Gas solubility, diffusivity and permeability in poly(ethylene oxide)

Journal of Membrane Science 239 (2004) 105–117

Gas solubility, diffusivity and permeability in poly(ethylene oxide)

H. Lin, B.D. Freeman∗

Department of Chemical Engineering, Center for Energy and Environmental Resources, The University of Texas at Austin,10100 Burnet Road, Building 133, Austin, TX 78758, USA

Received 14 March 2003; received in revised form 7 August 2003; accepted 25 August 2003

Available online 6 May 2004

Abstract

The effect of pressure on the solubility, diffusivity, and permeability of He, H2, O2, N2, CO2, CH4, C2H4, C2H6, C3H6 and C3H8 inpoly(ethylene oxide) (PEO) is reported at 35◦C. Additionally, the temperature dependence of permeability is reported. The effect of polarether linkages in PEO on gas transport is illustrated by comparing transport properties in PEO with those in polyethylene (PE). For example,at 35◦C and infinite dilution, semi-crystalline PEO exhibits CO2 permeability coefficient of 12 Barrers, and CO2/H2 and CO2/N2 pure gasselectivities of 6.7 and 48, respectively. In contrast, at similar conditions, the permeability of PE to CO2 is 13 Barrers, but the CO2/N2 selectivityis only 13. In addition to good separation properties for quadrupolar–nonpolar gas pairs, PEO also shows interestingly high selectivity forolefins over paraffins, which is ascribed to favorable interaction between the polar ether groups in PEO and olefins. For example, the infinitedilution permeability of PEO to propylene is 3.8 Barrers and pure gas propylene–propane selectivity is 2.7 at 35◦C. At similar conditions, PEexhibits propylene–propane selectivity of only 1.4.© 2004 Elsevier B.V. All rights reserved.

Keywords: Poly(ethylene oxide); Carbon dioxide; Separation; Solubility; Permeability

1. Introduction

The use of membranes to selectively remove CO2 frommixtures with H2, CO, N2 and CH4 is of interest for a widevariety of applications such as syngas processing, flue gasrectification, and natural gas separations[1,2]. One particu-lar example is hydrocarbon reforming, which is the dominanttechnology for H2 production[3]. This process producesmixtures of H2 and CO2 that must be separated. Unfortu-nately, conventional membranes are usually hydrogen selec-tive [4]. In such membranes, the desired hydrogen productis produced at low pressure in the permeate stream of themembrane, but it is typically utilized at pressures equal toor higher than feed pressure. The cost of repressurizing thehydrogen to feed pressure can be prohibitive and contributesto the use of alternative processes, such as liquid absorption,to remove acid gases such as CO2 from such streams.

Polymers containing polar moieties, such as ether groups,have an affinity for CO2 due to dipole–quadrupole interac-

∗ Corresponding author. Tel.:+1-512-232-2803;fax: +1-512-232-2807.

E-mail address: [email protected] (B.D. Freeman).

tions[5]. This affinity may be harnessed to prepare materialsthat are more permeable to CO2 than to H2. Such membranescould be used to selectively remove CO2 and other acid gasesfrom mixtures with H2. Using such membranes, H2 wouldbe produced in the high-pressure residue stream, possiblyreducing or eliminating expensive recompression steps.

Because of the interest in improving CO2 separationperformance, there have been many recent studies of poly-mer membranes containing poly(ethylene oxide) (PEO),poly(ethylene glycol) (PEG) or other groups bearing polarether segments that can interact favorably with acid gasessuch as CO2 [6–21]. For example, blending PEG with cel-lulose nitrate or cellulose acetate increased both CO2 per-meability and CO2/N2 selectivity [6,8]. Block copolymerscontaining PEO segments exhibit high CO2 permeabilityand high CO2/N2 and CO2/H2 selectivity[9–13,15–18,20].For example, Bondar et al. studied poly(ether-b-amide)copolymers; they observed a CO2 permeability of 120 Bar-rers and a CO2/H2 pure gas selectivity of 9.8 at 35◦C anda feed pressure of 1.0 MPa (10 atm)[17]. Table 1presentsCO2 permeability and CO2/N2 selectivity in some blockcopolymers containing roughly the same weight percentof PEO segments and different hard segments. While the

0376-7388/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.memsci.2003.08.031

106 H. Lin, B.D. Freeman / Journal of Membrane Science 239 (2004) 105–117

Table 1Gas transport properties in block copolymers containing similar amountsof poly(ethylene oxide) segments and a variety of hard segments

Hard segmenta PEO (wt.%) PCO2 [Barrer] PCO2/PN2

PolyimidePMDA-pDDS [10] 68.6 238 49BPDA-ODA [10] 62.3 117 51

PolyamideIPA-ODA [10] 68.3 58 53PA12 [17] 55 120 51PA6 [17] 57 66 56

PolyurethaneMDI-BPA [10] 60.5 48 47

a The detailed chemical structures are available in the correspondingreferences. The gas permeability was measured at 35◦C and 200 kPa(2 atm) in [10], and at 35◦C and 1.0 MPa (10 atm) in[17].

gas selectivity is similar among all these materials, gaspermeability varies significantly. These results suggest thatthe PEO phase is the continuous path for gas permeation[10,17], and gas permeability depends strongly on the de-tailed morphology, such as domain shape and interspatialarrangement, which could be influenced by the hard seg-ment composition and the length of PEO and hard segmentblocks.

Despite this interest in PEO-based materials for acid gasselective separations, a systematic study of the solubility, dif-fusivity, and permeability properties of pure poly(ethyleneoxide) has not been reported, due in large measure to its highcrystallinity and, consequently, low transport property val-ues. In this study we present physical characterization andgas transport properties of solution cast PEO films. The ef-fect of pressure on gas permeability, diffusivity and solubil-ity is reported for a variety of nonpolar gases (He, H2, O2,N2), a series of olefinic and aliphatic hydrocarbons (CH4,C2H6, C2H4, C3H8, C3H6), and CO2. The effect of tem-perature on permeability is also reported. Relevant physicalproperties of these penetrants, which will be used later inthe discussion, are recorded inTable 2.

Table 2Penetrant parameters characterizing size (critical volume) and condens-ability (critical temperature)

Size (critical volume[39] (cm3/mole))

Condensability (criticaltemperature[39] (K))

He 57.4 5.19H2 65.1 33.24O2 73.4 154.6N2 89.8 126.2CO2 93.9 304.21CH4 99.2 191.05C2H4 130.4 282.40C2H6 148.3 305.35C3H6 181.0 364.9C3H8 203.0 369.8

2. Background

The permeability of a polymer to a gas A,PA, is [4]:

PA ≡ NA l

p2 − p1(1)

whereNA is the steady-state flux of gas through the film,lis the film thickness, andp2 andp1 are the upstream (i.e.,high) and downstream (i.e., low) partial pressures of gasA, respectively. If the diffusion process obeys Fick’s law,and the downstream pressure is much less than upstreampressure, the permeability is given by[4]:

PA = DASA (2)

where DA is the average effective diffusivity through thefilm, andSA is the apparent sorption coefficient[4]:

SA = C2

p2(3)

whereC2 is the concentration of gas dissolved in the polymerwhen the gas pressure in contact with the polymer isp2.

The ideal selectivity of a membrane for gas A over gas Bis the ratio of their pure gas permeabilities[4]:

αA/B = PA

PB=

[DA

DB

] [SA

SB

](4)

whereDA/DB is the diffusivity selectivity, the ratio of thediffusion coefficients of gases A and B. The ratio of the solu-bilities of gases A and B,SA/SB, is the solubility selectivity.Diffusivity selectivity is strongly influenced by the size dif-ference between the penetrant molecules and the size-sievingability of the polymer matrix, whereas solubility selectivityis controlled by the relative condensability of the penetrantsand the relative affinity between the penetrants and the poly-mer matrix[4].

Gas transport properties in a semi-crystalline polymersuch as PEO are usually modeled by assuming that the crys-tals act as an impermeable dispersed phase imbedded in anamorphous phase and by then developing models for the in-fluence of crystallinity on solubility and diffusivity. In a rub-bery polymer, the effect of crystallinity on penetrant sorp-tion is typically represented as follows[22]:

SA = SA,aφa (5)

whereSA is the observed solubility coefficient,SA,a is thesolubility coefficient in the amorphous polymer, andφa isthe amorphous phase volume fraction.

The influence of crystallinity on diffusivity is traditionallydescribed as follows[23]:

DA = DA,a

τβ(6)

where DA,a is the diffusion coefficient in the amorphouspolymer, τ is a tortuosity factor, andβ is a chain im-mobilization factor.τ characterizes the tortuosity of theamorphous phase caused by the presence of impermeable

H. Lin, B.D. Freeman / Journal of Membrane Science 239 (2004) 105–117 107

crystallites dispersed in it. Simple models from compos-ites theory, such as the one given below, are often used todescribe the influence of crystallinity on tortuosity[23]:

τ = 1

φa(7)

The chain immobilization factor,β, accounts for the re-stricted segmental mobility in the amorphous phase bycrystallites. In the simplest case, whenβ = 1 (i.e., no chainimmobilization), gas permeability is given by[23]:

PA = SADA = PA,aφ2a (8)

wherePA,a is the estimated permeability of penetrant A inamorphous phase polymer.

Generally, crystallites decrease both gas diffusivity andsolubility. By reducing amorphous phase polymer chain mo-bility, crystallites can also increase activation energy of dif-fusion, especially for larger penetrants[23]. These effectsbecome more pronounced as the crystalline volume fractionincreases or as crystallite size decreases[23].

3. Experimental

3.1. Materials and sample preparation

Poly(ethylene oxide) with a weight-average molecularweight of approximately 1,000,000 was purchased fromAldrich Chemical Company, Milwaukee, WI and used as-received. The gases and vapors used in pure gas permeationand sorption measurement had a purity of at least 99% andwere obtained from National Specialty Gases (Raleigh, NC).

Gas permeation and sorption experiments were conductedusing dense PEO films of uniform thickness, prepared bydissolving solid PEO in ultrapure water, which is producedby a Milli-Q water purification system (Millipore Corpora-tion, Bedford, MA). Films were cast from 3 wt.% water so-lutions into plastic or Teflon flat-bottomed Petri dishes. Af-ter air-drying at ambient conditions for 3–7 days, films wereremoved from the dish and placed on a Teflon plate. PEOfilms were stored under vacuum in an oven at room temper-ature for 24 h to assist in removal of residual water and thenannealed at 70–80◦C for 2 h. After annealing, samples wereremoved from the oven and cooled at ambient conditionsbefore being placed in a desiccator, where they were storeduntil use. Film thicknesses were in the range of 100–300�m.

Initially, it was difficult to prepare defect free PEO films.We arrived at the film preparation protocol described in theprevious paragraph after trying several solvents (acetoni-trile, chloroform, and water), concentrations and evaporationrates. However, these variables did not have as much impacton the ability to prepare defect free samples as annealing.Generally, samples prepared without annealing were defec-tive (i.e., they showed similar permeabilities to all gases).In contrast, annealing solvent cast films above the polymermelting temperature resulted in defect free films. Because

PEO is susceptible to oxidative degradation, due to the pres-ence of weak C–O bonds in the backbone[24], the anneal-ing time needed to be as short as possible and the annealingtemperature needed to be as low as possible. Therefore, tominimize the degradation and prepare a nonporous film, wedecided to anneal the sample under vacuum just above itsmelting temperature for 2 h.

3.2. Density

Polymer film density was determined by hydrostaticweighing using a Mettler Toledo balance (Model AG204,Switzerland) and a density determination kit[25]. In thismethod, a liquid with a known density (ρo) (the so-calledauxiliary liquid) is needed, and the film density (ρ) iscalculated as follows:

ρ = MA

MA − MLρo (9)

where MA is the film weight in air, andML is the filmweight in the auxiliary liquid. Iso-octane was used as theauxiliary liquid because PEO is reported to be insoluble iniso-octane[26]. The film weight determination in iso-octanewas performed as quickly as possible to reduce any swellingof PEO due to iso-octane sorption.

3.3. Thermal characterization

Thermal transitions were determined using a PerkinElmer (Shelton, CT) DSC 7 differential scanning calorime-ter (DSC). Experiments were performed at a heating rate of20◦C/min over temperatures ranging from 0 to 120◦C. Thedegree of crystallinity was evaluated from the area underthe melting endotherm in the first scan[27].

3.4. Permeation measurements

The pure gas permeation properties in PEO were deter-mined using a constant volume/variable pressure apparatus[17]. The permeation cell is a stainless steel filter holder fromMillipore Corporation (47 mm disc filter, Bedford, MA) withan area of 13.8 cm2. PEO samples were partially masked us-ing impermeable aluminum tape on the upstream face, or onthe upstream and downstream faces as described by Mogriand Paul[28]. Both masking methods gave very similar per-meability values, consistent with the observations of Mogriand Paul[28]. The o-ring in the permeation cell was in directcontact with the aluminum tape so that the soft rubbery PEOfilm would not be damaged by the o-ring. After aluminumtape masking, the surface area of the sample available forgas transport was 5.1 cm2.

After a film was mounted in the system, both upstreamand downstream volumes were exposed to vacuum overnightto degas the film. The leak rate in the system was alwaysmeasured before starting the permeation experiments, andthen the pressure increase in the downstream volume was


recorded. Gas permeability (cm3(STP) cm/(cm2 s cm Hg))was calculated from the steady-state rate of pressure in-crease in a fixed downstream volume:

PA = Vdl

p2ART

[(dp1

dt

)ss

−(

dp1

dt

)leak

](10)

whereVd is the downstream volume (cm3), l is the film thick-ness (cm),p2 is the upstream absolute pressure (cm Hg),Ais the film area available for gas transport (cm2), the gasconstant,R the 0.278 cm Hg cm3/(cm3(STP) K),T is the ab-solute temperature (K) and (dp1/dt)ssand (dp1/dt)leak are thesteady-state rates of pressure rise (cm Hg/s) in the down-stream volume at a fixed upstream pressure and under vac-uum, respectively. (dp1/dt)leak was usually less than 10% of(dp1/dt)ss. The downstream pressure was always less than2 cm Hg, which was very low compared with lowest up-stream pressure considered (400 kPa (4 atm)).

3.5. Sorption measurements

Gas solubility was determined using a dual-volume, dual-transducer apparatus based on the barometric, pressure-decay method[16]. Polymer samples were degassed byexposure to vacuum in the sorption cell overnight beforebeginning sorption measurements and between each gas.

Because PEO is highly crystalline and, therefore, exhibitslow solubility, the uncertainty in the measured solubility co-efficients of the low sorbing permanent gases was high. Forexample, the uncertainty in solubility was estimated to be±50% for N2, O2 and CH4, and less than 10% for the otherpenetrants. Solubilities of H2 and He at 35◦C were too lowto measure. Uncertainty was estimated by a standard propa-gation of errors analysis[29], where uncertainties of all rel-evant measured parameters propagate and contribute to theuncertainty of the solubility. The dominant contribution tothe uncertainty comes from the uncertainty in measuring thepressure in the sorption cell. For this measurement, we usethe two Sensotec pressure transducers (Model Super THE),and the uncertainty in the measured pressure is±1.7 kPa(±0.017 atm). The full pressure range of the transducer is0–3.4 MPa (0–34 atm).

4. Results and discussion

4.1. Thermal and physical characterization

Fig. 1presents a first scan DSC thermogram of PEO. Thepeak of the melting endotherm is 68◦C, which is near thevalue of 66◦C reported for PEO with a molecular weight of1,000,000[30]. The weight fraction crystallinity in the film,χc, was estimated as follows[27]:

χc = �H

�Hc(11)

Fig. 1. First scan differential scanning calorimetry thermogram of poly(ethylene oxide).

where�H is the melting enthalpy, obtained from the areaunder the melting endotherm, and�Hc is the melting en-thalpy of 100% crystalline PEO. From the DSC experiment,�H was 121 J/g, which is close to the literature value of125 J/g for PEO with a molecular weight of 4,000,000[27].A variety of values of�Hc exist in the literature rangingfrom 166.4 to 265 J/g[26]. In this study, we used the valueof 166.4 J/g suggested by Simon and Rutherford[30]. Us-ing this value inEq. (11) yields a crystallinity value of72.7 wt.%.

Volume fraction crystallinity,φc, was calculated as fol-lows:

φc =(

ρ

ρc

)χc (12)

whereρ is the measured PEO density andρc is the crystaldensity calculated from the unit cell dimensions of a PEOcrystallite, which is 1.234 g/cm3 at room temperature[30].PEO film density,ρ, was 1.209 g/cm3, which is consistentwith values (1.20–1.22 g/cm3) reported in the literature forPEO[25]. UsingEq. (12), the crystallinity was 71 vol.%.

The volume percent crystallinity can also be estimatedfrom the density using the following relation:

φc = ρ − ρa

ρc − ρa(13)

whereρa is the density of amorphous PEO (1.124 g/cm3)[30]. Theφc value calculated fromEq. (13)was 0.77, whichis consistent with that obtained fromEq. (12). In the remain-der of this report, the crystallinity calculated from the DSCresult will be used to estimate amorphous phase permeabil-ity and solubility values.

Transport properties in polymers are sensitive to theamount of free volume in the polymer matrix[4]. In semi-crystalline polymers such as PE and PEO, transport ispresumed to occur only in the amorphous regions of thepolymers, so it is of interest to compute the fractional free


Table 3Physical property comparison between poly(ethylene oxide) andpoly(ethylene)

Polymer Tga (◦C) FFVb Densityc

(g/cm3)Crystallinity(vol.%)

Solubilityparameter(MPa1/2)[26]

PEO −50 0.139 1.124 71 19.8PE −44 0.188 0.854 43d 16.6

a In these polymers,Tg depends strongly on the degree of crystallinity[50]. The value reported for PEO corresponds to 74 vol.% crystallinity[50]. The value reported for PE corresponds to a sample with 43 vol.%crystallinity; in a PE sample having 71 vol.% crystallinity, theTg would be−10◦C [50]. If one extrapolates to hypothetical wholly amorphous PEOand PE, the estimatedTg values are−85 and−80◦C, respectively[50].

b FFV values based on estimated density of amorphous PE and PEO.c Estimated density of wholly amorphous polymer at room temperature.d Alathon 14 polyethylene was chosen from the reference by Michaels

and Bixler [22]. Later in this report, gas transport properties of Alathon14 are compared with those of PEO.

volume in the amorphous regions of such polymers. Theamorphous density data were used to estimate the frac-tional free volume (FFV) of the amorphous phase using thefollowing group contribution method[31]:

FFV = V − Vo

V(14)

whereV is the specific volume of the amorphous polymer atthe temperature of interest andVo is the specific occupiedvolume at 0 K, which was estimated as 1.3 times the vander Waals volume[32]. The densities of amorphous PEOand PE were taken to be 1.124 g/cm3 at 20◦C [30] and0.854 g/cm3 at 25◦C [22], respectively. Using these values,the FFV of the amorphous phase of PEO is 0.139. Thisvalue is significantly lower than that of PE, which has anamorphous phase FFV of 0.188. These values are recordedin Table 3.

4.2. Permeability

Fig. 2a and bpresent permeability coefficients for gasesat 35◦C as a function of upstream pressure. For the perma-nent gases (He, H2, O2, and N2), permeability coefficientsare essentially independent of pressure, while the permeabil-ity coefficients of CO2 and hydrocarbons such as C3H8 in-crease with increasing pressure. This behavior is consistentwith gas permeation properties in rubbery polymers[33].For strongly sorbing penetrants, such as CO2 and C3H8, highpenetrant concentrations can plasticize the polymer matrixby increasing polymer local segmental motion, thus enhanc-ing penetrant diffusion coefficients and, in turn, permeabil-ity [34]. Additionally, the solubility of condensable compo-nents typically increases with increasing pressure, and thisfactor also acts to increase permeability coefficients[35].

For the data inFig. 2a,b, the pressure dependence of thepermeability coefficients may be described by the following

Fig. 2. (a) Permeability coefficients of penetrants in semi-crystalline PEOat 35◦C as a function of upstream pressure. The scale for gas permeabilityvalues is shown on the lefty-axis for all gases except CO2, whose scale isin the right y-axis. (b) Permeability coefficients of hydrogen and severalhydrocarbons in semi-crystalline PEO at 35◦C as a function of upstreampressure.

simple empirical model[33]:

PA = PA,o(1 + m �p) = PA,o(1 + mp2) (15)

wherePA,o is the permeability coefficient at an upstreampressure,p2, of 0 (i.e., infinite dilution permeability),m theadjustable constant, and�p is the difference between theupstream and downstream pressure,�p = p2 − p1. Sincedownstream pressure,p1 is much less than upstream pres-surep2, �p can be replaced byp2. Infinite dilution perme-ability coefficients for different penetrants were calculatedusing Eq. (15). Estimated amorphous phase permeabilitycoefficients were estimated usingEq. (8). This calculationpresumes that tortuosity obeysEq. (7) andthat the chainimmobilization factor,β, is unity. Because we did not havePEO samples with varying levels of crystallinity, neither ofthese assumptions can be tested. As a result, the estimated


Table 4Penetrant permeation parameters in semi-crystalline and amorphous poly(ethylene oxide) and in amorphous polyethylene[22,23]

Gas PEO PE

PA,oa (Barrer) m × 103 (atm−1) PA,a

b (Barrer) Ep (kJ/mole) PA,o (Barrer) PA,ab (Barrer)

He 1.7± 0.1 −4 ± 8 20 84± 3 4.9 34H2 1.8 ± 0.1 −2 ± 7 21 76± 5O2 0.68 ± 0.05 −0.4 ± 7 8.1 89± 6 2.9 18N2 0.25 ± 0.02 −10 ± 7 3.0 95± 5 0.97 6.7CO2 12 ± 1.0 34± 10 143 70± 7 13 78CH4 0.60 ± 0.05 12± 8 7.1 133± 6 2.9 23C2H4 2.9 ± 0.5 8 ± 22 34 50± 10C2H6 1.6 ± 0.3 23± 21 19 75± 9 6.8 66C3H6 3.8 ± 1.6 250± 90 45 58± 11 14 147C3H8 1.4 ± 0.6 180± 70 17 70± 16 9.5 108

a Infinite dilution permeability in semi-crystalline PEO.b Estimated infinite dilution amorphous phase permeability coefficients at 35◦C in PEO and 25◦C in PE. Permeability coefficients in amorphous phase

PE are calculated as the product of solubility coefficients in amorphous PE[22] and diffusion coefficients in amorphous PE estimated withEq. (6) [23].

amorphous phase permeability coefficients should be re-garded as rather crude estimates of the actual permeationproperties of the amorphous material. These data are re-ported inTable 4. The permeability coefficients decrease inthe following order:

CO2 > C3H6 > C2H4 > H2 ≈ He > C3H8

≈ C2H6 > CH4 ≈ O2 > N2

Except for CO2 and the olefins, this order of permeabilitycoefficients is typical for rubbery polymers[33]. Generally,penetrants with higher critical temperature are more con-densable and, therefore, more soluble; however, more con-densable penetrants often have larger critical volume values(cf. Table 2), which reduces diffusion coefficients. Perme-ability reflects the tradeoff between these often conflictingcontributions from solubility and diffusivity.

The gas transport properties of polyethylene (PE) havebeen well studied[22,23]. Polyethylene provides an inter-esting material for comparison with PEO because PE isessentially PEO without the polar ether linkages. Severalphysical properties of these two polymers are compared inTable 3. The amorphous phase FFV of PEO is significantlylower than that of PE, and the solubility parameter of PEOis higher than that of PE. These trends are qualitativelyconsistent with the much more polar nature of PEO.

Table 4presents a comparison of infinite dilution perme-ability coefficients in amorphous PEO and PE. Unlike PEO,literature values for tortuosity and chain immobilization fac-tors are available for PE[23], and these data were used toestimate amorphous phase permeability coefficients in PE.With the exception of CO2, PE exhibits higher permeabilityvalues than PEO, even though the PE data were determinedat lower temperature (25◦C, rather than 35◦C for PEO).CO2 is the only gas exhibiting higher permeability in PEOthan in PE. Interestingly, CO2 is much more permeable thanall of the other gases considered, including H2, which, inconventional glassy gas separation polymers, always has ahigher permeability coefficient than CO2 [4]. The estimated

CO2 permeability in amorphous phase PEO is within therange of values reported for block copolymers containingPEO (cf. Table 1). The CO2/H2 pure gas selectivity in PEOis 6.7 at infinite dilution and increases to 9.9 at 1.5 MPa(14.7 atm), which is similar to values reported for polyether-b-polyamide segmented block copolymers[17]. To empha-size the effect that this difference in properties for CO2 hason separation, one can also consider the CO2/N2 selectivity.In PE, the pure gas CO2/N2 selectivity at infinite dilution isapproximately 12. However, in polar PEO, the CO2/N2 puregas selectivity at infinite dilution is 48, which is essentiallyequivalent to the selectivity in block copolymers containingPEO, as shown inTable 1. These results are consistent withenhanced solubility of quadrupolar CO2 in PEO.

It is also of interest to explore the difference betweenolefin and paraffin transport in these two polymers becauseof the importance of this separation to the petrochemicalindustry[36]. In amorphous PE, propane and propylene havevery similar permeability coefficients, and the C3H6/C3H8selectivity is only 1.4 (cf.Table 5). However, in amorphousPEO, olefins exhibit significantly higher permeability thantheir paraffin analogues. The pure gas C3H6/C3H8 selectivityat infinite dilution and 35◦C is 2.7, which is almost 100%

Table 5Estimated amorphous phase propylene permeability, diffusivity and sol-ubility, and C3H6/C3H8 selectivity in PE at 25◦C and PEO at 35◦C atinfinite dilution

Propylene sorption andtransport properties

Propylene–propaneselectivity

PEb PEO PE PEO

PAa 147 45 P=/P c 1.4 2.7

Daa × 107 3.2 1.7 D=/D c 1.5 1.6

SAa 3.5 2.0 S=/S c 0.89 1.7

a The units for permeability (P), diffusivity (D) and solubility (S) areBarrer, cm2/s, and cm3(STP)/(cm3 polymer atm), respectively.

b Michaels and Bixler[22,23].c The subscripts “=‘’ and “ ” represent propylene and propane, respec-

tively.


Table 6Effect of pressure and temperature on pure gas permeability coefficientsin semi-crystalline PEO

Pressure (atm) Permeability (Barrer)

25◦C 35◦C 45◦C

N2

4.4 0.24 0.997.8 0.07 0.24 1.0

14.6 0.22 1.0

O2

4.4 0.26 0.68 2.57.8 0.26 0.68 2.6

14.6 0.26 0.68 2.5

CH4

4.4 0.63 3.87.8 0.16 0.65 3.9

14.6 0.19 0.70 3.8

H2

4.4 1.8 6.47.8 0.85 1.8 6.6

14.6 0.81 1.8 6.7

CO2

4.4 13 407.8 8.1 15 46

14.6 9.5 17 52

C2H4

4.4 1.4 3.0 5.37.8 1.6 3.2 5.7

10 1.7 3.2 5.9

C2H6

4.4 0.62 1.7 3.37.8 0.78 1.9 3.5

11.2 0.88 1.9 3.5

C3H6

3.0 3.2 6.6 125.0 5.6 8.6 147.8 8.3 11 17

C3H8

4.0 1.1 2.4 5.16.4 1.6 3.0 5.97.8 1.9 3.5 6.5

larger than that in PE. This result suggests the possibilityof specific interactions between the polar ether linkages andolefins. Sorption data will be presented later to support thishypothesis.

The effect of temperature on permeation properties wasdetermined. Permeability coefficients were measured at 25,35 and 45◦C. Table 6presents representative permeabilitycoefficients at different temperatures and pressures. All pen-etrants exhibit higher permeability at higher temperature. Af-ter experiments at 45◦C, which was the highest temperatureexplored and was, therefore, closest to the melting point ofPEO, H2 permeability at 35◦C was re-measured to confirmthat PEO transport properties had not changed as a result ofperforming experiments at 45◦C. No significant differencein H2 permeability coefficients was observed.

At each temperature, with the exception of N2 at 25◦C,the permeability coefficients were extrapolated to infinitedilution by fitting the data toEq. (15). Since there is only onedata point for N2 at 25◦C, this value was used as the effectiveinfinite dilution permeability coefficient for this case. Thisshould be a reasonable approximation since N2 permeabilityis essentially insensitive to pressure. Using these infinitedilution permeability coefficients, the activation energy ofpermeation was estimated as follows[37]:

PA = PAoexp

(−Ep

RT

)(16)

wherePAo is a pre-exponential factor,R is the gas constant,T is the absolute temperature, andEp is the activation energyof permeation. The results of this calculation are presented inTable 4. Based on the solution–diffusion model,Ep is [37]:

Ep = Ed + �HS (17)

whereEd is the activation energy of diffusion and�HS isthe enthalpy change of sorption. Sorption is typically con-sidered to be comprised of two hypothetical thermodynamicsteps, i.e., condensation of the pure penetrant and mixingof the hypothetical pure condensed penetrant with polymersegments. Within the context of this picture, the above equa-tion can be rewritten as follows[37]:

Ep = Ed + �Hcond+ �Hmix (18)

Activation energy of permeation values in PEO were posi-tive, so permeability coefficients increased with increasingtemperature. Generally, penetrant activation energy of dif-fusion (Ed) is positive and increases with increasing pene-trant size[4]. Condensation is exothermic (i.e.,�Hcond <

0), and the magnitude of the enthalpy change on conden-sation increases with increasing penetrant condensability,as characterized by properties such as critical temperature.The enthalpy of mixing (�Hm) can be negative or positive,depending on the energetic interactions between the con-densed penetrant and the polymer. If penetrant moleculeshave favorable interactions with polymer segments, such asdipole–quadrupole interaction, the mixing enthalpy can benegative. As shown inTable 4, there is no monotonic trendof Ep values with penetrant size, which suggests that eachterm inEq. (18)may have an important influence onEp.

Based on the data presented inTable 6, pure gas selectiv-ity values were calculated as a function of temperature andpressure, and these data are recorded inTable 7. In general,selectivity increases as temperature decreases. For example,the pure gas selectivity of CO2/H2 at 790 kPa (7.8 atm) is6.9 at 45◦C and increases to 9.5 at 25◦C. These results sug-gest that operation of a PEO membrane at lower temperatureshould result in better CO2/H2 separation performance.

4.3. Solubility

Fig. 3a,bpresent sorption isotherms of various penetrantsat 35◦C in semi-crystalline PEO. For less soluble penetrants,


Table 7Pure gas selectivity in semi-crystalline poly(ethylene oxide) as a functionof pressure and temperature

Pressure (atm) Pure gas selectivity

25◦C 35◦C 45◦C

O2/N2

4.4 2.8 2.57.8 3.7 2.8 2.6

14.6 3.1 2.5

CO2/N2

4.4 55 407.8 140 63 48

14.6 79 52

CO2/CH4

4.4 21 107.8 51 23 12

14.6 50 25 13

CO2/H2

4.4 7.4 6.27.8 9.5 8.4 6.9

14.6 12 9.9 7.7

C2H4/C2H6

4.4 2.3 1.8 1.67.8 2.4 1.7 1.6

11.2 1.9 1.7 1.7

C3H6/C3H8

4.4 3.9 3.0 2.67.8 4.4 3.1 2.7

such as O2, N2, CH4, C2H6 and C2H4, the isotherms are lin-ear and solubility,SA, is constant. We represent the averagesolubility for these gases asS∞. The more soluble pene-trants, such as C3H6, C3H8 and CO2, exhibit slightly convexisotherms which may be described by the Flory–Hugginstheory[38]:

lnp

p0= lnΦ + (1 − Φ) + χ(1 − Φ)2 (19)

where p0 (atm) is the penetrant saturation vapor pressureat the temperature of the sorption experiment; it is esti-mated from the Antoine or Wagner equation[39]. χ is theFlory–Huggins interaction parameter, andΦ is the volumefraction of dissolved gas in the amorphous phase of the poly-mer, which is given by:

Φ = CV̄

φa + CV̄(20)

whereφa is amorphous phase volume fraction in the poly-mer, andV̄ is the partial molar volume of the penetrant(cm3/cm3(STP)), which is approximated as the mean valueof the partial molar volume data reported by Kamiya et al.[38]. χ values were obtained by fitting experimental mea-surements ofC as a function ofp to Eqs. (19) and (20). Atinfinite dilution, Eqs. (19) and (20)can be simplified to:

S∞ = φa

p0V̄exp(−1 − χ) (21)

Fig. 3. (a) Sorption isotherms in semi-crystalline PEO at 35◦C. Thescale for gas sorption values is shown on the lefty-axis for all gasesexcept CO2, whose scale is on the righty-axis. (b) Sorption isotherms insemi-crystalline PEO at 35◦C.

Using Eq. (21), infinite dilution solubility coefficients,S∞,of CO2, C3H6 and C3H8 in semi-crystalline PEO were esti-mated. These values, along with infinite dilution solubilitycoefficients for the other gases are recorded inTable 8. Gen-erally, solubility coefficients increase with increasing criticaltemperature. CO2 and the olefins (ethylene and propylene)show higher solubility coefficients than expected based ontheir condensability (i.e., critical temperature). The solubil-ity data were corrected to an amorphous basis usingEq. (5).Fig. 4 presents the estimated solubilities at infinite dilutionin amorphous PEO at 35◦C as a function of penetrant criticaltemperature. These data are compared with solubility valuesin amorphous PE at 25◦C [22]. For permanent gases (N2,O2, and CH4), PEO has similar solubility values to those inPE if the uncertainty in solubility is considered. Therefore,the higher permeability coefficients of permanent gases inPE are due to higher diffusion coefficients.


Table 8Solubility coefficients of gases in semi-crystalline poly(ethylene oxide) at35◦C

Gas p0 (atm) V̄ c × 103

(cm3/cm3(STP))χ S∞

(cm3(STP)/(cm3 atm))

N2 0.036± 0.018O2 0.041± 0.017CH4 0.078± 0.037C2H4 0.17 ± 0.02C2H6 0.12 ± 0.02CO2 81.9a 2.01 0.56 0.37± 0.02C3H6 14.68b 3.26 1.4 0.58± 0.02C3H8 12.1b 3.57 2.0 0.34± 0.01

a This value is hypothetical, estimated from the Wagner equation[33].b Calculated using the Wagner equation for C3H8, and the Antoine

equation for C3H6 [39].c Kamiya et al.[38].

The infinite dilution CO2 solubility coefficient is1.3 cm3(STP)/(cm3 atm) at 35◦C in amorphous PEO. Thisresult is compared with the result of Bondar et al.[16], whostudied gas sorption in a series of phase separated blockcopolymers containing PEO segments. Using solubility datain copolymers, they estimated, by extrapolation, a value of1.4 cm3(STP)/(cm3 atm) for the solubility of CO2 in whollyamorphous PEO, which is in excellent agreement with thevalue determined in this study. High pressure phase equilib-ria data for CO2 and poly(ethylene glycol) (PEG) with an av-erage molecular weight of 200 have also been reported[40].At 40◦C and CO2 pressure of 5.71 MPa, CO2 solubility inPEG was 1.3 cm3(STP)/(cm3 atm), which is also consistentwith our estimate of CO2 solubility in amorphous PEO.

Fig. 4. Estimated amorphous, infinite dilution solubility coefficients inpoly(ethylene oxide) (35◦C) (�) and poly(ethylene) (25◦C) (�) [22]. Theline represents the best fit of the poly(ethylene) data to a model in whichthe logarithm of solubility increases linearly with critical temperature[4].

Fig. 4 further demonstrates the extraordinarily high levelof CO2 sorption in PEO relative to solubilities of penetrants,such as C2H6, that have similar critical temperatures butcannot participate in specific interactions with the polymermatrix. In PE, for example, the CO2/C2H6 solubility selec-tivity is 0.35. However, in more polar PEO, the CO2/C2H6solubility selectivity is 3.1, which is nearly an order ofmagnitude higher than that observed in PE. This result sug-gests that CO2 experiences favorable interactions with theether groups in PEO. The interaction between quadrupolarCO2 and polar groups in polymers is well known[41]. VanAmerongen studied the effect of polar acrylonitrile contentin butadiene/acrylonitrile copolymers on CO2 solubility andfound that polymers with higher concentrations of polaracrylonitrile had higher CO2 sorption[42]. Koros suggestedthat the solubility selectivity for the CO2/CH4 system in-creases as the mass density of polar carbonyl or sulfonegroups in the polymer system increases[43]. Bondar et al.studied gas sorption in a series of copolymer (Pebax)containing polyether segments; they found that solubilityselectivity of carbon dioxide over nonpolar gases increasesas ether linkage concentration in the polymer increases[16].

Interestingly, olefins exhibit higher solubility than theirparaffin analogs in PEO. Often, an olefin (e.g., propy-lene) exhibits lower solubility than its paraffin analog(e.g., propane) in polymers (e.g., PE) due to the slightlylower critical temperature of the olefin. However, PEOexhibits the opposite behavior. As shown inTable 5, thepropylene–propane solubility selectivity at infinite dilutionis 1.7, which, together with a propylene–propane diffusivityselectivity of 1.6, gives an overall selectivity of 2.7. Onthe other hand, in amorphous PE, the propylene–propanesolubility selectivity is approximately a factor of two lowerthan that in PEO, which diminishes the propylene–propanepermeability selectivity to 1.4. Both polymers have sim-ilar diffusivity selectivity values (1.5 in PE and 1.6 inPEO). Additionally, the C2H4/C2H6 solubility selectivityin PEO is 1.4, even though C2H4 has a lowerTc valueand, on this basis, would be expected to be less solublethan C2H6. Together, these results indicate that olefins un-dergo favorable interaction with the polar ether oxygenin PEO.

Olefin solubility is also enhanced in liquids such astetrahydrofuran, a cyclic ether. Polar organic solvents, suchas tetrahydrofuran (THF), are Lewis acids and, as such, theycan interact with Lewis bases, such as theπ electrons inaromatic hydrocarbons or olefins[44,45]. Therefore, suchpolar solvents form solubility-enhancing complexes witholefins but not with paraffins[44,45].

To better illustrate the interesting behavior of olefin sorp-tion in polar and nonpolar polymers, olefin and paraffin sol-ubilities in a polar solvent were compared with those in anonpolar solvent. THF was selected as the polar solvent sinceit has an ether oxygen, and its interactions with aromatichydrocarbons have been documented[44]. Hexane, a well-


Fig. 5. (a) Effect of temperature on C2H4 and C2H6 solubility in liquidtetrahydrofuran (THF)[47]. (b) Effect of temperature on C2H4 and C2H6

solubility in liquid n-hexane[48,49].

studied paraffin, was chosen as a typical nonpolar hydrocar-bon solvent.Fig. 5apresents the solubilities of C2H4 andC2H6 in THF as a function of temperature. The solubilitiesof C2H4 and C2H6 in n-hexane as a function of temperatureare illustrated inFig. 5b. In THF, C2H6 has somewhat highersolubility at higher temperature. However, C2H4 solubilityincreases more rapidly than that of C2H6 as temperaturedecreases. As a result, at 0◦C, C2H4 is significantly moresoluble than C2H6 in this polar, ether-containing solvent. Incontrast, over the entire range of temperatures investigated,C2H6 is more soluble than C2H4 in n-hexane, consistent withthe higher critical temperature of C2H6. These results sug-gest that olefins are more soluble than paraffins in polar liq-uids such as THF as long as the temperature is low enough toallow specific interactions to play a dominant role in the ther-modynamic interactions between the olefin and the liquid.

Table 9Diffusion coefficient comparison in semi-crystalline (DA) and amorphous(DA,a) poly(ethylene oxide) at 35◦C and poly(ethylene) at 25◦C

Gas PEO PE

DA × 107

(cm2/s)DA,a × 107

(cm2/s)DA × 107

(cm2/s)DA,a × 107

(cm2/s)

O2 1.3 ± 0.5 4.5 4.6 18N2 0.53 ± 0.27 1.8 3.2 12CO2 2.5 ± 0.2 8.6 3.72 13CH4 0.58 ± 0.28 2.0 1.93 8.6C2H4 1.3 ± 0.2 4.5C2H6 1.0 ± 0.2 3.4 0.68 3.9C3H6 0.50 ± 0.20 1.7 0.58 3.2C3H8 0.31 ± 0.10 1.1 0.32 2.1

4.4. Diffusivity

Based onEqs. (2), (6) and (7), amorphous phase diffu-sion coefficients for various penetrants at infinite dilutionin PEO at 35◦C were estimated and are given inTable 9,where the gases are arranged in order of increasing criti-cal volume. The diffusivity in PEO was also compared withthat in amorphous phase PE at 25◦C [23]. Generally, diffu-sion coefficients decrease with increasing critical volume ex-cept for CO2 which, due to its strongly non-spherical shape,presents a significantly smaller effective cross-section fordiffusion than indicated by its critical volume. Ethylene alsoshows similar behavior; its diffusivity is higher than that ofmethane, despite ethylene’s larger critical volume. Gener-ally speaking, diffusion coefficients are higher in PE than inPEO. However, there are several complicating factors thatmake a direct comparison difficult. First, the data for PEand PEO are at different temperatures and different crys-tallinities. Additionally, diffusivity is very sensitive to thedistribution of inter-crystalline spacings in semi-crystallinepolymers[23], which is dependent on the solid film prepa-ration process. The crystallite structure in the PE samplewas not discussed in the paper in which the transport datawere reported[23]. Nevertheless, it is unlikely that the PEOstudied in this paper would necessarily have similar macro-crystalline structure. For example, polyethylene crystalliteshave dimensions in the 4–30 nm range[46], while PEO maycontain macrospherulites with diameters up to 2 cm[24].Therefore, tortuosity and chain immobilization factors char-acterizing the effect of crystallites on penetrant diffusioncould well be different in PE and PEO. Since, in this study,we do not have tortuosity and chain immobilization factorsfor different penetrants in PEO, it is impossible to directlycompare amorphous phase diffusivity in these two polymers.

Local effective diffusion coefficients,Deff , characterizingthe penetrant diffusivity in the polymer at a penetrant con-centration ofC2, can be evaluated using the following stan-dard equation[33]:

Deff(C2) =[PA + p

dPA

dp

]p2

(dp

dC2

)p2

(22)


Fig. 6. Local effective diffusion coefficient in semi-crystalline poly(ethy-lene oxide) at 35◦C as a function of penetrant concentration. The lineswere calculated usingEqs. (22) and (24)for C2H4 and C2H6, and usingEqs. (22) and (25)for CO2, C3H6 and C3H8.

SubstitutingEq. (15) in Eq. (22) results in the followingexpression for the local diffusivity:

Deff(C2) = PA,o (1 + 2mp2)

(dp

dC2

)p2

(23)

The solubility of less soluble penetrants is independent ofpressure, which leads to:(

dp

dC2

)p2

= 1

S∞ (24)

For CO2, C3H6 and C3H6, the following equation can bederived fromEqs. (19) and (20):

(dp

dC2

)p2

= eχΦ2−2χΦ−Φ

S∞(2χΦ2 − 2χΦ − Φ + 1

)

×(

1

1 + C2V̄ /φa

)2

(25)

Fig. 6 presents calculated effective diffusion coefficients insemi-crystalline PEO as a function of local concentrationfor several hydrocarbons and CO2. For all of the penetrantsshown,Deff increases with increasing local concentration,suggesting that these penetrants plasticize the polymer ma-trix. This behavior is consistent with our previous argumentthat higher penetrant contacting pressure can increase per-meability by enhancing penetrant average diffusivity throughthe film. Interestingly, poly(dimethylsiloxane) (PDMS),which does not exhibit a particular affinity for CO2, exhibitsplasticization to C2H6 and C3H8 but not to CO2, even atCO2 concentrations as high as 80 cm3(STP)/cm3 [33,34];on the other hand, PEO was significantly plasticized by CO2even at concentrations of the order of 10 cm3(STP)/(cm3

amorphous polymer).

5. Conclusion

Permeation and sorption properties of a variety of gaseswere determined in poly(ethylene oxide), a polar rubberypolymer. Relative to its nonpolar analog, polyethylene, PEOexhibits much higher CO2/H2 pure gas selectivity due tohigh CO2/H2 solubility selectivity, which is qualitativelyconsistent with the notion that polar, basic ether linkagesinteract favorably with acidic penetrants such as CO2, thusincreasing CO2 sorption. Interestingly, PEO is more perme-able to olefins than to paraffins due, in part, to enhancedolefin–paraffin solubility selectivity. Presumably, the doublebonds in the olefins interact favorably with the polar etherlinkages, and paraffins cannot access this interaction.

Acknowledgements

The authors gratefully acknowledge partial support ofthis project by the United States Department of Energyunder grant number DE-FG02-99ER14991. This researchwork was also partially supported with the funding fromthe United States Department of Energy’s National EnergyTechnology Laboratory under a subcontract from ResearchTriangle Institute through their Prime Contract No.: DE-AC26-99FT40675.

Appendix A. List of symbols

A film area available for gas transport (cm2)C2 concentration of gas A dissolved in the

polymer (cm3(STP)/cm3)(dp1/dt)leak rate of pressure rise in the downstream

volume during leak test (cm Hg/s)(dp1/dt)ss steady-state rate of pressure rise in the

downstream volume (cm Hg/s)DA average effective diffusivity of gas A (cm2/s)DA,a diffusion coefficient in the amorphous

polymer (cm2/s)DA/DB diffusivity selectivity of gas A to gas BDeff local effective diffusion coefficient (cm2/s)Ed activation energy of diffusion (kJ/mole)Ep activation energy of permeation (kJ/mole)�H melting enthalpy, calorimetry data (J/g)�Hc melting enthalpy of 100% crystalline

polymer (J/g)�Hcond enthalpy of condensation (kJ/mole)�Hm enthalpy of mixing (kJ/mole)�HS enthalpy change of sorption (kJ/mole)l film thickness (cm)m adjustable constant inEq. (15)(atm−1)MA polymer film weight in air (g)MB polymer film weight in the auxiliary liquid (g)NA steady-state flux of gas A (cm3(STP)/(cm2 s))


�p pressure difference across the polymerfilm (atm)

p1 downstream partial pressure of gas Ap2 upstream partial pressure of gas APA permeability of a polymer to gas A (Barrer)PA,a estimated amorphous phase permeability at

infinite dilution (Barrer)PAo pre-exponential factor (Barrer)PA,o infinite dilution permeability (Barrer)p0 penetrant saturation vapor pressure (atm)R gas constantS∞ infinite dilution solubility (cm3/(cm3 atm))SA observed solubility of gas A in a polymer

(cm3(STP)/(cm3 atm))SA,a estimated solubility of gas A in wholly

amorphous polymer (cm3(STP)/(cm3 atm))SA/SB solubility selectivity of gas A to gas BT absolute temperature (K)Vd downstream volume (cm3)V specific volume of amorphous polymer

at a temperature (cm3/g)V̄ penetrant partial molar volume

(cm3/cm3 (STP))Vo specific volume of amorphous polymer

at 0 K (cm3/g)

Greek lettersαA/B permeability selectivity of gas A to gas Bβ chain immobilization factorχ Flory–Huggins interaction parameterχc weight fraction crystallinity in the polymerφa amorphous phase volume fraction

of a polymerφc crystalline phase volume fraction

of a polymerΦ volume fraction of dissolved gas

in the amorphous polymerρ observed film densityρa density of amorphous polymer (g/cm3)ρc crystal density calculated from unit

cell dimensions (g/cm3)τ tortuosity factor

Subscriptsa amorphous phaseA gas AB gas Bc crystalline phase1 downstream side2 upstream side

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Gas solubility, diffusivity and permeability in poly(ethylene oxide)

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