Molecular simulation of [P8883][Tf₂N] ionic liquid decorated silica in 6FDA-ODA based mixed matrix membrane for enhanced CO₂/CH₄ separation

Abstract

Mixed-matrix membranes (MMMs) have been reported to have considerable scope in gas separation applications because of their merged inherent strength of a durable polymer matrix and the exceptional performance capabilities of inorganic fillers. The selection of comparatively suitable polymers with fillers that can match each other and boost interfacial compatibility while ensuring uniform dispersion of filler within the polymer is still intensively demanding and is challenging at the experimental scale. Ionic liquids (ILs) are effective in promoting better dispersion and compatibility, leading to improved separation performance. A computational molecular simulation approach is employed in current work to design a hybrid membrane having Trioctapropyl phosphonium bis(trifluoromethylsulfonyl)imide [P8883][Tf₂N] IL decorated silica as a filler and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride-4,4′-oxydianiline (6FDA-ODA) polymer for carbon dioxide (CO₂) separation from methane (CH₄). Thermophysical and gas transport properties under pure and mixed gas condition (30, 50, and 70% CO₂/CH₄) within the MMMs with varying filler loadings (5, 10, and 15 wt% IL-silica) are examined via Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) simulations. Membrane characteristics like glass transition temperature (T_g), Fractional Free Volume (v_f), X-Ray Diffraction (XRD), solubility, diffusivity, permeability, and selectivity for neat and IL-silica filled 6FDA-ODA are computed. The results show that the T_g of the composite membrane with 5 wt% IL-silica is found to be considerably higher (with 305 °C) than that of the pure 6FDA-ODA polymer having 298 °C. A higher T_g value highlights the effective dispersion and higher adhesion between the filler and polymer membrane. Additionally, CO₂ permeability for 5 wt% IL-silica/6FDA-ODA MMM is significantly improved, measuring 319.0 barrer while maintaining a CO₂/CH₄ selectivity of 16.2. These values are 89% and 56% respectively, greater than the corresponding values of neat 6FDA-ODA membrane. Published data from the literature review is used to validate the findings and guarantee their reliability. The obtained results exhibited an error in the range of 0.7–9%. Hence, it is concluded from the study that molecular simulation can be used to design IL decorated silica incorporated within 6FDA-ODA matrix, which is able to boost the interfacial compatibility, with elevated CO₂/CH₄ selectivity and CO₂ permeability.

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1 Introduction

Raw natural gas, a fuel source of considerable global importance, contains a high level of CO₂, requires its purification to prevent issues such as pipeline degradation, increased compression costs, reduced heating efficiency, and increased greenhouse gas emissions.^1,2 Among the various separation technologies, membrane separation offers several advantages, including environmental friendliness, simple fabrication, trouble-free application, low capital cost, low energy consumption, well-space utility, and excellent thermal suitability.³ However, polymeric membranes have some shortcomings to meet industrialization standards due to the well-known “trade-off” between permeability and selectivity.⁴

Mixed matrix membranes (MMMs) are designed to exceed Robeson's upper bounds to get around the tradeoff between permeability and selectivity. MMMs consist of a polymer matrix with distributed inorganic components, allowing them to possess the advantageous characteristics of both inorganic and polymer membranes.⁵ In the MMM, the dispersed inorganic filler disrupts the effective packing of polymer for the creation of void channels to facilitate gas transport while also enhancing affinity for a specific molecule to improve separation performance.⁶ This gives MMMs a significant performance boost over a basic polymeric membrane.⁷ However, improper filler dispersion and low interfacial compatibility between the filler and polymer led to a tradeoff between permeability and selectivity, common issues faced by MMM, causing a bottleneck in its further enhancement. To tackle this concern and improve CO₂/CH₄ separation, supporting ionic liquids onto the surface of fillers or polymers has been proposed.^8,9

To date, several studies have been conducted to support ionic liquids (ILs) on polymers and fillers to improve their CO₂ separation performance. There are various methods to support ILs on the surface of polymer and filler,¹⁰ which encompass impregnation,¹¹ physical stirring,¹² supercritical fluid deposition (SCFD),¹³ blending,¹⁴ and grafting.¹⁵ A study was conducted on the synthesis of Ethyl Cellulose (EC) supported with 1-carboxymethyl-3-methylimidazolium tetrafluoroborate [HOOCMIM][BF₄]. The resulting EC exhibited a permeability of 199 barrer, which was significantly higher than that of the pure EC (46.8 barrer). Furthermore, the selectivity for CO₂/CH₄ increased from 9.0 to 19.¹⁶ A. S. Aquino et al.¹⁷ studied methyl-3-(3-trimethoxysylilpropyl) imidazolium chloride [MTMSP-Im][Cl] supported on mesoporous material (MCM-41) and found that at 25 °C and 1 bar, the CO₂ absorption capacity of IL supported on MCM-41 was 57% higher than that of the bare MCM-41 with merely 0.62 mmol CO₂ per g sorbent. Wang et al.¹⁸ synthesized 1-n-butyl-3-methylimidazolium chloride [BMIM][Cl] decorated Santa Barbara Amorphous-15 (SBA-15) and observed that under similar conditions, the CO₂ adsorption of SBS-15-IL was 63% higher than that of the neat SBA-15. Using the same method, Vishwanath Hiremath et al.¹⁹ studied four amino acid (AA) functionalized 1-methyl-3-ethyl-imidazolium [EMIM] based IL supported on ordered mesoporous silica (OMS-IL (AA)) and compared its CO₂ sorption capacity with bare silica (0.11 mmol g⁻¹). They observed that the CO₂ sorption capacity of OMS-IL (AA) was 63% higher than that of the neat silica. Bahadori et al.²⁰ prepared 1-(2-aminoethyl)-3-methyl imidazolium bromide [NH₂-EMIM][Br] grafted on MIL-101(Cr) and found that the CO₂ sorption capacity of the grafted sample was 7.84 times higher than the MOFs present at that time. Zhu et al.¹⁵ synthesized trioctapropyl phosphonium bis(triflimide) [P8883][Tf₂N] grafted silica and obtained the CO₂ capture performance increased from 0.07 mmol g⁻¹ to 0.99 mmol g⁻¹.

Preparing MMMs using the incorporation of IL modified filler in the polymeric matrix is another widely used method. Ilyas et al.²¹ conducted a study where they developed a mixed matrix membrane consisting of zeolite 4A filler supported by an IL called 3-(trimethoxysilyl)propan-1-aminium acetate [APTMS][AC] and polysulfone (PSF) polymer. Their research revealed that incorporating a filler content of 34 wt% in the membrane led to an enhanced separation performance. Specifically, the modified filler demonstrated an increase in the selectivity of CO₂/CH₄ by 37% and CO₂/N₂ by 43% as compared to the original unmodified filler in the MMMs. Li et al.²² synthesized 1-butyl-3-methylimidazolium bis(triflimide) [Bmim][Tf₂N] embedded in ZIF-8/Pebax-1657 based MMM and observed membrane performance at various loadings of [Bmim][Nf₂T]@ZIF-8. They reported the highest CO₂ permeability of 104.9 barrer at 15 wt% loading, which was 28% greater than that of the pure Pebax-1657 (72 barrer) and the selectivity was also increased from 18 to 34.5. To separate CO₂ from CH₄ and N₂, Ahmad et al.²³ employed 1-ethyl-3-methylimidazolium bis(triflimide) [EMIM][Tf₂N] supported on zeolite SAPO-34, which was subsequently integrated into PSF. Compared to the unmodified MMM, they observed a substantial improvement in the CO₂ separation ability of a composite containing SAPO-34 modified with the IL, with an approximately 486% rise in CO₂/CH₄ and a 232% increase in CO₂/N₂ selectivity. Nevertheless, the process of identifying an appropriate filler and polymer that complement one another, as well as an ionic liquid that can enhance the surface-to-surface compatibility and propagation of the filler within the polymer, will inevitably involve numerous attempts and mistakes. Additionally, membrane morphology and performance of the new generation hybrid materials are difficult to measure in situ, causing testing of membranes on an experimental scale to be potentially costly, labor-intensive, and time-consuming. For instance, Liu et al.²⁴ synthesized a MMM consisting of a fluorinated metal organic framework (NbOFFIVE-1-Ni) filler and 4,4′-(hexafluoroisopropylidene) diphthalic anhydride-2,4,6-trimethyl-1,3-diaminobenzene (6FDA-DAM) polymer. The composite membrane (NbOFFIVE-1-Ni/6FDA-DAM) exhibited diminished CO₂/CH₄ selectivity compared to the base 6FDA-DAM membrane, likely due to incompatibility between the polymer and filler materials.

Computational chemistry has grown as an effective tool that provides fast, atomistic-level elucidation of material properties in the creation and analysis of different materials. It offers modeling and simulation environment that can be used to anticipate and understand the connections between molecular structure of a material and its properties while circumventing the difficulty, cost, or time associated with lab-scale manufacturing.^25,26 Several computational studies have been conducted on polymers and MMMs. Velioğlu et al.²⁷ conducted a comprehensive investigation on the molecular simulation of gas transport on three distinct polyimides, namely 4,4-hexafluoroisopropyli-dene-diphthalic anhydride-2,4,6-trimethyl-m-phenylene diamine (6FDA-DAM), 4,4-hexafluoroisopropyli-dene-diphthalic anhydride-4,4-oxydianiline (6FDA-ODA), and 4,4-hexafluoroisopropyli-dene-diphthalic anhydride-2,5-dimethyl-p-phenylenediamine (6FDA-DPX). Their investigation involved the computation of diffusion and sorption coefficients of CO₂, CH₄, N₂, and O₂ gases within these polymers, employing simulation conditions of temperature and pressure set at 35 °C and 10 bar for CO₂ and CH₄, and 35 °C and 2 bar for N₂ and O₂. They were able to closely replicate the experimental findings. Karim et al.²⁸ conducted a simulation study on silica/PSF based mixed matrix membrane under pure gases condition, which included O₂, N₂, CO₂, and CH₄ and observed that for 20 wt% silica, the CO₂ permeability was 22.5 barrer, which was 470% higher compared to permeability of pristine PSF (3.95 barrer) and the simulated results were in close agreement with the experimental values. Khadija et al.²⁹ further conducted molecular simulation study on CO₂/CH₄ separation in silica/PSF based MMM. They varied silica filler loadings (15, 20, 25, and 30 wt%) to observe its effect on the gas transport properties of MMM and found that the permeability and selectivity were consistently increasing with incorporation of silica in PSF membrane until 25 wt%, which further decreased for 30 wt%. The same group later functionalized silica with amine and embedded it in PSF membrane and resulted optimum permeability (60 barrer) and selectivity (10.9) at 20% loading, which was higher than the unfunctionalized silica/PSF MMM.³⁰ Ban et al.³¹ conducted experimental and molecular dynamic study on [Bmim][Tf₂N]@ZIF-8/PSf MMMs and observed a significant enhancement in CO₂/CH₄ separation performance. They found that with incorporation of 6 vol% of ionic liquid decorated filler, the CO₂ permeability increased from 228 to 307 barrer at 303 K and 6 bar. The selectivity also increased from 23.1 ± 2.6 to 36.9 ± 1.7 and both the simulation and experimental results were consistent. Hence, it can be concluded that a suitable computational model accurately predicts the separation capability of existing membranes and can subsequently be employed for the next generation membranes that can be used in macroscopic process simulation.

In summary, based on review of the literature, the supported IL membranes (SILMs) have higher gas separation performance than pristine polymeric membranes and IL-MMMs have even higher levels than SILMs. Instead of countless, expensive laboratory experiments, molecular simulation offers a virtual replica of a system, unlocking its unexplored properties. This not only saves time and money but also reduces the handling of hazardous materials.

Therefore, the objective of this study is to establish a computational structure for MMM that exhibits enhanced dispersion, compatibility, and separation capabilities. To accomplish this, a MMM consisting of an IL-decorated filler and a polymer is formulated. Due to prominent characteristics of polyimides, i.e., outstanding thermal, chemical, and mechanical properties, as well as better CO₂/CH₄ separation capabilities,³² 6FDA-ODA polyimide has been employed as polymer in this study, while silica as a filler due to its prominent characteristics that can help to enhance the properties of gas transport (i.e., permeability and selectivity³³). Meanwhile, trioctapropyl phosphonium-bis(triflimide) [P8883][Tf₂N] has been selected as an ionic liquid to decorate the silica filler, in which [Tf₂N]⁻ is favorable for CO₂ adsorption.³⁴ Along with this, phosphonium based ionic liquids (PILs) are more thermally stable,³⁵ stable towards nucleophilic and basic conditions,³⁶ have lower densities than water, low viscosity, high productivity, and low manufacturing cost than the rest of the ILs.³⁷ The concept based on pre-modification technique is used to construct the MMM via molecular simulation approach through which first IL is supported on silica surface and then embedded into polymer matrix. Design via grafting method is used to support ionic liquid on silica surface as reported earlier,^10,15 in which ionic liquids are chemically supported, that not only maintains the porous structure and surface of the substrate, but also offers good affinity with CO₂. In the grafting method, the cations present are mainly responsible for chemically modified ILs based adsorbents.³⁸

To understand how varying gas concentration affects transport properties in a mixed gas system, the interaction between gas molecules and IL-silica/6FDA-ODA based MMM should be explored. Even though it has been demonstrated that for single gas (CO₂, CH₄, N₂, H₂, and O₂), IL-filler concentration boosts the membrane's solubility and diffusion coefficient relative to its pristine membrane,³⁹ investigation under the mixed gas environment at molecular level, which reflects actual natural gas sweetening process is still unresolved. Therefore, this study investigated the effect of immobilization of IL [P8883][Tf₂N] on silica surface with varying weight percentages (i.e., 5, 10, and 15) on the permeation characteristics of CH₄/CO₂ under single and a gas mixture of CO₂ and CH₄ (i.e., 70, 50, and 30 vol.%) at constant temperature (40 °C) and pressure (1 atm). Therefore, the distinctive characteristic of this investigation is to develop an innovative composite membrane and to elucidate the impact of diverse concentrations of CO₂/CH₄ on the transportation properties in IL-silica/6FDA-ODA founded MMMs at varying IL-silica loadings using molecular simulation.

2 Methodology

In this work, atomistic simulations were performed utilizing Materials Studio (MS). Interactions were represented by empirical models so as to develop the essential motion equations.⁴⁰ The configuration of the system is followed to record position of each atom.^41–43 This process generates the temporal trajectory of the system, which can be utilized to analyze membrane framework and behavioral properties through the application of computational mechanics techniques.^44,45 Khadija et al.,²⁹ Karim et al.,³⁹ and Ahn et al.⁴⁶ compared experimental and simulation data to authenticate the methodology employed in their investigation of gas movement behavior.

2.1 Force field

The term “force field” refers to a computational model used in molecular simulation to estimate the forces between and within molecules specifically in molecular mechanics or Monte Carlo simulations. The force field uses the functional form and parameter sets to determine the potential energy of a system of atoms.⁴⁷ To replicate a system precisely, a force field is utilized to generate a collection of model configurations that are strictly consistent with a fully quantum mechanical description.^48–51 The potential energy (ν) in the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) is represented by eqn (1).⁵²

All the terms in the equation, with the exception of the final two terms, can be classified as valence terms. These terms are dependent on the lengths of bonds (b), the angles between bonds (θ), the angles of torsion (θ′), or the out-of-plane angles (x) formed by pair of atoms i and j that are bonded together. The inclusion of these terms is crucial for accurately predicting vibrational frequencies and variations in the geometry of bonded molecules that are connected to conformational changes.⁵³ In contrast, the last two terms are nonbonded interaction terms. These terms rely on the distances (r_ij) between pairs of atoms that are separated by three or more bonds or that belong to different molecules. The coulombic contributions, which are dependent on the partial charges (q) on atoms, play a vital role in the interactions between polar groups.⁵⁴ For homoatomic pairs, LJ-9-6 parameters (ε₀, r⁰) are provided.

The present study employed the COMPASS II force field,^29,30 which has exhibited notable efficacy in simulating polymeric systems.^55,56 The COMPASS model has been comprehensively parameterized for various organic and inorganic compounds.⁵⁷

2.2 Molecular simulation on IL-silica/6FDA-ODA MMM

The first step for performing molecular simulation on MMM, was the construction of the polymer repeat unit. The 6FDA-ODA repeat unit, depicted in Fig. 1, was constructed utilizing the visualizer and collection module of MS following the method described by Velioglu et al.²⁷

Fig. 1 The single chain structure of 6FDA-ODA repeat unit.

The length of the polymer chain was set to 20 repeat units as reported by Chen et al.⁴⁸ Shorter chains are better for ensuring an efficient physical system since they increase the polymeric chain's mobility regardless of the size of the cell.^58,59 The methodology for the construction of spherical α-quartz silica with radius 6.1 Å is in accordance with the approach as reported by Karim,³⁹ while its ionic liquid modification mechanism is the same as described in the simulation by Khadija et al.³⁰ and experimentally by Zhu et al.,¹⁵ and is shown in Fig. 2.

Fig. 2 Procedure to support IL on silica surface.

The second step is construction of the hybrid membrane structure using the amorphous cell module of MS. Before embedding the polymer chain and ionic liquid modified silica, the structures were subjected to energy minimization and geometry optimization using COMPASS II along with smart minimizer approach that combines the conjugate gradient, steepest descent and, Newton methods to optimize the geometry and minimize the energy of the system.^60,61 An amorphous cell was generated with an initial density (g cm⁻³) of 0.987, which accounted for 70% of the recognized experimental density of 6FDA-ODA.^62–65 A 2000-steps energy minimization was then performed to optimize the geometry and reduce the energy of the first created atomic structure to remove any unwanted interactions, such as overlaps and close contacts. The incorporation of ionic liquid modified silica into 6FDA-ODA polymer is shown in Fig. 3 with the atomic representations as: red: oxygen, white: hydrogen, dark grey: carbon, blue: nitrogen, yellow: sulfur, vivid orange: silicon, pale cyan: fluorine, and pale magenta: phosphorus.

Fig. 3 Illustration of embedment of IL-silica into 6FDA-ODA polymer to form IL-silica/6FDA-ODA MMM amorphous cell.

The system was subsequently annealed utilizing the temperature cycle protocol implemented in the Forcite module. The system was subjected to temperature variations between 300.15 K and 553.15 K, which is considerably greater than the T_g value of the polymer,⁶² and then cooled back at steps of 293.15 K. The cell was then subjected to 100 picosecond (ps) NPT dynamics at each step. To achieve stable structures and to evaluate whether the membrane system has reached an equilibrated condition that resembles properties similar to the real configuration, a 500 ps NPT ensemble MD was performed. The NPT ensemble maintains a constant quantity of particles (N), pressure (P, 1 atm), and temperature (T, 298.15 K). NPT thermodynamic package changes cell volume according to material to provide a realistic density of the material. Using the COMPASS II force field, non-bonded responses, including coulombic and van der Waals attractions, were computed. The Ewald model was employed to compute coulombic interactions with accuracy of 0.0001 kcal mol⁻¹ while van der Waals interactions were considered using Lennard-Jones 9-6 function via atomic method. A Nose–Hoover thermostat and Bendersen barostat were used for controlling temperature and pressure, respectively, while maintaining the cutoff distance between 12.5 and 19 Å (less than half of the cell length) at a time step of 1 fs.²⁷ In order to ascertain the stability of each structure, eqn (2) was utilized to derive the binding energy (E_b).⁶⁶

E_b = −E_I = E_total − (E_polymer + E_IL-silica) (2)

where E_b is the binding energy, E_total is the overall energy for the hybrid membrane structure, E_polymer shows energy of the polymer (6FDA-ODA), and E_IL-silica is energy of the IL-silica.

A fundamental characteristic of a more stable system is that it possesses a higher negative adhesive energy.⁶⁷ When the binding energy is negative, this indicates that the composite's total energy is less than the combined energy values of its constituent parts. Therefore, achieving a complicated system with increased stability is enabled. On the contrary, a system's intrinsic instability is indicated by positive binding energy. In sum, the stability of a membrane system is directly proportional to the decrease in its binding energy.⁶⁸

2.3 Physical properties

The approach employed in this study to evaluate the physical parameters, such as the fractional free volume and X-ray diffraction pattern, and glass transition temperature (T_g), is covered in the sections 2.3.1, 2.3.2, and 2.3.3, respectively.

2.3.1 Fractional free volume (v_f). Free volume in a polymer is the volume of the total mass that is not occupied by the polymer chains themselves, which allows the movement of diffusing molecules.⁶⁹ It is commonly used to describe the spaces or pores between polymer strands. Connolly surface task, employing a probe radius of 0 nm, was utilized to determine the cell and van der Waals volumes.⁷⁰ Fractional free volume (v_f) is ratio of estimated specific free volume and the polymer specific volume and can be calculated from group-contribution method as depicted in eqn (3):⁷¹where v is polymer molar volume and v_o is molar occupied volume of the repeat unit of a polymer at 0 K and can be obtained from the van der Waals volume (v_vdv) as provided in eqn (4):⁷²

v_o = 1.3v_vdv (4)

2.3.2 X-ray diffraction (XRD) pattern. The FORCITE Scattering Analysis module of MS is utilized to estimate the material's crystallography.³⁰ The XRD data was obtained using X-ray radiation with wavelength of 1.542 Å and 2θ ranging from 10 to 50°. The angle of diffraction is used to determine the difference among the atomic planes and can be calculated by using Bragg's law:

nλ = 2d sin θ (5)

where n is number of beams, θ is angle of diffracted beam, λ is wavelength of the incident beam, and d is the distance between the plane atoms, which is used to determine the crystallinity of the material by generating diffraction patterns.³⁹ The cutoff value, and the range of interest of 2θ are defined to generate an XRD graph. The cut off number specifies how often a data point is recorded throughout the span of the analysis.²⁹

The diffracted intensity (I(Q)) of beam for the XRD of the simulated membranes can be obtained in the periodic boundary state and is connected to the radial distribution function via a Fourier transform operation,⁷³ as shown in eqn (6):

where f_i and f_j are structure factor, r is distance between i and j atom and Q is scattering angle magnitude and can be calculated as:

2.3.3 Glass transition temperature. The temperature at which an amorphous polymer material changes from a hard and somewhat brittle “glassy” state into a softer or rubbery state, which is similar to supercooled liquid, is known as the glass transition temperature (T_g).^39,74,75 T_g of each polymer with an amorphous structure varies, and this property helps to distinguish the temperature range at which a polymer is thought to remain stable and maintain its mechanical properties.⁷⁶ After performing all the simulations, the final structure was cooled from 723 K to 473 K with steps of 293 K and the specific volume at different temperatures was recorded and plotted against temperature. The temperature at which an abrupt change in slope of a specific volume is observed is considered as glass transition temperature (T_g) of the material. This similar procedure was applied to all structures to find their T_g.

2.4 Simulation of transport properties for gas

The elaboration on methodologies used to compute the gas transport properties, which include solubility, diffusivity, permeability, and selectivity, are covered in sections 2.4.1, 2.4.2, and 2.4.3.

2.4.1 Solubility. Grand Canonical Monte Carlo method (GCMC) was used to calculate solubility of a gas in a membrane. For this, amorphous cells were constructed embedding neat polymer chains or polymer with filler. For each molecule in the amorphous cell, the non-bonded energy was computed utilizing the COMPASS II force field. Using the same force field, both coulombic and van der Waals forces were employed to simulate the sorption process.⁷⁷ The probability of determining the concentration of the permeable gas was computed utilizing the energy difference (E) of the before and after the configurations in the GCMC method.⁷⁸ A widely recognized Metropolis algorithm is employed to decide whether a gas molecule's movements should be accepted or rejected. The translational movement's acceptance probability for construction and destruction (P_acc) was computed by displacing gas molecules randomly in all x, y, and z directions, as per eqn (8):⁷⁸where ΔE is the sum of non-bonded potential terms, V is the volume of membrane cell, k is the Boltzmann's constant, f_i is the fugacity, and N_i is number of i components in the membrane.

The solubility for an equilibrated gas-polymer system is ratio of the concentration (C, measured in cm³ (STP) per cm³ polymer) to the pressure (P_i) (or partial pressure for mixed gas system) of the gas i. Hence the solubility (S_i) of gas in a membrane can be calculated as follows:⁷⁹

2.4.2 Diffusivity. The diffusivity, which determines with what rate the gas molecules can move within the polymer is another important parameter of the gas transport properties. In order to determine the diffusivity of individual gases through the final membrane constructions of pure 6FDA-ODA and IL-silica/6FDA-ODA nanocomposites, ten molecules of CO₂ and CH₄ were introduced. Geometry optimization and energy minimization stages were conducted prior to the embedding process. In order to attain equilibrated density, the most effective amorphous cell of every membrane, in conjunction with the penetrant gases, underwent relaxation process for 500 picoseconds NPT ensemble MD at constant temperature of 308.15 K and pressure 1 atm. Following this, we conducted an NPT ensemble MD simulation for a duration of 5000 ps using simulated membrane structures of a satisfactory density. As a result, the precise trajectory of the gas molecules within each cell could be detected. The Forcite mean square displacement (MSD) analysis module was utilized to record the trajectories at 5000 ps. The slope of the plot (MSD vs. time) was used to determine the diffusivity coefficients of the selected gas molecules. The diffusion coefficient at normal regime was calculated when the slope of the plot logarithmic MSD vs. time approached to unity and were calculated using the Einstein relation,³⁹ as shown in eqn (10):where D_i is diffusion coefficient of atom i, N is the quantity of diffusing components, and |r_i(t) − r_i(o)|² is average mean square displacement of atom i and r_i(t) and r_i(o) are position vectors, representing final and initial positions of atom i. The anomalous diffusion for different regimes is distinguished by using power-law.^80,81

Δt ∝ D_it^N (11)

Different diffusion regimes are distinguished based on the value of the exponent n: n = 1, a normal diffusion region, and anomalous regime for n ≠ 1.

2.4.3 Permeability & selectivity. Transport of gases in the polymeric membranes is based on ‘solution–diffusion’ concept and the model were formulated in the 19th century by Graham and later by Mitchell.⁸² The permeability is the product of solubility (S) and diffusivity (D), for i component can be calculated using eqn (12):^83,84

P_i = S_i × D_i (12)

The selectivity of gas separation membranes is another significant property which can be defined as the ability of a membrane to separate a gas from a gas mixture. According to this definition, the ideal selectivity is the ratio of the permeabilities of the gases^85,86 and can be calculated as follows:

α_ij = P_i/P_j (13)

where P_i and P_j are the permeabilities of two gases (i and j) evaluated under similar conditions.

3 Results and discussions

3.1 Physical characteristics

3.1.1 Equilibrated amorphous cells. The amorphous cells for neat and incorporated ionic liquid modified silica in 6FDA-ODA co-polymer are illustrated in Fig. 4.

Fig. 4 Equilibrated amorphous cell for (a) neat 6DA-ODA, (b) 5 wt% IL-silica/6FDA-ODA MMM, (c) 10 wt% IL-silica/6FDA-ODA MMM, (d) 15 wt% IL-silica/6FDA-ODA MMM.

In order to authenticate the amorphous cells, the equilibrium density and potential and non-bonded energies status of the true membrane structures were applied. From Fig. 5(a) and (b), it was observed that after performing 500 ps NPT molecular dynamics, the system has acquired equilibrium. It was evident that the time-dependent curves of density and energy were approximately stable with fluctuations of <10% typically after 400 ps, suggesting that equilibrated structures had been achieved. The energy was minimized too during the molecular dynamic simulation process, suggesting evolution towards stable and equilibrated structures. The same judging methodology had been employed in previous published literature when evaluating the equilibrium time for their respective molecular dynamics simulation.^87,88 Additionally, the equilibrated density for neat 6FDA-ODA was 1.39 g cm⁻³, which was in close agreement with experimental density (1.40 g cm⁻³), yielding error of only 0.7%.⁸⁹ For 5 wt% of filler in simulated cell, the density decreased because of increased free volume. Conversely, the densities rose as the weight percentages of modified filler in simulated structures increased. The aforementioned effect was noted due to the filler's (silica) greater density (2.2 g cm⁻³) in comparison to the 6FDA-ODA polymer. The minimal fluctuations in negative values of potential and non-bonded energy for an equilibrated system confirmed that the system is thermally stable and has attained equilibrium as shown in Fig. 5(b). The potential and non-bonded energies of a membrane with 5 wt% IL-silica are lower than that of the pristine polymeric membrane which shows that the prior is more stable.

Fig. 5 Molecular dynamic simulation of (a) equilibrated density for all the structures; (b) potential and non-bonded energies for pristine polymeric membrane and 5 wt% IL-silica MMM.

To further affirm stability of the system, the binding energy of the MMM with different wt% of IL-silica is calculated using eqn (2). As shown in Table 1, the binding energies of neat 6FDA-ODA and IL-silica were −459.26 and −963.48 kcal mol⁻¹, respectively. When 5 wt% IL-silica is added to 6FDA-ODA polymer, its binding energy was reduced to −9466.26 kcal mol⁻¹. It was noted that a relatively more stable membrane system was achieved as MMM with 5 wt% IL-silica possessed 95% lower binding energy than the neat polymeric membrane. The octyl sidechain of the trioctapropyl phosphonium cation, which is chemically supported on the silica surface, is most likely oriented in a direction that is away from the silica surface. This nonpolar segment of the ionic liquid interacts with the nonpolar 6FDA-ODA polymer. Consequently, enhanced attraction between polymer and filler was achieved and hence stabilized the membrane system. For higher wt% of IL-silica the flexibility of the polymer increases consequently reduces the structure stability.

Table 1 Binding energy of membrane systems consisting of different filler loadings

Membrane	Model system	Total energy (kcal mol^−1)	Binding energy (kcal mol^−1)
Neat 6FDA-ODA		−459.26	—
IL-silica		−963.48	—
5 wt% IL-silica		−10889.83	−9466.26
10 wt% IL-silica		−2792.48	−1369.74
15 wt% IL-silica		−2100.47	−677.73

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3.1.2 Glass transition temperature (T_g). After having the optimized structure, it was cooled from 450 °C to 100 °C with steps of 20 °C and the specific volume at different temperatures was recorded. For 6FDA-ODA membrane and 5 wt% IL-silica/6FDA-ODA MMM, Fig. 6 illustrates the variations in specific volume with respect to temperature.

Fig. 6 T_g of neat 6FDA-ODA and 5 wt% IL-silica/6FDA-ODA MMM.

After a linear increase in specific volume, an abrupt change was observed between 250 °C and 300 °C. The temperature at which an abrupt change in specific volume was observed is considered as the glass transition temperature (T_g) of 6FDA-ODA and its IL-silica MMM. The obtained T_g results for neat 6FDA-ODA from simulation (298 °C) were in close consistency with the experimental values (303 °C) with 1.7% error. The simulated values of T_g for neat 6FDA-ODA and IL-silica/6FDA-ODA based MMM, calculated in similar way, are shown in Table 2.

Table 2 Physical properties of 6FDA-ODA based membrane with varying weight percentages of IL-silica^a

Membrane	Tg (°C)	Density (g cm^−3)	Fractional free volume	d-Spacing
a Experimental values are shown in brackets.^89,90
0	298 (303)	1.39 (1.40)	0.34 (0.32)	5.57 (5.6)
5	305	1.21	0.41	5.87
10	301	1.41	0.315	6.11
15	300	1.43	0.30	6.25

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The T_g for neat 6FDA-ODA and 5 wt% IL-silica are 298 °C and 305 °C, respectively. An increase in the glass transition temperature (T_g) for 5 wt% IL-silica supports the stability of the composite due to flat ring structure and polar CF₃ groups along the surface of 6FDA-ODA that allows IL-silica to be in close contact with it, which results in relatively stronger van der Waals interactions between polymer and filer. The recent studies on polymer–filler interactions called the surface polarity of filler and polymer as a key driving force to change interfacial interactions.⁹¹ The glass transition temperature (T_g) of the IL-silica/6FDA-ODA based MMM increased slightly in comparison to the pristine polymeric membrane. This can also be related to the introduction of the filler, which leads to an increment in rigidity. However, the T_g further decreases with an increase in IL-filler content (10 and 15 wt%). This is because the IL not only enhanced the flexibility of the polymer matrices but also reduced the contact area between the two materials as can be seen in Fig. 4(d) (black circle).⁹² Consequently, the T_g for higher contents of IL-silica decreased.⁸¹ However, when compared to the pristine polymeric membrane, the 10 and 15 wt% IL-silica/6FDA-ODA based MMM exhibits a relatively higher T_g value. This behavior is supported by the decrease in binding energy as the weight fraction of IL-silica rose.

3.1.3 Fractional free volume (v_f) in IL-silica/6FDA-ODA MMMs. The transport mechanism of the permeable gas molecules in polymer membranes can be better understood with an understanding of the fractional free volume.⁹³ v_f for equilibrated IL-silica/6FDA-ODA MMM was averaged throughout the final five frames. The v_f values increased up to 40% (0.34 to 0.40) with incorporation of 5 wt% of IL-silica and then decreased in the following order: 10 wt%, 15 wt%, the similar effects on occupied and free volume are evident in the literature,^31,89 and is depicted in Fig. 7. The effective polymer packing creates gaps at the interface, which raises the free volume of the membrane structure that leads to improved gas transport.^94,95 The maximum free volume was recorded for incorporation of 5 wt% of IL-silica. For higher wt% (10 and 15) of IL-silica filler loadings, a notable reduction in free volume is observed because of the cavity occupation by ionic liquid. However, with not a considerable variation in the free volume values of IL-silica/6FDA-ODA MMMs are shown in Table 2.

Fig. 7 Fractional free volume (a) for neat 6FDA-ODA (b) 5 wt% IL-silica (c) 10 wt% IL-ilica (d) 15 wt% IL-silica.

For higher wt% of IL-silica (i.e., 10 and 15 wt%), it is postulated that there exists a boundary free from defects between the dispersed particles and the polymer interface.⁹⁶ The robust adhesion between the polymer and filler leads to a decrease in the available volume within the polymer,⁹⁷ a phenomenon commonly referred to as polymer rigidification. In the majority of instances, this rigidification enhances the selectivity of the system while concurrently diminishing its permeability.⁹⁸

3.1.4 X-ray diffraction analysis. The Forcite scattering module of the simulation software was used to find the XRD patterns of the neat 6FDA-ODA polymer and IL-silica filled 6FDA-ODA structures. Fig. 8 presents the XRD patterns of all simulated structures. 6FDA-ODA is an amorphous polymer since its structure lacks a regular arrangement. Several investigations indicate that the polymer chains of 6FDA-ODA are not tightly packed. This leads to the chains being challenging to organize in a consistent manner, resulting in the lack of a clearly defined, extensive arrangement in the structure.^62,99–102

Fig. 8 X-ray scattering patterns for 6FDA-ODA polymer with different weight percentages of IL-silica (experimental XRD data for neat 6FDA-ODA is extracted from the graph⁸⁹).

As the 2θ was varied from 10° to 50°, a sharp peak was generated for each membrane, indicating the crystalline region of the membrane. The main peak for neat 6FDA-ODA is at 2θ ≈ 15.9° which is well consistent with the published literature (15.5°) having a 2.6% error.¹⁰² The diffraction peak for IL-silica filled structure coincided with the neat structure with a negligible shift in main peak. It was evident that the ionic liquid has the capability to disrupt the ordered arrangement of molecules in 6FDA-ODA, resulting in a lower degree of crystallinity in the membrane matrix by demonstrating decreased intensity of the XRD peak.¹⁰³ The peak got broader with increment in the IL-silica content and became flattened for 15 wt% IL-silica. A similar trend was observed in the previous studies.^104–106 Introducing the filler with IL decorated on its surface into the membrane matrix may potentially increase the free volume with efficient disruption in the polymer chain. However, the ionic liquid to be located between the polymer chains causes lubrication effect between the filler and the polymer, which can effectively avoid the aggregation of filler. Under such condition, the increment in d-spacing is not apparent when the filler amount is not sufficient. However, at higher amount of IL-modified silica, the 2-theta is further shifted to the left and resulted bigger d-spacing values due to creation of more free volume.¹⁰⁷ The d-spacing values for the structures are calculated by using eqn (4) and are presented in Table 1.

3.2 Gas transport study

The majority of pressure-driven polymer membranes employ a solution–diffusion mechanism for gas transport, which are consisted of three stages: sorption, diffusion, and desorption. The gas molecules firstly adsorb on the polymer's upstream surface. Next, they diffuse through the membrane's pores, and lastly, they desorb on the membrane's downstream side.^108–110

3.2.1 Gas solubility CO₂/CH₄. This section elucidates the sorption characteristics of IL-silica/polyimide-based membranes with respect to gas molecules. The sorption module of the MS with utilizing the adsorption isotherm task has been performed to ascertain the solubility of gases within the membrane. The solubility results obtained for CO₂ in 6FDA-ODA (0.311 mmol g⁻¹) and silica supported [P883][Tf₂N] (0.74 mmol g⁻¹) are consistent with the experimental data (0.33 mmol g⁻¹ at 35 °C and 1 bar (ref. 102) and 0.8 mmol g⁻¹ at 40 °C and 1 atm,¹⁵ with 5.7% and 7.5% error, respectively). Fig. 9 plots the predicted solubility and sorption energy distribution values for IL-silica/6FDA-ODA MMM structures for CO₂ and CH₄ in mixed and pure gas conditions at 40 °C and 1 atm and shows that CO₂ is more soluble than CH₄, with solubility increasing in proportion to gas concentration within the membrane structure.

Fig. 9 For 50% CO₂ and 50% CH₄ in 5 wt% IL-silica/6FDA-ODA nanocomposite membrane (a) adsorption isotherm, (b) density distribution at interface, (c) sorption energy distribution, and (d) density distribution of binary gas mixture of CO₂ (red points) and CH₄ (green points) molecules; under different mixed gas concentrations and filler weight percentages (e) CO₂/CH₄ solubility, (f) CO₂/CH₄ solubility–selectivity.

Fig. 9(a) demonstrates that CO₂ is more soluble than CH₄. For all weight percentages of filler, the solubility results for pure gases were higher than the mixed gas conditions. This is because the pure gases have no competition for adsorption sites and uniform and well-defined interactions with the membranes over the mixed gases flowing through the membrane, shown in Fig. 9(e). Fig. 9(b) shows the largest density of CO₂ adsorbed onto interface between the silica surface and polymer chain. Fig. 9(d) shows two different absorption sites for CO₂ and CH₄ and is confirmed from different energy peaks for CO₂ (−6.8 kcal mol⁻¹) and CH₄ (−4.8 kcal mol⁻¹) shown in Fig. 9(c). The sorption capacity can go up if the energy distribution shows higher and wider peaks. This shows how the CO₂ and CH₄ sorbates interact with the membrane material.

The membrane with 5% weight percentage of filler showed the highest solubility for pure gas and mixed gas feed under 70% CO₂. This pattern is in line with earlier research on the mixed gas trend of CO₂/CH₄ because as the percentage of CO₂ in the membrane rises, it suppresses the route of CH₄ gas molecules.¹¹¹ Incorporation of ionic liquid modified silica into 6FDA-ODA polymer increased the solubility of CO₂. The interfacial adhesion between the polymer and filler was enhanced by ionic liquid modified silica, which also increased the number of polymer–filler pores and enhanced gas solubility. Thus, based on the results obtained in this work, it can be said that the solubility of CO₂ gas in the membrane is increased by adding the ionic liquid modified silica particles. However, the gas solubility decreased as the quantity of IL-silica nanoparticles increased beyond a certain point. For instance, for the 6FDA-ODA/5 wt% IL-silica MMM, the solubility of CO₂ is 50.23 cm³ (STP) per cm³ atm, but for the 6FDA-ODA/10 wt% IL-silica MMM, it is reduced to 35.85 cm³ (STP) per cm³ atm. This indicates that the solubility decreases with increasing IL-silica content as shown in Fig. 9(e). The decrease in solubility is because of the blockage effect of the ionic liquid, which may act as a potential barrier against the entry of gas molecules, reducing the number of molecules with sufficient energy to pass through and reach to the active sites of the membrane. This behavior was also supported by the fractional free volume which decreased as the weight percentage of IL-silica increased.¹¹² The solubility selectivity values of gases with different compositions in MMM with varying filler loadings, shown in Fig. 9(f), demonstrate that increase in filler loadings makes MMM more selective. The highest solubility–selectivity was obtained at 15 wt% IL-silica due to confined pore volume that makes MMM more selective, the same effect was also noted in earlier research.^28,113

3.2.2 Diffusivity of CO₂/CH₄. Fig. 10(a)–(c) provide a visual representation to demonstrate that the simulation was executed over a duration of 5000 picoseconds in order to establish the distinctiveness of the anomalous region from the Einstein diffusion region for a 5 wt% IL-silica under a 50% CO₂ gas concentration. Following this, the inclination of the Einstein normal diffusion regime was employed to ascertain the diffusivity. The diffusivity results obtained for mixed gas (50%/50% CO₂/CH₄) in 6FDA-ODA under similar conditions (at 35 °C, 10 atm, 2.28 × 10⁻⁸, 0.263 × 10⁻⁸ cm² s⁻¹) are replicable with the experimental data (2.1 × 10⁻⁸, 0.24 × 10⁻⁸ cm² s⁻¹) with 8.6 and 9% error, respectively.¹¹⁴

Fig. 10 (a) Mean square displacement (MSD), (b) logarithmic plot for determination of Einstein diffusion region, (c) normal region plot for evaluation of diffusivity coefficients, and (d) diffusion coefficients of CO₂/CH₄ in IL-silica/6FDA-ODA MMM with varying mixed gas concentrations and different filler weight percentage.

The membrane's pores are precisely sized in relation to the gas molecule's kinetic (sieving) diameter. Due to this, smaller gases can now diffuse far more quickly than molecules of bigger gases. In this case, the CO₂ has smaller kinetic diameter (3.3 Å) than CH₄ (3.8 Å) causing separation of CO₂/CH₄ gases.¹¹⁵ One could assume that CH₄ is unable to enter the tiny pores because CH₄ has substantially larger diameter. Even the more open pores, where CO₂ diffuses more freely, are practically impossible for the larger CH₄ molecule to pass through.¹¹⁵ As the fractions of IL-silica in the membranes increased to 5 wt%, there was an observed increase in the diffusion coefficients of the gases. This phenomenon can be attributed to the disruption of the polymer chains caused by IL-silica nanoparticles, resulting in the creation of voids in the configuration of the 6FDA-ODA.²⁸ For greater weight proportions of IL-silica, the diffusivity of penetrant gases exhibited a decline; however, the selectivity of diffusivity demonstrated an enhancement. This phenomenon can be attributed to the pore occupancy either by polymer chains or by ionic liquid, resulting in a diminished pathway for the transportation of gas molecules.³¹ The existence of filler nanoparticles within the polymer phase generally produces a physical barrier within the membrane, rendering the permeation of gas molecules challenging.¹¹⁶ It was observed that the diffusivity of CO₂ was higher than that of CH₄ in all the structures, this can be attributed to smaller kinetic diameter of CO₂ as compared to CH₄.¹¹⁷ The dissimilarity in size between the penetrants and their respective diffusing capacities resulted in the enhanced diffusivity of CO₂ gas molecules than CH₄ molecules.¹¹⁸ The presence of ionic liquid, possessing a higher affinity for CO₂ molecules in comparison to CH₄, can be an additional contributing factor to the notable augmentation in the diffusion of CO₂ gas molecules.^119–121 In general, the strong affinity between CO₂ molecules and the ionic liquid can lead to the formation of transient complexes or enhanced solvation states. These interactions can facilitate the movement of CO₂ through the membrane matrix by reducing the energy barrier for diffusion. Additionally, the higher affinity leads to a greater local concentration of CO₂ molecules, which forms augmented concentration gradient as a driving force for diffusion to occur within the membrane matrix. Overall, the enhancement of weight percentages of silica modified with ionic liquid across diverse gas concentrations led to an improvement in both diffusion and diffusion selectivity.

3.2.3 Permeability and permselectivity in IL-silica/6FDA-ODA based MMMs. The permeability and selectivity of the simulated structure was calculated using eqn (12) and (13) and the results are shown in Fig. 11. Fig. 11 presents the permeabilities of CO₂ and CH₄, as well as the permeability selectivity for ionic liquid decorated silica/6FDA-ODA MMMs. Additionally, it depicts the position of the gas permeability data of IL-silica/6FDA-ODA MMMs with reference to the Robeson upper bounds.^122–124

Fig. 11 Transport properties under different gas composition in a membrane with varying filler loadings (a) CO₂ gas permeability, (b) CH₄ gas permeability, (c) CO₂/CH₄ permeability–selectivity; (d) membrane performance as compared with Robeson upper bounds.

As can be seen from Fig. 11, CO₂ exhibits a higher level of permeability compared to CH₄ owing to its higher diffusivity due to smaller size and greater condensability, as signified by its critical temperature (T_c), for instance, T_c,CO2 = 304 K, T_c,CH4 = 191 K,¹²⁵ indicating CO₂ is more soluble than that of the CH₄. As mentioned in section 3.2.2, the increased condensability also further results in a higher local concentration of CO₂ molecules, thereby enhancing the concentration gradient that drives diffusion within the membrane matrix.¹²⁶ The permeability of gas molecules increased to 89% with an increasing 5 wt% filler as compared to pure polymer. A reduction in permeability was noticed for a higher weight percentage (10 and 15 wt%) of modified filler The subsequent factors may contribute to the observed reduction in permeability. (1) As previously mentioned, 6FDA-ODA exhibits a significant degree of gas permeability, particularly towards CO₂. Consequently, the incorporation of fillers with lesser permeability would result in reduced gas permeabilities throughout the MMMs. (2) The clustering of the alkyl chains of ionic liquid supported on silica surface with the 6FDA-ODA layer. (3) The inclusion of filler in the polymeric matrix causes a larger tortuosity, which disrupts gas diffusion and lengthens the pathlength through the MMMs.¹²⁷ (4) The mobility of penetrant gas molecules is hampered by polymer rigidification adjacent to the porous particles.¹²⁸ (5) The filler's pores may get smaller due to pore blockage by the polymer chains or alkyl chains of IL which may result a chocked gas flow.¹²⁹ (6) A completely blocked set of pores due to heavily adsorbed gas molecules results in a jammed sieve.¹³⁰

Based on the obtained results it can be said that utilizing smaller amounts of inorganic fillers is a better choice in gas separation in mixed matrix membranes (MMMs). Earlier studies have also experienced a similar effect.^29,30,39 Nonetheless, regardless of the noticed clustering, the permeability values of 10 wt% IL-silica for pure gas conditions still remained greater than those for the pure 6FDA-ODA polymer. Under identical conditions, the permeability values for pure gases are greater than that of the gases in mixed condition, depending on the solubility and diffusivity coefficients. The gas permeability in mixed gas decreased as the concentration of that gas decreased can be attributed to the occurrence of the completive gas transport within the membrane.

The CO₂/CH₄ selectivity was observed to be correlated with the membrane physical properties through inclusion of IL-silica, typically with respect to the effect of free volume and cavity size distribution.¹³¹ At higher loadings, reduced fractional free volume but increasing d-spacing was observed, implying the number of voids was reduced but created at bigger size due to agglomeration.^132,133 At 15 wt% IL-silica, void size effect was dominant at higher CO₂ concentrations, which contributed to an increment in the CO₂/CH₄ selectivity, as seen from Fig. 11(c). At higher concentrations of CO₂ (70% and 50%), the increase in the number of CO₂ molecules enhanced the interaction with the voids within the membrane, which facilitated the selective transport of CO₂ over CH₄. In contrast, the membrane's permeability towards CH₄ was decreased via competitive transport, resulting in enhanced selectivity ultimately.¹²⁶ On the other hand, for reduced CO₂ concentration at 30%, there was a reduced driving force for entrance of CO₂ within the limited number of microvoids, which further decreased its transport performance. Additionally, the ionic liquid at higher loading could potentially serve as a barrier due to its blocking effect,^134,135 effectively reducing the number of gas molecules with sufficient energy to penetrate and reach the active sites of the membrane that reduced gas permeability, typically at low concentration with reduced driving force. The decrease in CO₂ gas permeability will ultimately result in a decrease in gas perm-selectivity.¹³⁶

The highest permeability and selectivity were observed at 5 wt% and 15 wt%, respectively. It became evident that the addition of IL-silica nanoparticles to the membrane enhanced the characteristics of the membrane as well as the solubility of gases. This enhancement demonstrated that when combined with the 6FDA-ODA polymer, the IL decorated silica nanoparticles may be able to address the flaws in the inter-crystalline structure of the membrane surface. Furthermore, the presence of an ionic liquid improved the dispersion of the nanofillers on the membrane surface, improved polymer–filler compatibility and exhibited a strong affinity for CO₂ due to the prevalence of an anionic group of the ionic liquid. Due to the complex pathways that impose restrictions on the transportation of CH₄, the combined effects of the interaction between polymer and ionic liquid modified filler result in a selective transport mechanism that effectively limits the loss of CH₄.^137–140 Compared to the pristine polymeric membrane, the increase in permeability and selectivity for 15 wt% ionic liquid modified filler based MMMs was found to be 22% and 68%, respectively for pure gas condition. The gas permeability and selectivity of the pristine 6FDA-ODA polymer and the IL-silica MMMs were compared to the upper bounds set by Robeson.^30,141–143 Fig. 11(d) illustrates that the IL-silica/6FDA-ODA based MMMs exhibited significantly greater permeability and selectivity compared to the pristine 6FDA-ODA membrane and were found to be in closer proximity to the Robeson plot.

3.2.4 Comparison of optimized MMM with previously studied MMMs. A comparison was conducted to assess the performance of the IL-silica/6FDA-ODA based MMMs in the context of CO₂/CH₄ separation. This benchmarking exercise involved a review of relevant literature (i.e., IL@filler/polymer), the findings of which are presented in Table 3. For example, an MMM composite was created by incorporating 30 wt% of [APTMS][AC]@zeolite-4A into PSF. The MMM exhibited CO₂ permeability of 16 barrer and CO₂/CH₄ selectivity of 30.²⁹ The [BMIM][Tf₂N]/ZIF/Pebax mixed matrix membrane with 15 wt% IL-filler exhibited a CO₂ permeability of 104 barrer and a CO₂/CH₄ selectivity of 34. The [P8883][Tf₂N]-silica/6FDA-ODA with 5 wt% IL-silica demonstrated a 20-fold increase in CO₂ permeability (319 barrer) and a 1.85-fold decrease in CO₂/CH₄ selectivity (16.2) compared to the [BMIM][Tf₂N]/ZIF/Pebax MMM. There was no notable difference in CO₂/CH₄ selectivities between the two materials.²¹ The outcomes regarding the gas mixture of CO₂/CH₄ demonstrate that the presence of [P8883][Tf₂N] supported on silica enhances the permeability of CO₂ in the membrane. This enhancement can be attributed to the presence of [Tf₂N] ions,¹⁴⁴ which are CO₂ philic groups, as well as the longer alkyl chain on the cation, which slightly increases the solubility. Furthermore, the combination of these groups and the molecular sieving ability of the MMM leads to an improved permeability with a satisfactorily selective nature.

Table 3 Comparing CO₂ separation efficiency of IL@filler/polymer based MMMs

Membrane	Filler (wt%)	Operating conditions		PCO2 (barrer)	Selectivity (PCO2/PCH4)	References
		T (°C)	P (bar)
[Emim][Tf2N]@silica/PC	3	25	2	34.6 GPU	86.5	106
NH2@silica/PSF	20	35	1	62	11	30
[Emim][Tf2N]@SAPO-34/PSF	5	25	3.75	7.24 GPU	20.3	23
[APTMS][AC]@ZIF-67/PSF	30	25	10	20.12	67	145
[Bmim][Tf2N]@ZIF-8/Pebax1657	15	25	1	104	34.8	22
[APTMS][AC]@zeolite 4A/PSF	30	25	10	16	30	21
PAMAM@CTS/PSF	10	40	1	61 GPU	—	146
[BMIM][PF6]@ZIF-8/PEBAX	25	40	1	117	84.5	147
[P8883][Tf2N]@silica/6FDA-ODA	5	40	1	319	16.2	This work

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The permeability and selectivity of the [P8883][Tf₂N]-silica/6FDA-ODA based MMM in this investigation, particularly with 5 wt% IL-silica loading, surpasses all previously reported literature results, as shown in Table 3. The permeability and selectivity data presented here indicate enhanced CO₂ permeability and CO₂/CH₄ selectivity, showcasing the potential of integrating phosphonium-based IL-silica filler in polymers to create IL-silica/polymer MMMs. In general, the present study aimed to enhance the gas permeability of CO₂ and the selectivity of CO₂/CH₄ by utilizing a silica substrate decorated with an IL. This innovative design successfully addressed the common tradeoff problem encountered in gas separation membranes. The improved CO₂ permeability and selectivity have the potential to be applied in offshore separation processes with high levels of contaminants. This would lead to increased flux while minimizing the required membrane area in confined locations.

4 Conclusion

In conclusion, MMM consisting of a gas-selective silica modified with [P8883][Tf₂N] IL (IL-silica) filler, and 6FDA-ODA polymer, has been effectively designed and simulated. The NPT ensemble, energetic based cavity-sizing algorithm, grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation techniques using the COMPASS force field with 500 ps simulation time were performed to calculate the density and glass transition temperature, fractional free volume, diffusivity, and solubility respectively. The impact of IL-filler loading and feed gas concentration on the performance of the MMM has been examined. The results demonstrated that the incorporation of IL-silica led to a reduction in inter-crystallinity and free volume of the structure with improved T_g value, resulting in a more stable and selective gas separation process. The modification of the filler with IL has significantly enhanced the separation performance of membrane. By incorporating 5 wt% IL-silica, the IL-silica/6FDA-ODA MMM has demonstrated an approximate 80% improvement in permeability and a 56% improvement in selectivity. The observed enhancement can be ascribed to the improved interfacial compatibility between the polymer and filler at the interface, enhanced dispersion of the ionic liquid-modified filler within the polymer, and increased carbon dioxide attraction with the ionic liquid. Using molecular simulation, this study highlights the potential for supporting IL into silica via a straightforward grafting technique to construct MMM with acceptable separation performance. The results obtained from the model's validation indicated a satisfactory level of precision in predicting the permeability of CO₂ and CH₄. The mean percentage error, when compared to experimental results, was found to be less than 10%. This article describes the techniques to improve the filler and polymer's performance and emphasizes the benefits of using molecular simulation to ascertain the features of gas permeation in order to further evaluate the correlation's applicability. This approach offers the benefits of reduced error, time commitment, and cost-effectiveness, which can be valuable in material screening and the optimization of process conditions to enhance the separation performance of the membrane. Furthermore, this concept can be extended to optimize other factors that influence the physical properties and performance of IL-modified silica-based MMMs, such as IL selection, temperature, and pressure variations.

Author contributions

Mehtab Ali Darban: writing original manuscript, software, formal analysis. Serene Sow Mun Lock: supervision, formal analysis, writing – review & editing. Suhaib Umer Ilyas: visualization, investigation. Dun-Yen Kang: writing – review & editing. Mohd Hafiz Dzarfan Othman: writing – review & editing. Chung Loong Yiin: resources; writing – review & editing. Sharjeel Waqas: writing – review & editing. Zunara Bashir: writing – review & editing.

Conflicts of interest

The authors assert that they do not possess any recognized conflicting financial concerns or personal bonds that may have seemed to affect the research presented in this manuscript.

Acknowledgements

We want to acknowledge the financial support provided by the Ministry of Higher Education, Malaysia, under Fundamental Research Grant Scheme (FRGS) (Ref. No. FRGS/1/2022/TK09/UTP/03/3, Cost Centre: 015MA0-153), The Murata Science Foundation (Grant No. 23MP07, Cost Centre: 015ME0-351) and YUTP-Fundamental Research Grant (Cost Centre: 015LC0-498). Moreover, we would also like to acknowledge the technical support from the Institute of Sustainable Energy and Resources, Centre of Carbon Capture, Utilisation and Storage (CCCUS).

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