Dual synergistic modification of Pebax 2533 membranes with sorbitol and silver nanoparticles for enhanced CO₂ separation efficiency

Abstract

CO₂ separation from N₂ and CH₄ is increasingly important due to environmental and industrial concerns. Membrane-based separation using polymeric materials offers advantages such as energy efficiency, easy processing, and cost-effectiveness. In this study, mixed matrix membranes (MMMs) based on CO₂-philic Pebax 2533 were fabricated and modified in two steps to enhance CO₂ separation performance. In the first step, Sorbitol was incorporated at various loadings (5–20 wt%), with 15 wt% found to be optimal, achieving CO₂ permeability of 394.5 Barrer and selectivities of 13.11 (CO₂/CH₄) and 48.70 (CO₂/N₂) at 30 °C and 2 bar. Sorbitol enhanced membrane crystallinity and thermal stability, as confirmed by FTIR, DSC, and TGA. In the second step, Ag nanoparticles (AgNPs) were introduced (up to 5 wt%) into the Pebax/Sorbitol matrix to exploit facilitated CO₂ transport mechnisem. FESEM showed changes in morphology and increased chain rigidity. The optimized membrane (P/S-15/Ag-5) exhibited a 19.5% increase in CO₂ permeability compared to P/S-15, while maintaining the selectivities. The combined effect of Sorbitol and AgNPs led to improved thermal and separation properties, making the developed MMMs promising candidates for efficient CO₂ separation applications.

Introduction

Fossil fuel combustion releases greenhouse gases, primarily carbon dioxide (CO₂), an acidic gas that contributes to acid rain and is a major driver of global warming^1,2. Additionally, in natural gas and biogas processing, the presence of CO₂ poses challenges due to its corrosive nature, which can reduce the lifespan of processing equipment. Thus, CO₂ separation is essential to mitigate these adverse effects³. Conventional separation methods—such as adsorption, absorption, and cryogenic distillation—are energy-intensive and costly^4,5. In recent decades, however, membrane technology has emerged as a promising alternative, offering advantages like lower capital and operational costs, operational simplicity, and material versatility^6,7. Among membrane types, polymeric membranes dominate due to their low cost, ease of fabrication, and wide availability^8–10. Dense membranes are morphologically ideal for gas separation, where permeation follows the solution-diffusion mechanism¹¹. However, as established by Robeson (1991), polymeric membranes face an inherent trade-off between permeability and selectivity, limiting their performance¹². To overcome this, recent research has focused on strategies such as polymer/polymer blending, polymer/non-polymer modification (e.g., mixed-matrix membranes), crosslinking, grafting^13,14. Modifying polymers with non-polymeric organic compounds is a cost-effective approach that can enhance separation performance while simultaneously improving mechanical and thermal stability^15–17.

Another strategy to overcome the permeability-selectivity trade-off is the use of mixed-matrix membranes (MMMs)^18,19. In this approach, a filler (dispersed phase) is incorporated into a polymer (continuous phase) to enhance selectivity, permeability, or both²⁰. The compatibility between MMM components critically impacts membrane performance, necessitating careful material selection^19,21,22. Intermolecular interactions (e.g., dipole-dipole, ion-dipole, hydrogen bonding) promote cohesion among membrane constituents^23,24. A wide range of additives can be employed, including metals, metal oxides, and metal-organic frameworks (MOFs)^25–27. Stabilized metal nanoparticles, for instance, boost gas permeability via facilitated transport, a three-step mechanism:

• Complexation of gas molecules with metal nanoparticles.

• Diffusion of the gas-metal complex across the membrane.

• Decomplexation and gas release at the downstream side²⁸.

For CO₂, this process involves coordination between metal orbitals and CO₂ electron pairs, enhancing permeability beyond the solution-diffusion mechanism²⁹. Nanoparticles also disrupt polymer chain packing, increasing interchain spacing and gas permeation³⁰. While this may reduce selectivity, the CO₂-facilitated transport mechanism can significantly compensate for the drawback^31,32.

Both glassy and rubbery polymers are used in CO₂ separation membranes, but each has inherent limitations³³. A promising solution is the use of block copolymers combining rigid (glassy) and soft (rubbery) segments. Poly(ether-block-amide), commercially known as Pebax, is one such copolymer, consisting of polyamide (PA) blocks (rigid segments) and polyether (PE) blocks (soft segments)³⁴. Pebax is available in various grades, depending on the PA/PE ratio and composition³⁵. Its excellent mechanical properties and CO₂-philic functional groups (amide, ether, and hydroxyl) make it particularly suitable for CO₂ separation membranes, especially Pebax 1657 and 2533 grades³⁶. Several studies have explored Pebax modification using nanoparticles to enhance its performance. For example: Sanaeepur et al. used Cu nanoparticles to improve the performance of Pebax 1657/glycerol membranes. At 10 bar and 25 °C, pure Pebax showed CO₂ permeability of 65.71 Barrer and CO₂/N₂ selectivity of 81.9. The Pebax/glycerol (15 wt%) membrane exhibited values of 50.42 Barrer and 222.7, while the Pebax/glycerol (15 wt%)/Cu (1.5 wt%) MMM achieved 63.6 Barrer and 200 for permeability and selectivity, in that order²⁵.

Nobakht and Abedini investigated the effects of maltitol and zeolitic imidazolate framework-8 (ZIF-8) on the separation performance of Pebax 1657 membranes. Gas permeation test results showed that the optimal maltitol loading was 20 wt%, and this membrane composition was selected as the base for MMM preparation. The highest CO₂/N₂ (69.31) and CO₂/CH₄ (26.59) selectivities were achieved with 5 wt% ZIF-8 loading. Meanwhile, a 10 wt% ZIF-8 loading yielded the maximum CO₂ permeability (429.57 Barrer). All measurements were conducted at 30 °C and 10 bar³⁷.

Ansari et al. blended Pebax 2533 with Matrimid and polystyrene CO₂/N₂ separation. The best performance was achieved for the membrane containing 5 wt% of Matrimid which improved CO₂ permeability by 21% and CO₂/N₂ selectivity by 76% ³⁸.

Nafisi and Hägg used modified Si nanoparticles as a modifier for Pebax 2533. They found that the nanoparticles increased the permeability of CO₂, CH₄, N₂, and O₂ while the selectivity of CO₂/N₂ and CO₂/CH₄ decreased at lower loading of filler. By increasing the loading of inorganic filler, the selectivity values did not change and it was attributed to the nanogap formation around the nanoparticles in the Pebax matrix³⁹.

Casadei et al. incorporated different types of graphene oxide (GO) in a Pebax 2533 matrix. According to their report, 0.02 wt% loading of porous GO nanofiller into the Pebax matrix, improved the permeability of CO₂ by 10% and its value was 400 Barrer at 35 °C and 1 barg; while the CO₂/N₂ selectivity remained approximately constant (about 25)⁴⁰.

The incorporation of silver nanoparticles (AgNPs) into MMMs has gained attention due to their special physicochemical properties and strong affinity toward polarizable gases such as CO₂. AgNPs can enhance the gas transport behavior by interacting with the quadrupole moment of CO₂, thereby facilitating its sorption and diffusion through the membrane matrix. Furthermore, the high surface area of AgNPs may promote microstructural modifications in the polymeric phase, such as increased chain mobility, contributing to improved gas permeability. In addition, silver-based fillers are known for their antimicrobial properties and thermal stability, which can be advantageous for membrane longevity and operational robustness. Thus, AgNPs represent a multifunctional additive that not only improves gas separation performance but also adds functional value to the membrane system^41,42.

In this study, Pebax 2533 (20 wt% PA and 80 wt% PE) was used as the main polymer matrix due to its good permeability, inherent CO₂ selectivity, and suitable mechanical properties. To enhance membrane performance, Sorbitol was first incorporated into Pebax to improve CO₂/CH₄ and CO₂/N₂ selectivity, owing to its six hydroxyl (O─H) groups. The Lewis acid-base interaction between CO₂ and O─H groups increases CO₂ permeation and improves its selectivity over other gases. In the secondary modification step, silver nanoparticles (AgNPs) were added to the optimized Pebax/Sorbitol matrix, as confirmed by gas permeation tests. These nanoparticles can occupy spaces between Pebax chains in the membrane matrix, thereby increasing the diffusion path length. Additionally, AgNPs facilitate CO₂ transport through the membrane while maintaining selectivity at acceptable levels. The prepared membranes were characterized using FESEM, FT-IR, TGA, and DSC, as detailed in the following sections.

Experimental

Materials

Pebax 2533, the membrane matrix main material, was supplied by Arkema (France). Sorbitol (99% purity, molecular weight: 182 g/mol), used as the main modification agent, was purchased from Merck (Germany). Ethanol (99.9% purity), employed as the solvent for Pebax, was also obtained from Merck. Silver nanoparticles (average size: 20 nm, 99.99% purity), utilized as the secondary modification material, were supplied by US Nano (USA).

Membrane fabrication

Pebax/Sorbitol membrane Preparation

First, a homogeneous 3 wt% Pebax 2533 solution in ethanol was prepared by stirring at 60 °C for 4 h. Separately, Sorbitol was dissolved in deionized water at room temperature for 1 h to obtain a 20 wt% solution. The two solutions were then mixed and stirred for 6 h at 60 °C to ensure uniformity. The final solution was cast onto a glass Petri dish and left at room temperature for 24 h to allow solvent evaporation. Finally, to achieve complete solvent removal, the membranes were oven-dried at 60 °C for 12 h.

Pebax/Sorbitol/Ag membrane Preparation

This step was conducted after identifying the optimal Pebax/Sorbitol membrane composition. First, a specified amount of AgNPs was added to ethanol, and the mixture was stirred for 15 min. After partial dispersion was achieved, the mixture was sonicated in a 150 W sonicator (vCLEAN-L02, Backer (Iran)) for 20 min to ensure complete and stable nanoparticle dispersion. Next, a 3 wt% Pebax 2533 solution was prepared by dissolving the polymer in ethanol under stirring at 60 °C for 4 h. Concurrently, a 20 wt% Sorbitol solution was prepared in deionized water by stirring for 1 h at room temperature. The two solutions were then combined and mixed at 60 °C for 6 h, followed by 1 h of sonication to homogenize the AgNPs distribution. After degassing (30 min at rest) and cooling, the solution was cast onto a Petri dish. Solvent evaporation was carried out in two stages: 24 h at room temperature, followed by 12 h in an oven at 60 °C to eliminate residual solvent.

All fabricated membranes, containing varying loadings of Sorbitol and AgNPs, are coded and summarized in Table 1.

Table 1.

The Pepared membranes abbreviation.

Membrane	Pebax 2533 content (wt%)	Sorbitol content (wt%)	AgNPs content (wt%)
PP	100	–	–
P/S-5	95	5	–
P/S-10	90	10	–
P/S-15	85	15	–
P/S-20	80	20	–
P/S-15/Ag-0.5	84.5	15	0.5
P/S-15/Ag-1	84	15	1
P/S-15/Ag-2	83	15	2
P/S-15/Ag-5	80	15	5

PP: Pure Pebax, P: Pebax, S: Sorbitol, Ag: Silver nanoparticles (AgNPs).

Characterization

To characterize the functional groups and identify intermolecular interactions within the prepared membranes, Fourier-transform infrared (FTIR) analysis was performed using a BRAIC instrument (China) across a wavenumber range of 400–4000 cm⁻¹.

The surface and cross-sectional morphology of the membranes, along with the dispersion quality of AgNPs, were examined by field-emission scanning electron microscopy (FESEM). Cross-sectional samples were prepared by cryofracturing the membranes in liquid nitrogen. All samples (surface and cross-section) were gold-coated to achieve electrical conductivity prior to imaging. FESEM was conducted using a TESCAN MIRA3 instrument (Czech Republic) at varying magnifications. Differential scanning calorimetry (DSC) was employed to determine the melting point, glass transition temperature, and potential phase transitions of the membranes. Heat capacity was measured as a function of temperature under constant pressure. Samples of known mass underwent heating-cooling cycles, with heat flow differences used to calculate heat capacity changes. DSC was performed using a TA Q600 instrument (USA) under a nitrogen atmosphere, with a temperature range of − 100 to 250 °C and a heating rate of 10 °C/min (dual scanning mode). Thermogravimetric analysis (TGA) assessed the thermal stability of the membranes and their components. Samples were first dried at 70 °C for 24 h to eliminate residual moisture. Subsequently, they were heated in a TA Q600 instrument (USA) from 25 °C to 650 °C at 10 °C/min, with continuous weight monitoring.

Membrane permeability measurement

A constant-volume system was employed to measure the permeability of pure gases (CO₂, N₂, and CH₄) under single-gas conditions. Experiments were conducted at temperatures of 30, 50, and 70 °C and the feed pressures of 2, 6, and 10 bar. The test gas was introduced to the membrane cell, and permeated gas was collected in the downstream chamber. Permeability was calculated by monitoring the pressure increase in the downstream chamber over time. The slope of the linear region of the pressure-versus-time curve was inserted into Eq. 1 to determine the gas permeability coefficient⁴³.

1

In which, P is the gas permeability Barrer (1 Barrer = 10^− 10 cm³ (STP) cm/ (cm² cmHg s)), V is the volume of downstream chamber (cm³, L is the thickness of membrane (cm), A is the effective surface of membrane in cell (cm², T is the operating temperature (K), p₀ is the feed gas pressure (atm) and (dp/dt) is the downstream pressure increment at steady state condition (atm/s)⁴³.

The ideal selectivity (α) can be calculated using Eq. 2 with having A and B pure gases permeability⁴³:

2

To perform mixed-gas experiments for each binary system (CO₂/CH₄ and CO₂/N₂) a 10 vol% CO₂ containing mixture was fed to the permeation measurement setup which was coupled via a gas chromatograph (Agilent 7890 A). The values of permeability in this case, were calculated by Eqs. (3) and (4).

3

4

The selectivity of gas mixture can be obtained using Eq. (5).

5

where x and y represent the mole fractions in feed side and permeate side, respectively.

Results and discussion

FTIR

The FTIR spectra of pure Pebax, Sorbitol, AgNPs, and the modified membranes are shown in Fig. 1. According to this figure, Pebax spectrum exhibits eight peaks representing its functional groups. The N─H stretching peak is observed at 3289 cm⁻¹, and the ═C─H stretching vibration appears at 3091 cm^-1. A peak in the range of 2832–2948 cm^-1 corresponds to C─H stretching. The stretching vibrations of C═O in O─C═O and H─N─C═O are indicated by peaks at 1730 cm^-1 and 1635 cm^-1, respectively. The peaks at 1542 cm⁻¹ and 1469 cm⁻¹ are attributed to the bending vibrations of N─H and C─H. The final characteristic peak appears at 1105 cm^-1, which corresponds to the stretching of C─O─C^44–46.

Fig. 1.

FTIR spectra of Pebax, Sorbitol, Ag and the prepared membranes.

The characteristic peaks of Sorbitol are clearly identifiable; At 3394 cm^-1, a broad peak appears, which can be attributed to the O─H stretching vibration. Additionally, the C─H stretching is evident with a peak at 2930 cm^-1. Other bands at 1641, 1410, and 1087 cm^-1 correspond to O─H bending, C─H bending, and C─O stretching vibrations, respectively^44,47,48.

In the case of AgNPs, two peaks are observed at 3415 and 1633 cm^-1, which are consistent with previous reports^49,50. These peaks are associated with adsorbed moisture and the stabilizing agents used during the synthesis process⁵¹.

The spectra of Sorbitol-modified membranes show all the characteristic peaks of both Pebax and Sorbitol without any additional peaks. This suggests that all interactions are physical, and no new functional groups have formed. In some regions, slight shifts to higher wavenumbers are observed. For example, the peaks at 3289 and 1635 cm^-1 in the Pebax membrane (PP) shift to 3299 and 1641 cm^-1 in the P/S-10 membrane, respectively. These shifts may be attributed to interactions between the hydroxyl groups of Sorbitol and the amide and ether groups of Pebax^25,44.

For the Pebax/Sorbitol/Ag membranes, the characteristic peaks of all components are visible, with only slight changes in the intensity of peaks related to AgNPs. The interaction between AgNPs and other components in the mixed matrix membrane (MMM) is illustrated in Fig. 2. Due to their positive surface charge, AgNPs are attracted to oxygen atoms, which possess non-bonding electron pairs and a partial negative charge, resulting in their incorporation into the polymer matrix via dipole–dipole interactions²⁵.

Fig. 2.

Schematic of Pebax, Sorbitol, and AgNPs in MMMs and their interaction with CO₂ and each other.

FESEM

The FESEM images of the prepared membranes, showing both surface and cross-sectional morphologies, are presented in Fig. 3. As can be seen, the PP membrane has a smooth surface without any impurities or defects. Additionally, the cross-sectional image of the PP membrane shows a regular and dense structure. By incorporating Sorbitol, its molecules are embedded within the polymer matrix, and some white regions appear on the membrane surface. This can be attributed to the compression of Pebax chains due to the formation of hydrogen bonds between Pebax and Sorbitol. The cross-sectional images of the P/S-5 and P/S-15 membranes also show this effect, evident from the shrinkage observed in their textures. In the surface images of the MMMs, a dense structure with a uniform dispersion of AgNPs can be observed. A direct relationship between the loading of AgNPs and increased non-uniformity in the membrane structure is evident in the cross-sectional images. This can be explained by the mutual interaction between AgNPs and the polymeric matrix. AgNPs disrupt the packing of polymer chains, leading to a less densely packed structure, which in turn enhances gas permeation. According to the surface and cross-sectional images of the P/S-15/Ag-5 membrane, the surface roughness is higher compared to the other membranes. This increase in roughness is caused by the presence of AgNPs, which leads to a larger surface area and increased contact with gas molecules. As a result, gas permeation—especially for CO₂—is enhanced. In the cross-sectional images, a key parameter of the membranes, namely their overall thickness, can also be measured and used for permeability calculations. For all prepared membranes, the overall thickness was approximately 21 ± 0.5 μm, as shown in Fig. 3a.

Fig. 3.

Cross-sectional and surface images of pure and modified membranes.

In the cross-sectional images at 50,000x magnification, as shown in Fig. 4, the structure of the Pebax/Sorbitol/Ag MMMs can be observed. In Fig. 4a, corresponding to the P/S-15/Ag-0.5 membrane, white regions indicate chain compactness resulting from interactions between AgNPs and the membrane matrix. As the loading of AgNPs increases, this accumulation becomes more pronounced, leading to a more uneven and irregular membrane structure. Such structural irregularities directly impact the membrane’s gas permeability performance. According to Fig. 4b, a free space has formed within the membrane matrix, in which gas molecules encounter minimal resistance, allowing them to permeate through the membrane more easily.

Fig. 4.

50000x magnification cross-sectional image of (a) P/S-15/Ag-0.5 and (b) P/S-15/Ag-5 membranes.

DSC and TGA

To investigate the thermal properties and degree of crystallinity of the prepared membranes, DSC analysis was conducted, and the results are presented in Fig. 5; Table 2. According to the figure, for Pebax 2533, the glass transition temperature (T_g), melting temperature (T_m) of the polyethylene segment, and T_m of the polyamide segment were observed at -77.3 °C, 9.8 °C, and 135.2 °C, respectively, which are consistent with previously reported values^40,52,53.

Fig. 5.

DSC curves of prepared membranes.

Table 2.

DSC results Fo prepared membranes.

Membrane	Tg (°C)	Tm, PTMO (°C)	Tm, PA (°C)	XC, PTMO (%)	XC, PA (%)	XC (%)
PP	-77.3	9.8	135.2	16.65	32.76	19.88
P/S-5	-73.8	10.1	135.8	17.05	32.94	20.23
P/S-15	-66.9	10.7	136.4	17.51	33.82	20.77
P/S-15/Ag-1	-66.3	11.4	136.9	17.77	33.95	21.00
P/S-15/Ag-5	-65.5	11.9	137.1	17.93	34.18	21.18

Sorbitol, with a Tg around − 5 °C, can act as a rigidifier for Pebax and reduce its chain mobility⁵⁴. As shown in Fig. 5, the T_g values of the P/S-5 and P/S-15 membranes shifted to higher temperatures, which is directly attributed to Sorbitol loading. This shift can be explained by the formation of hydrogen bonds between the hydroxyl groups of Sorbitol and the nitrogen and oxygen atoms in the Pebax chains, which restricts their mobility. Moreover, it is clear that the addition of Sorbitol does not significantly affect the T_m values, and only one T_g is observed, indicating good miscibility between Pebax and Sorbitol in the modified membranes with Sorbitol loadings of 5–15 wt%.

Upon incorporation of AgNPs, the upward trend in T_g continues, reaching − 65.5 °C for the P/S-15/Ag-5 membrane. As described in previous sections, AgNPs act as a restrictor of chain flexibility in the polymeric matrix, causing the MMMs to exhibit more glassy behavior. According to Fig. 5, there is no significant change in T_m values compared to the PP, P/S-5, and P/S-15 membranes, confirming the successful synthesis and compatibility of the MMMs.

From the crystallinity point of view, as reported in Table 2, the addition of Sorbitol led to an increase in crystallinity for the P/S-5 and P/S-15 membranes. This enhancement is attributed to the hydrogen bonding between Pebax and Sorbitol. For the P/S-15 membrane, the crystallinity reached 20.77%, which is 0.89% higher than that of the pristine PP membrane. Furthermore, the incorporation of AgNPs into the optimal Pebax/Sorbitol membrane (P/S-15) further increased the crystallinity. For the P/S-15/Ag-5 membrane, the crystallinity reached 21.18%. The effect of AgNPs on crystallinity is similar to that of Sorbitol in that both restrict chain mobility, thus promoting crystallization. As a result, when the nanoparticles are properly dispersed throughout the membrane (see FESEM section), they facilitate crystal growth.

The thermal resistance of the prepared membranes and the effect of each modifier’s loading were studied using TGA, and the results are shown in Fig. 6. As can be observed, pure Pebax exhibits three stages of degradation. The first stage occurs between 50 and 355 °C and is attributed to the removal of solvent and moisture. The second stage, from 355 to 480 °C, corresponds to the thermal degradation of the polymer chains. The third stage, above 480 °C, involves the carbonization of the degraded polymer chains.

Fig. 6.

TGA curves of Pebax, Sorbitol, AgNPs and the prepared membranes.

Sorbitol shows a degradation temperature (T_d) around 500 °C, resulting in a 95% weight loss of the sample. The obtained curves for both Pebax and Sorbitol are consistent with the literature^39,44,45,55. When Sorbitol was added to Pebax, the T_d increased to 364 °C and 378 °C for the P/S-10 and P/S-20 membranes, respectively.

According to the TGA curve for AgNPs, the sample lost about 2 wt% of its weight up to 195 °C, likely due to the removal of adsorbed moisture. Between 195 and 280 °C, an additional weight loss of approximately 7% occurred, which can be attributed to the decomposition of organic stabilizing agents. A further weight loss of about 3% was observed at 730 °C, potentially related to the degradation of carbon residues or inorganic impurities. At 800 °C, approximately 89% of the initial sample mass remained, corresponding to metallic Ag^56,57.

In AgNPs-containing MMMs, the degradation range broadened and occurred between 220 and 530 °C, which is directly influenced by the presence of all components. This suggests a heterogeneous degradation pattern—an inherent feature of MMMs—and highlights the effective interaction and compatibility among Pebax, Sorbitol, and AgNPs.

Gas permeation results

The effect of adding Sorbitol and AgNPs on the separation performance of the prepared membranes was evaluated at 30 °C under a feed pressure range of 2–10 bar. As previously mentioned, the optimum Sorbitol loading was first determined, followed by the fabrication of MMMs. In the following sections, the results of gas permeation tests—considering the effects of Sorbitol and AgNPs loadings as well as feed pressure—are discussed in detail for both CO₂/N₂ and CO₂/CH₄ gas pairs over the modified Pebax membranes.

Pebax/Sorbitol membranes

According to Fig. 7, which presents the gas permeation test results for pure Pebax and Pebax/Sorbitol membranes at 2 bar and 30 °C, the permeability of CO₂ is significantly higher than that of N₂ and CH₄. This is attributed to CO₂’s smaller kinetic diameter, higher condensability, and greater quadrupole moment^58,59. As shown in Fig. 7a, the addition of Sorbitol up to 10 wt% reduces the permeability for all tested gases. For instance, in the P/S-10 membrane, the CO₂, N₂, and CH₄ permeabilities were 290.7, 7.6, and 28.4 Barrer, respectively, whereas for the pure Pebax membrane, the values were 328.3, 9.4, and 38.4 Barrer. This reduction is due to the increased rigidity and crystallinity of the polymer chains (see Table 2), which limits chain mobility and consequently restricts gas permeation. The increase in crystallinity can be attributed to strong hydrogen bonding interactions formed between the hydrogen atoms of Sorbitol’s hydroxyl groups and the oxygen atoms (from hydroxyl, ether, and amide groups) and nitrogen atoms (from amide groups) in the Pebax backbone. In the P/S-15 membrane, crystallinity continued to increase, and N₂ and CH₄ permeability further decreased. However, in the case of CO₂, the increased presence of hydroxyl groups promoted Lewis acid–base interactions between CO₂ and the hydroxyl functionalities, enhancing CO₂ permeability via the solubility mechanism. In the P/S-20 membrane, the disruption of hydrogen bonding between Pebax and Sorbitol resulted in reduced crystallinity, which led to increased permeability for all tested gases.

Fig. 7.

Effect of Sorbitol loading on (a) CO₂, CH₄, and N₂ permeability and (b) CO₂/CH₄ and CO₂/N₂ selectivity.

According to Fig. 7b, the CO₂/N₂ and CO₂/CH₄ selectivities increased with the addition of Sorbitol to Pebax up to 15 wt%, and then decreased in the P/S-20 membrane. For the pure Pebax, P/S-15, and P/S-20 membranes, the CO₂/N₂ selectivity values were 34.92, 46.49, and 45.72, respectively, while the CO₂/CH₄ selectivity values were 8.55, 12.39, and 11.47. The decrease in selectivity observed in the P/S-20 membrane can be attributed to the disruption of hydrogen bonding, which led to increased permeability of N₂ and CH₄. Based on these results, a Sorbitol loading of 15 wt% was identified as the optimum value and was selected as the base formulation for the second-stage modification with AgNPs.

Effect of AgNPs content

The permeability values of CO₂, N₂, and CH₄ gases, along with the CO₂/N₂ and CO₂/CH₄ selectivities for Pebax/Sorbitol/Ag MMMs, are presented in Fig. 8. According to Fig. 8a, the permeability of all three gases increased with the addition of AgNPs. Embedding AgNPs within the polymer chains disrupts the packing of the chains and increases the free space, which facilitates the diffusion of gas molecules through the membrane. Additionally, the incorporation of AgNPs can weaken some of the hydrogen bonds formed between Pebax and Sorbitol molecules, thereby enhancing the mobility of the polymer chains. The increase in permeability was more pronounced for CO₂ than for N₂ and CH₄. This can be attributed to the ability of AgNPs to facilitate CO₂ transport by altering the local concentration through a facilitated transport mechanism, involving reversible complexation between the empty orbitals of Ag and the non-bonding electron pairs of the electron-donating CO₂ molecules. The trend of selectivity changes for CO₂/N₂ and CO₂/CH₄ is illustrated in Fig. 8b. As shown, the selectivity values for the Pebax/Sorbitol/Ag MMMs remained nearly unchanged compared to the base modified membrane (P/S-15). Thus, it can be concluded that the addition of AgNPs effectively improved membrane performance by increasing permeability while maintaining selectivity. For instance, at 2 bar and 30 °C, the CO₂ permeability, CO₂/N₂ selectivity, and CO₂/CH₄ selectivity values were 320.8 Barrer, 46.49, and 12.38, respectively, for the P/S-15 membrane. These values changed to 359.8 Barrer, 45.54, and 12.36, respectively, in the P/S-15/Ag-5 MMM.

Fig. 8.

Effect of AgNPs content on (a) CO₂, N₂, and CH₄ permeabilities and (b) CO₂/N₂ and CO₂/CH₄ selectivities.

The values of diffusivity and solubility coefficients were also obtained for the prepared membranes and the results are shown in Table 3. Moreover, the CO₂ permeation behavior of Pebax/Sorbitol/AgNPs membranes is illustrated in Fig. 9. In the MMMs, increasing AgNP loading from 0 to 5 wt% resulted in a clear upward trend in gas diffusivity: CO₂ diffusivity increased from 1.90 to 2.06 × 10^− 6 cm²/s, while CH₄ and N₂ diffusivities rose from 1.31 to 1.47 and 1.20 to 1.37 × 10⁻⁶ cm²/s, respectively. This trend is attributable to the increased free space and disruption of polymer chain packing in the MMMs (see Fig. 9). Meanwhile, CO₂ solubility increased modestly (from 168.8 to 174.7 cm³(STP)/(cm³·cmHg)×10⁴), whereas CH₄ and N₂ solubilities remained nearly unchanged—indicating selective affinity of Sorbitol and AgNPs towards CO₂ due to specific polar or π-complexation interactions. As a result, although diffusivity selectivity decreased slightly from 1.45 to 1.40, solubility selectivity increased from 8.54 to 8.82, yielding a net preservation of overall CO₂/CH₄ selectivity. A similar, trend was observed for CO₂/N₂ selectivity, which improved from 29.4 to 30.3. These findings reflect a synergistic enhancement mechanism whereby AgNPs elevate diffusivity for all gases, while specifically maintaining or enhancing CO₂ sorption, thereby balancing permeability and selectivity in line with established MMM transport models⁶⁰.

Table 3.

Diffusivity and solubility coefficients of the prepared membranes (values rounded to two decimal points).

Membrane	Diffusivity (cm2/s×106)			Solubility (cm3(STP)/cm3.cmHg×104)
	CO2	CH4	N 2	CO2	CH4	N 2
P/S-15	1.90	1.31	1.20	168.84	19.77	5.75	1.45	8.54	1.58	29.36
P/S-15/Ag-0.5	1.92	1.34	1.22	169.06	19.70	5.74	1.43	8.58	1.57	29.47
P/S-15/Ag-1	1.96	1.37	1.25	169.23	19.78	5.76	1.43	8.56	1.57	29.38
P/S-15/Ag-2	2.00	1.41	1.30	169.55	19.71	5.77	1.42	8.60	1.54	29.39
P/S-15/Ag-5	2.06	1.47	1.37	174.66	19.79	5.77	1.40	8.82	1.50	30.29

Fig. 9.

Schematic view of CO₂ permeation in Pebax/Sorbitol/Ag membranes.

Effect of feed pressure

In membrane separation processes, the pressure difference across the membrane primarily acts as the driving force for gas transport. Therefore, increasing the feed pressure generally enhances gas permeation through the membrane. However, the extent of this enhancement depends on the penetrants’ size, shape, and their interactions with the membrane matrix. Additionally, increased pressure can lead to tighter polymer chain packing, which in turn may reduce the permeability. Another critical factor to consider is the plasticization effect, an undesirable phenomenon in gas separation membranes. Under high pressures, gas molecules are more readily absorbed on the membrane surface and diffuse into the polymer, increasing the chain mobility at higher gas concentrations. This enhanced mobility softens and swells the polymer, reducing its selectivity. Plasticization can significantly compromise the membrane’s performance by lowering selectivity. Moreover, the accumulation of gas molecules on the membrane surface may increase interactions between specific gases and the membrane’s selective sites, thereby enhancing gas permeation via the solubility mechanism. Given these potential effects, investigating the influence of feed pressure on membrane performance is essential. Therefore, gas permeation tests were conducted at 2, 6, and 10 bar to evaluate the effect of pressure on membrane behavior.

Figure 10 shows the effect of feed gas pressure on the performance of the prepared MMMs. With increasing pressure, due to the higher driving force, the permeability of all gases increases. In addition, CO₂ molecules, owing to their quadrupole moment, are capable of forming quadrupole–dipole interactions with the dipole moments of oxygen atoms in hydroxyl and carbonyl groups, as well as nitrogen atoms in amide groups. These interactions enhance CO₂ permeability through the solubility mechanism. Increasing the pressure leads to the accumulation of CO₂ molecules on the membrane surface, facilitating their permeation more effectively than other gases.

Fig. 10.

Effect of feed pressure on (a) CO₂ permeability, (b) CH₄ permeability, (c) N₂ permeability, (d) CO₂/CH₄ selectivity, and (e) CO₂/N₂ selectivity.

Furthermore, the increased concentration of CO₂ molecules at the membrane surface due to higher feed pressure can enhance permeability via the facilitated transport mechanism. For instance, for the P/S-15/Ag-5 membrane at 10 bar, the permeability values for CO₂, N₂, and CH₄ were 471.2, 9.6, and 36.1 Barrer, respectively, compared to 359.8, 7.9, and 29.1 Barrer at 2 bar. This clearly indicates a relatively greater enhancement in CO₂ permeability compared to N₂ and CH₄.

Figures 10 d and e show the changes in selectivity for CO₂/N₂ and CO₂/CH₄ gas pairs, respectively. In both cases, it is evident that selectivity increases with pressure. For example, in the P/S-15/Ag-5 membrane, the CO₂/N₂ selectivity increased from 45.54 at 2 bar to 49.08 at 10 bar. Similarly, the CO₂/CH₄ selectivity gained from 12.36 to 13.05 over the same pressure range. This enhancement is directly related to the more efficient interaction of CO₂ with the membrane and the facilitated transport effect of AgNPs. In contrast, N₂ and CH₄ are primarily influenced by the increase in driving force.

In terms of plasticization, these results are also valuable. Since the selectivity of all prepared MMMs increases with pressure, it indicates that plasticization does not occur in the fabricated membranes up to 10 bar of feed pressure.

Effect of temperature

Effect of temperature on CO₂ permeability and CO₂/CH₄ and CO₂/N₂ selectivity, presentend in Fig. 11. As shown in Fig. 11-a, for all membranes, when the temperature raised from 30 to 70 °C, the permeability of CO₂ enhanced; in can be mainly caused by more polymer chain mobility at higher temperatures. The increased mobility of polymer chains at elevated temperatures increases the diffusion of all gases through the membranes. On the other hand, CO₂, due to its high negative heat of sorption, exhibits a reduced solubility in the membranes at higher temperatures. This results in a smaller increase—or even a relative decrease—in CO₂ permeability compared to less condensable gases⁹. Consequently, the CO₂/N₂ and CO₂/CH₄ selectivities decrease with rising temperature, although the overall selectivity trend remains consistent across different AgNPs loadings.

Fig. 11.

Effect of temperature on (a) CO₂ permeability, (b) CO₂/CH₄ selectivity, and (c) CO₂/N₂ selectivity at 2 bar of feed pressure.

Mixed-gas permeation

The results of the mixed-gas separation performance evaluation are presented in Table 4. As shown, the measured permeabilities and selectivities are lower than those obtained from single-gas tests. This reduction is attributed to competitive sorption and plasticization effects under mixed-gas conditions. Specifically, CO₂ exhibits a stronger sorption affinity than CH₄ or N₂ in the Pebax matrix, which enhances CO₂ uptake but also induces swelling and increased segmental mobility in the polymer chains. As a result, the permeability of all gases increases, while the selectivities decrease accordingly. Moreover, in a gas mixture system, diffusivity selectivity is reduced due to the competition of penetrant–membrane interactions at sorption sites, further diminishing the observed separation performance. It should be noted that P/S-15/Ag-5 still retains favorable CO₂ permeability (339.1 Barrer), demonstrating that the nanoparticles help mitigate—but do not fully eliminate—these mixed-gas effects.

Table 4.

Mixed gas separation results at 30 °C and 2 bar.

Membrane	CO2 Permeability (Barrer)	CH4 Permeability (Barrer)	N2 Permeability (Barrer)	CO2/CH4 selectivity	CO2/N2 selectivity
PP	302.3	36.3	8.9	8.33	33.97
P/S-15	295.7	24.5	6.6	12.07	44.80
P/S-15/Ag-5	339.1	28.3	7.6	11.98	44.62

Long-term stability

To develop a promising membrane for efficient separation of CO₂, its stability is the key parameter. The must important factor in stability and performance serving of a typical membrane is the compatability of its constituent materials. So, for evaluating the durability of the optimum MMM, a long term test was performed over 10 days at 30 °C and 6 bar and the result depicted in Fig. 12. As can be seen, the CO₂ permeability declines with a gentle slope and at the end of the duration, CO₂ permeability reduced by about 1% (433.5 → 428.9 Barrer); which provides an acceptable stability for this membrane. The reduction can be related to the slight physical aging of the membrane during the test.

Fig. 12.

CO₂ permeability of P/S-15/Ag-5 membrane over the time; T = 30 °C, P = 6 bar.

Comparison with other studies

Table 5 compares the gas permeation results of the prepared membranes in this study with those of similar reported works. As shown, AgNPs act effectively as a modifier in the Pebax/Sorbitol matrix and demonstrate comparable performance with other types of fillers.

Table 5.

Comparison of the findings of this study with previous works on Pebax-based ternary MMMs.

Main matrix (wt% content in membrane)	Filler	Filler content (wt%)	Test condition		CO2 permeability (Barrer)	Selectivity		References
			T (°C)	P (bar)		CO2/CH4	CO2/N2
Pebax1657 (84)/PVA (10) Pebax1657 (79)/PVA (15)	Graphene oxide	6 6	30	10	236.50 228.30	33.64 -	- 124.09	9
Pebax 1657 (83.5)/Glycerol (15)	Cu	1.5	25	10	63.60	-	200	25
Pebax 1657 (84)/ [HMIM][NTf2] (10)	γ–Al2O3	6	25	10	173.90	24.29	77.98	61
Pebax 1657 (75)/Maltitol (20)	ZIF-8	5	30	10	397.85	26.59	69.31	37
Pebax 1074 (52)/PEG-200(40)	MgO	8	25	10	292.71	29.24	65.74	62
Pebax 2533 (80)/Sorbitol(15)	Ag	5	30	10	471.20	13.05	49.08	This work

Comparison with the upper bound

A useful criterion for evaluating the overall membrane performance in terms of both permeability and selectivity is the comparison with Robeson’s upper bound. Accordingly, for the CO₂/N₂ and CO₂/CH₄ gas pairs, the base plots were adopted from the 2008 revision of the upper bound, and the performance data of the PP, P/S-15, and P/S-15/Ag membranes at 10 bar were added. Figure 13 presents these plots; As shown in Fig. 13-a, the P/S-15/Ag-5 membrane surpassed the upper bound in CO₂/N₂ separation. The addition of AgNPs resulted in a significant increase in permeability while maintaining nearly constant selectivity, thereby enhancing the overall membrane performance. For the CO₂/CH₄ pair (Fig. 13-b), a similar improvement trend was observed, and the reduced distance between the performance points and the upper bound further confirms the positive impact of AgNPs on the separation capabilities of the MMMs.

Fig. 13.

Performance evaluation of the prepared membranes with Robeson upper bound; (a) CO₂/N₂, and (b) CO₂/CH₄ gas pair.

Conclusion

In this study, mixed matrix membranes (MMMs) composed of Pebax 2533, Sorbitol, and AgNPs were fabricated using the phase inversion method. As the first modification step, Sorbitol was incorporated into the Pebax matrix at loadings of 5, 10, 15, and 20 wt%. The best CO₂ separation performance was achieved with the membrane containing 15 wt% Sorbitol. At 30 °C and a feed pressure of 2 bar, this membrane exhibited CO₂ permeability of 320.8 Barrer, and CO₂/CH₄ and CO₂/N₂ selectivities of 12.39 and 46.49, respectively; while the corresponding values for the pristine Pebax membrane were 328.3 Barrer, 8.55, and 34.93. These improvements were attributed to hydrogen bonding between Pebax and Sorbitol, which increased crystallinity, as confirmed by FTIR spectroscopy and DSC analysis. The membrane morphology was influenced by Sorbitol loading, and a wrinkled surface pattern was observed. TGA results indicated enhanced thermal stability with Sorbitol incorporation. In the second modification step, a facilitated transport strategy was applied by embedding AgNPs into the optimized Pebax/Sorbitol (15 wt%) matrix. AgNPs were added at concentrations of 0.5, 1, 2, and 5 wt%. With increasing AgNP loading, CO₂ permeability increased while selectivity for both gas pairs remained nearly unchanged. For the membrane with 5 wt% AgNPs, at 30 °C and 10 bar, CO₂ permeability reached 471.2 Barrer, with CO₂/CH₄ and CO₂/N₂ selectivities of 13.05 and 49.08, respectively. The addition of AgNPs led to reduced polymer chain mobility, which was visually confirmed in FESEM images as white nodules. DSC analysis showed an increase in glass transition temperature (Tg) and crystallinity, indicating increased chain rigidity. TGA revealed heterogeneous degradation behavior due to the presence of two distinct phases. Comparison with similar studies demonstrated that the fabricated MMMs in this work exhibit competitive CO₂ separation performance for both CO₂/N₂ and CO₂/CH₄ gas pairs.

Author contributions

Hossein Hassanzadeh: Methodology, Validation, Formal Analysis, Investigation, Writing – Original Draft, Visualization. Reza Abedini: Conceptualization, Methodology, Validation, Formal Analysis, Resources, Data Curation, Writing – Review & Editing, Supervision, Project Administration, Funding Acquisition. Mohsen Ghorbani: Validation, Formal Analysis, Investigation, Writing – Original Draft, Visualization.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.