Synthesis, characterization and gas separation properties of novel copolyimide membranes based on flexible etheric–aliphatic moieties

Abstract

The structural properties and gas permeation of a group of copolyimide membranes were investigated. The copolyimides used in this study were prepared using 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA) and 4,4′-oxydianyline (ODA) as aromatic diaminens and 4,9-dioxa-1,12-dodecanediamine (DODD), 1,13-diamino-4,7,10-trioxatridecane (TODD) and 1,8-diamino-3,6-dioxaoctane (DOO) as aliphatic diamines. Polymers were synthesized using random and block copolymerization methods via thermal imidization in a two step procedure. Reflectance-Fourier transform infrared spectroscopy (ATR-FTIR), dynamic mechanical thermal analysis (DMTA), thermal gravimetric analysis (TGA) and X-ray diffraction analysis (XRD) have been performed to characterize the synthesized copolyimides. The copolyimide with BTDA–ODA diamines showed higher T_g compared to the other polymers due to its fully aromatic structure. Gas permeation results reveal that the type of aliphatic diamines and polymer morphology can greatly affect the permeability of membranes for pure CO₂, CH₄, O₂ and N₂ gases. The gas permeability and selectivity of random copolyimides were higher than those of block copolyimides. The effects of temperature and feed pressure were also investigated. The permeability of all gases decreases slightly with increasing pressure. The results revealed that an increase in the temperature of the polymer matrix is able to increase the diffusivity and permeability of the membrane.

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1. Introduction

Membranes offer an attractive alternative to cryogenic or pressure swing adsorption processes for gas separation applications.^1–3 Polymeric gas separation membranes are used in a wide variety of areas such as air separation, separation of carbon dioxide from natural gas and removal of hydrogen from mixtures with hydrocarbons in petrochemical processing.^4,5

Some glassy polymers such as polyimides, polysulfones, polycarbonates and cellulose acetates and some rubbery polymers such as polyurethanes and polydimethylsiloxanes are introduced as proper polymers in manufacturing of gas separation membranes. Satisfactory results have been obtained in gas separation properties particularly for polyimides and polyurethane in glassy and rubbery polymers.^6–9 The improvement of the gas separation property of the polymeric membrane is the target of most research in this area.^10,11 Polymeric membranes with high permeability and high selectivity are desired for gas separation, but most materials known for this application follow trade off relation between permeability and selectivity.^12,13 Changing the chemical structure of polymer is the most common way to increase the membrane permeability without reduction in selectivity.^14–16

A lot of researches have been carried out to find the relationship between the chemical structure and gas separation properties of polyimides.^17–24 Polyimide membranes are synthesized using various diamines and dianhydrides in order to achieve better gas separation properties. These properties are directly related to the structure of polyimides, including the fractional free volume and inter chain distances that is affected by crystallinity of the polymer.^25–30

Up to now, many polyimide structures have been synthesized, however few of them are commercialized.^31,32 One of the famous commercial polyimide membrane is matrimid 5218 with permeabilities of about 2 and 4 barrer for O₂ and CO₂ gases, respectively.^33,34

Copolyimide structures can provide particular membranes by combining two monomers with different properties that cannot be achieved by homopolyimides.^35–40 Copolyimide structures are mostly synthesized using aromatic diamines but there are a few researches were reported on copolyimides with aliphatic diamines.

Tena et al. studied a set of copoly(ether-imide)s, synthesized by the reaction between an aromatic dianhydride (BPDA), a polyoxyalkyleneamine(poly(ethylene oxide)diamino terminated) (PEO-2000) and various aromatic diamines (PPD, BNZ, and ODA) under different thermal treatments. Results showed that increasing molecular weight of PEO from 6000 to 2000 g mol⁻¹ in the analogous copolyimides can lower the permeability significantly and slightly increase the selectivity for all studied gases.⁴¹

In another study, the semi aliphatic BTDA–DAH polyimide and its blends were synthesized using BTDA–ODA and BTDA–DDS polyimides in order to improve the H₂ gas selectivity. Their findings showed a decrease in chain packing for blend membranes compared with pure polyimide which leads to both higher fractional free volumes (FFV) and gas permeation rate. Also, their results revealed that, H₂/CH₄ separation factor of polyimide blends was among the highest reported data by other researchers using traditional membrane materials.⁴²

Regarding the literature, polyimide gas separation membranes have high selectivity and relatively low permeability. As a result, increasing permeability of polyimide membranes needs to be taken into consideration to improve gas separation performance. Aliphatic diamines have higher mobility and flexibility compared to aromatic diamines thus, they can be respected to improve gas permeability of polyimide membranes. Considering this fact that aromatic diamins have high selectivity, we have employed aliphatic–aromatic copolymers to achieve an enhanced gas separation performance.

In this study, block and random copolymerization methods were applied to investigate the effect of aliphatic ether moieties on gas permeation properties of copolyimides. Furthermore, the effects of pressure and temperature on permeability, diffusion and solubility coefficients of prepared copolyimides were investigated.

2. Experimental

2.1. Materials

The dianhydride monomer, 3,3′,4,4′-benzophenonetetracarboxylic dianhydride (BTDA), was purchased from Sigma-Aldrich (USA). The aliphatic diamine monomers, 4,9-dioxa-1,12-dodecanediamine (DODD), 1,13-diamino-4,7,10-trioxatridecane (TODD), 1,8-diamino-3,6-dioxaoctane (DOO), and aromatic diamine monomer, 4,4′-oxydianyline (ODA), were obtained from Merck (Germany). All of the monomers were purified by vacuum distillation prior to use. The dimethylacetamide (DMAc) supplied by Merck (Germany) was used as solvent. CO_2, N₂ and O₂ gases (purity 99.99) were purchased from Roham Gas Co. (Tehran, Iran) and CH₄ (purity 99.9) was obtained from Air Products Co.

2.2. Synthesis of poly(amic acid)

A series of homo and random copolyimides were synthesized based on ODA and three aliphatic diamines via conventional two-step procedure. Also for the comparison purpose, a block copolyimide was synthesized. The difference between the formation methods of block and random copolyimides was in the way of preparation of polyamic acid (PAA).

2.2.1. Random copolymerization. Initially, ODA was dissolved in a 100 ml three neck flask with 10 ml of dried DMAc under nitrogen atmosphere and at room temperature (25 °C). When ODA had completely dissolved in the solvent, aliphatic diamine was added to the mixture. The mixture was stirred continuously for 15 min at room temperature. In order to obtain polyamic acid, a stoichiometric proportion of anhydride/diamine(s) containing solvent was added to the reaction vessel and the reaction mixture was stirred for an additional 18 h (Fig. 1a).

Fig. 1 (a) Random copolymer (b) block copolymer.

2.2.2. Block copolymerization. ODA and DMAc were charged into a three neck flask and stirred for 15 min at room temperature (25 °C) until a homogeneous solution is achieved. Then, anhydride was added to the mixture. The mixture was stirred for 12 h until the reaction between anhydride and ODA was completed. In order to obtain polyamic acid, aliphatic diamine was added to reaction vessel and the reaction mixture was stirred at room temperature for an additional 12 h (Fig. 1b).

2.3. Polyimide synthesis and membrane preparation

Thermal imidization process was chosen to convert polyamic acid to polyimide. The PAA solution was spread out on the glass plate and baked at 80 °C during the night to remove the residual solvent. The films were imidized under vacuum by sequential heating at specified temperature for 1 h and up to 200 °C. Then films were heated up to 220 °C under atmospheric pressure and for 30 min. Films thicknesses were measured 30–50 μm. The synthetic route of polyimide is shown at Scheme 1. Table 1 shows the synthesized polyimides with their components molar ratio.

Scheme 1 Copolyimide synthetic route with different aliphatic diamines.

Table 1 Prepared membranes name with various aliphatic diamines

Polymer	Mole fraction of ODA	Mole fraction of aliphatic diamine	Type of polymerization
BTDA–ODA	100	0	—
BTDA–ODA–DOO	80	20	Random
BTDA–ODA–TOTD	80	20	Random
BTDA–ODA–DODD(80–20)(R)	80	20	Random
BTDA–ODA–DODD(80–20)(B)	80	20	Block
BTDA–ODA–DODD(60–40)(R)	60	40	Random
BTDA–ODA–DODD(60–40)(B)	60	40	Block

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2.4. Measurements of permeability and selectivity

The pure-gas permeation properties of synthesized copolyimides were measured using time-lag constant pressure/variable volume apparatus.^43,44

The permeability coefficients, P, diffusion coefficients, D, and solubility coefficients, S, were measured in temperature and pressure ranges of 25–45 °C and 3–10 bar, respectively. The effective permeation area (A) was about 13.1 cm². The volume of downstream side was constant (19.7 cm³) that comprised from a pressure transducer to show the total amount of gas which passed through the membrane.⁴³ At steady state, with a constant rise in the downstream pressure rate, eqn (1) was used to determine the permeability coefficient. The permeability coefficient is expressed in barrer, where 1 barrer = 10⁻¹⁰ cm³ (STP) cm cm⁻² s⁻¹ cmHg⁻¹. T₀ and P₀ are the standard temperature and pressure (T₀ = 273.15 K, P₀ = 1.013 bar), d is the thickness of the film (cm), T is the temperature and (dp/dt)_s is the slope of the plot of downstream pressure change versus time.

The diffusion coefficient (D) was determined by the time lag method, represented as:⁴⁵

where, θ is the time lag (s), i.e. the intercept obtained from extrapolating the linear region of the q versus the time plot. D is the diffusion coefficient (cm² s⁻¹).

The solubility coefficient (S) was then calculated from eqn (3):

S = P/D (3)

The ideal selectivity, α_A/B (the ratio of single gas permeabilities) of membranes was calculated from pure gas permeation experiments:

2.5. Characterization methods

Reflectance-Fourier transform infrared analyses (ATR-FTIR) were carried out using Tensor27 FT-IR (ATR, Bruker) in the range of 600–4000 cm⁻¹ to investigate the formation of imide groups in the synthesized polyimides. The thermogravimetric-differential thermal analysis (TG/DTA) curves of polymer films were recorded using Perkin Elmer Pyris Diamond TG/DTA thermal analyzer. Measurements were conducted under nitrogen atmosphere at the heating rate of 10 °C min⁻¹ from room temperature to 800 °C. Thermomechanical analysis (TMA) was carried out using diamond dynamic mechanical Perkin-Elmer pyris analyzer. Rectangular samples of 10 mm width and 20 mm length were cut from films. Tension tests were carried out from ambient temperature at 5 °C min⁻¹ under 1 Hz frequency. X-Ray diffraction analysis was carried out on a Philips X'Pert (Netherlands) using Cu radiation under a voltage of 40 kV, current of 40 mA and diffraction angle (2θ) of 5° to 60°. The average d-spacing was determined based on the Bragg's law:

nλ = 2d sin(θ) (5)

where, d is the d-spacing, λ is wavelength of radiation (λ = 1.54 Å), θ the scattering angle and n is an integer number (1, 2, 3…) related to the Bragg order. The obtained d-spacing reported in Table 2.

Table 2 Thermal and physical properties

Polymer	Mole fraction of diamine	ρ (g cm^−3)	FFV	d-Spacing (Å)	Tg (°C)	Tgg (°C)
BTDA–ODA	100–0	1.417	0.124	2.82, 3.20	272	120
BTDA–ODA–DOO	80–20	1.33	0.203	2.39, 3.56	197	—
BTDA–ODA–TOTD	80–20	1.228	0.241	2.29	230	115
BTDA–ODA–DODD(R)	80–20	1.220	0.240	2.23, 3.70	218	84
BTDA–ODA–DODD(B)	80–20	1.197	0.250	2.13, 3.20	228	85
BTDA–ODA–DODD(R)	60–40	1.18	0.270	2.13, 2.68	176	—
BTDA–ODA–DODD(B)	60–40	1.17	0.270	2.13, 3.20	211	71

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Polymer density (ρ) was measured by picknometer instrument. Fractional Free Volume (FFV) was calculated from the density data using the eqn (6).⁴⁶

where, V is the polymer specific volume (cm³ g⁻¹) and V_w is van der Waals volume (cm³). V_w was estimated by Hyperchem 7.0 software. This method has the advantage over bondi method due to optimization of polymer structure.⁴⁷

3. Results and discussion

3.1. ATR-FTIR spectra

ATR-FTIR spectra of synthesized polyimides (Fig. 2), display bands for symmetric and asymmetric C=O bonds of imide groups at 1720 and 1780 cm⁻¹, respectively. Also, the peak at 1690 cm⁻¹ which is related to poly(amic acid), was completely removed after imidization. The observations confirmed the occurrence of imidization process in the polymers.⁴¹ ATR-FTIR shows a peak around 1356 cm⁻¹ which corresponds to C–N bonds. Characteristic bands observed for CH₂ and CH groups (2920, 2860 cm⁻¹) in linear polyimides were not appeared in fully aromatic BTDA–ODA polyimide (Fig. 2b).⁴²

Fig. 2 ATR-FTIR spectra of synthesized polyimides.

3.2. Thermal analysis

Fig. 3 represents the decomposition behavior of the prepared membranes using TG/DTA. A similar trend was seen for synthesized copolymers, except for fully aromatic BTDA–ODA sample. Three plateaus could be seen in this graph. The first one (almost 2% weight loss) corresponds to the evaporation of remaining solvent and adsorbed water in the membranes (300–350 °C). This plateau happens at about 450 °C for fully aromatic BTDA–ODA sample that shows its higher thermal stability than other samples. The second plateau occurred at the range of 350–550 °C which corresponds to the degradation of aliphatic etheric groups (30–40% of weight loss). The polymer carbonization occurs at the temperature range of 550–800 °C in the final degradation step.⁴¹ It should be noted that the residual weight of completely aromatic membrane (BTDA–ODA) was greater than the other samples. Existence of aromatic groups in the polymer chain increase the ratio of carbon remained in the carbonized membranes and consequently residual polymer weight in the final degradation step.

Fig. 3 TGA curves for copolymer membranes.

Derivative thermal gravimetric (DTGA) was further used to study the thermal stability of polyimide polymers. These curves represent the degradation intensity in different temperatures. Fig. 4 shows these curves for BTDA–ODA, block and random BTDA–ODA–DODD membranes. Except for fully aromatic BTDA–ODA sample, two degradation peaks were observed for all of membranes; the first one is appeared at 400–450 °C and the other one at 570–600 °C which might be due to the degradation of aliphatic–etheric groups and aromatic groups in the polymer chains, respectively. In the case of BTDA–ODA sample, only one peak was observed at 572 °C (Fig. 4a). BTDA–ODA polymer does not have the aliphatic groups and the degradation was observed only at 572 °C while, all the polymers containing aliphatic groups demonstrate another degradation peak at 400–450 °C. These results reveals that the degradation of aliphatic groups happens at lower temperatures compared to aromatic groups which degrade at higher temperatures. DTGA curve for random and block copolymer structure BTDA–ODA–DODD(80–20) was shown in Fig. 4b. There are two distinctive peaks at the range of 410–435 °C and 560–580 °C in both copolymers. Also, the small peak has been appeared between these two peaks in random copolymers. In random copolymer, the intensity of the peak is greater at lower temperature compared to higher temperature, while it is vice versa for block copolymer. These differences in thermal degradation behavior of block and random copolymers could be explained via the phase segregation properties of the polymer chains. Random copolymers due to their lower phase segregation have more inter-connections between linear and aromatic moieties and the effect of each part on the other one is greater than those of block copolymers. So, the degradation temperatures of soft linear and aromatic hard segments in random copolymers would shift to higher and lower temperatures, respectively. In the case of block copolymer due to its higher phase segregation, the difference between degradation temperature of soft and hard moieties are higher than in random one. Comparison of the curves for BTDA–ODA–DODD(60–40)(B) and BTDA–ODA–DODD(80–20)(B) revealed that the degradation intensity at temperature range of 400–450 °C increases with the amount of aliphatic groups in the chain. Also, the degradation peak intensities in both low and high temperatures for BTDA–ODA–DODD(60–40)(B) are the same (Fig. 4c).

Fig. 4 TG/DTA curves of (a) BTDA–ODA, (b) BTDA–ODA–DODD(80–20) and (c) BTDA–ODA–DODD(B).

There is a strange peak appeared as a noise in BTDA–ODA–DODD copolymers which may be related to the inhomogeneity created by phase segregation of these kind of copolymers.

Dynamic mechanical analysis (DMA) has been applied to illustrate the thermal behavior of the synthesized polyimides (Fig. 5). In DMTA analysis tan δ shows the ratio of the loss modulus per storage modulus. The maximum peak shows the T_g of polymer and the other smaller peak in lower temperatures represents the secondary transitions. In glass transition temperature, because the most of the stress could damp by chain mobility the loss modulus shows a maximum and this maximum also appear at tan δ. In this study we reported the changes occurred on tan δ versus temperature (Fig. 5)

Fig. 5 DMA analysis for copolyimide membranes.

Table 2 represents the glass transition temperatures (T_g) and secondary transition temperatures (T_gg) of the prepared polymers.

The former could be used to compare chain mobility and free volume of the polymers.⁴⁸ Existence of linear groups in the polymer chains leads to lower glass transition temperature.

As expected, the BTDA–ODA sample has higher T_g than other structures due to its fully aromatic structure. It is also expected that T_g of BTDA–ODA–TOTD membrane be lowest among all the samples due to its longer aliphatic segment and more etheric group's content. However an opposite trend was observed which could be attributed to its higher molecular weight that dominates the flexibility. Since, the density of etheric groups in the chain of BTDA–ODA–DOO is higher than that of BTDA–ODA–DODD(80–20)(R), T_g of the former is lower than that of the latter. This implies that the etheric groups is dominant factor compared to the chain length for the purpose of flexibility improvement and consequently T_g reduction. Comparison of random and block copolymer structures revealed that the block copolymer has higher T_g than random one.⁴⁹ The isolation of soft and hard segments in the block structure put limits on long term chain mobility and leads to higher T_g. Also, it has been shown that the increase in the amount of aliphatic diamine improved the chain mobility and consequently caused more reduction in T_g. Data shows 10 °C difference between T_g value of block and random structures in the BTDA–ODA–DODD(80–20) copolymers, which is 35 °C for BTDA–ODA–DODD(60–40) copolymers. This could be attributed to the chain mobility of random BTDA–ODA–DODD(60–40) structure. It is worthwhile to note that T_gg has not been observed in BTDA–ODA–DODD(60–40)(R) copolymer while it has been appeared in the BTDA–ODA–DODD(60–40)(B) copolymer. By incorporation of soft aliphatic groups into block copolymer, the values of T_g and T_gg decreased 42 and 14 °C respectively.

3.3. Gas separation properties

3.3.1. Addition of aliphatic diamines to the polymer structure. To investigate the effect of aliphatic amines on structure of polymer and therefore the gas separation property, some physical properties of polyimides such as fractional free volume (FFV), density (ρ) and glass transition temperature (T_g) have been analyzed which are shown in Table 2. It is observed that the addition of aliphatic diamine to the polyimide structure can increases the FFV drastically (0.203–0.27) which could be attributed to increase in the mobility of polymer chains in presence of flexible aliphatic–etheric groups. Polyimides usually show the FFV value in the range of 0.12–0.19.⁵⁰

Gas permeability data are listed in Table 3. As shown in this table, the gas permeability increased by addition of aliphatic moieties in the polymer structure. Aliphatic diamines have small inter-chain separation due to their spatial arrangement and planar structure configuration. This phenomenon causes the small increment in gas permeability in spite of high increment in FFV.

Table 3 Permeability coefficients and selectivities at 10 bar and 35 °C

Structure	Permeability (barrer)^a				Selectivity
	CH4	N2	O2	CO2	CO2/CH4	CO2/N2	O2/N2	N2/CH4
a 1 barrer = 10^−10 cm^3 (STP) cm cm^−2 s^−1 cmHg^−1.
BTDA–ODA	0.0062	0.012	0.073	0.226	36.45	18.83	6.08	1.93
BTDA–ODA–DOO	0.0073	0.014	0.077	0.228	31.23	16.28	5.5	1.91
BTDA–ODA–TOTD	0.0090	0.015	0.080	0.236	26.22	15.73	5.33	1.66
BTDA–ODA–DODD(80–20)(R)	0.0140	0.027	0.133	0.576	41.14	21.33	4.92	1.92
BTDA–ODA–DODD(80–20)(B)	0.0125	0.024	0.110	0.433	36.64	18.04	4.58	1.92
BTDA–ODA–DODD(60–40)(R)	0.0350	0.056	0.176	0.587	16.77	10.48	3.14	1.60
BTDA–ODA–DODD(60–40)(B)	0.0330	0.052	0.161	0.488	14.78	9.38	3.09	1.57

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Diffusivity and solubility coefficients of studied membranes are reported in Tables 4 and 5. The obtained results show that the diffusivity coefficients of membranes were increased by incorporation of aliphatic diamine into polymer structure.

Table 4 Diffusion coefficients^a and diffusion selectivities at 10 bar and 35 °C

Structure	Diffusion coefficient				Selectivity
	CH4	N2	O2	CO2	CO2/CH4	CO2/N2	O2/N2	N2/CH4
a D (10^−10 cm^2 s^−1).
BTDA–ODA	1.75	6.36	20.95	9.61	5.49	1.51	3.29	3.63
BTDA–ODA–DOO	1.95	6.98	28.67	9.89	5.07	1.41	4.1	3.58
BTDA–ODA–TOTD	2.72	9.08	32.37	12.42	4.56	1.36	3.56	3.33
BTDA–ODA–DODD(80–20)(R)	3.31	12.76	49.87	24.65	7.44	1.93	3.90	3.85
BTDA–ODA–DODD(80–20)(B)	3.71	10.02	36.52	16.12	4.34	1.60	3.64	2.70
BTDA–ODA–DODD(60–40)(R)	5.21	18.38	52.34	25.65	4.92	1.39	2.85	3.52
BTDA–ODA–DODD(60–40)(B)	4.71	15.88	43.56	19.14	4.06	1.2	2.74	3.37

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Table 5 Solubility coefficients^a and solubility selectivities at 10 bar and 35 °C

Structure	Solubility coefficient				Selectivity
	CH4	N2	O2	CO2	CO2/CH4	CO2/N2	O2/N2	CH4/N2
a S (10^−3 cm^3 cm^−3 (cmHg)^−1).
BTDA–ODA	3.54	1.90	3.47	23.5	6.63	12.36	1.82	1.86
BTDA–ODA–DOO	3.74	2.01	2.68	23.05	6.16	11.46	1.33	1.86
BTDA–ODA–TOTD	3.31	1.65	2.47	19	5.74	11.51	1.49	2
BTDA–ODA–DODD(80–20)(R)	4.23	2.12	2.66	23.37	5.52	11.02	1.25	1.99
BTDA–ODA–DODD(80–20)(B)	3.37	2.40	3.01	26.86	7.97	11.19	1.25	1.40
BTDA–ODA–DODD(60–40)(R)	6.72	3.05	3.36	22.88	3.40	6.53	1.10	2.20
BTDA–ODA–DODD(60–40)(B)	7.01	3.27	3.70	25.50	3.63	7.79	1.13	2.14

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Diffusivity generally increased with the kinetic diameter of molecules except for CO₂ as following order:⁵¹

CH₄ (3.80 Å) < N₂ (3.64 Å) < CO₂ (3.30 Å) < O₂ (3.46 Å)

Two following major reasons are explaining why the diffusivity of O₂ is greater than that of CO₂. The first, asymmetric arrangement and twisting motion of CO₂ molecules make them more engaged with the polymer chain and the second, the interaction between the CO₂ molecules and polar groups of polyimide prevents the free motion of CO₂ within the polymer chain. This limitation decreases with increasing inter-chain separation.⁴

The solubility coefficients varied according to the critical temperature in the following order:

CO₂ > CH₄ > O₂ > N₂

The higher solubility of polar CO₂ gas is mainly due to its higher condensability and reactivity to polymer chains.

BTDA–ODA–DODD(80–20)(R) has greater FFV and consequently higher permeability than BTDA–ODA–DOO which could be attributed to its longer aliphatic diamines. The CO₂ and O₂ permeabilities in BTDA–ODA–DODD(80–20)(R) were 152 and 72% higher than BTDA–ODA–DOO sample. The pair gas selectivity for CO₂/CH₄ and CO₂/N₂ were increased 31.7 and 31% respectively. However, O₂/N₂ selectivity reduced 11.7% which can be attributed to the inter-chain separations (d–s). The permeability of CO₂ increased drastically in BTDA–ODA–DODD(80–20)(R) due to 3.7 Å d-spacing in this polymer. This amount of d-spacing may cause to significant restriction in penetration of large N₂ (3.64 Å) and CH₄ (3.8 Å) molecules and therefore reduction in permeability. Consequently the pair gas selectivities of CO₂/N₂ and CO₂/CH₄ increased. BTDA–ODA–DOO has the d-spacing of 3.56 Å which is bigger than the kinetic diameter of O₂ (3.46 Å) and smaller than the kinetic diameter of N₂ (3.64 Å). This leads to the higher O₂/N₂ selectivity in BTDA–ODA–DOO membrane compared to BTDA–ODA–DODD(80–20)(R) membrane. Also, diffusivity and diffusivity selectivity increased in this sample compared to BTDA–ODA–DODD(80–20)(R). However, solubility remained almost unchanged.

Results showed higher the etheric group's content and longer the chains, more flexible chain and consequently higher the permeability. There is an exception in our results which is not entirely clear now. Although BTDA–ODA–TOTD has higher etheric group's content and longer chains than BTDA–ODA–DOO, however they have the same permeability as.

BTDA–ODA–DODD(80–20)(R) has both improved permeability and selectivity than the other membranes which could be explained by the changes occurred in the polymer structure. The inter-chain separation in the structure of this polymer is about 3.7 Å which is larger and smaller than the kinetic diameters of CO₂ (3.3 Å) and CH₄ (3.8 Å) respectively and very close to kinetic diameter of N₂ (3.64 Å). So, the penetration of CH₄ and N₂ molecules across the polymer pores is more difficult than small CO₂ molecules. Table 3 shows that CO₂ gas had the highest promotion in permeability that leads to most efficient separation for CO₂/CH₄ and CO₂/N₂ pair gases. For example, the permeability of CO₂ and CH₄ raised 154 and 125% compared to the BTDA–ODA, respectively. Also, CO₂/CH₄ selectivity increased 12.8%. Diffusivity through BTDA–ODA–DODD(80–20)(R) sample increased based on the kinetic diameter of gases (Table 4). This increment was lower for CH₄ than the other gases due to the similarity between inter-chain separation and the size of molecule.

The increase in gas diffusivity of BTDA–ODA–DODD(80–20)(R) with respect to the BTDA–ODA polyimide is in the following order:

CO₂ (156%) > O₂ (138%) > N₂ (100%) > CH₄ (89%)

By increasing the amount of aliphatic amine from 20 to 40% in BTDA–ODA–DODD(R), the permeability coefficients increased while the gas selectivities dropped significantly as a result of increasing in FFV. E.g. the CO₂ permeability improved only 2% while the CO₂/CH₄ selectivity reduced by remarkable value of 60%. Moreover, diffusivity and solubility coefficients increased significantly for O₂, N₂ and CH₄ gases but solubility of CO₂ showed a slight reduction (less than 2%). The increasing in gas permeability and diffusivity of the studied gases were in the same trend with their molecular size.⁵²

The increase in gas permeability and diffusivity in the BTDA–ODA–DODD(80–20)(R) sample with respect to the BTDA–ODA–DODD(60–40)(R) polyimide structure are in the following order, respectively:

CH₄ (150%) > N₂ (107.4%) > O₂ (32.33%) > CO₂ (1.87%)

CH₄ (36.46%) > N₂ (30.57%) > O₂ (4.72%) > CO₂ (3.9%)

Fig. 6 shows a brief correlation between enhancements of transport properties, diffusion and permeability coefficients, versus molecular size of studied gases for BTDA–ODA–DODD(80–20)(R) and BTDA–ODA–DODD(60–40)(R) samples. As shown in this figure, the diffusivity and permeability of larger gas molecules enhanced more than smaller ones.

Fig. 6 Enhancement of transport properties versus molecular size of studied gases.

Fig. 7 shows the variation of diffusivity versus kinetic diameter of gases. Diffusivity of O₂, N₂ and CH₄ varied linearly (R-square of greater than 0.99) for all structures and were in good agreement with previously reported data.^51–54

Fig. 7 Correlation of diffusion coefficients to kinetic diameter of gases in membranes.

3.3.2. Random and block copolymerization. The effect of the copolymerization type on gas separation properties of synthesized copolyimides has been evaluated by comparing two type of random and blocks copolyimides. The FFV is identical in both block and random structures (Table 2). However, the higher permeability in random copolymers indicate further FFV and inter-chain separation in random structure than block structure. Most of the soft aliphatic diamines accumulate in one side of polymer chain and more phase segregation has been occurred in the block copolymers. Existence of phase separation between aliphatic soft and aromatic hard moieties in block copolymers causes gas molecules to pass through the soft portions of the chain and consequently a lower space is accessible for gas transport. However, in random copolymers the required space exists all over the structure due to the uniform distribution of soft segments in polymer structure. Increasing in the amount of aliphatic diamine up to 40% may change separation properties of block structure and makes it similar to that of random structure. The raised efficient volume and the further amounts of space provided for gas transfer through BTDA–ODA–DODD(60–40)(B) than BTDA–ODA–DODD(60–40)(R) sample accounts for this increment in phase separation. Also, higher diffusivity and lower solubility was observed for random structures. Diffusivity and solubility of block and random copolymers got closer to each other by increasing in aliphatic diamine content. The differences in gas diffusivities were more than solubilities which indicated that the type of copolymerization significantly affects diffusivities of gases.

3.3.3. Effect of pressure on performance of gas separation. Permeabilities of O₂, N₂, CH₄ and CO₂ were measured for BTDA–ODA–DODD(80–20)(B) membrane at temperature of 35 °C and pressures of 3, 5, 6.5 and 10 bar in order to evaluate the effect of pressure. The results are depicted in Table 6.

Table 6 Permeability coefficients and permselectivities as a function of feed pressure at 35 °C^a

Pressure	Permeability (barrer)				Selectivity
	CH4	N2	O2	CO2	CO2/CH4	CO2/N2	O2/N2	N2/CH4
a 1 barrer = 10^−10 cm^3 (STP) cm cm^−2 s^−1 cmHg^−1.
3	0.017	0.034	0.16	0.69	40.58	20.29	4.7	2
5	0.016	0.031	0.143	0.594	37.12	19.16	4.61	1.93
6.5	0.014	0.027	0.122	0.505	36.07	18.7	4.51	1.92
10	0.0125	0.024	0.11	0.433	34.64	18.04	4.58	1.92

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The permeability of all gases reduced with increasing pressure based on dual mode theory.⁵⁵ More reduction in permeability was observed for CO₂ (37.2%) which is the most condensable gas among the others. The obtained results showed that the permeability of gases has been reduced in proportion to their kinetic diameter. Furthermore, the selectivity of all gases decreased with increasing in pressure. The most and least decrease in selectivity was for the CO₂/CH₄ (14.6%) and O₂/N₂ (2.6%) pair gases, respectively.

Also, the solubility selectivity decreased while the diffusivity selectivity increased with increase in the pressure for CO₂/CH₄ pair gases. The reduction in amount of solubility selectivity was higher than the increase in diffusivity selectivity, and consequently the permeability pair gas selectivities reduced by pressure.

This can be explained by dual mode sorption model, which is a combination of Henry and Langmuir models.

C_A = C_DA + C_HA (7)

where, C_D and C_H represent the Henry and Langmuir's absorptions. The Henry's model is applied for the gas absorption in dense polymer while the Langmuir's model is related to absorption of gases in vacant spaces or trapped micro-volumes in glassy polymers. Eqn (7) can be rewritten in terms of pressure, as follow:where, K_D represents the Henry's law coefficient and is a measure of intrinsic interaction of polymer chains and gas molecules, C′_H is Langmuir absorption capacity, amounts of gas molecules that can saturate the pores of polymer matrix, and b is affinity constant or the ratio of rate constants for adsorption and desorption.

According to this model, gas absorption in the glassy polymer can be described as combination of absorption in dense polymer (Henry's models) and in vacant spaces of polymer matrix (Langmuir's model). Langmuir model which is related to free volumes of glassy polymer may play an important role in variations of gas permeability in glassy polymers with pressure. Langmuir's absorption is related to the solution of gas molecules in vacant sites and so the gas molecules need lower driving force to get absorbed in these regions. Therefore, Langmuir's absorption occurred more easily at low pressures compared to the Henry's absorption. Absorption in Henry's mode plays a significant role at high pressures when the Langmuir's regions have been saturated. Solubility coefficient is reduced as a result of increase in feed pressure. This reduction is higher for most soluble gases (Fig. 8). Based on the Koros and Paul partial immobilization theory,⁵⁶ the gas molecules that absorbed in Langmuir's regions have lower diffusivity than the ones absorbed in Henry's mode. So, the gases diffusivity coefficients in glassy polymers are lower at low pressures as absorption is dominated at Langmuir regions (Fig. 9). On the other hand, diffusivity begins to increase with increase in pressure and absorption at Henry's region. The permeability is defined as the multiplication of solubility coefficient and diffusivity. The solubility reduction with addition of pressure is greater than diffusivity raising, thus, the permeability has been decreased with increase in pressure.

Fig. 8 Pressure dependence on solubility coefficients in BTDA–ODA–DODD(80–20)(B) at 35 °C.

Fig. 9 Pressure dependence of diffusion coefficients in BTDA–ODA–DODD(80–20)(B) at 35 °C.

3.3.4. Effect of temperature on the performance of gas separation. The permeability, diffusivity and solubility coefficients of N₂, O₂, CH₄ and CO₂ were measured in BTDA–ODA–DODD(80–20)(B) membrane at 10 bar and temperatures of 25, 35, 45 °C. The results are shown in Fig. 10–13. The permeability and diffusivity of all gases increased, but the solubility decreased with temperature. Increasing temperature and therefore activation energy causes the increase in diffusivity while the solubility reduces due to the absorption of negative heat. Diffusivity is a stronger function of temperature than solubility (E_d + H_s > 0) and that is the main reason for the increase in permeability. Generally the permeability, diffusivity and solubility are described as function of temperatures by Arrhenius equations:

P = P₀ exp(−E_p/RT) (9)

D = D₀ exp(−E_d/RT) (10)

S = S₀ exp(−H_s/RT) (11)

where P₀, D₀ and S₀ are pre-exponential factors, E_p is activation energy for permeation, E_d is activation energy for diffusion and H_s is apparent absorbed heat. Table 7 shows the amounts of these coefficients.

Fig. 10 Temperature dependence of permeability coefficients in BTDA–ODA–DODD(80–20)(B) at 10 bar.

Fig. 11 Temperature dependence of selectivity in BTDA–ODA–DODD(80–20)(B) at 10 bar.

Fig. 12 Temperature dependence of diffusion coefficients in BTDA–ODA–DODD(80–20)(B) at 10 bar.

Fig. 13 Temperature dependence of solubility coefficients in BTDA–ODA–DODD(80–20)(B) at 10 bar.

Table 7 Arrhenius equation parameters for all gases

	CO2	O2	N2	CH4
P0 (barrer)	0.188	0.09	0.0026	0.0011
Ep (kcal mol^−1)	6.37	11.62	24.79	28.51
D0 (cm^2 s^−1)	5.34 × 10^−6	1.38 × 10^−5	14.43 × 10^−4	20 × 10^−4
Ed (kcal mol^−1)	20.7	20.98	36.34	39.85
S0 (cm^3 cm^−3 (cmHg)^−1)	10 × 10^−5	8 × 10^−5	2.8 × 10^−5	4.4 × 10^−5
Hs (kcal mol^−1)	−14.32	−9.33	−11.44	−11.32

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Selectivity reduced for various gas pairs as a result of temperature increase. Larger the size of penetrating gas, higher the permeation activation energy is. Therefore, permeation of larger gases grows more rapidly with temperature than the smaller ones and as a result the pair gas selectivities reduce. This reduction is more significant for CO₂/CH₄ compared to O₂/N₂ due to the higher difference in molecular size of CO₂ and CH₄. The selectivity of CO₂/CH₄ was reduced up to 44% while this was 38% for O₂/N₂ selectivity. The dependence of selectivity to the temperature is examined quantitatively by measuring the differences between gas diffusivity activation energies (ΔE_d,A,B). The negative amount of activation energy indicates the reduction in selectivity. Also, the reduction in gas selectivity can be explained by the changes in the mobility and the amount of free volumes in polymer. As known, the free volume and chain mobility increase as temperature increases. Consequently, separation of large and small molecules is less efficient.

4. Conclusion

In this research, a series of novel copolyimide membranes were synthesized based on aromatic and aliphatic–ether moieties. Also, the block and random structures of BTDA–ODA–DODD have been synthesized. TGA analysis showed two degradation steps for all membranes except for BTDA–ODA, one which was in the temperature range of 400–450 °C and the other at 570–600 °C. DTGA plot for block and random BTDA–ODA–DODD(80–20) structures showed two distinctive peaks at the range of 410–435 °C and 560–580 °C in both copolymers. The results showed that the influence of etheric groups is more important than the chain enlargement in increasing the flexibility and consequently T_g reduction. Aliphatic etheric parts improved the chains movement and consequently T_g shifts to lower temperatures. Comparison of BTDA–ODA–DODD(R) and BTDA–ODA–DODD(B) copolyimodes reveals that the latter has higher amount of T_g.

Random-copolymers have a better gas separation performance compared to block-copolymers due to uniform distribution of soft segments of aliphatic diamines in their matrix. Therefore, gas molecules have a good tendency to pass through matrix of random-copolymers. As a result, almost the whole polymer matrix is active for gas separation process.

TDA-ODA–DODD(80–20)(R) copolyimide membrane had the best performance in gas separation. The enhancement in selectivity of CO₂/CH₄ and CO₂/N₂ in this polymer in comparison to fully aromatic BTDA–ODA was 12.87% and 13.27%, respectively. Random copolyimide structure has higher permeability than block copolyimide due to more segmental mobility of the polymer chain. Also, the effect of pressure and temperature on gas permeation properties of BTDA–ODA–DODD(80–20)(B) membrane were studied. Results showed that increasing in pressure caused reduction of permeability, pair gas selectivity and solubility. Also, permeation and diffusion coefficients of all gases increased with increasing gas temperature, while solubility coefficients of gases decreased with increasing gas temperature.

Acknowledgements

The authors wish to thank National Iranian Gas Company (NIGC) for financial support of this study.

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