Separation of Carbon Dioxide from Natural Gas by Matrimid-Based Mixed Matrix Membranes

With respect to the expected growth in the demand for natural gas, it is necessary to upgrade low-quality natural gas by gas sweetening processes in order to  decrease CO₂ and H₂S content thereof (Hao, Rice, & Stern, 2002). In case of CO₂, it causes corrosion in presence of any moisture and increases the cost of gas transportation (Colin A. Scholes, Stevens, & Kentish, 2012). In addition, the separation of CO₂ from industrial stack gases, is vital from the environmental point of view(Bhide, Voskericyan, & Stern, 1998). Nowadays, MMMs are the subjects of many studies conducted in natural gas sweetening field because they combine the polymer advantages of processability, flexibility and availability with good separation property as well as the thermal/mechanical stability of inorganic fillers. Among many existing polymers studied in gas separations, the focus is on polyimides due to their high gas permeability, high intrinsic permselectivity, appropriate mechanical strength and chemical stability as compared with other conventional membranes (Sridhar, Veerapur, Patil, Gudasi, & Aminabhavi, 2007). Matrimid^® is a thermoplastic polyimide, widely applied as a commercial grade for gas separation processes (Tin et al., 2003). This polymer, is plasticized by CO₂ at pressures around 10 bar at room temperature leading to an increase in permeabilities of all separating gases, thus, deterioration of selectivity. When the CO₂ concentration is high enough to interact with polymer chains, it can increase the segmental mobility and the free volumes within the macromolecules (Bos, Pünt, Strathmann, & Wessling, 2001). Plasticization can be suppressed by cross‐linking, polymer blending and applying inorganic fillers in polymer matrix, that is, fabrication of MMMs (Dong, Li, & Chen, 2011; Gh & Navarchian, 2016; Hosseini, Peng, & Chung, 2010; Hosseini, Teoh, & Chung, 2008; Ismail & Lorna, 2002; Perez, Balkus Jr, Ferraris, & Musselman, 2014; Shahid & Nijmeijer, 2014b; Su et al., 1997; Xiao, Low, Hosseini, Chung, & Paul, 2009).

Various fillers like zeolites (Shahid & Nijmeijer, 2014a; Y. Zhang, Balkus Jr, Musselman, & Ferraris, 2008), silica (Ahn, Chung, Pinnau, & Guiver, 2008), alumina (Tena et al., 2010), clay (Bhole, Wanjale, Kharul, & Jog, 2007; Defontaine et al., 2010; Gh & Navarchian, 2016) and metal oxides (Hosseini, Li, Chung, & Liu, 2007) are applied in MMMs for gas separation. These fillers are appropriate candidates in overcoming the plasticization phenomenon and the permselectivity limitations of polymeric membranes for gas separation as presented by Robeson upper bound (Noble, 2011; Robeson, 2008). They may control the chain mobility by mutual interactions that prevent plasticization of polymer matrix at high feed pressures (Ismail & Lorna, 2002). The tortuosity of diffusion path increases by applying these fillers into the polymer matrix that improve the selectivity in the favor of smaller penetrant (Bertelle, Gupta, Roizard, Vallières, & Favre, 2006). This is due to the fact that the selectivity of polymers at temperatures below their glass transition temperature (T_g) is mainly dominated by diffusivity term (Yampolskii, Pinnau, & Freeman 2006). While the fillers, may disrupt the polymer chain packing which leads to an increase in polymer free volume and generate voids in the polymer matrix that improve permeability of gaseous penetrants (Gh & Navarchian, 2016; Hashemifard, Ismail, & Matsuura, 2011; He, Pinnau, & Morisato, 2002; Liang et al., 2012).

Several authors have assessed the effect of fillers on CO₂/CH₄ separation behavior of MMMs. Hashemifard et al. reported significant increase in permeability of CO₂ and CH₄ by applying montmorillonite clays with different types of interlayer cations to the polyetherimide matrix (Hashemifard et al., 2011). Applying montmorillonite in polyethersulfone is reported by Liang et al (2012) to increase permeability values of both CO₂ and CH₄ gases. They attributed this improvement mainly to extra gas transport paths produced on the polymer-clay interface (Liang et al., 2012). Montmorillonite modified by PAni was incorporated into Matrimid matrix, where, an enhanced permeability of CO₂ and CH₄ is observed as the small voids production in the polymer/clay interfaces (Gh & Navarchian, 2016). The plasticization pressure is postponed to higher pressures when PC particles are applied.

Gas permeability in dense membrane is subject to solution-diffusion mechanism(Baker, 2004). Although, the selectivity of glassy polymers at temperatures below T_g is influenced mainly by the fillers with high aspect ratio like montmorillonite, that increase the diffusion path (Yampolskii et al., 2006), it is suggested that applying fillers with special functional groups, like magnesium oxide (MgO) nanoparticles with hydroxyl groups on the surface, can interact with polar gases including CO₂ which would improve its solubility and gas permeability (Cong, Radosz, Towler, & Shen, 2007; Hosseini et al., 2007; Hu et al., 1997; Pacchioni, 1993). The polymer-particle interactions may reduce the chain mobility that results in less plasticization. It can be assumed, that applying these two kinds of fillers may enhance the permselectivity and plasticization behavior of dense membranes.

To the best of authors’ knowledge, here, there exist no report suggesting simultaneous application of both modified silicate layer and MgO nanoparticles in the Matrimid matrix. In this study, two fillers with different geometry and chemical properties including flake-like PC and spherical MgO nanoparticles are applied in order to improve both permeability and selectivity of MMMs and their plasticization resistance in the CO₂/CH₄ separation process. Chemical structure, morphology and thermal properties of fabricated membranes are analyzed through FTIR-ATR, XRD, FESEM, DSC and TGA. The gas permeation tests are run at different pressures to evaluate permselectivity and plasticization behavior of MMMs. The effects of MgO and PC contents on the permselectivity and plasticization resistance of Matrimid membranes are assessed as well.

2. Methods and Materials

2.1. Materials

Matrimid^®5218 (Hunstman LLC Corporation, Canada, CAS number 62928-02-6) and MgO nanoparticles (average size 1-5 nm, US NANO company, USA), are consumed preparation of MMMs. The TEM image of MgO nanoparticles is shown in Fig. (1-a). PC nanocomposite (Table 1) is consumed as synthesized by in-situ polymerization of aniline in the presence of Cloisite 30B^®(Gh & Navarchian, 2016). The solvent, NMP is purchased from Merck Company (Germany). The purchased chemicals are consumed upon receive.

Table 1. Characteristics of PAni/clay (PC) powder used in this study(Gh & Navarchian, 2016)

Figure 1. (a) TEM image of MgO nanoparticles prepared by the manufacturer, and (b) SEM image of PC powder (Gh & Navarchian, 2016).

2.2. Membrane Fabrication

Matrimid-based membranes containing different contents of MgO (0-10 wt%) and PC (0-10 wt%) fillers are fabricated through solution casting method (Hashemifard et al., 2011; Hosseini et al., 2007). The required volumes of Matrimid and MgO are dissolved in NMP by magnetic stirring and ultrasonication in a separate manner, next, the specified mass of PC is dispersed in NMP, stirred, ultrasonicated and then mixed with Matrimid/NMP and MgO/NMP solutions, followed by further stirring, ultrasonication and filtration. The filtrate is casted in 8 cm-diameter Petri dishes and then dried completely in the oven at 120˚C for sufficient time. Finally, the films are pilled from the glass and are dried at 200˚C for 2-3 days to obtain membranes with the thickness of 60-70 microns. Fabricated samples are coded as PCxMy, where, M is the MgO, and x and y are the PC and MgO weight percents, respectively, (e.g. PC5M5 membrane contains 5 wt% of each fillers).

2.3 Membrane Characterization

There exist many techniques for characterization of fabricated MMMs

2.3.1 Fourier Transform Infrared

The chemical structure of fabricated membranes is analyzed through FTIR-ATR spectrophotometer (JASCO FT/IR-6300, Japan) equipped with attenuated total reflection (ATR) accessory at room temperature from 4000 to 400 cm⁻¹ with a spectral resolution of 4 cm⁻¹ and averaged over 32 scans.

2.3.2 X-Ray Diffraction

The microstructures of membranes are analyzed through XRD technique where a Bruker diffractometer (D8 ADVANCE, Germany) at the scan range of 5^˚-80^˚ is applied.

2.3.3 Thermal Analysis

A simultaneous TGA/DSC system (STA 449F3 Jupiter, Netzsch, Germany) with a silicon carbide furnace is applied to assess the thermal properties of fabricated membranes. The samples of 5-10 mg weight are heated from 60 to 540°C at 10°C/min rate in the N₂ atmosphere. The Netzsch Proteus Thermal Analysis software is applied for DSC and TGA data analysis.

2.3.4 Field Emission Scanning Electron Microscopy

FESEM (ZEISS SUPRA 35VP, Germany) is applied in analyzing the MMMs morphology. The samples are frozen and fractured in liquid nitrogen in order to monitor the membrane cross-section. The fractured samples are mounted on carbon tape masked on stainless steel stand and sputter-coated with 15 nm of gold prior to FESEM analysis.

2.4 Gas Permeability Tests

Gas permeability of all fabricated membranes are measured through a variable-pressure constant-volume apparatus (Model NM1390, Iran) by the following equation (Chung, Chan, Wang, Lu, & He, 2003):

where P_A is the permeability coefficient of the membrane to gas A in Barrer (1 Barrer= 10^-10 cm³(STP).cm/cm².s.cmHg), V is the volume of the downstream chamber (12 cm³ ± 0.002 cm³), A is the effective area of the film (17.1 cm² ± 0.0014 cm²), L is the thickness of the membrane (0.007 cm  ± 0.0001 cm), T is the absolute temperature in measurement (298.15 K ± 0.1K), and dp/dt is the pressure rate measured at downstream chamber (mbar/s) which is calculated in of 3θ to 7θ time range (θ  is the time lag in downstream pressure-time diagram)(Y. Zhang et al., 2008). The uncertainty pressure (p or p₀) and time (t) measurements is ±0.1 mbar and ±0.1 sec, respectively. The relative uncertainty of permeability of gas A (P_A) is less than 1.6% based on Taylor equation (Taylor, 1997).

The ideal selectivity (α) of a membrane for gas A to gas B is assessed through the following equation:

(2)

where D (cm²/sec) and S (cm³(STP)/cm³(polymer).atm) are diffusivity and solubility of penetrants in the membrane matrix. Symbols α_D and α_S are the diffusivity-based and solubility-based selectivity values, respectively. The permeability tests are run at 4-10 bar and 25°C for all samples. The samples are examined at 4-30 bar pressure range to determine p_plast of MMMs and the effect of pressure on permeability and selectivity. The diffusion coefficient is obtained from the t-intercept, θ, of the plot p against t, as suggested by Barrer (Crank, 1975; Taveira, Mendes, & Costa, 2003):

The gas fluxes A (J_A)(cm³(STP)/cm².sec) through the membranes are calculated through the following equation (Baker, 2004):

where, Δp_A is the pressure difference across the membrane.

3. Results and Discussion

3.1. Chemical Structure

Chemical structure of pristine Matrimid, PC0M5 and PC5M5 membranes, the PC powder and MgO nanoparticles are illustrated in Fig. (2). As observed in Fig. (2-c), the peaks at 1778 cm^-1 (C=O stretching of ketonic groups), 1716 cm^-1 (C=O anti-symmetric stretching of imide groups), 1669 cm^-1 (C=O stretching of imide groups), 1425 cm^-1 (bending vibrations of aliphatic C–H bonds), and 3484 cm^-1 (N-H bonds) constitute the characteristic peaks of Matrimid (Dong et al., 2011; Gh & Navarchian, 2016; Moghadam, Omidkhah, Vasheghani-Farahani, Pedram, & Dorosti, 2011; Pavia, Lampman, Kriz, & Vyvyan, 2015 ; Zhao et al., 2008). In the FTIR spectra of Matrimid-MgO and Matrimid-MgO-PC membranes and MgO nanoparticles, (Fig. (2-c_), the peak at 487-490 cm^-1 is attributed to the symmetric Mg=O bond (Figs 2 (b, d and e)). The FTIR spectrum of Matrimid-PC-MgO membrane is shown in (Fig. (2-c)). The peak at 1509 cm^-1 (stretching bonds of benzenoniod rings) (Kang, Neoh, Tan, Khor, & Tan, 1990; Tang, Jing, Wang, & Wang, 1988) and the peak at 1377 cm^-1 (weak stretching of C-N bond in quinonoid-benzenoniod-quinonoid (QBQ) successive units) (Cao, Li, Xue, & Guo, 1986) are the characteristic transmittance of emeraldine base PC powder which are also visible in FTIR spectrum of PC powder (Fig. (2-a)) (Gh & Navarchian, 2016). The peaks of clay 30B at 400-600 cm^-1 (ascribed to Si-O bending and Al-O stretching), and 1035 cm^-1 (attributed to Si–O stretching) are observed in FTIR spectra of PC powder (Fig. (2-a)) and Matrimid-PC-MgO membrane (Kataria, 2005). Some shifts in  Matrimid appearance peaks (the peak at 1294 cm^-1 for bending of C–CO–C groups) and PC  (the C-H stretching at 1302 cm^-1 and stretching bonds of quinonoid rings at 1587 cm^-1) may indicate the possible compatibility of these two polymers because of hydrogen bonding between carbonyl groups of Matrimid and N-H group in secondary amine functional groups of PAni (Jiang, Wang, Chung, Qiao, & Lai, 2009).

Figure 2. FTIR spectra of (a) PC powder, (b) MgO nanoparticles, (c) Matrimid membrane, (d) PC0M5 and (e) PC5M5.

3.2 Microstructure

The X-ray spectra of Matrimid membrane and corresponding MMMs are shown in Fig. (3). A broad peak observed at 2θ about 20°indicates the amorphous nature of Matrimid (Ebadi Amooghin, Omidkhah, & Kargari, 2015; Hosseini et al., 2007; Sridhar et al., 2007). Presence of this peak is often interpreted as a measure of the average intersegmental distance between the polymer chains (Aziz & Ismail, 2010; Ghosal & Freeman, 1994). Appearance of the same peak with the same broadness and strength in the XRD spectra of MMMs reveals that the incorporation of the neither of fillers in general alter the microstructure of the Matrimid matrix. As observed in Fig. (3), there exists no sharp peak representing the peaks of MgO nanoparticles. As decleared by Hosseini et al. (Hosseini et al., 2007), this is attributed to the low concentration of MgO in membrane matrix.

3.3 Thermal Properties

The DSC/TGA graphs of Matrimid-PC (sample PC5M0) and Matrimid-PC-MgO (sample PC5M5) membranes are shown in Fig. (4), where all endothermic peaks shown in DSC curves of the samples below 150°C are attributed to the evaporation of trace amount of volatile compounds including water, HCl, NH₄OH, etc. with a weight loss less than 1% as seen in TGA curves (Gh & Navarchian, 2016; Narayanan et al., 2010). For both membranes, the weight loss from 150°C to 200°C (1-2%) is mainly due to the evaporation of NMP (boiling point: 202 to 204°C (Rajiv Mahajan, Burns, Schaeffer, & Koros, 2002)). The extra weight loss of about 8% at 200-455°C (for sample PC5M0) and 200-473°C (for sample PC5M5) ranges with an endothermic peak at 280-290°C is probably attributed to the loss of organic cation of 30B clay, evaporation and/or decomposition of low molecular weight polyaniline oligomers of the PC particles (Anadão, Sato, Wiebeck, & Valenzuela-Díaz, 2010; Ansari, Yadav, Cho, & Mohammad, 2013). An exothermic peak at 495-496°C is attributed to the thermal decomposition of PC and Matrimid observed in both samples. The onset of thermal decomposition of PC5M0 and PC5M5 are 455°C and 473°C which is higher than that of neat Matrimid (410°C), reported by (Perez et al., 2014). This represents an enhanced thermal stability of the membranes by incorporating PC (Anadão et al., 2010; Shi & Gan, 2007) and MgO (Moaddeb & Koros, 1997). The dispersed clay platelets probably act as barriers caused by labyrinth effect (tortuous path) (Lu, Hu, Li, Chen, & Fan, 2006) for both heat and mass transfer (Anadão et al., 2010). As for MgO, it is assumed that high stiffness MgO nanoparticles may hinder long-range mobility of polymer chains which increase thermal stability of the polymer (Moaddeb & Koros, 1997). This phenomenon can be verified by analyzing the glass transition temperature (Tg) of the samples. As observed in Fig 4, the Tg of PC5M0 is about 310°C, corresponding to that of the Matrimid Tg. The Tg of PC5M5 is enhanced at 335°C where the stiffness of the polymer is enhanced by applying MgO nanoparticles.

Figure 3. XRD patterns of pristine Matrimid, PC0M5, PC5M0 and PC5M5 membranes, in the range of 5º-80°.

Figure 4. TGA (solid lines) and DSC (dashed lines) thermographs of samples PC5M0 (a) and PC5M5 (b).

3.4 Morphology

The FESEM images of MMMs are shown in Fig. (5), where in sections 5 )a, b and c(, there is no significant accumulation of MgO or PC particles on the membrane surface. This is due to the appropriate of concentration (and, viscosity) and temperature of casting solution rates (Aroon, Ismail, Matsuura, & Montazer-Rahmati, 2010; R. Mahajan, 2000).

As observed in Figs 5 (d, e and f), the cross-sections of MMMs have a crater-type morphology (Ge, Zhou, Rudolph , & Zhu, 2013; Gh & Navarchian, 2016; Shahid & Nijmeijer, 2014b). The creation of elongated matrix around the crater edges is probably because of the interfacial stress concentrations between polymer and fillers (Y. Zhang et al., 2008). Several authors suggest similar morphology for different kinds of nanosized fillers like metal-organic frameworks (MOFs) (Dorosti, Omidkhah, & Abedini, 2014; Ge et al., 2013; Shahid & Nijmeijer, 2014a, 2014b) and ordered mesoporous silica spheres (Khan, Klaysom, Gahlaut, Khan, & Vankelecom, 2013) in various polymer matrices including polyimides. A different morphology is observed, for MMMs containing a micron-size MOF (Ploegmakers, Japip, & Nijmeijer, 2013), Probably indicating that the filler size plays a more important  than the chemical/physical nature of components in formation of this morphology.

Here, the presence of particles smaller than 0.1 µ in the center of the craters is probably due to some minor aggregation of MgO particles not present in PC5M0. As to similar particle size in these two membranes, it is assumed that addition of both 5 wt% PC and 5 wt% MgO do not lead to particles’ interference, thus, more agglomeration. This is most probably because of difference in the nature of chemical and physical properties of the two fillers. It is assumed that PAni acts as a sizing agent on clay minerals and prohibits their interaction with MgO nanoparticles (Aroon et al., 2010). This can assist the successful incorporation of the fillers at relatively high concentrations in improving the Matrimid gas separation properties.

A few pores are observed in the membranes cross sections. Because these pores are not observed in the FESEM images of the membrane surfaces (Figs (5-a, b and c)), it is assumed that they are not formed along the gas permeation direction and do not make short-cut paths for gas molecules, thus, keeping sufficient gas selectivity for the membrane. The unconnected-pores in the cross section of the membranes are mainly the result of the residual stresses imposed during solvent evaporation and depend on volume of solvent left to be removed when the nascent polymer matrix is vitrified (Moore & Koros, 2005)

Figure 5. FESEM images of PC5M0 (a and d), PC0M5 (b and e) and PC5M5 (c and f). The left and right photos indicate the membranes surface and cross-section, respectively. Magnifications of all images are 20 kX. (The arrows illustrate MgO agglomerates)

3.5 Permeability and Selectivity of Membranes

3.5.1 Matrimid-MgO Membranes

The images of permeability and selectivity of Matrimid-based membranes containing 0-10 % (wt.) MgO are illustrated in Figs 6 (a, b and c). Permeabilities of CO₂ and CH₄ in pristine Matrimid membrane at 4 bar feed pressure are 7.8 and 0.26 Barrer, respectively, and both increase to about 14 and 0.5 Barrer, respectively, together with increasing MgO concentration to 10%. This phenomenon can probably be attributed to the fact that MgO nanoparticles interaction with Matrimid macromolecules, leading to chain packing within the polymer chains, an increase in their free volume and enhance gas permeabilities (Matteucci, Kusuma, Kelman, & Freeman, 2008). The fact that the CO₂/CH₄ selectivity is kept high at 28-38 range for various MgO contents and different pressures is expressed in Fig. (6-b). Smaller dynamic molecular diameter and higher condensability of CO₂ molecules in comparison with those of CH₄ lead to higher diffusion and solubility coefficients of this gas, ending in relatively high CO₂/CH₄ selectivity values (Chung et al., 2003; Colin A Scholes, Tao, Stevens, & Kentish, 2010). As observed in Fig (6-c), the CO₂/CH₄ selectivity is enhanced gradually by applying up to 5 % MgO and then a slight fall. This can be explained by two contradicting effects of MgO nanoparticles on CO₂/CH₄ selectivity. MgO has basic property and may have specific interactions with acidic CO₂ leading to an increase in CO₂/CH₄selectivity at a specified MgO content (Mekhemer, Halawy, Mohamed, & Zaki, 2004). At higher MgO contents, excess free volume and generated voids together with possible agglomeration of particles, deteriorate the CO₂/CH₄ selectivity (Perez et al., 2014). The sample with 5% MgO (sample PC0M5) is of the best performance among the examined samples, because the CO₂ permeability increases up to 35-40% and CO₂/CH₄ selectivity enhances by 3±0.3 units as compared with that of Matrimid membrane at the test pressures of 4-10 bar, Figs 6(a, b and c).

Figure 6. Effect of MgO content on (a) permeability of CO₂, (b) permeability of CH₄ and (c) selectivity of CO₂/CH₄ for Matrimid-based membranes at 4-10 bar and 298 K. Effect of PC content on (d) permeability of CO₂, (e) permeability of CH₄ and (f) selectivity of CO₂/CH₄ for Matrimid-MgO (5 wt%) membranes at 4 bar and 298 K. Relative uncertainties are less than 1.6% and 3.2% for permeability and selectivity, respectively.

The permeability of Matrimid-MgO membranes for both gases decreases subject to an increase in pressure from 4 to 10 bar. The permeability of gas through a dense membrane is a product of its solubility and diffusivity coefficients (Baker, 2004):

The gas sorption capacity is defined Eq.(6) (Yampolskii et al., 2006):

where, S is the solubility coefficient and p is the gas pressure. The three-parameter dual-mode sorption isotherm model can describe gas sorption in glassy polymers (Paul, 1979):

where, K_d is the Henry’s law parameter,  is the Langmuir sorption capacity, and b is the Langmuir affinity parameter. The solubility coefficient is calculated through Eqs. (6 and7):

The solubility decreases subject to pressure, and approaches to the Henry’s law parameter at very high pressures. In glassy polymers, the diffusion coefficient for a gaseous penetrant increases slowly at relatively low pressures. This behavior corresponds to the transport model based on dual-mode concepts (Koros, Paul, & Rocha, 1976). The solubility and diffusion coefficient correlation with pressure determines, the permeability pressure behavior. Since the former is dominant, the dual-mode sorption and the mobility models predict a decrease in permeability with an increase in pressure which is mainly due to the lower solubility of gases at higher pressure (Bos, Pünt, Wessling, & Strathmann, 1998; Duthie et al., 2007; Ismail & Lorna, 2002; Wind, Staudt-Bickel, Paul, & Koros, 2002; L. Zhang, Xiao, Chung, & Jiang, 2010).

The effect of MgO content and pressure on the gas permselectivity of membranes, can be analyzed by computing the gas sorption properties of a mixed-matrix membrane based on the additive model as follows (Barrer, Barrie, & Rogers, 1963; Matteucci, Kusuma, Sanders, Swinnea, & Freeman, 2008):

(9)

where C_MMM, C_F and C_polymer are the gas concentration (the amount of adsorbed gas per volume) in the nanocomposite (MMM), the filler and the polymer (cm³(STP)/cm³), respectively. C_V is the gas concentration in the polymer/particle interfacial voids, obtained by the ideal gas law for a given pressure (p) and temperature (T):

Gas concentration in a void is, obtained as being 0.88 cm³(STP)/(cm³ void) at standard conditions. In Equation 9, is the void volume percentage and is the volume percentage of filler, that is:

where, ρ_F and ρ_P are the density of filler and polymer, and ω_F and ω_P are the filler weight and polymer, respectively.

Gas sorption capacity of filler (MgO) is described as a function of pressure by the Freundlich isotherm (Matteucci, Raharjo, Kusuma, Swinnea, & Freeman, 2008):

where, K and n are the fitting parameters as reported by Matteucci (Table 2) (Matteucci, Kusuma, Kelman, et al., 2008). As discussed, MgO indicate a greater sorption capacity for CO₂, due to acid-base interaction. Substitution of gas concentration values with each one of the MMM component (from equations 7, 10 and 12) in Equation 9, yields:

The last term (void contribution on gas uptake) in Eq. (13) is neglected when compared with filler and polymer contributions (Matteucci, Kusuma, Kelman, et al., 2008), thus:

Here, the gas sorption capacity of MMMs can be assessed at any pressure and filler concentration. For this purpose, first, diffusion coefficients of both gas types in Matrimid membrane at different pressures are calculated by the time lag experimental method (Equation 3). The gas sorption data of pristine Matrimid are then obtained from permeability data through Eq.s (5 and 6) and finally, the dual-sorption parameters (K_d, C'_H, and b) of Matrimid are extracted by fitting Eq. (7) according to Table 2.

In the next step, the effect of MgO nanoparticles on gas sorption properties of MMMs at two different pressures (1 and 4 bar) are calculated through Eq. (14), Table 3, where, the concentration of gaseous penetrants on the MMMs (C_MMM) is higher than that of neat Matrimid (C_polymer), thus the reason for enhanced permselectivity of MMMs when MgO nanoparticles are applied.

Table 2. Freundlich isotherm parameters for gas adsorption onto MgO (Matteucci, Kusuma, Swinnea, & Freeman, 2008) and dual-mode sorption parameters of pristine Matrimid at 25 °C

Table 3. Gas sorption data (cm³ gas in STP/cm³)of MgO, Matrimid and MMMs at two different pressures (1 and 4 bar)

3.5.2 Matrimid-MgO-PC membranes

Permeability and selectivity of Matrimid-MgO-PC membranes (PCxM5) with 5 wt% MgO and different PC loadings are illustrated in Figs 6 (d, e and f) for a typical feed pressure (4 bar). These samples are analyzed in order to assess the incorporation effect of two kinds of fillers on the gas separation properties of Matrimid membranes it is observed that applying PC particles enhances the membrane permeability in both gases types. As observed in Table 1, PC powder is comprised of 80 wt% emeraldine-base PAni. Rebattet and et. al (Rebattet, Escoubes, Pinéri, & Geniès, 1995) have already suggested that the sorption capacities of CO₂ and CH₄ on emeraldine-base PAni at 1 bar pressure are 4 and 1.5 cm³ in STP/cm³ polymer,respectively. These values are almost in the same order of Matrimid gas sorption capacity reported in Table 3 and also those mentioed in other references (Chung et al., 2003; Moghadam et al., 2011). It is suggested that any possible interaction between penetrating gas types with silicate layers (e.g. Si-OH) do not affect the solubility of CO₂ or CH₄ on the membranes (Ahn et al., 2008; Anadão et al., 2010; Bhole et al., 2007; Defontaine et al., 2010; Hashemifard et al., 2011; Liang et al., 2012). Thus, the polyaniline/clay (PC) particles do not probably make any significant change in gas sorption properties of fabricated membranes and the enhanced membrane permeability for both gas types at higher PC content is probably mostly attributed to the diffusion term. The SEM analysis of PC indicate a flower-petal like morphology of about 7 nm average pore size (Gh & Navarchian, 2016). The effect of the generated voids at polymer-filler interface is discussed for mixed-matrix membranes by Mahajan. It is found that presence of nonselective permeable regions in the polymer-filler interphase,  results in selectivity of MMMs to drop to the selectivity of pristine polymer membrane level (R. Mahajan, 2000). Consequently, due to contradicting effects of tortuosity and void formation on diffusivity of gaseous penetrants, the CO₂/CH₄selectivity remains almost unchanged upto 5% PC content and then drops when the PC loading is increased to 10 wt% (Fig. (6-f)).A close examination of Fig. (6), indicates that the sample PC5M5 is assumed to have the best performance among the examined samples because its CO₂/CH₄ selectivity is enhanced by 3.3 units (by MgO nanoparticles), and its permeability for CO₂ is increased by 70 % (due to presence of PC) compared to pristine Matrimid membrane. Comparing pristine membrane with three MMMs, each containing totally 10 wt% filler (samples PC5M5, PC0M10 and PC10M0), confirms that the sample PC5M5 has the best permselectivity performance on the Robeson chart (Fig. (7)). This can be verified by FESEM analysis that represents the same distribution of the fillers in sample PC5M5 with samples PC0M5 and PC5M0. This finding declares that incorporation of two kinds of fillers at lower concentrations (5 wt% PC and 5 wt% MgO) resulted in less agglomeration when compared with the membrane with only one type of filler at higher concentration (10 wt% PC or 10 wt% MgO). Here, it can be deduced that the applying PC and MgO with different geometry and physicochemical properties enhance Matrimid permeability and selectivity in CO₂ from CH₄ separation.

Figure 7. The comparison of permselectivity results of fabricated Matrimid and corresponding MMMs in Robeson chart. All symbols are related to different MgO and/or PC contents. (data for PC10M0 are adopted from our previous work
(Gh & Navarchian, 2016)).

3.6 Effect of fillers on plasticization resistance of the MMMs

The effect of MgO content on plasticization resistance is analyzed. As pressure increases, Matrimid is plasticized by CO₂ at 10 bar pressure at room temperature (Bos et al., 2001; Bos et al., 1998; Bos, Pünt, Wessling, & Strathmann, 1999). As observed in Fig. (8-a), plasticization pressure of the Matrimid-based membrane containing only MgO (without any PC) is increased slightly from 10 bar to 15 bar as the MgO content in the polymer is increases from zero (in pristine Matrimid) to 10 wt%. The reported maximum p_plast of Matrimid/nanofiller systems is up to 21 bar in Matrimid/MOF system (Shahid & Nijmeijer, 2014b). Matrimid-PC membranes (without MgO) have plasticization pressure of 30 bar as found in our previous work (Gh & Navarchian, 2016). In other Matrimid-based systems the plasticization has been postponed to 30-40 bar by thermal treatment (Bos et al., 1998), crosslinking (Tin et al., 2003) or polymer blending(Khan, Li, & Vankelecom, 2011) while the permeability and/or selectivity parameters faced significant deterioration.

Plasticization pressure of Matrimid-PC membranes containing 5 wt% MgO (PCxM5)- (Fig. (8-d)) is slightly higher than that of Matrimid-PC membranes (MgO-free) with the same PC content (PCxM0), Table 4. It is suggested that the improvement of plasticization pressure is mainly the result of introducing high modulus rigid silicate layers (Joulazadeh & Navarchian, 2010, 2011) which can entangle with Matrimid matrix and increase the chain stiffness (Ismail & Lorna, 2002), applying high plasticization resistant PAni (Gupta, Hellgardt, & Wakeman, 2006). MgO nanoparticles may hinder intrasegmental mobility of polymer backbone and so suppress plasticization (Ismail & Lorna, 2002).

Because of the plasticization phenomena in the glassy polymers, their gas separation capacity is limited, while one of the important characteristics of a membrane is its operating pressure. The fluxes of treated CO₂ in fabricated MMMs (calculated by Equation 4) indicate that by applying 5% PC and 5% MgO in Matrimid, CO₂ permeability and p_plast improve by 76% and 200%, respectively, while the selectivity is almost unchanged. For this membrane, the membrane capacity (the flux of the treated CO₂ through the membrane) can be obtained as 46.8×10^-5 cm³(STP)/cm², Eq. (4), where it is 425% when compared to the flux of CO₂ through thepristine membrane in natural gas processing at p_plast (30 bar) with the selectivity of 39.7, Table 4.

Table 4. Permeability, selectivity, and flux of CO₂ permeate through fabricated MMMs atplasticization pressure (p_plast). Data for Matrimid-PC membranes (PCxM0) are adopted from our previous work (Gh & Navarchian, 2016).

3.7 Effect of Pressure on Selectivity of the MMMs

Permeability of CH₄ at PC0Mx Fig. (8-b) and PCxM5 samples Fig. (8-e), respectively at 4-30 bar gas pressure are measured to determine the effect of presure on CO₂/CH₄ selectivity as illustrated in Figs 8 (c and f). It is observed that the selectivity increases with pressure upto 10-12 bar, then remains almost constant at higher pressures. The same behavior is observed in Matrimid-PC samples without any MgO(Gh & Navarchian, 2016). Selectivity is composed of two terms, α_D and α_S Eq. (2); the former is  the most dominant factor in the selectivity of glassy polymers (Yampolskii et al., 2006) and is a function of penetrant concentration in the polymer matrix (Ghosal & Freeman, 1994; Koros et al., 1976). As CO₂ is more condensable and diffusive than CH₄, its concentration in polymer matrix is higher than that of CH₄. At low pressures, concentration of CO₂ isjust high enough in the polymer matrix to increase its diffusion coefficient, thus, the selectivity increase with pressure. An increase in pressure increases both, the CH₄ concentration in the polymer and its diffusivity, which lead to a constant selectivity at higher pressure.

Figure 8. Effect of pressure on permeability of (a) CO₂, (b) CH₄ and (c) selectivity of CO₂/CH₄ for Matrimid membranes with different MgO content at 298 K. Effect of pressure on permeability of (d) CO₂, (e) CH₄ and (f) selectivity of CO₂/CH₄ for Matrimid-MgO (5 wt%) membranes with different PC content at 298 K. Relative uncertainties are less than 1.6% and 3.2% for permeability and selectivity, respectively.