Effect of macrovoids in nano-silica/polyimide mixed matrix membranes for high flux CO₂/CH₄ gas separation

Abstract

Macrovoid structured mixed matrix membranes (MMMs) composed of nano-size (200 nm) silica particles and co-polyimide were prepared from 6FDA–ODA–DAM (6FDA = 4,4′-(hexafluoroiso-propylidene)diphthalic anhydride; ODA = 4,4′-oxidianiline; DAM = 1,3,5-trimethyl-2,6-phenylenediamine) with different proportions (1 : 1 and 1 : 4) and tetraethoxysilane (TEOS) via the sol–gel method. The separation performance of MMMs with 6FDA–ODA–DAM treated at high temperature (450 °C) was excellent for CO₂/CH₄ separation (for 6FOD–ODA–DAM (1 : 1): CO₂ permeability ∼265 Barrer and CO₂/CH₄ selectivity ∼32; for 6FOD–ODA–DAM (1 : 4): CO₂ permeability ∼302 Barrer and CO₂/CH₄ selectivity ∼25). Remarkably, the best membrane could resist pressure up to 600 psi without any loss of permselectivity. The CO₂/CH₄ separation performance of a series of silica–6FDA–ODA–DAM(11) MMMs with different SiO₂ loadings is theoretically predicted using a modified Maxwell model where both gas permeability and macrovoid shape factor are simultaneously considered as adjustable parameters. Applying the optimized values, the modified Maxwell model predictions were in excellent agreement with experimental permeability data (less than 2% deviation).

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1. Introduction

Membrane-based gas separations are attractive because of their simplicity, low energy costs, and ability to operate in remote locations. Full utilization of the advantages of membrane technology, however, will require new membranes with increased permeabilities and selectivities.¹ Today, membrane-based CO₂/CH₄ gas separation has mainly four important fields of application in petroleum industries,² natural gas purification,³ bio-gas purification,⁴ and CO₂ capture.⁵ Mixed matrix membranes (MMMs) combine the potential advantages of inorganic particles and polymer matrix, which are superior permeability or selectivity of the former and good processability and mechanical properties of the latter.^6–12 In this regard, the development of these organic–inorganic hybrids focused on structure and composition modification of polyimides to improve their gas selectivity and/or permeability.^13–17 In this study, physical and gas transport properties of macroporous hybrid membranes with novel 6FDA–ODA–DAM co-polyimide containing silica were investigated. The hybrid membranes were prepared via a sol–gel technique using this co-polyimide and tetraethoxysilane (TEOS) silica.

2. Literature review

Mixed matrix membranes, which are composed of an inorganic nanofiller dispersed in a polymer matrix, have been investigated for gas separation and have the potential to provide a solution to the limiting trade-off between permeability and selectivity of polymeric membranes.^18,19 For example, some membranes, in which SiO₂ or TiO₂ particles are dispersed in polyimide, show much higher gas permeabilities and similar or even improved gas selectivities compared to their corresponding neat polymer membranes.^20–26 The sol–gel method is the most widely used preparation technology for nanocomposite membranes. In this method, polymers and inorganic nanoparticle precursors are mixed together in solution. The inorganic precursors then hydrolyze and condense into well-dispersed nanoparticles in the polymer matrix. The advantage of this method is obvious: the reaction conditions are moderate (usually room temperature and ambient pressure) and the concentrations of organic and inorganic components are easy to control in the solution. Additionally, the organic and inorganic ingredients are dispersed at the molecular or nanometer level in the membranes, and thus the membranes are homogeneous.^27–30

For example, Iwata et al. reported that by using the sol–gel method, a nanocomposite membrane of polyacrylonitrile (PAN) with hydrolyzate of tetraethoxysilane (TEOS) as the inorganic phase showed O₂ permeability of 2.2–2.5 Barrer and ideal selectivity of 13–17 (silica contents from 3–20 wt%) in O₂/N₂ separation.³¹

Gomes et al. prepared poly(1-trimethylsilyl-1-propyne) (PTMSP)/silica nanocomposite membranes by sol–gel copolymerization of TEOS with different organoalkoxysilanes in tetrahydrofuran solution of PTMSP.³²

Joly et al. fabricated polyimide/silica membranes containing 32 wt% silica via the sol–gel method by adding tetramethoxysilane (TMOS) to poly(amic acid) (PAA) solution and subsequently imidizing at 60–300 °C. The nanocomposite membrane had a higher permeability for CO₂ (from 0.8 to 2.0 Barrer) and a lower CO₂/CH₄ selectivity (from 40 to 25) compared to the pure polyimide membrane.²¹

Kusakabe et al. reported that CO₂ permeability of polyimide/SiO₂ hybrid nanocomposite membranes was 15 times larger than that of the corresponding polyimide. Permeability also increased with increasing mass fraction of silica, while permselectivity of CO₂ to N₂ decreased.³³

Suzuki et al. reported that hyperbranched polyimide (HBPI)–silica hybrid membranes were prepared via a sol–gel technique using poly(amic acid), water, and tetramethoxysilane.^24,34,35 Amine-terminated 6FDA–TAPOB hyperbranched polyimide (HBPI) (HBPI(6FDA-TAPOB)) was prepared by polycondensation of 1,3,5-tris(4-aminophenoxy) benzene (TAPOB) and 6FDA in N,N-dimethylacetamide (DMAc), followed by an addition of a silane coupling agent, 3-aminopropyl-trimethoxysilane (APTrMOS) to modify the end groups.^24,34 6FDA-HAB hydroxy polyimide (HPI) (HPI(6FDA-HAB)) was synthesized from 6FDA and 3,3′-dihydroxybenzidine (HAB) in DMAc. Finally, 6FDA-TAPOB hyperbranched polyimide (HBPI(6FDA-TAPOB))/6FDA-HAB hydroxy polyimide (HPI(6FDA-HAB)) blend-silica hybrid membranes were prepared by blending HBPI and HPI polymers, adding of appropriate amounts TMOS and deionized water, followed by imidizing and hybridizing in an oven under N₂ flow.³⁵ The results showed that both gas permeabilities and CO₂/CH₄ selectivities were increased with increasing silica content.

Recently, Suzuki et al. used the same method to obtain hyperbranched polyimide-silica hybrid membranes followed by heat-treatment in nitrogen at 450 °C. These membranes have both excellent gas permeability (134–369 Barrer) and selectivity (32–68), particularly for CO₂/CH₄ under the tested conditions (76 cm Hg and 25 °C).³⁶

Fardad studied the influence of various catalysts on the structure of silica sol–gel films based on the hydrolysis and condensation of TEOS with 2 moles of water, and in the presence of 2 moles of ethanol. This investigation showed that film thickness, shrinkage, porosity, and optical quality depended on the type of catalysts used in the preparation of the solution precursor.³⁷

Kayser et al.³⁸ prepared amine functionalized nano-spherical silica particles by a modified Stöber method³⁹ and grafted 3-aminopropyl-dimethylmethoxysilane (APDMS) on their surface. These particles were used as inorganic fillers in silica/SPEEK mixed matrix membranes. The results indicated that the main effect of the inorganic filler on proton conductivity is related to changes in the microstructure of the water channels in the wet polymer related to the distribution of nanoparticles in their lattice.

In the above-described investigations, most authors prepared the silica particles in situ in acid conditions (for example, poly(amic acid) (PAA)), with the acid acting as a catalyst in the hydrolysis/condensation reactions. In some cases, silica particles were first produced and then mixed with polymer solution before casting. The polymer morphology changes associated with particle introduction in the MMMs, and their effects on membrane performance in gas separation were seldom discussed. In this work, silica particles were simultaneously generated with membrane fabrication by a simple method. The focus is made on the relationship between morphology, affected by silica particles, and membrane separation performances of the MMMs in CO₂/CH₄ separation.

3. Experimental

3.1. Materials

Materials for synthesis of co-polyimide compounds: 6FDA = 4,4′-(hexafluoroiso-propylidene)diphthalic anhydride (>99% purity) was provided by Chriskey Company, ODA = 4,4′-oxidianiline (97% purity) was purchased from Sigma-Aldrich, and DAM = 1,3,5-trimethyl-2,6-phenylenediamine (98% purity) was obtained from TCI America. All three compounds were then purified by vacuum sublimation. 1-Methyl-2-pyrrolidone (NMP) was purchased from TCI America and purified by vacuum distillation. Acetic anhydride and triethylamine were obtained from Sigma-Aldrich. Chloroform (CHCl₃, 99.8% assay by GC analysis) was obtained from VWR International LLC, and methanol was obtained from Fisher Scientific. Tetraethylorthosilicate (TEOS, 98%) was obtained from Sigma-Aldrich Co. Matrimid® 5218 and Ultem®1000 were purchased from Huntsman Advanced Materials (Switzerland) GmbH and WS Hampshire Inc, respectively.

3.2. Co-polyimide synthesis

6FDA-ODA-DAM co-polyimides were synthesized by a two-step method as described elsewhere.⁴⁰ In the first step, poly(amic acid) (PAA) derived from equimolar amounts of solid 6FDA and DAM diamines (ODA : DAM molar ratios are 1 : 1 and 1 : 4) were prepared by solution condensation in NMP. Both reaction mixtures were stirred using a power drill (Mastercraft) connected to a variable autotransformer (The Superior Electric co. Bristol Conn, USA) stirrer under an argon atmosphere and placed in an ice–water mixture for 15 h. In the second step, poly(amic acid) was then imidized to form polyimides by chemical imidization under an argon atmosphere at room temperature for 24 h by adding acetic anhydride (dehydrating agent) and triethylamine (catalyst). The reaction scheme of co-polyimide synthesis is shown in Fig. 1. The polyimide solution was then precipitated with methanol, washed several times with methanol, and dried at 200 °C in a vacuum oven for 24 h.

Fig. 1 Reaction scheme for copolyimides synthesis.

3.3. Silica/polyimide MMM preparation

The hybrid membranes were prepared by the sol–gel reaction and dense film casting method.³⁵ First, 0.4–0.5 g of polyimide was dissolved in 5–10 ml of chloroform. The obtained solution was then filtered to remove un-dissolved materials and dust particles. Then, appropriate amounts of TEOS (eqn (1), M_SiO2 and M_TEOS is the molecular weight of SiO₂ and TEOS. W_TEOS and W_polyimide are the weight of TEOS and PI used in this experience) and excess water were added in the polymer solution. This hydrolysis reaction is an example of a sol–gel process. The side product is ethanol. The reaction proceeds via a series of condensation reactions that convert the TEOS molecule into a mineral-like solid via the formation of Si–O–Si linkages (eqn (2)). The rate of this conversion is sensitive to the presence of acids and bases, both of which serve as catalysts. The Stöber process allows the formation of mono-dispersed silica particles. The size of silica particles is between 50 and 2000 nanometers depending on type of silicate ester used, type of alcohol used and volume ratios.³⁹ The slurry was agitated for 24 h to obtain a good homogenization and produce macrovoids during this period. A nascent film was cast from the solution onto a clean polyester plate using a small metal container with a cover to delay solvent evaporation from the nascent membrane. The membrane was further dried for 15 h at 200 °C under vacuum. Ethanol evaporated with the high heating temperature. The average thickness of MMMs was 40–85 μm, measured with a micrometer.

Si(OC₂H₅)₄ + 2H₂O → SiO₂ + 4C₂H₅OH (2)

3.4. Thermal treatment of MMMs

The hybrid membranes were further heated under nitrogen at 300 °C and 450 °C for 1 hour each time, thereby obtaining gas separation membranes for further analysis.

3.5. Characterization

FT-IR spectra were recorded using a Nicolet Magna 850 Fourier transform infrared spectrometer (Thermo Scientific, Madison, WI) equipped with a liquid-nitrogen-cooled narrow-band MCT detector using Golden-Gate (diamond IRE) ATR accessories (Specac Ltd., London, U.K.). Each spectrum was obtained from the acquisition of 128 scans at 4 cm⁻¹ resolution, from 4000 to 700 cm⁻¹ using Happ-Genzel apodization.

The weight loss curves (TGA-DTG) were recorded using a TA Instruments TGA model Q5000IR from 100 to 850 °C at a heating rate of 10 °C min⁻¹ under nitrogen.

The glass transition temperature (T_g) and Young's modulus of MMM were determined using a dynamic mechanical thermal analyzer (TA Instruments, RSA-3, New Castle, DE) on samples having dimensions of 25 × 6 × 0.02 mm³. For T_g measurements, the temperature was increased from 30 to 350 °C at a rate of 10 °C min⁻¹ with a strain of 0.05% and a frequency of 1 Hz.

The membrane density (ρ) is simply defined by the ratio between mass (M) and volume (V). The mass is weighed with an analytical balance Mettler AE200 with a sensitivity of 10⁻⁴ g. The volume is then calculated from the diameter (d) (constant at 55 mm) and the average of 8 thicknesses (l) of the membrane.

SEM images were recorded to determine crystal size and to characterize morphology of the dispersed phase, using a JEOL JSM-840A operated at 15–20 kV. From the SEM micrographs, the average diameter of macrovoids, their number and surface were obtained using image analysis software (Image Pro Plus). The average diameter was measured at 2 degree intervals and passing through the centroid giving an average of 90 measurements for each macrovoid.

The cell density is determined from the number of cells per unit section area. It is calculated assuming that the surface distribution is the same in all three dimensions and eqn (3) is the mathematical expression of cell density.⁴¹

where N is the number of cells and A is the area in which the cells are counted.

3.6. Membrane properties

The pure gas transport properties were measured using the variable pressure (constant volume) method.^11,12 In the measurements, the permeate pressure was varied from 10⁻³ to 30 Torr. For each membrane, gas permeability, CO₂/CH₄ selectivity, and separation factor were averaged over three replicate permeation tests. The reported data correspond to averages of these results.

For the transport of individual components A and B through a membrane, the permeability P_i of penetrant i can be expressed as follows:

The ideal selectivity can be written as the ratio of permeabilities:

where P_A and P_B are the permeabilities of pure components A and B, respectively. A is the membrane area (cm²), l is the membrane thickness (cm), Δp is the upstream pressure (psi), V is the downstream volume (cm³), R is the universal gas constant (6236.56 cm³ cm Hg mol⁻¹ K⁻¹), T is the absolute temperature (K) and dp/dt is the permeation rate (psi s⁻¹).

The separation factor (α^*_AB) represents the ability of a membrane to separate a binary gas mixture, and is defined as:

α^*_AB = (y_A/y_B)/(x_A/x_B) (6)

where, y_A and y_B are the mole fractions of the components in permeate, while x_A and x_B are their corresponding mole fractions in the feed. The values of molar compositions are average values of at least five measurements after steady composition was reached, in an experiment in which permeates composition was measured by gas sampling and gas chromatography (GC) analysis at different times. The relative error of these values is less than 2%. The time to reach stable composition was well over 12 time lags (12θ).

4. Results and discussion

4.1. Thermal analysis

Characteristic temperatures from TGA curves were determined as the low temperature peak in the DTG analysis and the values are listed in Table 1. The neat polymer membranes from 6FDA-ODA-DAM co-polyimide are designated 6FOD, whereas the ODA : DAM molar ratio is labelled 11 or 14 (for 1 : 1 and 1 : 4, respectively). For example: 6FOD(11)-n%-200, n% is wt% SiO₂ loading, and 200 is the treatment temperature. The treatment temperatures are 200, 300 and 450 °C. The temperatures to reach 5% and 10% weight loss of 5–15 wt% SiO₂/polyimide MMMs were increased (by about 5–30 °C). Those of MMMs after thermal treatment at 300 and 450 °C were generally lower by about 10–40 °C. DTG peak temperatures also give information on the pyrolysis rates. Thermal stability of the MMM materials prepared via TEOS hydrolysis reaction is believed to be sufficient for gas separation applications, even through the stability value is very close compared to that of the pure polyimide.⁴² For example, the highest temperature used for hydrogen separation was 300–500 °C. At the natural gas well, the gas pressure is rather high (in excess of 1000 psi) and the gas temperature is on the order of 30–50 °C. All the TGA curves show a plateau, which indicates no remnant hydroxyl groups. There was no residual absorbed solvent or hydroxyl group having low decomposition temperature. At the latter temperature, most chemical decomposition reactions of the material took place. These weight losses are mostly due to the conversion of carbonyl groups (C=O) to either CO or CO₂.⁴³

Table 1 TGA-DTG properties of MMMs

Membrane^a	Td5% (°C)	Td10% (°C)	DTG peak (°C)
a 6FOD(11), 6FOD(14) : 6FDA-ODA-DAM (1 : 1) and 6FDA-ODA-DAM (1 : 4). n%: wt% SiO2 loading, at treatment temperature of 200, 300 and 450 °C.
6FOD(11)-0%-200	488	508	529
6FOD(11)-5%-200	495	529	550
6FOD(11)-10%-200	501	531	553
6FOD(11)-15%-200	504	535	554
6FOD(11)-10%-300	450	511	549
6FOD(11)-10%-450	503	532	552
6FOD(14)-0%-200	489	508	523
6FOD(14)-10%-200	447	484	520
6FOD(14)-10%-300	451	484	520
6FOD(14)-10%-450	464	485	520
Matrimid-0%-200	474	508	511
Matrimid-10%-200	440	486	518
Matrimid-10%-450	452	492	523

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4.2. FTIR analysis and mechanism of reaction

To explore the mechanism of TEOS hydrolysis reaction during MMM casting, FT-IR measurements were used to confirm this reaction. The possible TEOS hydrolysis reaction is displayed in eqn (2).

As shown in Fig. 2, the appearance of absorption bands at 1725 cm⁻¹ (asymmetric stretch of the carbonyl group, imide I band) and 1782 cm⁻¹ (symmetric stretch of the carbonyl group, imide II band), 1377 cm⁻¹ (C–N stretch), 1117 cm⁻¹ (imide III band) and 720 cm⁻¹ (deformation of the imide ring or imide IV carbonyl group) confirmed the formation of imides for all membranes.⁴⁴ Usually, siloxanes show one or more very strong infrared bands in the region 1000–1130 cm⁻¹. Disiloxane and small-ring cyclosiloxanes show a single Si–O–Si band. As the siloxane chains became longer or branches the Si–O–Si absorption becomes broader and more complex showing two or more overlapping band.⁴⁵ From Fig. 2, carbonyl (C=O) peaks were found at 1100 cm⁻¹ in the 6FOD(11) membrane, silica (Si–O) vibrations are found between 1080 and 1060 cm⁻¹ in the others membrane. The 6FOD(11)-20%-ambient has two peaks at 1060–1080 cm⁻¹. Thus these peaks to some extent overlap with the C–O frequencies of polyimides. Other weak vibrations are found in between 2900 and 3000 cm⁻¹ in Fig. 2 for membrane 6FOD(11)-20% at ambient temperature. This membrane is the nascent film and was not heated. These distinctive bands at 2927–2983 cm⁻¹ correspond to the symmetric and asymmetric vibrations of CH₂ methylene and CH₃ methyl groups. It is thought that these groups belong to the ethanol generated in reaction (2).

Fig. 2 FT-IR spectra of neat polyimide 6FOD(11), 10 wt%, 15 wt%, 20 wt% SiO₂ loading membranes treated at 200 °C, and 20 wt% SiO₂ loading membrane treated at ambient temperature. Spectra are shifted upward by 0, 50, 100, 150, and 200, respectively.

4.3. Dynamic mechanical testing (DMA) analysis

DMA testing is a versatile and sensitive technique enabling the complete exploration of the relaxation mechanisms in viscoelastic materials.⁴⁶ The most common use of DMA is for the determination of the glass-transition temperature (T_g), where the maximum loss of applied energy is observed, usually as a peak, in the traces of the loss factor versus temperature.^9,11,40 Young's modulus is obtained from the slope of stress–strain curves at low deformation (linear elastic) and represents the rigidity of materials (Fig. 3).

Fig. 3 Young's modulus as a function of temperature for selected MMMs.

Table 2 summarizes the glass transition temperature and Young's modulus of 6FOD(11) polyimide, and 6FOD(11) with TEOS MMM. Compared to the neat 6FOD(11) membrane (Table 2), the T_g values of MMMs decreased with increasing MOF loading (from 5 to 20 wt%). This decrease might be explained by the presence of macrovoids (see below), which can enhance the movement of the polymer chains. In the preparation of polymer foams, carbon dioxide and ethanol (EtOH) mixtures can be used as blowing agents as already proposed.^47,48 Gendron at al. studied the effect of blending CO₂ with ethanol (EtOH) as a co-blowing agent for polystyrene (PS) foaming.⁴⁸ The results showed that viscosity and glass transition temperature obviously decreased with increasing amount of foaming agents. The T_g values of treated MMMs are higher than that of the neat polyimide membrane. This may be due to polymer chains becoming more rigid after rearrangement upon high temperature treatment.⁴⁹ Moreover, Young's modulus of MMM membranes decrease with increasing SiO₂ loading (Fig. 3 and Table 2). This behaviour is usually associated with highly reduced densities and low mechanical properties of foamed polymers.⁵⁰

Table 2 T_g and Young's modulus neat 6FOD(11) and SiO₂-6FOD(11) membranes with different SiO₂ loadings and treatment temperatures

Membrane	Tg (°C)	Young's modulus (MPa) (50 °C)
6FOD(11)-0%-200	319	150
6FOD(11)-5%-200	318	67
6FOD(11)-10%-200	317	66
6FOD(11)-15%-200	305	48
6FOD(11)-20%-200	283	31
6FOD(11)-10%-300	327	56
6FOD(11)-10%-450	353	72

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4.4. Morphology of macrovoid structured MMMs

Typical images of the macrovoid structured MMMs for SiO₂ loading varying from 5 to 20 wt% are given in Fig. 4. It is seen that these macrovoids are non-circular and non-uniform until 1–20 micron in diameter; the number of cells and their sizes vary with increasing SiO₂ loading. It is thought that the hydrolysis reaction is favoured in the weak acid polyimide solution during membrane casting, but no reaction between PI and TEOS was evidenced (see Section 4.2). The ethanol generated by the hydrolysis reaction was only slightly evaporated during stirring and mostly during dry heating (200 °C) the membrane. The macrovoids were then generated due to ethanol evaporation.

Fig. 4 SEM micrographs showing the macrovoid structure of 6FOD(11)-200 MMMs with: (a) 5 wt%; (b) 10 wt%; (c) 15 wt%, and (d) 20 wt% SiO₂ loading.

Fig. 5 shows the distribution of macrovoid average diameter in each membrane. Table 3 summarizes the membrane density, average macrovoid diameter and macrovoid density of MMMs. Membrane density was decreased slowly with increasing SiO₂ loading compared with the original membrane. The average macrovoid diameter and macrovoid density changed with SiO₂ loading. The morphology of macrovoid structure is complex and could be affected by many factors during membrane fabrication such as ambient temperature, pH value of solution, stirring time, etc. These results are consistent with higher void size and lower void number as reported in ref. 48.

Fig. 5 Macrovoid average diameter distribution of MMMs: (a) 6FOD(11)-5%-200; (b) 6FOD(11)-10%-200; (c) 6FOD(11)-15%-200, and (d) 6FOD(11)-20%-200.

Table 3 Morphological properties of neat 6FOD(11) and SiO₂-6FOD(11) membranes with different SiO₂ loadings and treatment temperatures

Membrane	Membrane density (g cm^−3)	Average diameter (μm)	Macrovoid density (cm^−3)
6FOD(11)-0%-200	1.38	—	—
6FOD(11)-5%-200	1.08	5.95	2.0 × 10^7
6FOD(11)-10%-200	1.06	7.45	1.3 × 10^7
6FOD(11)-15%-200	0.71	4.48	1.0 × 10^8
6FOD(11)-20%-200	0.51	5.27	3.9 × 10^7
6FOD(11)-10%-300	0.79	4.02	3.0 × 10^7
6FOD(11)-10%-450	0.96	5.04	3.5 × 10^7

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The size of silica particles was dependent on the conditions of hydrolysis solution.³⁹ In the present work, 200 nm silica particles were observed for MMM in very weak acid solution. Fig. 6 shows an example for 6FOD(11)-10%-200 membrane. This result is in agreement with ref. 39.

Fig. 6 SEM images of SiO₂ particles of 6FOD(11)-10%-200 membrane with different magnifications: (a) 10 000×; and (b) 20 000×.

4.5. Gas transport properties

4.5.1. CO₂/CH₄ separation performance of macrovoid structured MMMs. The membrane performance of macrovoid structured MMMs (thickness: 30–80 μm), i.e. permeability, ideal selectivity and separation factor, for pure CO₂ and CH₄ gases, and their blends (50/50 CO₂/CH₄) were measured at 25 °C and 15 psi (Table 4). For the Matrimid 5218 commercial polymer, MMMs containing 10 wt% SiO₂ with two different heating temperatures showed high permeability for both gases and kept about the same selectivity. Their permeabilities are up by 300% compared to the original Matrimid. Unfortunately, Ultem 1000 could not resist the higher heating temperature.

Table 4 Gas permeability (Barrer), ideal selectivity, and 50/50 CO₂/CH₄ mixed gas selectivity of neat 6FOD(14) membrane and SiO₂-6FOD(14) MMMs with different silica loadings at 25 °C and 15 psi

Membrane	PCO2 (Barrer)	PCH4 (Barrer)	PCO2/PCH4	(50/50%) CO2/CH4 mixed gas selectivity
6FOD(14)-0%-200	130	7.10	23.2	22.9
6FOD(14)-10%-200	290	21.8	13.3	21.8
6FOD(14)-10%-450	300	12.2	24.8	22.3
Matrimid-0%-200	10.0	0.28	35.3	35.0
Matrimid-10%-200	41.0	1.10	38.0	38.0
Matrimid-10%-450	34.0	0.92	36.7	38.2
Ultem-0%-200	1.45	0.037	38.8	36.8
Ultem-10%-200	2.78	0.15	17.5	18.2

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Two co-polyimides with different ODA : DAM (1 : 1 and 1 : 4) molar ratios were used as polymer matrices for macrovoid structured MMMs. The CO₂/CH₄ separation performances of neat and their macrovoid structure membranes are summarized in Tables 4 and 5. The co-polyimide 6FOD(14) with 10 wt% SiO₂ has both higher values of CO₂ and CH₄ permeability compared to those of neat co-polyimide. The macrovoid membranes of 6FOD(14)-10%-450 and 6FOD(11)-10%-450 with heating temperature of 450 °C showed very high CO₂ permeability of 302 and 265 Barrer, and their selectivity improved to 24.8 and 32 from 23 and 24, respectively. The separation factor for mixed gas also showed high values from 22 to 34.

Table 5 Gas permeability (Barrer), ideal selectivity, and 50/50 CO₂/CH₄ mixed gas selectivity of neat 6FOD(11) membrane and SiO₂-6FOD(11) MMMs with different silica loadings at 25 °C and 15 psi

Membrane	PCO2 (Barrer)	PCH4 (Barrer)	PCO2/PCH4	(50/50%) CO2/CH4 mixed gas selectivity
6FOD(11)-0%-200	51.8	1.80	24.2	21.9
6FOD(11)-5%-200	200	12.5	18.2	24.5
6FOD(11)-10%-200	235	12.5	16.8	24.6
6FOD(11)-15%-200	420	76.9	6.3	—
6FOD(11)-20%-200	810	695	1.2	—
6FOD(11)-10%-300	245	13.1	18.7	25.7
6FOD(11)-10%-450	265	8.6	31.8	34.2

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4.5.2. Effect of heat treatment temperature. The effect of heat treatment temperature (200, 300, and 450 °C) on membrane properties for co-polyimide 6FOD(11) with 10 wt% SiO₂ was examined. The CO₂ permeability as a function of heating temperature is reported in Tables 4 and 5 Compared to the neat polyimide membrane (6FOD(11)), CO₂ permeability is significantly increased up to 340% (for 6FOD(11)-10%-450), and the ideal selectivity and separation factor of the latter are also enhanced. The effect of thermal rearrangement (TR) on CO₂/CH₄ separation of polymer membranes in ref. 51 showed that CO₂ permeability was increased, while ideal selectivity was decreased with increasing heating temperature. In the present work, the results combine both macrovoid and thermal rearrangement effects, which produce this significant improvement in membrane properties.

4.5.3. Effect of SiO₂ loading. To determine the effect of SiO₂ particle loading in the MMMs, the SiO₂ content of 6FOD(11) MMMs was varied from 5 to 20 wt%. The corresponding volume fractions are 3.2, 6.5, 9.7 and 13.0%. The results are summarized in Table 5, where both CO₂ and CH₄ permeabilities are shown to increase with increasing SiO₂ loading, whereas ideal selectivity decreased. This behaviour is related to low compatibility between SiO₂ particles and the polymer matrix. Fig. 7 shows CO₂ permeabilities, membrane density, average diameter of macrovoids, and cell density as a function of SiO₂ loading.

Fig. 7 CO₂ permeability, membrane density, average macrovoid diameter and void density as a function of SiO₂ loading for 6FOD(11)-200 membrane.

4.5.4. Effect of feed pressure. Fig. 8 shows CO₂ and CH₄ permeabilities and ideal selectivity as a function of feed pressure for 6FOD(11)-10%-450 membrane. CO₂ permeability first decreases and then increases with feed pressure. The observed variation of CO₂ permeability under pressure may be attributed to the “breathing effect” of the MIL-53 phase. Moreover, it is clear that CH₄ permeability is almost constant. In the mixed matrix membranes, the effect of pressure on permeability is different in the polymer phase where plasticization induces an increase in permeability, while in the MOF phase, the “breathing effect” results in a lower one. It is possible that for the membranes studied in this work both variations cancel each other out. As a result, the CO₂/CH₄ ideal selectivity is accordingly increased and this membrane could then be used until a feed pressure of 600 psi.

Fig. 8 CO₂ and CH₄ permeability and ideal selectivity as a function of feed pressure for 6FOD(11)-10%-450 membrane.

4.5.5. Comparison with Robeson's upper bound curve. The performances of these membranes on permeability-selectivity chart are compared with Robeson's upper bound curves in Fig. 9. Both macrovoid structured MMMs with thermal rearrangement yield data points above the 1991 limit at high CO₂ permeability. Compared to pure polyimide membranes, the macrovoid structured MMMs from 6FOD(11), 6FOD(14), Matrimid® 5218 and Ultem®1000 with TEOS have higher permeability. Higher CO₂ permeabilities compared to MMMs made from PI/MOF and PI/zeolite determined in our earlier works were also observed.

Fig. 9 Performance of MMMs with respect to Robeson's upper limit curves.

4.6. Modelling of MMM permeation properties

4.6.1. Selection of predictive model. As mentioned above, due to the hydrolysis of ethanol during MMM casting, MMMs with macrovoid structure were obtained. Comparing to other reported MMM morphologies, to the best of our knowledge, this macrovoid structure defines a new kind of MMMs. In contrast to a typical filler-polymer MMM, in which the dispersed fillers are surrounded by polymer layers with/without interfacial defects, the macrovoid MMMs are made of macrovoids generated within dispersed filler-polymer layers (Fig. 4). In addition from Fig. 4, because the silica particles are well dispersed in the 6FOD polymer, the macrovoid MMMs can be considered as an ideal MMM, which contains macrovoids as the dispersed phase and silica-6FOD polymers as the continuous phase.

Coupling a theoretical modelling with experimental separation data provides an opportunity to understand the transport properties of these MMMs. As reported in our recent review,⁵² the particularly useful Maxwell model developed in 1873, originally derived from the estimation of the dielectric properties of particulate composite materials, has been widely accepted as a simple and effective tool for predicting permeation properties of a two-phase ideal MMM as:

In eqn (7), P_eff describes the effective steady-state permeability of a gaseous penetrant through a MMM, P_f and P_c are the effective permeability of pure filler membrane and polymer matrix, respectively, ϕ_d is the volume fraction of the dispersed filler.^52,53 In this equation, P_c and ϕ_d are often known experimental parameters, while P_f can be considered as either an un-known or a known parameter. The shape factor n depends on the shape of the dispersed filler. Various definitions of n were proposed in the literature. Hamilton and Crosser have, for example, proposed n = 3/ψ, where the sphericity ψ is defined as the ratio between the surface area of a sphere having a volume equal to the particle volume and the particle surface area.⁵⁴ For near-spherical fillers, the value is therefore taken as n = 3, and eqn (7) reduces to the well-known original Maxwell model.⁵³ Kang et al. reported a shape factor n = 6 for cylindrical or tubular fillers in a polymer matrix.⁵⁵ In this case, eqn (7) is an expression of the Hamilton-Crosser model.⁵⁴ For a general case of filler shape, the shape factor n can accept a variety of integer values up to infinity.⁵⁴

It is clear that in order to mathematically solve eqn (7), both the shape factor n and the filler permeability P_f can be considered as adjustable parameters and optimized by minimizing the differences between experimental data and calculated ones. This difference, namely the average absolute relative error (%AARE), is expressed as follows:

where, NDP is the number of data points. P^cal_i and P^exp_i are the calculated and experimental permeabilities, respectively. The optimized parameter is chosen to best fit the experimental data according to the minimized %AARE. For fitting, a MATLAB optimization program was developed.

4.6.2. Application to macrovoid MMM morphology. For macrovoid structured MMMs, the CO₂/CH₄ separation performance can be predicted using the Maxwell model for the ideal case of MMM morphology. While macrovoids are considered as the dispersed filler, the gas permeability P_v and volume fraction ϕ_v of macrovoid are then replaced for the P_f and ϕ_d terms, respectively. Eqn (7) can be re-written as follows:

Generally, gas permeability in the interfacial void (P_v) of a typical zeolite-polymer MMM is assumed to be the product of Knudsen diffusivity through a pore with the same hydraulic diameter as the void and sorption coefficient of the gas in the void.^52,54 In the present case, because of the mean free paths (λ) of penetrant gas (λ_CO2 = 0.082 μm and λ_CH4 = 0.062 μm calculated based on ref. 56 at 25 °C and 15 psi) are much smaller than the average macrovoid diameter (Table 3), the gas transport through the macrovoids is assumed to be by molecular or bulk diffusion.⁵⁷ Thus, coupling with the shape factor n, the macrovoid permeability P_v will be considered as adjustable parameters. First, all the macrovoid MMMs with different SiO₂ loadings were assumed to have the same shape factor n and macrovoid permeability P_v. After calculating the membrane permeability P_M using eqn (9), the average absolute relative error (%AARE) was then determined using eqn (8). The optimized value of P_v corresponding to the average shape factor n_avg was obtained for the minimum value of %AARE. Second, owing to a large difference in macrovoid diameter of these silica-6FOD MMMs (see Fig. 4 and Table 3), an optimized shape factor n must be determined for each MMM membrane. This is obtained by using eqn (8) and (9), but only the shape factor n is considered as an adjustable parameter while P_v has the value determined in the previous step. Table 6 summarizes the estimated model parameters obtained from Maxwell model fitting the experimental data of CO₂/CH₄ separation through the silica-6FOD(11) MMMs with different SiO₂ loadings.

Table 6 Estimated model parameters obtained from Maxwell model fitting the experimental data of the CO₂/CH₄ separation through the silica-6FOD(11) MMMs with different SiO₂ loadings

Membrane	ϕv (vol%)	Pv (Barrer)	navg	nop	PCO2 (Barrer)				%AARE
					Exp.	n = 3	n = 6	nop	n = 3	n = 6	nop
6FOD(11)-5%-200	24	3185	11	11	200	98	139	197	53.9	29.3	1.3
6FOD(11)-10%-200	28			12	235	107	156	237
6FOD(11)-15%-200	53			8	420	209	339	414
6FOD(11)-20%-200	67			11	810	326	537	798

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As can be seen in Table 6, the value of the optimized CO₂ permeability of macrovoids P_v predicted by the Maxwell model using our MATLAB optimization program is 3815 Barrer. Compared to the CO₂ permeability values calculated based on the Knudsen diffusion for a void space with average diameter of 5 nm (15 200 Barrer) or a pinhole with average diameter of 50 nm (152 000 Barrer),⁵⁴ this value is significantly smaller, although the average macrovoid diameters of the studied MMMs are ranging from 4.58 to 7.45 μm (Table 3). This result confirms the above assumption for the gas diffusion mechanism through the macrovoids.

Fig. 10 illustrates a comparison between the CO₂ permeability predicted by the Maxwell model with different shape factors n and the experimental data. Both n = 3 (spherical) and n = 6 (cylindrical or tubular) show a significant divergence with the experimental data. Their %AAREs are 53.9 and 29.3%, respectively. Interestingly, better agreement between the Maxwell model predictions and experimental data was observed when applying the optimized shape factors n_op (%AARE = 1.3%, see Table 6).

Fig. 10 Comparison between the CO₂ permeability predicted by the modified Maxwell model with different shape factors n and CO₂/CH₄ experimental data of the silica-6FOD(11) MMMs with different SiO₂ loadings.

The relation between macrovoid diameter and shape factor n is demonstrated in Fig. 11. The optimized shape factor n_op is a linear function of the average macrovoid diameter. This result is remarkably significant for the application of the Maxwell model to predict the gas permeation performance of any kind of MMM morphology.

Fig. 11 Shape factor (n) as a function of macrovoid average diameter.

5. Conclusions

Macrovoid structured mixed matrix membranes with nano-size (200 nm) silica particle and 6FDA-ODA-DAM co-polyimide were produced, which after high temperature treatment showed excellent performance for CO₂/CH₄ gas separation. These membranes have improved gas permeability (from 52 to 265 Barrer), ideal selectivity (from 24 to 32), and separation factor (from 22 to 34) compared to the original neat polymer membrane. Moreover, 6FOD(11)-10%-450 membrane could withstand pressure up to 600 psi without any loss of permselectivity. CO₂ and CH₄ permeabilities were found to increase with increasing SiO₂ loading (from 5 to 20 wt%), while ideal selectivities decreased due to low compatibility between SiO₂ particles and the polymer matrix. It is believed that a compatibilizing agent would be necessary at high loading to solve this problem. Also, membrane density and mechanical properties were found to decrease, while total void area or volume in the MMM increased with increasing SiO₂ loading.

A special use of shape factor n in the Maxwell equation was developed to predict the gas transport properties through MMMs for this new macrovoid MMM morphology. This work is an additional step to our recent comprehensive computational strategy to fit experimental permeation data of MMMs.⁵⁸ In this study, the modified Maxwell model predictions were in excellent agreement with experimental data having less than 2% deviation. Both intrinsic gas permeability of the dispersed phase (macrovoid) and shape factor (n) were simultaneously considered. The shape factor (n) was found to be strongly dependent on the foam-like morphology of these MMMs.

Notes and references

1. W. J. Koros and G. K. Fleming, J. Membr. Sci., 1993, 83, 1.
2. G. R. Pastor, J. F. Peters, W. K. Larsen and A. C. Iakovakis, U.S. Pat., 4753,666, 1988.
3. http://en.wikipedia.org/wiki/Natural_gas, accessed on 05.04.13.
4. S. Basu, A. L. Khan, A. Cano-Odena, C. Liu and I. F. J. Vankelecom, Chem. Soc. Rev., 2010, 39, 750.
5. W. J. Schell, J. Membr. Sci., 1985, 22, 217.
6. C. Liu and S. Kulprathipanja, Mixed-matrix membranes, in Zeolites in Industrial Separation and Catalysis, Wiley-VCH Verlag GmbH & Co., 2010, p. 329.
7. A. F. Ismail, P. S. Goh, S. M. Sanip and M. Aziz, Sep. Purif. Technol., 2009, 70, 12.
8. R. Mahajan and W. J. Koros, Ind. Eng. Chem. Res., 2000, 39, 2692.
9. O. G. Nik, X. Y. Chen and S. Kaliaguine, J. Membr. Sci., 2011, 379, 468.
10. H. Vinh-Thang, S. Kaliaguine, MOF-based mixed matrix membranes for industrial applications, in Coordination polymers and metal organic frameworks: Properties, types and applications, ed. O. L. Ortiz and L. D. Ramírez, Nova Science Publishers, Hauppauge, N. Y., USA, 2011, pp. 129–168.
11. X. Y. Chen, H. Vinh-Thang, D. Rodrigue and S. Kaliaguine, Ind. Eng. Chem. Res., 2012, 51, 6895.
12. X. Y. Chen, O. G. Nik, D. Rodrigue and S. Kaliaguine, Polymer, 2012, 53, 3269.
13. C. Joly, S. Goizet, J. C. Schrotter, J. Sanchez and M. Escoubes, J. Membr. Sci., 1997, 130, 63.
14. C. J. Cornelius and E. Marand, J. Membr. Sci., 2002, 202, 97.
15. C. Hibshman, C. J. Cornelius and E. Marand, J. Membr. Sci., 2003, 211, 25.
16. M. Iwata, T. Adachi, M. Tomidokoro, M. Ohta and T. Kobayashi, J. Appl. Polym. Sci., 2003, 88, 1752.
17. C. Hibshman, M. Mager and E. Marand, J. Membr. Sci., 2004, 229, 73.
18. F. Peng, L. Lu, H. Sun, Y. Wang, H. Wu and Z. Jiang, J. Membr. Sci., 2006, 275, 97.
19. F. Peng, L. Lu, H. Sun, Y. Wang, J. Liu and Z. Jiang, Chem. Mater., 2005, 17, 6790.
20. T. C. Merkel, B. D. Freeman, R. J. Spontak, Z. He, I. Pinnau, P. Meakin and A. J. Hill, Science, 2002, 296, 519.
21. C. Joly, M. Samaihi, L. Porcar and R. D. Noble, Chem. Mater., 1999, 11, 2331.
22. M. Moaddeb and W. J. Koros, J. Membr. Sci., 1997, 125, 143.
23. C. Hibshman, C. J. Cornelius and E. Marand, J. Membr. Sci., 2003, 211, 25.
24. T. Suzuki and Y. Yamada, Polym. Bull., 2005, 53, 139.
25. Y. Kong, H. Du, J. Yang, D. Shi, Y. Wang, Y. Zhang and W. Xin, Desalination, 2002, 146, 49.
26. J. H. Kim and Y. M. Lee, J. Membr. Sci., 2001, 193, 209.
27. R. H. Brzesowsky, G. de With, S. van den Cruijsem, I. J. M. Snijkers-Hendrickx, W. A. M. Wolter and J. G. van Lierop, J. Non-Cryst. Solids, 1998, 241, 27.
28. J. Livage and C. Sanchez, J. Non-Cryst. Solids, 1992, 145, 11.
29. A. Kioul and L. Mascia, J. Non-Cryst. Solids, 1994, 175, 169.
30. M. Smaihi, T. Jermoumi, J. Marignan and R. D. Noble, J. Membr. Sci., 1996, 116, 211.
31. M. Iwata, T. Adachi, M. Tomidokoro, M. Ohta and T. Kobayashi, J. Appl. Polym. Sci., 2003, 88, 1752.
32. D. Gomes, S. P. Nunes and K. V. Peinemann, J. Membr. Sci., 2005, 246, 13.
33. K. Kusakabe, K. Ichiki, J. Hayashi, H. Maeda and S. Morooka, J. Membr. Sci., 1996, 115, 65.
34. T. Suzuki, M. Miki and Y. Yamada, Eur. Polym. J., 2012, 48, 1504.
35. M. Miki, T. Suzuki and Y. Yamada, J. Appl. Polym. Sci., 2013, 130, 54.
36. T. Suzuki and Y. Yamada, US Pat., 20120202953, 2012.
37. M. A. Fardad, J. Mater. Sci., 2000, 35, 1835.
38. M. J. Kayser, M. X. Reinholdt and S. Kaliaguine, J. Phys. Chem. B, 2010, 114, 8387.
39. W. Stöber, A. Fink and E. Bohn, J. Colloid Interface Sci., 1968, 26, 62.
40. X. Y. Chen, D. Rodrigue and S. Kaliaguine, Sep. Purif. Technol., 2012, 86, 221.
41. R. Gosselin and D. Rodrigue, Polym. Test., 2005, 24, 1027.
42. Y. Liu, R. Wang and T. S. Chung, J. Membr. Sci., 2001, 189, 231.
43. S. Zhao, Z. Q. Shi, C. Y. Wang and M. M. Chen, J. Appl. Polym. Sci., 2008, 108, 1852.
44. K. P. Pramoda, S. L. Liu and T. S. Chung, Macromol. Mater. Eng., 2002, 287, 931.
45. L. J. Bellamy, The infra-red spectra of complex molecules, 3rd edn, Chapman and Hall, London, ch. 20, 1975.
46. T. M. Nair, M. G. Kumaran, G. Unnikrishnan and V. B. Pillai, J. Appl. Polym. Sci., 2009, 112, 72.
47. H. Voelker, G. Alicke, H. Schuch, M. Weilbacher and R. Weber, US Pat., 5,182,308, 1993.
48. R. Gendron, M. F. Champagne, Y. Delaviz and M. E. Polasky, J. Cell. Plast., 2006, 42, 127.
49. H. Kawakami, M. Mikawa and S. Nagaoka, J. Membr. Sci., 1996, 118, 223.
50. X. Y. Chen and D. Rodrigue, J. Cell. Plast., 2009, 45, 405.
51. H. B. Park, C. H. Jung, Y. M. Lee, A. J. Hill, S. J. Pas, S. T. Mudie, E. van Wagner, B. D. Freeman and D. J. Cookson, Science, 2007, 318, 254.
52. H. Vinh-Thang and S. Kaliaguine, Chem. Rev., 2013, 113, 4980.
53. J. C. Maxwell, Treatise on Electricity and Magnetism, Oxford University Press, London, 1873.
54. R. L. Hamilton and O. K. Crosser, Ind. Eng. Chem. Fundam., 1962, 1, 187.
55. D. Y. Kang, C. W. Jones and S. Nair, J. Membr. Sci., 2011, 381, 50.
56. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/menfre.html#c3.
57. D. D. Do, Adsorption Analysis: Equilibria and Kinetics, Series on Chemical Engineering, Imperial College Press, London, 1998, vol. 2.
58. H. Vinh-Thang and S. Kaliaguine, J. Membr. Sci., 2014, 452, 271.

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