gas transport properties of poly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluoropropane) diimide...

Journal of Membrane Science 199 (2002) 191–202

Gas transport properties ofpoly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluoropropane)

diimide (6FDA-1,5-NDA) dense membranes

R. Wanga,b, S.S. Chana,c, Y. Liu a, T.S. Chunga,c,∗a Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602, Singapore

b Environmental Technology Institute, 18 Nanyang Drive, Singapore 637723, Singaporec Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent,

Singapore 119260, Singapore

Received 30 March 2001; accepted 27 July 2001

Abstract

The intrinsic gas transport properties of permeation, diffusion and sorption for He, O2, N2, CH4 and CO2 in aromaticpolyimide, poly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluoropropane) diimide (6FDA-1,5-NDA) dense membranes wereinvestigated. The permeation of pure gases of He, O2, N2, CH4 and CO2 was measured with a temperature-controlledpermeation cell while the sorption isotherm was obtained from the Cahn 2000 microbalance sorption cell.

The 6FDA-1,5-NDA membrane has a selectivity of 49 for CO2/CH4 with a permeability of 22.6 Barrers for CO2 under10 atm at 35◦C. The Henry’s diffusivity holds a dominating effect over the Langmuir diffusivity and decreases in the order ofO2 > CO2 > N2 > CH4, in fair agreement with the apparent diffusivity. The activation energies of permeation and diffusionincrease with increasing gas kinetic diameters in the order of CO2, O2, N2 and CH4.

The solubility of gases tested adopts a parallel trend with their critical temperatures. Upon pressure acceleration, the gasdiffusivity increases while the solubility decreases. The overall gas permeability of 6FDA-1,5-NDA decreases with increasingpressure, which can be explained by using the dual-mode sorption model and the partial immobilisation model. More than50% of the entire total gas sorbed is distributed in the Langmuir environment when pressure is less than 25 atm. The fractionalmobility of Langmuir species decreases while the fractional mobility of the Henry species increases when the feed pressureincreases. CO2 exhibits the most significant pressure-dependent properties due to its the strongest interaction and highestcondensability. © 2002 Elsevier Science B.V. All rights reserved.

Keywords: 6FDA-1,5-NDA polyimide; Gas separation membrane; Permeation; Diffusion; Sorption

1. Introduction

The intrinsic properties of permeation, diffusionand sorption of polymers largely control many physi-cal and chemical processes especially in gas separa-tion applications [1–3]. Typical examples include the

∗ Corresponding author. Fax:+65-779-1936.E-mail address: [email protected] (T.S. Chung).

enrichment of O2 for biomedical purposes, recoveryof H2 from syngas and removal of CO2 form naturalgas, etc. Permeation of a penetrant via a polymericmembrane occurs by the solution–diffusion mecha-nism [2,4], in which the gas molecules first dissolveat the membrane surface, then diffuse through thematerial due to the concentration gradient, and finallydesorb at the other side of the membrane. In principle,to select a polymeric material for membrane-based

0376-7388/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0376-7388(01)00697-4

192 R. Wang et al. / Journal of Membrane Science 199 (2002) 191–202

separations, its mass transfer properties should be firsttaken into consideration.

As reported in the abundance of literatures, poly-imides with 2,2′-bis(3,3′-decarboxyphenyl) hexafluo-ropropane dianhydride (6FDA) have been identified asattractive and promising membrane materials becausethey exhibit high gas permeability and selectivity,excellent thermal resistance and mechanical strength[5]. Being one of this series polymers, aromaticpoly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluo-ropropane) diimide (6FDA-1,5-NDA) is believed topossess these impressive characteristics due to its stiffmolecular chain, disrupted intersegmental packing,and weak interchain interaction [6].

There have been active studies on the relation-ships between the chemical structure of polyimidesand their gas separation properties [7–9]. Addition-ally, the fabrication of high performance asymmet-ric and composite 6FDA-based membranes are alsofrequently reported [10–17]. However, relatively lim-ited information is available on the gas transport of6FDA-based polymers, in particular the temperature-and pressure-dependent aspects [18–22], especiallyfor 6FDA-1,5-NDA polyimide.

The objective of this paper is to investigate theintrinsic gas transport properties of 6FDA-1,5-NDAfrom the permeation and sorption measurements. Themotivation of this work is to meet the need to developa fundamental database of transport properties ofpolymers which are of interest in the development ofmembrane materials for gas separations. Fundamentalstudies focus on the evaluation of the varying effectsof temperature and pressure on gas permeability, dif-fusivity and solubility. The analysis of the activationenergies of permeation and diffusion as well as heatsof sorption for He, O2, N2, CH4 and CO2 are includedin this work. Additionally, the dual-mode sorptionparameters, the gas mobility and distribution in theHenry and Langmuir sites of the polymer matrix arealso discussed.

2. Experimental

2.1. Materials

6FDA-1,5-NDA polyimide used in this study wassynthesised by chemical imidisation method in our

Fig. 1. Chemical structure of 6FDA-1,5-NDA.

laboratory. Its chemical structure is shown in Fig. 1.Prior to chemical synthesis, (2,2′-bis(3,4-carboxyl-phenyl) hexafluoropropane dianhydride) (6FDA) and(1,5-naphthalanediamine) (1,5-NDA) were purifiedby sublimation. NMP (N-methyl-pyrrolidone) wasdistilled at 42◦C/10 mbar after dried with molecularsieve. Other chemical reagents were used as received.

Equal mole of 6FDA was added to a NDA solu-tion of NMP with stirring under Argon environment.After reaction for 24 h, acetic anhydride and triethy-lamine (with a 4:1 molar ratio of acetic anhydrideto triethylamine) were slowly added to the solutionto perform imidisation for 24 h. After precipitation inmethanol, the polymers were filtered and dried under150◦C/10 bar for 24 h.

2.2. Dense membranes preparation

The dense membranes were prepared by employinga solvent evaporation method [22]. The evapora-tion temperature used was 75◦C for 24 h and thefinal drying temperature used was 250◦C. Four dif-ferent solvents namely dichloromethane (CH2Cl2),chloroform (CHCl3), tetrahydrofuran (THF) andN,N-dimethylformamide (DMF) were used for trials.The final membranes for the gas permeation test wereprepared by using DMF as a solvent.

2.3. Pure gas permeation tests

The pure gas permeability coefficients were mea-sured by using a constant volume method. The detailsof the apparatus design and testing procedures couldbe found in the publication elsewhere [20]. In short,the gas permeability coefficient was calculated fromthe following equation when the permeation reachesa steady state.

P = 273.15× 1010Vl

760AT((p0 × 76)/14.7)

(dp

dt

)(1)

R. Wang et al. / Journal of Membrane Science 199 (2002) 191–202 193

where P is the permeability of a membrane toa gas and its unit is in Barrer (1 Barrer= 1 ×10−10 cm3 (STP)/cm/cm2 s cmHg),V the volume ofthe down-stream chamber (cm3), A the effective areaof the membrane (cm2), and T is the experimentaltemperature (K) and the pressure of the feed gas inthe up-stream chamber is given byp0 in psia.

The apparent diffusion coefficient (cm2/s) was esti-mated from the time lag method by using the follow-ing equation:

Dapp = l2

6θ(2)

whereθ is the time lag andl is the membrane thick-ness. The permeabilityP is the product of appar-ent diffusivity Dapp and solubilitySapp. Based on thediffusion–solution mechanism, the apparent solubilitycoefficient,Sapp can be calculated from the followingequation:

Sapp = P

Dapp(3)

The separation efficiency of two components (i, j)may be evaluated from the ratio of their permeabilitythat is known as the separation factor or selectivity,αij . Apparently the overall selectivity may be analysedfrom the view of diffusivity selectivity and solubilityselectivity as follows:

αij =(

Pi

Pj

)=

(Dapp,i

Dapp,j

) (Sapp,i

Sapp,j

)(4)

The temperature dependence of gas permeability,diffusion and solubility coefficients of polymers canbe described by the Arrhenius relationship in regionsfar from thermal transition [23]:

P = P0 exp

(−EP

RT

)(5)

Dapp = D0 exp

(−ED

RT

)(6)

Sapp = S0 exp

(−�HS

RT

)(7)

whereP0, D0 and S0 are the pre-exponential factorsindependent of temperature,EP, ED and�HS the ac-tivation energies for permeation, diffusion and heat

Table 1Physical properties of pure gases

Gas

He O2 N2 CH4 CO2

Kinetic diameter,σ (Å)

2.55 3.46 3.64 3.80 3.30

Critical temperature,Tc (K)

5 155 126 191 304

of solution, respectively,R the universal gas constant,andT is the absolute temperature.

Combining Eq. (3) with Eqs. (5)–(7),P0 is D0×S0,EP is related toED and�HS as follows:

EP = ED + �HS (8)

The six parameters,P0, D0, S0, EP, ED and�HS maybe determined by the least square data fitting based onexperimental results.

The pure gas permeability of 6FDA-1,5-NDA weredetermined in the sequence of He, O2, N2, CH4 andCO2 as a precaution to reduce possible inaccuracyof the measurement caused by the plasticisation phe-nomenon when the polymer is exposed to CO2 at highpressures. The physical properties of these gases arelisted in Table 1. For each gas, measurements were firstconducted by changing the up-stream pressure from3.5, 5, 10, 15 to 20 atm at a constant temperature of35◦C. Then, the gas permeability measurements weremade by varying the temperature ranging from 30, 35,40, 45 to 50◦C while maintaining the up-stream pres-sure at 10 atm.

2.4. Pure gas sorption tests

Sorption test for O2, N2, CH4 and CO2 in6FDA-1,5-NDA dense membranes were conductedusing the Cahn D200 microbalance sorption cellwhich consists of one sample pan and one referencepan. The balance was first calibrated with each in-dividual pure gas in order to eliminate the influenceof buoyancy on the pans. Approximately 200 mg ofsample were loaded on the sample pan and the wholesystem was evacuated for 24 h before testing. Puregas was fed into the sample camber from 0 to 25 atmat 23◦C and was allowed to sorb in the polymersample until sorption equilibrium was established. The


equilibrium sorption value obtained should be cor-rected by accounting buoyancy force.

3. Results and discussion

3.1. Dense membrane preparation

The chemical structure of the material used in thisstudy is confirmed by the FTIR spectrum of syn-thesised 6FDA-1,5-NDA shown in Fig. 2, in whichthe characteristic peaks of imide group appeared at1786 cm−1 (asymmetric stretch of C=O in the imidegroup), 1713 cm−1 (symmetric stretch of C=O inthe imide group) and 1350 cm−1 (stretch of C–N inthe imide group). Experimentally, 6FDA-1,5-NDAcan be dissolved in THF but neither does it dissolvein CH2Cl2 nor CHCl3. After drying, the membraneformed using THF as a solvent was visibly brownishand opaque, which may be attributed to the phaseseparation within the polymer solution. It was foundthat 6FDA-1,5-NDA has a good solubility in DMF.However, when the polymer was dissolved in DMFand left for slow solvent evaporation at ambienttemperature, the polymer solution became white in

Fig. 2. FTIR spectrum of 6FDA-1,5-NDA.

colour. This may be caused by the absorption ofenvironmental moisture by the polymer. Due to therelatively high boiling point of DMF (153◦C), therewas no visible sign of membrane formation for thesolution at ambient temperature. A brownish and visi-bly pristine film was finally obtained when the solventevaporation temperature was meticulously controlled.This is because phase inversion was induced in thethermodynamically stable 6FDA-1,5-NDA solutionby varying its temperature, which leads to a decreasein Gibbs free energy of the solution.

3.2. Effect of temperature on the gas transportproperties of 6FDA-1,5-NDA dense membranes

The gas permeability and permselectivity of6FDA-1,5-NDA dense membranes measured at 35◦Cwith an up-stream pressure of 10 atm are shown inTable 2. It can be seen that 6FDA-1,5-NDA mem-brane has an excellent selectivity of 49 for CO2/CH4with a good permeability of 22.6 Barrers for CO2.The temperature dependence of the gas permeabilityfor He, O2, N2, CH4 and CO2 is depicted in Fig. 3.Apparently, the gas permeability for all the pure gasestested are improved by raising the temperature.


Table 2Gas permeability and permselectivity of 6FDA-1,5-NDA dense membranes measured at 35◦C with 10 atm

Permeability (Barrer) Permselectivity

He O2 N2 CH4 CO2 He/N2 O2/N2 CO2/N2 CO2/CH4

77 6.4 1.1 0.46 23 71 5.9 21 49

Fig. 3. The change of permeability coefficients with absolute temperature.

Table 3 summarises the values forP0, D0, S0, EP, EDand�HS. The positive activation energies of diffusionfor all the gases imply activated diffusion processes,whereas the negative values of molar heats of sorptionfor all the gases suggest exothermic adsorptions.

3.2.1. Effect of temperature on the diffusionand sorption

Fig. 4 depicts that the diffusion coefficients of O2,N2, CH4 and CO2 increase with increasing tempera-ture from 30 to 50◦C. The percentages of increment

Table 3Pre-exponential factors and activation energies for permeation, diffusion and solution of different gases

Gas

O2 N2 CH4 CO2

Pre-exponential factor,P0 × 108 (cm3 (STP)/cm/cm2 s cmHg) 1.02 1.41 5.15 1.07Pre-exponential factor,D0 × 104 (cm2/s) 1.68 4.16 1.89 0.13Pre-exponential factor,S0 × 104 (cm3 (STP)/cm3 cmHg) 0.60 0.40 2.27 8.21Activation energy for permeation,EP (kJ/mol) 7.08 12.46 17.97 4.00Activation energy for diffusion,ED (kJ/mol) 21.05 27.42 30.11 16.12Molar heat of solution,�HS (kJ/mol) −13.99 −14.53 −12.63 −12.13

are 41, 49, 53 and 33% for O2, N2, CH4 and CO2, re-spectively. Slow gases such as N2 and CH4 have higherpermeability increments than O2 and CO2 because theformer has higher activation energies than the latter.In contrast with that observed for diffusivity, the datafrom Fig. 4 also suggest that when the temperatureis progressively increased, the apparent solubility (asdefined by Eq. (3)) for each gas, O2, N2, CH4 andCO2 is slowly decreased. This descending trend is rea-sonable because of the exothermic adsorption for allthe gases.


Fig. 4. The changes of apparent diffusivity and solubility with absolute temperature.

3.2.2. Synergistical impacts of the diffusion and thesorption on the permeation

At low temperatures, permeation is diffusion-restricted, because gas diffusion is much slower thanthat at higher temperatures. Meanwhile, at high tem-peratures the process is solution-restricted, becausegas dissolution in the polymer is slower than thatat low temperatures.EP is the sum of bothED and�HS, the effect of temperature on diffusivity is morepronounced asED � |�HS|, thereby outweighing therole of the solubility to the overall permeability.

3.2.3. Comparison of the diffusivity and solubilityof four gases

It is believed that the activation energy of a penetrantfor diffusion increases with its kinetic diameter [24].With reference to Table 3, the activation energy fordiffusion (ED) obtained in our work follows a similartrend in the order of

ED(CH4) > ED(N2) > ED(O2) > ED(CO2)

which is in the same sequence as the penetrant kineticdiameter:

σk(CH4) = 3.8 Å > σk(N2) = 3.64 Å > σk(O2)

= 3.46 Å > σk(CO2) = 3.3 Å

Fig. 4 illustrates a comparison of all the diffusivitydata of these four pure gases, it is observable thatwith exception to CO2, the magnitude of the dif-fusivity of the three non-interacting gases increaseswith the order of O2 > N2 > CH4. Based on theStoke–Einstein equation [25], the molecules with alarger radius exert more frictional resistance and ren-der an adverse impact on diffusion. Therefore, smallergas molecules tend to diffuse more rapidly than theirlarger counterparts.

On the other hand, it is noticed that the solubilityof gases adopts a parallel trend with their critical tem-peratures. As reported in Table 1, the magnitude ofcritical temperature grows in the order of

Tc(N2) < Tc(O2) < Tc(CH4) < Tc(CO2)

The gas solubility is therefore being enhanced in thesame gas sequence:

Sapp(N2) < Sapp(O2) < Sapp(CH4) < Sapp(CO2)

Referring to the Table 3 again, the activation en-ergy of permeation,EP is highest for CH4, trailed byN2, O2 and finally CO2, which is in the similar trendof activation energy of diffusion. This indicates againthat the diffusion plays a more prominent role in de-termining the overall permeation of the gases.


Table 4Effect of temperatures on gas permselectivity and diffusivityselectivity at 10 atm

T (◦C) PO2/PN2 PCO2/PCH4 DO2/DN2 DCO2/DCH4

30 6.1 53 5.1 1835 5.9 49 4.8 1640 5.8 45 4.7 1545 5.6 42 4.5 1450 5.3 38 4.4 13

3.2.4. Effect of temperature on the permselectivityThe permselectivities for the gas pairs, O2/N2 and

CO2/CH4 at various temperatures are summarised inTable 4. According to Table 4, both gas pairs of O2/N2and CO2/CH4 have lower permselectivities at highertemperatures as a result of larger activation energiesof N2 and CH4 for permeation as compared to O2and CO2, respectively. Additionally, a decline is ob-served in the changes of the diffusivity selectivity withtemperature.

3.3. Effect of pressure on the gas transportproperties of 6FDA-1,5-NDA dense membranes

Fig. 5 shows that the permeability decreases uponpressure rising for all the four pure gas tested. Theextent of decrease appears more prominent in the orderof kinetic diameters of the gases. Again the evaluationof this result is addressed in terms of their diffusivityand solubility.

Fig. 5. The change of permeability coefficients with pressure.

Fig. 6. The change of apparent diffusivity with pressure.

3.3.1. Effect of pressure on the diffusion and sorptionFigs. 6 and 7 show that with increasing pressure, the

apparent diffusivity increases while the apparent sol-ubility decreases, respectively, for all the gas tested.The apparent diffusivity of CO2 depicts the most sig-nificant degree of increment, because a higher pressuremay tend to weaken the polarity interactions betweenCO2 and the polymer. Similarly, CO2 also shows themost significant degree of decrement in the solubilitywhen the pressure is increased.

The above observation may be explained by thedual-mode sorption model [26–33]:

C = CD + CH = kDp + C′Hbp

1 + bp(9)

where the total amount of gas sorbed in the poly-mer (C) is the sum of the gas concentrations in the

Fig. 7. The change of apparent solubility with pressure.


Fig. 8. Pure gas sorption isotherm for 6FDA-1,5-NDA at 23◦C.

Henry’s mode (CD) and the Langmuir sites (CH), kDthe Henry’s law constant,C′

H the Langmuir capacityconstant andb is the Langmuir affinity constant. Thus,the solubility may be expressed as a function of pres-sure:

S = C

p= kD + C′

Hb

1 + bp(10)

The Henry’s sorption occurs in the densified poly-mer area, whereas the Langmuir’s sorption occurs inthe molecular-scale microvoids originally present inthe polymer matrix when the polymer is quenchednon-equilibriumly through its glass transition tem-perature. Adopting the partial immobilisation model[27,30,31], which assumed that the Langmuir’s pop-ulation is partially mobilised and characterised bya diffusion coefficientDH, the permeability may bere-written as follows:

P = kD

(1 + FK

1 + bp

)DD (11)

whereDD is the diffusion coefficient of the Henry’spopulation,F viewed as the moving fraction of theLangmuir’s population or alternatively defined asDH/DD [34] and K is a combination of sorption pa-rameter defined asC′

Hb/kD. From above Eqs. (10)and (11) we can deduce that solubility and perme-ability decrease when pressure is raised, as illustratedin Figs. 5–7, respectively.

3.3.2. Sorption analysisPure gas sorption isotherms for N2, O2, CH4 and

CO2 are given in Fig. 8. The parameters ofkD, C′H and

b are calculated by a non-linear least squares fit of thesorption using Eq. (9), whereasF andDD are obtainedby a non-linear least squares fit of the permeation datausing Eq. (11) afterkD, C′

H and b are known. Theyare tabulated in Tables 5 and 6. Here it should bepointed out that parameters ofkD, C′

H andb obtainedat 23◦C were used to estimate the values ofF andDDat 35◦C due to the limitation of temperature controlof the sorption cell. We assume that possible errorsoccurring from the temperature dependence of theseparameters is negligible.

Table 5Sorption parameters for 6FDA-1,5-NDAa

Gas kD (cm3 (STP)/cm3 atm)

C′H (cm3

(STP)/cm3)b (1/atm)

N2 (i) 0.29 12.25 0.086(ii) 0.30 12.15 0.087

O2 (i) 0.31 17.24 0.099(ii) 0.33 16.95 0.100

CH4 (i) 0.33 27.58 0.14(ii) 0.37 27.23 0.14

CO2 (i) 1.38 42.80 0.93(ii) 1.65 40.46 1.04

a Values calculated using (i) pressure and (ii) fugacity.


Table 6Parameters ofK, F, DH and DD for various gases

Gas K F DH (cm2/s) DD (cm2/s)

N2 3.59 0.092 2.21× 10−9 2.39 × 10−8

O2 5.40 0.039 5.54× 10−9 1.42 × 10−7

CH4 11.6 0.037 3.25× 10−10 8.83 × 10−9

CO2 28.9 0.065 6.55× 10−9 1.01 × 10−7

Table 5 shows that CO2, has the largest value forkD and b, followed by CH4, O2 and N2. The valuesof kD andb correlate with the physical properties ofthe penetrant molecules such as the critical tempera-tures as well as condensibility. Among the four gasestested, CO2 has the highest condensibility followedby CH4, O2 and N2. Table 5 also shows the values ofsorption parameters calculated using pressure and fu-gacity to account for the deviation of gases from idealgas behaviour. The differences are minor.

In fair agreement with the concept of the partial im-mobilisation model [30],DD is greaterDH as shownin Table 6. Thus, the overall gas diffusivity increaseswith increasing pressure as the result of the dominat-ing DD. A similarity in the gas sequence is observedin the Henry’s diffusivity and the apparent diffusivityformerly obtained in which theDD for O2 > CO2 >

N2 > CH4. Table 7 shows the comparison between thesolubility (S) estimated from sorption measurement at23◦C with the apparent solubility (Sapp) obtained fromthe permeability measurement at 35◦C. The differ-

Fig. 9. Pure gas sorption in various modes as a function of pressure.

Table 7Comparison of theSapp (at 35◦C) with S estimated from sorptionmeasurements (at 23◦C) at 10 atm

Gas Sapp (102 cm3

(STP)/cm3 cmHg)S (102 cm3

(STP)/cm3 cmHg)

N2 1.28 1.15O2 1.55 1.54CH4 3.37 2.61CO2 9.94 6.39

ences of the values ofS andSappare mainly caused bytheir definitions. However, both results show a similartrend in the gas order where the solubility of CO2 >

CH4 > O2 > N2.

3.3.3. Effect of pressure on the gas sorption andmobility in the different sorption modes

The gas sorption in the polymer matrix that consistsof Henry’s and Langmuir’s fractional concentration,CD/C andCH/C as a function of pressure are shownin Fig. 9. With the increase of pressure, the fractionalconcentration of Langmuir sites decreases gradually.But for CO2 and CH4 at 25 atm, more than 50% of theentire total gas sorbed are distributed in the Langmuirenvironment. The saturation fraction of Langmuir site,CH/C′

H is depicted as a function of pressure in Fig. 10.For CO2, because of its high condensability, its satura-tion fraction reaches more than 90% rapidly, showingthat almost all the microvoids are filled with Langmuirspecies.


Fig. 10. Saturation fraction of Langmuir isotherm.

Fig. 11. Fractional mobility of Langmuir and Henry isotherms.

The fractional mobilities of Henry and Langmuirspecies may be characterised byCD/(CD + FCH)andFCH/(CD + FCH), respectively. As illustrated inFig. 11, the fractional mobility of Langmuir speciesdecreases, while the fractional mobility of the Henryspecies increases when the feed pressure increases.Obviously, when all the Langmuir sites are no longeravailable, the gas dissolves in the Henry mode pri-marily takes charge.

4. Conclusion

We have studied the permeability and selectivityof 6FDA-1,5-NDA polyimide membranes as afunction of temperature and pressure. The 6FDA-1,5-NDA membrane has an excellent selectivityof 49 for CO2/CH4 with a good permeability of22.6 Barrers for CO2 under the pressure of 10 atm at35◦C.


When the temperature is raised, the overall per-meability of the membrane increases as a result ofthe increasing gas diffusivity despite of the decreaseof the gas solubility. Experimental data strongly sug-gest that the effect of diffusivity is more pronounced,thereby diluting the role of the solubility conse-quences to the overall permeability. The activationenergy of permeation for CH4, N2, O2 and CO2 is inthe similar trend of the activation energy of diffusion,which is consistent with the order of their kineticdiameters.

The solubility of gases and their respective sorptionparameters adopt a parallel trend with their criticaltemperatures. CO2 demonstrates the highest sorptionlevel followed by CH4, O2 and N2. CO2 also has thehighest dissolution in the Henry’s environment andthe highest affinity for the Langmuir sites. The gassolubility calculated from the sorption measurementsshows a similar trend to the apparent solubility ob-tained from the permeability measurement in the gasorder where the solubility of CO2 > CH4 > O2 >

N2.Upon pressure acceleration, the gas diffusivity in-

creases while the solubility decreases. In spite of thecontradicting effect of pressure on diffusivity and solu-bility, the overall gas permeability of 6FDA-1,5-NDAdecreases with increasing pressure, which may beexplained by using the dual-mode sorption modeland the partial immobilisation model. More than 50%of the entire total gas sorbed is distributed in theLangmuir environment. The fractional mobility ofLangmuir species decreases, while the fractional mo-bility of the Henry species increases when the feedpressure increases. CO2 exhibits the most significantpressure-dependent properties due to its the strongestinteraction and highest condensability.

Acknowledgements

The authors would like to thank British Gas AsiaPacific Pte. Ltd. (BG), Institute of Materials Researchand Engineering (IMRE), Environmental Technol-ogy Institute (ETI), Economic Development Boardof Singapore (EDB) and the National Science andTechnology Board of Singapore (NSTB) for fundingthis project. Special thanks are due to Dr. Cheng forher kind help on the sorption study.

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gas transport properties of poly(1,5-naphthalene-2,2′-bis(3,4-phthalic) hexafluoropropane) diimide...

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