Materials Science of Synthetic Membranes - ACS Publications

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Partial Solubility Parameter Characterization of Interpenetrating Microphase Membranes SONJA KRAUSE Department of Chemistry, Rensselaer Polytechnic Institute, Troy, NY 12181

Ion exchange membranes and the dense layer of reverse osmosis membranes act as i f they were composed of two interpenetrating microphases. One of these microphases consists of the ionic groups and/or the principal H -bonding groups (-OH, -NH , or > NH) of the membrane polymer with sufficient water to make a continuous pore-like phase. The other microphase consists of the remaining hydrophobic (principally hydrocarbon, ester and carbonyl) portions of the membrane polymer. On the one hand, water, ions, and the principal H-bonding groups, if any, of the organic molecules which go through these membranes are assumed to travel through the aqueous microphases. On the other hand, small organic molecules without major Η-bonding groups and the hydrophobic portions of the other molecules are assumed to be transported through the hydrophobic microphases. It is proposed that solubility para meters calculated for only the hydrophobic portions of the membrane polymers and the hydrophobic portions of the small molecules of interest can be used to deter mine which small molecules can be sorbed by a particu lar membrane and, in some cases, be preferentially transported across the membrane. Some experimental data in the literature are examined using these ideas. 2

Both reverse osmosis and ion exchange membranes may be used to sepa rate ions from water, and both types of membranes can also be used to separate organic solutes from water. Depending on the membrane used, some organic solutes remain mainly on the feed side of the membrane, while others are p r e f e r e n t i a l l y transported through the membrane; i . e . , the concentration of solute on the permeate side of the membrane becomes greater than that on the feed side. Since i t i s generally assumed that transport of these organic solutes cor r e l a t e s with p r e f e r e n t i a l sorption of the solute by the membrane, a simple method for predicting such p r e f e r e n t i a l sorption would be use f u l . A rather complex, semi-empirical method for making such

0097-6156/85/0269-0351$06.00/0 © 1985 American Chemical Society Lloyd; Materials Science of Synthetic Membranes ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

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predictions has been developed by Sourirajan and coworkers (1). It nevertheless seems desirable to develop a simpler, less empirical method to calculate p r e f e r e n t i a l sorption and, i f possible, d i s t r i bution c o e f f i c i e n t s for organic solutes between a membrane and an aqueous solution.

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The Interpenetrating Microphase Model To develop such a method, a physical model f o r the "active" portion of the membrane of interest i s necessary. Membrane models that have been developed previously f o r various purposes have been reviewed elsewhere (see f o r example References^ and 3). A s l i g h t l y different model i s being proposed i n this paper; t h i s model i s based on a number of experimental observations on polymers and polymeric mem branes, some of which are summarized below: 1. The dense layer of reverse osmosis membranes transports water as i f through pores, but no pores are observed i n electron micrographs of the dried membranes. This implies either that the pores are too small to be observed by electron microscopy or that they only exist i n the presence of water, not i n the dried polymer. 2. Ion exchange membranes also transport water as i f through pores, but no pores have been observed d i r e c t l y . 3. Although most reverse osmosis membranes are not crosslinked, they do not dissolve i n water; nevertheless, they absorb about 10-15 wt. % water. Ion exchange membranes are usually crosslinked and absorb s i m i l a r amounts of water. 4. C y l i n d r i c a l structures of f i n i t e thickness were consistent with the small angle l i g h t scattering (SALS) data obtained on hydrated poly(2-hydroxyethyl methacrylate), a polymer similar to those used f o r reverse osmosis membranes (4). 5. The properties of poly(methacrylic acid) show that consid erable association of the ot-methyl groups occurs i n aqueous solu tions of t h i s polymer (5) · This association i s often referred to as a hydrophobic interaction. Some properties of other polymers, such as the polycondensate between L-lysine and 1,3-benzenedisulfonyl chloride (6), are also attributed to hydrophobic interactions be tween parts of the polymer chains. These five sets of observations, plus knowledge of the phenome non of microphase separation i n block copolymers leads to a model of reverse osmosis or ion exchange membranes i n which the hydrophobic portions of the polymer chains have come together to form one more or less continuous microphase, while the hydrophilic portions of the polymer chains ( i o n i c groups, -OH groups, -NH or > NH groups) have "dissolved" i n a small amount of water to form another more or less continuous microphase when the membrane i s swollen i n water. The hydrophilic groups, i n most cases, probably form clusters but not continuous microphases i n the dried membranes. Such i o n i c clusters have been studied i n ionomers such as Nafion poly(perfluoropropylene oxide sulfonic acid) membranes; clusters i n ionomers have been reviewed recently by Mauritζ and Hopfinger (7). These reviewers also quote a model f o r hydrated Nafion proposed by T. D, Gierke at the October, 1977, meeting of the Electrochemical Society, Atlanta, Georgia, i n which aqueous spher i c a l microphases % 40 Â i n diameter are connected by short, ^ 10 A 2

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


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353

d i a m e t e r c o r r i d o r s t o form a c o n t i n u o u s aqueous microphase, Gierke a p p a r e n t l y observed s m a l l a n g l e X-ray s c a t t e r i n g p a t t e r n s o f N a f i o n which were c o n s i s t e n t w i t h 40 A d i a m e t e r s p h e r i c a l c l u s t e r s , b u t t h e 10 A c o r r i d o r s were c o n j e c t u r e d r a t h e r than o b s e r v e d . There i s s u f f i c i e n t e v i d e n c e f o r i n t e r p e n e t r a t i n g microphases i n w a t e r - s w o l l e n , w a t e r - t r a n s p o r t i n g membranes t o use t h i s as a w o r k i n g model f o r t h e membranes. U s i n g t h i s model, one may assume t h a t w a t e r and i o n s t r a n s p o r t e d t h r o u g h such a membrane t r a v e l through t h e aqueous m i c r o p h a s e s i n which t h e i o n i c and h y d r o p h i l i c groups i n t r i n s i c t o t h e membrane polymer a r e a l s o embedded. M o l e c u l e s c o n t a i n i n g no major h y d r o p h i l i c groups may then t r a v e l t h r o u g h t h e h y d r o p h o b i c microphases i f they t r a v e l t h r o u g h t h e membrane a t a l l . These m i c r o phases a r e much s m a l l e r ( o f t h e o r d e r o f 10 A t o 30 A) than t h e phases found i n i m m i s c i b l e polymer b l e n d s , s e m i c r y s t a l l i n e p o l y m e r s , or b l o c k copolymers. Models used t o e x p l a i n s o r p t i o n o r p e r m e a b i l i t y i n t h e s e l a r g e r phases (j8) may n o t n e c e s s a r i l y be extended w i t h o u t change t o t h e much s m a l l e r ( m o l e c u l a r d i a m e t e r ) microphases p o s t u l a t e d h e r e f o r r e v e r s e osmosis and i o n exchange membranes. To u n d e r s t a n d the s o r p t i o n o f s m a l l o r g a n i c m o l e c u l e s c o n t a i n i n g no major h y d r o p h i l i c groups by a r e v e r s e osmosis o r i o n exchange membrane , and thus t h e t r a n s p o r t o f these m o l e c u l e s t h r o u g h t h e membrane , i t i s n e c e s s a r y t o c o n s i d e r t h e i n t e r a c t i o n o f t h e h y d r o p h o b i c m o l e c u l e w i t h o n l y t h e h y d r o p h o b i c p o r t i o n o f t h e membrane polymer. I t i s a l s o u s e f u l t o c o n s i d e r the i n t e r a c t i o n o f s m a l l m o l e c u l e s cont a i n i n g h y d r o p h i l i c groups as w e l l as h y d r o p h o b i c groups w i t h t h e membranes and t h e i r t r a n s p o r t t h r o u g h the membranes. I t i s l i k e l y t h a t such m o l e c u l e s i n t e r a c t w i t h b o t h t y p e s o f microphases w i t h i n the membrane and move through t h e membrane more o r l e s s a t t h e " i n t e r f a c e " between microphases. The concept o f such an " i n t e r f a c e " i s hazy s i n c e t h e d i a m e t e r o f any o f t h e microphases i s p r o b a b l y v e r y s m a l l , most l i k e l y below 30 A. A "phase" w i t h such dimension i s a s m a l l system i n t h e sense o f H i l l (9) and t h e f l u c t u a t i o n s o f i t s p r o p e r t i e s from t h e i r averages a r e l a r g e . W i t h t h i s caveat i t i s s t i l l p o s s i b l e t o c o n s i d e r t h e average p r o p e r t i e s o f t h e s e microphases and t o assume t h a t a s m a l l m o l e c u l e w i t h a h y d r o p h i l i c and a h y d r o p h o b i c p a r t i s s i t u a t e d , on t h e average, w i t h i t s h y d r o p h i l i c p o r t i o n i n the aqueous microphase and i t s h y d r o p h o b i c p o r t i o n i n t h e h y d r o p h o b i c microphase of t h e membrane polymer. The H i l d e b r a n d S o l u b i l i t y

Parameter

In t h e above c o n s i d e r a t i o n s , t h e h y d r o p h o b i c p o r t i o n s o f b o t h t h e membrane polymer and the s m a l l m o l e c u l e s t h a t e n t e r t h e membrane a r e e x p e c t e d t o i n t e r a c t i n t h e h y d r o p h o b i c microphases i n t h e membrane. I t t h e r e f o r e becomes u s e f u l t o f i n d a n u m e r i c a l measure o f t h e m i s c i b i l i t y o f t h e s e h y d r o p h o b i c p o r t i o n s o f m o l e c u l e s . I n t h e case o f complete m o l e c u l e s , b o t h s m a l l and p o l y m e r i c , t h e s o l u b i l i t y parame t e r concept has been u s e f u l i n t h e p a s t . T h i s concept i s r e l a t e d t o the e n t h a l p y change which o c c u r s on m i x i n g i n r e g u l a r s o l u t i o n t h e o r y as developed by H i l d e b r a n d and coworkers (10) and a s used f o r polymer s o l u t i o n t h e o r y by F l o r y ( 1 1 ) . The H i l d e b r a n d s o l u b i l i t y parameter i s a measure o f t h e a t t r a c t i o n between m o l e c u l e s o f t h e same k i n d , i n c l u d i n g d i s p e r s i o n f o r c e s , p o l a r f o r c e s , and hydrogen bonding



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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

interactions. In general, the closer the values of the Hildebrand s o l u b i l i t y parameters of two molecules, the more soluble i n each other they are expected to be. Because of entropy considerations, the exact degree of proximity needed between the s o l u b i l i t y para meters of two molecules i n order to expect m i s c i b i l i t y i s greater between a polymer and a small molecule than between two small molecules. The Hildebrand s o l u b i l i t y parameter concept has worked well f o r molecules that contain no major Η-bonding groups, but many exceptions to the predictions occur when major Η-bonding groups are present, even i n only one of the molecules being considered. For t h i s reason, Hansen (12) developed the so-called three-dimensional s o l u b i l i t y parameter i n which the contributions of dispersion forces, polar forces, and Η-bonding are considered as separate contributions to the s o l u b i l i t y parameter. Bagley (13) developed a two-dimensional s o l u b i l i t y parameter i n which the Η-bonding contribution i s considered separately from the other two contributions which are lumped together. One-, two- and three-dimensional s o l u b i l i t y parameters have been useful to membrane s c i e n t i s t s and engineers (14-20) and have fewer exceptions to their predictions than the simple Hildebrand s o l u b i l i t y parameter. The s o l u b i l i t y parameters of insoluble polymers are often deter mined by swelling the polymer i n a series of solvents with d i f f e r e n t s o l u b i l i t y parameter values. Maximum swelling of the polymer then occurs i n those solvents whose s o l u b i l i t y parameters are closest to that of the polymer. It i s interesting to note that swelling data for Nafion, when interpreted i n t h i s way, indicate the presence of two s o l u b i l i t y maxima; that i s , t h i s ionomeric polymer acts as i f i t had two d i f f e r e n t s o l u b i l i t y parameters (21). This seems reasonable for a polymer that i s composed of two d i f f e r e n t phases; neither s o l u b i l i t y maximum, however, i s very close to the s o l u b i l i t y param eter of water. The P a r t i a l S o l u b i l i t y Parameter of the Hydrophobic Portion of a Molecule The simplest c r i t e r i o n f o r a t h e o r e t i c a l c a l c u l a t i o n of the misci b i l i t y of the hydrophobic portions of small molecules with the hydrophobic microphase of a membrane polymer appears to be a p a r t i a l s o l u b i l i t y parameter; that i s , calculation of the s o l u b i l i t y param eter of only the hydrophobic portions of the molecules. This can be done using a group contribution approach in which each group (for example, a CH -group) i n the molecule contributes a certain a t t r a c tive force and a c e r t a i n volume to the molecule. In t h i s way, a s o l u b i l i t y parameter may be estimated f o r e i t h e r a portion of a molecule or for a whole molecule. The s o l u b i l i t y parameter of the hydrophobic molecule or portion of a molecule, δ^ρ, may be calculated using the relationship 3

δ, HP

(1) ι


17.

KRAUSE


355


where the F-^ are group c o n t r i b u t i o n s t o the molar a t t r a c t i o n cons t a n t o f the m o l e c u l e and the V-^ r e p r e s e n t group c o n t r i b u t i o n s t o the molar volume of a rubbery polymer o r of a s m a l l m o l e c u l e cont a i n i n g t h a t group. A l t e r n a t i v e l y , 6 ^ can be e s t i m a t e d by u s i n g the r e l a t i o n s h i p

where the U-^ are m o l a r group c o n t r i b u t i o n s t o t h e c o h e s i v e energy of the polymer o r s m a l l m o l e c u l e . Some i n v e s t i g a t o r s have t a b u l a t e d F i , w h i l e o t h e r s use t h e U^. T a b u l a t i o n s o f F-^, U i , and V i t h a t have been made by a v a r i e t y o f i n v e s t i g a t o r s have been shown and d i s c u s s e d by Van K r e v e l e n and H o f t y z e r (22) and by B a r t o n ( 1 6 ) , Van K r e v e l e n and H o f t y z e r (22) have made the most r e c e n t t a b u l a t i o n of F i and V i , w h i l e F e d o r s (23) c o m p i l a t i o n of U i w i t h accompanying V-^ i n c l u d e s v a l u e s f o r the l a r g e s t number of m o l e c u l a r groups. The two s e t s of t a b l e s g i v e r a t h e r d i f f e r e n t v a l u e s f o r the 6^p of m o l e c u l e s and p a r t s o f m o l e c u l e s as w i l l be seen below. T h i s means t h a t both s e t s of p a r a m e t e r s w i l l have t o be e v a l u a t e d a g a i n s t exp e r i m e n t a l d a t a . Van K r e v e l e n and H o f t y z e r * s v a l u e s g i v e v a l u e s f o r s o l u b i l i t y parameters n u m e r i c a l l y s i m i l a r t o those o b t a i n e d from the F i v a l u e s from the r e v i s e d S m a l l s Table (24) o r Hoy's Table ( 2 5 ) , Note t h a t R e f e r e n c e s 24_ and 2^5 g i v e no v a l u e s f o r V-£. O r d i n a r i l y , when c a l c u l a t i o n s are made f o r complete m o l e c u l e s o r polymer r e p e a t u n i t s , the m o l a r volume of the l i q u i d o r rubbery polymer can be used i n t h e c a l c u l a t i o n s i n s t e a d of ZV±. This molar volume i s e a s i l y c a l c u l a t e d from the d e n s i t i e s and m o l e c u l a r weights. In c a l c u l a t i o n s of ôjjp f o r a p o r t i o n o f a m o l e c u l e , however, group c o n t r i b u t i o n s t o V i are n e c e s s a r y . In some p r o p r i e t a r y p u b l i c a t i o n s , Hoy (26) has c a l c u l a t e d group c o n t r i b u t i o n s t o V i f o r polymers a t t h e i r g l a s s t r a n s i t i o n temperatures. Table I g i v e s the v a l u e s of F± and V i used i n t h i s work i n conn e c t i o n w i t h E q u a t i o n 1, and T a b l e I I g i v e s the v a l u e s of U i and V i used i n t h i s work i n c o n n e c t i o n w i t h E q u a t i o n 2. T

1

Comparison w i t h E x p e r i m e n t a l

Data

I t s h o u l d be e x p e c t e d t h a t c a l c u l a t e d v a l u e s of 6jjp c o r r e l a t e b e t t e r w i t h e q u i l i b r i u m p r o p e r t i e s o f t h e membranes i n aqueous s o l u t i o n than w i t h t r a n s p o r t p r o p e r t i e s . Che of the few such e q u i l i b r i u m measurements t h a t have been p u b l i s h e d i s by Anderson e t a l (27). T h e i r measured p a r t i t i o n c o e f f i c i e n t s (Κ), d i f f u s i o n c o e f f i c i e n t s (D), and r e v e r s e osmosis r e j e c t i o n (R) of the o r g a n i c s o l u t e s are shown i n T a b l e I I I f o r c e l l u l o s e a c e t a t e membranes. T h e i r d a t a f o r c e l l u l o s e acetate butyrate was s i m i l a r and i s not shown here. Aqueous so l u t i o n s of the o r g a n i c s o l u t e s , u s u a l l y at c o n c e n t r a t i o n s of about 10""^ l " , were used i n the measurement of p a r t i t i o n c o e f f i c i e n t s by UV a b s o r p t i o n . In Table I I I , 1


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


Table I. Group Molar Attraction Constant, F-^, and Molar Volume Group Contributions V-^, of Rubbery Amorphous Polymers and Small Molecules at 25°C According to Van Krevelen (16,22J

Group -CH -CH -CH< >C< -CH(CH )-C(CH ) -CH=CH>C=CH -C(CH )=CHphenyl p-phenylene -F -CI -0-C003

2

3

3

3

-s-

-Br -N0

2

2

F. 1 -1/2 3/2 -1 J cm mol 420 280 140 0 560 840 444 304 724 1517 1377 164 471 256 512 460 695* 900*

V. 1 3

1

ι" cm22.8 mol 16.45 9.85 4.75 32.65 50.35 2 7.75 20.0 42,8 64.65 61.4 10.0 18.4 8.5 24.6 (21.0 a c r y l i c ) 15.0 25.3** 12.9+

From Reference 24-. From Reference 26>, t Estimated from Chapter 6, Table 9 of Reference 16.


17. KRAUSE

357


Table II, Group Contributions to the Cohesive Energy, U i and and Molar Volume Group Contributions, V i , at 25°C according to Fedors (23) U

Group

V

1

-CH 4.71 -CH 4.94 -CH< 3.43 >C< 1.47 H C= 4.31 -CH= 4.31 >C= 4.31 HCE 3.85 -CE 7.07 phenyl 31.9 phenylene (o,m,p) 31.9 phenyl(tri subs tituted) 31.9 pheny(tetrasubstituted) 31.9 ring closure (5 or more atoms) 1.05 ring closure (3 or 4 atoms) 3.14 conjugation i n ring (per double bond) 1.67 halogen attached to C atom with double bond 20% of halogen Ui -F 4.19 -F (disubstituted) 3.56 -F ( t r i s u b s t i t u t e d ) 2.30 -CF - (in perfluoro compound) 4.27 -CF3 (in perfluoro compound) 4.27 -CI 11.55 -CI (disubstituted) 9.63 -CL ( t r i s u b s t i t u t e d ) 7.53 -Br 15.49 -OH 29.8 -03.35 -CHO 21.4 17.4 -co18.0 -co 2 -CO3 17.6 -NH 12.6 -NH8.4 -N< 4.2 -N= 11.7 -N0 ( a l i p h a t i c ) 29.3 -N0 (aromatic) 15.36 -S14.15 3


i kJ mol

2

2

2

2

2

2

i cirr* mol""l 33.5 16.1 - 1.0 -19.2 28.5 13.5 - 5.5 27.4 6.5 71.4 52.4 33.4 14.4 16 18 - 2.2 —

18.0 20.0 22.0 23.0 57.5 24.0 26.0 27.3 30.0 10.0 3.8 22.3 10.8 18.0 22.0 19,2 4.5 - 9.0 5.0 24,0 32.0 12



3

2

cl

--

5

0.3±0.1

-0.33

1.5

33217

—

-

+0.04 -0.09

-

-0.06

3.8

1.8

20 10 8.0

-

150

-

+0.17

16512

129112

2012 3711 5414

3.510.2

2.110.5

0.7

75

300

at pH 5.6

+

1

*

3

2

3

24.0(23.2) 26.0(22.3)**

21.9 23.6

24.3

m

>

00

m

η

Η

m

Χ

Η

31.4

2

24.7

22.9

2

22.4

11.9

18.1

21.9

18.6

24.3

1

J /*,. '

18.4

2

H p

* (Eq. >

26.0*

21.9

*

20.3

2

Ο

J ' ™" '

H p

* (Eq.

* Taken from Reference 24. t Taken from Reference 27. **Calculated by using only 80% of the l i s t e d f o r the halogen; t h i s halogen i s not r e a l l y attached to a C atom with a double bond but t h i s idea was used i n the c a l c u l a t i o n .

2,4-Dichlorophenol

p-Bromophenol

2

OOCC H

0

OOCC H

3,5-Di(Carbethoxy)phenol

0

Phenyl Phenyl Nitrobenzene

H0-@-

Phenylene

3

CH -

CH N0

Aniline Phenol Nitrobenzene

Hydroquinone

Nitromethane

c

Pyridine

2

(CH ) CO

Acetone

3

Calculated as

Molecule

K

Dxl0 2 -1 cm sec

1 0 t

Table I I I . P a r t i t i o n C o e f f i c i e n t s , D i f f u s i o n C o e f f i c i e n t s , Reverse Osmosis Rejection at 68 atm, and

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