Hydrogels for Medical and Related Applications - ACS Publications

4 The Role of Water in the Osmotic and Viscoelastic

Downloaded by UNIV OF CALIFORNIA SANTA CRUZ on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch004

Behavior of Gel Networks MU SHIK JHON,* SHAO MU MA, SACHIKO HATTORI, DONALD E. GREGONIS, and JOSEPH D. ANDRADE Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112 The existence of an ordered structure at water/solid inter faces has been generally accepted. A structured molecule possess certain preferred orientations and cannot move independent of its neighboring molecules. In the case of water the word "structured" should not be misinterpreted; we do not mean that water possess long range orderness. By "structure" we mean the orderness rela tive to that in bulk water. In a strict sense, even the molecules in bulk water are structured because of hydrogen bonding and other near neighbor interactions. Drost-Hansen (1_) has discussed a three-layer model for the structure of water near certain water/solid interfaces. According to this model, water molecules near the solid surface are struc tured; those sufficiently far away from the surface have bulk water structure and those in between have decreasing orderness as a function of distance from the interface. Others (2,3) have indicated the existence of three states of water in natural macro molecular gels (2) or in membranes of cellulose acetate (3). Jhon and Andrade (4) proposed a three-state model of water in hydrogel systems. They suggested that three classes of water exist in hy drogels, namely X water (bulk water), Ζ water (bound water), and Y water (intermediate forms or interfacial water). Following this, Lee, Jhon and Andrade (5,6) tested the model by thermal expansion, specific conductivity, differential scanning calorimetry, and proton spin-lattice nuclear magnetic relaxation studies for poly(hydroxyethyl methacrylate) (PHEMA gels). Very recently, Choi, Jhon and Andrade {7) again extended the model by means of thermal expansion, specific conductivity, and dielectric relaxation studies for (2,3-dihydroxypropyl methacrylate) gels (DHPMA gels). In this paper theories for the osmotic and viscoelastic behavior of hydrogels are developed in terms of water structure. Some experimental results on the viscoelastic behavior of hydrogels are presented. *0n leave from Korea Advanced Institute of Science, Seoul, Korea; to whom correspondence should be addressed. 60

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

4.

JHON

ET AL.

S w e l l i n g and O s m o t i c


61

Water in the Behavior of Gel Networks

Pressure

A c c o r d i n g t o F l o r y (8), t h e n e t w o r k s t r u c t u r e mav have s e v e r a l roles. I n a s o l v e n t t h e n e t w o r k d i s s o l v e s and t a k e s t h e r o l e o f a solute. In a s o l u t i o n i t p e r m i t s t h e p a s s a g e of solvent mole c u l e s and keeps o u t o t h e r d i s s o l v e d m a t e r i a l s a n d , h e n c e , a c t s as a membrane. As t h e n e t w o r k s w e l l s t h e p o l y m e r c h a i n s a r e e l o n g a t e d and e x e r t a f o r c e i n o p p o s i t i o n t o t h e s w e l l i n g . In t h i s c a s e , t h e n e t w o r k a c t s as a p r e s s u r e g e n e r a t i n g d e v i c e . His t h e o r y o f s w e l l i n g i s based on t h e b a l a n c i n g o f t h e o s m o t i c p r e s s u r e by t h e m e c h a n i c a l c o n t r a c t i o n . To o b t a i n h i s f o r m a l e x p r e s s i o n , F l o r y u t i l i z e s the Flory-Huggins polymer s o l u t i o n t h e o r y a s s u m i n g random m i x i n g between s o l u t e and s o l v e n t and a rigid lattice. The e x p r e s s i o n i n c l u d e s two t e r m s , an e n t r o p y t e r m ( c o m b i n a t i o n a l ) and a h e a t t e r m due t o i n t e r m o l e c u l a r f o r c e s (non-combinational). L a t e r , Prigogine e t a l . (£) develoned a c o r r e s p o n d i n g s t a t e t h e o r y f o r p o l y m e r s o l u t i o n s w i t h a more rigorous expression f o r t h e non-combinational c o n t r i b u t i o n than the Flory-Huggins approach. However, t h e c o m b i n a t i o n a l t e r m i s s t i l l used i n i t s o r i g i n a l f o r m . In t h e s w e l l i n g o f h y d r o g e l s , t h e random m i x i n g a s s u m p t i o n between h i g h p o l y m e r and w a t e r i s n o t g e n e r a l l y v a l i d , b e c a u s e o f t h e h i g h d e g r e e o f s t r u c t u r i n g o f w a t e r i n some g e l n e t w o r k s . The P r i g o g i n e t h e o r y , w h i c h i s l i m i t e d t o n o n - p o l a r and m o d e r a t e l y p o l a r s y s t e m s w i t h no h y d r o g e n b o n d i n g , i s a l s o n o t g e n e r a l l y applicable. In t h i s p a p e r , a new s e m i - e m p i r i c a l i n t e r a c t i o n p a r a m e t e r , Δ , i s i n t r o d u c e d and used i n an e q u a t i o n o f s w e l l i n g b a s e d on a " S o l u b i l i t y M o d e l " (TOJ t o a v o i d t h e a b o v e - m e n t i o n e d d i f f i c u l t i e s . The e q u i l i b r i u m c o n d i t i o n f o r i s o t r o p i c s w e l l i n g (9J c l a s s i c a l l y requires that 2

\ 3Ni/T,P

\ 3Ni / T , P

L

1

J

where A F and àF ^ a r e t h e f r e e e n e r g y o f m i x i n g and e l a s t i c b e h a v i o r , r e s p e c t i v e l y , and N i i s t h e mole f r a c t i o n o f s o l v e n t . The " S o l u b i l i t y M o d e l " (10) s t i l l c a r r i e s t h e same e l a s t i c t e r m , b u t t h e f i r s t t e r m i s m o d i f i e d . The p r o c e s s o f t r a n s f e r r i n g one mole o f w a t e r from b u l k t o g e l network i n v o l v e s t h r e e s t e p s ( F i g u r e 1 ) : m


62

HYDROGELS

Water i n Gel W a t e r

2nd

FOR MEDICAL

A N D RELATED APPLICATIONS

Step

Water i n Vapor


(energy t o d i g holes i n solvent)

1st

Step ΔΗ (heat o f vaporization)

3rd

Step Δ (polymer-solvent interaction) 2

Water i n bulk

Water i n |Gel Network

Figure 1. A schematic of the process of transferring one mole of water from bulk to gel network

F i r s t Step. To b r i n g a mole o f w a t e r f r o m t h e b u l k phase t o t h e vapor phase: T h i s r e q u i r e s an e n e r g y w h i c h e q u a l s t h e h e a t o f vaporization o f water, Δ Η : ν

ΔΗ

γ

= ΔΗ °

+ £

ν

T

Cp d T ,

[2]

where Δ Η ° i s t h e h e a t o f v a p o r i z a t i o n a t some r e f e r e n c e t e m p e r a t u r e , T , and Cp i s t h e s p e c i f i c h e a t . Second s t e p . To b r i n g w a t e r m o l e c u l e s from t h e vapor phase t o t h e e x i s t i n g g e l water: A t o r n e a r e q u i l b r i u m t h e g e l n e t w o r k i s expanded w i t h w a t e r , w h i c h c o n s i s t s o f X , Y and Ζ t y p e s , f i l l i n g t h e empty spaces. The e n e r g y , Δ ι , r e q u i r e d i n t h i s s t e p i s f o r c r e a t i n g a mole o f c a v i t y o f t h e s i z e o f t h e s o l u t e m o l e c u l e ( w a t e r i n v a p o r ) ag a i n s t t h e s o l v e n t ( g e l w a t e r ) s u r f a c e t e n s i o n : γ

Δ! = 4 i r r 2

2

(γ Ζ + γ Y + γ Χ ) / ( 1 ζ y χ

+ Κ),

where 4lïr

[3]

i s the surface area of the water molecule; γ , γ , χ y γ , a r e t h e s u r f a c e t e n s i o n s and Χ , Υ, Ζ a r e t h e w e i g h t f r a c t i o n s o f t h e three types o f water, Χ , Υ, Ζ r e s p e c t i v e l y . The t e r m 1/(1 + K) needs a l i t t l e more e x p l a n a t i o n . Jhon, G r o s h , Ree and E y r i n g ( 1 1 ) p r o p o s e d a model i n w h i c h ( b u l k )



4.

JHON ET AL.


63

w a t e r i s v i s u a l i z e d as c o n t a i n i n g a t l e a s t t w o s o l i d - l i k e s t r u c t u r e s , t h e i c e - I - l i k e open s t r u c t u r e a n d t h e i c e - I I I - l i k e c l o s e d s t r u c t u r e , i n e q u i l i b r i u m w i t h each o t h e r and w i t h t h e g a s - l i k e m o l e c u l e s (A g a s - l i k e m o l e c u l e r e f e r s t o a m o l e c u l e w h i c h i s s u r r o u n d e d by h o l e s ) . A t e r m 1/(1 + K) i s i n t r o d u c e d i n e q u a t i o n [ 3 ] on t h e a s s u m p t i o n t h a t t h e e n e r g y o f c a v i t y formation i s neglible i n the i c e - I - l i k e part of the l i q u i d s t r u c t u r e , and Κ i s t h e e q u i l i b r i u m c o n s t a n t between i c e - I - l i k e and i c e - I I I - l i k e d o m a i n s . Third step. To b r i n g w a t e r m o l e c u l e s in g e l water t o gel network: T h i s s t e p r e q u i r e s an e n e r g y o f i n t e r a c t i o n between t h e p o l y m e r m o l e c u l e s a n d t h e s u r r o u n d i n g water molecules, Δ ( 1 2 ) : 2

A =fn 2

/~

B

U(R) < S

A + R + B

>

dR.

A v

[4]

where A and Β d e n o t e w a t e r and h i g h p o l y m e r , r e s p e c t i v e l y ; η i s t h e number d e n s i t y o f s o l v e n t m o l e c u l e s ; f i s t h e q u a n t i t y w h i c h takes account o f t h e f a c t t h a t t h e d i s t r i b u t i o n o f s o l v e n t m o l e c u l e s o f t h e p o t e n t i a l minimum i s d e n s e r t h a n t h e a v e r a g e d e n s i t y ; U(R) i s t h e i n t e r m o l e c u l a r p o t e n t i a l o f A and Β m o l e c u l e s a t a s e p a r a t i o n d i s t a n c e , R; a n d ^ / \ + R ^ the

1

+r

S

v

a v e r a g e v a l u e o f t h e s u r f a c e a r e a . To e v a l u a t e U(R) a n d /\ ^ 3 /\ » the reader should consult the c i t e d references (10, < s

>

+

+

v

12), A l t h o u g h t h e new i n t e r a c t i o n p a r a m e t e r Δ i s d i f f i c u l t t o e v a l u a t e d i r e c t l y , i t c a n be o b t a i n e d f o r a v a i l a b l e s y s t e m s i n the i n p u t d a t a i n E q u a t i o n [ 2 ] , E q u a t i o n [ 3 ] and second terms i n Equation [ 1 ] a r e provided. Experiments t o support t h i s s e m i - e m p i r i c a l s o l u b i l i t y t h e o r y w o u l d be f i r s t , t o d e t e r m i n e t h e i n t e r a c t i o n p a r a m e t e r , Δ , f o r v a r i o u s g e l - w a t e r s y s t e m s . T h e s e c a n be o b t a i n e d b y m e a s u r i n g s w e l l i n g d e g r e e s as t h e o n l y i n p u t d a t a , t h e r e s t being a v a i l a b l e i n the l i t e r a t u r e . S w e l l i n g e x p e r i m e n t s on PHEMA n e t w o r k s made o f c o n t r o l l e d p u r i t y a r e underway. The o b t a i n e d Δ w i l l be compared t o t h e F l o r y i n t e r a c t i o n p a r a m e t e r χ ( 8 ) . O t h e r s o l v e n t s y s t e m s s u c h as a l c o h o l s s h o u l d a l s o be studied. S e c o n d , a phase d i a g r a m may be c o n s t r u c t e d f o r t h e water-polymer system. P e r f e c t symmetry a t t h e c o n s o l u t e t e m p e r a t u r e w i l l s u p p o r t t h e h y p o t h e s i s o f random m i x i n g o f w a t e r and p o l y m e r m o l e c u l e s . D e v i a t i o n s from i t would i n d i c a t e support of the s o l u b i l i t y theory. The t h r e e - s t a t e model o f w a t e r s t r u c t u r e c a n a l s o be a p p l i e d t o osmotic pressure o f polymer s o l u t i o n s . The u s u a l e x p r e s s i o n f o r o s m o t i c p r e s s u r e c a n be u s e d e x c e p t t h a t t h e volume s h o u l d be r e p l a c e d by V ( X f x ) , where f x i s t h e r a t i o between t h e s o l u b i l i t y o f s o l u t e i n X o r b u l k w a t e r t o t h a t i n g e l w a t e r . We b e l i e v e t h a t o n l y t h e p o r t i o n o f w a t e r a v a i l a b l e f o r o s m o t i c p r e s s u r e s h o u l d be i n c l u d e d i n t h e o s m o t i c p r e s s u r e e q u a t i o n . T y i n g both s w e l l i n g and o s m o t i c p r e s s u r e e x p e r i m e n t s t o g e t h e r w i t h t h e t h r e e - s t a t e t h e o r y , one may 2

2

2


64

HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

perform a s w e l l i n g and/or osmotic p r e s s u r e experiment o f pure w a t e r as a f u n c t i o n o f t e m p e r a t u r e . As w a t e r i s h e a t e d f r o m - 30°C t o 1 0 0 ° C , any change i n s w e l l i n g a n d / o r o s m o t i c p r e s s u r e w o u l d be p a r t l y due t o m e l t i n g o f i c e - I - l i k e c l u s t e r s ( 1 1 ) .


Viscoelastic

Properties

The e f f e c t o f s o l v e n t on t h e v i s c o e l a s t i c b e h a v i o r o f h y d r o g e l s has been w i d e l y r e p o r t e d i n t h e l i t e r a t u r e ( 1 3 , 1 4 , 1 5 ) . In c r e e p and s t r e s s r e l a x a t i o n m e a s u r e m e n t s , t h e r e t a r d a t i o n t i m e and r e l a x a t i o n t i m e a r e f u n c t i o n s o f s o l v e n t . In dynamic s t u d i e s t h e s o l v e n t r e d u c e s t h e γ r e l a x a t i o n p r o c e s s and s h i f t s the β process to lower temperatures. Furthermore, the c o n c e n t r a t i o n and t h e n a t u r e o f low m o l e c u l a r w e i g h t compounds a f f e c t t h e s i z e and shape o f t h e s e c o n d a r y l o s s maximum as w e l l as t h e a p p a r e n t a c t i v a t i o n e n e r g y . In e q u i l i b r i u m s t u d i e s , C i n t h e M o o n e y - R i v l i n e n u a t i o n i s a f f e c t e d by t h e solvent. H y d r o g e l s , i n t h e r u b b e r y r e g i o n , behave much l i k e r u b b e r . T h e r e f o r e , i n t h i s study, a theory f o r the s t r e s s - s t r a i n r e l a t i o n i n h y d r o g e l s was d e v e l o p e d by m o d i f y i n g t h e t h e o r y of rubber e l a s t i c i t y . Consider a f r e e l y o r i e n t i n g chain which c o n t a i n s η segments. The f o r o e F needed t o m a i n t a i n t h e c h a i n a t an a v e r a g e e l o n g a t i o n L i s g i v e n by t h e expression: 2

F

L

= i7 * Φ

or

τ-Μ,ιφ.

[5]

The s t r e s s σ needed t o m a i n t a i n a r u b b e r n e t w o r k a t h i g h e l o n g a t i o n i s g i v e n by (16) σ/vkT = 1 n\*{a/n ) h

-α"

2

,

[6]

where v , a , l , k and Τ a r e , r e s p e c t i v e l y , t h e number o f c h a i n s p e r u n i t v o l u m e , t h e e x t e n s i o n r a t i o , t h e seament l e n g t h , B o l t z m a n n ' s c o n s t a n t , and t h e a b s o l u t e t e m p e r a t u r e . L and L* a r e t h e L a n g e v i n f u n c t i o n and i n v e r s e L a n g e v i n f u n c t i o n , r e s p e c t i v e l y w h i c h a r e d e f i n e d by χ = L ( y ) = c o t h y - 1/y and y = L * ( x ) , r e s p e c t i v e l y . F o r a h y d r o g e l w i t h m a i n l y X w a t e r , i t i s r e a s o n a b l e t o assume t h a t t h e p o l y m e r c h a i n s can r o t a t e f r e e l y and E q u a t i o n s [ 5 ] and [ 6 ] a p p l y . However, f o r h y d r o g e l s w i t h m o s t l y Ζ w a t e r , due t o t h e c o n s t r a i n e d s t a t e , o n l y two l i m i t e d c o n f o r m a t i o n s can o c c u r , i . e . , i n t e r n a l i s o m e r i z a t i o n between two c o n f o r m e r s k e e p i n g t h e p o s i t i o n o f e a c h c h a i n end f i x e d . In m a g n e t i c t h e o r y , i t i s known t h a t t h e m a g n e t i c f i e l d s h i f t s t h e r e l a t i v e amount o f two o r i e n t a t i o n s . F o r M mag n e t i c d i p o l e s e a c h o f w h i c h can e x i s t e i t h e r i n t h e d i r e c t i o n o f t h e m a g n e t i c f i e l d , H, o r a g a i n s t t h e f i e l d , t h e r e l a t i o n between t h e m a g n e t i z a t i o n , I, and t h e m a g n e t i c f i e l d t a k e s Q


4.

Water

JHON ET AL.

in the Behavior

of Gel

65

Networks

t h e f o r m [ 1 7 ] I/m M = t a n h (|γ ), where m i s t h e m a g n e t i c moment. In p o l y m e r e l a s t i c i t y t h e f o r c e p l a y s a c o r r e s p o n d i n g role. The e q u i v a l e n t e x p r e s s i o n f o r p o l y m e r e l a s t i c i t y c a n be written as: .

hL\

7(

£ e

°

F

/

k

0


e

We s h a l l

-£ F/kT

T

" *oF/kT ;

k T

refer to Ζ ( ^ γ )

e

JUF/kT

-

t

a

n

h

^/kT).

ill

as t h e Ζ f u n c t i o n .

F o r h y d r o g e l s w i t h m o s t l y Y w a t e r s t r u c t u r e , we e x p e c t t h a t b o t h t h e L f u n c t i o n and t h e Ζ f u n c t i o n s h o u l d f a i l t o a p p l y and a Y f u n c t i o n s h o u l d g o v e r n :

π YUoF/kT) = /

s i n e cose tanh ( H F cose/kT)

de .

0

[8]

0 In t h i s c a s e , n o t o n l y two o r i e n t a t i o n s ( c o n f o r m e r ) a r e p e r m i t t e d , b u t t h e p o s i t i o n o f each c h a i n end i s n o t f i x e d . With t h e same argument t h e n u m e r i c a l v a l u e o f a Y f u n c t i o n l i e s between t h e c o r r e s p o n d i n g X f u n c t i o n and Ζ f u n c t i o n . H e n c e , e q u a t i o n [ 6 ] c a n be m o d i f i e d as f o l l o w s : α/vkT = i r\ lXL*(a/n ) h

+ W*{a/n )

h

h

+ ZZ*(a/n^) - a " \

[9]

where Y * , Z* a r e t h e i n v e r s e Y f u n c t i o n and i n v e r s e Ζ f u n c t i o n , respectively. To t e s t o u r h y p o t h e s i s , t h e s t r e s s - e l o n g a t i o n c u r v e s f o r three poly(hydroxyethy1 methacrylate) gels with d i f f e r e n t w a t e r c o n t e n t s were o b t a i n e d f r o m s t r e s s - s t r a i n measurements a t room t e m p e r a t u r e ( 2 3 ° C ) ( F i g u r e 2 ) . The o b s e r v e d d a t a a r e g i v e n by t h e s o l i d l i n e s i n t h e f i g u r e . The v a l u e s o f X , Y and Ζ a r e t a k e n f r o m Lee ( 5 , 6 ) . C h o o s i n g η = 100 (we f o u n d t h a t r e s u l t s o b t a i n e d f o r η = 100 and η = 1000 do n o t d i f f e r s i g n i f i c a n t l y ) , t h e v a l u e s o f σ c a n be c a l c u l a t e d as a f u n c t i o n o f a . The c o n s t a n t s , v k T , needed f o r f i t t i n g t h e e x p e r i m e n t a l c u r v e s a r e 1.09 χ 1 0 d y n e s / c m ( G e l I, 45% w a t e r ) ; 6 . 0 3 χ 1 0 d y n e s / c m ( G e l I I , 31% w a t e r ) ; and 2 . 5 9 χ 1 0 d y n e s / c m ( G e l I I I , 2 9 . 9 % w a t e r ) . The c a l c u l a t e d p o i n t s a r e i n d i c a t e d i n t h e figure. G e l s I and I I were p r e p a r e d w i t h t h e i n d i c a t e d amount o f w a t e r i n t h e p o l y m e r i z a t i o n m i x w h i l e G e l I I I was p r e p a r e d w i t h 100% h y d r o x y e t h y l m e t h a c r y l a t e monomer and t h e n s w e l l e d t o 29.9% water c o n t e n t . Although t h e w a t e r c o n t e n t i n G e l II and G e l I I I a r e a b o u t t h e same, t h e f o r m e r i s c o n s i d e r a b l y tougher than t h e l a t t e r . I t i s p o s s i b l e t h a t , a t 23°C, t h e behavior o f Gel II i s n o t w i t h i n i t s r u b b e r y r e g i o n , s i n c e t h e a g r e e m e n t between t h e c a l c u l a t e d and measured a v a l u e s f o r t h i s g e l i s l e s s 7

2

2

7

7

2




66


4.

JHON ET AL.


s a t i s f a c t o r y t h a n t h o s e f o r t h e o t h e r two

67

gels.


Summary A theory i s developed to i n t e r p r e t the osmotic, s w e l l i n g and v i s c o e l a s t i c b e h a v i o r o f h y d r o g e l n e t w o r k s i n t e r m s o f a t h r e e - s t a t e model o f w a t e r s t r u c t u r e . For i s o t r o p i c s w e l l i n g under e q u i l i b r i u m c o n d i t i o n s , F l o r y assumed random m i x i n g between t h e s o l v e n t m o l e c u l e s and t h e p o l y m e r m o l e c u l e s . Since water molecules i n hydrogels possess h i g h e r degrees o f orderness than those i n the b u l k , i t i s b e l i e v e d t h a t the s o l u b i l i t y t h e o r y (10) s h o u l d be used i n s t e a d o f t h e c l a s s i c a l Flory theory. T h i s i s because s o l u b i l i t y t h e o r y c o n s i d e r s the f r e e energy of mixing of water w i t h the gel network, which i n c l u d e s the heat of v a p o r i z a t i o n of w a t e r , the energy r e q u i r e d t o c r e a t e h o l e s i n t h e g e l w a t e r and t h e e n e r g y o f i n t e r a c t i o n between w a t e r and p o l y m e r . In o u r t h e o r y o n l y t h e p o r t i o n o f w a t e r a v a i l a b l e f o r o s m o t i c p r e s s u r e was i n c l u d e d i n the osmotic pressure e q u a t i o n . For the v i s c o e l a s t i c b e h a v i o r o f h y d r o g e l s , t h e t h e o r y o f r u b b e r e l a s t i c i t y was m o d i f i e d t o accommodate t h e e f f e c t o f t h r e e t y p e s o f w a t e r on t h e i r s t r e s s strain relationship. P o l y m e r c h a i n s w i t h m a i n l y X w a t e r can r o t a t e f r e e l y , t h o s e w i t h m a i n l y Ζ w a t e r can o n l y have two r e s t r i c t e d c o n f o r m a t i o n s and t h o s e w i t h m a i n l y Y w a t e r can have intermediate behavior. In a c t u a l c a s e s , t h e c o n t r i b u t i o n s f r o m a l l t h r e e t y p e s o f w a t e r s h o u l d be c o n s i d e r e d s i n c e t h e y a r e c o e x i s t i n g i n any p o l y m e r - w a t e r s y s t e m . A few e x p e r i m e n t s a r e proposed. A c c o r d i n g t o some e x p e r i m e n t a l r e s u l t s , t h e t h e o r y p r o v i d e s good a g r e e m e n t .

Acknowledgement We g r a t e f u l l y a c k n o w l e d g e s u p p o r t o f t h i s work by NIH HL1692K)! and NSF G r a n t GH33996X.

Grant

Abstract A three-state model of water structure in hydrogels has been extended to describe the osmotic, swelling and viscoelastic be havior of gel networks. The solubility theory modification of the classical Flory theory is proposed to explain the osmotic and swelling behavior of gel networks. In describing the viscoe lastic behavior of hydrogels, three functions, governed by the three types of water, are used to explain the stress-strain relations in the rubbery region.



68


Literature Cited 1. Drost-Hansen, W., Indust. Eng. Chem. (1969) 61, 10. 2. Aizawa, Μ., and Suzuki, S., Bull. Chem. Soc. Japan (1971) 44, 2907. 3. Krishnamurthy, S., McIntyre, D., and Santee, E. R., Jr., J. Polym. Sci. (1973) 11, 427. 4. Jhon, M. S., and Andrade, J. D., J. Biomed. Mater. Res. (1973) 7, 509. 5. Lee, H. B., Andrade, J. D., and Jhon, M. S., Polymer Preprints (1974) 15, 706. 6. Lee, H. B., Jhon, M. S., and Andrade, J. D., J. Colloid and Interface Sci. (1974) 51, 225. 7. Choi, S. H., Jhon, M. S., and Andrade, J. D., Submitted for publication. 8. Flory, P. J. "Principles of Polymer Chemistry," Cornell University Press, Ithaca, New York (1953). 9. Prigogine, I., Belleman, Α., and Englert-Chowles, Α., J. Chem. Phys. (1956) 24, 518. 10. Jhon, M. S., Eyring, H., and Sung, Y. K., Chem. Phys. Letters (1972) 13, 36. 11. Jhon, M. S., Grosh, J., Ree, T., and Eyring, H., J. Chem. Phys (1966) 44, 1465. 12. Kihara, T., and Jhon, M. S., Chem. Phys. Letters (1970) 7, 559. 13. Janacek, S., and Kolarik, J., Coll. Czech. Chem. Comm. (1965) 30, 1597. 14. Janacek, J., and Ferry., J. D., J. Poly. Sci. (1969) Part A-2, 7, 1681. 15. Ilavsky, M., and Prins, W., Macromolecules (1970) 3, 415. 16. Bueche, F., J. Appl. Poly. Sci. (1960) 4, 107. 17. Hill, T. L., "An Introduction to Statistical Thermody namics," Addison-Wesley Publishing Company, Inc., Reading and London (1960).


Hydrogels for Medical and Related Applications - ACS Publications

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