Water in Polymers - ACS Publications

0 where Bq2 is proportional to solute cross sectional area (nr 2 ) , D0 ... (1) urea; (2) thiourea; (3) glucose; (4) inositol; (5) sucrose; (6) lactos...
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20 Solute Permeation Through Hydrogel Membranes Hydrophilic vs. Hydrophobic Solutes

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S. W. KIM, J. R. CARDINAL, S. WISNIEWSKI, and G. M. ZENTNER Department of Pharmaceutics, University of Utah, Salt Lake City, UT 84112

P o l y ( 2 - h y d r o x y e t h y l m e t h a c r y l a t e ) (p-HEMA) i s a h y d r o p h i l i c m e t h a c r y l a t e p o l y m e r w h i c h was f i r s t p r e p a r e d b y W i c h t e r l e and L i m OJ. T h i s p o l y m e r , a n d many o t h e r s y n t h e t i c h y d r o g e l s , has been e x t e n s i v e l y examined f o r p o t e n t i a l b i o m e d i c a l a p p l i c a t i o n s (2J. A l t h o u g h many s t u d i e s have f o c u s e d on t h e p h y s i c o c h e m i c a l n a t u r e o f t h e s e h y d r o g e l s , many q u e s t i o n s r e m a i n u n a n s w e r e d . Among t h e s e a r e t h e n a t u r e , o r g a n i z a t i o n , and r o l e o f w a t e r i n d e t e r m i n i n g s u c h p r o p e r t i e s a s i n t e r f a c i a l a n d t r a n s p o r t phenom­ ena. Problems which deal w i t h t h e presence o f water and t h e s t r u c t u r e o f water a t t h e m o l e c u l a r l e v e l a r e o f t e n complex. F o r h y d r o g e l s , i t h a s been p r o p o s e d ( 3 ) t h a t w a t e r c a n be t r e a t e d i n terms o f a t h r e e s t a t e m o d e l . These i n c l u d e : bound, i n t e r f a c i a l , and " b u l k - l i k e " w a t e r . Bound w a t e r i s s t r o n g l y a s s o c i a t e d w i t h the polymer, probably as water h y d r a t i n g t h e h y d r o p h i l i c groups of t h e polymer. I n t e r f a c i a l water i s probably associated with h y d r o p h o b i c i n t e r a c t i o n s between t h e p o l y m e r s e g m e n t s . Finally, " b u l k - l i k e " water i s t h a t w i t h p r o p e r t i e s which a r e s i m i l a r t o t h a t o f b u l k w a t e r i n aqueous s o l u t i o n . S e v e r a l s t u d i e s have been d e s i g n e d i n an e f f o r t t o v e r i f y t h i s m o d e l . The t o t a l g e l w a t e r c o n t e n t was e s t i m a t e d s e m i q u a n t i t a t i v e ^ u s i n g NMR (4,_5). Simi­ l a r a p p r o a c h e s were made t o i n v e s t i g a t e t h e s t a t e o f " w a t e r i n p HEMA g e l s u s i n g t h e t e c h n i q u e s o f d i l a t o m e t r y , s p e c i f i c c o n d u c t i ­ v i t y and d i f f e r e n t i a l s c a n n i n g c a l o r i m e t r y ( 6 ) . R e c e n t l y , we have examined s o l u t e p e r m e a t i o n t h r o u g h h y d r o g e l membranes i n a n e f f o r t t o d e v e l o p m o d e l s w h i c h d e s c r i b e i n d e t a i l t h e t r a n s p o r t phenomena w i t h p a r t i c u l a r e m p h a s i s on t h e r o l e o f water i n t h i s process. These s t u d i e s have u t i l i z e d p HEMA a n d i t s c o p o l y m e r s , and b o t h h y d r o p h o b i c a n d h y d r o p h i l i c solutes (7*8,9). I t was d e t e r m i n e d t h a t p-HEMA a n d i t s c o p o l y ­ mers a r e p e r m e a b l e t o b o t h h y d r o p h o b i c a n d h y d r o p h i l i c s o l u t e s . The f a c t o r s w h i c h i n f l u e n c e t h e p e r m e a b i l i t i e s i n c l u d e t h e n a t u r e and p e r c e n t o f c r o s s l i n k e r s a n d t h e w a t e r c o n t e n t o f t h e h y d r o gel . In t h i s m a n u s c r i p t , t h e p e r m e a b i l i t i e s o f w a t e r s o l u b l e n o n -

Ameriean Chemical

In Water in Polymers; Rowland, S.; Washington, D. C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

WATER IN P O L Y M E R S

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348

e l e c t r o l y t e s and h y d r o p h o b i c s o l u t e s i n p-HEMA and c r o s s l i n k e d pHEMA a r e examined f r o m a m e c h a n i s t i c p o i n t o f v i e w . For hydro­ p h i l i c s o l u t e s , i t was f o u n d t h a t p e r m e a t i o n p r o b a b l y o c c u r s v i a the " b u l k - l i k e " water regions of the hydrogels. For hydrophobic s o l u t e s , analyses of permeation data i n d i c a t e t h a t solutes d i f ­ f u s e p r e d o m i n a n t l y v i a a " p o r e " t y p e mechanism i n p-HEMA and v i a a " p a r t i t i o n " mechanism i n p-HEMA h i g h l y c r o s s l i n k e d w i t h e t h y l ­ ene g l y c o l d i m e t h a c r y l a t e (EGDMA). The a n a l y s e s o f p e r m e a t i o n d a t a was based on t h e a s s u m p t i o n t h a t t h e p o r o u s f l u x o f a s o l u t e i s a s s o c i a t e d w i t h the " b u l k - l i k e " water r e g i o n s o f the hydrogels and t h e p a r t i t i o n f l u x w i t h t h e p o l y m e r m a t r i x , " i n t e r f a c i a l " and "bound" water regions o f the hydrogels. M a t e r i a l s and Methods Materials. HEMA was a h i g h l y p u r i f i e d sample ( g i f t o f Hydron L a b o r a t o r i e s , New B r u n s w i c k , N . J . ) c o n t a i n i n g t h e f o l l o w i n g l e v e l s of i m p u r i t i e s : m e t h a c r y l i c a c i d 0.06%, e t h y l e n e g l y c o l dimetha­ c r y l a t e 0 . 0 2 4 % , and d i e t h y l e n e g l y c o l m e t h a c r y l a t e 0 . 2 4 % . EGDMA (Monomer P o l y m e r L a b o r a t o r i e s , P h i l a d e l p h i a , PA) was p u r i f i e d by b a s e e x t r a c t i o n and d i s t i l l a t i o n . The i n i t i a t o r , a z o b i s ( m e t h y l i s o b u t y r a t e ) was p r e p a r e d by t h e method o f M o r t i m e r ( 1 0 ) . PolyHEMA f i l m s and f i l m s c o n t a i n i n g 1 mole % EGDMA were s y n t h e s i z e d i n the presence of t h e i r e q u i l i b r i u m water contents. F i l m s w i t h 5.25 m o l e % EGDMA were s y n t h e s i z e d i n 40% ( v / v ) e t h a n o l as t h e s o l v e n t . A l l f i l m s were e q u i l i b r a t e d i n w a t e r (changed r e p e a t e d l y ) f o r t h r e e t o f o u r weeks p r i o r t o u s e . A l l s o l u t e s were u s e d as r e c e i v e d . A l l s t e r o i d s p r o d u c e d a s i n g l e s p o t f r o m TLC. R a d i o l a b e l e d s t e r o i d s had t h e same Rf v a l u e s as t h e u n l a b e l e d m a t e r i a l s w i t h >95% o f t h e d e t e c t a b l e a c t i v i t y a s s o c i a t e d w i t h the primary spot. Methods. The d i f f u s i o n e x p e r i m e n t s were p e r f o r m e d a t room t e m p e r a t u r e (23°C) u t i l i z i n g a g l a s s d i f f u s i o n c e l l c o n s i s t i n g o f two c o m p a r t m e n t s e a c h w i t h a volume o f 175 m l . Each chamber was s t i r r e d a t a c o n s t a n t r a t e t o reduce boundary l a y e r e f f e c t s . So­ l u t e c o n c e n t r a t i o n s were m o n i t o r e d by H o r * C t r a c e r s , r e f r a c ­ t i v e i n d e x , o r U.V. s p e c t r o s c o p y . P a r t i t i o n c o e f f i c i e n t s , defined as t h e r a t i o o f t h e c o n c e n t r a t i o n s i n t h e membrane and i n t h e b u l k aqueous phase were d e t e r m i n e d by s o l u t i o n d e p l e t i o n t e c h n i q u e . The t h i c k n e s s o f w a t e r s w o l l e n membranes were measured u s i n g a l i g h t w a v e m i c r o m e t e r (Van Kueren C o . , W a t e r t o w n , MA). P e r m e a t i o n c o e f f i c i e n t s f o r h y d r o p h i l i c s o l u t e s were o b t a i n e d t h r o u g h t h e use o f t h e f o l l o w i n g e q u a t i o n {]}): 3

lnO-2

C /C ) = t

0

-0/ν

α

k

+ 1/V ) 2

AUt

Eq. 1

where C t = c o n c e n t r a t i o n a t t i m e t ; Co = i n i t i a l c o n c e n t r a t i o n ; = V = compartment volume (175 m l ) ; A = membrane a r e a ( 1 4 . 9 c m ) ; U = p e r m e a b i l i t y ( c m / s e c ) ; and t = t i m e ( s e c o n d s ) . D i f f u s i o n 2

2

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20.

K I M ET A L .

Hydro gel

Membranes

349

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c o e f f i c i e n t s a r e g i v e n by Dm = Ud/Ko where d = wet membrane t h i c k ­ n e s s and Ko i s t h e p a r t i t i o n c o e f f i c i e n t . Under t h e c o n d i t i o n s o f t h e e x p e r i m e n t s used i n o u r l a b o r a ­ t o r i e s , E q . 1 i s n o t v a l i d f o r h y d r o p h o b i c s o l u t e s due t o h i g h p a r t i t i o n i n g o f t h e s e s p e c i e s i n t o t h e membrane. In a p r e v i o u s p u b l i c a t i o n ( 8 ) , i t was shown t h a t t h e f o l l o w i n g e q u a t i o n i s v a l i d f o r the hydrophobic s o l u t e s : l

n , n

(CiV (CiV -

(2V + Kp/Vm) C t ) _ 2 UA ( t - t ) (2V + KD/Vm) Co) " " V 0

Eq. 2

where C i = i n i t i a l c o n c e n t r a t i o n i n compartment I; Co = c o n c e n t r a ­ t i o n i n compartment II a t t h e o n s e t o f s t e a d y s t a t e ( t o ) , C t = c o n c e n t r a t i o n i n compartment II a t any t i m e t w h i c h i s g r e a t e r t h a n t o ; V = membrane v o l u m e , and V = compartment volume (175 ml). In t h e l i m i t t h a t Kp i s s m a l l , E q . 2 r e d u c e s t o E q . 1. m

Results

and

Discussion

1) Hydrophilic Solutes. The mechanisms o f p e r m e a t i o n o f h y d r o p h i l i c s o l u t e s i n h y d r o g e l f i l m s has been c o n s i d e r e d p r e v i ­ o u s l y by Yasuda e t a l . ( 1 2 J . These a u t h o r s u t i l i z e d t h e " f r e e v o l u m e " model f o r s o l u t e p e r m e a t i o n i n h y d r o g e l f i l m s i n w h i c h i t was assumed t h a t : i ) t h e e f f e c t i v e f r e e volume f o r s o l u t e d i f f u ­ s i o n c o r r e s p o n d s t o t h e f r e e volume o f t h e aqueous p h a s e ; i i ) t h e s o l u t e d i f f u s e s t h r o u g h " f l u c t u a t i n g p o r e s " by s u c c e s s i v e jumps through " h o l e s " which are l a r g e r than the s o l u t e ; i i i ) the s o l u t e p e r m e a t e s o n l y t h r o u g h aqueous r e g i o n s and s o l u t e - p o l y m e r i n t e r ­ a c t i o n s a r e m i n i m a l . Based on t h i s m o d e l , t h e d i f f u s i o n c o e f f i ­ c i e n t , Dm, i n t h e h y d r a t e d membrane i s g i v e n b y :

Do

Vf

IH

/

t

q

'

0

where B q i s p r o p o r t i o n a l t o s o l u t e c r o s s s e c t i o n a l a r e a ( n r ) , D i s the d i f f u s i o n c o e f f i c i e n t f o r the s o l u t e i n water, Vf i s the f r e e v o l u m e , and H i s t h e volume f r a c t i o n o f w a t e r i n t h e h y d r a t e d membrane. From E q . 3 i t i s a p p a r e n t t h a t Dm s h o u l d be d e p e n d e n t upon b o t h t h e c r o s s s e c t i o n a l r a d i u s o f t h e d i f f u s i n g s o l u t e s and t h e membrane h y d r a t i o n . V a l u e s o f Dm f o r t h e h y d r o p h i l i c s o l u t e s i n p-HEMA and p-HEMA c r o s s l i n k e d w i t h 1 m o l e % EGDMA a r e shown i n T a b l e s I and I I . It i s e v i d e n t t h a t t h e Dm v a l u e s i n t h e c r o s s l i n k e d membrane a r e s m a l l e r t h a n i n p-HEMA. P l o t s o f t h e s e v a l u e s a c c o r d i n g t o E q . 3 a r e shown i n F i g . 1. A s e m i e m p e r i c a l e q u a t i o n d e v e l o p e d by W i l k e and Chang (13) was u t i l i z e d t o c a l c u l a t e Do. The m o l a r volume o f t h e s o l u t e was e s t i m a t e d f r o m a t o m i c c o n t r i b u t i o n s a c c o r d i n g t o LeBas ( 1 4 J . The m o l e c u l a r r a d i i , r , g i v e n i n T a b l e I were c a l c u ­ l a t e d a s s u m i n g t h a t t h e s o l u t e s were s p h e r i c a l ( 1 5 ) . 2

2

0

0

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

WATER IN P O L Y M E R S

350

TABLE

I

Transport Parameters of H y d r o p h i l i c Solutes

D x 10 (cm /sec)

D

Dm χ Ι Ο " (cn^/sec)

5. 57 0. 23 0. 22 0. 20 0. 23 1. 27 0. 14 0. 53

1.95 4.96 3.28 17.4 26.0 97.0 1.81 149.

5

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0

Solute

(&)

Na M e t h o t r e x a t e Sucrose Lactose Inositol Glucose Thiourea Raffinose Urea

27.7 27.4 18.1 18.1 8.8 35.7 8.1

2

0.38 0.41 0.41 0.64 0.64 1.30 0.31 1.39

TABLE

i n p-HEMA

K

Dm χ 1 0 (cnf/sec) 8

Solute Na M e t h o t r e x a t e Sucrose Lactose Inositol Glucose Thiourea Raffinose Urea

D

5.84 0.25 0.21 0.18 0.24 1.14 0.12 0.48

I n Pja Do -5. -4. -4. -3. -3. -2. -5. -2.

27 41 75 61 47 59 14 23

II

Transport Parameters of H y d r o p h i l i c Solutes p-HEMA w i t h 1 M o l e % EGDMA

K

8

1.09 3.53 2.45 13.1 15.6 88.0 1.31 128

in

"ft -5.85 -4.75 -5.12 -3.89 -3.71 -2.70 -5.47 -2.39

From t h e p l o t s shown i n F i g . 1, i t i s e v i d e n t t h a t Eq. 3 i s v a l i d f o r t h e h y d r o p h i l i c s o l u t e s examined i n t h e p r e s e n t s t u d y . The d e p e n d e n c e o f Dm on c r o s s s e c t i o n a l r a d i u s i s e v i d e n t f r o m t h e l i n e a r i t y of the p l o t s . The w a t e r c o n t e n t s o f p-HEMA and p-HEMA c r o s s l i n k e d w i t h 1 m o l e % EGDMA a r e 42% (w) and 37% (w) r e s p e c t ­ ively. T h i s e f f e c t o f membrane h y d r a t i o n i s c o n t a i n e d i n t h e s l o p e o f t h e p l o t s g i v e n i n F i g . 1. I t i s a p p a r e n t t h a t as t h e membrane h y d r a t i o n i s i n c r e a s e d , Dm i s l e s s s e n s i t i v e t o c h a n g e s i n the s i z e o f the permeating s o l u t e . From t h e s e r e s u l t s , i t may be c o n c l u d e d t h a t h y d r o p h i l i c s o ­ l u t e s p e r m e a t e p-HEMA and p-HEMA c r o s s l i n k e d w i t h 1 mole % EGDMA p r i m a r i l y v i a the water f i l l e d channels or "pores" w i t h i n the h y d r o g e l f i l m s . T h i s c o n c l u s i o n d o e s n o t a p p e a r t o be v a l i d ,

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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KIM ET A L .

Hydrogel

Membranes

35

Figure 1. Dependence of diffusion coefficients of hydrophilic solutes on molecular size in (—) p-HEMA and (---) p-HEMA crosslinked with 1 mol % EGDMA: (1) urea; (2) thiourea; (3) glucose; (4) inositol; (5) sucrose; (6) lactose; (7) raffinose.

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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352

WATER IN POLYMERS

h o w e v e r , f o r p-HEMA c o n t a i n i n g h i g h e r c o n c e n t r a t i o n s o f t h e c r o s s l i n k e r EGDMA. F o r e x a m p l e , i n f i l m s c o n t a i n i n g 2.5 m o l e % EGDMA d e v i a t i o n s f r o m l i n e a r i t y i n p l o t s o f t h e t y p e shown i n F i g . 1 were n o t e d . F o r f i l m s p r e p a r e d f r o m 5 m o l e % EGDMA, no d e t e c t a b l e d i f f u s i o n was f o u n d a f t e r two weeks f o r t h e s o l u t e s r a f f i n o s e and inositol. From t h e d a t a shown i n T a b l e s I and I I , and t h a t g i v e n i n a t h e s i s by Sung ( 5 ) , i t i s p o s s i b l e t o f u r t h e r d e f i n e t h e model f o r h y d r o p h i l i c s o l u t e p e r m e a t i o n i n h y d r o g e l f i l m s v i a an a n a l y s i s o f t h e KD v a l u e s . The p a r t i t i o n c o e f f i c i e n t s f o r w a t e r i n p-HEMA and p-HEMA c r o s s l i n k e d w i t h 1 m o l e % EGDMA a r e 0.52 and 0.51 r e s p e c t i v e l y . However, f r o m S u n g ' s d a t a ( 5 ) , i t i s p o s s i b l e t o d e f i n e p a r t i t i o n c o e f f i c i e n t s f o r water i n t o the various subclasses of water i n the h y d r o g e l membranes. F o r p-HEMA, t h e s e v a l u e s o f KD a r e : bulk w a t e r 0 . 3 0 , b u l k + i n t e r m e d i a t e w a t e r 0 . 4 1 , and b u l k + i n t e r m e d i ­ a t e + bound w a t e r 0 . 5 2 . F o r p-HEMA w i t h 1 m o l e % EGDMA, t h e v a l u e s a r e : b u l k w a t e r 0 . 2 1 , b u l k + i n t e r m e d i a t e w a t e r 0 . 3 6 , and b u l k + i n t e r m e d i a t e + bound w a t e r 0 . 5 0 . A comparison o f these v a l u e s w i t h t h e e x p e r i m e n t a l v a l u e s f o u n d i n T a b l e s I and II i n ­ d i c a t e s t h a t the sugars p a r t i t i o n p r i m a r i l y i n t o bulk water of b o t h membranes a n d , t h e r e f o r e , t h a t t h e d i f f u s i o n o f t h e s e s o l u t e s o c c u r s p r i m a r i l y i n t h e b u l k w a t e r o f t h e membranes. This r e s u l t i s c o n s i s t e n t w i t h the observed very low p e r m e a b i l i t y o f i n o s i t o l and r a f f i n o s e i n p-HEMA w i t h 5 mole % EGDMA. These membranes have l i t t l e o r no b u l k w a t e r ( 5 ) . T h i o u r e a and Na m e t h o t r e x a t e show l a r g e d e v i a t i o n s f o r Kp f r o m v a l u e s e x p e c t e d based on p a r t i t i o n s o l e l y i n t o t h e w a t e r f r a c t i o n o f t h e membrane. T h i s phenomena may be due t o s p e c i f i c i n t e r a c t i o n s of the s o l u t e s w i t h the macromolecular chains. The i n c r e a s e i n p o l a r i z a b i l i t y i n g o i n g f r o m u r e a t o t h i o u r e a and t h e p r e s e n c e o f p o l a r i z a b l e a r o m a t i c g r o u p s i n Na m e t h o t r e x a t e i n d i ­ c a t e s t h a t t h i s i n t e r a c t i o n may be d i s p e r s i v e i n n a t u r e . From t h e s e r e s u l t s , i t may be i n f e r r e d a l s o t h a t some p o r t i o n o f t h e t o t a l t r a n s p o r t o f t h e s e s o l u t e s may o c c u r i n r e g i o n s o t h e r t h a n t h e b u l k w a t e r r e g i o n s o f t h e h y d r o g e l membranes. It is i n t e r ­ e s t i n g t o n o t e t h a t t h e t o t a l volume f r a c t i o n o f H 0 i n p-HEMA and p-HEMA w i t h 1 mole % EGDMA may be a v a i l a b l e f o r t h e t r a n s p o r t of urea. 2

2) Hydrophobic S o l u t e s . The v a l u e s o f D , Kp, Dm and In Djp/D f o r s e v e r a l h y d r o p h o b i c s o l u t e s i n p-HEMA and p-HEMA c r o s s l i n k e d w i t h 5.25 mole % EGDMA a r e g i v e n i n T a b l e s I I I and IV. 0

0

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20.

κίΜ

ET AL.

Hydrogel

Membranes

TABLE

III

Transport Parameters o f Hydrophobic Solutes

D x 10 (cm /sec)

D

Dm x 1 0 (cm /sec)

48 70 129 83 177 27

18.8 13.5 7.04 10.6 5.48 8.86

9

6

0

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Solute

2

6.04 5.83 5.59 5.56 6.41 5.55

Testosterone Norethindrone Progesterone 17-Hydroxy progesterone Estradiol Cortisol

TABLE

i n p-HEMA

K

In

2

Dm Do

-5.78 -6.06 -6.68 -6.27 -7.07 -6.44

IV

Transport Parameters o f Hydrophobic S o l u t e s i n p-HEMA C r o s s l i n k e d w i t h 5.25 M o l e % EGDMA

Dm x 1 0 (cn^/sec) 9

D

l

n

l

n

Dm Do"

Solute

K

Testosterone Norethindrone Progesterone 17-Hydroxy progesterone Estradiol Cortisol

89 131 232 132

2.70 1.16 1.12 1.53

-7.71 -7.91 -8.52 -8.20

235 20

1.21 1.78

-8.57 -8.04

By c o m p a r i s o n o f Dm v a l u e s g i v e n i n T a b l e s I I I and IV w i t h t h o s e f o u n d i n T a b l e s I and I I , i t may be n o t e d t h a t Dm v a l u e s f o r h y d r o p h o b i c s o l u t e s a r e a p p r o x i m a t e l y two o r d e r s o f m a g n i t u d e l e s s than f o r the h y d r o p h i l i c s o l u t e s . C o n v e r s e l y , Kp v a l u e s a r e a b o u t two o r d e r s o f m a g n i t u d e g r e a t e r f o r t h e h y d r o p h o b i c s o l u t e s i n d i c a t i n g t h a t v e r y s t r o n g i n t e r a c t i o n s o c c u r between t h e s e h y d r o p h o b i c s o l u t e s and t h e m a c r o m o l e c u l a r segments o f t h e h y d r o ­ g e l membranes. In a p r e v i o u s p u b l i c a t i o n (7.) i t was c o n c l u d e d t h a t h y d r o ­ p h o b i c s o l u t e s , s u c h as p r o g e s t e r o n e , p e r m e a t e p-HEMA p r i m a r i l y v i a t h e " p o r e " mechanism. However, f o r p r o g e s t e r o n e i n p-HEMA w i t h 5.25 m o l e % EGDMA, i t was f o u n d t h a t t h e " p a r t i t i o n " m e c h a n ­ ism d o m i n a t e s p e r m e a t i o n . In t h i s m e c h a n i s m , i t i s presumed t h a t t h e s o l u t e s p e r m e a t e by d i s s o l u t i o n and d i f f u s i o n w i t h i n t h e m a c r o m o l e c u l a r segments o f t h e p o l y m e r b a c k b o n e . In t h e " p o r e " mechanism v a l u e s a r e e x p e c t e d t o be l e s s t h a n one and r e f l e c t

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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t h e d i s t r i b u t i o n o f s o l u t e between membrane s o l v e n t and b u l k s o l v ­ ent. In t h e " p a r t i t i o n " mechanism p o l y m e r s e g m e n t / s o l u t e i n t e r ­ a c t i o n i s h i g h w h i c h l e a d s t o w i d e r a n g e o f Kp v a l u e s w h i c h a r e much g r e a t e r t h a n o n e . From t h e d a t a g i v e n i n T a b l e s I I I and I V , i t i s a p p a r e n t t h a t Kp v a l u e s f o r b o t h membranes a r e much g r e a t e r t h a n o n e . These h i g h KD v a l u e s f o r p-HEMA a p p e a r t o be i n c o n s i s t e n t w i t h t h e " p o r e " mechanism f o r s o l u t e t r a n s p o r t . T h i s c o n t r a d i c t i o n c a n be s o l v e d a s s u m i n g t h a t KD i s d o m i n a t e d by t h e h i g h s o l u b i l i t y o f t h e hydrophobic s o l u t e w i t h i n the hydrophobic region of the hydrogel, w h e r e a s , p e r m e a t i o n i s c a r r i e d by d i f f u s i o n w i t h i n " f l u c t u a t i n g p o r e s " as d e s c r i b e d i n h y d r o p h i l i c s o l u t e p e r m e a t i o n . It i s , t h e r e f o r e , i m p o r t a n t t o s e p a r a t e " p o r e " and " p a r t i t i o n " c o n t r i b u ­ t i o n s t o the t o t a l permeation i n o r d e r t o determine the dominant mechanisms f o r h y d r o p h o b i c s o l u t e s i n p-HEMA. As n o t e d i n p r e v i o u s s e c t i o n s o f t h i s m a n u s c r i p t , i t has been proposed t h a t t h r e e types o f water e x i s t w i t h i n hydrogel f i l m s , n a m e l y , b o u n d , i n t e r m e d i a t e , and b u l k w a t e r . From t h i s m o d e l , i t i s p r o p o s e d t h a t h y d r o g e l membranes p r e p a r e d w i t h o u t c r o s s l i n k e r a r e composed o f two domains d e s i g n a t e d A and Β ( 8 ) . Domain A c o n ­ s i s t s o f p o l y m e r s e g m e n t s , bound w a t e r and i n t e r f a c i a l w a t e r . Domain Β i s c o n s i d e r e d t o be b u l k w a t e r w h i c h f o r m s t h e " f l u c t u a ­ ting pores." P-HEMA w i t h 5 . 2 5 mole % EGDMA, h a v i n g no " b u l k - l i k e " w a t e r , i s assumed t o be composed e n t i r e l y o f A t y p e d o m a i n s . T r a n s p o r t i n t h e A domains o f t h e h y d r o g e l o c c u r s t h r o u g h t h e bound and i n t e r f a c i a l w a t e r a n d / o r t h r o u g h t h e h y d r o p h o b i c p o l y ­ meric regions. T h e r e f o r e , p e r m e a t i o n i n t h e A domains w i l l o c c u r v i a t h e " p a r t i t i o n " mechanism as p r e v i o u s l y d e s c r i b e d . KD v a l u e s f o r t r a n s p o r t i n A domains v a r y w i d e l y d e p e n d i n g on t h e s o l u t e solubilities. T r a n s p o r t i n t h e Β domains o c c u r s by d i f f u s i o n o f the s o l u t e i n " b u l k - l i k e " water. KD v a l u e s a r e i d e a l l y one i n t h i s case s i n c e the s o l u t e i s s i m p l y p a r t i t i o n i n g from bulk water i n t o hydro'gel domains o f " b u l k - l i k e " w a t e r . D i f f u s i o n composed e x c l u s i v e l y o f A - t y p e d o m a i n s , as p o s t u l a t e d i n p-HEMA w i t h 5 . 2 5 m o l e % EGDMA, o c c u r s o n l y by t h e p a r t i t i o n mechanism w h i c h has no " b u l k - l i k e " water. T h i s model was s u c c e s s f u l l y a p p l i e d t o e s t i ­ mate t h e c o n t r i b u t i o n o f e a c h domain t o t h e t o t a l p e r m e a b i l i t i e s o f s t e r o i d s i n h y d r o g e l membranes. I t c a n be shown t h a t p-HEMA c o n t a i n s 2 2 . 8 % " b u l k - l i k e " w a t e r ( 8 ) . As n o t e d , KD f o r p a r t i t i o n i n t o t h i s w a t e r must be 1 . 0 . W i t h t h i s i n f o r m a t i o n , t h e r a t i o o f s o l u t e d i f f u s i o n due t o Β domains t o t o t a l s o l u t e p e r m e a b i l i t y , DB/PT> w h i c h r e p r e s e n t s t h e f r a c t i o n o f " p o r e - t y p e " p e r m e a t i o n i n p-HEMA membranes, can be d e t e r m i n e d ( 8 ) . These v a l u e s a r e g i v e n i n T a b l e V. I t may be n o t e d t h a t t h e v a l u e s o f D B / Ρ Τ a r e a l l approximately 0 . 8 0 except C o r t i s o l which i s 0 . 8 8 . This i n d i c a t e s t h a t t h e " p o r e " c o n t r i b u t i o n t o t r a n s p o r t i n p-HEMA i s s i m i l a r f o r a l l hydrophobic s t e r o i d s except the r e l a t i v e l y water s o l u b l e s t e r ­ o i d , C o r t i s o l , w h i c h p e r m e a t e s by " p o r e s " t o a g r e a t e r e x t e n t .

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20.

K I M ET AL.

Hydrogel

Membranes

355

TABLE V

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Transport Parameters o f S t e r o i d s i n p-HEMA by M o d e l i s t i c A n a l y s i s

D i f f u s i o n C o e f f i c i e n t (Dg) i n " B u l k - l i k e " Water (cm /sec)

Solute

2

Testosterone Norethindrone Progesterone 17-Hydroxy progesterone Estradiol Cortisol

7.20 7.29 5.59 5.56

χ χ χ χ

10" 10" 10 10"

6.41 5.95

χ x

10" 10'

7

7

- 7

7

7

7

-5.78 -6.06 -6.68 -6.27

0.80 0.77 0.76 0.82

0.54 0.54 0.56 0.63

-7.07 -6.44

0.77 0.88

0.75 1.35

The r e l a t i v e l y h i g h f r a c t i o n s o f D B / P T f o r a l l s t e r o i d s s u g ­ g e s t t h a t p e r m e a t i o n t h r o u g h p-HEMA membrane i s d o m i n a t e d by t h e " p o r e " mechanism. The h i g h KD v a l u e s a r e c o n s i s t e n t w i t h t h e p r o ­ posed m o d e l . A c c o r d i n g t o t h e model and d a t a o b t a i n e d i n t h e p-HEMA membrane, p a r t i t i o n i n g o f h y d r o p h o b i c s o l u t e s i s g o v e r n e d p r e d o m i n a n t l y by A t y p e d o m a i n s . S o l u t e w i t h i n t h e s e domains makes a s m a l l c o n t r i b u t i o n t o p e r m e a b i l i t y . S o l u t e p e r m e a t i o n i s d o m i n a t e d by t h e " p o r e " m e c h a n i s m . The a s s u m p t i o n made i n t h e model i s t h a t A domains a r e o f t h e same n a t u r e i n b o t h p-HEMA and c r o s s l i n k e d p-HEMA. If t h i s is s t r i c t l y t r u e , t h e p a r t i t i o n c o e f f i c i e n t s w h i c h a r e d o m i n a t e d by A t y p e domains i n p-HEMA s h o u l d be r e l a t e d t o p a r t i t i o n c o e f f i ­ c i e n t s i n p-HEMA w i t h 5.25 mole % EGDMA a c c o r d i n g t o t h e volume f r a c t i o n o f A t y p e domains p r e s e n t i n p-HEMA. ( T h i s volume f r a c ­ t i o n i s 0.772 s i n c e " b u l k - l i k e " w a t e r i s 2 2 . 8 % i n p-HEMA.) These v a l u e s a r e g i v e n i n T a b l e V as t h e r a t i o K p ( I ) / K p ( I I ) . K D ( H and K D C I I ) a r e p a r t i t i o n c o e f f i c i e n t s o f s t e r o i d s i n p-HEMA and p HEMA w i t h 5.25 m o l e % EGDMA r e s p e c t i v e l y . The e s t r a d i o l v a l u e o f 0.75 i s i n c l o s e agreement w i t h t h e p r e d i c t e d v a l u e o f 0 . 7 7 2 . However, t h i s r a t i o f o r t h e o t h e r s t e r o i d s e x c e p t C o r t i s o l i s a p p r o x i m a t e l y 0.54 t o 0 . 6 3 . Though t h e q u a n t i t a t i v e a g r e e m e n t i s not good, q u a l i t a t i v e agreement w i t h t h e p r e d i c t e d v a l u e i s o b ­ tained. T h i s i n d i c a t e s t h a t d i f f e r e n c e s e x i s t between t h e A domains i n p-HEMA and p-HEMA c r o s s l i n k e d w i t h EGDMA. I t was d i s c u s s e d p r e v i o u s l y t h a t d i f f u s i o n c o e f f i c i e n t s o f h y d r o p h i l i c s o l u t e s i n p-HEMA a c c o r d i n g t o E q . 3 showed a s t r a i g h t l i n e c o r r e l a t i o n p r o v i d e d t h e f r e e volumes a c c e s s i b l e t o t h e v a r i ­ ous s o l u t e s a r e e q u a l . D i f f u s i o n c o e f f i c i e n t s of these s t e r o i d s (from Table I I I ) are p l o t t e d i n F i g . 2 using the r v a l u e o f 11.45 % (16). E x p e r i m e n t a l v a l u e s o f I n Dm/Do f o r t h e s e s t e r o i d s d e v i a t e s u b s t a n t i a l l y from the l i n e a r l i n e o b t a i n e d from hydro2

2

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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356

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POLYMERS

Figure 2. Dependence of diffusion coefficients on solute molecular size in p-HEMA: (—) correlation of steroid diffusion in Β-type domains with water-soluble solutes; (—) experimental values of steroid diffusion

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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20.

κίΜ E T A L .

Hydrogel

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philic solutes. However, i f t h e c a l c u l a t e d v a l u e s o f I n D B / D O a r e f i t w i t h t h e l i n e a r c o r r e l a t i o n o b t a i n e d from t h e h y d r o p h i l i c s o ­ l u t e s , e x c e l l e n t a g r e e m e n t i s o b t a i n e d ( F i g . 2 ) . These r e s u l t s p r o v i d e f u r t h e r s u b s t a n t i a t i o n o f t h e model p r e s e n t e d a b o v e , i . e . , t h a t h y d r o p h o b i c s o l u t e s p e r m e a t e p-HEMA membranes p r i m a r i l y v i a the " b u l k - l i k e " water r e g i o n s . In c o n c l u s i o n , 1} H y d r o p h i l i c s o l u t e s p e r m e a t e p-HEMA and p-HEMA c r o s s l i n k e d w i t h l o w e r m o l e % EGDMA v i a t h e " p o r e " m e c h a n ­ ism. T h e d i f f u s i o n c o e f f i c i e n t s o f t h e s o l u t e s depend on t h e m o l e c u l a r s i z e a n d may u t i l i z e t h e " b u l k - l i k e " w a t e r i n t h e h y d r o gels. As t h e water content o f hydrogel i n c r e a s e s , t h e s o l u t e p e r ­ meability increases. 2 ) H y d r o p h o b i c s o l u t e s p e r m e a t e p-HEMA and p-HEMA c r o s s l i n k e d w i t h EGDMA v i a e i t h e r t h e " p o r e " o r " p a r t i t i o n " mechanisms. D i f f u s i o n c o e f f i c i e n t s a r e lower than those o f hydro­ p h i l i c s o l u t e s ; h o w e v e r , s t e r o i d s c a n p e r m e a t e even i n p-HEMA w i t h 5 . 2 5 m o l e % EGDMA d u e t o t h e p r e d o m i n a n t " p a r t i t i o n " m e c h a n ­ i s m f o r h y d r o p h o b i c s o l u t e p e r m e a t i o n i n t h i s membrane. Hydro­ p h i l i c s o l u t e s f a i l t o permeate t h e high c r o s s l i n k e d h y d r o g e l s . 3) B a s e d on p a r t i t i o n c o e f f i c i e n t d a t a , t h e h y d r o p h i l i c s o l u t e s examined a p p e a r t o p e r m e a t e p-HEMA and p-HEMA w i t h 1 m o l e % EGDMA v i a " b u l k - l i k e " water regions. Partition coefficients of steroids i n p-HEMA a r e d o m i n a t e d by t h e i r h i g h s o l u b i l i t y o f t h e s t e r o i d s i n t h e hydrophobic regions o f t h e hydrogels o r A domains, whereas, p e r m e a t i o n i s d o m i n a t e d by d i f f u s i o n w i t h i n " f l u c t u a t i n g p o r e s . " Acknowledgements S t i m u l a t i n g d i s c u s s i o n s w i t h D r s . J . D. A n d r a d e , D. G. G r e g o n i s , and J . F e i j e n made t h i s work p o s s i b l e . We g r e a t f u l l y a c k n o w l e d g e D r . S. R o n e l , Hydron Med. S c i . , I n c . , f o r h i s g e n e r o u s d o n a t i o n s o f p u r e HEMA. S u p p o r t e d by NIH g r a n t s HD 09791 and HL 13738. Abstract The permeabilities of water soluble nonelectrolytes and sev­ eral hydrophobic steroids in poly(hydroxyethyl methacrylate) hydrogel films were determined. The effects of crosslinking and variations in equilibrium water content of the films, on the ob­ served permeabilities, were investigated. For hydrophilic solutes the permeation and partition coefficients are consistent with transport via the "bulk-like" water regions of the hydrogel films. These "bulk-like" water regions probably exist within the porous regions of the film. Decreases in the "bulk-like" water via copolymerization or crosslinking reduce both the partition and per­ meation coefficients, indicating exclusion of hydrophilic solutes from non "bulk-like" water regions. For hydrophobic solutes, per­ meability coefficients are smaller and partition coefficients are much larger relative to the hydrophilic solutes. For the hydro­ phobic solutes modelistic analysis of the permeation and partition

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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data indicate permeation occurs predominantly by a pore-type mechanism in poly(hydroxyethyl methacrylate) and by a partition mechanism in highly crosslinked poly(hydroxyethyl methacrylate) films. The porous flux was associated with the "bulk-like" water regions of the hydrogel films and the partition flux with the collective polymer matrix, "interfacial" and "bound" water region of the films.

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RECEIVED January 4, 1980.

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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