tr><tr><td>T3H</td><td>282</td><td>295</td><td>268</td><td>267</td><td>5</td><td>15</td><td>5</td><td>17</td></tr><tr><td>T5H</td><td>68</td><td>108</td><td>157</td><td>130</td><td>11</td><td>16</td><td>94</td><td>104</td></tr><tr><td>T6H</td><td>302</td><td>389</td><td>318</td><td>294</td><td>9</td><td>7</td><td>10</td><td>13</td></tr><tr><td>T1</td><td>50</td><td>44</td><td>55</td><td>53</td><td>2</td><td>6</td><td>2</td><td>8</td></tr><tr><td>T2</td><td>372</td><td>272</td><td>418</td><td>408</td><td>15</td><td>50</td><td>60</td><td>63</td></tr><tr><td>T3</td><td>786</td><td>1128</td><td>741</td><td>726</td><td>46</td><td>46</td><td>62</td><td>55</td></tr><tr><td>T4</td><td>55</td><td>14</td><td>50</td><td>49</td><td>21</td><td>6</td><td>20</td><td>27</td></tr><tr><td>T5</td><td>59</td><td>32</td><td>59</td><td>40</td><td>13</td><td>23</td><td>47</td><td>71</td></tr><tr><td>T6</td><td>1086</td><td>898</td><td>876</td><td>658</td><td>31</td><td>39</td><td>68</td><td>54</td></tr></tbody></table>

For the T1H to T6H series, the single gas dry test provides better selectivity or similar with the exception of T5H.

When membranes were tested with a mixture of gasses, relatively small differences are observed for CO₂ permeabilities between wet and dry gas conditions: (i) T1H to T6H membranes (except T5H) show a small decrease in permeability, due to competitive water-CO₂ sorption, as typical for glassy polymers, and (ii) T1 to T6 membranes (except T3 and T6) show similar or higher CO₂ permeabilities under wet conditions. The fact that T3 and T6 have similar or lower permeabilities when tested with humidified gas may be correlated with the water sorption where T3 and T6 showed the smallest water uptake.

The CO₂/N₂ selectivities show a substantial increase when using humidified feed gas for all membranes and feed pressures, the difference being even more pronounced at 5 bar (Fig. 2D). Unexpectedly, for the T1H to T6H series, the more glassy membranes, despite the CO₂ permeability being depressed under humid conditions, the CO₂/N₂ selectivity is similar or slightly increased. Another obvious trend is that T1H to T6H membranes, except T5H, show lower CO₂/N₂ selectivity than T1 to T6 membranes under both dry and humid conditions. This is not unexpected because the hydrated imidazoles limit their interactions with the permeant CO₂ to provide a decreased permeability for T1H to T6H membranes (31). The fact is that the CO₂ permeability increases with pressure from 1.2 to 5 bar and may indicate a limited contribution of facilitation transport (characterized by higher permeability and selectivity at lower feed pressures) for overall CO₂ transport mechanism in T1H to T6H series (6–8).

An important conclusion based on the results, obtained using humidified and dry mixed gases, is that water vapors have a positive effect both on CO₂ permeability and especially on CO₂/N₂ selectivity except a small decrease of the CO₂ permeability for the most glassy series T1H to T6H and T3 and T6. This is beneficial for industrial implementation, as all CO₂ industrial flue gas, biogas, and natural gas streams are fully humidified and are opposite to the behavior in the presence of humidity of glassy polymer membranes, MOF, and zeolite mixed matrix membranes where the water vapors have a considerable negative effect on membrane performances.

The CO₂ sorption experiments enabled us to relate the gas transport phenomena with the structure of the membranes (figs. S11 to S13 and table S7). The gas solubility and the diffusion coefficients of CO₂ are close to the values reported for similar membranes in literature (32, 33). The hysteresis can be observed for most of the T1H to T6H membranes except the most rubbery ones T6H and T3H, as a result of the increase of the free volume during the sorption. The more elastic/rubbery T1 to T6 membranes do not show a hysteresis, and both sorption and desorption follow Henry's law. The CO₂ solubilities obtained through Henry's law or dual sorption model data fitting are similar for T1 to T6 and T1H to T6H (table S7). This trend is different when compared with water sorption (table S5) as T1H to T6H membranes adsorb much more water than T1 to T6. Lower CO₂ permeabilities and CO₂/N₂ selectivities for T1H to T6H series compared to T1 to T6 series (except the T5/T5H pair), under both dry and humid testing conditions (Table 2), indicate that neither the water nor the CO₂ sorption is the determinant factor for CO₂ separation. Despite similar CO₂ solubilities in both series, an order of magnitude difference can be observed for the diffusion coefficients of T1/T1H and T5/T5H compared with the rest of the membranes. As in the case of single gas permeation, the separation performances are correlated with structural differences induced by the length of polyTHF and polyPPO chains: Longer chains give higher diffusion. The combination of star shape and long polyPPO chains seems to be beneficial as it provides higher CO₂ diffusion coefficient. Overall, it can be concluded that diffusivity has the biggest contribution to CO₂ permeability and is responsible for the observed differences in membrane performances leading to highest CO₂ permeability for the rubbery membranes T3H, T6H, T2, and T3.

## Atomistic-scale molecular simulations

To gain further insight on the structure-property relationship of these ROFs, atomistic-scale simulations were carried out for two representative ROFs: T5 and T6, with shorter (polyPPO₅) and longer (polyPPO₃₂) linear connectors, respectively (Fig. 3A). For T5, two atomistic models were constructed associated with different degrees of cross-linking, i.e., T5a (30%) and T5b (100%) varying
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Single and mixed gas experiments. Single gas permeation performances (A) CO₂/N₂ and (B) CO₂/CH₄ at 5 bar and 25°C; the arrows show the correlation between membrane with the same composition with (●) and without (o) histamine. (C) Comparison of mixed and single gas CO₂ permeability and CO₂/N₂ selectivity at 5 bar and 25°C. (D) CO₂ permeability and CO₂/N₂ selectivity of mixed gas experiments at 1.2- and 5-bar feed and 25°C with dry and 100% humidified feed. (E) Selectivity-permeability trade-off Robeson graphs; the solid line depicts the 2008 and 2019 upper bounds (35). Solid points are showing performances obtained with 10% CO₂ to 90% N₂ gas mixture at 1.2 bar, 25°C, humidified feed gas 100% RH. Data for thermal rearranged (TR), fixed site carrier, and PIMs were extracted from literature (36). PDMS, polydimethylsiloxane.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Atomistic-scale simulations. (A) Schematic 3D fully interpenetrated cross-linked T5 ROFs, where the spheres are the BTA centers and the stick are the PPO connectors. (B) Simulated CO₂ sorption isotherms at 298 K in ROF-T5 and ROF-T6 models in comparison to experimental data. (C) Radial distribution function (RDF) between the carbon atom of the CO₂ molecule and selected sites of the T5a structure. The relevant sites are labeled on the structure fragment in the inset.</figcaption></figure>

from a partial to a three imine moieties on BTA center. These atom-
istic models first identified the effect of the PPO connector length
on the rigidity of the ROFs based on the differences of calculated T<sub>g</sub>
values of T<sub>5</sub> and T<sub>6</sub>, which are estimated as -12°C for T<sub>5a</sub>, 8°C for
T<sub>5b</sub>, and -30°C for T<sub>6</sub>, through the simulated cooling via NPT and
NVT-molecular dynamic (MD) simulations describing the system
at constant particle number (N), pressure (P), volume (V), and tem-
perature (T) (figs. S14 and S15). When compared to the experimen-
tal data (-28° and -56°C, respectively), the simulation reproduced
the effect of the structural differences on the T<sub>g</sub> values consistently.
It should be noted that a faster cooling rate in molecular simulations
leads to overprediction of T<sub>g</sub> by ~30°C, according to the Williams-
Landel-Ferry model (32).

Figure 3B reports the calculated CO₂ sorption isotherms at 298 K via a strategy integrating grand canonical Monte Carlo simulations and NPT- and NVT-ensemble MD simulations (more details in the Supplementary Materials) for the two **T5** models and compared them to the experimental sorption isotherm collected for the **T5** membrane. The cross-linking of **T5** implies, as expected, a reduction in the CO₂ sorption capacity. The resulting Henry's constants are 1.353 and 0.921 cm³/atm for **T5a** and **T5b**, respectively, with respect to the experimental value of 1.421 cm³/atm. The comparison between experimental and simulated sorption isotherms suggests that the polymer **T5** is therefore partially cross-linked. Radial distribution function analyses reported in Fig. 3C for different CO₂/T5 atom pairs shows that the CO₂ affinity exhibited by **T5** is associated to preferential interactions between the carbon atom of CO₂ and the oxygen atom of the carbonyl group. The simulated CO₂ sorption isotherm in **T6** is also shown in Fig. 3B. This simulation shows that **T6** has a higher CO₂ sorption capacity due to its longer PPO chain, which makes it more flexible and exhibits a greater swelling tendency. In addition, Henry's constant of 1.825 cm³/atm is higher than the values obtained for both **T5** models, in line with a stronger interaction between CO₂ and **T6**.

MD simulations performed at 298 K and at the equilibrium load-
ings at 5 bar, in line with the experimental protocols, further re-
vealed that CO₂ diffuses faster in **T6** (D<sub>s,CO₂</sub> = 5.47 × 10<sup>-6</sup> cm²/s)
than in both **T5** models (D<sub>s,CO₂</sub> = 0.133 × 10<sup>-6</sup> cm²/s for T5a and
D<sub>s,CO₂</sub> = 0.611 × 10<sup>-6</sup> cm²/s for T5b), in line with the experi-
mental CO₂ diffusivity data reported in table S7. This trend is asso-
ciated with the more pronounced chain mobility of **T6** that enables

generation of free volume and diffusion pathway for the gas. The separation performances of T5 and T6 were further evaluated in terms of CO₂ permeability and CO₂/N₂ and CO₂/CH₄ selectivity based on single components and binary mixture conditions. For a better insight of the separation mechanism of these polymers, it is of interest to break down the permselectivity (αₚ) into solubility selectivity (αₛ) and diffusion selectivity (αₔ), based on the solution-diffusion model. Moreover, comparison of ideal and mixed gas solubility selectivities allows identifying the presence of any competitive sorption phenomenon. Table 3 summarizes the calculated single gas and binary mixture separation properties for CO₂/N₂ and CO₂/CH₄ gas pairs in T6 at 298 K and 5 bar that are in excellent agreement with the experimental data presented as well in this table. For binary mixtures, CO₂:N₂ ratio was set to 10:90 in line with the experimental work, where as a 50:50 mixture was assumed for the CO₂/CH₄ pair. These simulations show that gas diffusivity increases with the length of the PPO chains. As typical with rubberby polymers (33, 34), the membranes are not selective in terms of diffusivity, and the CO₂/N₂ separation in T6 is governed primarily by sorption selectivity. High diffusivity and high sorption selectivity result in high permselectivity, confirming the experimental observation that T6 is a promising candidate for CO₂/N₂ separation. On the other hand, the relatively poorer performance of this polymer in CO₂/CH₄ separation is due to lower solubility selectivity.

DISCUSSION

ROF membranes reported here present high CO₂ permeabilities and unexpectedly high selectivity for a rubbery-based membrane under various gas transport conditions, including changes in pressure, humidity, and single and mixed gas transport experiments. This suggests that the ROFs designed from low molecular components are intrinsically promoting the preferential selective transport and separation of CO₂ presenting higher selectivity (CO₂/N₂, 50 to 100) compared to classical elastomeric polymers.

In addition, when compared to glassy polymers and MOF or
zeolite mixed matrix membranes (35–37), the ROF membranes
are not negatively affected by the water sorption, water vapors
having a positive effect on CO₂/N₂ selectivity. The high CO₂ perme-
abilities (500 to 1000 Barrer) can be explained by the rubbery state
of the polymer. Hysteresis phenomena were observed during CO₂
<table><caption>Table 3. Simulated single gas transport properties of T6 at 298 K.</caption><thead><tr><th rowspan="2"></th><th colspan="4">Simulation</th><th colspan="2">Experimental</th></tr><tr><th>S<sub>i</sub> (cm<sup>3</sup>/cm<sup>3</sup>)</th><th>D<sub>5,1</sub> (10<sup>-6</sup> cm<sup>2</sup>/s)</th><th>P<sub>i</sub> (Barrer)</th><th>α<sub>S</sub></th><th>α<sub>D</sub></th><th>α<sub>P</sub></th><th>P<sub>i</sub> (Barrer)</th><th>α<sub>P</sub></th></tr></thead><tbody><tr><td>CO<sub>2</sub></td><td>9.75</td><td>5.47</td><td>1404</td><td></td><td></td><td></td><td>898</td><td></td></tr><tr><td>N<sub>2</sub></td><td>0.0902</td><td>4.28</td><td>51</td><td>21.6*</td><td>1.28*</td><td>27.7*</td><td>27</td><td>33*</td></tr><tr><td>CH<sub>4</sub></td><td>1.41</td><td>2.89</td><td>111</td><td>6.95†</td><td>1.96†</td><td>12.7†</td><td>104</td><td>8.6†</td></tr></tbody></table>

sorption experiments and corroborated with the generation of a transient high free volume into ROF matrix resulting in increased diffusivity. High CO₂ permeability is related as well to high affinity of CO₂ to the PPO chains in T3 and T6 due to chemical interactions, pointing toward the possibility of a facilitated transport contribution to the overall transport mechanism. Robeson diagram for CO₂/N₂ separation, with both 2008 and 2019 proposed upper bonds, shows that three membranes of this study, T3, T6, and T5H, are above the 2019 upper bond (Fig. 2E) (35, 38). This implies excellent permeability performances when compared with other (i) polymeric rubbery poly(dimethylsiloxane)(PDMS) or poly(1-trimethylsilyl-1-propyne) (PTMSP) or glassy polyimide (PI) or PEBAX membranes or (ii) porous polymer of intrinsic microporosity (PIM) and TR polymeric or mixed matrix MOF and POF membranes showing synergetic high permeabilities and selectivity. It also suggests an excellent structural homogeneity, a necessary requisite to manufacture seamless membranes without defects. The excellent film formation processability and stability of ROFs make these membranes excellent candidates for upscaling and implementation in industrial CO₂ separation processes.

# MATERIALS AND METHODS

## Chemicals

All reagents were obtained from Sigma-Aldrich and used without further purification. All organic solutions were routinely dried by using sodium sulfate (Na₂SO₄).

## General procedure for the synthesis of ROF membrane films

One mole of the BTA and 0.66 mol of difunctional connectors 1, 2, 5, and 6 or 1 mol of trifunctional connectors 3 and 4 were solubilized in 80 ml of methanol or chloroform. The reaction was vigorously stirred overnight at reflux. The mixture was concentrated to almost the half volume, 40 ml. Then, 7 ml of solution was poured into a Teflon dish (6 cm in diameter) and slowly dried at 25°C for 4 days to give yellow films. In the final step, the films were heated at 70°C in an oven for two more days. ¹H NMR spectra were recorded on an ARX 300 MHz Bruker spectrometer in CDCl₃ using the residual solvent peak as reference.

## Characterization of the membranes

The membranes T1H to T6H and T1 to T6 have been characterized by differential scanning calorimetry, FTIR, AFM, gas permeation, and gas and water sorption. A summary of the experiments made is presented in table S1 (39).

## Swelling experiments

The membranes in this study are intended to be used for CO₂ capture from flue gas, natural gas, and biogas. For all these applications, the gas is fully humidified. In addition, water plays an important role in material durability, as membranes can excessively swell and degrade. It is known that water can play a favorable role in CO₂ transport as in the case of facilitate transport membranes, and here, it can interact with donor-acceptor H-bonding groups and easily solvates acidic gases as CO₂. It can therefore be useful to know to which extent the polymer is able to uptake water. To measure the amount of water absorbed by the membranes, swelling experiments have been performed in a controlled water vapor fully saturated atmosphere. The membranes have been dried for 90 hours in a vacuum oven at 50°C, and dried weight was measured and recorded. The membranes were installed in a “humidity box” together with an open recipient filled with water. The box was covered with aluminum foil to guarantee a 100% humidity atmosphere (more details in the Supplementary Materials).

## Gas permeation experiments

The membranes investigated were prepared as self-standing films and were supported on filter paper for facile manipulation during testing. The membranes with filter paper were mounted in a sandwich mode, between two discs of aluminum tape. For the most flexible membranes, which easily deform when tightened in the testing membrane cell, smaller membrane areas were used. The diameter of the hole in aluminum was at least 4 mm smaller than the membrane diameter. A rubber O ring is used on top to hold the membrane sandwich on top of a stainless-steel sinter filter in the bottom of the cell. Very often, gas transport properties of new membrane materials are tested by single gas permeation using the time-lag method, relatively high feed pressure, and hard vacuum on permeate side (below 10 mbar). Although in real life, a mixture is always present, often containing water vapors (fully water saturated), with the interest component to be removed in low concentration present (i.e., CO₂, 0.4% in air to 15% in flue gas from coal fired power plants), single gas permeation can provide valuable indications about the gas transport mechanism, gas solubilities, and diffusivities. In our experiments, after an overnight evacuation, a feed pressure of 5 bar of nitrogen was applied during approximately 2 hours, and permeation was measured. After 4 hours of evacuation, 5 bar of methane was applied, again followed by 4 hours of evacuation before the application of 5 bar of carbon dioxide. For the purpose of screening, feed pressure was maintained constant at 5 bar and the temperature at 25°C. In a second step, for some selected membranes, the pressure

<footnote>*CO₂/N₂ selectivity. †CO₂/CH₄ selectivity.</footnote>
influence on gas permeability was investigated additionally at 3-, 8-, and 10-bar feed pressure.

## Single gas permeation experiments

The single gas permeation setup is presented in fig. S8. The feed gas is provided from gas cylinders, and a pressure sensor enables the control and check the applied pressure. Vacuum is applied on the permeate side of the membrane using a vacuum pump. After placing the cell in the gas permeation setup, a certain evacuation time was needed to be sure that all the gases adsorbed on the membrane and on the tubes of the apparatus were desorbed. For this, all the valves were opened, and the vacuum pump was running. An overnight evacuation was performed, at the installation of the cell. A leakage test has been performed for the permeate side: After evacuation, all the valves were closed, and the pressure in the permeate side was followed. Then, the slope of the pressure versus time gives the permeate side leakage rate. Each membrane was tested at 5 bar with different gases. The gases used were nitrogen ($N_2$), methane ($CH_4$), and carbon dioxide ($CO_2$), in this order, to avoid modifications of the membrane due to the strongest adsorbing gases. The pressure was set in the feed side using the first pressure sensor (between V1 and V3), the valve V6 was opened after that, and valves V10, V11, and V12 have been closed. The second pressure sensor (in the permeate side before V11) enabled to follow the increasing pressure. Between two gases, the whole system was evacuated, for at least twice the time of exposure to gas.

## Mixed gas permeation experiments

The membranes used were the same membranes used for the single gas experiments. Each membrane was tested with a 10% $CO_2$ to 90% $N_2$ at 1.2 and 5 bar in both dry and wet conditions. The dry experiments were run first, and then exposure to wet gases was performed overnight before taking measurements. The sweep gas used was pure methane or pure helium at a flow of 5.6 ml/min and an absolute pressure of 1.02 bar. A leakage test was run with pure $CO_2$ or $CH_4$ to measure the nitrogen amount leaking into the setup during the experiments. The permeate gas was sent to the chromatograph, and the permeate composition was recorded at steady state. A schematic representation of the testing setup used for mixed gas permeation experiments is presented in fig. S10. A pressure indicator enables the measurement of the feed pressure. The retentate gas flow rate is measured with bubble flow meter. The sweep gas pressure is set to atmospheric pressure, and the flow can be adjusted and recorded via a flow meter or a flow controller. The permeate gas is sent to a gas chromatograph to analyze its composition. Two different configurations are possible: using dry gas or humidified gas. In case of humidified, wet gas, both feed and sweep gases follow are passed through a diffuser in a metallic cylinder filled with water. The membranes used were the same membranes used for the single gas experiments. Each membrane was tested with a 10% $CO_2$ to 90% $N_2$ at 1.2 and 5 bar in both dry and wet conditions. The dry experiments were run first, and then exposure to wet gases was performed overnight before taking measurements. The sweep gas used was pure methane or pure helium at a flow of 5.6 ml/min and an absolute pressure of 1.02 bar. A leakage test was run with pure $CO_2$ or $CH_4$ to measure the nitrogen amount leaking into the setup during the experiments. The permeate gas was sent to the chromatograph, and the permeate composition was recorded at steady state (more details in the Supplementary Materials).

## Gas sorption experiments

A gravimetric method was used to characterize the sorption of the different gases in the membranes. The experiments were conducted using a Rubotherm magnetic suspension balance. The specificity of this instrument is that the sample and the holder are not directly linked to the balance, and so very extreme conditions of pressure and temperature can be applied. The holder is maintained suspended by a permanent magnet. The system is presented in fig. S11. The system enables the measurement of the variation of weight of a sample holder and the sample under different conditions of pressure and/or temperature. This variation can be related to the specific gas uptake. The plot of specific gas uptake at one given temperature versus pressure is called sorption isotherm of the gas in the membrane. To avoid perturbations due to non-ideality, the fugacity was used instead of the pressure. Before all experiments, the weight of the holder and the volume of the holder are measured. A "blank" measurement is run using different pressures of helium, which is considered as a non-adsorbent gas, which are applied to the holder only without sample (more details in the Supplementary Materials).

## Atomistic simulations

The nonbonded interactions between the ROF atoms were represented by the Transferable Potentials for Phase Equilibria-United Atom (TraPPE-UA) force field (40), while bonded interactions were taken from the General Amber Force Field (GAFF) (41). A 14-Å cutoff was applied for both Lennard-Jones (LJ) and electrostatic interactions, accompanied by tail corrections for LJ interactions and Ewald correction for the long-range electrostatic interactions (42). Partial electrostatic charges of the polymer atoms were estimated by density functional theory calculations using the Dmol3 tool of the Materials Studios 5.5 simulation package (BIOVIA Dassault Systems, San Diego) based on the repeat unit of ROF-T5. To represent the permeant molecules, the Elementary Physical Model EPM2 force field was adopted for $CO_2$ (43), whereas methane was represented as spherical united atom (40). For $N_2$, the three-site model was used with a dummy charge at the center of mass of the molecule (44). For the ROF-type polymers with short PPO chains, such as ROF-T5, the representation of the cross-linking between the carbonyl group of the BTA and the amine group of the PPO could be important, since the degree cross-linking controls the chain mobility of the polymers and their sorption capacities. To understand the extent of this effect, we considered two different cross-linking schemes for the ROF-T5: (i) hyperbranching and (ii) fully cross-linking. For the hyperbranched ROF-T5 model, a repeat unit containing trialkylhyde and PPO groups was used to grow a hyperbranched copolymer of ~31 kDa using the polymer builder tool of the Materials Studio software package. This procedure led to a cross-linking degree of 30%, which was defined on the basis of the ratio of $NH_2$ to N=O groups. Two of these chains were used to construct a cubic simulation cell using the Amorphous Cell module of the software package. The matrix was then equilibrated using a series of NVT- and NPT-MD simulations. The fully, 100%, cross-linked ROF-T5 model was constructed by inserting three repeat units orthogonally leading to a 3D network as represented in the cartoon in Fig. 3A, which forms a unit cell. The unit cell was then extended in all three dimensions by creating a 2 by 2 by 2 super cell. The resulting supercell underwent a series of NVT- and NPT-MD simulations. For the ROF-T6 polymer, only an uncross-linked model was constructed because of the higher chain length of the PPO, which makes the effect of the cross-linking
negligible. Two hyperbranched T6 chains of ~30 kDa were con-
structed and terminated by NH₂ groups. These chains were used to
obtain a simulation box with a final density of 1.05 g/cm³ after the
equilibration procedure. For polymers, the Tg is an important de-
scriptor of the chain flexibility. As an initial validation of the poly-
mer models, the glass transition temperatures (Tgs) of the ROF-T5
and ROF-T6 polymers were estimated by calculating the specific
volume (v) of each polymer over the temperature range (160 to 360 K)
using NPT-MD simulations. Starting from 360 K, each polymer
is cooled down from with 20 K decrements, which mimicked the
experimental cooling procedure. The temperature at which the slope
of the "v" versus T" curve changed was identified as the Tg for the
polymer. The open-source Large-scale Atomic/Molecular Massively
Parallel Simulator (LAMMPS) software was used in all molecular
simulations (Monte Carlo and MD). All postprocessing analyses
were carried out by using either the modules available in LAMMPS
or in-house codes unless otherwise stated (more details in the
Supplementary Materials).

**Supplementary Materials**

The PDF file includes:

Supplementary Text

Tables S1 to S8

Figs. S1 to S15

Legends for data S1 and S2

References

**Other Supplementary Material for this manuscript includes the following:**

Data S1 and S2

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**Acknowledgments:** We would like to thank to J. C. Jansen, CNR-ITM, Italy, for the useful discussions regarding sorption results. **Funding:** This work was supported in part by the project "Evolution" funded by European Union–NextgenerationEU and Romanian Government, under National Recovery and Resilience Plan for Romania, contract no.760033/23.05.2023/23.05.2023, cod PNRR-C9-I8-CF16, through the Romanian Ministry of Research, Innovation and Digitalization, within Component 9, Investment I8; by the M-ERA NET 2021 project no. ANR-22-MER3-0002-01, COFFEE; and by the Research Council of Norway through the POLYMEM project (grant no. 254791) in the CLIMIT program. The computational work was performed using HPC resources from GENCI-CINES (grant A0160907613). **Author contributions:** Conceptualization: M.B. and M.S. Methodology: M.S., L.C., M.G.A., and T.M. Investigation: M.P, T.M., and L.C. Visualization: G.M. and M.G.A. Supervision: M.B., M.S., G.M., and M.-B.H. Writing—original draft: M.B., M.S., and G.M. Writing—review and editing: All authors. **Competing interests:** The authors declare that they have no competing interests. **Data and materials availability:** All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

Submitted 16 May 2024

Accepted 11 October 2024

Published 13 November 2024

10.1126/sciadv.adq5024