Hydrogels for Medical and Related Applications

9 Rotational Viscometry Studies of the Polymerization of Hydrophilic Methacrylate Monomers

Downloaded by TUFTS UNIV on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch009

SHAO M. MA, DONALD E. GREGONIS, CHWEN M. CHEN, and JOSEPH D. ANDRADE Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112 T h e r e i s c o n s i d e r a b l e l i t e r a t u r e on t h e m e c h a n i c a l b e h a v i o r o f p o l y ( 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) g e l s (1_). To o u r k n o w l e d g e , no s t u d y has been made on t h e f l o w p r o p e r t i e s o f t h i s polymer during the course of p o l y m e r i z a t i o n . I n t h i s s t u d y we a t t e m p t e d t o use t h i s e a s i l y o b t a i n e d p r o p e r t y t o o b t a i n knowledge c o n c e r n i n g (1) t h e r e l a t i v e r a t e o f p o l y m e r i z a t i o n w i t h v a r i o u s i n i t i a t o r s ; ( 2 ) t h e e f f e c t o f p o l y m e r i z a t i o n t i m e on t h e f l o w p r o p e r t i e s o f PHEMA; ( 3 ) t h e r e l a t i o n s between t h e f l o w c u r v e , m o l e c u l a r w e i g h t and t h e m o l e c u l a r w e i g h t d i s t r i b u t i o n . At a given temperature the v i s c o s i t y (η) v s . shear r a t e ( § ) c u r v e f o r c o n c e n t r a t e d p o l y m e r s o l u t i o n s and p u r e p o l y m e r s depends on t h e m o l e c u l a r w e i g h t and m o l e c u l a r w e i g h t d i s t r i b u t i o n o f t h e system. However, an i n c r e a s e i n v i s c o s i t y o f t h e p o l y m e r i z a t i o n mixture indicates only that conversion i s i n c r e a s i n g . How v i s c o s i t y changes d u r i n g t h e c o u r s e o f p o l y m e r i z a t i o n f r o m N e w t o n i a n t o n o n - N e w t o n i a n as a f u n c t i o n o f m o l e c u l a r w e i g h t o r m o l e c u l a r weight d i s t r i b u t i o n i s not t o t a l l y understood. Q u a l i t a t i v e l y , t h e p o l y m e r i z a t i o n m i x t u r e behaves as a N e w t o n i a n f l u i d d u r i n g t h e e a r l y s t a g e o f p o l y m e r i z a t i o n . As t h e degree o f p o l y m e r i z a t i o n o r t h e c o n c e n t r a t i o n o f t h e p o l y m e r i c f r a c t i o n i n c r e a s e s , t h e v i s c o s i t y a l s o i n c r e a s e s and t h e s y s t e m becomes n o n - N e w t o n i a n . Polymers w i t h broad m o l e c u l a r weight d i s t r i b u t i o n s show a h i g h e r v i s c o s i t y dependency on s h e a r r a t e ( 2 , 3 ) ; non-Newtonian b e h a v i o r s t a r t s t o o c c u r a t l o w e r shear r a t e s than s i m i l a r polymers w i t h narrow m o l e c u l a r weight d i s tributions. T h e r e f o r e , the e f f e c t of p o l y m e r i z a t i o n time a t t h i s s t a g e w o u l d depend on t h e p o l y d i s p e r s i t y o f t h e p o l y m e r p r o d u c e d . F u r t h e r p o l y m e r i z a t i o n e n c o u n t e r s b r a n c h i n g and g e l f o r m a t i o n . G r a e s s l e y (4) r e p o r t e d t h a t l o n g - c h a i n b r a n c h i n g a f f e c t s t h e v i s c o s i t y - s h e a r r a t e c u r v e i n a s i m i l a r way as b r o a d e n i n g o f t h e molecular weight d i s t r i b u t i o n . However, t h e e f f e c t s o f b r a n c h i n g c a n n o t be s e p a r a t e d f r o m t h e e f f e c t o f p o l y d i s p e r s i t y i n v i s c o m e t r y measurements. The v i s c o s i t y o f a b r a n c h e d p o l y m e r may be h i g h e r o r lower than a l i n e a r polymer. T h i s depends on w h e t h e r the molecular weight i s higher or lower than the m o l e c u l a r weight

119

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


120

HYDROGELS

FOR MEDICAL

AND RELATED APPLICATIONS

of t a n g l i n g segments. Because o f t h e c o m p l i c a t e d n a t u r e o f t h e p r o b l e m , no s i n g l e t h e o r y can a d e q u a t e l y d e s c r i b e t h e m e c h a n i c a l behavior of the p o l y m e r i c system during the course of p o l y m e r i z a tion. However, , s e v e r a l t h e o r i e s ( 5 - 7 ) have w o r k e d w e l l f o r l i n e a r p o l y m e r s , w h i c h m i g h t be t h e c a s e f o r PHEMA p r o d u c e d w i t h very l i t t l e c r o s s l i n k i n g agent i n a r e l a t i v e l y poor s o l v e n t s u c h as w a t e r . The p r e s e n t i n v e s t i g a t i o n c o n s i s t s o f : (1) f l o w c u r v e s o b t a i n e d f o r h y d r o x y e t h y l m e t h a c r y l a t e (HEMA)-water m i x t u r e s , p o l y m e r i z e d a t 60°C as f u n c t i o n s o f p o l y m e r i z a t i o n t i m e and i n i t i a t o r ; (2) t h r e e t h e o r i e s o f n o n - N e w t o n i a n v i s c o s i t y , t h e B u e c h e - H a r d i n g method ( 5 j , R e e - E y r i n g a c t i v a t e d - s t a t e t h e o r y (6) and B a r t e n e v ' s e m p i r i c a l method ( 7 ) , a r e b r i e f l y d e s c r i b e d and t h e f l o w p a r a m e t e r s o f o u r s y s t e m s a r e a n a l y z e d w i t h t h e s e t h e o r i e s ; (3) t h e r e l a t i o n s between i n i t i a t o r s and p o l y m e r i z a t i o n r a t e and between f l o w c u r v e , m o l e c u l a r w e i g h t , m o l e c u l a r w e i g h t d i s t r i b u t i o n and p o l y m e r i z a t i o n t i m e a r e d i s c u s s e d . Material

and

Methods

The m o n o m e r - s o l v e n t m i x t u r e used i n t h i s s t u d y c o n s i s t e d o f s i x p a r t s o f HEMA and t h r e e p a r t s o f w a t e r , by v o l u m e . The i n i t i a t o r s used i n c l u d e ammonium p e r s u l f a t e , a z o b i s i s o b u t y r o n i t r i l e (AIBN), azobis(methyl i s o b u t y r a t e ) , azobis(methoxyethyl i s o b u t y r a t e ) , and a z o b i s ( m e t h o x y d i e t h o x y e t h y l i s o b u t y r a t e ) . A c o n c e n t r a t i o n o f 5.71 m m o l / l i t e r was used f o r ammonium p e r s u l f a t e and 5.21 m m o l / l i t e r f o r t h e o t h e r s . The s y n t h e s i s , p u r i f i c a t i o n and c h e m i c a l c h a r a c t e r i z a t i o n o f t h e PHEMA a r e g i v e n e l s e w h e r e (8). I t s h o u l d be n o t e d t h a t a l t h o u g h HEMA monomer i s c o m p l e t e l y m i s c i b l e w i t h w a t e r , PHEMA i s n o t w a t e r s o l u b l e . A Haake R o t o v i s c o r o t a t i o n a l v i s c o m e t e r was u s e d f o r v i s c o s i t y measurement. P o l y m e r i z a t i o n was c a r r i e d o u t i n a c o a x i a l c y l i n d e r s e n s o r s y s t e m , w i t h a MV cup and a MVI b o b . Temperature was k e p t a t 60°C w i t h a Lauda K-2/R c i r c u l a t i n g b a t h . F l o w c u r v e s were d e t e r m i n e d as f u n c t i o n s o f t i m e a t s h e a r r a t e s f r o m 0 t o 685 s e c " . To a v o i d permanent m e c h a n i c a l b r e a k d o w n , l o w e r r a t e s were used as t h e p o l y m e r i z a t i o n i n c r e a s e d . Non-Newtonian

shear

Viscosity

In n o n - N e w t o n i a n f l o w t h e c h a n c e i n a p p a r e n t v i s c o s i t y as a f u n c t i o n o f s h e a r r a t e ( § ) g e n e r a l l y t a k e s t h e f o r m η η

0

= f(xS),

(η)

Cl]

where η i s t h e v i s c o s i t y a t z e r o s h e a r r a t e , § > and τ i s t h e c h a r a c t e r i s t i c r e l a x a t i o n t i m e , which i s molecular weight-depend ent. 0

0


9.

Polymerization of Hydrophilic Methacrylate Monomers

M A E T AL.

121


Many t h e o r i e s have been p r o p o s e d t o e x p l a i n n o n - N e w t o n i a n b e h a v i o r i n condensed systems. M o l e c u l a r t h e o r i e s b a s e d on t h e e q u i v a l e n c e h y p o t h e s i s ( 9 j , on t h e e n t a n g l e m e n t c o n c e p t ( 1 0 ) , and on t h e a c t i v a t e d - s t a t e model (6) have g a i n e d c o n s i d e r a b l e acceptance. Bueche-Harding Standard Curve. Bueche i n t r o d u c e d a s h e a r r a t e dependence t o Rouse t h e o r y ( 1 1 ) . A c c o r d i n g t o h i s h y p o t h e s i s , macromolecules i n s o l u t i o n under dynamic d e f o r m a t i o n a r e assumed t o behave s i m i l a r l y t o t h o s e u n d e r s t e a d y s h e a r i n g . The change i n v i s c o s i t y w i t h s h e a r r a t e s i s c o n s i d e r e d as due t o t h e r e s u l t s o f d e f o r m i n g and r o t a t i n g o f t h e c o i l i n g p o l y m e r m o l e c u l e s under a s h e a r i n g f o r c e . Below a c e r t a i n c h a r a c t e r i s t i c t i m e , t ^ , (which equals a p p r o x i m a t e l y t h e r e c i p r o c a l o f z e r o shear r a t e , s ) the v i s c o s i t y decreases r a p i d l y w i t h i n c r e a s i n g s h e a r r a t e , w h i l e above i t t h e v i s c o s i t y a p p r o a c h e s i t s maximum value. T h i s r e l a x a t i o n t i m e c a n be c a l c u l a t e d f r o m t h e p r o p e r t i e s of the system at low shear r a t e s . Bueche has i g n o r e d t h e e f f e c t o f c h a i n e n t a n g l e m e n t s on n o n - N e w t o n i a n b e h a v i o r and assumed t h a t t h e l o c a l p r o p e r t i e s o f t h e s y s t e m , s u c h as t h e r e l a x a t i o n t i m e d i s t r i b u t i o n , a r e i n d e pendent o f i t s s t a t e o f m o t i o n . H i s t h e o r y , t h e r e f o r e , does n o t c o r r e l a t e well with experimental data (4, 12-14). G r a e s s l e y ( 1 0 ) p r o p o s e d a t h e o r y by a s s u m i n g t h a t t h e v i s c o s i t y o f a p o l y m e r i c s y s t e m i s c o n t r o l l e d by i n t e r m o l e c u l a r c h a i n e n t a n g l e m e n t s and t h a t an i n c r e a s e i n s h e a r i n d u c e s changes i n t h e n e t w o r k o f e n t a n g l e m e n t s and hence c a u s e s t h e v i s c o s i t y to decrease. T h i s e n t a n g l e m e n t a p p r o a c h has a sound theoretical basis. However, i n f o r m a t i o n c o n c e r n i n g t h e p o l y d i s p e r s i t y and t h e e n t a n g l e m e n t d e n s i t y a r e needed t o c a r r y o u t actual computation. For a l i n e a r c o i l i n g polymer, B u e c h e - H a r d i n g , l a t e r , s u g g e s t e d a method f o r d e t e r m i n i n g i t s a b s o l u t e m o l e c u l a r w e i g h t f r o m i t s f l o w c u r v e ( 5 j . In t h i s method t h e y u s e d a s t a n d a r d curve which f o l l o w s the e m p i r i c a l equation 0

n / n = 1.00 + 0 . 6 0 ( T S ) o

3 / 4

,

[2]

t o match t h e i r e x p e r i m e n t a l d a t a . The v a l u e o f η and s a r e d e t e r m i n e d by s u p e r i m p o s i n g t h e s t a n d a r d c u r v e i n t h e f o r m o f l o g ( η / η ο ) v s . l o g ( S T ) w i t h an e x p e r i m e n t a l c u r v e i n t h e f o r m o f l o g ( η ) v s . l o g ( s ) w h i l e b o t h c u r v e s were p l o t t e d on t h e same scale. The m o l e c u l a r w e i g h t o f t h e p o l y m e r i s t h e n c a l c u l a t e d from t h e e x p r e s s i o n 0

M = 7T NckT/12n

0

s , [3] ο o where N, c , k, and Τ a r e A v o g a d r o ' s number, t h e c o n c e n t r a t i o n o f p o l y m e r i n g / c c , 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 ture, respectively. 2

o


122

HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

B u e c h e s r e l a x a t i o n t i m e {tw = l / s ) , as p o i n t e d o u t by G r a e s s l e y ( 1 5 ) , g o v e r n s t h e m a g n i t u d e o f t h e s h e a r r a t e when t h e v i s c o s i t y begins to decrease. I t s h o u l d be an i m p o r t a n t p a r a meter f o r those p r o p e r t i e s i n which the l o n g e r r e l a x a t i o n times a r e d e t e r m i n i n g f a c t o r s . The B u e c h e - H a r d i n g s t a n d a r d c u r v e , w h i c h a g r e e d m o d e r a t e l y w e l l w i t h d a t a on u n f r a c t i o n a t e d p o l y s t y r e n e i n benzene and p o l y ( m e t h y l m e t h a c r y l a t e ) (PMMA) i n c h l o r o f o r m , s h o u l d p r e d i c t t h e n o n - N e w t o n i a n b e h a v i o r o f any l i n e a r p o l y m e r i c system w i t h not too broad a m o l e c u l a r weight d i s t r i b u tion (5). PHEMA and PMMA have t h e same backbone s t r u c t u r e . S i n c e t h e s h e a r r a t e used i n t h i s s t u d y i s r e l a t i v e l y l o w ; and t h e s y s t e m i s e x p e c t e d t o have low e n t a n g l e m e n t d e n s i t y ( w a t e r i s a p o o r s o l v e n t ) , low b r a n c h i n g and c r o s s l i n k i n g ( t h e d i e s t e r c o n c e n t r a t i o n i s l o w ) , t h e B u e c h e - H a r d i n g method s h o u l d work w e l l f o r our system. 1


0

R e e - E y r i n g s ' s A c t i v a t e d - S t a t e M o d e l . T h i s model (6) assumes t h a t t h e r e e x i s t s i g r o u p s o f f l o w u n i t s w h i c h d i f f e r i n r e l a x a t i o n t i m e and i n g e o m e t r i c a l d i m e n s i o n s . Some o f t h e s e flow u n i t s are Newtonian, others are non-Newtonian. A Newtonian f l o w u n i t i s a m o l e c u l e o r a group o f m o l e c u l e s i s o l a t e d f r o m o t h e r u n i t s , w h i l e a non-Newtonian u n i t i s a Newtonian u n i t bonded ( o r e n t a n g l e d ) w i t h a n o t h e r N e w t o n i a n u n i t o r u n i t s . T h u s , f o r f l o w o f n o n - N e w t o n i a n u n i t s , t h i s bond ( o r e n t a n g l e ment) must be b r o k e n ( o r d i s e n t a n g l e d ) . Based on t h i s c o n c e p t , t h e g e n e r a l i z e d v i s c o s i t y e q u a t i o n i s χ . β. Σ , -^-1 i

η =

1

sinh"

β.s

1

,

Γ4]

β^

a

where χ · i s t h e f r a c t i o n a l a r e a o c c u p i e d by t h e i t h f l o w u n i t on t h e s h e a r s u r f a c e , and η

cu = (λ X X 3 ) . / 2 k T

;

[5]

β. = [(A/X )2k ]T

;

[6]

2

l

Ί

1

1

a., and β. a r e t h e c h a r a c t e r i s t i c s h e a r volume d i v i d e d by kT w h i c h i s r e l a t e d t o t h e i n v e r s e o f t h e s h e a r modulus and t h e r e l a x a t i o n t i m e , r e s p e c t i v e l y , β./α· i s t h e N e w t o n i a n v i s c o s i t y . λ is

the jumping d i s t a n c e ,

λ ι , λ , and λ 2

3

are the m o l e c u l a r

d i m e n s i o n s o f a f l o w u n i t , k' i s t h e j u m p i n g f r e q u e n c y o f t h e f l o w u n i t when t h e r e i s no s t r e s s . According to the theory of rate processes (16): k

'

=

ΊΪ

IT

e

x

p

m , are mostly non-Newtonian i n b e h a v i o r . F o r two s y s t e m s w i t h t h e same m o l e c u l a r w e i g h t i t f o l l o w s t h a t 2

(62)1

(f ) 2

(m )î

2

2

=

(62)2 Downloaded by TUFTS UNIV on October 14, 2014 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0031.ch009

(Γ )?

2

=

=

.

Ml

(f )i 2

[13]

(Â )i 2

The s u b s c r i p t 2 i n s i d e t h e p a r e n t h e s e s r e f e r s t o t h e n o n N e w t o n i a n f l o w u n i t s and t h e s u b c r i p t s 1 and 2 o u t s i d e t h e p a r e n t h e s e s r e f e r t o s y s t e m s 1 and 2 , r e s p e c t i v e l y . Equation [13] i n d i c a t e s t h a t the average l e n g t h or the m o l e c u l a r w e i g h t o f t h e t a n g l i n g segments i s p r o p o r t i o n a l t o t h e s q u a r e r o o t o f t h e r e l a x a t i o n t i m e o f t h e f l o w u n i t s w h i c h c o n t a i n s u c h segments. T h i s w o u l d a p p r o x i m a t e l y be t h e c a s e when t h e same d e a r e e o f p o l y m e r i z a t i o n was r e a c h e d f r o m d i f f e r e n t i n i t i a l HEMA-water mixtures. On t h e o t h e r hand we can w r i t e (19) Bp = 6

S

(M/m ) (M/rn^ 2

1

/

3

and

^s a

p

(MM,)

[14] (M/m ) 2

where t h e s u b s c r i p t s ρ and s r e f e r t o p r o p e r t i e s f o r t h e p o l y m e r and u n a t t a c h e d k i n e t i c s e g m e n t s , r e s p e c t i v e l y . I f the degree of p o l y m e r i z a t i o n i s s u f f i c i e n t l y l a r g e , i . e . , i f M > m , the v a l u e o f nu , m s h o u l d n o t be a f f e c t e d by f u r t h e r p o l y m e r i z a tion. It follows that 2

2

(0p)ti

where t i and t

2

(M

V t ,

" '

V t .

.

A I B N ; (3) Both R e e - E y r i n g ' s t h e o r y o f n o n - N e w t o n i a n f l o w and B u e c h e H a r d i n g ' s method can d e s c r i b e t h e b e h a v i o r o f HEMA-water mixtures d u r i n g the course of p o l y m e r i z a t i o n . Bartenev's e m p i r i c a l e x p r e s s i o n works l e s s w e l l presumably because t h e r a t i o n/no f o r o u r s y s t e m i s s t i l l some f u n c t i o n o f m o l e c u l a r w e i g h t and c a n n o t be assumed t o depend on s h e a r s t r e s s alone; (4) The m o l e c u l a r w e i g h t o f l i n e a r PHEMA can be o b t a i n e d by u s i n g t h e B u e c h e - H a r d i n g method w i t h i n d e p e n d e n t i n f o r mation concerning c o n c e n t r a t i o n of the polymer. However, we have n o t c a r r i e d o u t c o n c e n t r a t i o n measurements i n t h i s

(1)


HYDROGELS

FOR

MEDICAL

AND RELATED

APPLICATIONS


136



9. M A E T AL.

Polymerization

of Hydrophilic

Methacrylate

Monomers

137

s t u d y and o n l y t h e r a t i o VM i s e s t i m a t e d . The r e l a t i v e m o l e c u l a r w e i g h t a t d i f f e r e n t p o l y m e r i z a t i o n t i m e s c a n be obtained from E y r i n g ' s r e l a x a t i o n t i m e ; (5) Nakagima's theory (20) c o r r e l a t e s t h e f l o w curve w i t h t h e cumulative molecular weight d i s t r i b u t i o n curve o f l i n e a r polymers. One c a n e x p l o r e t h i s t h e o r y f u r t h e r and s e e whether i t i s a p p l i c a b l e t o o u r systems. The work p r e s e n t e d h e r e i s o n l y a p r e l i m i n a r y s t u d y . The d a t a o b t a i n e d w i t h a Haake R o t o v i s c o v i s c o m e t e r a r e n o t a s u f ficient test. To f u r t h e r t e s t t h e a p p l i c a b i l i t y o f t h e t h e o r i e s requires that: ( 1 ) e x p e r i m e n t a l d a t a be o b t a i n e d o v e r a w i d e range o f r a t e s o f s h e a r , a t s e v e r a l d i f f e r e n t t e m p e r a t u r e s and u s i n g v a r i o u s s o l v e n t s ; ( 2 ) c o n c e n t r a t i o n and p o l y d i s p e r s i t y be d e t e r m i n e d s i d e by s i d e w i t h v i s c o m e t r i c measurement s o t h a t r e s u l t s f r o m t h e s e measurements c a n be d i r e c t l y c o m p a r e d .

Abstract Flow curves for hydroxyethyl methacrylate-water mixtures were determined as functions of polymerization time and initia tor. The non-Newtonian behavior of these systems was analyzed by a Bueche-Harding standard curve, by the Ree-Eyring generalized viscosity equation and by Bartenev's empirical equation. The relative rate of polymerization initiated with AIBN and various AIBN esters and the relationships between flow curves, molecular weight, molecular weight distribution and polymerization time are discussed. Literature Cited 1. Janacek, J., J. Macromol. Sci.-Revs. Macromol. Chem. (1973) C9 (1) 1-47. 2. Rudd, J. F., J. Poly. Sci. (1960) 44, 459. 3. Sabia, R., J. Appl. Poly. Sci. (1964) 8, 1053. 4. Graessley, W. W., and Prentice, J. S., J. Poly. Sci., A-2 (1968) 6, 1887. 5. Bueche, F., and Harding, S. W., J. Poly. Sci. (1958) 32, 177. 6. Ree, T., Eyring, H., J. Appl. Phys. (1955) 26, 793, 800. 7. Bartenev, G. Μ., Vysokomolekyluarnye Soedineniya (1964) 6, 2155. 8. Gregonis, D., Chen, C. M., and Andrade, J. D., this symposium. 9. Bueche, F., F. J. Chem. Phys. (1954) 22, 1570. 10. Graessley, W. W., J. Chem. Phys. (1965) 43, 2696. 11. Rouse, P. E., J. Chem. Phys. (1953) 21, 1272. 12. Ballman, R. L., and Simon, R. M., J. Poly. Sci. A-2 (1964) 2, 3557. 13. Graessley, W. W., Hazleton, R. L., and Lindeman, L. R., Trans. Soc. Rheology, (1967) 11, 267.



138

HYDROGELS FOR MEDICAL AND RELATED APPLICATIONS

14. Shih, C. K., Tran. Soc. Rheology (1970) 14, 83. 15. Graessley, W. W., J. Chem. Phys. (1967) 47, 1942. 16. Glasstone, S., Laidler, K., and Eyring, Η., "The Theory of Rate Processes," p. 483, McGraw Hill Book Company, New York, 1941. 17. Jhon, M. S., and Eyring, H., private communication. 18. Ma, S. M., Eyring, H., and Jhon, M. S., Proc. Natl. Acad. Sci. (USA) (1974) 71, 3096. 19. Eyring, H., Ree, T., and Hirai, N., Proc. Natl. Acad. Sci. (USA) (1958) 44, 1213. 20. Nakajima, Ν., Proc. 5th Intl. Cong. on Rheology, Ed. by Shigeharu Onogi, (1968) 4, 295. 21. Gabrysh, A. F., Eyring, H., Shimizu, M., and Asay, J., J. Appl. Phys. (1963) 34, 261. 22. DeWitt, T. W., Markovitz, H., Padden, F. J., and Zapas, L. J., J. Colloid Sci. (1955) 10, 174.


Hydrogels for Medical and Related Applications

Recommend Documents