Investigation of the Gas Separation Properties of Polyurethane Membranes in Presence of Boehmite Nanoparticles

In this study, the effect of boehmite nanoparticles on the CO2, CH4, O2, and N2 permeability in polyurethane membranes was investigated. Boehmite nanoparticles were synthesized by the hydrothermal method using the salt of aluminum nitrate Al (NO3)3 and diethanolamine as a precipitating agent. Different temperatures (110, 160, and 200) °C and times (18–24 h) in synthesizing boehmite nanoparticles are also investigated. The characteristics of the synthesized nanoparticles were analyzed with X-ray diffraction (XRD), Field-emission scanning electron microscopy (FESEM), and Transmission electron microscopy (TEM). The analysis results represented that increasing the temperature to 200 °C as well as high duration time at this temperature (24 h) result in nanoparticles with high purity and high crystallinity. Polyurethane was synthesized by bulk two-step polymerization using hexamethylene diisocyanate (HMDI) and 1,4-butanediol (BDO) as hard segments and poly(tetramethylene glycol) (PTMG, 2,000 g/mol) as the soft segment. The synthesized polymer was in a molar ratio: PTMG: HMDI: BDO = 1:3:2. PU membranes and PU-boehmite nanocomposite membranes were prepared using solution casting and solvent evaporation technique. The characteristics of the synthesized nanocomposite membranes were analyzed with Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), Field-emission scanning electron microscopy (FESEM), and differential scanning calorimetry (DSC). The results of characterization analyses indicated that there is a strong interaction between boehmite nanoparticles and polymer and also the appropriate distribution of boehmite nanoparticles in the prepared samples. Gas permeation properties of polyurethane—boehmite nanocomposite at different boehmite loadings (0, 5, 10, 15, and 20 wt.%) were studied for pure CO2, CH4, O2, and N2 gases at 8 bar and 30 °C. The obtained results indicated that the reduction in permeability of all gases but enhancement in CO2/N2, CO2/CH4, and O2/N2 selectivities were observed as boehmite content increases. In the membrane with 20 wt.% boehmite content, enhancement of CO2/N2 (65.33%) and CO2/CH4 (55.37%) selectivities were observed in comparison with pure polyurethane, while the CO2 permeability reduction of polyurethane–boehmite membranes was 22.08%.


Introduction
Today, membrane technology has been considered in many industries such as oil, gas, petrochemical, pharmaceutical, semiconductor, biotechnology, and the environment. Since the cost of energy consumption is increasing rapidly, the use of membrane technology is increasing, especially in the gas separation industry. Due to its unique features such as stability, high efficiency, and process simplicity, the membrane process plays a very influential role in reducing costs and environmental problems [1,2]. Materials usually used to make membranes for the gas separation process include carbon, ceramics, and polymers [2]. Polymeric membranes with favorable selectivity and permeability are those used mostly for gas separation applications.
Polymeric membranes used in gas separation can be classified into two categories: rubber and glass. Polyurethanes (PUs) are a well-known class of rubbery polymer structures [3]. Recent research shows that PU membranes are good candidates for gas separation membranes because of their 1 3 high mechanical properties, thermal stability as well as high gas separation performance.
PU polymeric materials consist of a group of hard and soft segments [4]. Components of PU polymers include complex urethane or urea segments and soft segments based on polyester or polyether [5].
The two main characteristics of membranes are permeability and selectivity. Studies of gas transfer properties with PU membranes show that permeability increases with decreasing urethane segment content and increasing molar mass of polyether segments [6].
The performance of polymeric membranes in gas separation is the most effective factor in the economy of separation. Therefore, many attempts by different researchers have been made in the past years to maximize membrane performance [7].
The chemical modification of polymer structures and embedding of inorganic fillers into polymer matrix have been proposed by different researchers as an efficient technique to improve gas separation properties of different polymeric membranes. The most important of these fillers include porous metal-organic frameworks (MOFs), polyhedral oligomeric silsesquioxane (POSS), zeolites, carbon molecular sieves, alumina, and nonporous silica [3,[7][8][9][10][11]. By incorporating inorganic filler with favorable gas separation properties into the polymer matrix, it is expected that an increase in overall selectivity can be achieved with a minimal reduction in permeability or vice versa [12].
Sadeghi et al. investigated the effect of silica nanoparticles on gas penetration properties based on polyurethane membrane polyester. The transfer properties of polyurethane-silica nanocomposite membranes with silica content of 2.5, 5, 10, and 20% by weight for pure CO 2 , CH 4 , N 2 , and O 2 were studied. The results show a decrease in the permeability of all gases but an increase in the selectivity of CO 2 / N 2 , CO 2 /CH 4 , and O 2 /N 2 . In polyurethane-silica nanocomposite membrane (20% by weight), CO 2 /N 2 selectivity was 1.65 times that of pure polyurethane. While the reduction of CO 2 permeability of polyurethane-silica membranes compared to pure polyurethane was 35.6% [6].
Sadeghi et al. looked into the impact of silica nanoparticles on the gas permeability capabilities of polycaprolactone-based polyurethane membranes in 2013. The capabilities of these mixed membranes for pure CO 2 , CH 4 , N 2 , and O 2 gases were investigated. The results demonstrated a decrease in gas permeability but an increase in ideal selectivity for CO 2 /N 2 , CO 2 /CH 4 , and O 2 /N 2 [13].
Santos et al. synthesized and characterized a variety of PU/silica xerogels functionalized with RTILs (bmim Cl and bmim TF2N). The pressure-decay approach was used to determine CO 2 sorption capacity and reusability at 298.15K and 1 bar. According to the findings, the filler aggregation in the PU matrix enhanced the loss of mechanical characteristics. The addition of silica xerogels functionalized with RTILs to the PU matrix, on the other hand, resulted in higher CO 2 uptake [14].
Sadeghi et al. studied the effect of TiO 2 nanoparticles on the gas separation properties of PU. At 10 bar and 25 °C, gas permeation capabilities of PU-TiO 2 nanocomposite membranes with TiO 2 concentrations up to 30 wt.% were investigated for N 2 , O 2 , CH 4 , and CO 2 . As the TiO 2 content increases, the permeability of the investigated gases decreases, and gas selectivities increase [7].
Ghalei et al. used tetraethoxysilane (TEOS) as a silica monomer and a low concentration of polyethylene oxidepolypropylene oxide block copolymer (pluronic) with polyvinyl alcohol (PVA) as templating agents to make siliconbased particles. Compared to typical silica particles, the synthesized particles had a greater polarity. The results of gas transport properties of CO 2 , CH 4 , O 2 , and N 2 showed that when the modified silica concentration increased, the permeabilities of CH 4 and CO 2 increased while those of other gases declined [3].
In this work, we used boehmite for the first time to improve the performance of PU membranes in the gas separation process. For this purpose, boehmite nanoparticles were first synthesized. In the synthesis of boehmite by the hydrothermal method which is a controllable method, the salt of aluminum nitrate Al(NO 3 ) 3 and diethanolamine as a precipitating agent was used. The effect of different temperatures and times in synthesizing boehmite nanoparticles is also investigated. The synthesized boehmite nanoparticles were applied to modify the structure of the polyurethane membranes. Polyurethane was synthesized using hexamethylene diisocyanate (HMDI) and 1,4-butanediol (BDO) as hard segment and poly(tetramethylene glycol) (PTMG, 2,000 g/mol) as the soft segment. The synthesized polymer was in a molar ratio: PTMG: HMDI: BDO = 1:3:2. PU membranes were prepared by solution casting and solvent evaporation method. Structural characteristics of these membranes were studied by FTIR, DSC, and FESEM.

Synthesis of Boehmine Samples
First, Al (NO 3 ) 3 . 9H 2 O (14 gr) was added to 100 ml of deionized water under vigorous magnetic stirring at room temperature to achieve solution A. Ethylenediamine (8 ml) was dissolved into 50 ml of deionized water at room temperature under vigorous stirring to obtain solution B. Solution B was subsequently added drop by drop to the solution A to give lacteous precipitates immediately. At this point, the pH value of the reaction mixture was 8-8.5. The obtained suspension was transferred into a 300 ml stainless steel autoclave and heated for (18 and 24) hours at (110, 160, and 200) °C. The autoclave was subsequently allowed to cool in the air at room temperature with natural convection. The resultant colloidal product was centrifuged and washed several times with deionized water and ethanol and dried at 60 °C in a vacuum for 12 h. The detailed experimental parameters concerning heating temperature and reaction time for corresponding boehmite samples are listed in Table 1.

Polyurethane Synthesis
The polyurethanes are synthesized by the bulk two-step polymerization method as explained elsewhere [15,16]. Microdiisocyanate prepolymer was synthesized by reacting poly tetramethylene glycol (PTMG, MW = 2000 g. mol −1 ) and hexamethylene diisocyanate (HMDI), for 2.5 h at 85-90 °C under nitrogen atmosphere. 1.0 wt.% DBTDL solution in THF was used as a catalyst. The chain extension of the prepolymer was performed by adding 1,4-butanediol (BDO), to the reaction media at room temperature. To obtain a linear polymer, the NCO/OH molar ratio of 1 was used in the reaction. The molar ratio of the reaction components has been adjusted as follows: PTMG: HMDI: BDO = 1:3:2.

Preparation of PU Membrane
PU membranes were prepared by a solution casting and a solvent evaporation technique. Synthesized thermo-plastic PU was dissolved in DMF to obtain a 10 wt.% solution at 70 °C and the polymer solution was cast on a Teflon petridish and maintained for 2 days at ambient temperature to allow the solvent to evaporate. In order to completely remove the solvent, prepared membranes were detached from the glass plates and dried in a vacuum oven at70 °C for12 h.
The mixture was then stirred to form a homogeneous solution at 70 °C. Then the dope solution was filtered and cast on a petri dish. The resultant was maintained for 2 days at ambient temperature to allow the solvent to evaporate. Finally, the prepared film was placed in a vacuum oven at 70 °C for 12 h for complete removal of the solvent.

Characterization
X-ray diffraction (XRD) patterns of boehmite samples and PU-boehmite nanocomposite membranes were recorded on a Bruker D8 Advance X-ray diffractometer with a Cu Kα anode (λ = 0.1542 nm) operating at 40 kV and 30 mA. The morphology of the boehmite nanoparticles and PUboehmite nanocomposite membranes are observed using Field emission scanning electron microscopy (FESEM, HITACHI S-4160) images.
TEM images of boehmite samples were obtained using a Philips CM30 microscope operating at 250 kV to investigate the dispersion and metal particle size of the particles.
FTIR spectra for PU-boehmite nanocomposite membranes were performed in the absorbance mode. WQF-510 Fourier transforms spectrometer (Rayleigh Optics, China) equipped with a KBr beam splitter and DLA TGS (deuterated Lanthanide triglycine sulfate) detector and μMAX IR microscope (PIKE Technologies, USA). The spectra were scanned in the mid-IR range from 400 to 4000 cm −1 .
The glass transition temperature (T g ), and melting temperature (T m ) of the PU-boehmite nanocomposite membranes were determined by differential scanning calorimetry (DSC) analysis. It was performed by using a DSC (model 823 e, Mettler Toledo, Switzerland) instrument. In this case, the samples (8 mg) were heated from −100 to 250 °C at a rate of 10 °C/min under the nitrogen atmosphere.

Gas Permeation Measurements
The permeability of pure gases O 2 , N 2 , CH 4 , and CO 2 is measured by the constant pressure method. The feed side pressure of the membrane cell is kept at a pressure of 8 bar and a temperature of 30 °C whereas the permeate side was maintained at atmospheric pressure. Also, the effective membrane surface area is 17.72 cm 2 . The permeability of pure gases was calculated from the following equation: where P is gas permeability expressed in barrer (1 barrer = 10 -10 cm 3 (STP) cm/cm 2 S.cmHg), q is the gas flow flux that passes through the membrane (cm 3 /s), L is membrane thickness (cm), P 1 and P 2 is the absolute pressure on the feed side and the gas side passing through the membrane (cmHg), and A is effective membrane area (cm 2 ). The permselectivities ( A∕B ) of membranes, was calculated from pure gas permeation experiments as follows: All data are based on pure gas measurements at steadystate conditions.

XRD Analysis
Assisted with the XRD technique, we characterized the phase, purity, and crystallinity of the as-prepared boehmite samples synthesized by the hydrothermal method. The X-ray diffraction patterns of the boehmite sample at different times and temperatures of hydrothermal reaction are presented in Fig. 1. The boehmite crystal phase in the XRD analysis shows that all the diffraction peaks of the synthesized sample are orthorhombic and are in complete agreement with diffraction card no γ -AlOOH (JCPDS 21-1307). No peaks for other phases such as Al(OH) 3 or Al 2 O 3 were observed, indicating its high purity and crystallinity. The main peaks of γ-AlOOH in the XRD pattern (020, 120, 031, 131, 051, 220, 151, 080, 231, 171, and 251) [17] are narrowed implying that the γ-AlOOH nanostructures are well crystallized.
According to Fig. 1, it is clear that with increasing reaction time and temperature, samples tend to crystallite. More specifically, it can be observed that the intensity of the peak corresponding to the (020) crystal plane is extraordinarily strong as compared to other peaks. Therefore, it can be concluded that increasing the temperature to 200 °C as well as high duration time at this temperature (24 h) results in nanoparticles with high purity and high crystallinity.  Table 1 with different magnifications (1 µm, 500 nm, and 300 nm). The effect of time and temperature of hydrothermal reaction on the morphology of synthesized boehmite was also shown in Figs. 2, 3, 4, 5. Figure 2 represents a synthesized boehmite at a temperature of 110 °C for 24 h. The reason for the synthesis of boehmite particles at this temperature is the reduction of initial production costs and ultimately the production cost. According to the images, it can be observed that the obtained sample is in the form of nanorod particles that have a very high aggregation and adhesion. High magnification images show that the synthesized samples have collapsed and become clumpy. The bright spots, which are seen as light bulbs, indicate the presence of impurities in the sample. According to the image with a magnification of 300 nm, it can be seen that the depression between the particles is such that the nanoparticles stick to each other and form a non-uniform plate. Figure 3 shows the boehmite nanoparticles synthesized at 160 °C for 18 h. According to the images, it can be seen that the boehmite samples synthesized at this temperature still retained the rod-shaped structure, but the particle size became smaller and the nanorods did not accumulate as in Fig. 3, indicating an increase in efficiency at 160 °C compared to 110 °C. Images at 300 nm magnification also show that the nanorods are stacked next to each other. Figure 4 shows the FESEM images synthesized at 200 °C and 24 h. According to the images, it can be seen that in this sample, nanoparticles are also in the form of rods. High magnification images show that the synthesized nanostructures are partly separate. The main reason is the appropriate temperature and time of the hydrothermal reaction.

FTIR Analysis
FTIR spectra were used for characterizing the structure of the pure PUs, and PU-boehmite nanocomposite membranes. The FTIR results are shown in Fig. 7. As can be seen, the strong peak at 555 and 855 cm −1 which belongs to boehmite, is observed in all PU-boehmite membranes, confirming the presence of nanoparticles in hybrid membranes [18]. The absence of the NCO peak at 2270 cm −1 indicates the completion of the reaction. N-H stretching of urethanes and C=O peaks appears at around 3300 and 1730-1670 cm −1 , respectively. The peak of urethane ether linkage is at 1117-1100 cm −1 . [19]. According to Fig. 7, by comparing the spectra of pure PU and PU-boehmite nanocomposite membranes, the effects of boehmite nanoparticles on the phase separation of hard and soft segments of prepared membranes, and possible interactions between boehmite and polyurethane membrane since changes in the hydrogen bonding character of polyurethane matrix by the incorporation of boehmite nanoparticles can be easily detected.
For this purpose, we focus on specific regions in Fig. 7, where strong absorptions were observed by the urethane group (specifically N-H and C=O absorption bands), and the ether group. Peak shifts and shape changes especially at the hydroxyl and amine, carbonyl, and ether regions, for the hard and soft segments are indications of an interaction between the boehmite and the PU membrane [16].
As shown in Fig. 7, No dramatic change in the peak shape or position of the absorption band at the 3300 cm −1 (N-H) for PU-boehmite nanocomposite membrane containing 10% by weight of boehmite is seen. On the other hand, the width of the peak corresponding to N-H groups increases with an increasing amount of boehmite up to 20% by weight in the polymer. The OH groups on the boehmite surface may form a hydrogen bond with carbonyl groups or/ and N-H groups of urethane in the hard segment or ether groups in soft segments [16]. The broadening of the peaks is attributed to the overlap of N-H and OH frequencies and/or also due to the distribution of hydrogen bonds with urethane N-H groups by incorporation of a part of boehmite. [19,20]. For a more accurate investigation of hydrogen bonding between hard and soft segments in these PU synthesized membranes, in the FT-IR spectra, peaks of carbonyl groups were assessed. As seen in Fig. 7, the FTIR spectrum of pure and hybrid membranes shows a peak with a maximum at 1683 cm −1 with a shoulder at 1726 cm −1 , which were attributed to the H-bonded and free urethane carbonyl bands [21]. As seen in Fig. 7, for PU the intensity of these two bonds is approximately equal. Moreover, with increasing boehmite nanoparticles to 10 wt.% the intensity of the hydrogen-bonded carbonyl bond increases dramatically. Finally, at 20 wt.% the intensity of these two bonds does not much change compared to 10% by weight.
This increase in the peak intensity of bonded carbonyl group may be related to the hydrogen bond between boehmite particles and ether groups in soft segments of PU. As OH groups in boehmite interact with ether groups in the soft segments of polyol in polyurethane, the number of available ether groups of soft segments to create hydrogen bond with the N-H groups reduces, and hence urethane N-H groups interact more with carbonyl groups of hard segments of urethane. In this situation reduction in hydrogen bonding between ether groups of soft segments and urethane groups of hard segments result in intensification of bonded carbonyl peak and increasing microphase separation [3,6,7,16].
The FTIR spectrum in the ether region is also shown in Fig. 7. As mentioned above, the band observed at 1117 cm −1 in FTIR spectra of PU was attributed to the hydrogen bonding interaction between N-H and C-O-C groups [16]. As shown in Fig. 7, when the ether region of the FTIR spectra is investigated, the peaks at the ether region of the spectrum shift to lower wavenumbers as a function of the amount of boehmite incorporation. This observation indicates with an increasing amount of boehmite nanoparticles in the PU, hydrogen bonding between the hydroxyl groups on the boehmite surface and the oxygen atoms in the ether linkages of the PTMG due to an increase in the surface contact area, and several hydroxyl groups exist formed [16].
It is well known that in PU (N-H) groups form hydrogen bonds with both the carbonyl (C=O) of the hard segments and the oxygen (-O -) in the polyether soft segment [16]. Considering the FTIR results, it can be concluded that by increasing boehmite nanoparticles to 10 wt.%, nanoparticles tend to be more dispersed in the soft segments compared to hard segments of the polymer. Result in the replacement of hydrogen bonding between N-H groups and ether groups with the hydrogen bond between the boehmite's OH groups and the ether groups of polyol in a soft segment of PU. Therefore, the amount of available ethereal pieces of soft segments groups to create hydrogen bond with the N-H groups reduces, and hence urethane N-H groups interact more with carbonyl groups of hard segments of urethane which lead to the intensification of peaks at region 1683 cm −1 (bonded C=O) and shift peak to right at ethereal region (1107 cm −1 (C-O-C)) in the FTIR spectra.
FTIR results were also indicated that with increasing the content of boehmite nanoparticles to 20wt.%, a portion of the boehmite nanoparticles is distributed in soft segments of the polymer by the interaction of OH groups in boehmite with ether groups of polyol which lead to shifted the peak of the ethereal region to lower wavenumbers as a function of the amount of boehmite incorporation (1100 cm −1 ). On the other hand, the other portion of the boehmite may interact with N-H groups of the hard segment of PU and disrupt the hydrogen bonding between urethane carbonyl groups and the urethane N-H groups in the hard segments resulting in the broadening of the N-H peak by adding 20 wt.% boehmite to PU.

DSC Analysis
Thermal analysis of the polyurethane membranes was performed by DSC measurements. The DSC thermograms of pure PU and PU-boehmite nanocomposite membranes are depicted in Fig. 8. The glass transition temperature (T g ) of PU is between −79.81 °C and −76.49 °C which is related to PTMG, the soft segment in PU structure (Fig. 8). Higher Tg of PUs compared to pure PTMG (around −88 °C) is ascribed to the phase mixing between the soft and hard segments [3].
The glass transition temperature is one of the most important criteria for comparing the chain mobility of the polymers. According to Fig. 8, the T g of hybrid membranes shows a slight increase with the increase of boehmite content. In comparison with PU, the T g of PU + 10 wt.% boehmite nanoparticles, and PU + 20wt.% boehmite nanoparticles shift from −79.81 to −78.45 °C and −77.49 °C. This should be attributed to the hydrogen bonding between boehmite nanoparticles and polyol chains; a decrease in the mobility of chains was expected. These interactions enhance the rigidity of the soft segments [22] and limit the movement or motions of the soft segments. Therefore, the introduction of nano-particles results in a slight increase in glass transition temperatures of the soft segments. Figure 8 also shows an endothermic peak at the temperature of 10-35 °C that may be attributed to the crystals formed in the soft segments. Due to the higher molecular mobility of the soft segments, this T m appeared at lower temperatures. The results indicated that by increasing the boehmite concentration, the crystalline peak of the soft segments appears at a higher temperature compared to the PU. This behavior is related to strong interactions and hydrogen bonding between the hydroxyl groups on the surface of particles and PU chains which may be restricting the mobility of PU chains. Therefore, it can be concluded that most boehmite nanoparticles are distributed in soft segments [20].

XRD Analysis
The effects of the nanoparticles on the morphological behavior of the prepared PU membranes were investigated using XRD analysis. A broad peak, at 2θ = 22.02°, can be identified by considering the spectra of the pure PUs in Fig. 9, indicating the existence of amorphous structure or small crystalline regions of prepared PU membrane. From Fig. 9, a sharp and strong peak appearing at 2θ = 19.8° in pure PU also relate to the crystalline structure of PTMG (as shown in the DSC thermograms) in the structure of pure PU [23].
With the insertion of boehmite into the PU matrix, the intensity of the broad peaks in the structure of PU decreases, implying that the ordered structure in PU chains is reduced. This is reasonable because the presence of the boehmite in the soft segments disrupted the chain packing and crystallinity. The dispersion of the boehmite nanoparticles in the soft segment might likely weaken the hydrogen bond interaction between the soft and hard segments. Instead, it creates a strong interaction between PU and boehmite. This observation was reported elsewhere [23,24].
The results from the XRD pattern of boehmite with PUboehmite composite membranes in Fig. 9 show that boehmite particles existed in the nanocomposite membranes. By increasing the amounts of nanoparticles in the samples, the intensity of the peaks related to boehmite becomes slightly stronger. The increase in the intensity of peaks suggests that the interface adhesion is strong between inorganic additives and organic polymer structure due to the structural modification [7,25].  Figure 10 shows the FESEM photographs of the PU and PU-boehmite composite membranes. To investigate the dispersion and compatibility between the nanoparticles and the polymer matrix cross-sectional micrographs of the polyurethane-boehmite hybrid membranes with 0, 10, and 20 wt.% boehmite nanoparticles were used and presented in Fig. 10. As can be seen, the membranes are quite dense and the presence and distribution of boehmite nanoparticles in prepared membranes are evident. The approximate average size of boehmite nanoparticles in the membrane is also estimated at 50 nm. As demonstrated in the FESEM images, there are two types of dispersion of boehmite nanoparticles in the polymers. There are some particles with no aggregation which indicates effective nanoscale mixing and homogeneous dispersion into the polymer matrix. Some of the particles, however, aggregated together to form larger particles within the polymer. As shown in the FESEM images most of the aggregated particles are smaller than 180 nm in size. Moreover, aggregation and roughness increase with the increasing percentage of boehmite nanoparticles in PU membranes.

Gas Permeation Performance
The permeability of nitrogen, oxygen, methane, and carbon dioxide gases and the permselectivities of gas pairs in PU and PU-boehmite nanocomposite membranes were measured at a pressure of 8 bar and a temperature of 30 °C. Figure 11 represents the permeability results of the gases in pure PU and PU-boehmite composite membranes. As can be elucidated from Fig. 11, the permeability of gases in pure PU membrane varies in the following order: P(CO 2 ) > > P ( CH 4 ) > P(O 2 ) > P(N 2 ).
The higher permeability of CO 2 in comparison with other gases is related to its low kinetic diameter and high condensability, which facilitate the penetration of this gas in the membranes [26]. In addition, CO 2 as a polar gas can interact with the polar ethereal groups in the soft segments of the synthesized PUs [20]. Table 2, shows the condensability and kinetic diameter of pure gases [27]. As shown in Table 2, the kinetic diameter of methane is greater than nitrogen and oxygen molecules, but the permeability   Fig. 11 indicates more permeation of methane in comparison with oxygen and nitrogen. The difference observed in the permeability results of the membranes can be explained through the solution-diffusion mechanism [6].
The diffusivity is dependent on the kinetic diameter of the permeant gases through the membranes so that the diffusivity of a gas is increased upon the reduction of the kinetic diameter of the gas [28].
The solubility is dependent on the condensability of the permeate gases within the membrane, and the condensability itself is related to the critical temperature of the gases. In other words, solubility coefficients of gases well correlate with their critical temperature. According to the critical temperature of carbon dioxide, methane, oxygen and nitrogen (T C , CO2 = 304.2K T C , CH4 = 190.6K, T C , O2 = 154.6K, and T C , N2 = 126.2K), synthesized polyurethane membranes are permeable to methane than to nitrogen. Therefore, CO 2 with the highest condensability would be expected to have the highest permeability and N 2 with the lowest condensability would be expected to have the lowest permeability [3,21] This behavior reveals the predominance of a solution mechanism for the gas permeation process in the PUs membranes. In the rubbery polymer matrix, solubility is the dominant mechanism in the permeation of gases through a rubbery polymer matrix; consequently, the permeability of these polymers is controlled by solubility. Therefore, the synthesized PUs in this study exhibit typical rubbery polymer properties. The above results are consistent with the work of other researchers [3,6,7,19].
As shown in Fig. 11, the permeability of all gases decreased by increasing the number of boehmite nanoparticles in the polyurethanes.
In PU membranes, soft segment domains are formed as a result of microphase separation. Soft and flexible polyol segments of PU alone have the necessary flexibility and movement to create space for the movement of gas molecules and are permeable to gases, whereas the hard segment domains act as an impermeable barrier [29]. In the case of PU-boehmite nanocomposite membranes, there are two hard and soft segment regions for the distribution of boehmite nanoparticles. From an entropic point of view, it appears that boehmite nanoparticles prefer to distribute in the hard segment of PU [30]. However, FTIR and DSC (increase in Tg of the soft. segments) results indicated that the particles were mostly located in the soft regions. Also, the decrease in permeability of all gases by increasing the number of boehmite nanoparticles in the polyurethanes as shown in Fig. 11, is the main reason for the distribution of the greatest number of boehmite nanoparticles in the soft segments.
So, gas permeability reduction could be attributed to two factors: the presence of additional dense particles such as boehmite nanoparticles decrease the free volume, restrain the polymer chain movements, and makes the diffusion path a tortuous one for gas molecules to pass through the membrane. Therefore, the diffusion of larger molecules size of gas molecules becomes more limited. The second is the decrease in free volume, which reduces the sorption and diffusion of penetrants in the polymer matrix [31].
By adding boehmite to 10 wt.%, the solution mechanism remains the dominant mechanism. This claim is further emphasized after comparing the permeability reduction of the 5 and 10 wt.% boehmite containing PU nanocomposite membranes with respect to the pure PU membranes, which clarifies the lesser reduction of permeability for methane than O 2 and N 2.
By adding boehmite from 10 to 20 wt.%, a greater reduction in methane permeability compared to O 2 is observed. The higher permeability reduction of CH 4 represents some alterations in the rubbery properties of the polymer, which weaken the role of the solution mechanism in gas permeation at higher boehmite loading of polyurethane membranes. The presence of boehmite nanoparticles in the soft segments decreases the chain mobility of the polymer, which in turn reduces the rubbery properties of the polyurethane [20].
In the case of CO 2 , as mentioned above, the lower permeability reduction with increasing boehmite content compared to other gases results from its smaller molecular size, higher condensability, and good interactions with polar -OH groups on the boehmite surface [20]. Figure 12 also shows the CO 2 /N 2 , CO 2 / CH 4 , and O 2 / N 2 permselectivities of PU-boehmite nanocomposite membranes. According to Fig. 12, increasing the number of boehmite nanoparticles in membranes up to 20wt.% increases the selectivity of CO 2 /N 2 , CO 2 /CH 4 , and O 2 /N 2 gases from 16.45, 6.005, and 1.67 in pure PU to 27.2, 9.33, and 2.16 for polyurethane-boehmite (20 wt.%). The permselectivity of all pair gases improved by increasing the number of boehmite nanoparticles in the membranes.
The order of increment in gas selectivity of the mentioned nanocomposite membranes by addition of 20 wt.% boehmite nanoparticles are as follows: CO 2 /N 2 (65.35%) > CO 2 /CH 4 (55.37%) > O 2 /N 2 (29.34%). As seen, the CO 2 /N 2 and CO 2 /CH 4 pair gases present higher selectivities than O 2 /N 2 pair gas. Considering the solution-diffusion mechanism, the selectivity of gases in polymers is the product of diffusivity and solubility selectivity which enables the polymer chains to separate small molecules from large ones, condensable molecules from non-condensable ones, and polar molecules from non-polar ones [32].
By the addition of the boehmite nanoparticles into the membranes, as mentioned before, most of the particles may disperse in the soft segments. Therefore, the presence of the particles should affect the mobility of the polymer chains in soft segments and also may reduce the free spaces trapped in the soft segments. These two events would increase the molecular sieving property of the composite membrane and domination of the diffusion mechanism increase. These changes lead to more diffusivity selectivity in polymers.
Therefore, the permeation of larger molecular size gases is more restricted than that of small ones, except when good interactions between the nanoparticles and the polymer chains would be available.
Considering O 2 /N 2 gases, the lowest improvement in the selectivity of PU nanocomposite was observed for this gas pair. These results are related to the same condensability of these two gases and no interactions with polymer chains and OH groups of the particles. The molecular size difference plays an important role. Therefore, the improvement of diffusivity selectivity due to better molecular sieve property of nanocomposite membranes cause the selectivity increment, and finally, the total selectivity increment is not very great.
In the case of CO 2 /N 2 gases, the biggest improvement in selectivity by adding boehmite nanoparticles in PU matrix is due to more condensable property and also more interaction of CO 2 molecule with polymer chains in comparison with nitrogen. It means that the solubility selectivity also plays an effective role in enhancement of selectivity of pair gases (especially at low concentration of boehmite nanoparticles).
Finally, the increase of CO 2 /N 2 selectivity in comparison with CO 2 /CH 4 is attributed to the very low condensability of nitrogen in comparison with methane. As mentioned, the suitable sorption sites on polymer-boehmite interface offer more solubility of condensable gases and solution of methane due to its condensable nature which is significantly more than that of nitrogen. Therefore, despite the larger molecular size of the methane which could offer higher diffusivity selectivity of CO 2 /CH 4 in comparison with CO 2 /N 2 , domination of the solution mechanism causes the high solution of methane and lowers the solubility selectivity. Table 3 offers a comparison of the performance of various membranes filled with particles for the experimental data obtained in this work and literature data. As can be detected, the percentage enhancement permselectivity of pair gases have been affected by the operational conditions, i.e., T and P, as well as the type of filler content. According to Table 3, the results presented here indicate that polyurethane-boehmite composite membranes have reasonable percentage enhancement permselectivity among reported polymers-filler.
Even though membrane separation is, in general, a very attractive technology, it shows some limitations for the gas separation application. It has to be considered that an efficient separation process needs polymers with higher permeability to lead to higher productivity and lowers capital cost due to minimum membrane area, and higher selectivity affords more efficient separations in a lesser number of stages, higher purity of end product, and lower power costs.
Unfortunately, the inherent trade-off between permeability and selectivity demonstrated by Robeson in 1991 and 2008 remains to be the biggest challenge in the development of polymeric membranes. Polymers with high permeability will exhibit low selectivity and vice versa. In Fig. 13, the results obtained from the prepared PU-boehmite membranes were compared with Robeson's upper bound line [33]. As shown in this Fig. 13, the prepared membrane series investigated shows good separation ability, high permeation, and selectivity for CO 2 /N 2 . All of the synthesized membranes lie close to the upper bond line. The good separation ability of these membranes indicates the suitable potential of these membranes for industrial applications.

Modeling of Gas Permeability in the Polyurethane-Boehmite Composite Membranes
Various models can be utilized in order to predict the gas permeation in hybrid membranes. One of the models that used for the prediction of the permeability in membranes is Higuchi model. In the Higuchi model, it is assumed that spherical particles are randomly distributed in a polymer matrix. The general form of this equation is shown as the following equation: where P eff is the effective permeability of mixed matrix membrane, P c is the permeability of the polymer, φ is the volume fraction of boehmite in the composite membrane, and K H is the Higuchi constant. The volume fraction φ of boehmite in composite membranes was calculated by the following equation: where w boehmite and w pu refer to the weight of boehmite and polyurethane, and boehmite and PU are the density of boehmite and polyurethane, respectively. The density of boehmite and polyurethane were 3.03 and 1.1 g/cm 3 , respectively. The Higuchi constant, K H , was selected at 0.78 by Higuchi for the best fit of the experimental data to the model [26]. There is no significant correlation between model and experimental results supposing, K H = 0.78 in the model, especially phenomena such as preferential agglomeration, sedimentation and surface effects would take place [26]. However, using the least square method, the model fitted very well with the experimental data and   Table 4. As presented in Table 4, K H increases as the molecular size of the gases increase, except in the case of nitrogen and methane which may refer to the higher condensability of methane. The order of K H is in good agreement with the order of reduction values of gas permeability of prepared nanocomposite membranes in respect to pure polyurethane.
As shown in Figs. 14, 15, 16, 17, the Maxwell model [20] was also applied to the obtained data and compared with the Higuchi model. Because the permeability of gases is zero in boehmite particles, the Maxwell model is reduced to: As shown in Figs. 14, 15, 16 the Higuchi model fits better to the experimental data.

Conclusions
This work evaluated the permeability of CO 2 , CH 4 , O 2 , and N 2 in polyurethane (PU) membranes as a function of boehmite content. FTIR, DSC, XRD and FESEM characterize the prepared PU-boehmite nanocomposite membranes using solution casting and solvent evaporation method.  Comparing the performance of the synthesized polyurethanes with Robeson's upper bound line shows that these membranes appear near the line because of increased boehmite content. The polyurethane-boehmite membranes' permeability behaviors were evaluated during the Maxwell and Higuchi models. The Higuchi model showed an appropriate correlation to experimental results for the permeability of studied gases in nanocomposite membranes.

Author Contributions
The authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by somayeh tourani and fatemeh akbarbandari. The first draft of the manuscript was written by somayeh tourani and all authors commented on revised versions of the manuscript. All authors read and approved the final manuscript.
Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data Availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.