Enhanced permeation performance of polyether-polyamide block copolymer membranes through incorporating ZIF-8 nanocrystals☆

Longwei Xu,Long Xiang,Chongqing Wang*,Jian Yu,Lixiong Zhang,Yichang Pan*

State Key Laboratory of Materials-Oriented Chemical Engineering,College of Chemical Engineering,Nanjing Tech University,Nanjing 210009,China

1.Introduction

Removing CO2from natural and flue-gas is of great importance to cut down the emissions of greenhouse gas.Membrane-based CO2separation is a promising alternative in terms of energy and environmental issues to conventional cryogenic distillation and reversible adsorption techniques[1,2].The majority of commercially available polymeric membranes for CO2separation is made from glassy polymers,for example,polyimide,cellulose acetate and poly(phenylene oxide)[3,4].However,the permeation rates of CO2on those membranes are not sufficient for large-scale separation applications,even if they have good selectivity.As emphasized by Merkel and co-workers[5],very high selectivity is not of the primary concern for industrial membrane application,because the downstream concentration of the more permeable component plateaus increases as the selectivity continues.

Polyether-polyamide block copolymers(Pebax),a series of commercial and low-cost copolymer materials,have great potential for use in CO2separation because of their excellent selectivity but moderate CO2permeability[6-9].For example,Pebax?1657,composited of 60 wt%polyethylene oxide(PEO)and 40 wt%polyamide(PA6),is of a satis fied selectivity for CO2/CH4but a relatively low CO2permeability(several tens of Barrer)[9-11].In order to enhance the gas permeability of polymeric membranes,one of the most promising strategies was developed to incorporate highly permeable fillers into the polymer matrices,leading to a hybrid materials referred as mixed matrix membranes(MMMs)[12].When the gas permeability on inorganic fillers is two-order higher than that on the polymer matrix[13,14],the gas permeability on the resulting MMMs,free of interfacial defects,will be substantially improved.However,the compatibility between conventional inorganic fillers(zeolites and carbon molecular sieves)and polymeric matrix for interfacial adhesion is challenging,always resulting in an increase of the gas permeability but a sharp decrease of the gas selectivity.

This issue can be effectively mitigated using porous metal-organic framework(MOF)materials as fillers,because the organic linkers in MOFs can provide better affinity with polymer matrix[11,15-20].In this sense,ZIF-8[21],constructed from zinc(II)cations and 2-methylimidazole anions was selected to be served as the filler to improve the intrinsic CO2permeability of Pebax?1657 matrices,because of its high porosity and high CO2permeability(～3000 Barrer)[22].In addition,ZIF-8 with ultra-microporous window is also attractive for its facile synthesis procedure and low-cost precursor,as well as its exceptional thermal and chemical stability,and thus has been extensively applied in gas-based adsorbents,separating membranes and sensors[23-27].Besides,blending of ZIF-8 nano- fillers in polymeric membranes has also been demonstrated for enhancing either gas permeability or selectivity(or sometimes both)of the parentpolymeric matrices[28-35].However,almost all reports are focused on the glassy polymeric matrices,such as polyimide and polysulfone,which are of intrinsic low gas permeability.Recently,Na fisi and H?gg have incorporated ZIF-8 fillers into the high-permeable Pebax?2533 matrices,which is composited of 80 wt%polytetramethylene oxide(PTMO)and 20 wt%polyamide(PA12)[36].Even though the CO2permeability was further improved,the selectivity for CO2/CH4(～9)is not satis fied for the potential separation application.Compared with Pebax?2533,Pebax?1657 not only exhibits higher CO2/light-gas selectivity but also provides stronger mechanical strength due to its higher content of polyamide[8].Therefore,in this study,rubbery Pebax?1657 polymeric membrane with relative-high gas permeability was blended with ZIF-8 nano- fillers to further enhance the gas permeation.The good interfacial interaction between ZIF-8 fillers and Pebax matrices was verified by several physical measurements.The CO2permeability on the 18 wt%ZIF-8/Pebax membrane was improved to 178 Barrer,which is 300%higher than that on pristine Pebax membrane,and the CO2/CH4selectivity still maintained at～18.The transport mechanism on the ZIF-8/Pebax MMMs was also explored.The mixed-gas separation performance for CO2/CH4mixtures on the ZIF-8/Pebax MMMs is very close to the Roberson upper bound,and thus is technologically attractive for purification of natural gas.Finally,the mixed-gas permeation performances on the optimized 18 wt%ZIF-8/Pebax membrane were also investigated.

2.Experimental

2.1.Materials

Allchemicals were used as received withoutfurtherpurification.Both zinc nitrate hexahydrate(Zn(NO3)26H2O,99%)and 2-methylimidazole(Hmim,99%)were purchased from Sigma-Aldrich.Pebax?1657 was purchased from Arkema Inc.,France.Analytical grade ethanol was supplied from Sinopharm Chemical Reagent Co.,Ltd.The water used in all experiments was treated by the Millipore Milli-Q purification system.

2.2.Synthesis of ZIF-8 nanocrystals

ZIF-8 nanocrystals were synthesized following our reported procedure[37].In a typical synthesis,Zn(NO3)2·6H2O(1.17 g)and Hmim(22.70 g)were dissolved in deionized(DI)water(88 ml),and the resulting mixture was stirred at room temperature(～25°C)for 6 h.The as-prepared turbid solution was centrifuged and washed with DI water three times,followed by directly re-dispersing in ethanol/water mixture(mass ratio 7:3).

2.3.Fabrication of ZIF-8/Pebax MMMs

The flat-sheet dense ZIF-8/Pebax MMMs with different ZIF-8 loadings were fabricated using a solution-casting method.Firstly,Pebax polymer pellets were dissolved in an ethanol/water mixture(mass ratio 7:3)under re flux at 80°C for 2 h to prepare an 8 wt%Pebax solution.Secondly,proper amount of above ZIF-8 suspension was added to the Pebax solution,followed by an indirect ultrasonic dispersion for 30 min.Finally,the bubble-free casting solution was rapidly casted onto a Te flon plate with a doctor-blade knife at ambient condition.The just-casted film was dried atroomtemperature forsolventevaporation,followed by further drying in a vacuum oven at 70°C for 24 h.As a comparison,pristine Pebax membranes were also fabricated from pure Pebax solution using above same casting and drying processes.The weight loading of ZIF-8 in the MMMs was de fined as:

while the volume fraction of ZIF-8 in MMMs was de fined as:

where ρPebaxand ρZIF-8refer to the density of polymer Pebax and ZIF-8 crystals,and are 1.14 and 0.95 g·cm-3[10,14].

2.4.Characterization

X-ray diffraction(XRD)patterns of all samples were acquired on a Rigaku Smartlab TM 9 kW powder diffractometer(CuKαsource)at 40 kV and 40 mA.The BET surface area of ZIF-8 nanocrystals was derived from the nitrogen adsorption isotherms at 77 K using a BELSORP-max machine.The particle size distribution of ZIF-8 nanocrystals in the water/ethanol suspension was measured by means ofdynamic lightscattering(DLS)using a Brookhaven 90 plus particle size analyzer at 25°C.Thermogravimetric analysis(TGA)was conducted on a NETZSCHSTA 449 instrument under air atmosphere from 25 to 800°C with a heating rate of 10 °C·min-1.Scanning electron microscope(SEM)characterization was performed on a ZEISS SUPRA 55 at 10 kV to examine the morphology of ZIF-8 crystals and membranes.The membrane samples were artificially broken in liquid nitrogen to investigate the cross-sectional morphology.Energy dispersive X-ray spectroscopy(EDX)wasused to analyze the TGAresidues of ZIF-8 and mixed matrix membrane samples.All samples were coated with Au using a Denton Vacuum Desk II sputter coater before SEM analysis.Differential scanning calorimeter(DSC)measurements were conducted on NETZSCHDSC 204 F1 Phoenix to determine the glass transition temperature(Tg)ofallmembrane samples.The measurement was operated under nitrogen from-80 to 250°C using a standard heating-cooling-heating procedure with a rate of 10 °C·min-1.Density measurements of the MMMs were performed using hydrostatic weighing with a density determination kit(Mettler Toledo).High-pressure adsorption isotherms of N2,CH4and CO2on membrane samples were recorded on a Belsorp-HP adsorption apparatus at 298-323 K with pressure up to 1 MPa.Prior to the test,membrane sample(～300 mg)cut into small pieces was activated under vacuum(10-5Torr)at 100°C for 24 h.At each point,an equilibration time of at least 1 h was used.

2.5.Gas permeation experiments

Both single and mixed gas permeation experiments were conducted on a home-made setup by the Wicke-Kallenbach technique,as shown in Fig.1.Allgases with 99.99%purity were supplied by Nanjing Sanle group Co.,Ltd.A flat-sheet permeation cell with effective membrane area of 2.84 cm2was used for all tests.Helium was used as the sweep gas.In all tests,the stage-cut(i.e.,ratio of permeate flow to feed flow)less than 1%was maintained to avoid the concentration polarization.Unless otherwise specified,the feeding pressure was maintained at 0.4 MPa.The compositions of the steady-state feed,retentate and permeate were all tested by gas chromatography(Agilent 7890)equipped with a thermal conductive detector.To guarantee the reliability of testing,three duplicated membrane samples fabricated under the same condition were used for permeation.The permeation results were averaged as the final data with deviations.Prior to the test,residual gas present in the membranes and the pipeline was removed by vacuum pump.The gas permeation under the steady-state can be written as:

whereLrefers to the membrane thickness(cm),measured with a digital micrometer(Mitutoyo,Japan),Niis the flux through the film(cm3·s-1).TheArepresents the effective membrane area(cm2),the pressure drop,Δpi,is the difference between the feed and permeate side(cmHg,1 cmHg=1333.22 Pa).The unit of permeability(Pi)and permeance(Ji)are commonly expressed as Barrer and GPU,respectively(1 Barrer=10-10cm3(STP)·cm·(cm2·s·cmHg)-1,1 GPU=1 × 10-6cm3(STP)·(cm2·s·cmHg)-1).The gas permeation experiments for each membrane sample were repeated for three times.The measurement results of three samples were averaged as the final data with deviations shown in table as error bars.The ideal selectivity and separation factor of a membrane were calculated as shown in the equation below:

Fig.1.Schematic diagram of the set-up for gas permeation measurements.

3.Results and Discussion

3.1.Characterization of ZIF-8 fillers

The as-synthesized ZIF-8 fillers were firstly characterized by various physical measurements.As shown in Fig.2(a),XRD patterns of the synthesized fillers are excellent agreement with the simulated pure-phase ZIF-8 structure[21].The DLS measurement shows that the particle size of as-synthesized fillers ranges from 80 to 200 nm with a mean particle size of 129 nm(Fig.2(b)).The fillers from SEM images exhibit the polyhedral morphology(Fig.2(c)).The N2adsorption measurement of ZIF-8 fillers exhibits a type I isotherm(Fig.2(d)).The BET surface area is calculated to be 1608 m2·g-1,which is close to the previous reported values of ZIF-8 nanocrystals[31,38,39].From above characterizations,it was concluded that highly crystalline ZIF-8 nanocrystals were successfully prepared.

3.2.Characterization of ZIF-8/Pebax MMMs

Robust Pebax membranes containing various ZIF-8 loadings were successfully fabricated.The fresh as-synthesized ZIF-8 nanocrystals without drying were used as fillers,because drying process was prone to induce the non-reversible agglomeration of fillers[40,41].In order to determine the accurate loadings ofZIF-8 in MMMs,TGA characterizations of the membrane samples in air were firstly conducted(Fig.3(a)).The final solid residues were only zinc oxide by EDX analysis[42].Table 1 lists the determined mass percentages of ZnO by TGA and calculated ZIF-8 loadings in corresponding MMMs.Higher mass percentage of zinc was found in the final residues,indicating that higher ZIF-8 loadings are in the MMMs.The mass percentage of zinc elements in pure ZIF-8 fillers determined by TGA(27.67%)was close to the theoretical mass percentage calculated by molecular mass(28.5%).The actual mass loadings of ZIF-8 fillers in MMMs are 11 wt%,18 wt%,21 wt%and 33 wt%,respectively,in good agreement with the nominal calculated compositions,and are employed in the remaining discussion.

The interfacial interaction between fillers and polymeric matrices was first investigated by DSC measurements.As shown in Fig.3(b),the glass transition temperature(Tg)of the ZIF-8/Pebax MMMs gradually increases with the ZIF-8 loadings,suggesting a favorable interfacial interaction between fillers and matrix.TheTgvalue ofthe pristine Pebaxmembrane is-55.5°C,consistent with the values from other reports[6-9].TheTgvalue of MMMs shifts to-52.9°C when the ZIF-8 loading increases to 33 wt%.This positive shift is due to the reduced mobility of polymer chain and the rigidification of polymer chains on the filler's surface[41].We speculate that this interaction comes from the hydrogen bonding between imidazolate group of ZIF-8 fillers and ether group in the Pebax polymer.

Table 1Analysis results of TGA residues and calculated ZIF-8 loadings

Fig.3.(a)TGA curves in air,(b)DSC curves,(c)density testing and(d)XRD patterns of ZIF-8 nanocrystals,pristine Pebax membrane and ZIF-8/Pebax MMMs with various filler loadings.

In addition,the good interfacial interaction was also con firmed by the bulk density measurements.As shown in Fig.3(c),the MMMs exhibit a clear linear relationship between density and ZIF-8 loading,suggesting that voids or “sieve-in-a-cage”are not presented in the fabricated MMMs.Furthermore,it is also found that XRD patterns of ZIF-8 fillers after integrating into the Pebax matrices are slightly different with those of the original ZIF-8 structure(Fig.3(d)).The crystal structure of ZIF-8 fillers inside the Pebax matrices at(112)and(013)becomes the strongest diffraction intensity,while the diffraction peaks at(011)and(112)are the strongest in the original ZIF-8 structure.This change of XRD patterns from the crystal orientation should be eliminated,because of the random distribution of spherical fillers inside the matrices.On the contrary,this phenomenon is attributed to the chemical interaction between Pebax and ZIF-8 crystals,as demonstrated by the facilitated preparation of ZIF-8 crystals with the aid of Pebax polymer[43].Cross-sectional SEM images of the membranes(Fig.4)also show the good interfacial interaction between fillers and polymer,owing to the inherently organic property of ZIF-8 framework.The small white spots are the spherical ZIF-8 nanocrystals,and homogeneously dispersed in the polymer matrices.Even the loading of ZIF-8 fillers up to 33 wt%,larger clusters or aggregates of fillers were not observed,which bene fits from the utilization of undried and fresh as-synthesized ZIF-8 nanocrystals.However,further increasing ZIF-8 loadings will result in the mechanical failure of the MMMs.Overall,above characterizations present the good interfacial interaction between ZIF-8 nanocrystals and Pebax matrices.

3.3.Separation performance on ZIF-8/Pebax MMMs

Table 2 lists the single-gas permeation results of CO2,CH4and N2on the pristine Pebax and ZIF-8/Pebax MMMs with various ZIF-8 loadings.The permeation temperature and feeding pressure are 25°C and 0.4 MPa,respectively.The permeability of all gases experiences the same increase-and-decrease pattern.As the ZIF-8 loading increases up to 18 wt%,the permeability of all gases increases to three times compared with that on the pristine Pebax membrane.Further increasingthe ZIF-8 loading to 21 wt%,the permeability of all gases on MMMs obviously decreases,butstillexhibitnearly 2.5-fold higherthan thaton the pristine Pebax membrane.However,the simultaneous amplification of gas permeability on MMMs results in the similar selectivity for both CO2/N2and CO2/CH4to the pristine Pebax membrane.However,when the ZIF-8 loading was increased to 33 wt%,the permeability of CO2sharply decreases from 137.8 to 84.4 Barrer.This phenomenon is possibly attributed to the rigidification of polymer chains on the filler's surface[12],as demonstrated by the obvious increase of Tg value(Fig.3(b)).In contrast,the permeability of both CH4and N2decreases moderately,resulting in an obvious reduction of selectivity for both CO2/N2and CO2/CH4.

Table 2Single-gas permeation results of CO2,CH4 and N2 on the pristine Pebax membrane and ZIF-8/Pebax MMMs with various ZIF-8 loadings

3.4.Transport mechanism on ZIF-8/Pebax MMMs

In order to understand the transport role of the added ZIF-8 filler,the diffusion and solubility coefficients of all gases through MMMs were investigated.As shown in Fig.5,high-pressure adsorption isotherms of all gases on the pristine Pebax membrane and ZIF-8/Pebax MMMs all exhibit linear shape,and the concentration of adsorbed gas increases with the ZIF-8 loading in MMMs.Therefore,the solubility coefficient of the gas was determined by the following equations[44]:

whereCi(cm3·cm-3)is the concentration for adsorbed componenti,p(cmHg)is the gas pressure at adsorptive equilibrium,kD(cm3·cm-3·cmHg-1)is the Henry's solubility coefficient.Si(cm3·cm-3·cmHg-1)is the solubility coefficient.

Based on the solution-diffusion mechanism in polymeric membrane,the diffusion coefficient of the gas can be determined by:

whereDiis the average effective diffusion coefficient(cm2·s-1),andPiis the gas permeability obtained from the single-gas permeation.As shown in Fig.6(a),the solubility coefficients of all gases in MMMs increase with the ZIF-8 loadings,attributed to the higher adsorption capacities of gas in ZIF-8 than those in Pebax.In contrast,the diffusion coefficients of three gases exhibit slightly different trends as a function of ZIF-8 loading,although they all experience an increase-and-decrease pattern (Fig.6(b)).Compared with the pristine Pebax membrane,both diffusion and solubility coefficients raise on the 18 wt%ZIF-8/Pebax MMMs,resulting in the significant improvement of gas permeability.However,the diffusion coefficients of all gases sharply decrease with the increase of ZIF-8 loading from 21 wt%to 33 wt%.This phenomenon is possibly due to the rigidification or blockage of filler's pores by the polymer chain[12].

In order to further understand the permeation performance in the ZIF-8/Pebax MMMs,we perform analysis using the Maxwell model[45],which is often applied to predict the gas permeation behavior of MMMs with spherical fillers.

Fig.5.High-pressure sorption isotherms of CO2,N2 and CH4 on pristine Pebax membrane and ZIF-8/Pebax MMMs at 25°C.

wherePeffis the effective permeability ofthe MMMs,PcandPdrepresent the permeability of the continuous(polymer)and dispersed phase( fillers),respectively.The intrinsic permeability of CO2,N2and CH4on ZIF-8 fillers(Pd)was 3300,1000 and 270 Barrer,respectively,reported by Koros'group[22].

Fig.6.(a)Solubility coefficients and(b)diffusion coefficients of all gases at 4 bar and 25°C as a function of ZIF-8 loadings in MMMs.

As shown in Fig.7(a),when the ZIF-8 loading in MMMs is below 12 vol%,the experimental permeability of all gases matches well with the Maxwell prediction.With increasing of ZIF-8 loading from 21 vol%to 24 vol%,the experimental values of gas permeability are above the Maxwell prediction,possibly due to the good interfacial interaction between ZIF-8 and Pebax matrices.However,as the loading furtherincreases to 37 vol%,the experimentalvalue of CO2permeability falls below the Maxwell curve.On the other hands,the experimental selectivity for both CO2/N2and CO2/CH4on MMMs also matches well with the Maxwell prediction,with the exception of those on membrane with 37 vol%loading(Fig.7(b)).The almost constant selectivity is possibly attributed to the large difference ofgas permeability between polymer matrix and porous fillers[13].In contrast,the severely decreased selectivity on MMMs with 37 vol%loading could arise from one of two possibilities.First is the rigidification or blockage of filler's pores by the polymer chain,as demonstrated by above the gas permeation tests and physical measurements.Second is thatthe volume fraction of fillers in MMMs is far beyond the application threshold of the Maxwell model(～20 vol%)[45].

3.5.Effect of temperature on separation performance

The effectofpermeating temperature(298-323 K)on the separation performance of the pristine Pebax membrane as well as ZIF-8/Pebax MMMs was further explored.As shown in Figs.8 and 9,the permeability of N2,CH4and CO2all increases with the permeating temperature,whereas the selectivity for both CO2/CH4and CO2/N2decreases.The increase in gas permeability with temperature indicates that diffusion dominates the transport of gas through the membrane,instead of solubility,because adsorption of gases is all greatly reduced with the increase of temperature.However,the increase in CO2permeability was less than that of other gases(CH4or N2),resulting in a decrease in selectivity for both CO2/CH4and CO2/N2.The relationship between gas permeability and temperature can be described with the Arrhenius equation in terms of the permeation activation energy:

wherePois the pre-exponential factor,Epis the apparent activation energy for permeation (kJ·mol-1),Ris the gas constant(8.314 J·K-1·mol-1),andTis the absolute temperature(K).

Fig.7.Comparison between Maxwell model and experimental data of ZIF-8/Pebax MMMs with various ZIF-8 loadings:(a)gas permeability and(b)selectivity.

Table 3 presents the calculatedEpfor all gases through the pristine Pebax membrane and ZIF-8/Pebax MMMs with various ZIF-8 loadings.TheEpvalues of CO2,CH4and N2on the pristine Pebax membrane are 23.8,40.8 and 44.4 kJ·mol-1,respectively,which are consistent with the reported values for Pebax?1657 membrane[46].In addition,theEpvalues ofallgases on ZIF-8/Pebax MMMs with various ZIF-8 loadings are all lower than those on the pristine Pebax membrane,indicating that the addition of ZIF-8 fillers can facilitate the permeation of gas through the polymer matrices[47].Furthermore,due to its smallestEpvalue for CO2,it was the least favorable for CO2when temperature increased compared with CH4and N2.Therefore,the raise of CO2permeability was less than that of other gases(CH4and N2)with increase in permeating temperature,resulting in a decrease in selectivity for both CO2/CH4and CO2/N2systems.

Fig.8.Effect of operating temperature on the gas permeability through pristine Pebax membrane and MMMs with various ZIF-8 loadings:(a)N2,(b)CH4,and(c)CO2.

Fig.9.Effect of operating temperature on selectivity through pristine Pebax membrane and MMMs with various ZIF-8 loadings:(a)CO2/CH4 and(b)CO2/N2.

3.6.Mixed-gas permeation

The mixed-gas permeation on the 18 wt%ZIF-8/Pebax MMMs was also conducted at 25°C to probe the CO2permeation in the presence of another component.Compared with the single-gas permeation,a reduction in CO2permeability is observed,whereas the permeability of both N2and CH4are slightly higher in the mixed-gas permeation(Fig.10(a and b)).As a result,the separation factor is slightly lower than the ideal selectivity.The observed slight difference between single-component and mixed-gas permeations was also found in several duplicated membranes from different batches.Therefore,this phenomenon should be attributed to the multicomponent competitive sorption[48],rather than the experimental deviation.The presence of CH4(or N2)with CO2in gas mixture could prevent further adsorption of CO2on ZIF-8 fillers and also prohibit the extra condensation of CO2,resulting in the reduction of CO2solubility.As shown in Fig.10(c),the mixed-gas separation performance for CO2/CH4is very close to the Roberson upper bound[49,50],and thus are technologically attractive for purification ofnatural gas.

4.Conclusions

In summary,enhanced permeation performance of CO2on Pebax?1657 polymeric membranes by incorporating ZIF-8 nano-fillers was successfully achieved,without compromising the separating selectivity.The interfacial interaction between ZIF-8 fillers and Pebax matrices was satis fied,as demonstrated by several physical characterizations.The CO2permeability on the 18 wt%ZIF-8/Pebax membrane can reach to 178 Barrer,～300%higher than that on the pristine Pebax membrane,and the CO2/CH4selectivity still maintains at 18.The improved gas permeability on the 18 wt%MMMs was attributed to the raise of both gas solubility and diffusivity by the addition of ZIF-8 nano- fillers.For the mixed-gas(CO2/CH4)permeation,the separation performances are very close to the Roberson upper bound,and thus are technologically attractive for purification of natural gas.

Table 3Activation energies of permeation for CO2,CH4 and N2 on all membranes

Fig.10.(a,b)Single and mixed-gas permeation results on the 18 wt%ZIF-8/Pebax MMMs at 25°C and(c)comparison with Roberson upper bound[49].

Nomenclature

Aeffective membrane area,cm2

Ciconcentration for adsorbed gas,cm3·cm-3

Diaverage effective diffusion coefficient,cm2·s-1

Epapparent activation energy for permeation,kJ·mol-1

Jigas permeance,GPU

kDHenry's solubility coefficient,cm3·cm-3·cmHg-1

Lmembrane thickness,cm

mmass,g

Niflux through the film,cm3·s-1

Pcpermeability of the continuous phase,Barrer

Pdpermeability of the dispersed phase,Barrer

Peffeffective gas permeability of the MMMs,Barrer

Pigas permeability,Barrer

ΔPidifference between the feed and permeate side,cmHg-1

ppressure at adsorptive equilibrium,cmHg-1

Rgas constant(=8.314 J·K-1·mol-1)

Sisolubility coefficient,cm3·cm-3·cmHg-1

Tabsolute temperature,K

αA/Bgas selectivity on the membrane

ρ density,g·cm-3

?volume fraction of ZIF-8 in mixed matrix membrane

ω mass loading of ZIF-8 in the MMMs

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