Materials selection guidelines for membranes that remove CO2 from gas mixtures

Materials selection guidelines for membranes

that remove CO2 from gas mixtures

Haiqing Lin, Benny D. Freeman*

Center for Energy and Environmental Resources, Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78758, USA

Received 30 May 2004; revised 13 July 2004; accepted 20 July 2004

Available online 26 November 2004

Abstract

Membrane technology has been investigated for removing CO2 from mixtures with light gases such as CH4, N2 and H2, and optimal

membranes with high CO2 permeability and high CO2/light gas selectivity are of great interest. This overview describes the material science

approaches to achieve high CO2 solubility and CO2/light gas solubility selectivity by introducing polar groups in polymers. CO2 solubility

and CO2/N2 solubility selectivity in both liquid solvents and solid polymers containing a variety of polar groups are discussed. Optimum

materials appear to have a solubility parameter of about 21.8 MPa0.5 to achieve both high solubility and high solubility selectivity. However,

the introduction of polar groups can decrease CO2 diffusion coefficients and can make a material more size-selective, which is detrimental to,

for example, CO2/H2 separation properties. So far, ether oxygens in ethylene oxide (EO) units appear to provide a good balance of CO2

separation and permeation properties. One drawback of using pure poly(ethylene oxide) (PEO) is its strong tendency to crystallize. This

report reviews strategies for incorporating high concentrations of EO units into polymers while suppressing crystallization. A simple model,

based on free volume theory, is used to correlate a wide range of CO2 permeability coefficients in PEO containing materials, and the results

are satisfactory, particularly given the simplicity of the model. Crosslinked poly(ethylene glycol) acrylate (XLPEO) containing branches

with methoxy end groups exhibit the highest CO2 permeability (i.e. 570 Barrers) and highest CO2/H2 selectivity (i.e. 12) at 35 8C and infinite

dilution among all PEO containing materials reported to date. Because such materials do not crystallize at typically accessible temperatures,

CO2/H2 selectivity can be further improved by decreasing temperature. For example, at an upstream pressure of 4.4 atm, CO2/H2 pure gas

selectivity reaches a value of 40 at K20 8C while maintaining a CO2 permeability of 52 Barrers.

q 2004 Elsevier B.V. All rights reserved.

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

1. Introduction

Carbon dioxide is an impurity that must be removed from

mixtures with light gases such as CH4, N2 and H2, and the

scale of these separations is enormous [1]. For example, the

annual US production of natural gas is 5.6!1011 m3 (STP),

and approximately 20% of this gas contains CO2 at

concentration above the allowable US pipeline specifica-

tion, which is 2 vol% or less.[2] Similarly, hydrogen is a

basic chemical in the fertilizer and refinery industries, and

its annual production is 8.1!109 kg in the US alone [3]. H2

is usually produced via steam reforming of hydrocarbons

and, as such, it is contaminated with CO2 during production;

0022-2860/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.molstruc.2004.07.045

* Corresponding author. Tel.: C1 512 232 2803; fax: C1 512 232 2807.

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

the CO2 must be removed to produce highly purified H2 [1].

Hydrogen production is expected to increase as refinery

demands for H2 increase and as H2 applications (e.g. fuel

cells) increase. Additionally, CO2 recovery from flue gas

(primarily in mixtures with N2) is becoming more important

due to global warming, and there are initiatives that might

eventually require CO2 removal from flue gas [4]. These

applications could sharply increase the demand for more

energy-efficient, cost-effective strategies for CO2 removal

from gas streams.

Currently, CO2 is removed from gas mixtures mainly by

absorption technology (such as amine or hot potassium

carbonate aqueous solutions), pressure swing adsorption

and membrane technology [1]. Economically, membranes

may be advantageous in small and medium scale separations

and when product purity requirements are not extremely

Journal of Molecular Structure 739 (2005) 57–74

www.elsevier.com/locate/molstruc

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7458

stringent [5]. Membrane technology enjoys inherent advan-

tages, such as small footprint, mechanical simplicity, and

high energy efficiency, relative to traditional acid gas

treatment technologies [6]. For membrane-based separ-

ations in the applications mentioned above, it is highly

desirable to selectively remove CO2 from mixtures with

light gases such as H2, N2 and CH4, thereby maintaining the

light gas at or near feed pressure (in the case of H2 and CH4)

to avoid expensive recompression of the desired light gas

product. For CO2 removal from N2, selectively removing

CO2 avoids permeation of the major component (N2) across

the membrane, which could vastly reduce membrane area

requirements.

The emergence of membrane technology for CO2

removal from natural gas in the 1980s resulted from several

breakthroughs. Although gas permeation in membranes has

been studied since the 1940s, membrane fabrication

technology was not sufficiently developed to provide high

enough gas flux for industrial applications until Loeb and

Sourirajan introduced techniques to prepare high flux

anisotropic membranes with selective layer thicknesses of

less than 0.5 mm and often less than 0.1 mm [5]. The second

breakthrough came with the development of high surface-

to-volume membrane module designs, such as spiral-wound

and hollow-fiber modules [5]. These designs accommodate

large membrane area in small volumes, significantly

reducing the footprint of membrane systems. These two

advances contributed to the successful development of

reverse osmosis membrane systems. However, Loeb–

Sourirajan type anisotropic membranes could not be directly

used for gas separations, because pinholes or defects are

always introduced during the membrane preparation

process, and they diminish selectivity substantially. Henis

and Tripodi [7] resolved this limitation by applying a thin

layer of silicon rubber to the membrane (e.g. polysulfone) to

eliminate non-selective convective flow through pinholes.

The composite membrane exhibited separation and per-

meation properties similar to those of polysulfone since

silicon rubber has much higher gas permeability than

polysulfone. These achievements allowed membrane tech-

nology to become a viable alterative to conventional gas

separation technologies such as absorption and adsorption.

Recent efforts have focused on membrane materials

optimization to achieve better separation performance and

better stability in process environments [8].

The steady-state permeability of gas A, PA, through a

film of thickness l is defined as [9]

PA hNAl

p2A Kp1A

(1)

where NA is the steady state flux of gas through the film

(cm3 (STP)/cm2 s), l is the film thickness (cm), and p2A and

p1A are the upstream (i.e. high) and downstream (i.e. low)

partial pressures (cmHg), respectively. Permeability coeffi-

cients are commonly expressed in units of Barrers, where

1 BarrerZ10K10 cm3 (STP) cm/(cm2 s cmHg). If diffusion

obeys Fick’s law and the downstream pressure is much less

than the upstream pressure, the permeability can be

expressed as [9]

PA Z DA !SA (2)

where DA is the average effective diffusivity, and SAZC2A/

p2A is the ratio of gas concentration sorbed in the upstream

face of the polymer, C2A, to the upstream pressure, which is

also called the apparent solubility of penetrant A in the

polymer. The ideal selectivity of a membrane for gas A over

gas B is the ratio of their pure gas permeabilities [5]

aA=B ZPA

PB

ZDA

DB

� �!

SA

SB

� �(3)

where DA/DB is the diffusivity selectivity, which is the ratio

of the diffusion coefficients of gases A and B. The ratio of

the solubility of gases A and B, SA/SB, is the solubility

selectivity.

Generally, penetrant solubility increases with increasing

condensability (i.e. higher critical temperature or higher

normal boiling point) and more favorable interactions with

the polymer, while gas diffusivity is enhanced by decreasing

penetrant size, increasing polymer fractional free volume,

increasing polymer chain flexibility, and decreasing poly-

mer–penetrant specific interactions. Table 1 summarizes the

condensability and molecular size of CO2 and several other

gases of interest. In polymers and liquids, CO2 typically

exhibits higher solubility than light gases in large measure

due to its higher condensability (as characterized by Tc).

Based on relative molecular size difference alone, CO2

diffusivity should be higher than that of CH4, similar to that

of N2, and lower than that of H2. For CO2/CH4 separation,

membrane materials with high diffusivity selectivity have

been extensively pursued by designing relatively rigid

polymers with high glass transition temperatures, and high

CO2 permeability has been sought by maintaining or

increasing fractional free volume [10]. Another avenue,

which has received much less attention, is materials with

higher values of CO2/light gas solubility selectivity. This

strategy is absolutely required for CO2/H2 separation, which

exhibits unfavorable diffusivity selectivity, and may be

necessary for CO2/N2 separation where the penetrant size

difference is not large. This report describes structure–

transport property guidelines for designing polymers with

high CO2 permeability and CO2/light gas selectivity; it

focuses mainly on materials that achieve high selectivity as

a result of high solubility selectivity. CO2 is the target gas in

these examples because there is great interest in CO2

separations and also because there are more experimental

data for CO2 than for any other acid or polar gas. However,

the materials design considerations discussed here may also

be applicable for removing other acid or polar gases (e.g.

H2S, SO2, H2O, NH3, etc.) from mixtures with light gases.

In this regard, special attention will be paid to H2S, since it

is an acid gas (like CO2) and is often a contaminant that

Table 1

Physical properties of penetrants of interest

Penetrant Vca (cm3/mol) V2

a (cm3/mol) Tcb (K) psat

b (atm) d2c (MPa0.5)

H2 65.1 33.24 6.6

N2 89.8 126.20 5.3

CH4 99.2 191.05 11.6

CO2 93.9 45 304.21 63.4 12.2

H2S 98.5 39 373.53 19.8 18.0

a Vc is critical volume [70]. �V2 is the partial molar volume of condensed penetrant at 25 8C. For CO2, �V2 is the average value given by Kamiya et al. [25] and

by Xu et al. [71] for H2S.b Tc is critical temperature [70], and psat is the penetrant saturation vapor pressure at 25 8C [26].c Solubility parameters, which are estimated for the hypothetical liquids at 25 8C and 1 atm. The values are taken from [18], except that of H2S [26].

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 59

must also be removed from the gas streams of interest. More

specifically, the effect of various polar groups on CO2

solubility, diffusivity and permeability and CO2/light gas

selectivity is discussed. The present report focuses primarily

on rubbery polymers. Because ethylene oxide units provide

the best combinations of CO2 permeability and CO2/N2 and

CO2/H2 selectivity known to date, we review various

strategies of incorporating high concentrations of ethylene

oxide groups or poly(ethylene oxide) in polymers while

avoiding crystallization of ethylene oxide units, which

substantially decreases gas permeability.

2. Structure–gas solubility correlation

Penetrant solubility in rubbery polymers is often

described using the Flory–Huggins model [11]

ln a Z ln f2 C ð1 K1=mÞð1 Kf2ÞCcð1 Kf2Þ2 (4)

where a is penetrant activity, c is the Flory–Huggins

interaction parameter, m is the ratio of polymer to penetrant

partial molar volumes ð �V1= �V2Þ, and f2 is the volume

fraction of gas dissolved in the polymer matrix. For ideal

gases, the activity is p/psat, where psat (atm) is the penetrant

saturation vapor pressure at the temperature of the

experiment. The gas volume fraction, f2, can be written

as [11]

f2 ZðC=22414Þ �V2

1 C ðC=22414Þ �V2

(5)

where C is the penetrant concentration in the polymer (cm3

(STP)/cm3 polymer), and �V2 (cm3/mol) is the partial molar

volume of penetrant in the polymer. In the limit of infinite

dilution, when the sorbed gas concentration is very low (i.e.

f2/1), Eqs. (4) and (5) reduce to Henry’s law, CZkDp,

where kD (cm3 (STP)/(cm3 atm)) is the infinite dilution

solubility coefficient [12]:

kD Z22414

psat�V2

eKð1CcK1=mÞ (6)

Therefore, penetrant solubility depends not only on gas

physical properties, such as saturation vapor pressure and

partial molar volume, but also on its interactions with

the polymer matrix. As interactions become more favorable

(i.e. as c decreases), penetrant solubility increases expo-

nentially, according to this simple model.

The Flory–Huggins interaction parameter, c, is typically

related to the penetrant solubility parameter as follows [13]

c Z b C�V2ðd1 Kd2Þ

2

RT(7)

where R is the ideal gas constant, T is absolute temperature,

b is a constant which, in the original Flory–Huggins theory,

is set to zero [13], and d1 and d2 are the solubility parameters

of the polymer and penetrant, respectively. Based on this

model, maximum values of gas solubility would be

observed when the polymer has a solubility parameter

equal to that of the gas of interest (e.g., CO2).

Generally, the effect of liquid solvent chemical structure

on gas sorption has been used as a guideline for designing

highly solubility selective polymers, because the solubility

selectivity of polymers is presumed to be similar to that of

liquid solvents with similar structure [12]. One rationale for

this approach is that, in the limit of infinite dilution, the

Flory–Huggins model, together with Eq. (7), is consistent

with solubility predictions from regular solution theory,

which is widely used for correlating gas solubility in liquids.

For liquids, regular solution theory provides the following

expression for the mole fraction of gas dissolved in a liquid

solvent at 1 atm, x2, as a function of the solubility parameter

difference between the liquid solvent and the gas [14]

x2 Z1

f L2

expK �V2ðd1 Kd2Þ

2

RT

� �(8)

where f L2 (atm) is the fugacity of the pure liquid penetrant

(i.e. hypothetical condensed gas) at atmospheric pressure.

As d1, the liquid solubility parameter, approaches d2, x2

reaches a value of 1=f L2 , or 1/psat, which is Raoult’s Law. If

the liquid solvent and penetrant have the same partial molar

volume (i.e. �V1Z �V2 or, equivalently, mZ1), then x2ZkD

�V2=22414 according to Eq. (6). Under these circum-

stances, Eq. (8) can be derived from Eqs. (6) and (7), so the

expression for the Henry’s Law coefficient is:

ln kD Z ln22414�V2psat

� �K

�V2ðd1 Kd2Þ2

RT(9)

Fig. 1. (a) Effect of solvent solubility parameter on CO2 solubility and

CO2/N2 solubility selectivity at 25 8C; (b) N2 solubility at 25 8C as a

function of the square of liquid solubility parameter; and (c) effect of

solvent solubility parameter on H2S solubility and H2S/N2 solubility

selectivity at 25 8C. Detailed information about solvents and values of

solubility and solubility selectivity are summarized in Table 2. The best fit

line in Fig. 1b is ln kD ZK1:07K0:0022d21. The units of kD and d1 are cm3

(STP)/(cm3 atm) and MPa1/2, respectively.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7460

This equation predicts that gas solubility reaches a

maximum value when d1 equals to d2. This concept has been

successfully applied to obtain, for example, xenon’s

solubility parameter. Steinberg and Manowitz graphed

xenon solubility as a function of solvent solubility

parameter and found a sharp maximum at a solvent

solubility parameter of 16 MPa0.5 [15,16]. This value is in

good agreement with the solubility parameter of xenon,

estimated from an empirical correlation between d2 and Tc

proposed by Hildebrand et al. [14]. While Eq. (9) is a

satisfactory model for describing gas solubility in solvents

with solubility parameters near that of the gas considered,

Steinberg and Manowitz’s results also show that Eq. (9)

enormously overestimates the decrease of gas solubility

with increasing d1 when d1 is far from d2 [15]. When d1 and

d2 differ substantially, the following empirical equation is

often used to correlate the solubility coefficients of a gas in a

series of liquids of varying solubility parameter [14]

ln kD Z a Cbd21 (10)

where a and b are treated as empirical adjustable constants.

Fig. 1a presents CO2 solubility and CO2/N2 solubility

selectivity at 25 8C in liquid solvents containing a spectrum

of polar groups. Detailed information regarding the

chemical structure and solubility data is recorded in

Table 2. In this example, N2 is used as a marker for non-

polar gases (e.g. CH4 and H2), and liquid solvents are used

because there are many more data for gas solubility in

liquids than in polymers. The solubility parameter values for

the liquids are calculated from the definition, i.e.

dhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDHvap KRTÞ=V

p, where DHvap is the enthalpy of

vaporization, and V is the liquid molar volume at 25 8C [14].

Historically, these parameters are evaluated at 25 8C, but

they can be evaluated at any convenient temperature as long

as it is well below Tc and as long as all parameters are

evaluated at the same temperature. These d1 values,

recorded in Table 2, are very close to the estimated Hansen

solubility parameters, which consider the effect of polar

groups and even hydrogen bonding on solubility parameter

values [16]. As the solvent solubility parameter increases,

CO2 solubility increases to a maximum before decreasing.

This behavior can be approximately modeled using Eq. (9)

by setting the CO2 solubility parameter, d2, to

21.8G0.2 MPa0.5. The uncertainty in d2 is estimated using

the propagation of errors technique [17] and assuming that

the CO2 solubility data in Table 2 have an uncertainty of

G10%. The values of �V2 and psat used in this calculation are

recorded in Table 1.

The model fit, with the CO2 solubility parameter as the

only adjustable parameter, is the solid curve in Fig. 1a. This

result is unexpected because the solubility parameter of

hypothetical liquid CO2 at 25 8C is reported to be much

lower than 21.8 MPa0.5. Prausnitz and Shair [18] report a

value of 12.2 MPa0.5, and Lawson [19] reports 6.8 MPa0.5.

These values were obtained by treating d2 as an adjustable

Table 2

Pure gas solubility and solubility selectivity in various liquid solvents at 25 8C

Solvents Structure d1a FFVb SCO2

b SH2Sb SCO2

=SN2SCO2

=SH2SCO2

=SCH4SH2S=SN2

Reference

C6 n-Hexane 15.0 0.324 2.1 7.3 8.8 20 2.4 31 [21]

TCM Chloroform CHCl3 19.0 0.328 3.6 31 29 59 248 [21]

THF Tetrahydro-

furan

19.1 0.263 6.2 31 45 79 10 224 [38,72,

73]

MAc Methyl acet-

ate

19.4 0.307 6.0 36 70 11 [21]

AN Acetone 19.8 0.312 6.6 22 40 74 12 138 [21,23,73,

74]

DMF N,N-Dimethyl

formamide

24.0 0.214 4.1 38 65 86 15 613 [21]

ACN Acetonitrile H3C–CbN 24.1 0.302 7.1 21 64 94 14 188 [38,75–

77]

PC Propylene

carbonate

26.0 0.244 3.9 13 57c 118c 17 194 [75,78]

DMS Dimethyl

sulfoxide

26.3 2.9 32 [21,75,

79]

MeOH Methanol H3C–OH 29.5 0.306 3.6 16 23 40 7.2 101 [21,74,80,

81]

H2O Water HOH 48.0 0.179 0.76 2.3 52 43 24 156 [21]

a Solubility parameter in units of MPa0.5.b Gas solubility in units of cm3 (STP)/(cm3 atm), and when necessary, solvent density is taken from [26].c Values were estimated using models in [75].

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 61

parameter and then fitting CO2 solubility data to equations

similar to Eq. (9), which is a typical method for estimating

gas solubility parameter values since the CO2 critical

temperature (i.e. 31 8C) is very close to 25 8C, so d2 cannot

be calculated from dhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðDHvap KRTÞ=V

p[14,20].

To understand this enormous discrepancy between the

reported CO2 solubility parameter values and the apparent

value that we find, a closer examination of the calculation of

CO2 solubility parameter is useful. The value of 12.2 MPa0.5

was obtained from CO2 solubility in toluene at 25 8C, where

the CO2 mole fraction was 0.0105 at a CO2 partial pressure

of 1 atm [21]. In fact, fitting this mole fraction to Eq. (8)

yields two d2 values since Eq. (8) is second order in d2; these

values are 12.2 and 24 MPa0.5. The higher value is rather

similar to what we have obtained, but it was not mentioned

in the earlier reference [18]. The value of 6.8 MPa0.5 was

calculated using CO2 solubility in various polar and non-

polar liquids with solubility parameters ranging between 12

and 20.4 MPa0.5 [19]. The reference for this value does not

provide the experimental solubility values used and does not

provide any comparison between experimental and calcu-

lated values. However, the fitting results could not be good,

since it would predict that CO2 solubility would decrease

monotonically as liquid solubility parameter increases,

which is not the case, as shown in Fig. 1a. For example, at

25 8C, CO2 solubility in n-hexane is only 2.1 cm3 (STP)/

(cm3 atm) [22], but it is 6.6 cm3 (STP)/(cm3 atm) in acetone

[23], which has a solubility parameter of 19.8 MPa0.5.

Lawson [19] also used a value of 105 cm3/mol for the partial

molar volume of liquid CO2, which is approximately three

times higher than typical reported values (i.e. about 45 cm3/

mol [24–26]). Additionally, the value of 6.8 MPa0.5 is rather

low compared with values of 10.4 MPa0.5 for the solubility

parameter of H2 and 10.6 MPa0.5 for the solubility parameter

of N2 reported in the same paper and obtained using the same

model fitting method [19]. More importantly, the values of

12.2 or 6.8 MPa0.5 cannot predict a maximum in CO2

solubility where it is observed experimentally, and this

ability to predict a maximum in solubility when the

solubility parameters of the solvent and solute are similar

is a key concept of regular solution theory [16]. On the other

hand, Fig. 1a suggests that a solubility parameter value of

21.8 MPa0.5 for CO2 does capture its tendency to dissolve in

the liquids considered [14].

As illustrated in Fig. 1a, CO2/N2 solubility selectivity

reaches a maximum at a solubility parameter value quite

near that associated with the maximum in CO2 solubility.

Since light gases such as N2 have much lower solubility

parameters than any of the liquid solvents shown (cf. Tables

1 and 2) and no specific interactions with these liquids,

increasing the solvent solubility parameter should mono-

tonically decrease their solubilities, which is often described

using the empirical model given by Eq. (10). As illustrated

in Fig. 1b, the model fit describes quite well most of the gas

solubility data except that of methanol. Consequently, CO2/

N2 solubility selectivity can be modeled using Eqs. (9) and

(10), and the result is shown as the dashed line in Fig. 1a.

It appears that the change in CO2 solubility from one liquid

to another dominates the solubility selectivity and, there-

fore, CO2/N2 solubility selectivity exhibits a peak at a

similar d2 value as that of CO2 solubility.

Fig. 1a contains many common polar groups and

demonstrates that ether oxygens (cf. tetrahydrofuran),

nitriles (cf. acetonitrile), carbonyls (cf. acetone), acetates

Fig. 2. The effect of polymer solubility parameter on CO2 solubility

(unfilled symbols) and CO2/N2 solubility selectivity (filled symbols) at

35 8C in polymers containing polar groups. The squares represent

copolymers of butadiene and acrylonitrile [32], and the triangles represent

polymers containing carbonate groups [33]. PB, polybutadiene; PTMO,

poly(tetramethylene oxide) [29]; PEO, poly(ethylene oxide) [29,35]; and

PVAc, poly(vinyl acetate) [31].

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7462

(cf. methyl acetate) and amides (cf. N,N-dimethylforma-

mide) are more useful for improving CO2 solubility and

CO2/N2 selectivity than polar groups such as halogens (cf.

trichloromethane or chloroform), carbonates (cf. propylene

carbonate), sulfoxides (cf. dimethyl sulfoxide) and

hydroxyls (cf. methanol). It is worth mentioning that

propylene carbonate and methanol are used as physical

absorbents to remove acid gases such as CO2 and H2S from

light gases [1]. Table 2 also presents CO2/H2 and CO2/CH4

solubility selectivity values, and they exhibit trends similar

as those of CO2/N2 as the matrix solubility parameter

changes. Gas solubility values in water are also listed in

Table 2; water has the highest solubility parameter and the

lowest CO2 solubility among all of the liquids considered.

Fig. 1c presents H2S solubility and H2S/N2 solubility

selectivity in liquids containing various polar groups. H2S is

also an acid gas and has a reported solubility parameter of

18 MPa0.5, however, the method to obtain this value was not

discussed in detail [27]. As illustrated in Fig. 1c, H2S

solubility also reaches a maximum at a liquid solvent

solubility parameter of approximately 22.3G0.2 MPa0.5,

based on fitting Eq. (9) to the data and treating the H2S

solubility parameter as an adjustable constant. The uncer-

tainty is estimated using the propagation of errors technique

[17] and assuming that the H2S solubility data have an

uncertainty of G10%. The dashed line in Fig. 1c was

calculated using the calculated H2S solubility values from

using Eq. (9) and N2 solubility values from Eq. (10).

Similar to CO2, THF, which contains polar ether oxygens,

also exhibits high H2S solubility and high H2S/N2 solubility

selectivity. Fig. 1a and c clearly indicate the discrepancy

between the reported solubility parameter of CO2 and H2S

and the practical effective solubility parameter value, which

is taken to be the value of the solvent with the highest CO2

and H2S solubility, respectively. Unfortunately, there are few

data for solvents with solubility parameters in the range from

20 to 25 MPa0.5, which is a very interesting range since,

presumably, a maximum in solubility and solubility

selectivity would be observed there. This fact also means

that the apparent effective solubility parameter values for

CO2 and H2S are somewhat approximate.

Fig. 2 presents CO2 solubility and CO2/N2 solubility

selectivity at 35 8C in various rubbery polymers. The

polymer solubility parameters were estimated by Fedor’s

group contribution method [28]. The polymers selected for

this comparison are basically polyethylene (PE) containing

various types and amounts of polar groups. Four polar

groups are present in these polymers: ether oxygens [29,30],

acetates [31], nitriles [32] and carbonates [33]. For example,

poly(ethylene oxide) is polyethylene with an ether oxygen

separating each pair of carbon atoms; polyacrylonitrile may

be viewed as PE containing a nitrile substituent on every

other carbon, etc. Although the data are somewhat more

scattered than those for the liquids, both CO2 solubility and

CO2/N2 solubility selectivity appear to peak at a polymer

solubility parameter value of about 22 MPa0.5, similar to

that of the liquids (cf. Fig. 1a). Polymers with the highest

CO2 solubility contain polar groups such as ether oxygens,

nitriles and acetates. Unfortunately, even though carbonyl

groups can improve CO2 sorption and CO2/N2 solubility

selectivity, there has been no systematic study of gas

sorption in rubbery polymers containing high concen-

trations of such groups to the best of our knowledge.

Instead, these groups, along with carbonates and amides, are

typically used to improve barrier properties by increasing

chain rigidity and, in turn, lowering diffusion coefficients.

Polymers containing these groups are usually glassy at

35 8C, which removes them from the scope of this study [31,

34]. The survey of both liquid solvents and polymers

suggests that incorporation of ether oxygens or nitrile

groups may be useful for improving CO2 sorption and CO2/

light gas solubility selectivity. Additionally, increasing the

concentration of these polar groups in the polymers might

help. For example, as ether oxygen concentration increases

from polybutadiene to poly(tetramethylene oxide) to

poly(ethylene oxide), CO2 solubility increases monotoni-

cally from 0.89 to 1.4 cm3 (STP)/(cm3 atm) [29,32,35]. In

copolymers of butadiene and acrylonitrile [32], CO2

solubility and CO2/N2 selectivity increase systematically

with increasing acrylonitrile content [32].

Qualitative correlations between the concentration of

polar moieties in the polymer matrix and CO2/light gas

solubility selectivity have been mentioned previously

[12,29,36]. Koros [12] suggested that CO2/CH4 solubility

selectivity increases as the mass density of carbonyl or

sulfonyl groups in polymers increases. Bondar et al. [29]

proposed that CO2/light gas solubility selectivity increases

as the concentration of ether linkages or carbonyl groups

Fig. 3. Comparison of (a) CO2 and (b) N2 solubility at 35 8C in polymers

and at 258C in liquids.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 63

increases. However, such simple correlations fail in some

circumstances. For example, Morisato et al. studied CO2/

CH4 solubility selectivity in a series of polyamides

containing sulfonyl groups; they found that the CO2/CH4

selectivity was much lower than predicted based on the total

concentration of carbonyl and sulfonyl groups. They

explained this finding by arguing that the carbonyl groups

preferred to interact with amide linkages on adjacent chains

to form hydrogen bonds rather than interact with CO2 [37].

The current work might explain this phenomenon in a more

systematic way. Strong hydrogen bonding in polymers

increases the solubility parameter to values beyond

22 MPa1/2, which would increase the Flory–Huggins

interaction parameter, c, thereby decreasing CO2 solubility

and CO2/CH4 solubility selectivity.

While Eq. (6) suggests a correlation of gas solubility in

low molar mass solvents with that in analogous polymers,

this result cannot fully account for the differences between

gas solubility in these two matrices. Fig. 3a and b replot the

CO2 and N2 solubility data in liquids from Fig. 1a and

polymers from Fig. 2. Polymers exhibit much lower gas

solubility than liquids, even if the polymer has the same

solubility parameter as a liquid. Koros found that Eq. (6)

gives 1.36 as the ratio for CO2 solubility in n-heptane to that

in high molecular weight polyethylene using 1/m values of

1/3 and 0 for heptane and polyethylene, respectively.

However, CO2 solubility in heptane is 260% higher than

that in polyethylene [12]. This trend is also observed for

CO2 sorption in liquid tetrahydrofuran (THF) and in the

analogous polymer, poly(tetramethylene oxide) (PTMO).

CO2 solubility in THF [38] and in PTMO [29] is 5.12 and

1.12 cm3 (STP)/(cm3 atm) at 35 8C, respectively. However,

Eq. (6) predicts a factor of only 1.6 for this solubility ratio

using 1/m values of 1/2 and 0 for THF and PTMO,

respectively. Koros argued that other factors might

contribute to the difference between the model prediction

and the experimental data. For example, the inadequacies of

lattice representations of Flory–Huggins theory, and the

differences between �VCO2and c for liquid solvents and solid

polymers were thought to play a role in this discrepancy

[12]. In our opinion, an important reason for the observed

differences could be fractional free volume (FFV) differ-

ences between liquids and polymers. The Flory–Huggins

and regular solution theories do not allow empty lattice sites

(i.e. free volume), and this shortcoming has been cited as a

major drawback of these models [39]. Generally, liquids

have higher free volume than polymers, and higher free

volume provides more space to accommodate penetrant

molecules, so solubility might be expected to be correlated

with the amount of free volume in the matrix that is

absorbing the gas molecules.

FFV is usually estimated using Bondi’s group contri-

bution method [34]

FFV ZV KV0

V(11)

where V is the specific volume of the amorphous polymer at

the temperature of interest, and V0 is the specific occupied

volume at 0 K, which is estimated as 1.3 times the van der

Waals volume [28]. This simple equation assumes that the

occupied volume does not change with temperature, which

might not be true in reality [13]. Nevertheless, this definition

of fractional free volume is widely used to correlate gas

diffusion and permeability values and often yields satisfac-

tory results [34]. In Fig. 3a and b, all of the polymers have

FFV values lower than 0.21 while most liquids have

FFV much larger than 0.21, except N,N-dimethylforamide,

which has a FFV value of 0.21 and dimethyl sulfoxide,

whose FFV is not known since the van der Waals volume

of sulfoxide group is not available (cf. Table 2). Clearly,

liquids exhibit much larger gas solubility than polymers,

due, presumably, to the much greater free volume in liquids.

To provide some indication of the magnitudes of differences

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7464

in free volumes for liquids and polymers, THF would have

an estimated FFV of 0.292, while PTMO has a value of only

0.188 if the densities of THF and PTMO are taken as 0.88

and 1.01 g/cm3 [26,29], respectively. As a result, THF

exhibits much higher CO2 sorption than PTMO, although

PTMO has an estimated solubility parameter (i.e.

18.5 MPa0.5) very close to that of THF (i.e. 19.1 MPa0.5).

Fig. 4. The effect of polymer solubility parameter on (a) CO2 diffusion

coefficient and (b) CO2/N2 diffusivity selectivity at 35 8C in polymers

containing various polar groups. The definition of the symbols is given in

the caption of Fig. 2. PTMC1093: crosslinked poly(tetramethylene

carbonate) diol [33].

3. Structure–gas diffusivity and permeability

correlations

Gas diffusion in polymers is often qualitatively under-

stood to depend sensitively on free volume [40]

DA Z A0 exp Kg

hVf iV�

A

� �(12)

where A0 is a pre-exponential factor, g is a numerical factor

introduced to account for possible overlap of free volume

elements, V�A is the minimum free element size needed to

accommodate a gas molecule, which is dependent on

penetrant size, and hVfi is the average free volume in the

polymer. Based on this model, higher free volume would

generally increase gas diffusion coefficients and diminish

the effect of penetrant size on diffusion coefficients.

Therefore, one might expect that as free volume decreases,

CO2 diffusivity would decrease while CO2/CH4 diffusivity

selectivity would increase, and CO2/H2 diffusivity selectiv-

ity would decrease.

In general, addition of polar groups to polymers increases

the solubility parameter, which decreases free volume and

increase polymer chain rigidity [13]. Therefore, while polar

groups might increase CO2 sorption, they could decrease

CO2 diffusion coefficients. Fig. 4a and b present CO2

diffusion coefficients and CO2/N2 diffusivity selectivity

values in various polymers as a function of the polymer

solubility parameter. Roughly speaking, gas diffusion

coefficients decrease with increasing polymer solubility

parameter. In addition to the effect of polar groups on

polymer free volume and chain rigidity, the affinity of polar

groups for CO2 might further retard CO2 diffusion. For

example, as acrylonitrile content increases from 0 to 39 wt%

in copolymers with butadiene, CO2/N2 diffusivity selectiv-

ity decreases from 0.93 to 0.62 (i.e. by 30%), presumably

due a combination of these factors [32].

Fig. 4b suggests that CO2/N2 diffusivity selectivity may

have a minimal value at a polymer solubility parameter of

about 22 MPa0.5, where the affinity between polymer

segments and CO2 reaches a maximum. However, the data

are somewhat scattered, so this judgment needs to be tested

by more experimental results.

The result in Fig. 4b is interesting since CO2 is similar in

size to N2 (based on critical volume values) or slightly

smaller than N2 (based on the kinetic diameter of CO2

(3.3 A) relative to that of N2, 3.64 A) [41]. So, materials

with solubility parameters either much greater or lower than

22 MPa0.5 exhibit CO2/N2 diffusivity selectivity values that

are near to or greater than 1. Materials with solubility

parameters near 22 MPa0.5 can exhibit diffusivity selectivity

values substantially lower than one, suggesting significant

restriction of CO2 mobility beyond that experienced by N2.

There is no diffusion theory currently available to explain

such mobility reduction of penetrants due to specific

interactions with polymers [42], even though this phenom-

enon has been observed for other systems [42,43]. For

example, Davies and Griffiths [42] measured penetrant (i.e.

toluene, aniline and phenol) diffusion in solutions of

poly(vinyl acetate) dissolved in D-methanol using nuclear

magnetic resonance; they reported a decrease in all

Fig. 5. The effect of polymer solubility parameter on (a) CO2 pure gas

permeability and (b) CO2/N2 pure gas permeability selectivity at 35 8C in

polymers containing various polar groups. The symbols are defined in the

caption of Fig. 2. Gas permeability values for PTMO and PEO are

calculated based on Eq. (19) and are recorded in Table 3 [30].

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 65

penetrant diffusion coefficients as polymer content

increased. For toluene, which does not interact specifically

with poly(vinyl acetate), the reduction in its diffusion

coefficient could be explained, using free volume theory, by

the decrease of fraction free volume of the polymer solution

as polymer content increased. However, for aniline or

phenol, where hydrogen bonds are formed between the

polymer and the penetrant, their diffusion coefficient

reductions were much more significant than that of toluene

and could not be fully ascribed to the decrease of fraction

free volume [42]. In this latter case, interaction of the aniline

or phenol molecules with the polymer slowed their

diffusion rates, qualitatively similar to the reduction in

CO2 mobility in solvents with similar solubility parameters

to that of CO2.

Fig. 5a and b present CO2 permeability and CO2/N2

selectivity as a function of polymer solubility parameter,

respectively. Roughly speaking, the permeability decreases

as polymer solubility parameter increases, and this

decrease is similar to the trend of diffusion coefficients

with solubility parameter (cf. Fig. 4a). This result suggests

an important role of the effect of solubility parameter on

free volume, diffusion coefficients, and, in turn, per-

meability coefficients. The effect of polymer solubility

parameter on CO2/N2 selectivity represents a tradeoff

between solubility selectivity and diffusivity selectivity.

Solubility selectivity has a maximum value at approxi-

mately 22 MPa1/2, and the lowest values of diffusivity

selectivity are observed at approximately the same polymer

solubility parameter value. Except for ether oxygens, all

polar groups tend to decrease CO2 permeability. For

example, as acrylonitrile content increases from 0 to

39 wt% in copolymers with butadiene, CO2 permeability

decreases from 180 to 13 Barrers [32]. On the other hand,

the addition of ether oxygens improves CO2 permeability.

For example, amorphous poly(tetramethylene oxide) has an

estimated CO2 permeability of 300 Barrers [30] compared

with 180 Barrers in polybutadiene [32]. Interestingly, the

addition of ether oxygens does not significantly reduce

polymer chain flexibility as characterized by glass

transition temperature (Tg). In fact, the hypothetical Tg of

wholly amorphous poly(ethylene oxide) is K89 8C, which

is slightly lower than the hypothetical Tg of wholly

amorphous polyethylene (i.e. K80 8C) [44]. In contrast,

as acrylonitrile content in copolymers with butadiene

increases from zero to 39 wt%, Tg increases significantly

from K80 to K26 8C [32].

The effect of polar groups on CO2/CH4 separation is

more subtle: polar groups increase solubility selectivity and

should increase diffusivity selectivity if polar groups do not

retard CO2 transport too strongly. Ghosal et al. [43] found

that aryl substituent of basic –CH2–NH2 groups in

polysulfone increased CO2/CH4 solubility selectivity,

restricted sub-Tg torsional motion, and decreased fractional

free volume, which should contribute to improvements in

size sieving ability and, therefore, CO2/CH4 diffusivity

selectivity. However, CO2/CH4 diffusivity selectivity actu-

ally decreased due to the affinity between the amine

moieties and CO2, and this combination of somewhat

higher solubility selectivity coupled with much lower

diffusivity selectivity resulted in a decrease in CO2/CH4

permselectivity [43].

On the other hand, CO2/H2 separation always faces

unfavorable diffusivity selectivity, and this would become

even more detrimental if the size sieving ability of the

polymer were increased by, for example, introducing polar

groups into the polymer which brought about an overall

reduction in polymer free volume. Furthermore, if the polar

groups enjoy specific and sufficiently strong interactions

Fig. 6. Effect of polar acrylonitrile content in copolymers with butadiene on

CO2 and H2 transport properties at 25 8C: (a) CO2 solubility; (b) CO2/H2

solubility, diffusivity and permeability selectivity [32].

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7466

with CO2, CO2/H2 diffusivity selectivity will be further

reduced. As illustrated in Fig. 6a and b, the increase of polar

acrylonitrile content in copolymers with butadiene results in

systematically higher CO2 solubility and CO2/H2 solubility

selectivity. However, the decrease in CO2/H2 diffusivity

selectivity is larger than the increase in solubility selectivity,

leading to a sharp decrease in permselectivity as polar

acrylonitrile content increases. So far, polar ether oxygens

appear to be the only well-known groups which improve

CO2/H2 permselectivity. For example, polymers of poly-

butadiene, PTMO and PEO, in order of increasing ether

oxygen content, exhibit CO2/H2 permselectivity values of

about 3.0 (at 35 8C and 1 atm [32]), 3.7 (at 35 8C and 10 atm

[30]) and 6.7 (at 35 8C and infinite dilution [35]),

respectively.

4. Structural design of poly(ethylene oxide) containing

polymers

The unique property of polar ether oxygens for CO2

separation has attracted much interest. There have been

numerous efforts to design polymers containing poly(ethyl-

ene oxide) (PEO) for CO2/N2 and CO2/H2 separations [4,29,

30,45–56], in part because ethylene oxide units have a high

concentration of ether oxygens and are relatively easy to

fabricate. In comparison, poly(methylene oxide) would

have an even higher ether oxygen content. However, it has

extremely high crystallinity and is very difficult to process

into gas separation membranes. Indeed, gas transport

properties in poly(methylene oxide) have not been reported

to the best of our knowledge. PEO is also subject to a similar

disadvantage, i.e. a strong tendency to crystallize, which is

deleterious for gas permeability. The following sections

discuss the effect of crystallinity on gas permeation and then

review three main techniques to reduce crystallinity in PEO:

(1) using low molecular weight liquid PEO or poly(ethylene

glycol) (PEG); (2) designing phase separated block

copolymers with runs of ethylene oxide (EO) segments

that are too short to crystallize effectively at room

temperature; and (3) designing highly branched, crosslinked

networks with high concentrations of PEO.

4.1. Poly(ethylene oxide)

Generally, polar groups in a polymer matrix improve

polymer chain packing efficiency and promote chain

crystallization. Until recently, there was no systematic

study of gas transport properties in pure PEO [35], although

pure PEO is an ideal base material to use for comparison.

However, it can be very challenging to prepare defect-free

films of PEO for gas permeation studies. To circumvent this

problem, annealing PEO films above the melting tempera-

ture was found to be critical for preparing defect-free films

[35]. Such PEO films have a crystallinity of 71 vol% and a

glass transition temperature of K52 8C. At 35 8C and

infinite dilution, PEO exhibits a CO2 permeability of

12 Barrers, and the pure gas selectivities of CO2 over H2,

N2, and CH4 are 6.7, 48 and 20, respectively [35].

A simple model proposed by Michaels and Bixler [57,58]

to adjust measured gas transport properties in semi-crystal-

line polymers to those in wholly amorphous polymers is

based on assuming a two phase system (i.e. crystalline and

amorphous) where the crystals act as a nonsorbing and

impermeable dispersed phase imbedded in an amorphous

matrix. Therefore, in a rubbery polymer, the measured

solubility (i.e. SA) is typically related to amorphous phase

solubility (i.e. SA,a) as follows [57]

SA Z SA;aFa (13)

where Fa is the amorphous phase volume fraction. The

influence of crystallinity on diffusivity was described as

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 67

follows [58]

DA ZDA;a

tb(14)

where DA,a is the diffusion coefficient in the amorphous

polymer, t is a tortuosity factor, and b is a chain

immobilization factor. t characterizes the tortuosity of the

amorphous phase caused by the presence of dispersed

impermeable crystallites. Simple models from composites

theory, such as the one below, are often used to describe the

influence of crystallinity on tortuosity [58]:

t Z1

Fa

(15)

The chain immobilization factor, b, accounts for the

restricted segmental mobility in the amorphous phase by

crystallites. In the simplest case, when bZ1 (i.e. no chain

immobilization), gas permeability is given by [58]

PA ZPA;a

tbFa Z PA;a !F2

a (16)

where PA,a is the estimated permeability of penetrant A in

the amorphous phase of a polymer. Further analysis of the

immobilization factor will be presented later. According to

this model, CO2 permeability in amorphous PEO is

estimated to be 140 Barrers at 35 8C and infinite dilution

[35], which is about one order of magnitude higher than in

semi-crystalline PEO. Clearly a logical way to improve

separation performance of PEO would be to inhibit or

totally depress crystallization.

4.2. Liquid poly(ethylene glycol)

A natural approach to obtaining the beneficial separation

performance of PEO without crystallinity is to use low

molecular weight PEO or poly(ethylene glycol) (PEG),

which is a liquid at temperatures such as 35 8C. For

example, PEG with a molecular weight of 600 g/mol has a

melting temperature of 17–22 8C, according to the Aldrich

catalogue. PEG has been fabricated into membrane systems

in two ways: as liquid membranes and as blends with solid

polymers [45–47,49,59,60].

Kawakami et al. [45,46] impregnated PEG (MWZ300 g/mol) into the microporous regions of a cellulose

membrane filter with an average pore size of 0.2 mm. This

membrane exhibited a CO2 permeability of 49 Barrers and

CO2/N2 selectivity of 13 at 25 8C and 0.2 atm. The addition

of inorganic salts to PEG can improve CO2 separation

efficiency. For example, liquid membranes of PEG contain-

ing KF exhibited a CO2 permeability of 100 Barrers and

CO2/N2 selectivity of 45 at 25 8C and 0.2 atm. However,

liquid membranes are subject to two inherent disadvantages:

potential instability resulting from liquid lost due to the

pressure difference across the film and lower gas per-

meability due to the tortuosity of the micropores in the solid

substrate.

Blends of liquid PEG with a compatible solid polymer

can provide the necessary mechanical integrity to sustain

significant pressure differences across the membrane.

Heterogeneous PEG blends such as those with poly

(dimethyl siloxane) (PDMS) [59] or poly(1-trimethylsi-

lyl-1-propyne) (PTMSP) [60], and homogeneous PEG

blends such as those with cellulose nitrate [49] or cellulose

acetate have been reported [47]. Generally, the non-PEG

component (i.e. the second component) needs to be

carefully chosen because blends generally exhibit transport

properties intermediate between those of the two constitu-

ent components. In heterogeneous blends, the second

component is usually the continuous phase to maintain

good mechanical properties. Therefore, this component

should have lower gas permeability so that the blends will

exhibit gas selectivity similar to that of PEG. On the other

hand, the barrier property of the second component will

reduce CO2 permeability in the blend. The balance needs

to be critically evaluated. The underlying rationale will be

further discussed in Section 4.3. Currently PDMS and

PTMSP have been used in such studies, and they are

among the most permeable polymers known. For example,

CO2 permeability is 3200 and 28,000 Barrers in PDMS

[61] and PTMSP [60], respectively, but only 140 Barrers

in estimated amorphous PEO. The addition of 30 wt%

PEG (MWZ300 g/mol) to PTMSP increases CO2/N2

selectivity from 5.6 to 25, and the CO2 permeability of

the blend is 146 Barrers at 30 8C. Entrapping liquid PEG

(MWZ600 g/mol) within solid PDMS yields a CO2/H2

selectivity of about 7.5 at 25 8C, compared to 4 in PDMS

alone [59].

In a homogeneous blend, gas transport properties, X,

such as permeability or selectivity, are usually expressed

empirically as follows [62]

ln Xb Z F1 ln X1 CF2 ln X2 (17)

where Fi is the volume fraction of component i, and the

subscripts 1, 2 and b represent component 1, 2 and the

blend, respectively. Eq. (17) predicts that CO2 separation

performance in a blend would approach that of PEG as the

PEG content increases; however, mechanical properties

would also approach those of PEG. For example, as PEG

(MWZ300 g/mol) content increases from zero to 50 wt%

in blends with cellulose nitrate, CO2 permeability increases

from about 20 Barrers to about 120 Barrers, and CO2/N2

selectivity increases from about 20 to about 45 at 25 8C. On

the other hand, the films become tacky, fragile, and finally

too weak to test for gas permeation properties when the

PEG content reaches 60 wt% [49]. In general, by carefully

choosing the proper components and compositions in

blends containing PEG, one might achieve CO2 separation

performance close to that of PEG membranes with

sufficient mechanical integrity to withstand high pressure.

However, this has yet to be demonstrated.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7468

4.3. Block copolymers

Block copolymers containing PEO segments have been

extensively investigated for CO2 removal from light gases.

These copolymers typically have microphase separated

structures containing soft PEO segments and hard segments

such as polyamides [29,30,51,54] and polyimides [48]. The

hard segments provide mechanical stability and inhibit

crystallization of PEO. For example, in a commercial

PEBAXw copolymer containing 57 wt% PEO and 43 wt%

Nylon 6, the melting temperature of the PEO phase is 13 8C,

which is much lower than that of high molecular weight

PEO (65 8C) [29]. Although block copolymers are more

difficult to prepare than polymer blends, they present a more

efficient opportunity to incorporate a high content of PEO

while still maintaining good mechanical properties, since

PEO is directly connected to relatively immobile and tough

hard segments by chemical bonds. For example, a polymer

blend of cellulose nitrate and PEG becomes too weak for gas

permeation test when the PEG content reaches 60 wt% [49].

In contrast, PEBAXw containing 57 wt% PEO can form a

robust film capable of sustaining gas pressures well in

excess of 15 atm [30].

Petropoulos reviewed approaches for evaluating gas

permeability in binary composite polymeric materials and

observed that the Maxwell model could be used over the

whole composition range for a dispersion of isometric

particles of such shape and mode of packing that the

interparticle gaps are uniformly maximized [63]

Pb Z Pc

Pd C2Pc K2FdðPc KPdÞ

Pd C2Pc CFdðPc KPdÞ

� �(18)

where Fd is the volume fraction of the discontinuous phase,

and Pb, Pc and Pd are gas permeability in the composite,

continuous phase and discontinuous phase, respectively.

The composite could be heterogeneous polymer blends or

phase separated block copolymers. Eq. (18) predicts that gas

permeation properties of the composite would be dominated

by the continuous phase, suggesting that optimal phase

separated materials should have amorphous PEO as the

continuous phase. Table 3 presents gas transport properties

in various phase separated block copolymers containing

PEO. The detailed chemical structures are recorded in

Table 4. The values of CO2/N2 selectivity are quite similar

to that of PEO in all of these materials, suggesting that the

PEO phase in these block copolymers is the continuous path

for gas diffusion [30,50]. On the other hand, the widely

varying gas permeability values demonstrate that gas

permeability depends strongly on the detailed morphology,

such as the domain shape and spatial arrangement, which

could be influenced by the hard segment composition and

the lengths of the PEO and hard segment blocks.

In most copolymers reported to date, the rigid phase has a

much lower permeability than the PEO phase [30,48]. For

example, at 35 8C, Nylon 6 exhibits a CO2 permeability of

0.21 Barrers [31], compared with 66 Barrers at 10 atm for

PEBAXw containing 57 wt% PEO and 43 wt% Nylon 6

[30]. On this basis, Eq. (18) can be simplified by letting Pd/

PcZ0

Pb Z Pc

1 KFd

1 CFd=2

� �(19)

This model has been applied to the reported block

copolymer data to provide a crude estimate of effective gas

permeability in the PEO phase, and these values are

summarized in Table 3. Some copolymers, such as B1,

exhibit incomplete phase separation, i.e. the PEO phase is

partially miscible with the hard phase [50]. The estimated

CO2 permeability in the PEO phase of B1 is only 7 Barrers

(cf. Table 3), which suggests the existence of an intermixed

phase that has properties between those of pure, amorphous

PEO and the hard segment component (cf. Tables 3 and 4).

Table 3 illustrates that the hard phase affects physical

properties of the soft phase; for example, the measured Tg in

the PEO phase varies by 30 8C depending on the hard phase

composition and amount. The deviation of Tg in a

microphase of a block copolymer from its bulk value has

been well documented and has been ascribed to the

existence of a zone of material, near the interface between

the PEO phase and the hard segment phase, where both

components coexist and intermix [64]. Another view

proposed by Bares [64] is that the interface of the PEO

phase and the hard phase imposes constraints on the

mobility of PEO chains and thus influences Tg. He was

able to quantitatively relate the Tg change in one phase to the

surface area per unit volume of the phase undergoing the

change in Tg [64]. In both of these scenarios, the Tg of a

microphase in a block copolymer depends on the block

molecular weight and microphase morphology. Table 3 also

suggests a general trend, i.e. gas permeability in the PEO

phase increases as the Tg of PEO phase decreases.

The Maxwell model is not generally applicable for semi-

crystalline polymers, because often the crystalline phase

cannot be represented as spheres uniformly dispersed in an

amorphous polymer phase [13,63]. Instead, crystalline

phases are often found to be lamellar-shaped dispersions

[13]. Therefore, using the Maxwell model would under-

estimate the restriction of gas diffusion in semi-crystalline

polymers. The model given by Eq. (16) is more often used to

account for the effect of crystals on permeability [58].

4.4. Crosslinked poly(ethylene oxide)

Graham [65] proposed empirically that significant

crystallinity in crosslinked PEO is not evident when

the molecular weight between crosslinks lower than

1500. Various techniques are available to crosslink PEO

[65]. For instance, radiation or radical crosslinking of high

molecular weight PEO has been reported, and crosslinking

by reactions of end groups such as hydroxyl or vinyl

Table 3

Pure gas CO2 permeability and CO2/N2 selectivity in PEO containing polymers at 35 8C

Polymera PEO content

(wt%)

Dpb (atm) Bulk polymerc PEO phased

PCO2[Barrer] aCO2 =N2

Reference Tg [8C] PCO2[Barrer] FFV

Semi-crystalline PEO 100 0 12 48 [35] K52 140 0.129

Block copolymers

55PEO/PA6 55 10 120 52 [30] K55 263 0.130

57PEO/PA12 57 10 66 55 [30] K53 146 0.129

M1: MDI-BPA/PEG(75) 53.6 2 31 44 [50] K42 71 0.120

M2: MDI-BPA/PEG(80) 60.5 2 48 47 [50] K41 95 0.119

M3: MDI-BPA/PEG(85) 66 2 59 49 [50] K41 104 0.119

L3: L/TDI(20)-BPA/PEG(90) 64.5 2 47 51 [50] K43 80 0.120

I4: IPA-ODA/PEO3(80) 68.3 2 58 53 [50] K45 88 0.122

B5: BPDA-ODA/DABA/PEO2(70) 43.3 2 14 57 [50] K42 34 0.120

B6: BPDA-ODA/DABA/PEO2(80) 53.4 2 36 56 [50] K44 71 0.121

B7: BPDA-ODA/PEO3(75) 52.3 2 75 52 [50] K56 154 0.131

B13: BPDA-mPD/PEO4(80) 53.1 2 81 54 [50] K61 158 0.136

P5: PMDA-mPD/PEO3(80) 55.9 2 99 50 [50] K62 176 0.136

P6: PMDA-APPS/PEO3(80) 68.3 2 159 51 [50] K55 234 0.130

P7: PMDA-APPS/PEO4(70) 61.2 2 136 53 [50] K66 234 0.140

P8: PMDA-mPD/PEO(80) 58.9 2 151 52 [50] K61 259 0.136

P9: PMDA-ODA/PEO4(80) 66.6 2 167 52 [50] K62 252 0.136

P10: PMDA-pDDS/PEO4(80) 68.6 2 238 49 [50] K62 345 0.136

B1: BPDA-ODA/DABA/PEO1(75) 41.2 2 2.7 56 [50] K36 7 0.114

Crosslinked poly(ethylene oxide)

PEGDA/PEGMEA(0) 83 0 112 52 [66] K38 112 0.116

PEGDA/PEGMEA(20) 83 0 150 58 [66] K44 150 0.121

PEGDA/PEGMEA(50) 82 0 250 41 [66] K52 250 0.128

PEGDA/PEGMEA(70) 82 0 320 47 [66] K56 320 0.131

PEGDA/PEGMEA(91) 81 0 520 41 [66] K61 520 0.136

PEGDA/PEGMEA(99) 81 0 570 41 [66] K64 570 0.138

DM14/MM9(0) 80 1 65 53 [4] K42 65 0.120

DM14/MM9(10) 80 1 85 54 [4] K44 85 0.121

DM14/MM9(30) 80 1 129 51 [4] K51 129 0.127

DM14/MM9(50) 79.9 1 185 50 [4] K56 185 0.131

DM14/MM9(70) 79.9 1 260 48 [4] K62 260 0.136

DB30/MM9(0) 78.4 1 128 49 [4] K47 128 0.124

DB30/MM9(10) 78.5 1 140 50 [4] K49 140 0.125

DB30/MM9(30) 78.8 1 185 51 [4] K54 185 0.130

DB30/MM9(50) 79.1 1 231 48 [4] K58 231 0.133

DB30/MM9(70) 79.4 1 308 47 [4] K62 308 0.136

DM9/MM9(10) 72.8 1 28 53 [4] K34 28 0.113

DM23/MM9(10) 86.1 1 194 52 [4] K57 194 0.132

DB10/MM9(10) 57.2 1 12 48 [4] K14 12 0.096

a Detailed polymer structures are provided in Table 4. For block copolymers from [50], the numbers in parentheses refer to the feed composition (wt%) of

PEG, PEO diamine, and TDI to total diols, diamines, and isocyanates, respectively. For crosslinked PEO samples, the numbers in parentheses represent the

weight percentage of the last component in the names of these polymers.b Dp is the pressure difference across the membrane, which is essentially the upstream pressure since the downstream pressure in near zero in all the

measurements.c Measured transport properties in PEO containing polymers.d Physical properties of the PEO phase in these materials. Except for semi-crystalline PEO, all other PEO phases are amorphous at 35 8C. This list of

properties includes the measured glass transition temperature ascribed to this phase, the estimated CO2 permeability from Eq. (16) for PEO and Eq. (19) for

block copolymers and the estimated fractional free volume from Eq. (21). For materials that are not semi-crystalline or block copolymers, the permeability

values reported in this section of the table are equal to those reported in the ‘bulk polymer’ section of this table.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 69

groups has been studied. Hirayama et al. [4] prepared

crosslinked PEO from mixtures of poly(ethylene glycol)

methacrylate (a monomer containing nine EO units)

and poly(ethylene glycol) dimethacrylate (a crosslinker

containing 14 EO units) by plasma irradiation. They

reported that CO2 permeability increases as monomer

content increases while CO2/N2 selectivity remains almost

unchanged. They prepared a polymer containing 70 wt%

monomer; it exhibited a CO2 permeability of 260 Barrers

and a CO2/N2 selectivity of about 48 at 35 8C and 1 atm.

Such separation properties represent a significant improve-

ment over those exhibited by block copolymers.

We prepared crosslinked PEO by UV photopolymeriza-

tion of poly(ethylene glycol) diacrylate (PEGDA)

Table 4

Chemical structures of PEO containing polymers in Table 3

Name Structure Notes

Block copolymers

55PEO/PA6 (nZ5)

57PEO/PA12 (nZ11)

M and L series hard segment:

polyurethane

General formula

RZL, MDI or TDI

I series hard segment: polyamide X and Y: see below.

B and P series hard segment:

polyimide

General formula

RZBPDA or PMDA

X: PEO

YZODA, DABA, mPD, pDDS or

APPS

Monomers for crosslinked poly(ethylene oxide)

PEGDA

PEGMEA

DM14

MM9

DB30

L, TDI (see below) adduct of trimethylol propane; COLONATE L. MDI, 4,4 0-diphenyl-methane diisocyanate. BPA, bisphenol A (structure is included in the

general formula of M and L series). TDI, 2,4-toluene-diisocyanate. IPA, isophthalic acid (structure is included in the general formula of I series). BPDA,

3,3 0,4,4 0-biphenyltetracarboxylic dianhydride. PMDA, pyromellitic dianhydride. ODA, 4,4 0-oxydianiline. DABA, 3,5-diaminobenzoic acid. mPD, 1,3-

phenylenediamine. pDDS, 4,4 0-diaminodiphenyl sulfone. APPS, p-aminophenoxy phenyl sulfone.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7470

containing 14 EO units and poly(ethylene glycol) methyl

ether acrylate (PEGMEA) containing about 8.5 EO units

[66]. PEO crystallinity was completely absent in these

copolymers at temperatures as low as K90 8C (the lowest

limit of the calorimeter used) due, presumably, to the short

nature of the EO branches in the side chains of these

materials and to the frustration of crystallization by

crosslinking. The average number of EO units per acrylate

group is approximately 7, which is the minimum number of

monomers required for the unit cell of a PEO crystal [31].

Therefore, using these starting materials, network polymers

can be prepared which are non-crystalline and have a high

Fig. 7. Fractional free volume of crosslinked PEO prepared from PEGDA

and PEGMEA as a function of (TKTg), where T is 308 K and Tg is the glass

transition temperature of the corresponding copolymer. The best fit line is

FFVZ0:055C0:00084!ðT KTgÞ.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 71

concentration of EO units. The use of acrylate groups

instead of methacrylate groups provides higher chain

flexibility (or lower glass transition temperature), which

can increase gas diffusion coefficients and, in turn,

permeability [32]. For example, crosslinked PEO prepared

from 70 wt% PEGMEA and 30 wt% PEGDA exhibits a

CO2 permeability coefficient of 320 Barrers at 35 8C and

infinite dilution. The analogous polymer, prepared from a

methacrylate monomer and crosslinker, has a CO2 per-

meability of only 260 Barrers [4]. Additionally, acrylate

groups polymerize more efficiently than methacrylate

groups because of their lower steric hindrance. For example,

unlike its methacrylate analog, pure PEGMEA monomer

can polymerize to completion, forming a crosslinked film

that can be used for permeation testing. This material is

crosslinked because commercial sources of PEGMEA

monomer contain low levels of residual diacrylate monomer

that act as crosslinking sites. The inclusion of methyl ether

chain end groups in the monomer (as opposed to hydroxyl

end groups) increases free volume and improves CO2/H2

separation performance of copolymers of PEGMEA and

PEGDA. As PEGMEA monomer content increases from 0

to 99 wt%, CO2 permeability increases about four-fold,

reaching 570 Barrers and CO2/H2 selectivity increases by

50%, up to 12 at 35 8C and infinite dilution [66]. If the

–OCH3 end groups are replaced by –OH end groups, CO2

permeability and CO2/H2 selectivity remain unchanged as

the –OH end group content changes across the entire

composition window [66].

In general, the crosslinked network materials formed

from PEG acrylates and diacrylates provide the best

permeation and separation properties of PEO-containing

materials so far. Crosslinking insures good chemical

resistance, simply because crosslinked networks are not

soluble. It is straightforward to incorporate more than

80 wt% PEO in crosslinked polymers from acrylate

monomers and/or crosslinkers, which is higher than the

maximum value (about 60%) reported for block copolymers

and blends [48,50]. Crosslinked PEO can be further

modified to give much higher CO2 permeability and CO2/

H2 selectivity than block copolymers or blends by

introducing methyl ether chain end groups [66]. Finally,

crosslinking could completely suppress crystallization at all

temperatures of practical interest [66], while block copoly-

mers or blends would still exhibit a melting temperature at

temperatures near ambient [29]. Consequently, with the

crosslinked PEO materials, temperature can be lowered to

optimize CO2 separation performance because lower

temperatures favor CO2/light gas solubility selectivity

[66]. For example, in a copolymer prepared from 70 wt%

PEGMEA and 30 wt% PEGDA, CO2/H2 pure gas selectiv-

ity increases from 11 to 40 as temperature decreases from 35

to K20 8C at 4.4 atm, while CO2 permeability is still

52 Barrers at these conditions [66]. These separation

properties are the best results reported to date for solid

non-facilitated transport polymeric membranes.

5. Discussion

Table 3 summarizes CO2 permeability and CO2/N2

selectivity in various PEO containing materials at 35 8C

along with the glass transition temperature, estimated CO2

permeability and fractional free volume of the PEO phase.

For consistency, all of the permeability data are reported at

35 8C, based on either direct measurement or interpolation

using data from the corresponding references. While CO2/

N2 selectivity remains relatively constant, indicating that

PEO is continuous and provides the dominant contribution

to the permeation properties, CO2 permeability ranges from

7 to 570 Barrers. Clearly, understanding the underlying

mechanism leading to such a wide range of gas permeability

might lead to materials design rules to further improve acid

gas separation performance.

Interestingly, Tg seems to be correlated with CO2

permeability, as illustrated in Table 3. Tg characterizes

chain mobility, and it has been correlated with fractional

free volume in rubbery PEO as follows [13]

FFV Z FFVg CarðT KTgÞ (20)

where FFV and FFVg are the fractional free volume values at T

and Tg, respectively, and ar is the thermal expansion

coefficient of rubbery PEO. This equation assumes that the

occupied volume of the polymer is independent of tempera-

ture, which is an approximation [13]. Eq. (11), which is widely

used to estimate FFV, is also based on this assumption.

Using copolymers prepared from PEGDA and PEGMEA

as base materials, a series of copolymers with systematically

varying fractional free volume and glass transition tem-

perature are produced, as illustrated in Table 3. Fig. 7

presents the correlation between FFV and (TKTg), where

Fig. 8. CO2 permeability at 35 8C measured in crosslinked PEO prepared in

our laboratory (C) [66] and by Hirayama et al. (B) [4], and estimated in

amorphous PEO phase for block copolymers (6) based on Eq. (19) and for

semi-crystalline PEO (&) based on Eq. (16) as a function of (a) Tg of the

amorphous PEO phase and (b) 1/FFV in the amorphous PEO phase

estimated using Eq. (20). All data are recorded in Table 3. The curve fitting

in (b) describes all data except that of B1: PZ1:129!106

expðK1:135=FFVÞ.

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–7472

FFV is estimated using Eq. (11) and T is 35 8C. Assuming ar

to be independent of copolymer composition, the straight

line fit of the data yields a value of 0.055G0.001 for FFVg

and (8.4G2.6)!10K4 KK1 for ar. The uncertainties are

estimated using the propagation of errors technique [17].

The uncertainty of FFV is estimated as G1% since polymer

density has an uncertainty of G1%, and (TKTg) is assumed

to have an uncertainty of G2% or about G2 K. The value

of FFVg is comparable with other reported experimental and

theoretical values, such as the ‘universal’ values of 0.025

reported by Ferry and coworkers and 0.12 reported by

Simha and Boyer [13]. ar is defined as follows [28]

ar Z1

V

vV

vT

� �p

(21)

where V is the specific volume of amorphous rubbery PEO,

and T is absolute temperature. From PVT measurements, the

value of ar is 7.8!10K4 KK1 for rubbery poly(ethylene

oxide) dimethyl ether with a molecular weight of 1000 g/

mol [67], which is very close to the value estimated from

Fig. 7. Therefore, Eq. (20), with parameters obtained from

these copolymers, might be a reasonable first approximation

to describe the PEO phase in other PEO containing

materials. Based on reported Tg values for the PEO phase,

FFV values were estimated using Eq. (20) for the PEO phase

of various PEO containing materials at 35 8C, and the results

are recorded in Table 3. Fig. 8a demonstrates the trend that

PEO phases with lower Tg values exhibit higher CO2

permeability. In Fig. 8a, the CO2 permeability coefficients

in the PEO phase were estimated using Eq. (19) for the

block copolymer and Eq. (16) for semi-crystalline PEO.

Fig. 8b presents the correlation of CO2 permeability with

1/FFV. Generally, gas solubility is a weak function of

polymer fractional free volume, which has been experimen-

tally observed in copolymers of PEGDA and PEGMEA

copolymers [66]. Therefore, by combining Eqs. (3) and

(11), there is a simple relationship between gas permeability

and FFV [34]

P Z A exp KB

FFV

� �(22)

where A and B are positive constants. This equation has

been applied to a wide range of data and, qualitatively, it

shows an encouraging ability to unify the data in Fig. 8b,

considering the simplicity of this equation. The much lower

permeability exhibited by block copolymer B1 (cf. Fig. 8b)

might be due to partial mixing of the PEO phase and the

hard phase as discussed above.

This simple model might be used to rationalize the

concept of the immobilization factor (b) used by Michaels

and Bixler [58] to characterize restricted segmental mobility

of amorphous polyethylene due to constraints imposed by

the presence of crystals. The following equation can be

derived from Eqs. (20) and (22)

ln b Z lnP0

PZ

Bar

FFV0

Tg KT0g

FFV0 KarðTg KT0g Þ

(23)

where P0 and FFV0 are the permeability and fractional free

volume of the wholly amorphous polymer, respectively. P

and Tg are for the PEO phase in PEO containing polymers.

Since high molecular weight, pure, amorphous PEO does

not exist at 35 8C, the polymer prepared from pure

PEGMEA is proposed as a model of amorphous PEO,

partially due to the similarities in densities and, therefore,

H. Lin, B.D. Freeman / Journal of Molecular Structure 739 (2005) 57–74 73

fractional free volume, of these two materials (i.e. 1.124 g/

cm3 for hypothetical amorphous PEO [35] and 1.13 g/cm3

for pure PEGMEA). In the original Cohen–Turnbull model

of diffusion that underlies Eq. (22), B is proportional to

penetrant size, so Eq. (23) clearly predicts that b would

increase as penetrant size increases and as Tg increases,

which is consistent with experimental results in the studies

of semi-crystalline polyethylene [58]. Michaels and Bixler

[58] found larger b values for larger penetrants and in

samples with higher crystallinity, which was inevitably

accompanied by higher Tg values.

Pure gas CO2/light gas selectivity, aCO2=LG, can be

derived from Eq. (22):

aCO2=LG ZACO2

ALG

exp KðBCO2

KBLGÞ

FFV

� �(24)

Since B values are presumably related to penetrant size,

the B values should decrease in the following order:

BCH4OBCO2

zBN2OBH2

. On this basis, increasing FFV

might decrease CO2/CH4 selectivity, but this should

increase CO2/H2 selectivity. CO2/N2 selectivity appears to

be quite constant in these PEO containing materials, as

shown in Table 3, which is consistent with BCO2zBN2

. The

increase of CO2/H2 selectivity with increasing free volume

has been experimentally observed in PEO containing

materials [66].

6. Conclusions

Structure/property guidelines have been extensively

explored in an effort to improve the separation performance

of polymer membranes for gas separation by increasing

polymer size sieving ability (i.e. diffusivity selectivity) [68,

69]. However, favorable solubility selectivity has not been

fully pursued as a route to enhance gas separation proper-

ties, probably due to the fact that penetrant diffusion

coefficients are often more sensitive than solubility to

polymer structure, and diffusion coefficients usually change

in a much broader range than penetrant solubility [69]. In

this report, we explore the possibility of harnessing

interactions between CO2 and polymers containing various

polar groups to improve permeability/selectivity properties.

By surveying CO2 and N2 sorption and/or transport in

liquids and polymers containing different types and amount

of polar groups, liquids and polymers with a solubility

parameter of about 21.8 MPa0.5 achieve the highest CO2

solubility and CO2/N2 solubility selectivity. So far, ether

oxygens in ethylene oxide (EO) units appear to be the most

useful groups for achieving high CO2 permeability and high

CO2/light gas selectivity (e.g. CO2/H2).

CO2 separation properties in various PEO containing

materials have been reviewed, and CO2 permeability ranges

from 7 to 570 Barrers. This wide change in CO2

permeability may be rationalized crudely using a very

simple model based on the free volume theory. Highly

branched, crosslinked PEO exhibits the highest CO2

permeability and highest CO2/H2 selectivity, due to

branches containing –OCH3 end groups, which increase

polymer fractional free volume and thus CO2 diffusivity and

CO2/H2 diffusivity selectivity. In particular, CO2/H2

selectivity values of 40 have been obtained, which is the

highest value reported in the literature for solid non-

facilitated transport membranes.

The approach of harnessing specific interactions of polar

groups in polymers with CO2 is an interesting route for

improving membranes for CO2/light gas separations.

However, more information about the nature of such

interactions is required and more polar groups or combi-

nations of various polar groups should be examined to

design optimized polymeric materials for CO2 removal

from light gases.

Acknowledgements

The authors gratefully acknowledge partial support of

this project by the United States Department of Energy

under grant number DE-FG02-99ER14991. This research

work was also partially supported with the funding from the

United States Department of Energy’s National Energy

Technology Laboratory under a subcontract from Research

Triangle Institute through their Prime Contract No.: DE-

AC26-99FT40675.

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