Diffusion through Hydrogel Membranes

6 Diffusion through Hydrogel Membranes I.

Permeation of Water Through Poly(2-hydroxyethyl methacrylate) and Related Polymers

S. J. WISNIEWSKI, D. E. GREGONIS, S. W. KIM, and J. D. ANDRADE

Downloaded by UNIV OF MINNESOTA on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch006

Departments of Applied Pharmaceutical Sciences and Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112

H y d r o g e l s a r e known f o r t h e i r u n i q u e p h y s i c a l p r o p e r t i e s and potential biomedical a p p l i c a t i o n s . The t r a n s p o r t phenomena o f some 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 o l y HEMA) membranes have been p r e v i o u s l y i n v e s t i g a t e d (1-4). R a t n e r and M i l l e r {5) have shown t h a t p o l y HEMA membranes have a h i g h p e r m e a b i l i t y t o u r e a due t o i n t e r a c t i o n between t h e s o l u t e and membrane, a n d , i n a d d i t i o n , c o n s i d e r t h e e x i s t e n c e o f p o r e s i n t h e p o l y HEMA g e l s t r u c t u r e , w i t h t h e w a t e r r e g i o n s o f t h e g e l a c t i n g as " p o r e s " for solute transport. R e c e n t l y Chen f o u n d (6_) t h a t t h e a b s o r p t i o n o f w a t e r by d e h y d r a t e d p o l y HEMA was a f u n c t i o n o f c r o s s ! i n k e r c o n t e n t . In h i s s t u d y d i f f u s i o n c o e f f i c i e n t s were c a l c u l a t e d f r o m a b s o r p t i o n k i n e t i c data using F i c k ' s law. Several f a c t o r s i n f l u e n c e the s t r u c t u r e o f h y d r o g e l s and s u b s e q u e n t l y t h e i r d i f f u s i o n c h a r a c teristics. These f a c t o r s i n c l u d e i n i t i a t o r , c r o s s l i n k i n g a g e n t s , c r o s s l i n k e r c o n t e n t , e q u i l i b r i u m w a t e r c o n t e n t and i m p u r i t i e s . Yasuda e t a l . ( 1 , 1 1 ) have u t i l i z e d a t h e o r y , b a s e d on a f r e e - v o l u m e c o n c e p t o f d i f f u s i v e t r a n s p o r t , f o r h y d r a t e d homogeneous membranes. They c o n c l u d e d t h a t t h i s c o n c e p t e x c e l l e n t l y e x p l a i n s t h e d i f f u s i v e t r a n s p o r t p a r a m e t e r s as a f u n c t i o n o f water c o n t e n t over a wide h y d r a t i o n range. In t h i s s t u d y , we have been c o n c e r n e d w i t h v a r y i n g c r o s s l i n k e r c o n c e n t r a t i o n s and w a t e r c o n t e n t . I t i s hoped t h a t t h i s d a t a w i l l p r o v i d e a d d i t i o n a l i n f o r m a t i o n on t h e b a s i c t r a n s p o r t mechanisms f o r w a t e r i n d i f f e r e n t g e l s y s t e m s and on t h e r o l e o f water i n the transport of other s o l u t e s . Experimental H y d r o x y e t h y l m e t h a c r y l a t e was o b t a i n e d as a g i f t f r o m Hydron L a b o r a t o r i e s (New B r u n s w i c k , New J e r s e y ) and was used w i t h o u t a d d i t i o n a l p u r i f i c a t i o n . M e t h o x y e t h y l m e t h a c r y l a t e and m e t h o x y e t h o x y e t h y l m e t h a c r y l a t e were p r e p a r e d i n o u r l a b o r a t o r i e s by base c a t a l y z e d t r a n s e s t e r i f i c a t i o n o f m e t h y l m e t h a c r y l a t e w i t h

80

In Hydrogels for Medical and Related Applications; Andrade, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.


6. wisNiEwsKi E T A L .

81

Diffusion through Hydrogel Membranes

t h e c o r r e s p o n d i n g a l c o h o l . E t h y l e n e g l y c o l d i m e t h a c r y l a t e (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 , P e n n s y l v a n i a ) and tetraethylene glycol dimethacrylate (Polysciences, Warrington, P e n n s y l v a n i a ) were p u r i f i e d by base e x t r a c t i o n t o remove i n h i b i t o r f o l l o w e d by d i s t i l l a t i o n . A z o b i s m e t h y l i s o b u t y r a t e , p r e p a r e d by t h e method o f M o r t i m e r Ç 7 ) , was used t o i n i t i a t e p o l y m e r i z a t i o n a t a c o n c e n t r a t i o n o f 7.84 m m o l e s / l i t e r monomer. Crosslinker c o n c e n t r a t i o n was c a l c u l a t e d on a m o l e - t o - m o l e b a s i s w i t h HEMA. The d e s i r e d monomer s o l u t i o n was m i x e d w i t h 45% v/v d i s t i l l e d w a t e r and p o l y m e r i z e d between g l a s s p l a t e s a t 60°C f o r 24 h o u r s . A g l a s s d i f f u s i o n c e l l , w h i c h c o n t a i n s two compartments o f e q u a l volume (175 m l ) , was d e s i g n e d . 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 . A t t h e b e g i n n i n g o f each e x p e r i m e n t , one compartment was f i l l e d w i t h t r i t i a t e d w a t e r , t h e o t h e r was f i l l e d w i t h d i s t i l l e d w a t e r . The i n c r e a s e i n t r i t i a t e d w a t e r was m o n i t o r e d by r e m o v i n g 50μ£ a l i q u o t s a t v a r i o u s times. These a l i q u o t s were p l a c e d i n 10 ml o f l i q u i d s c i n t i l l a t i o n " c o c k t a i l " ( A q u a s o l , New E n g l a n d N u c l e a r Company) and counted i n a Packard S c i n t i l l a t i o n c o u n t e r . The t h i c k n e s s o f t h e w e t membrane was measured u s i n g a l i g h t m i c r o m e t e r (Van Kauren Company). Membrane d e n s i t i e s were measured by w e i g h i n g s e c t i o n s o f w e t membrane o f known v o l u m e . Water c o n t e n t was o b t a i n e d f r o m t h e d i f f e r e n c e i n w e i g h t o f w e t and d r y membrane ( d r i e d t o c o n s t a n t w e i g h t u n d e r vacuum a t a b o u t 6 0 ° C ) . A l l e x p e r i m e n t s were r u n a t 23°C ± 1 ° C . Results

(8)

and D i s c u s s i o n

The e q u a t i o n used t o t r e a t o u r d a t a was d e r i v e d e l s e w h e r e and i s g i v e n as f o l l o w s : In

(1 - 2 C / C ) = T

Q

(J

+ \)

AUt,

where C t = H 0 c o u n t a t t i m e t ; C = H 0 c o u n t a t t i m e 0 ; V i = V = compartment volume = 175 m l ; A = membrane c o n t a c t a r e a = 14.9 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 ) . A p l o t o f In (1 - 2 C t / C ) v s . t i m e w i l l y i e l d a s t r a i g h t l i n e w i t h slope = -(1/V + 1/V )AU. S u b s t i t u t i n g our values of A , V and V g i v e s U = - 5 . 8 7 χ s l o p e (cm/sec). The d i f f u s i o n c o e f f i c i e n t s a r e g i v e n by D = Ud/Kp, where d = w e t membrane t h i c k n e s s and Kp 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 . By d e f i n i t i o n Kp = w a t e r c o n c e n t r a t i o n i n membrane/water c o n c e n t r a t i o n i n b u l k , w h i c h f o r o u r c a s e r e d u c e s t o Kp = ( j v | / y ) f · * 3

3

2

0

2

2

2

0

X

x

2

2

p

p

W

a n c

P^ a r e t h e w e t membrane d e n s i t y and t h e d e n s i t y o f w a t e r a t 23°C, r e s p e c t i v e l y . wet membrane and

W i s the weight f r a c t i o n of water i n the f

i s e q u a l t o W /W , where W i s t h e w e i g h t o f W

M

w

w a t e r and W i s t h e w e i g h t o f t h e w e t membrane. M


82

HYDROGELS

FOR MEDICAL

AND RELATED APPLICATIONS

Table 1 l i s t s the o b t a i n e d parameters f o r the v a r i o u s g e l s used. The d a t a f o r t h e ^ 0.2 m o l e - % d i e s t e r c r o s s ! i n k e r p o l y HEMA g e l s and u n r e p o r t e d d a t a on g e l s a p p r o x i m a t e l y 3-4 t i m e s t h i c k e r i n d i c a t e t h a t the p e r m e a b i l i t y U i s roughly p r o p o r t i o n a l t o 1/d, w h i l e D i s e s s e n t i a l l y i n d e p e n d e n t o f t h i c k n e s s . Variat i o n s i n D f o r t h e same g e l s a p p e a r t o be m a i n l y due t o e r r o r s i n t h e t h i c k n e s s measurement and a s m a l l d e g r e e o f n o n - u n i f o r m i t y in thickness. W.p and Kp d e c r e a s e as c r o s s l i n k i n g c o n t e n t i n c r e a s e s , as


expected.

However,

Kp seems t o i n c r e a s e a g a i n a t

approximately

6 mole-% c r o s s ! i n k e r . The i n c r e a s i n g Kp o f t h e h i g h e r c r o s s l i n k e d g e l s may be t h e r e s u l t o f g r e a t e r i n t e r a c t i o n between w a t e r and a h i g h l y c r o s s l i n k e d p o l y m e r n e t w o r k . This water, a r e l a t i v e l y small f r a c t i o n o f the t o t a l gel w a t e r , i s not a v a i l a b l e f o r t r a n s p o r t o r i s i n v o l v e d i n a much s l o w e r d i f f u s i o n p r o c e s s . (13,14), A p l o t o f d i f f u s i o n c o e f f i c i e n t s v s . p e r c e n t EGDMA and TEGDMA c r o s s ! i n k e r s i s shown i n F i g u r e 1. The d i f f u s i o n c o e f f i c i e n t s d e c r e a s e as t h e c r o s s ! i n k e r c o n t e n t i n c r e a s e s , a p p r o a c h i n g a l i m i t i n g v a l u e a t about 6 mole-% c r o s s l i n k e r . This behavior may i n d i c a t e a " p a r t i t i o n " t y p e membrane. Diffusion coefficients r a p i d l y i n c r e a s e w i t h d e c r e a s i n g c r o s s l i n k e r c o n t e n t below about 2.5 m o l e - % c r o s s l i n k e r , s u g g e s t i n g t h e d e v e l o p m e n t o f " l o o s e pores." Two b a s i c mechanisms have been c o n s i d e r e d i n e x p l a i n i n g s o l u t e t r a n s p o r t t h r o u g h a p o l y m e r membrane: 1) a m i c r o p o r o u s t y p e , w h i c h can a c t as a s i e v e w i t h t h e s o l u t e m o l e c u l e s b e i n g t r a n s p o r t e d t h o u r g h t h e m i n u t e p o r e s o f t h e membrane, and 2) a " p a r t i t i o n " t y p e membrane, w h i c h f u r t h e r a c t s t o s l o w t h e d i f f u s i o n p r o c e s s due t o t h e i n t e r a c t i o n between d i f f u s i n g s o l u t e and membrane m a t r i x o r membrane w a t e r . C r a i g ' s work (9) showed t h a t , i n g e n e r a l , a l i n e a r r e l a t i o n s h i p e x i s t s between m o l e c u l a r w e i g h t and h a l f t i m e r a t e s o f t r a n s f e r f o r p o r o u s membranes. However, t h e e f f e c t o f m o l e c u l a r w e i g h t on t h e h a l f t i m e r a t e s t h r o u g h c e r t a i n " p a r t i t i o n " membranes i n d i c a t e d no such t r e n d (10). R e c e n t l y , Chen ( 6 j has d e s c r i b e d t h r e e d i f f e r e n t d i f f u s i o n mechanisms f r o m h i s w a t e r a b s o r p t i o n s t u d i e s : 1) a d i s s o l u t i o n mechanism f o r h i g h e r c r o s s l i n k i n g c o n t e n t , 2) a p o r e f l o w mechanism f o r l o w c r o s s l i n k i n g c o n t e n t , and 3) an i n t e r m e d i a t e mechanism a t i n t e r m e d i a t e c r o s s l i n k e r c o n c e n t r a t i o n s . We have found s i m i l a r r e s u l t s from our s t u d y . Water d i f f u s e s t h r o u g h t h e c r o s s l i n k e d p o l y HEMA membranes v i a a p r e d o m i n a n t l y p o r e mechanism f r o m 0% c r o s s l i n k e r t o a p p r o x i m a t e l y 2.5 m o l e - % c r o s s l i n k e r . Above 4 m o l e - % c r o s s l i n k e r , w a t e r t r a n s p o r t i s m a i n l y c o n t r o l l e d by t h e i n t e r a c t i o n o f w a t e r w i t h t h e g e l m a t r i x . The i n t e r m e d i a t e r e g i o n l i e s between 2.5 t o 4 m o l e - % . A d e s c r i p t i o n o f t h e homogeneous membrane model and t h e t h e o r e t i c a l assumptions i n v o l v e d i n the d e r i v a t i o n of the r e l a t i o n between d i f f u s i o n c o e f f i c i e n t s and w a t e r c o n t e n t i s f o u n d


6.

WISNIEWSKI ET AL.

TABLE Diffusion


I.

C o e f f i c i e n t s , P e r m e a b i l i t i e s and H y d r o g e l

45% H2O-HEMA EGDMA-mole-% 7.5 5.3 3.8 2.3 0.75 0.38 =0.02

83


„ _D

u

d(cm)

P(g/cc)

_f

Composition

D χ 10 (cm /sec)

U χ 10* (cm/sec)

6

2

0.0777 0.0713 0.0717 0.0696 0.0739 0.0679 0.0717 0.0583 0.0638 0.0682

1.26 1.22 1.20 1.20 1.25 1.27 1.20 1.25 1.30 1.22

0.381 0.348 0.355 0.376 0.403 0.417 0.415 0.419 0.420 0.418

0.481 0.426 0.427 0.452 0.505 0.531 0.499 0.525 0.547 0.511

2.3 2.3 2.4 2.6 3.0 3.3 3.6 3.4 3.4 3.3

1.4 1.4 1.4 1.7 2.1 2.6 2.5 3.1 2.9 2.5

0.07-76 0.0736 0.0702 0.0697 0.0793

1.20 1.22 1.23 1.23 1.33

0.405 0.368 0.377 0.402 0.418

0.488 0.450 0.465 0.496 0.557

2.5 2.6 2.7 3.1 3.4

1.6 1.6 1.8 2.2 2.4

0.0660 0.0694 0.0686 0.0901 0.0733 0.0747

1.22 1.25 1.29 1.11 1.20 1.20

0.0348 0.173 0.308 0.631 0.504 0.444

0.0426 0.217 0.397 0.702 0.605 0.534

0.23 0.58 1.6 7.6 5.1 3.9

0.015 0.18 0.94 5.9 4.2 2.8

45% H2O-HEMA TEGDMA-mole-% 7.5 4.6 2.5 1.4 0.46

Copolymers: Volume-% MEMA 33% HEMA-67% MEMA 67% HEMA-33% MEMA MEEMA 33% HEMA-67% MEEMA 67% HEMA-33% MEEMA

MEMA

- methoxyethyl

methacrylate

MEEMA - m e t h o x y e t h o x y e t h y l HEMA

- hydroxyethyl

methacrylate

methacrylate


84

HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

elsewhere

(11 ), and t h a t r e l a t i o n i s g i v e n as f o l l o w s :

In D/D = β χ ( 1 - α ) / ( 1 + x a ) , Q

where χ = ( 1 - K p ) / K p ,

a = V / V , β = V*/V , D = experimental p

w

w

d i f f u s i o n c o e f f i c i e n t w i t h p a r t i t i o n c o e f f i c i e n t Kp, D


s i o n c o e f f i c i e n t o f water i n pure w a t e r , V

w

Q

= diffu

= f r e e volume i n

u n i t volume o f p u r e w a t e r , V = f r e e volume i n u n i t volume o f Ρ p o l y m e r p h a s e , and V * = a c h a r a c t e r i s t i c volume p a r a m e t e r d e s c r i b i n g t h e d i f f u s i o n o f a permeant m o l e c u l e i n t h e medium. It i s possible to rearrange t h i s equation i n order t o obtain a l i n e a r plot. That i s ,

A p l o t o f (In D/Do)" v s . x " s h o u l d y i e l d a s t r a i g h t l i n e w i t h s l o p e = - 1 / β ( 1 - α ) and i n t e r c e p t = - α / β ( 1 - α ) . T a b l e I I g i v e s v a l u e s o f _ ( l n D/Do) and x " f o r t h e g e l s s t u d i e d , u s i n g D = 2 . 4 χ 1 0 " c m / s e c f r o m (12). The v a l u e s f o r p o l y HEMA, u n c r o s s ! i n k e d (^ 0 . 0 2 m o l e - % ) , a r e an a v e r a g e o f f o u r d i f f e r e n t g e l s . Figure 2 i s a p l o t o f (In D/Do)" v s . x " f o r a l l b u t t h e c r o s s l i n k e d gels. L e a s t s q u a r e s f i t y i e l d s v a l u e s o f α = 0 . 6 9 and β = 11 with a c o r r e l a t i o n c o e f f i c i e n t of -0.998. The i n t e r c e p t y i e l d s a v a l u e o f 1.6 χ 1 0 " c m / s e c f o r t h e h y p o t h e t i c a l z e r o w a t e r content polymer. I n c l u s i o n o f c r o s s l i n k e d p o l y HEMA g e l s y i e l d s v a l u e s o f α = 0 . 7 2 and β = 13 w i t h a c o r r e l a t i o n c o e f f i c i e n t o f -0.988. Even t h o u g h a f a i r c o r r e l a t i o n i s o b t a i n e d w i t h t h e i n c l u s i o n o f t h e c r o s s l i n k e d g e l s , t h e s e g e l s seem t o e x h i b i t a t r e n d o f t h e i r own. These r e s u l t s and p r e v i o u s r e s u l t s ( 1 1 ) i n d i c a t e t h a t s t r u c t u r a l d i f f e r e n c e s o f t h e monomers used may p l a y some r o l e i n t h e d i f f u s i o n p r o c e s s o t h e r t h a n j u s t d e t e r mining water content. Changing o f t h e w a t e r c o n t e n t o f s w o l l e n g e l s f o r p u r e s y s t e m s by v a r y i n g p o l y m e r i z a t i o n w a t e r c o n c e n t r a t i o n may shed some l i g h t on s t r u c t u r a l e f f e c t s i n t h e d i f f u s i o n process. This study i s being continued. 1

1

1

1

0

5

2

1

7

1

2

Acknowledgements T h i s work was s u p p o r t e d by NHLI G r a n t No. HL 1 6 9 2 1 - 0 1 . The donations o f generous q u a n t i t i e s o f h y d r o x y e t h y l m e t h a c r y l a t e f r o m Hydro Med S c i e n c e s , I n c . , i s g r a t e f u l l y a c k n o w l e d g e d .

Abstract Water transport through fully swollen poly (2-hydroxyethyl methacrylate) (poly HEMA) hydrogels, containing varying concentra tions of ethylene glycol dimethacrylate (EGDMA) and tetraethylene


6.


WISNIEWSKI ET AL.

TABLE Values o f (In D/D )"

1

Q

(Using D

Q


Hydrogel (Copolymers i n volume-%) MEMA 33% HEMA-67% MEMA 67% HEMA-33% MEMA MEEMA 33% HEMA-67% MEEMA 67% HEMA-33% MEEMA HEMA

and x "

II. 1

f o r Hydrogels

= 2.4 χ 1 ( f

5

cm /sec) 2

IniD/D^"

1

Studied 1 2

χ

1

= K, D

-0.22 -0.27 -0.37 -0.87 -0.55 -0.65 -0.51

0.0445 0.277 0.658 2.36 1.15 1.53 1.09

-0.43 -0.43 -0.43 -0.45 -0.48 -0.50

0.927 0.742 0.745 0.825 1.02 1.13

-0.44 -0.45 -0.46 -0.49 -0.51

0.953 0.818 0.869 0.984 1.26

M o l e - % EDGMA 7.5 5.3 3.8 2.3 0.75 0.38

M o l e - % TEGDMA 7.5 4.6 2.5 1.4 0.46


HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

86

10.00

•

EGDMR

+

TEGDMR

00

θ

ο

+

ω ο

ε mm

ε

CROSSL INKER


ο

,

Η.

mm

2

mm

Β

2)0

a

ο

+

° 2.

m

2 .3 0

2 .3 0

2 .Β 0

D

Χ

10

0

α

ο

and TEGDMA

in

PHEMA

MEMR

•

-

3 . 5Γ0

(cm / s e c )

Figure 1. Plot of diffusion coefficients vs. mole % EGDMA hydrogel

0

3 . 2 0

.2

MEMR-HEMR

Χ κεΜΠ

. Η

Η

MEEMR—HEMR

Μ

MEEMR

c

.ε

Β

l ^0 0.

0

I . S

1 . 0

y

Figure 2. Plot of (In D/Do)'

1

2 . 0

2 . E

-1

vs. X' for hydrogels swollen to different water concentrations 1


equilibrium


6.

wisNiEwsKi E T A L .


87

glycol dimethacrylate (TEGDMA) crosslinkers, was investigated using tritiated water and a designed diffusion cell. Diffusion coefficients obtained in these experiments decrease as the concentration of crosslinker increases. This decrease is very sharp at crosslinker concentrations of 0-2.5 mole-%. At higher crosslinker concentrations (2.5-7.5 mole-%), the diffusion coefficients appear to reach a limiting value. This study indicates that a crosslinked poly HEMA membrane may provide both "partition" and "pore" mechanisms of solute transport based on crosslinker concentration. Hydrogels of varying water content were prepared to investi gate the relationship between water content and diffusion coefficient. Poly(methoxyethyl methacrylate) (poly MEMA), poly(methoxyethoxyethyl methacrylate) (poly MEEMA) and copolymers of MEMA and MEEMA with HEMA were formulated to give hydrogels with water content ranging from approximately 3% to 63%. The results of the diffusion experiments were examined in light of a free-volume model of diffusive transport. Excellent theoreticalexperimental correlation was obtained for the hydrogels used in this study. Literature Cited 1. Yasuda, H., Lamaze, C., and Ikenberry, L., Makromol. Chem. (1968) 118, 19. 2. Spacek, P., and Kubin, M., J. Poly. Sci., Part C, (1967) 16, 705. 3. Ikenberry, L., Yasuda, H., and Clark, H., Chem. Eng. Prog. Sym. Ser. (1968) 64 (84) 69. 4. Refojo, M. F., J. Appl. Poly. Sci. (1964) 9, 3417. 5. Ratner, B. D., and Miller, I. F., J. Biomed. Matl. Res. (1973) 7, 353. 6. Chen, R. Y. S., Polymer Preprints (1974) 15, No. 2, 387. 7. Mortimer, G. Α., J. Org. Chem. (1964) 30, 1632. 8. Mah, M. Y., Master's Thesis, University of Utah, 1972. 9. Craig, L. C., and Konigsberg, W., J. Phys. Chem. (1961) 65 116. 10. Lyman, D. J., Trans. Am. Soc. Art. Int. Org. (1964) 10, 17. 11. Yasuda, H., Lamaze, C. E., and Peterlin, Α., J. Poly, Sci., A-2 (1971) 9, 1117. 12. Wang, J. H., Robinson, C. V., and Edelman, I. S., J. Amer. Chem. Soc. (1953) 75, 466. 13. Chang, Y. J., Chen, C. T., and Tobolsky, J. Poly. Sci., Poly. Phys. Ed., (1974), 12, 1. 14. Hoffman, A. S., Modell, M., and Pan, P., J. Appl. Poly. Sci., 14, 285 (1970).


Diffusion through Hydrogel Membranes

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