Materials Science of Synthetic Membranes - American Chemical Society

2 Material Selection for Membrane-Based Gas Separations 1

R. T. CHERN, W. J. KOROS , H. B. HOPFENBERG, and V. T. STANNETT

Downloaded by UNIV QUEENSLAND on June 8, 2014 | http://pubs.acs.org Publication Date: December 12, 1985 | doi: 10.1021/bk-1985-0269.ch002

Department of Chemical Engineering, North Carolina State University, Raleigh, NC 27650

High membrane permselectivity for a gas mixture is wellknown to correlate with low permeability of the desired product through the membrane. Exceptions to this rule exist, however, and this suggests the possibility of improved membranes for a number of important applications. This paper suggests possible polymer structural changes which may allow control over the magnitudes of permeabilities and selectivities. These suggestions result from considering the permeability and selectivity in terms of their separate thermodynamic solubility and kinetic mobility contributions. The two contributions vary markedly with changes in the polymer structure and correlate with variations in penetrant and polymer physical properties. The feasibility of developing extremely selective high flux membrane materials is explored in terms of these correlations. The potential for such developments is shown to be fairly high for cases in which the permeant molecule is substantially more compact than the nonpermeant molecule if the resulting mobility advantage is not eliminated by a large solubility advantage favoring the nonpermeant. Several important examples of such systems are discussed including H2/CH4 and CO2/CH4. A short discussion of approaches to assess membrane materials for resistance to attack by components in the process stream is also presented.

Membrane-based gas separations have emerged as important chemical engineering unit operations for hydrogen recovery from purge and recycle streams (1-4) and f o r carbon dioxide and water removal from natural and land f i l l gases (5-9). Using asymmetric structures i n high surface area modules permits the use of higher s e l e c t i v i t y , lower permeability glassy polymers i n the place of rubbery materials. 'Current address: The Center for Energy Studies, The University of Texas at Austin, Austin, TX 78712. 0097-6156/85/0269-0025$06.50/0 © 1985 American Chemical Society In Materials Science of Synthetic Membranes; Lloyd, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


26

MATERIALS SCIENCE O F SYNTHETIC M E M B R A N E S

The f i r s t generation of gas separators has achieved an impressive penetration into markets t r a d i t i o n a l l y dominated by cryogenic, chemical and physical sorption processes. Competition from these processes i s strong. Membranes with higher permeabilities, select i v i t i e s and resistance to penetrant attack are required to meet challenges from these t r a d i t i o n a l processes and to permit expansion ?.nto a d d i t i o n a l application areas. Although no commercial examples exist currently i n the gas separation f i e l d , thin f i l m composite membranes such as those p i o neered by Cadotte and co-workers USD may ultimately permit the use of novel materials with unique transport properties supported on standard porous membranes. Therefore, the focus i n this paper w i l l be on suggesting a basis for understanding differences i n the permeability and s e l e c t i v i t y properties of glassy polymers. Presumably, i f such materials prove to be d i f f i c u l t to fabricate into convent i o n a l monolithic asymmetric structures, they could be produced i n a composite form. Even i f thin f i l m composite structures are used, however, the chemical resistance of the material remains an important consideration. For this reason, a b r i e f discussion of this topic w i l l be offered. T y p i c a l l y , membrane research e f f o r t s focus upon the determination of the permeability and s e l e c t i v i t y of candidate polymers without e x p l i c i t consideration of the s o l u b i l i t y and mobility terms comprising the permeability (.11-13) . This approach i s reasonably e f f e c t i v e for screening available polymers f o r a p a r t i c u l a r a p p l i cation but not optimum f o r providing guidelines to improve membrane performance by s c i e n t i f i c a l t e r a t i o n of the polymer structure. Moreover, i t may lead one to an overly pessimistic view of the select i v i t y and permeability properties achievable as a result of polymer s t r u c t u r a l v a r i a t i o n s . As an adjunct to this t y p i c a l approach, correlations of the penetrant d i f f u s i o n c o e f f i c i e n t s and s o l u b i l i t i e s with the physical and chemical natures of the polymers and penetrants w i l l be discussed. These correlations r a t i o n a l i z e the generally observed relationship between high s e l e c t i v i t y and low permeability. They also provide a p a r t i a l basis for understanding reports of several deviant cases i n which high s e l e c t i v i t y and permeability are observed for H2/CH4 and CO2/CH4 systems. I t i s these deviant cases that may lead the way to a new generation of more productive and s e l e c t i v e membranes. Background and Theory One-dimensional d i f f u s i o n through a f l a t membrane w i l l be treated i n the following discussion. The e f f e c t s of membrane asymmetry w i l l be neglected since the process of permselection occurs i n the thin dense layer of e f f e c t i v e thickness, at the membrane surface. In such a case, the expression for the l o c a l f l u x of a penetrant at any point i n the dense layer can be written as shown i n Equation 1 CU): dx

In Materials Science of Synthetic Membranes; Lloyd, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

(1)

2. CHERN ET AL.

27

Membrane-Based Gas Separations

where the d i f f u s i o n c o e f f i c i e n t , may be a function of l o c a l con centration, C, i n the membrane. The d i f f u s i o n c o e f f i c i e n t may be interpreted i n terms of a preexponential factor, D°, and an expo nential term that depends upon the a c t i v a t i o n energy f o r the d i f fusion process, Ε (14). β

D = D° expi- E /RT] D

(2)

To a f i r s t approximation, E i s the average energy that must be l o c a l i z e d next to the penetrant to generate an opening large enough to permit the molecule to execute a jump. If concentration depend ence of the d i f f u s i o n c o e f f i c i e n t e x i s t s , both D° and EQ may be functions of the amount of penetrant present. At low concentrations, the activation energy should be related strongly to the minimum cross section of the penetrant, since t h i s defines the c r i t i c a l opening size necessary f o r a jump to occur. The large effect on molecular mobility caused by differences i n penetrant size or shape i s i l l u s trated i n Figure 1 for a t y p i c a l rubbery and glassy polymer, respec* t i v e l y . The larger nonspherical penetrants tend to approach a p l a ~ teau d i f f u s i v i t y because the cross-sectional area of the molecule as well as i t s volume determine i t s a b i l i t y to f i n d a gap of s u f f i c i e n t size to permit a jump. Presumably, nonspherical penetrants move i n a somewhat oriented fashion, and the i n d i v i d u a l jump lengths may he only fractions of the t o t a l length of the molecule. Associated with the more highly r e s t r i c t i v e glassy environment comes a greater a b i l i ty to perform s i z e or shape discrimination between penetrants. This difference between the glassy and rubbery state i s i l l u s t r a t e d c l e a r ly by the much larger spread i n d i f f u s i o n c o e f f i c i e n t s i n the glassy polymer compared to the rubbery one. Recognition of the preceding facts often leads to the generalization that low membrane permeabil i t y i s necessary f o r high s e l e c t i v i t y . Although the two generally correlate, there appear to be a t t r a c t i v e exceptions to the rule that are worthy of serious investigation (11,13)· The permeability of a membrane to a penetrant i s defined by Equation 3:


n

P = . [p

S

2

* -

.

PjJ

(3)

where p and p^ are the upstream and downstream pressures of the com ponent acting across the e f f e c t i v e membrane thickness, £. Clearly, the permeability of the membrane i s not only determined by the mobi l i t y of the penetrant discussed above but also by i t s s o l u b i l i t y , be cause the higher the s o l u b i l i t y difference across the membrane, the higher w i l l be the observed f l u x and permeability. The contributions of the two factors can be seen c l e a r l y for the case where the down stream pressure, p^, i s n e g l i g i b l e . Substituting Equation 1 into Equation 3 and integrating leads to Equation 5: 2

(4)


28


10


10

Natural

Rubber

J

10

10

10

Έ

10

J-

10 20

40 van

Figure 1.

-L 60 der

-L

JL

80

100

Waals

120

140

160

180

Volume (cc/mole)

D i f f u s i o n c o e f f i c i e n t s f o r a variety of penetrants i n natural rubber at 25 °C and r i g i d p o l y ( v i n y l chloride) at 30 °C. The van der Waals volumes are taken from The Handbook of Chemistry and Physics, 35th ed., 1953-54, page 21-24 to 21-26, CRC, Cleveland, Ohio.


2.

CHERN ET AL.

29


- D S


where D =

(5)

defines an average measure of the pene trant's mobility i n the membrane between 2 ic the upstream concentration, C2> and down stream concentration, C^-O (14). The para meter, S = C2/p2> equal to the secant slope of the sorption i s o therm evaluated at the upstream conditions, i s a measure of the s o l u b i l i t y of the penetrant i n the membrane. The mobility factor i n Equation 5 i s k i n e t i c i n nature and largely determined by polymer-penetrant dynamics as discussed i n the context of Equation 2. The s o l u b i l i t y factor i n Equation 5 i s thermodynamic i n nature and i s determined by polymer-penetrant interactions and the amount of excess interchain gaps e x i s t i n g i n the glassy polymer (17). When the downstream pressure, p-^, i s n e g l i g i b l e compared to the upstream pressure, p2, the separation factor, α^β, defined by Equation 6 can be related to the r a t i o of the permeabilities of com ponents A and Β (18) as shown i n Equation 7: v

(Γ )

α

ΑΒ

=

[ y

A

/ y

B

]

[ X

A

/ X

B

]

a* = Ρ /P AB A' Β f

( 6 )

(7) '

K

J

where x ^ s and y^'s are the l o c a l mole fractions of components A and Β at the upstream and downstream membrane faces, respectively. The superscript * i n Equation 7 indicates that a* i s the so-called " i d e a l separation factor" which applies under the conditions de scribed above. The r a t i o of the component permeabilities i n such a case provides a useful measure of the i n t r i n s i c permselectivity of a membrane material for mixtures of A and B. When the i n t e r a c t i o n between one penetrant and the polymer i s not affected by the presence of another penetrant, the pure-com ponent permeabilities of the two penetrants i n the mixture can be used i n Equation 7. For rubbery polymers at low penetrant p a r t i a l pressures, this assumption of independent-permeation appears s a t i s factory (19-20). I t does not, however, appear to hold i n general f o r glassy polymer membranes (12,13,21-25). Moreover, i t also has been shown that p l a s t i c i z a t i o n of both rubbery (26) and glassy (27) polymers can occur at higher penetrant a c t i v i t i e s . Based on the recent study of the permeabilities of Kapton p o l y i mide to CO2/CH4 mixtures (21,22), i t i s expected that for systems which can be described by the generalized dual mode model (17), the permeability r a t i o of CO2 over CH4 i n a mixture can be approximated to within about 20% by using the respective pure component perme a b i l i t i e s . Consequently, f o r the present general discussion, purecomponent values w i l l be used i n Equation 7 i n the following sec tions f o r discussing t h i s important system.



30


Discussion General Considerations. Representative CO2 permeabilities f o r seve r a l glassy polymers at 35 C are plotted as a function of the upstream penetrant pressure i n Figure 2 (8). Except for c e l l u l o s e acetate, the permeabilities decrease monotonically with upstream pressure, consistent with the dual mode model predictions (17). The behavior of c e l l u l o s e acetate w i l l be addressed i n a l a t e r section i n terms of p l a s t i c i z a t i o n arguments. The i d e a l separation factors for CO2/CH4 at 20 atm, calculated using the pure-component permea b i l i t i e s , are plotted i n Figure 3 versus the s o l u b i l i t y parameters of the various polymers. The s o l u b i l i t y parameters of polymers (28-32) and the permeability data (5,6,33-35) were taken from a number of sources. A simple i n t e r p r e t a t i o n of Figure 3 might be that the higher intersegmental interactions associated with high s o l u b i l i t y parameter polymers create a mobility selecting environment by making i t more d i f f i c u l t to form a transient gap of s u f f i cient size to pass a bulky, spherical CH4 molecule compared to a streamlined, l i n e a r C0 molecule. As i l l u s t r a t e d i n l a t e r discussion of the separate mobility and s o l u b i l i t y factors i n Equation 5, t h i s argument based s o l e l y on mobility s e l e c t i v i t y appears to be oversimplified. E s p e c i a l l y i n the case of c e l l u l o s e acetate, i t w i l l be shown that s o l u b i l i t y considerations are of considerable importance. Examination of Figures 2 and 3 supports the previous observat i o n that low permeability and high s e l e c t i v i t y are generally r e lated. For example, the CO2 permeability of poly(phenylene oxide) (PPO) i s over twelve times higher than that of polysulfone, but i t s CO2/CH4 s e l e c t i v i t y i s less than h a l f that of polysulfone. Kapton, on the other hand, i s over twenty-five times less permeable to CO2 than polysulfone, yet i t s CO2/CH4 s e l e c t i v i t y i s more than twice as high as that of polysulfone. Such trends suggest that increases i n permselectivity could be achieved by substituting a polar or hydrogen-bonding group on the phenylene ring of PPO to increase i t s cohesive energy density at the expense of i t s high C02 permeability. A l t e r n a t i v e l y , one could introduce i r r e g u l a r i t i e s into the Kapton backbone through the use of one or more comonomers along with the standard bis-4(aminophenyl ether) used as the diamine i n Kapton production. Such modifications should i n h i b i t packing and thereby lower the e f f e c t i v e cohesive energy density. This "opening up" of the polymer structure would tend to markedly increase the CO2 permeability but on the basis of Figure 3, may also reduce the s e l e c t i v i t y . These concepts are der i v a t i v e of those pioneered by H. Hoehn of DuPont i n h i s work on the development of reverse osmosis membranes from aromatic polyamides (36). 2

S o l u b i l i t y and D i f f u s i v i t y Considerations. The preceding general discussion has been largely conjectural i n terms of the s p e c i f i c reasons f o r the relationship between v a r i a t i o n s i n the cohesive energy density and v a r i a t i o n s i n membrane s e l e c t i v i t y and permeability. To pursue these issues i n a more quantitative fashion, i t i s useful to consider the separpt-fi s o l u b i l i t y and mobility contributions, D and S , for the various polymers shown i n Figure 3.


2.

CHERN ET AL.


31

100 80 PPO(35%

60

Decrease)

12.5X Polysulfone


40

20 Cellulose Acetate (138%

Increase)

Polycarbonate (30%

decrease)

Polysulfone (38%

decrease)

K A P T O N (31% 1/26X

Decrease) Polysulfone

0.1 10

15 Feed Pressure

Figure 2.

20 (atm)

Pressure dependence of CO2 permeability i n a variety of glassy polymers at 35 °C. The c e l l u l o s e acetate data are estimated from a number of sources including Ref. 5 and 6 and "The Science and Technology of Polymer Films", ed. by 0. J . Sweeting, V o l . I I , Wiley Interscience, NY (1971).




32



2.

CHERN ET AL.

33


The sorption isotherms for most gases i n glassy polymers tend to have concave shapes l i k e those shown i n Figure 4. As a r e s u l t , the apparent s o l u b i l i t y (S = C2/p2) Is a decreasing function of the upstream penetrant pressure. On the other hand, the d i f f u s i o n coeff i c i e n t s , D, of gases i n glassy polymers t y p i c a l l y increase with sorbed concentration even i n the absence of p l a s t i c i z a t i o n (17). Such increases are moderate f o r a l l of the materials,in Figure 2 except c e l l u l o s e acetate and can be explained i n terms of saturation of excess volume i n the polymer as concentration increases. Strong p l a s t i c i z a t i o n , on the other hand, produces dramatic upswings i n the apparent mobility as appears to be the case with c e l l u l o s e acetate. The observed pressure dependence of the permeabilities shown_in _ Figure 2 are the net result of these two e f f e c t s related to D and S. In the case of cellulose acetate, the sorption isotherm for CO2 has the same ty_pe of concave shape as shown i n Figure 4, so a sharp i n crease i n D apparently overpowers the e f f e c t of the decreasing apparent s o l u b i l i t y c o e f f i c i e n t . The reason for c e l l u l o s e acetate's greater tendency to be p l a s t i c i z e d compared to the other polymers i n Figure 2 i s currently not well understood. Since p l a s t i c i z a t i o n tends to produce a more rubbery material, i t i s to be expected that s e l e c t i v i t y losses may attend the large upswing i n C02 permeability, but no published data are a v a i l a b l e to corroborate t h i s surgestion. The apparent s o l u b i l i t i e s and average d i f f u s i v i t i e s , S and D, for C0 and CH^ i n a number of glassy polymers at 30°C and 20 atm are shown i n Table I. The values reported for cellulose acetate were estimated from various sources i n the l i t e r a t u r e (5.6.37). In the case of c e l l u l o s e acetate where C02 p l a s t i c i z a t i o n i s apparently s i g n i f i c a n t , i t was assumed that the CH4 permeability i n CO2/CH4 mixtures w i l l increase by at least the same percentage as the C02 permeability. This assumption seems reasonable since the p l a s t i c i z e d matrix becomes more rubber-like and less discriminating f o r penetrants of different sizes and shapes (see Figure 1). According to Equation 7, the r a t i o of permeabilities i s given by Equation 8 a f t e r substitution from Equation 5 for components A and B: 2

°& •

P

V B

-

iVV

(8)

Equation 8 demonstrates that the i d e a l separation factor can be separated into a so-called " s o l u b i l i t y s e l e c t i v i t y " , [S^/Sg], and a "mobility s e l e c t i v i t y " , IDA/DB]· These two r a t i o s are also reported i n Table I. Evidently, the contribution of the "mobility s e l e c t i v i t y " i s the dominant factor for a l l of the polymers considered except c e l l u l o s e acetate i n which the opposite i s observed. The CO2 p l a s t i c i z a t i o n tendency of c e l l u l o s e acetate may, i n f a c t , be r e lated to this polymer's apparent high " s o l u b i l i t y s e l e c t i v i t y " . Clearly, the available data do not j u s t i f y more than a tentative suggestion at this point that high " s o l u b i l i t y s e l e c t i v i t y " such as that seen i n cellulose acetate may be associated with a tendency to be p l a s t i c i z e d with a subsequent loss i n g l a s s - l i k e s e l e c t i v i t y . More detailed sorption and d i f f u s i o n measurements using a single



34


Table I: Mobility and s o l u b i l i t y contributions to the permeability and s e l e c t i v i t y of typical glassy polymers at 35°C f o r a 20 atm pressure of both components based on pure component parameters. POLYMER

D

co

s 2

*

co

S

2

**

POLY(PHENYLENE OXIDE) (PPO)

2.2xl0"

POLYCARBONATE

3.2xl0~

7

8

*

CH

p 4

**

2.10

3.2xl0~

1.47

P

co CH

D 2

co

s 2

S 4

co

CH. 4

8

0.95

15.1

6.88

2.2

4.7xl0~

9

0.41

24.4

6.81

3.6

8

0.28

30.8

4.21

7.3

0.45

28.3

8.85

3.2

0.37

63.6

15.38

4.1

*** CELLULOSE ACETATE

5.9xl0~

8

2.05

1.4xl0~

POLYSULFONE

2.3xl0~

8

1.44

2.6xl0"

KAPTON

l.OxKf

9

1.53

6.5xl0"

9

n

*D has units of [cm /sec]. **S has units of {cc(SIP)]/[cc of polymer- atm]. ***Estimated values as indicated i n the caption of Figure 2.


2


2. CHERN ET AL.


35

well-characterized dense f i l m sample f o r the c e l l u l o s e acetate system are needed to better understand the factors responsible f o r i t s rather unusual behavior compared to the other polymers considered. Understanding these p r i n c i p l e s may permit expansion of the ranks of " s o l u b i l i t y s e l e c t i v e " materials for blending with more p l a s t i c i z ation resistant materials to enhance their s o l u b i l i t y s e l e c t i v i t y . Poly(phenylene oxide) i s an example of a material that might benefit from such a blending approach i f an appropriate miscible " s o l u b i l i t y s e l e c t i v e " polymer could be discovered. As shown i n Figure 2 and Table I, PPO i s highly permeable to C02 and has a respectable mobility s e l e c t i v i t y equal to 6.9 for the CO2/CH4 system. The o v e r a l l s e l e c t i v i t y of PPO for this system i s , however, rather low due to the low s o l u b i l i t y s e l e c t i v i t y (the lowest i n Table I ) . If blending could raise the s o l u b i l i t y s e l e c t i v i t y from two to four without a serious loss i n CO2 permeability, the resultant material would be quite a t t r a c t i v e as a membrane f o r CO2/CH4 separations. No data are available f o r evaluating this l a t t e r p o s s i b i l i t y , a l though i t has been reported that both the s o l u b i l i t y and permea b i l i t y of CO2 i n PPO are decreased when PPO i s blended with polystyrene (35). _ Apparent s o l u b i l i t y c o e f f i c i e n t s (S) evaluated at twenty a t mospheres at 35°C for various penetrants i n several glassy polymers are shown i n Figure 5 as functions of the c r i t i c a l temperatures of the gases. The plot demonstrates the d i f f i c u l t y i n achieving dramatic changes i n s o l u b i l i t y s e l e c t i v i t y using a f a i r l y large v a r i e t y of polymer types. The r e l a t i v e i n s e n s i t i v i t y of the s o l u b i l i t y ratios of d i f f e r e n t gases to changes i n polymer types i s due to the fact that the gas s o l u b i l i t y i s strongly dependent upon the inherent condensibility of the respective gases. Although the amount of unrelaxed volume between chain segments and_j>olymer~penetrant i n t e r actions enters into the determination of S, i t i s largely overshadowed by the condensibility of the gas which i s related d i r e c t l y to the c r i t i c a l temperature of the gas. Note that even i n polymers such as PPO with a large amount of unrelaxed intersegmental volume, the sorption l e v e l s of a l l components tend to be high, so the r a t i o s are not changed much. One must, therefore, r e l y primarily upon d i f ferences i n polymer-penetrant interactions to y i e l d the rather moderate differences i n s o l u b i l i t y s e l e c t i v i t y . The range of s o l u b i l i t y s e l e c t i v i t i e s f o r the CO2/CH4 system, for example, includes only the i n t e r v a l from 2.2 (for PPO) to 7.32 (for cellulose acetate). Although the s o l u b i l i t y s e l e c t i v i t y of c e l l u l o s e acetate i s considerable, i t i s not large enough by i t s e l f to be competitive without a substantial complementary factor of 4.2 contributed by i t s mobility s e l e c t i v i t y (Table I ) . I f this mobility contribution i s undermined by p l a s t i c i z a t i o n r e s u l t i n g from the i n t e r actions that enhance the C0 s o l u b i l i t y r e l a t i v e to that of CH4, then basing s e l e c t i v i t y enhancement on s o l u b i l i t y e f f e c t s i s somewhat questionable. Certainly, more data are required on c e l l u l o s e acetate and any other polymers that can be discovered with high s o l u b i l i t y s e l e c t i v i t i e s before such a negative conclusion i s adopted. The use of dopants i n polymers to increase the s o l u b i l i t y of one component r e l a t i v e to others has been discussed by Heyd and McCandless (38). If suitable nonmigrating additives can be found to provide s u f f i c i e n t ly high values of s o l u b i l i t y s e l e c t i v i t y , one could, i n p r i n c i p l e , 2


36


M A T E R I A L S SCIENCE O F S Y N T H E T I C M E M B R A N E S

0.1

0.01 100 Critical

Figure 5.

300

200 Temperature,

Κ

Correlation of the apparent s o l u b i l i t y at 20 atm and 35 °C with the c r i t i c a l temperatures of various pene trants i n a number of glassy polymers: φ polycarbonate, Ο poly(phenylene oxide), Q polysulfone, J | Kapton, φ c e l l u l o s e acetate, φ PMMA.



2.


CHERN ET AL.

37

preclude the need to r e l y upon mobility regulating mechanisms to a i d i n the separation process. This i s the basis f o r solvent extraction and l i q u i d membrane systems. The problems and considerations i n such cases are quite different from those i n standard bulk polymer systems and w i l l not be discussed here. Manipulation of the structure of standard bulk polymers to a l t e r their mobility s e l e c t i v i t y can be guided somewhat by correlations such as those shown i n Figures 6 and 7. Figure 6 shows a c o r r e l a t i o n of D f o r various penetrants i n a number of d i f f e r e n t glassy polymers. The correlating v a r i a b l e , the k i n e t i c diameter of the gas, i s related to the z e o l i t e window dimension that w i l l j u s t permit passage of the penetrant of interest (39). For molecules that are e s s e n t i a l l y spherical, such as methane, argon and helium, this dimension i s simi l a r to the Lennard-Jones diameter. For asymmetric molecules such as carbon dioxide and nitrogen, however, the k i n e t i c diameter corre sponds more closely to the minimum diameter of the molecule. This figure shows c l e a r l y the extremely strong effect on the penetrant mobility caused by small differences i n minimum penetrant diameter. A difference of less than 1.5 A distinguishes the k i n e t i c diameters of helium and methane; however, there are almost three orders of mag nitude difference i n their mobility i n polycarbonate. The spread i n the various d i f f u s i v i t y values f o r a given penetrant i n d i f f e r e n t polymers can be p a r t i a l l y understood i n terms of Figure 7. This figure shows the effects of v a r i a t i o n s i n the s p e c i f i c volume of the polymer on the observed d i f f u s i o n c o e f f i c i e n t s , D. While this cor r e l a t i o n i s useful and i n t u i t i v e l y s a t i s f y i n g , i t undoubtedly over s i m p l i f i e s the true differences i n molecular-scale environments sampled by a penetrant as i t moves through the polymers. The tend ency f o r glassy polymers to exhibit l o c a l variations i n the amount and d i s t r i b u t i o n of molecular scale intersegmental gaps trapped dur ing the quenching process from the rubbery state has been discussed i n d e t a i l (17). Nevertheless, the c o r r e l a t i o n i n Figure 7 i s useful i n depicting r e l a t i v e differences between extremes such as that r e presented by the highly open PPO environment and the rather compact Kapton environment. I t i s clear that the mobility s e l e c t i v i t y i s substantially higher for Kapton than f o r PPO. The r a t i o s of the ap parent d i f f u s i v i t i e s of (X>2 and CH4 increase from 6.9 f o r PPO to 15.4 for Kapton; however, the permeability f o r CO2 drops by more than two hundred f o l d i n going from PPO to Kapton. Such a dramatic penalty i n productivity c e r t a i n l y tends to confirm the general point of view that one cannot have both high s e l e c t i v i t y and high productivity i n the same membrane material. Fortunately, encouraging exceptions to such a point of view can be found i n the l i t e r a t u r e f o r both H /CH^ and CO2/CH4 systems (11,13). These studies suggest the p o s s i b i l i t y of increasing the product permeability while maintaining or even increasing s e l e c t i v i t y by proper design of the polymer molecular architecture. Examples of such exceptional polymers are given i n Table I I . Polymers A and Β are generically c l a s s i f i e d as polyimides and were formed by con densation of 4,4 - hexafluoroisopropylidene diphthalic anhydride with 3,5-diaminobenzoic acid and with 1,5-diaminonaphthalene, r e spectively (13). Note that the high permselectivities of polymers A and Β are consistent with correlations such as that i n Figure 3, since polyimides t y p i c a l l y exhibit high coehesive energies s i m i l a r 2

f


M A T E R I A L S SCIENCE O F SYNTHETIC M E M B R A N E S


38

Id

2.5

3.0

3.5 ο

Kinetic

Figure 6.

Diameter

,A

Correlation of the average d i f f u s i o n c o e f f i c i e n t , D, and the k i n e t i c diameters of several penetrants i n a number of glassy polymers at 35 °C f o r an upstream penetrant pressure of 20 atm: φ polycarbonate, poly(phenylene oxide), Q polysulfone, Β Kapton, c e l l u l o s e acetate.


39



2. C H E R N ET A L .

Polymer

Figure 7.

Specific

Volume

,(cc/gm)

Correlation of the average d i f f u s i o n c o e f f i c i e n t s of several penetrants with the s p e c i f i c volumes of the polymers f o r an upstream penetrant pressure of 20 atm at 35 °C.


40


Table I I .

Comparison of novel high flux, high s e l e c t i v i t y poly imides and polysulfones with standard polysulfone.

POLYMER

\

STRUCTURE

2


PcH

A

ρ co

p H

r

4

32

127

-

-

76

112

-

-

°"θΜ

6 8

CMt

POLYSULFONE

CF,

β

0

12

78

1.1

28

C

-

-

21

68

D

-

-

65

21


2


2.

C H E R N ET A L .


41

to Kapton. Surprisingly, however, both polymers A and Β exhibit not only the expected high s e l e c t i v i t i e s but also permeabilities that are markedly higher than those of c e l l u l o s e acetate or poly sulfone. A s i m i l a r l y encouraging exception to the general trend i n selec t i v i t y and productivity i s found i n the p o l y ( a r y l ether) family to which the standard polysulfone material belongs. Polymers C and D i n Table II are also c l a s s i f i e d as polysulfones and are referred to as poly(tetramethyl bis-A sulfone) and poly(tetramethyl bis-L s u l fone), respectively (11). One would have overlooked this group of materials i f an oversimplified c o r r e l a t i o n such as that shown i n Figure 3 were the only guideline used i n candidate s e l e c t i o n . As shown i n Table I I , polymers C and D are roughly f i v e and f i f t e e n times respectively more permeable to CO2 than standard polysulfone. The C O 2 / C H 4 s e l e c t i v i t i e s of these two polymers are roughly 2.4 and 0.9 times respectively, that of standard polysulfone. In both the polyimides and the a r y l ether cases, the backbones are comprised of bulky structures that r e s i s t compact packing of segments. The intersegmental separations i n these r i g i d bulky poly mers may be large enough to permit r e l a t i v e l y free movement of pene trants below a c e r t a i n c r i t i c a l s i z e . On the other hand, the sepa rations may be small enough and l o c a l chain motions r e s t r i c t e d enough to provide a substantial s i z e - and shape-discriminating a b i l i t y f o r s l i g h t l y less compact molecules. Although s o l u b i l i t y and d i f f u s i v i t y data are not available f o r these materials, the above i n t e r p r e tation appears to be reasonable. In the case of polymer D, the pre sence of the f l e x i b l e c y c l o a l k y l group presumably offsets the s t i f fening e f f e c t due to methylation and the s e l e c t i v i t y i s a c t u a l l y s l i g h t l y lower than that of standard polysulfone. P i l a t o et a l (11) suggested that densities of polymers C and D (1.15 and 1.10 g/cc, respectively) compared to standard polysulfone (1.24 g/cc) results i n the higher permeabilities of these complex sulfones compared to the standard material. Such a suggestion i s c l e a r l y consistent with the trends shown i n Figure 7. The preceding observations suggest that a loosely packed glassy polymer with s u f f i c i e n t cohesive energy and a r i g i d p l a s t i c i z a t i o n resistant backbone i s conducive to both high flux and high selec t i v i t y . Following this conclusion, even without synthesizing generic a l l y new polymers, r e l a t i v e l y high permeabilities and s e l e c t i v i t i e s may be achievable by s t r u c t u r a l modifications of p o l y ( a r y l ethers) polyimides, polyamides, polycarbonates, polyesters and polyurethanes. Environmental Factors. C l e a r l y , discovery of an e x t r a o r d i n a r i l y per meable and selective material that can survive only weeks or months i n the required operating environment w i l l be unacceptable. The present b r i e f discussion suggests approaches to consider i n evaluat ing environmental challenges to a candidate material. Such tests should be performed i n p a r a l l e l with detailed sorption and transport measurements soon after a candidate material i s found to have de s i r a b l e s e l e c t i v i t y and permeability properties. Complex stress d i s t r i b u t i o n s can exist i n quenched glassy poly mers and can make them subject to microscopic f a i l u r e . This i s es p e c i a l l y true i n the presence of thermal and penetrant l e v e l cycling because surface layer expansion can induce substantial t e n s i l e


MATERIALS SCIENCE OF SYNTHETIC MEMBRANES

42

stresses. Under t e n s i l e stresses, many glassy polymers develop a dense network of f i n e surface cracks or "crazes". Load bearing f i b r i l s , composed of bundles of chains, and having void volumes i n the 50% range (40), traverse the crazes. The basic sorption and trans port properties of such a material are d r a s t i c a l l y changed with es s e n t i a l l y complete loss of s e l e c t i v i t y i n the crazed region. A simple method for evaluating the stress cracking tendency of materials by environmental agents can be used as a screening t e s t . The test sample i s used i n the form of a cantilevered beam loaded with a weight as shown i n Figure 8 (41). By exposing the sample to a test environment containing various p a r t i a l pressures of agents such as C0 , H S and H 0, the p o t e n t i a l for stress-cracking of the polymer can be determined i n a quantitative manner. Because the stress i n the bar varies from the maximum at the clamped end to zero at the free end, a stress-cracking agent w i l l cause cracking down to the point where the stress i s i n s u f f i c i e n t to produce a l o c a l f a i l ure of the secondary bonds between polymer segments. This test can be performed as a function of temperature as well as composition to i d e n t i f y operating conditions where p o t e n t i a l problems can be a n t i cipated. The c r i t i c a l s t r e s s , S , i s calculated from Equation 9 where F i s the t o t a l force applied ( c l i p plus weight), L i s the d i s tance along the bar between the free end and the stress crack closest to i t . The dimensions b and d are the width and thickness of the bar i n Figure 8.


2

2

2

c

S

c

=

6 FL

(9)

The surface crazes observed are t y p i c a l l y on the order of a micron i n depth, so the e n t i r e sample bar thickness does not to be invaded for the test to be u s e f u l . Even rather large molecules can penetrate to the depth of a micron i n a matter of hours or days, and smaller mole cules l i k e (Χ>2 can do so i n a matter of minutes or seconds. True chemical attack, as opposed to the above physical process of crazing, can be predicted somewhat on the basis of known l a b i l i t y of chain backbone groups. For example, i t i s known that ester l i n k ages are p a r t i c u l a r l y susceptible to hydrolytic attack. Imide groups are, on the other hand, quite h y d r o l y t i c a l l y stable but are subject to aggressive attack by Lewis bases. A combined i n f r a r e d spectro scopic and gravimetric sorption study has been used to follow the progressive attack of ammonia on the imide ring of Kapton (42). The severity of the attack suggests that one should be cautious i n using materials such as the highly s e l e c t i v e imides i n Table II f o r separations where Lewis bases are present. The focus of t h i s paper and the m u l t i p l i c i t y of environmental hazards faced by a candidate membrane material make i t impossible to enumerate s p e c i f i c s i n greater d e t a i l than that discussed above. If strong stress-cracking tendencies are observed i n the tests described above (that i s , low values of S observed), p l a s t i c i z a t i o n tendencies may e x i s t for the polymer-penetrant p a i r . In such a case, care should be exercised to study the candidate material under conditions that include the most demanding environment anticipated i n actual use. G



2.

C H E R N ET A L .

Figure 8.


43

Simple apparatus f o r evaluating stress cracking p o t e n t i a l of candidate membrane materials.


44

materials science o f synthetic membranes


Conclusions There appears to be reasons f o r cautious optimism concerning the pos s i b i l i t y of developing more permeable and s e l e c t i v e membranes i n spite of the general inverse relationship between these two v a r i ables. Control of chain backbone r i g i d i t y and intersegmental pack ing density may provide a means of s e l e c t i v e l y permitting the pas sage of a r e l a t i v e l y compact permeant molecule while s u b s t a n t i a l l y r e s t r i c t i n g the nonpermeant. Reliance on s o l u b i l i t y s e l e c t i v i t y to provide the major means of discriminating between gas penetrants i n dense polymer films may be less promising. Cellulose acetate, the only material considered that i s strongly s e l e c t i v e for CO2 compared to CH4 on the basis of s o l u b i l i t y , appears to exhibit a strong p l a s t i c i z i n g response to increasing CO2 pressures. Such an e f f e c t i s expected to further reduce the mobility s e l e c t i v i t y of c e l l u l o s e ace tate and thereby cause i t to lose o v e r a l l s e l e c t i v i t y as C0 p a r t i a l pressure increases. A s i m i l a r trend may be observed f o r other glassy materials that r e l y strongly upon s o l u b i l i t y as the p r i n c i p a l basis for their s e l e c t i v i t y , however, considerably more research i s required before this tentative conclusion can be v e r i f i e d . A c o r r e l a t i v e approach such as that shown i n Figure 3 for the o v e r a l l s e l e c t i v i t y (or permeability) i s useful i n some senses but i n s u f f i c i e n t because i t would have led one to overlook the extremely interesting family of p o l y ( a r y l ethers) which i n some cases have both high s e l e c t i v i t y and high permeabilities. A detailed analysis of the mobility and s o l u b i l i t y contributions to the permeability and s e l e c t i v i t y properties of an homologous series of candidate materials can be extremely valuable i n membrane material s e l e c t i o n . Such an approach permits one to assess the true cause of changes i n the ob served permeability and s e l e c t i v i t y and can more e f f e c t i v e l y guide a systematic program to optimize membrane material transport properties. Environmental s e n s i t i v i t y of candidate materials must be asses sed under conditions of temperature, pressure and composition that simulate actual usage. F a i l u r e of a material i n t h i s context can severely l i m i t the range of a p p l i c a b i l i t y of a membrane that other wise has outstanding properties. 2

Acknowledgments The authors g r a t e f u l l y acknowledge support of this work under NSF Grant No. CPE08319285 and ARO contract No. DAAG29-81-0039. Also Dr. E. S. Sanders i s acknowledged f o r providing his data on the solu b i l i t y of various gases i n PMMA f o r use i n F i g . 5. Ms. Maxwell's assistance i n typing this manuscript i s also acknowledged.

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5. 6. 7. 8. 9. 10.


11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

29. 30. 31.


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46

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RECEIVED August 6, 1984


Materials Science of Synthetic Membranes - American Chemical Society

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