A group contribution approach to predict permeability and permselectivity of aromatic polymers

jourmdof MEMBRANE SCIENCE ELSEVIER

Journal of Membrane Science 132 (1997) 33-54

A group contribution approach to predict permeability and permselectivity of aromatic polymers Lloyd M. Robeson*, Carrington D. Smith, Michael Langsam Air Products and Chemicals, Inc. 7201 Hamilton Blvd., Allentown, PA 18195, USA Received 30 October 1996; received in revised form 16 January 19971 accepted 21 January 1997

Abstract Membrane separation of gases has evolved into an important separation technology for various gas mixtures (specifically O2fN2). Aromatic engineering polymers such as polysulfones, polycarbonates, and polyimides comprise commercially utilized membranes for these applications. The ability to predict permeability and permselectivity from polymeric structural units is highly desired in order to streamline synthetic approaches to optimum membrane candidates. A group contribution methodology is outlined in this paper which demonstrates excellent predictability of permeability (for 02, N2 and He) and good prediction of permselectivity for the O2/N2 and He/N2 gas pairs. This procedure utilizes the basic equation: ln P = ~-~i"--1Oi In Pi where ~)i=volume fraction of a structural unit i and Pi=the permeability contribution of the structural unit. Experimental permeability data are employed to set up an array of equations (of the above equation) solved by least squares fit. The values of ~)i are calculated using computer software programs to predict molar volume contributions. The structural units are chosen around the chemical bond. This procedure shows promising results when applied to aromatic polymers chosen from the classes of polysulfones, polycarbonates, polyarylates, poly(aryl ketones) and poly(aryl ethers). This procedure has been utilized to determine the contributions of 24 structural units employing 65 polymers which comprise the database. Excellent agreement within the database is observed and good agreement outside the database is also demonstrated. This procedure allows for a quantitative assessment of the structure/permeability (permselectivity) relationships for polymers of interest for membrane separation, and thus demonstrates group contribution methodology can be applied to both polymer permeability and permselectivity. Further refinements by addition of other polymeric classes (e.g. polyimides and polyamides) as well as additional expansion of the database should prove to be a valuable technique to predict the membrane separation potential of a wide variety of polymeric materials.

Keywords: Group contribution; Membrane separation; Permeability prediction; Permselectivity prediction: Structure/ permeability relationships

I. Introduction Membrane separation of gases has emerged into an important unit operations technique offering specific *Corresponding author. Fax: +1 610 481 6517. 0376-7388/97/$17.00 ;~g 1997 Elsevier Science B.V. All rights reserved. PII S0376-7388(97)0003 1-8

advantages over more conventional separation procedures (e.g. cryogenic distillation and adsorption). A number of books have summarized this field of technology [1-5]. The material science of gas separation by polymeric membranes has been largely empirical with a vast amount of experimental data on polymer

34

L.M. Robeson et aL /Journal of Membrane Science 132 (1997) 33-54

permeability and selectivity for the gas pairs of interest (e.g. O2/Na, H2/CH4, H2/N2, COa/CH4). Recently, literature references have appeared investigating the utility of molecular dynamics computer simulation to predict the diffusion coefficients of gases in simple polymeric systems (e.g. amorphous polyethylene, and silicone rubber) [6-9]. These results offer only a qualitative assessment of the permeability of simple gases in polymers; thus, significant improvements are desired before this technique will be able to appropriately predict permeability as well as permselectivity in more complex polymer systems. Group contribution methods have shown promise in the past for prediction of permeability, however, they do not allow for adequate permselectivity prediction. In addition, many of the polymers of present interest are not capable of being utilized in the database existing via these approaches. The most relevant group contribution method existing in the prior literature is by Salame [10] which will be briefly discussed later. In order to improve the predictability of polymer permeability and permselectivity and short-circuit the detailed synthesis programs to define the structure/ permeability relationships of new polymers, a group contribution method applicable to polymers of interest and capable of predicting permselectivity is highly desired. This has not realistically been possible until several years ago. The available database for polymers of interest has rapidly expanded to provide a sufficient database for a proper analysis (largely due to the structure/permeability program at the University of Texas, where much of the data utilized for the group contribution approach presented in this paper has been obtained). Group contribution methods are commonly employed to calculate specific properties of polymers and details of this methodology have been summarized by Van Krevelen [ 11 ]. The application of group contribution for predicting polymer permeability was first noted by Salame [10]. Salame noted a parameter called a Permachor (70 defined by the relationship: P(298 K) = P*(298 K) exp(-srr)

(1)

where P(298 K) is permeability of an arbitrary gas in an arbitrary polymer, P*(298 K) permeability of the same gas in a specific polymer and s is scaling factor to account for a specific gas.

The polymer Permachor 7r is equal to

7r= ( Z Tri)/n

(2)

where 7ri is incremental unit permachor value and n is number of characteristic groups per structural unit. The permeability is calculated from P = A exp(-sTr)

(3)

where A and s are constants for a particular gas. The structural units compiled by Salame do not include many of the polymers of interest for membrane separations (e.g. polysulfones, polycarbonates, polyarylates, polyimides). This approach yields a single value for o~(O2/N2) for all polymers with the same O2(or N2) permeability. As such, it offers no useful predictive capabilities for permselectivity of polymers for membrane separation. Another approach [ 12] for estimating polymer permeability has been noted by Jia and Xu. It was noted that the gas permeability could be predicted from the ratio of molar free volume/molar cohesive energy (Vf/Ecoh).Log P versus Vf/Ecohgave linear correlations for six gases over seven orders of magnitude for permeability. While this approach can yield an estimate of permeability, the accuracy is limited and of no value for predicting permselectivity as equal values of Vf/Ecohpredict equal separation factors. A recent publication by Park and Paul [13] addresses the limited success of prior correlations in predicting permselectivity as well as permeability. Using the basic equation noted: P = An exp (~FFvB -~)

(4)

where An and Bn are constants for a particular gas and FFV is the fractional free volume (V-VoW) where Vis the volume per mole of repeat unit, V0 is the dense volume. Park and Paul [ 13] employed modifications in order to achieve the desired predictive capability. The fractional free volume was assumed not to be constant for all gases for a specific polymer and the occupied volume was dependent upon both the gas and the structural unit. The results were correlated using a gas permeability database of 102 polymers to predict the empirical factors for 41 different groups. The results were shown to be a significant improvement over Bondi's methods [14] for both density and gas

35

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

permeability predictions. Good agreement of permselectivity was also demonstrated. Although the procedure by Park and Paul [13] is different than that employed in this study, the end result would be expected to be similar. The structural units and the database are overlapping, and a fit of the data thus will be similar. The approach chosen in this paper does not follow the fractional free volume route and has only two variables of importance for each structural unit; the molar volume and the permeability contribution of each subunit.

This will allow for combining units where symmetry is not observed. It is important to note that the position of the bond on the other side of the aromatic unit is very important, thus

I

I I

I

I

I I

or I

2. Group contribution methodology for permeability and permselectivity predictions

The key relationship for calculating polymer permeability employing the group contribution method proposed in this analysis is: In P = ~

i-1

(5)

0i In Pi

where Oi is the volume traction of a specific group i comprising the polymer repeat structure and Pi is the permeability contribution of a specific group i. This logarithmic relationship (shown in Eq. (5)) has been well established for copolymers and, as will be shown, is also valid for group contribution. One of the key elements for utilizing group contribution is the proper method of subdividing the segmental units. The chemical bond is an important link for synthetic polymer assembly and thus structural units will be chosen around each chemical bond. As applied to Bisphenol A polysulfone,

I I

I

I

I I

While molecular volumes of these groups are very similar (or equal), the Pi values for these groups are vastly different. For example, meta versus para linkages for aromatic groups have a pronounced effect on permeability, and this effect is addressed by the group contribution method noted herein. The group contribution approach noted here employed the Molecular Simulations, Inc. Quanta package to determine molecular volume in ~3 for each group. The advantage of this technique is that molecular volumes can be obtained for any polymeric unit. The Quanta method can easily calculate volumes of minimized energy molecules from which group contribution V/'s can be extracted. For example, to obtain the molecular volume of the segment noted below, the following procedure was used:

the structural units will be I

I

I I

I

2_~1~1 ~Clla?

and

I I

I

I

I I

~1

I I

OII-I

I I

First, the following structure was built in the Chemnote application and then transferred to the Quanta program where the molecular energy was minimized.

36

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

I

I CH3[

I CH3

I

I I NCI_I3 I

I

I

I

The molar volume of this molecule was computed by Quanta using the molecular similarity tool and found to be 214.37 ,~3. Next, the molecular volume of benzene (83.25 ,~3) was subtracted and the resulting value divided by two yielding 65.56 ~3 for the desired unit. Similar manipulations were performed to obtain molecular volumes of the other structures employed in this study. The structural units employed in this analysis are listed in Table 1 along with the molecular volumes determined as per the procedure described above. The polymers comprising the database, the permeability data and references are listed in the Appendix A. It must be emphasized that the success of any group contribution method is based upon reliable data utilized to calculate the individual group property values. The polymer permeability data was primarily from data published at the University of Texas (Paul and Koros and co-workers) measured at 35°C. In several cases data was utilized from sources at different temperatures (generally 25°C). Corrections were made using typical activation energies for glassy polymers. These corrections were relatively minor: P(O2)(35°C)=l.25P(O2)(25°C); oz(O2/N2) (35°C)=0.96c~(O2/N2)(25°C). This data was utilized for setting up equations as per the relationship in P = ~ i ~ ] 0i In Pi for a least squares fit to determine the volumes of Pi- An example of the equations employed is given for polysulfone.

The first phase of the analysis reported herein chose polymers from the class of polysulfones, polycarbohates, poly(aryl ketones), polyarylates and poly(aryl ethers). Polyimides have also been employed in this analysis but will not be presented herein. While polyimides show a good fit employing this approach, the data from the literature varies up to an order of magnitude for the same structure due to synthesis method, film preparation, and annealing to remove solvent; thus one must be selective to choose data from sources employing similar preparative procedures. The results of the least squares fit for the specific structural units are given in Table 2. The fit of the predicted and experimental data for the 65 polymers of the database are illustrated in Figs. 1-3, respectively for P(O2), P(N2) and P(He)

I00

o

p(o 2)

1o

o

BARRERS CALCULATED

0

~9

oo

1.0

0.t 0.1

,

....

-

1.0

P(O2) BARRERS

I0

I00

EXPERIMENTAL

Fig. 1. Comparison of predicted versus experimental values of the O2 permeability of polymers in the database.

O-s repeat unit s t r u c t u r a l units: 4 P 2 , 2 P 3 , 2P4.

In P(O2) = 0 . 4 2 8 In P 2 + 0.301 In P3 + 0.271 In P 4

37

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 1 Group contribution units and molecular volume ,~3

Vi(A 3)

Vi(A3) I

I

__l.__/CH3

P1

--(O~-0\

"T'-

/

65.56

51.07

P7 I

- -

~'\dI,

I I

I [

I

I

P2

-

39.0

x....l....d

]

--~Q)-~I [

I I

I I

! i

]

!

%~C!3

54.94

-?

P9

I

49.47

I

PIO

69.0 I I

I I I

73.19

Pll

i

Io

I I

I I

14.88

I

I

--~c~2-41.25 L_'T'_/ '! I I

44.32

I I

I

P6

!

o

i

0

!

]

I

P4

P,

54.82

I

A-,, &3

CH3

P8

I

I I

P3

! I

74.50

P12 I

38

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 1 (Continued).

VI(A3)

Vi(A 3) I I

I

P13

68.0

~

I

40.75

P17

-'\Ci I

I I

I

I I I

I

I

I

CH3

83.56

P18

68.0

P14 I I

I I

I I I

P19

I

P15

/~11

o

I I

I I

I I

--~~//~-~107.63

59.0

I

I

I [ CH3

i I I P16

o II

I I I I

I I

CH 3

\/I

P20

58.13 i

,

CH2~ _/

tL.

39

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 1 (Continued).

Vi(A 3)

V,{A 3)

I

I P21

~

P22

98.57

I /

I

CH 3 - - ~ - - C H 3

¢

I CH3 I I

II

0

I

CH3

~-'~1~o~/

P23

86.0 --kLL,'/-

r24

T

~

u

81.3

--

I

I

2OO

IO 0 o

IO0

o o

P(N21

I.O

P(He)

C A L C U L A T E D

BARRERS

O''O

0.01

Oo

o/

BARRERS

CALCULATED

0.01

/

O I :/ ,

i

030

i llitli

I

I

I I11111

1,0

1

I

I Illil

I0

P(N2) BARRERS EXPERIMENTAL Fig. 2. Comparison of predicted versus experimental values of the N2 permeability of polymers in the database.

4

i

=

t

I0

= ]

I

I

I

I

I

I

I

I

I00 200 I

P(He) BARRERS EXPERIMENTAL Fig. 3. Comparison of predicted versus experimental values of the He permeability of polymers in the database.

40

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 2 Predicted permeability and permselectivity data for structural units comprising the group contribution approach

Structural Unit

I

- ~ l

I

Permselectivity ~(02/NO

c~(He/N2)

CH3

-o,"-

P1

Permeability (Barrers) 02 N2 He

63.1

15.5

293

4.07

18.9

1.54

0.327

10.6

4.71

32.4

3.86

0.678

27.7

5.69

40.9

0.323

0.0394

6.81

8.20

173

104.0

27.5

589

3.78

21.4

1.71

0.337

12.7

5.07

37.7

c~

I P2

P3 c,H+ I

i

[

I

P4 I I I

P5

/-,~-,-Xc,F, M-IJCF

I I

i i

3

I

P6

-C.H 2I I

and in Figs. 4 and 5 for o~(O2/N2) and ce(He/N2) separation factors. The comparison of the fit of predicted versus experimental data can be obtained from the following expression:

O-=

/lnP//predicted) ( lnPi/observed))2) 'j2

LM. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

41

Table 2 (Continued).

Structural Unit

I

_ ~

Permeability (Barrers) 02 N2 He

Permselectivity a(O2/N2) a(He/N2)

CH3

-o-

P7

0.0781

0.00802

8.43

9.74

1051

0.0703

0.00952

5.64

7.38

592

0.0922

0.0134

3.20

6.88

239

9.67

2.15

29.9

4.50

13.9

0.00277

0.000637

0.192

4.35

301

4.52

0.508

52.1

8.89

103

- ~ C CH3

P8 I I

i

[

I

o

-?

P9

I I I

I

I I

I I

PIO

I Pll

i

o

- - O ~I

~ I I

I I

o--

I P12

I Gas 02 N2

He

a (residual norm) 1.426 1.687 0.9029

The predicted permeability versus experimental data shows excellent agreement for all gases. The separation factor for a(O2/N2) and t~(He/N2) also shows good agreement between experimental and predicted

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

42 Table 2 (Continued).

Permeability (Barrers) Structural Unit

Permselectivity

02

N2

He

¢x(O2/N2) ~t(He/Nz)

6.85

0.877

75.6

7.81

86.2

0.885

0.127

20.6

6.97

162

2.67

0.434

22.4

6.15

51.6

0.222

0.0340

4.84

6.53

142

0.00547

0.00139

6.21

3.94

4468

I P13 C1~

I

I I

I P14

I I

I I

/~ll

o

I

I

P15

I

P16

o II

- ~

BCIOI I I I

P17

I

I I I

I

I I results although not apparently as good as the permeability correlation. Note that the data are optimized for the best permeability fit, not the separation factor. One data point for c~(Oz/N2) does appear out of line (8.0/ 6.17; exp./calc) for polymer 42 (see Appendix A). In fact, the experimental value appears out of line and deserves independent verification. Generally, if the 02 predicted value is higher (or lower) than the experimental value, the N2 value shows the same trend. For

polymer 42, the reverse was true thus yielding a reasonable fit for permeability but a poor fit of the separation factor. From the data in Table 2 on the structural unit permeability values, a number of interesting comparisons can be made. The substitution of an ortho-methyl onto the phenyl ether group (P7) compared to (P2) leads to a dramatic lowering of the permeability contribution of the unit to the overall polymer perme-

43

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 2 (Continued).

Structural Unit

Permeability (Barrers) 02 N2 He

Permselectivity ¢x(O2/N2) (x(He/N2)

l I CIH3

l l

P18

4.39

0.746

25.6

5.88

34.3

19.3

3.46

81.4

5.58

23.5

84.6

20.3

293

4.17

14.4

1.94

0.350

25.3

5.54

72.3

I I l I

I

P19

I [ CH3

i

I CH 3

\/I

C,c

P20 I ="

I

I P21

I

c II O

I I

ability. Two methyl groups placed ortho to the phenyl ether however leads to a significant increase in permeability. The phenyl isopropylidene group (P3) shows a large increase in permeability with perfluorosubstitution (P5) of the isopropylidene group. The phenyl ether (P2) and phenyl methylene (P6) groups exhibit similar results.

The tere versus iso (para versus meta) placement of the phenyl ester group (P15) versus (P16) well illustrates the known effect of lowered permeability of isophthalate versus terephthalate based polyesters. Similar comparisons of para versus meta linkages can be made with (P2) and (P17) (phenylether) and (P3) and (P8) (phenyl isopropylidene) where meta

44

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 2 (Continued).

Permeability (Barrers) Structural Unit o

Permselectivity

02

N2

He

~(O2/N2)

or(tie/N2)

13.4

3.20

64.0

4.19

20.0

5.35

0.803

34.1

6.66

42.5

7.22

1.56

51.8

4.63

33.2

I

"_lo_

P22 I

CH3 - - c --CH3

I CH3 I I I

P23

CH3

P24

-

-T-

I

I

8

y

140 - -

120

7--

atUe' ' ~

a(O2/N 2) CALCULATED

lO0 -

o 0

0 _ Oo/ / o

6

_

CALCULATED

o o =X, oO o~q~e;Oo o

o 80 o 60--

o °

0(30 0

4

5

6

o o o

7

8

a(O:,/N 2) EXPERIMENTAL Fig. 4. Comparison of predicted versus experimental values of cKO2/N2) permeability of polymers in the database.

°

o o

o° ° oo0

yo

40

--

2(,

~

I

40

a(He/N.~

I

60

I

80

I

I00

I

120

I

140

EXPERIMENTAL

Fig. 5. Comparison of predicted versus experimental values of cffHe/N2) of polymers in the database.

LM. Robeson et al./Journal of Membrane Science 132 (1997) 33-54 20

I0-9 8 7 02

6

45

I0,000

BOUND

IOOO

0

o

o

oOO\ °

o

a-if2 5

0

4

00o ~ o

BOUND

a(He/Nz)

o~, ~

I00

3

o°

o

oo

o°

o o

o°

2 0001

I

0.01

l

0.1 P(O2)

I

1,0

I

I0

I

I00

I000

BARRERS

~ IIIIIll

Ol

Io

I

,

,llllll

IO

i

I

IIIIHI

IOO

I

I

]1111

IOOO

P(He) BARRERS

Fig. 6. Comparisonof the structuralunit valuesof In P(O2)versus In c~(O2/N2)with the upper bound relationshipof reference [ 16].

Fig. 7. Comparison of the structural unit values of In P(He) versus In c~(He/N2) with the upper bound relationship of reference [16].

yields much lower permeability. The substitution of bulky, rigid units in the main chain is known to lead to increased gas permeability without severe sacrifice of permselectivity. Comparisons of (P23), (P19) and (P20) with (P2) well demonstrate this observation. It is interesting to note that the trade-off of permeability and separation factor [16] is observed by the data for the structural units in Table 2. The plot of the structural unit values of In P(O2) versus In a(O2/N2) is shown in Fig. 6. The dibromophenylene ether group (P12) yields the best combination of P/c~ when compared to the upper bound relationship established by reference [16] and is positioned above the upper bound. Based on the analysis shown here, the polymer from P12; poly(2,3,5,6-tetrabromo- 1,4-phenylene oxide) would be expected to exhibit P/c~ values of 4.52 barrers/c~(O2/N2)=8.9. This is above the upper bound relationship established in reference [16]. Unfortunately, there does not seem to be any facile method for synthesizing this polymer. Other groups of interest include (P13) and (P19). The plot of the structural unit values of In P(He) versus In cffHe/ Ne) is given in Fig. 7 and compared with the upper bound relationship. While there is good agreement between the experimental and predicted values for the polymers in the database, the proof of the approach involves the ability to adequately predict permeability and permselectivity of polymers outside the database. Several examples are listed in Table 3. Generally good qualitative agreement is observed, however, the quantitative agreement

(with proper correction for temperature differences) does not appear as good as the fit of the polymers in the database. This analysis demonstrates the group contribution methodology can be applied to predict the permeability and permselectivity of polymers in the class of polycarbonates, polyarylates, polysulfones, poly(aryl ketones) and poly(aryl ethers). The analysis is only as good as the database. The results presented herein utilized data for polymers where 02, N2 and He data existed from the same source. As further data is added, the analysis will improve. In fact, for 02 and N2 a database involving over 180 different polymers and 67 groups has been compiled in our laboratories including polyamides and polyimides. There is generally good agreement between the data on the specific structural units except for the para-aromatic ester (P15) group. The expanded version yields a higher P(O2) contribution and a lower c~(O2/N2) value. This methodology has also been successfully employed to predict CO2 and CH4 permeabilities and o~(CO2/CH4) for a similar polymer database. Combination of the structural units in this database can yield polymers slightly above the upper bound relationship (e.g. poly tetrabromophenylene oxide), however, synthesis procedures for these specific cases are not readily available. In this and the expanded data base, the structural units establish a new 'upper bound' relationship slightly above the 'state-of-the-art' relationship noted in reference [16].

46

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Table 3 Comparison of experimental vs. calculated results on polymers outside the database P(O2) Barrers

©©_o} ~H3

CFj

"---7---/

CFj

IS

CHj

CF=

~

P(N2)

a(O~N 9

Reference

Barrers

Experimental (25°C) Calculated (35°C)

0.3 0.304

. . . . . . . .

17

Experimental (25°C) Calculated (35°C)

15.6 21.9

4.0 4.97

3.9 4.4

18

Experimental (25°C) Calculated (35°C)

52.5 41.4

13.5 9.7

3.9 4.27

18

Experimental (25°C) Calculated (35°C)

28.4 20.8

5.74 3.96

4.95 5.25

18

Experimental (25°C) Calculated (35°C)

8.97 11.4

1.775 2.0

5.08 5.7

18

Experimental (25°C) Calculated (35°C)

25.6 19.0

5.9 4.02

4.34 4.72

19

Experimental (25°C) Calculated (35°C)

1.56 1.68

0.240 0.294

6.5 5.7

19

//n

CF

I

3. C o n c l u s i o n s

Engineering polymers from the classes of aromatic polysulfones, polycarbonates, polyarylates, poly(aryl ketones) and poly(aryl ethers) have shown interesting properties as membranes for gas separation. Several members of these classes of polymers (e.g. polysulfone based on Bisphenol A, tetrabromo bisphenol A polycarbonates, and poly (2,6 dimethyl 1,4 phenylene oxide) have been utilized commercially in gas separation applications. Structure/property studies revealed predictable trends related to permeability and permselectivity. A group contribution approach using the

expression noted in Eq. (5) involves setting up an array of equations based on experimental data and solving for a least squares fit. The groups comprising the polymers in the experimental array are chosen around the chemical bond or in some cases around a specific group. The prediction of permeability for polymers in the database is excellent for 02, N2 and He. The permselectivity predictions are also quite good but exhibiting more scatter than with permeability. This procedure yields quantitative data for specific groups and allows for structure/permeability comparisons. The meta versus para linkage for aromatic groups well demonstrates the significantly lower

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

permeability qualitatively observed experimentally for meta linkage. This approach allows for a comparison of the groups which best offer permeability/ permselectively values to design polymers to approach 'upper bound' properties. This analysis is only as good as the database upon which this approach is based. The excellent agreement shown affirms the reliability of the large permeability database complied by investigators at the University of Texas (which comprises most of the database for this paper). The ability to predict permeability/permselectivity for polymers outside the database is also good. However, it will improve with an expanded database as has been demonstrated in our laboratories for 02 and N2. Until significant improvements occur in computer

47

simulations of diffusion (e.g. molecular dynamics), a group contribution approach such as proposed by Park and Paul [ 13] as well as the procedure outlined in this paper will be the best method for predicting permeability/permselectivity.

Acknowledgements The authors wish to acknowledge K.J. Anselmo who provided the assistance in solving the array of equations by least squares fit. Appendix A Permeability data (35°C) P(O2) Barrers

P(N2) Barrers

P(He) Barrens

Reference

'

1.4

0.25

13.0

20

3.4

0.666

33.0

21

1.1

0.20

10.0

21

1.1

0.196

10.0

21

1.8

0.321

14.0

20

3.2

0.571

32.0

20

0.584

0.0967

8.0

21,19

"

4"

,.

.

.

.

.

O--

"-S

--

48

LM. Robeson et aL/Journal of Membrane Science 132 (1997) 33-54

P(O2) Barrers

P(NT.) Barrers

P(He) Barrel's

Reference

5.6

1.06

41.0

20

0.64

0.914

12.0

20

14.6

3.5

82.3

22

0.69

O.11

11.7

20

1.1

0.21

11.8

23

2.4

0.44

26.4

23

10.

11.

12.

13.

(0-,-0-,0--0--0£ @-~0-,-0-~0--0,@-{ {o-~o+o-~o-oO-};?o-~.

14.

c~3

15.

3.7

0.76

42.0

23

18.0

4.0

113.0

24

3.3

0.610

29.0

24

1.8

0.321

21.0

20

1.3

0.224

12.0

25

0.75

0.129

8.9

26

/

16.

17.

©

e-o-o~

18.

19.

49

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

Reference

P(OT.)

P(N2)

P(He)

Barrers

Barrel's

Barrers

0.64

0.110

7.7

26

1.6

0.333

13.0

27

6.9

1.68

60.0

27

32.0

7.8

200.0

28

5.6

1.1

46.2

29

2.29

0.36

27.4

29

20.

21.

22.

23.

24.

25.

/CI

CI " ~

26. 1.36

0.182

17.6

29

9.7

1.8

100

27

5.8

1.208

36.0

25

0.74

0.114

11.7

20

0.41

0.0569

11.0

20

27.

cFs

~r

/n

28.

29.

30.

50

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

r~ -'-- CH'

~r

/0A; k r ~

C[F' x~----~r

P(O2) Barrers

P(N9 Barrers

P(He) Barrels

Reference

0.60

0.105

10.0

21

4.9

0.790

49.0

27

1.70

0.335

14.2

30

6.56

1.031

71.2

31

7.12

1.17

72.5

31

;.5

50•50 iso/tere 34.

35.

r

Br

r

CF3

Br

80/20 iso/tere 36.

Br

Br 11.25

1.94

93.7

31

7.05

1.215

68.75

31

31.18

0.592

21.8

32

2.76

0.484

21.3

32

1.84

0.361

13.9

32

25/75 iso/tere 37.

CI

CI

38.

39.

40.

51

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

P(O2) Barrers

P(N2) Barrers

POle) Barrers

Reference

41. 1.56

0.278

13.3

32

2.0

0.25

14.0

33

13.4

2.98

68.0

34

5.3

1.0

39.1

34

0.39

0.0661

9.3

20

1.6

0.250

18.2

35

7.2

1.44

61.7

35

1.3

0.180

16.3

36

5.63

0.901

41.6

36

22.1

4.474

124.0

36

42.

43.

C/•CH3 \ - - ' e ..c''

-°c-I(

31- - 7-,,

CH3cH3

44.

3c45.

-OfO-o©-,.-O-o:

46.

47.

48.

49.

I

50.

CF3 --O B/r

tr3

~r

~

'n

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

52

P(O9 Barrel's

P(N2) Barrers

P(He) Barrers

Reference

1,96

0.290

23.4

36

7.41

1.278

51.3

36

4.84

0.7045

38.5

36

16.8

2.94

94.4

36

53.

54.

55. 2.1

0.32

15.9

37

1.33

0.240

13.4

38

5.95

1.197

34.3

38

5.23

1.11

47.8

38

15.7

3.88

91.1

38

50/50 iso/tere 56.

( 0 ~__o__c~_~._o~*

58.

59.

c~3

53

L.M. Robeson et al./Journal of Membrane Science 132 (1997) 33-54

P(O2) Barrers

P(Nz) Barrers

P(He) Barrers

Reference

60. 1.53

0.276

14.7

38

5.60

1.09

35.6

38

3.03

0.570

22.3

38

9.55

1,93

45.9

38

61.

62.

63.

64.

65.

(~Hz

1.64

0.273

19.5

5.03

1.08

37.3

39

~H3 39

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54

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