Vapor Pressure and Swelling Pressure of Hydrogels

2 Vapor Pressure and Swelling Pressure of Hydrogels

Downloaded by COLUMBIA UNIV on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch002

MIGUEL F. REFOJO Eye Research Institute of Retina Foundation, Boston, Mass. 02114

H y d r o g e l s c o n s i s t o f two c o m p o n e n t s : the polymer network, w h i c h i s c o n s t a n t i n q u a n t i t y , and t h e aqueous c o m p o n e n t , w h i c h is variable. At e q u i l i b r i u m s w e l l i n g , the chemical p o t e n t i a l s of t h e w a t e r i n t h e g e l and t h e w a t e r s u r r o u n d i n g t h e g e l a r e e q u a l . The a d d i t i o n t o t h e s o l u t i o n s u r r o u n d i n g t h e g e l o f m a c r o m o l e c u l e s t h a t are too l a r g e to penetrate the gel lowers the chemical p o t e n t i a l of the water i n the s o l u t i o n . Water t h u s moves o u t o f t h e g e l and t h e n e t w o r k c o n t r a c t s , d e c r e a s i n g t h e c h e m i c a l p o t e n t i a l o f the water i n the network to the v a l u e o f the water i n the solution. Therefore, at e q u i l i b r i u m the osmotic pressure of the macromolecular s o l u t i o n equals the s w e l l i n g pressure of the hydrogel. The d e g r e e o f h y d r a t i o n t h a t can be a c h i e v e d by e q u i l i b r a t i o n w i t h a m a c r o m o l e c u l a r s o l u t i o n c a n a l s o be o b t a i n e d by compressing the g e l under a mechanical p r e s s u r e e q u i v a l e n t i n magnitude t o the osmotic p r e s s u r e o f the macromolecular s o l u t i o n . The m e c h a n i c a l p r e s s u r e r a i s e s t h e c h e m i c a l p o t e n t i a l o f t h e w a t e r i n t h e g e l , so w a t e r exudes f r o m t h e g e l u n t i l e q u i l i b r i u m i s reached. Thus t h e e q u i l i b r i u m w a t e r c o n t e n t depends on t h e mechanical pressure a p p l i e d to the g e l . The s w e l l i n g phenomena o f g e l s have been t h e o b j e c t o f t h e r m o d y n a m i c a n a l y s i s (1_,2). The o s m o t i c p r e s s u r e a t t r i b u t e d t o the polymer network ( π ) i s the d r i v i n g f o r c e o f s w e l l i n g . The s w e l l i n g p r o c e s s d i s t e n d s t h e n e t w o r k , and i s c o u n t e r a c t e d by t h e e l a s t i c c o n t r a c t i l i t y o f the s t r e t c h e d polymer network ( p ) . Hence t h e s w e l l i n g p r e s s u r e o f n o n i o n i c h y d r o g e l s ( Ρ ) i s t h e r e s u l t o f t h e i m b i b i t i o n o f s o l v e n t d r i v e n by an o s m o t i c p r e s s u r e , c o u n t e r a c t e d by t h e c o n t r a c t i l i t y o f t h e n e t w o r k w h i c h tends to expel the s o l v e n t : Ρ = π - p. A t e q u i l i b r i u m , π = ρ, and t h e s w e l l i n g p r e s s u r e i s z e r o (P = 0 ) . S w e l l i n g p r e s s u r e can be d e f i n e d as t h e p r e s s u r e e x e r t e d by a g e l when s w e l l i n g i s c o n s t r a i n e d b u t s w e l l i n g s o l v e n t i s a v a i l able. In g e n e r a l , t h e f o l l o w i n g e m p i r i c a l r e l a t i o n s h i p (I), d e v e l o p e d by P o s n j a k i n 1912 (3)> a p p l i e s t o a s w e l l i n g s u b stance:

37

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

38

HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS


Ρ = k X C

(I)

where Ρ i s t h e s w e l l i n g p r e s s u r e , k and η a r e c o n s t a n t s whose v a l u e s a r e u s u a l l y between 2 and 3 , and c i s t h e p o l y m e r n e t w o r k concentration. Since n>l, expression (I) i n d i c a t e s the w e l l known f a c t t h a t t h e s w e l l i n g p r e s s u r e , P, i n c r e a s e s r a p i d l y w i t h the c o n c e n t r a t i o n of the polymer i n the g e l . In t h i s p a p e r , t h e s w e l l i n g p r e s s u r e o f two c l a s s e s o f hydrogels of i n t e r e s t to ophthalmology i s i n v e s t i g a t e d . The f i r s t c l a s s i s a g r o u p o f h i g h l y h y d r a t e d h y d r o g e l s (above a b o u t 80% w a t e r a t s w e l l i n g e q u i l i b r i u m i n w a t e r ) w h i c h i s i n t e n d e d f o r s u r g i c a l use. The s e c o n d c l a s s c o n s i s t s o f h y d r o g e l s u s e d t o m a n u f a c t u r e c o n t a c t l e n s e s , and t h e s e g e l s a r e h y d r a t e d t o a b o u t 40 t o 75% w a t e r a t s w e l l i n g e q u i l i b r i u m i n w a t e r . E f f e c t o f t h e E x t e r n a l S o l u t i o n upon t h e H y d r a t i o n o f Hydrogels. The m a g n i t u d e o f e q u i l i b r i u m s w e l l i n g o f a h y d r o g e l i n an aqueous medium i s d e t e r m i n e d by t h e c h e m i c a l p o t e n t i a l o f water i n the outside s o l u t i o n . The c h e m i c a l p o t e n t i a l o f w a t e r i n t h e o u t s i d e s o l u t i o n i s d e t e r m i n e d by t h e n a t u r e and c o n c e n t r a t i o n of the solutes i n the s o l u t i o n . The s o l u t e s , d e p e n d i n g on t h e i r m o l e c u l a r s i z e , may o r may n o t p e n e t r a t e t h e p o l y m e r network. Some s o l u t e s w h i c h c a n p e n e t r a t e t h e n e t w o r k may i n t e r a c t w i t h t h e p o l y m e r s e g m e n t s , m o d i f y i n g t h e i r s t r e t c h i n g and contracting properties. Nevertheless, a l l solutes i n the gel w a t e r a f f e c t t h e g e l by l o w e r i n g t h e c h e m i c a l p o t e n t i a l o f i t s water. Solution t o n i c i t y i s a b i o l o g i c a l concept. It is related to osmotic p r e s s u r e , but i t l a c k s e x a c t p h y s i c o c h e m i c a l meaning. T h u s , v a r i o u s i s o t o n i c s o l u t i o n s may s w e l l o r d e s w e l l h y d r o g e l s d e p e n d i n g on t h e p e n e t r a t i o n and i n t e r a c t i o n o f t h e s o l u t e s w i t h t h e n e t w o r k segments ( £ ) ( F i g . 1 ) . S w e l l i n g Pressure o f High Water-Content G l y c e r y l Methac r y l a t e H y d r o g e l s and t h e i r O p h t h a l m i c A p p l i c a t i o n s . The s w e l 1 ing pressure-volume r e l a t i o n s h i p of p o l y ( g l y c e r y l methacrylate) h y d r o g e l s (PGMA) i s o f p r a c t i c a l i n t e r e s t f o r t h e d e v e l o p m e n t o f s w e l l i n g or expanding s u r g i c a l i m p l a n t s . A swelling implant i s a d e v i c e t h a t can be p l a c e d i n s i d e an o r g a n o r t i s s u e t h r o u g h a r e l a t i v e l y small i n c i s i o n . By i m b i b i n g a v a i l a b l e body f l u i d i t w i l l s w e l l t o f i l l a c a v i t y or to a l t e r the form of the s u r rounding t i s s u e s (5). To be u s e f u l , a s w e l l i n g i m p l a n t must s w e l l t o s e v e r a l tTmes i t s d r y volume u n d e r t h e c o n d i t i o n s o f implantation. In some a p p l i c a t i o n s , t h e i m p l a n t must e x e r t s u f f i c i e n t s w e l l i n g pressure to counteract the c o n s t r a i n i n g pressure of the surrounding t i s s u e s . Of i n t e r e s t i s a c o h e r e n t v i t r e o u s s u b s t i t u t e w h i c h c o u l d be used t o f i l l t h e v i t r e o u s c a v i t y o f t h e eye ( £ ) , and i n some c a s e s , t h e e n t i r e e y e b a l l (_7).



10

2CH

30Η

.9%

NaCI 2

CaCI 13% 2

UREA 1.63°/o

GLUCOSE 5.51%

SERUM

SERUM VITREOUS ULTRAFILTRATE

Figure 1. PGMA hydrogel, 98% H 0 at equilibrium swelling in distilled water. The bars repre sent the equilibrium swelling of the same hydrogel in diverse isotonic solutions and physiological fluids.

2

m

1 50Η

Τ- 6θΗ

Ζ ζ

80




40

A n o t h e r t y p e o f s w e l l i n g i m p l a n t i s used i n ophthalmology i n t h e s c l e r a l b u c k l i n g procedure i n r e t i n a l detachment s u r g e r y (8). G l y c e r y l m e t h a c r y l a t e monomer (GMA) p r e p a r e d by h y d r o T y s i s o f g l y c i d y l m e t h a c r y l a t e (9·) y i e l d s GMA w i t h s m a l l amounts o f some s t i l l u n i d e n t i f i e d c r o s s l i n k i n g a g e n t . However, h y d r o g e l s w i t h r e p r o d u c i b l e p h y s i c a l and c h e m i c a l p r o p e r t i e s c a n be o b t a i n e d f r o m GMA p r e p a r e d by t h i s p r o c e d u r e . Polymerization is c a r r i e d o u t i n g l a s s molds f i l l e d w i t h aqueous s o l u t i o n s o f GMA w i t h a redox i n i t i a t o r . The monomer d i l u t i o n i n t h e p r e p o l y m e r m i x t u r e determines the e q u i l i b r i u m degree of s w e l l i n g of the r e s u l t i n g hydrogel. The s w e l l i n g p r e s s u r e o f PGMA h y d r o g e l s was o b t a i n e d by e q u i l i b r a t i o n i n s o l u t i o n s o f d e x t r a n ( P h a r m a c i a , mol wt 2 3 6 , 0 0 0 ) , The PGMA s p e c i m e n s were p l a c e d i n d e x t r a n s o l u t i o n s and a l l o w e d t o e q u i l i b r a t e i n t i g h t l y c a p p e d j a r s a t room t e m p e r a t u r e . E q u i l i b r i u m s w e l l i n g was r e a c h e d a f t e r f o u r t o t e n w e e k s , d e p e n d i n g on t h e c o n c e n t r a t i o n o f t h e s o l u t i o n , and on t h e s i z e o f t h e specimen. When e q u i l i b r i u m s w e l l i n g was r e a c h e d , t h e d e x t r a n c o n c e n t r a t i o n was d e t e r m i n e d f r o m a l i q u o t s o f t h e s o l u t i o n . The o s m o t i c p r e s s u r e o f t h e d e x t r a n a t d i f f e r e n t c o n c e n t r a t i o n s was determined osmometrically (4). The d e x t r a n m o l e c u l e s Tn w a t e r s o l u t i o n have an e l l i p s o i d a l shape. The d i a m e t e r o f t h e d e x t r a n m o l e c u l e s u s e d i n t h e s e e x p e r i m e n t s i s a b o u t 270 Â ( 1 0 ) . The d e x t r a n m o l e c u l e s a r e n o t l i k e l y t o p e n e t r a t e i n t o PGMTThydrogels b o t h b e c a u s e a ) t h e average pore s i z e o f the hydrogels i s s m a l l e r than the s i z e of t h e d e x t r a n m o l e c u l e s ( f o r i n s t a n c e , PGMA h v d r o g e l s o f 94% H 0 have an a v e r a g e p o r e d i a m e t e r o f a b o u t 124 A)(1_1_), and b) when à h i g h l y hydrated gel i s placed i n a dextran s o l u t i o n , the osmotic d e h y d r a t i o n o f the gel i s f a s t e r than the d i f f u s i o n o f the dextran molecules i n t o the g e l . As a g e l d e h y d r a t e s , p o r e s i z e i s r e d u c e d , f u r t h e r l i m i t i n g p e n e t r a t i o n by l a r g e d e x t r a n m o l e c u l e s . F i g u r e 2 g i v e s t h e s w e l l i n g p r e s s u r e o f s e v e r a l PGMA h y d r o gels versus the " s w e l l i n g r a t i o " (q). The s w e l l i n g r a t i o i s d e f i n e d as t h e volume o f t h e s w o l l e n g e l o v e r t h e volume o f t h e same g e l i n t h e d r y s t a t e . The " s w e l l i n g r a t i o " was c a l c u l a t e d f r o m t h e " d e g r e e o f s w e l l i n g " ( γ ) , t h e d e n s i t y o f t h e s w o l l e n g e l ( d ) , and t h e d e n s i t y of the dry gel ( d ) , according to (II): 2

0

γ i s the r a t i o of the weights of the swollen gel to the dry gel (£). The d e n s i t i e s were o b t a i n e d f r o m F i g u r e 3 , w h i c h g i v e s t h e d e n s i t y o f a PGMA h y d r o g e l v e r s u s t h e w e i g h t f r a c t i o n o f w a t e r i n t h e s w o l l e n g e l (Cw = % H 0 / 1 0 0 ) . D e n s i t i e s w e r e d e t e r m i n e d by t h e h y d r o s t a t i c w e i g h i n g method. G e l s were weighed both i n a i r , 2


Vapor Pressure and Swelling

REFOJO

41

Pressure


2.

5

10 15 20

30

40

50

60

70

125.2

q = VOL. SWOLLEN GEL + VOL. DRY G E L

Figure 2. Swelling pressure vs. "swelling ratio" of several PGMA hydrogels. The equilibrium swelling of the PGMA hydrogels in distilled water is given for each swelling pressure curve in the graph.


42


and immersed i n η - h e p t a n e a t room t e m p e r a t u r e , Cw b y :


γ

=

γ i s r e l a t e d to

TO

The d e n s i t y o f t h e d i f f e r e n t PGMA h y d r o g e l s was o b t a i n e d from F i g u r e 3 assuming t h a t the d e n s i t i e s o f the d r y g e l s ( x e r o g e l s ) and h y d r o g e l s were n o t a f f e c t e d a p p r e c i a b l y by t h e amount of crosslinkage. The r e s u l t s g i v e n i n F i g u r e 2 show t h a t a s u b s t a n t i a l amount o f w a t e r i s removed f r o m h i g h l y h y d r a t e d h y d r o g e l s ( j e l l i e s ) when t h e y a r e s u b j e c t e d t o a s l i g h t c o m p r e s s i o n . Thus, the volume o f PGMA h y d r o g e l c o n t a i n i n g 9 8 . 9 % H 0 by w e i g h t (q = 1 2 5 . 6 ) was more t h a n h a l v e d i n volume (q = 45) u n d e r a b o u t 1 mm Hg o s m o t i c p r e s s u r e . T h e s e j e l l i e s exude l i q u i d w a t e r when t h e y a r e a l l o w e d t o s t a n d u n d e r t h e i r own w e i g h t i n t h e a i r . As t h e water content i n the hydrogel decreases, the pressure r e q u i r e d to compress w a t e r o u t o f t h e g e l i n c r e a s e s . H e n c e , PGMA w i t h 95% H 0 by w e i g h t (q = 30) a t e q u i l i b r i u m i n w a t e r l o s t a b o u t one t h i r d o f i t s volume o f w a t e r (q = 20) u n d e r o n l y a b o u t 4 mm Hg, b u t PGMA h y d r o g e l w i t h 82% H 0 by w e i g h t (q = 6.9) l o s t p r a c t i c a l l y no w a t e r u n d e r t e n t i m e s as much o s m o t i c p r e s s u r e . The r e l a t i o n s h i p o f h y d r a t i o n by w e i g h t , Cw, and s w e l l i n g r a t i o by volume ( q ) i s g i v e n b y : 2

2

2

q

"

(

T^CW~

(IV)

H e n c e , when t h e v a l u e o f Cw i s n e a r o n e , s u c h as i n j e l l i e s , s m a l l d i f f e r e n c e s i n h y d r a t i o n r e p r e s e n t s u b s t a n t i a l volume changes. The s w e l l i n g p r e s s u r e p r o p e r t i e s o f j e l l i e s and h y d r o g e l s a r e i m p o r t a n t f r o m t h e p o i n t o f v i e w o f t h e two k i n d s o f s w e l l i n g i m p l a n t s m e n t i o n e d a b o v e , a v i t r e o u s s u b s t i t u t e and a s c l e r a l b u c k l i n g d e v i c e . A v i t r e o u s s u b s t i t u t e must m i m i c t h e n a t u r a l v i t r e o u s body, which i s a h i g h l y h y d r a t e d j e l l y . The g e l i s implanted i n i t s dry s t a t e i n t o the e y e b a l l through the s m a l l e s t p o s s i b l e i n c i s i o n . Then i t a b s o r b s a v a i l a b l e i n t r a o c u l a r f l u i d , s w e l l i n g f r e e l y as l o n g as i t does n o t a d j o i n t h e w a l l s o f t h e eye, u n t i l i t f i l l s the v i t r e o u s c a v i t y . F u l l y swollen, the i m p l a n t must o c c u p y t h e v i t r e o u s c a v i t y w h i l e e x e r t i n g a minimum of pressure against the extremely s e n s i t i v e r e t i n a . The s e c o n d t y p e o f s w e l l i n g i m p l a n t i s p l a c e d on t h e o u t s i d e o f t h e e y e b a l l , i n t h e s c l e r a . T h i s i m p l a n t , upon s w e l l i n g , e x e r t s p r e s s u r e t o b u c k l e t h e w a l l o f t h e eye i n w a r d , t h e r e b y approximating the choroid that c a r r i e s the blood supply to a


2.

REFOJO

43

Vapor Pressure and Swelling Pressure


detached r e t i n a . Such an i m p l a n t must be s o f t t o a v o i d p r e s s u r e n e c r o s i s i n t h e s c l e r a , b u t n o t so f r a g i l e t h a t i t w i l l c r u m b l e under p r e s s u r e . About a f i v e - f o l d s w e l l i n g a g a i n s t t h e c o n s t r a i n ing t i s s u e i s s u f f i c i e n t . For t h i s a p p l i c a t i o n , a hydrogel w i t h 80 t o 85% w a t e r c o n t e n t a t e q u i l i b r i u m s w e l l i n g i n w a t e r a p p e a r s t o be most u s e f u l . V a p o r P r e s s u r e and S w e l l i n g P r e s s u r e o f H y d r o g e l C o n t a c t Lens M a t e r i a l s . S i n c e W i c h t e r l e and L i m ( 1 2 ) f i r s t p r o p o s e d t h e use o f h y d r o g e l s f o r c o n t a c t l e n s e s and otTiêr m e d i c a l d e v i c e s , many new h y d r o g e l s have been d e v e l o p e d ( 1 3 ) . The f i r s t commerc i a l h y d r o g e l c o n t a c t l e n s e s w e r e made o f s l i g h t l y c r o s s l i n k e d 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 ) (PHEMA), w h i c h i s s t i l l t h e m a t e r i a l most o f t e n used i n t h e s o f t l e n s i n d u s t r y . A second compound used t o make h y d r o g e l c o n t a c t l e n s e s i s v i n y l p y r r o l i d o n e ( V P ) , i n t h e f o r m o f a c o p o l y m e r o f HEMA and V P , P(HEMA/VP) ( T 4 ) . L e n s e s w h i c h c o n t a i n V P , b u t no HEMA a r e a l s o made, s u c h as a c o p o l y m e r o f m e t h y l m e t h a c r y l a t e and V P , P(MMA/VP) ( 1 5 ) . As d i f f e r e n t h y d r o g e l c o n t a c t l e n s e s become a v a T T a b l e , i t i s o f i n t e r e s t t o i n v e s t i g a t e and t o compare t h e i r r e l a t i v e w a t e r retention. Differences i n hydration at swelling equilibrium are i m p o r t a n t i n t h e e v a l u a t i o n o f t h e o p t i c a l and p h y s i o l o g i c a l performance o f t h e l e n s e s . This study determined the e q u i l i b r i u m s w e l l i n g o f s e v e r a l hydrogel c o n t a c t l e n s m a t e r i a l s under o s m o t i c and m e c h a n i c a l p r e s s u r e , as w e l l as t h e w a t e r a c t i v i t y o f t h e h y d r o g e l s under v a r i o u s s w e l l i n g c o n d i t i o n s . 1. D e t e r m i n a t i o n o f S w e l l i n g P r e s s u r e o f a PHEMA H y d r o g e l by E q u i l i b r i u m S w e l l i n g i n D e x t r a n S o l u t i o n . PHEMA I was o b t a i n e d by s o l u t i o n p o l y m e r i z a t i o n ( 1 6 ) . S t e q u i l i b r i u m s w e l l i n g i n d i s t i l l e d w a t e r , i t c o n t a i n s 40% H 0 by w e i g h t on a w e t b a s i s . PHEMA I s p e c i m e n s were p l a c e d i n d e x t r a n - 4 0 s o l u t i o n s and a l l o w e d t o e q u i l i b r a t e i n t i g h t l y capped j a r s a t room t e m p e r a t u r e [ D i f f e r e n t v a l u e s have been r e p o r t e d f o r a v e r a g e p o r e d i a m e t e r o f PHEMA I h y d r o g e l s ; t h e maximum i s 35 S ( 1 3 ) . D e x t r a n - 4 0 i n w a t e r has a m o l e c u l a r d i a m e t e r o f a b o u t 105 Â ( 1 0 ) ] . Equilibrium s w e l l i n g was r e a c h e d a f t e r two months. After e q u i l i b r a t i o n , the d e x t r a n c o n c e n t r a t i o n i n t h e j a r was d e t e r m i n e d g r a v i m e t r i c a l l y . The o s m o t i c p r e s s u r e ( π , i n a t m . ) o f d e x t r a n (mol wt 2 6 , 0 0 0 ) was calculated according to equation (V): 2

π = A-jC + A c

2

2

+ A c

(V)

3

3

where c i s t h e c o n c e n t r a t i o n ( i n g » c m " ) and A = 0 . 8 5 2 a t m » c m . g " , A = 1 3 . 5 2 a t m - c m g ~ , and A = 6 6 . 8 a t m - c m - g " a r e t h e v i r i a l c o e f f i c i e n t s a c c o r d i n g t o V i n k ( V 7 ) . The r e s u l t s o f t h e s w e l l i n g p r e s s u r e o f PHEMA I o b t a i n e d by t h i s p r o c e d u r e a r e g i v e n in Figs. 4,5. 3

3

x

1

6

2

2

9

3

3




1.4 -η

~t ι » ι » » » 11111 » 1111111M 111 f 1111111111 f 11111 111 > π 11111 i i ι » 111111 π 11 n 111 » 11 M » η ι n n I n ι n m 1 I M 11| 10

20

30

40

50

I

60

70

80

90

100

H 0 2

Figure 3. Density of PGMA hydrogel, 96% H 0 at equilibrium swelling, vs. hydration of the gel. The curve was printed by a computer using the least squares method applied to the data points. 2

Φ

I I I I I I

ι

I!

5°'

a of

SI

1/

/

Q

·/# 'ο

^ / /

4 I

Figure 4. Dehydration of two PHEMA hydrogeh under osmotic and mechanical pressure

- ι — ι — ι — r -1 -2 - 3 -4 WEIGHT

*. H

2

0 LOST


2.

REFOJO


45

2. D e t e r m i n a t i o n o f S w e l l i n g P r e s s u r e o f a PHEMA H y d r o g e l by E q u i l i b r i u m S w e l l i n g Under M e c h a n i c a l C o m p r e s s i o n . PHEMA I I was o b t a i n e d by b u l k p o l y m e r i z a t i o n ( 1 6 ) . I t c o n t a i n s 3 8 . 5 % H 0 a t e q u i l i b r i u m swelling i n d i s t i l l e d water. C i r c u l a r pieces o f PHEMA I I h y d r o g e l 20 mm i n d i a m e t e r (1 t o 2 mm t h i c k ) were p l a c e d between two s i n t e r e d g l a s s d i s k s i n a w a t e r b a t h u n d e r i r o n w e i g h t s ( f i v e t o t e n k i l o g r a m s ) , w h i c h were s e p a r a t e d f r o m t h e u p p e r s i n t e r e d g l a s s d i s c by a p l a s t i c c y l i n d e r p r o t r u d i n g above t h e s u r f a c e o f t h e w a t e r b a t h . The w a t e r b a t h c o n t a i n i n g t h e h y d r o g e l d i s c and t h e w e i g h t s on t o p o f i t were k e p t i n a c l o s e d chamber t o p r e v e n t e v a p o r a t i o n . Equilibrium swelling of t h e h y d r o g e l was o b t a i n e d a f t e r s e v e r a l weeks o f c o m p r e s s i o n . The r e l a t i o n s h i p between h y d r a t i o n and s w e l l i n g p r e s s u r e o f PHEMA I I o b t a i n e d by t h i s p r o c e d u r e i s shown i n F i g s . 4 , 5 . W h i l e a s l i g h t p r e s s u r e e a s i l y removes w a t e r f r o m t h e h i g h w a t e r - c o n t e n t h y d r o g e l s ( F i g . 2 ) , i t i s more d i f f i c u l t t o e x p e l w a t e r by o s m o t i c o r m e c h a n i c a l means f r o m h y d r o g e l s h a v i n g l o w w a t e r - c o n t e n t , s u c h as t h e commonly u s e d PHEMA c o n t a c t l e n s h y d r o g e l s , w h i c h c o n t a i n a b o u t 40% w a t e r a t e q u i l i b r i u m s w e l l i n g ( F i g s . 4 , 5 ) . S i m i l a r r e s u l t s a r e expected from hydrogels c o n t a i n i n g l e s s t h a n 80% w a t e r a t e q u i l i b r i u m ( F i g . 2 ) . Most h y d r o g e l c o n t a c t l e n s m a t e r i a l s c o n t a i n a b o u t 35 t o 75% w a t e r a t equilibrium in physiological saline solution. I t requires subs t a n t i a l p r e s s u r e t o remove w a t e r f r o m h y d r o g e l l e n s e s , w h i c h i s a d v a n t a g e o u s b e c a u s e i f l i d p r e s s u r e were t o s q u e e z e w a t e r f r o m the l e n s e s i n t h e eye t h e i r performance would s u f f e r . Of c o u r s e , t h e o p t i c a l p r o p e r t i e s , t h e s h a p e , and t h e s i z e o f a h y d r o g e l l e n s a r e a l l d e p e n d e n t on i t s w a t e r - c o n t e n t .


2

3. D e t e r m i n a t i o n o f Water A c t i v i t y i n H y d r o g e l s . One way to f a c i l i t a t e water l o s s from hydrogels i s t o decrease t h e r e l a t i v e humidity; t h i s decreases the chemical p o t e n t i a l o f the water vapor i n t h e s u r r o u n d i n g atmosphere t o a low v a l u e . It i s well known t h a t h y d r o g e l s c a n l o s e w a t e r r a p i d l y by e v a p o r a t i o n . When t h i s happens, t h e network, which i s under e l a s t i c t e n s i o n , w i l l contract. As t h e h y d r o g e l d e h y d r a t e s , t h e c h e m i c a l p o t e n t i a l o f t h e w a t e r r e m a i n i n g i n t h e g e l d e c r e a s e s and i s m a n i f e s t e d a s an i m b i b i t i o n p r e s s u r e , which i s equal i n magnitude t o t h e osmotic o r m e c h a n i c a l p r e s s u r e needed t o compress t h e g e l t o t h e same p a r t i a l l y dehydrated s t a t e . The w a t e r r e t e n t i o n , o r w a t e r e s c a p i n g t e n d e n c y ( f u g a c i t y ) o f h y d r o g e l s was d e t e r m i n e d ( F i g s . 6 , 7 ) by m e a s u r i n g t h e e q u i l i b r i u m r e l a t i v e h u m i d i t y (% ERH) o f t h e h y d r o g e l s a t 3 2 ° C , w h i c h i s approximately the surface temperature of the eye. F o u r d i f f e r e n t h y d r o g e l s were u s e d i n t h e s e e x p e r i m e n t s : ( a ) a PHEMA h y d r o g e l w i t h 4 2 . 5 % H 0 a t e q u i l i b r i u m s w e l l i n g ; ( b ) a c o p o l y m e r o f m e t h y l m e t h a c r y l a t e and v i n y l p y r r o l i d o n e , P(MMA/ V P ) , used i n t h e manufacture o f hydrogel c o n t a c t l e n s e s under t h e t r a d e name S a u f I o n ( c o n t a i n i n g a b o u t 70% H 0 a t e q u i l i b r i u m s w e l l i n g i n d i s t i l l e d w a t e r ) ; ( c ) a c o p o l y m e r o f HEMA and VP 2

2




46

-/•A-r 35

36

37

3 8 39

τ — ι 38 39

37

1 — - r 4 0 41

W E I G H T 7o H 2 O

Figure 5. Swelling pressure of two PHEMA hydrogels equilibrated under mechanical pres sure (PHEMA II, 38.5% H 0) and osmotic pressure (PHEMA I, 40% H 0), respectively 2

2

WATER ACTIVITY ia ) w

Figure 6.

Water sorption isotherms of hydrogel contact lens materials



2.

REFOJO

47


[P(HEMA/VP)], known as PHP and a l s o used i n c o n t a c t l e n s e s . It c o n t a i n s a b o u t 45% w a t e r a t e q u i l i b r i u m s w e l l i n g i n w a t e r ; and (d) a c o p o l y m e r o f MMA and GMA [P(GMA/MMA)] w h i c h c o n t a i n s 4 1 % water a t e q u i l i b r i u m s w e l l i n g . The e q u i l i b r i u m r e l a t i v e h u m i d i t y ( w a t e r a c t i v i t y ) was determined w i t h t h e hydrogel i n a c l o s e d c o n t a i n e r having a c a l i b r a t e d h u m i d i t y and t e m p e r a t u r e s e n s o r c o n n e c t e d by c a b l e t o a r e c e i v e r (Hygrodynamics U n i v e r s a l Hygrometer I n d i c a t o r , A m e r i can I n s t r u m e n t C o . , S i l v e r S p r i n g s , M a r y l a n d ) . The chamber c o n t a i n i n g t h e h y d r o g e l and t h e s e n s o r was m a i n t a i n e d i n a c o n s t a n t t e m p e r a t u r e d r y i n c u b a t o r a t 32°C. When r e l a t i v e h u m i d i t y r e a c h e d e q u i l i b r i u m , t h e w e i g h t o f t h e g e l was r e c o r d e d . The o p e r a t i o n was r e p e a t e d f o r d i f f e r e n t s t a t e s o f h y d r a t i o n t o o b t a i n t h e isotherms i n which t h e weight o f water sorbed per u n i t o f d r y p o l y m e r w e i g h t was p l o t t e d w i t h r e f e r e n c e t o w a t e r a c t i v i t y ( F i g . 6 ) . The w a t e r a c t i v i t y was o b t a i n e d u n d e r d e s o r p t i o n c o n d i t i o n s , e x c e p t f o r P(HEMA/VP), w h i c h was t e s t e d u n d e r r e s o r p tion conditions. The i s o t h e r m s o b t a i n e d have t h e s t a n d a r d s i g m o i d shape o f w a t e r s o r p t i o n i n p o l y m e r s . F i g u r e 7 shows t h e same r e s u l t s o f w a t e r a c t i v i t y v e r s u s w a t e r c o n t e n t i n t h e h y d r o g e l s , e x p r e s s e d i n p e r c e n t h y d r a t i o n on a w e t b a s i s , w h i c h i s c o n v e n t i o n a l l y used i n hydrogel l i t e r a t u r e . ERH ( r e l a t i v e h u m i d i t y o f t h e s p a c e a r o u n d t h e h y d r o g e l , when m o i s t u r e w i l l n e i t h e r l e a v e n o r e n t e r t h e h y d r o g e l ) i s a r a t i o o f e x i s t i n g p a r t i a l vapor pressure o f water i n t h e hydrogel (P ) t o t h e s a t u r a t i o n w a t e r v a p o r p r e s s u r e i n t h e a i r (P ). It i s given by:

% ERH =

15S. χ

100

(VI)

P /Ps i s , o f course, the "water a c t i v i t y " ( a ) i n t h e hydrogel a t the given temperature. Thus, t h e water a c t i v i t y i n hydrogels a t d i f f e r e n t l e v e l s o f h y d r a t i o n c a n be d e t e r m i n e d d i r e c t l y and c o u l d be u s e d t o c a l c u l a t e t h e s w e l l i n g p r e s s u r e ( P ) o f t h e hydrogels a t d i f f e r e n t hydrations according t o : e

w

P = P l n i w w

(VII)

where R i s t h e u n i v e r s a l gas c o n s t a n t , Τ t h e a b s o l u t e t e m p e r a t u r e , and V ^ t h e p a r t i a l m o l a r volume o f w a t e r . Under t h e e x p e r i mental c o n d i t i o n s ( F i g . 7 ) , small d i f f e r e n c e s i n water a c t i v i t y i n t h e h y d r o g e l s w e r e n o t d e t e c t a b l e a t h y d r a t i o n s above a b o u t 30% w a t e r . Not o n l y t h e hydrogels a t e q u i l i b r i u m s w e l l i n g i n w a t e r , b u t l i q u i d w a t e r a s w e l l , gave an ERH j u s t b e l o w t h e t r u e v a l u e o f 100%. T h i s i s a l i m i t a t i o n o f t h e h y g r o s e n s o r u s e d .

Amcnccn Chemical Socisîy Library 1155 16th St. N. 11

In Hydrogels for Medical and Related Applications; Andrade, J.; ACS Symposium Series; American Chemical Washington. 0. C. Society: 20036Washington, DC, 1976.

48


B e c a u s e o f t h e l a r g e v a l u e o f RT/V ( a b o u t 1390 a t m . a t 32°C) a v e r y s m a l l v a p o r - p r e s s u r e decrease can r e s u l t i n a s u b s t a n t i a l increase in swelling pressure. Thus, the hygrometer t e c h n i q u e c a n n o t be used t o d e t e r m i n e t h e s w e l l i n g p r e s s u r e o f h y d r o g e l s near e q u i l i b r i u m h y d r a t i o n . The s o r p t i o n i s o t h e r m s o f f o u r h y d r o g e l s a r e g i v e n i n F i g u r e 6. The s i g m o i d shape o f t h e c u r v e s may be an i n d i c a t i o n o f t h e t h r e e c l a s s e s o f w a t e r w h i c h , a c c o r d i n g t o L e e , J h o n , and A n d r a d e ( 1 8 ) , may be p r e s e n t i n t h e s e h y d r o gels. Because o f t h e d i f f i c u l t y o f o b t a i n i n g t h e e q u i l i b r i u m r e l a t i v e humidity of a x e r o g e l , the s e c t i o n of the curves at l o w e r h y d r a t i o n a r e n o t as s h a r p l y d e f i n e d as t h e o t h e r two sections. The ERH i s a measure o f " f r e e w a t e r - v a p o r p r e s s u r e " w h i c h i s , i n e s s e n c e , a measurement o f t h e " f r e e d o m o f w a t e r " o r i t s "escaping tendency" (19). T h e r e f o r e , the hygrodynamics e x p e r i ments do g i v e a good i n d i c a t i o n o f t h e p r o p o r t i o n o f " f r e e " w a t e r o f h y d r a t i o n i n h y d r o g e l s , t h a t i s , w a t e r i n t h e aqueous phase o f t h e h y d r o g e l w i t h t h e same v a p o r p r e s s u r e as l i q u i d w a t e r a t t h e same t e m p e r a t u r e . Water a c t i v i t y v e r s u s h y d r o g e l h y d r a t i o n ( F i g . 7) shows t h a t t h e w a t e r o f h y d r a t i o n i n h y d r o g e l s above a b o u t 25 t o 30% has a p p r o x i m a t e l y t h e same v a p o r p r e s s u r e as l i q u i d w a t e r . F i g u r e 8 , t h u s , r e p r e s e n t s t h e amounts o f " f r e e " w a t e r ( a - l ) and somewhat " b o u n d " w a t e r ( a < l ) i n h y d r o g e l s as r e p l o t t e d f r o m F i g u r e 6. The amount o f " b o u n d " w a t e r , a b o u t 30% o f w a t e r i n t h e h y d r o g e l s , i s s i m i l a r t o t h e amounts t h a t L e e , J h o n , and A n d r a d e (18) a s s i g n e d as " b o u n d " p l u s " i n t e r f a c i a l " w a t e r . The r e s t o f the water of hydration i n the hydrogels i s " f r e e " or " b u l k " water. T h u s , t h e c o n t a c t l e n s m a t e r i a l s examined a l l seem s u b j e c t t o l o s i n g s u b s t a n t i a l amounts o f w a t e r by e v a p o r a t i o n . The f a c t t h a t a b o u t 30% o f t h e w a t e r i s r e t a i n e d more t e n a c i o u s l y i n t h e l e n s m a t e r i a l s does n o t seem t o have any p r a c t i c a l i m p o r t a n c e f r o m t h e p o i n t o f v i e w o f w a t e r r e t e n t i o n o f h y d r o g e l l e n s e s and o p t i c a l performance. Of c o u r s e , f r e q u e n t b l i n k i n g and good t e a r s u p p l y a r e e s s e n t i a l f o r good r e s u l t s w i t h a l l h y d r o g e l c o n t a c t lenses.


W

w

w

O s m o t i c E f f e c t s Due t o t h e Aqueous Phase o f a H y d r o g e l Contact Lens. In a d d i t i o n t o t h e s w e l l i n g p r e s s u r e ( o r i m b i b i t i o n pressure) of h y d r o g e l s , which i s a p r o p e r t y of the polymer phase o f g e l s , t h e r e a r e o t h e r o s m o t i c e f f e c t s a t t r i b u t a b l e t o t h e aqueous p h a s e t h a t a r e o f p a r t i c u l a r i n t e r e s t i n t h e c o n t a c t lens f i e l d . Most o f t h e aqueous p h a s e o f a h y d r o g e l c a n be f r e e l y e x c h a n g e d w i t h t h e s u r r o u n d i n g aqueous media by d i f f u s i o n . The movement o f w a t e r , i o n s and o t h e r d i s s o l v e d s u b s t a n c e s i s r e s t r i c t e d t o some d e g r e e by f r i c t i o n w i t h t h e p o l y m e r n e t w o r k . H o w e v e r , due t o t h e l a r g e s u r f a c e a r e a o f c o n t a c t l e n s e s r e l a t i v e t o t h e i r t h i c k n e s s , most o f t h e aqueous phase w i l l i n t e r c h a n g e w i t h t h e t e a r s i n a few m i n u t e s .


REFOJO

Vapor


2.

Pressure and Swelling

49

Pressure

70

60

H

_i LU

Ο

s

5 0

RHEMA/VP) 1—1 PHEMA RGMA/MMA)

CL ^

40

WATER ACTIVITY ·

I » = 30

1

Η WATER ACTIVITY < 1

Figure 8. Amounts of "free" water (a ~ I) and "bound" water (a < 1) in hydrogel contact lens materials w

w



50


The aqueous phase i n a c o n t a c t l e n s can be i s o t o n i c , h y p o tonic or hypertonic with respect to tears. When a h y d r o g e l l e n s i s e q u i l i b r a t e d i n i s o t o n i c s a l i n e s o l u t i o n (0.9% N a C l ) , the aqueous phase o f t h e h y d r o g e l i s i s o t o n i c t o t h e normal t e a r s . When s u c h a l e n s i s p l a c e d i n t h e e y e , t h e r e w i l l be an i n t e r change o f i t s aqueous phase and t h e t e a r f i l m , b u t t h e t e a r t o n i c i t y w i l l n o t change i n t h e p r o c e s s o f e q u i l i b r a t i o n o f t h e lens. The p o s s i b l e change i n s i z e and o p t i c s o f a l e n s f r o m e q u i l i b r i u m s w e l l i n g i n i s o t o n i c s o l u t i o n and i n t e a r s i s n e g l i gible. I f the hydrogel lens i s wetted w i t h tap or d i s t i l l e d water p r i o r t o p l a c i n g i t i n t h e e y e , t h e aqueous phase o f t h e l e n s w i l l be h y p o t o n i c t o t e a r s . Water w i l l move f r o m t h e l e n s t o t h e tears. The l e n s w i l l t h e n c o n t r a c t , o f t e n a d h e r i n g t e n a c i o u s l y t o t h e c o r n e a and c a u s i n g much d i s c o m f o r t . Exchange o f t e a r s and t h e aqueous phase o f t h e g e l w i l l t a k e p l a c e u n t i l a s t a t e o f i s o t o n i c i t y i s r e a c h e d and t h e n t h e l e n s w i l l r e l e a s e f r o m i t s adhesion to the cornea. I f t h e l e n s i s p l a c e d i n a s o d i u m c h l o r i d e s o l u t i o n o f more t h a n 0 . 9 % , t h e aqueous phase o f t h e h y d r o g e l w i l l be h y p e r t o n i c to t e a r f i l m . As t h e l e n s i s p l a c e d i n t h e e y e , w a t e r w i l l be drawn o s m o t i c a l l y f r o m t h e t e a r f i l m i n t o t h e l e n s , b u t s a l t w i l l a l s o d i f f u s e from the lens i n t o the t e a r . T h i s w i l l change t h e t o n i c i t y of the tears to a hypertonic s t a t e . The l e n s e f f e c t can be q u i t e l a r g e as t h e t o t a l volume o f t h e t e a r f i l m and t h e t e a r meniscus i s roughly comparable to the water c o n t e n t of a hydrogel lens. The h y p e r t o n i c t e a r s w i l l d e h y d r a t e t h e c o r n e a l e p i t h e l i u m r e s u l t i n g i n o c u l a r d i s c o m f o r t ( i t c h i n g ) to the p a t i e n t . As t h e i s o t o n i c i t y of the tears i s r e - e s t a b l i s h e d through d i l u t i o n , the sensation of comfort i s again r e s t o r e d . The e x i s t e n c e o f a t h i n aqueous f i l m between a h y d r o g e l l e n s and t h e c o r n e a l e p i t h e l i u m i s a m a t t e r o f c o n t r o v e r s y . If the lens i s i n d i r e c t contact w i t h the cornea, the osmotic e f f e c t due t o t h e aqueous phase o f t h e h y d r o g e l l e n s w i l l be a c t i n g d i r e c t l y upon t h e c o r n e a l e p i t h e l i u m w i t h t h e same r e s u l t s d i s cussed above.

Abstract The swelling pressure of two types of hydrogels, which were classified according to application and hydration, were investigated. 1. Poly(glyceryl methacrylate) (PGMA) hydrogels which are intended for surgical uses in the eye, are divided into two subgroups, a) hydrogels of about 80 to 85%H Oat equilibrium swelling, for scleral buckling procedures in retinal detachment surgery, and b) hydrogels of above 98%H Oat equilibrium swelling, for vitreous implantation. The swelling pressure-volume relationship of these hydrogels was determined with dextran solutions. 2. Hydrogel contact lens materials (40-75%H Oat equilibrium). The swelling pressure of PHEMA hydrogels was determined by equilibration under osmotic and mechanical pressure. 2

2

2


2.

REFOJO

Vapor

Pressure and Swelling

Pressure

51

Although slight pressure will remove water from highly hydrated hydrogels, it is very difficult to expel water from medium hydra tion (40-80% HO) hydrogels. The equilibrium relative humidity at different states of hydration of PHEMA, P(HEMA/VP), P(MMA/VP), and P(GMA/MMA) was investigated. The results show that up to 30% HO, the water activity in the hydrogels is below the activity for pure water. However, all water above 30% hydration up to equilibrium swelling has the same vapor pressure as pure water. 2

2


Acknowledgements The author is indebted to Dr. F. Holly for his helpful discussion. Ms. F.L. Leong provided technical assistance. A. Seidman provided editorial assistance. This study was supported by PHS Grant EY-00327 of the National Eye Institute, National Institutes of Health. Literature Cited 1. 2. 3.

Katchalsky, Α.: Prog. Bioph. (1954) 4:1 Rijke, A.M., and Prins, W.: J. Polym. Sci. (1962) 59:171 Posnjak, E.: Kolloidchem. Beih. (1912) 3:417, in M.R. Kruyt, Ed. Colloid Science II. Elsevier Publishing Co., New York, 1949,p557 4. Refojo, M.F.: Anales Qui. (Madrid) (1972) 68:697 5. Refojo, M.F.: J. Biomed. Mater. Res. Symposium (1971) 1:179 6. Daniele, S., Refojo, M.F., Schepens, C.L., and Freeman, H.M.: Arch. Ophthal. (1968) 80:120 7. Dohlman, C.H., Refojo, M.F., Webster, R.G., Pfister, R.R., and Doane, M.G.: Arch. Ophthal. (Paris) (1969) 29:849 8. Calabria, G.A., Pruett, R.C., and Refojo, M.F.: Arch. Ophthal. (1971) 86:77 9. Refojo, M.F.: J. Appl. Polym. Sci. (1965) 9:3161 10. Senti, F.R., Hellman, N.N., Ludwig, N.M., Babcock, G.E., Tobin, R., Glass, C.A., and Lamberts, B.L.: J. Polym. Sci. (1955) 17:527 11. Refojo, M.F.: J. Appl. Polym. Sci. (1965) 9:3417 12. Wichterle, O. and Lim, D.: Nature (1960) 185:117 13. Refojo, M.F.: Encycl. Polymer. Sci. Technol. Supplement (in press) 14. Seiderman, M.: U.S. Patent 3,721,657 (1973) 15. Frankland, J.D., and Highgate, D.J.: Ger. Offen. (1973) No. 2,312,470 [in Chem. Abstr. 80:27872z] 16. Refojo, M.F., and Yasuda, H.: J. Appl. Polymer Sci. (1965) 9:2425 17. Vink, H.: European Polym. J. (1971) 7:1411 18. Lee, M.B., Jhon, M.S., and Andrade, J.D.: J. Colloid and Interface Sci. (1975) 51:225 19. Quinn, F.C.: Reprint No. 472, Am. Instrument Co., Div. Travenol Labs, Silver Springs, Md. In Hydrogels for Medical and Related Applications; Andrade, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

Vapor Pressure and Swelling Pressure of Hydrogels

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