Properties of Cellulose Acetate in Solution - ACS Symposium Series

6 Properties of Cellulose Acetate in Solution 1

Aggregation of Cellulose Triacetate in Dilute Solution G. C. BERRY and M . A. L E E C H

Downloaded by CORNELL UNIV on September 6, 2016 | http://pubs.acs.org Publication Date: April 21, 1981 | doi: 10.1021/bk-1981-0150.ch006

Department of Chemistry, Carnegie-Mellon University, 4400 Fifth Avenue, Pittsburgh, P A 15213

T h e r e a r e v e r y few p u b l i s h e d l i g h t s c a t t e r i n g i n v e s t i g a t i o n s o f d i l u t e s o l u t i o n s o f c e l l u l o s e t r i a c e t a t e , C ( 3 . 0 0 ) A [The n o t a t i o n C(D.S.)A i n d i c a t e s t h e d e g r e e o f a c e t y l s u b s t i t u t i o n (D.S.) o f t h e c e l l u l o s e a c e t a t e . ] A s t u d y b y P a t e l (1^) a n d c o w o r k e r s r e p o r t s l i g h t s c a t t e r i n g on f r a c t i o n s o f C(2.96)A i n a mixed s o l v e n t o f m e t h y l e n e c h l o r i d e a n d m e t h a n o l (50:50 v / v ) , u s i n g procedures s i m i l a r t o those employed b y Tanner and B e r r y ( 2 ) i n t h e i r s t u d y o n C ( 2 . 4 5 ) A i n t h e same m i x e d s o l v e n t . The a p p r o p r i a t e r e l a t i o n f o r the Rayleigh r a t i o R reads 6 2

2

!*• = ^ i + < s > h / 3 + 2 A c + ... 0 w (

L S

2

(1)

with K = K'CcWcc)

2 T

2

where ( s i s t h e l i g h t - s c a t t e r i n g a v e r a g e d mean-square r a d i u s o f g y r a t i o n , h = (4jtn/\) s i n 0/2, K i s a n o p t i c a l c o n s t a n t , a n d (^n/^c) i s t h e r e f r a c t i v e index increment o f t h e polymer m e a s u r e d a t c o n s t a n t c h e m i c a l p o t e n t i a l s o f s o l v e n t components and t e m p e r a t u r e . F o r m i x t u r e s c o n t a i n i n g a s o l u t e i n a twocomponent s o l v e n t , ( o i i / d c ) -j* i s r e l a t e d t o t h e c o n v e n t i o n a l r e f r a c t i v e i n d e x i n c r e m e n t ^ { c n / c c ) j P*T m e a s u r e d a t c o n s t a n t solvent composition by ^ 1

T

c

\

1

'JJ^T

\

' c ,p,T 3

\

3 /c ,p,T 2

This is the fourth work in a series by the authors. 0097-6156/81/0150-0061$05.00/0 © 1981 American Chemical Society Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

62

SOLUTION PROPERTIES OF POLYSACCHARIDES

w h e r e t h e s o l v e n t m i x t u r e h a s components 1 and 3 p r e s e n t i n v o l u m e f r a c t i o n cp^ and cp^ ( w i t h cpi+93 ^ * =

a n c

X = (dc«/dc )

(3)

9

( S e e , f o r e x a m p l e , t h e d i s c u s s i o n g i v e n b y E i s e n b e r g ( 3 ) . When d e a l i n g w i t h a m i x t u r e c o n t a i n i n g a s o l v e n t and a n o n s o l v e n t f o r t h e s o l u t e , we w i l l l e t component 3 d e n o t e t h e l a t t e r . In s t u d i e s o f C(2.45)A i n a methylene c h l o r i d e / m e t h a n o l m i x t u r e (50:50 v / v ) , T a n n e r and B e r r y f o u n d \ e q u a l t o -0.2 ( w i t h (^n/^C3> p T °«0982 m l / g ) , e . g . , t h a t m e t h y l e n e c h l o r i d e p r e f e r e n t i a l l y s o l v a t e d the polymer. Data o f P a t e l and c o w o r k e r s o n C ( 2 . 9 6 ) A f o r t h e same s o l v e n t m i x t u r e gave \ = - 0 . 3 , a l s o i n d i c a t i n g p r e f e r e n t i a l s o l v a t i o n o f t h e p o l y m e r by m e t h y l ene c h l o r i d e . Data o f S h a k h p a r o n o v e t a l . ( 4 ) f o r C ( 2 . 4 5 ) A i n methylene c h l o r i d e / m e t h a n o l mixtures c o n t a i n i n g 0 to 30% m e t h a n o l i n d i c a t e p o s i t i v e \, o r p r e f e r e n t i a l s o l v a t i o n b y metha n o l r a t h e r than methylene c h l o r i d e . T h e i r c o n c l u s i o n s a r e based on a p p a r e n t v a l u e s o f t h e m o l e c u l a r w e i g h t f r o m l i g h t s c a t t e r i n g , and a r e s u b j e c t t o e r r o r f r o m t h e e f f e c t s o f t h e a s s o c i a t i o n d i s c u s s e d b y T a n n e r and B e r r y . S i n c e the v a l u e s o f ( s ) / M f o r C(3.00)A a r e l a r g e , i t i s c o n v e n i e n t t o d i s c u s s them i n terms o f t h e w o r m - l i k e c h a i n m o d e l f o r which (5) =


C2

2

2

= ^

S(L/p

(4)

where L i s t h e c o n t o u r l e n g t h L = M/M

(5)

L

with t h e mass p e r u n i t c o n t o u r l e n g t h , p o f t h e p e r s i s t e n c e l e n g t h , and S ( L / p ) o f t h e f u n c t i o n 1

2

3

S(x) = l - 3 x " + 6 x " - h x " [ l - e x p ( - x ) ]

(6)

F o r L / p g r e a t e r t h a n a b o u t 10, S ( L / p ) i s e s s e n t i a l l y u n i t y . A p p r o x i m a t i n g M-^ by m / l , w h e r e t h e l e n g t h o f a r e p e a t i n g u n i t i s t a k e n t o be 0.545 nm, we g e t ML = 4 9 0 nm"! f o r C ( 3 . 0 0 ) A . The l i g h t s c a t t e r i n g d a t e on C ( 2 . 9 6 ) A o f P a t e l et_ a l . i n t h e 50/50 s o l v e n t m i x t u r e on f r a c t i o n s o v e r t h e m o l e c u l a r w e i g h t r a n g e 1 0 t o 1.7 x 1 0 g i v e 3 ( s ) / L e q u a l t o 65 nm. This e s t i m a t e i s much g r e a t e r t h a n t h e v a l u e p = 11 nm r e p o r t e d f o r C ( 2 . 4 5 ) A b y T a n n e r and B e r r y . T h u s , t h e d a t a o f P a t e l et a l . on C ( 2 . 9 6 ) A , s u g g e s t a much l e s s c o i l e d c h a i n c o n f o r m a t i o n t h a n i s i n d i c a t e d by r o t a t i o n a l i s o m e r i c s t a t e computations f o r c e l l u l o s i c c h a i n s . The v a l u e o f = 6 ( s ) / j ^ L computed w i t h t h e l a t t e r m o d e l i s r e l a t e d t o p by t h e e q u a t i o n Q

5

5

2

L S

w

2

Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.


6.

BERRY AND

LEECH

Cellulose

63

Triacetate

o r p = 2 . 7 3 CQQ f o r C ( 3 . 0 0 ) A . A c c o r d i n g t o Y a t h i n d r a and Rao ( 6 ) , e s t i m a t e s o f CQO v a r y i n t h e r a n g e 50 t o 80, d e p e n d i n g on the bond a n g l e a t t h e b r i d g e o x y g e n atom. C o n s e q u e n t l y , p i s e x p e c t e d t o be i n t h e r a n g e 13.1 t o 22 nm, i n r e a s o n a b l e a g r e e m e n t w i t h t h e d a t a o f T a n n e r and B e r r y o n C ( 2 . 4 5 ) A , b u t much l o w e r t h a n t h e e s t i m a t e f o r C ( 3 . 0 0 ) A b a s e d o n t h e d a t a o f P a t e l £ t al. I n some s y s t e m a t i c s t u d i e s o n C ( 3 . 0 0 ) A , M o o r e and R u s s e l l (_7) and l a t e r , F l o r y , S p u r r and C a r p e n t e r ( 8 ) i n v e s t i g a t e d t h e dependence o f [T|] o n s o l v e n t . I t was f o u n d t h a t [T\] was m a r k e d l y d e p e n d e n t o n s o l v e n t , b u t d i d n o t c o r r e l a t e w i t h the s e c o n d v i r i a l c o e f f i c i e n t A2 a s i s u s u a l f o r f l e x i b l e - c h a i n p o l y m e r s . Tanner and B e r r y showed t h a t t h e c h a i n e x p a n s i o n f a c t o r a i s c l o s e t o u n i t y f o r C(2.45)A on the b a s i s o f the v e r y s m a l l v a l u e s o f A2M /(s )3/2 b d experimentally. The low e x p a n s i o n o f C ( 2 . 4 5 ) A i s n o t n e c e s s a r i l y due t o s m a l l A 2 J b u t r a t h e r r e f l e c t s a l a r g e v a l u e o f < s ) / M , w h i c h has t h e c o n s e q u e n c e t h a t i n t r a m o l e c u l a r e x c l u d e d volume e f f e c t s may be s m a l l d e s p i t e l a r g e v a l u e s o f A2S i m i l a r e f f e c t s a r e d i s c u s s e d by H e l m i n i a k and B e r r y (£) i n r e l a t i o n t o s t u d i e s o n a p o l y m e r w i t h l i m i t e d f l e x i b i l i t y , i . e . , v e r y few a v a i l a b l e r o t a t i o n a l s t a t e s , s e p a r a t e d b y high barriers. As t h e y e m p h a s i z e d , t h e mere o b s e r v a t i o n t h a t a i s n e a r u n i t y d e s p i t e l a r g e v a l u e s o f A2 c a n n o t be t a k e n a s evidence f o r i n f l e x i b i l i t y . Presumably, a w i l l a l s o be n e a r l y u n i t y f o r C(3.00)A i n which case, as w i t h C(2.45)A, the v a r i a t i o n o f [T]] o r p w i t h s o l v e n t r e f l e c t s s h o r t - r a n g e s k e l e t a l e f f e c t s r a t h e r t h a n l o n g - r a n g e e x c l u d e d volume e f f e c t s . W o r m - l i k e c h a i n s t a t i s t i c s h a v e b e e n u s e d b y E i z n e r and P t i t s y n (1_0) f o r a bead m o d e l , and b y Yamakawa and F u j i i (11) f o r a c y l i n d e r m o d e l t o c a l c u l a t e [T|] a s a f u n c t i o n o f p , L and t h e c h a i n d i a m e t e r d. T h e i r r e s u l t s can be p u t i n t h e f o r m ([T|] i n dl/g). 2

2

0

s

e

r

v

e

2

M

L

[ T 1 ]

=

Tot

k f ( L / d , p/d)

(8)

The f u n c t i o n f ( L / d , p / d ) i s d i s c u s s e d i n more d e t a i l b y H e l m i n i a k and B e r r y , who p r o v i d e a g r a p h i c a l r e p r e s e n t a t i o n o f f ( L / d , p / d ) . I n t h e l i m i t a s L / p goes t o z e r o , t h e w o r m - l i k e c h a i n a d o p t s a r o d - l i k e c o n f o r m a t i o n and f ( L / d , p / d ) can be a p p r o x i m a t e d b y lim L/ =0

f(L/d, /d) p

= 0.0257 ( d / L ) °

-2

p

so

that


(9)

64

SOLUTION PROPERTIES OF

11m L/ =0

M_

~ 4.86

2

x 10 °

0

d

#

2

L

1

#

POLYSACCHARIDES

8

(10)

L

p

I n t h e o p p o s i t e e x t r e m e (and form


lim p/L=0

M

L

[

T

l

]=2

3

/

2

f o r l a r g e L ) Eqn. (8) t a k e s on

, p

3

/

2

L

1

/

2

the

(11)

L

21 w i t h $ a c o n s t a n t e q u a l t o 2.65 x 10 ( o f c o u r s e , i n Eqn. ( 1 1 ) , p i s independent of L ) . The d a t a o f P a t e l _et a l . on [T|] v e r s u s M f o r s o l u t i o n s o f f r a c t i o n s o f C ( 2 . 9 6 ) A i n c h l o r o f o r m g i v e [T|] L^*^. Consequentl y , even though p i s l a r g e f o r C(3.00)A, the c h a i n c o n f o r m a t i o n c a n n o t be c o n s i d e r e d t o be r o d - l i k e on t h e b a s i s o f the v i s c o metric data. N e i t h e r c a n [1]] be u n d e r s t o o d w i t h t h e l i m i t i n g f o r m Eqn. ( 1 1 ) f o r v e r y l a r g e L and s m a l l p / L . E v e n i f Eqn. (8) i s u s e d w i t h i n t e r m e d i a t e L / p , t h e dependence o f [T|] on M obs e r v e d by P a t e l e t a l . f o r c h l o r o f o r m s o l u t i o n s i s n o t c o n s i s t e n t w i t h t h e l a r g e v a l u e o f p c a l c u l a t e d f o r t h e i r d a t a on s o l u t i o n s i n the methylene c h l o r i d e / m e t h a n o l mixed s o l v e n t . For example, a p p l i c a t i o n o f Eqn. ( 8 ) g i v e s p e q u a l t o 3.5 nm f o r t h e v i s c o m e t r i c d a t a on c h l o r o f o r m s o l u t i o n s , compared w i t h 65 nm f o r t h e l i g h t s c a t t e r i n g d a t a on t h e s o l u t i o n s i n t h e m i x e d s o l v e n t . P o s s i b l e r e a s o n s f o r t h e d i s c r e p a n c y w i l l be c o n s i d e r e d b e l o w . Experimental Materials. S o l v e n t s used i n d i l u t e s o l u t i o n experiments w e r e f r e s h l y d i s t i l l e d p r i o r t o u s e , and t h e p o l y m e r was d r i e d u n d e r vacuum ( c a . 10" 5 mm Hg) f o r s e v e r a l days b e f o r e use i n t h e preparation of solutions. These p r e c a u t i o n s were taken to reduce t h e p o s s i b l e i n f l u e n c e o f a d s o r b e d w a t e r on t h e s o l u t i o n p r o p e r ties. The C ( 3 . 0 0 ) A p o l y m e r u s e d h e r e i s t h a t d e s c r i b e d by T a n n e r and B e r r y . S t u d i e s on D i l u t e S o l u t i o n s . The p r o c e d u r e s and i n s t r u m e n t a t i o n f o r d i f f e r e n t i a l refractometry l i g h t s c a t t e r i n g , viscometr y and s o l u t i o n d i a l y s i s a r e t h o s e g i v e n by T a n n e r and B e r r y . The d i a l y s i s e q u i p m e n t , shown s c h e m a t i c a l l y i n F i g u r e 1, i s s i m i l a r t o t h a t u s e d by T a n n e r and B e r r y , w i t h o u t e x p l i c i t description. D i l u t e s o l u t i o n s were b r o u g h t t o o s m o t i c e q u i l i b r i u m , u s i n g o s m o t i c p r e s s u r e membranes, o v e r a s e v e r a l h o u r p e r i o d by c o n t i n u o u s f e e d o f f r e s h m i x e d s o l v e n t w i t h t h e d e s i r e d c o n c e n t r a t i o n to the s o l v e n t s i d e of the d i a l y s i s c e l l . A b o u t 20 m l o f s o l u t i o n was r e t a i n e d on t h e s o l u t i o n s i d e , a g i t a t e d s l o w l y w i t h a magnetic s t i r r i n g bar. I n o r d e r t o a i d i d e n t i f i c a t i o n and a s s e s s m e n t o f p r e f e r e n t i a l l o s s o f one o f t h e m i x e d s o l v e n t components d u r i n g t h e


6.

BERRY A N D L E E C H

Cellulose

65

Triacetate

d i f f e r e n t i a l r e f r a c t i v e i n d e x measurement, a r e l a t i v e l y n o n v o l a t i l e s o l v e n t ( o r m i x e d s o l v e n t ) o f a b o u t t h e same r e f r a c t i v e i n d e x n was u s e d a s t h e r e f e r e n c e l i q u i d i n t h e r e f r a c t i v e i n d e x c e l l , r e p l a c i n g the mixed s o l v e n t used t o p r e p a r e t h e s o l u t i o n . The r e f r a c t i v e i n d e x A n b e t w e e n t h e m i x e d s o l v e n t u s e d f o r t h e s o l u t i o n and t h e r e f e r e n c e was d e t e r m i n e d p e r i o d i c a l l y d u r i n g e x p e r i m e n t s on t h e s o l u t i o n . S i n c e some o f t h e s o l v e n t s used o n t h i s s t u d y a r e m i x e d s o l v e n t s , w i t h b o t h components h a v i n g a h i g h v a p o r p r e s s u r e , i t was necessary t o study the v i s c o s i t y o f d i l u t e s o l u t i o n s w i t h sealed viscometers. C o m m e r c i a l l y a v a i l a b l e s u s p e n d e d - l e v e l Cannon v i s c o m e t e r s c o n s t r u c t e d t o p e r m i t s e a l i n g u n d e r vacuum were u s e d . The s o l u t i o n was f i l t e r e d i n t o t h e v i s c o m e t e r and d e g a s s e d b y s u c c e s s i v e f r e e z e - t h a w c y c l e s , a n d t h e v i s c o m e t e r was s e a l e d u n d e r vacuum. I n u s e , t h e v i s c o m e t e r was mounted o n a h o l d e r i n a constant temperature bath to permit the r o t a t i o n o f the v i s c o meter t o t h e h o r i z o n t a l t o f i l l the b u l b , and r o t a t i o n t o the v e r t i c a l f o r d e t e r m i n a t i o n o f the e f f l u x time.


Q

R e s u l t s and D i s c u s s i o n R e f r a c t i v e Index Increment. The r e f r a c t i v e i n d e x i n c r e m e n t fcn/^C2 o f t h e p o l y m e r (component 2 ) i n t h e s o l u t i o n was m e a s u r e d w i t h b o t h s i n g l e and two-component s o l v e n t s . W i t h t h e l a t t e r , t h e i n c r e m e n t was d e t e r m i n e d b o t h w i t h s o l u t i o n s a t c o n s t a n t s o l v e n t c o m p o s i t i o n and w i t h s o l u t i o n s d i a l y z e d t o o s m o t i c e q u i l i b r i u m o f t h e low m o l e c u l a r w e i g h t s o l v e n t s t o o b t a i n (OWC-C2)M»J

respectively. r

V a l u e s o f (^n/Bc2)cQ f ° s o l u t i o n s o f C ( 3 . 0 0 ) A i n s e v e r a l s o l v e n t s a r e g i v e n i n T a b l e I and F i g u r e 2. A v a l u e f o r c-n/&C2 Table I R e f r a c t i v e Index Increments (cW&C2) p f o r Cellulose Triacetate C

Component 1

Component 3

n Solvent (ml/g)

Methylene c h l o r i d e Methylene c h l o r i d e Methylene c h l o r i d e Methylene c h l o r i d e Chloroform s-Tetrachloroethane m-Cresol

Methanol Methanol Methanol

0.50 0.25 0.20 0 0 0 0

1.368 1.391 1.398 1.424 1.446 1.494 1.539

0.108 0.112 0.069 0.054 0.041 0.009 -0.028

V a l u e g i v e n By S h a r p i e s a n d Sweenton ( 1 2 )


a

66

SOLUTION PROPERTIES

O F POLYSACCHARIDES

Figure 1. Schematic of the equipment used to dialyze dilute solutions against a mixed solvent: solution chamber, C ; solvent chamber, C ; dialysis membrane, M; supporting glass frits, F; ground glass surface, S; teflon-coated magnetic stirrer, T; solvent inlet, I; outlet, O, teflon tubing, A; fresh solvent reservoir, R; and solvent waste, W. The chambers hold approximately 20 mL each.


t

2

0.20-

0.15-

Sn 8c

0.10

0.05

0.0 -0.05

-o.io 1.4

Refractive Index Figure 2. The refractive index increment (dn/dC )W3 for solutions of CTA in Tricresol (%); s-tetrachlorethane (%—); chloroform (w); methylene chloride (—and in mixtures of methylene chloride (1) and methanol (3) with cp = 0.20 (O); 0.25 (Q);and 0.50 (-O). 2

3


6.

BERRY AND

LEECH

Cellulose

67

Triacetate

f o r c h l o r o f o r m s o l u t i o n s due t o S h a r p i e s and Sweenton (12) i s i n c l u d e d i n F i g u r e 2 f o r c o m p a r i s o n . The d a t a i n F i g u r e 2 a r e compared w i t h t h e D a l e - G l a d s t o n e r e l a t i o n

= v ( n )

/ 2

C

2

V

(12)

s

3

where n i s t h e r e f r a c t i v e i n d e x o f t h e ( m i x e d ) s o l v e n t , t o g i v e t h e v a l u e s V £ = 0.746 m l / g and n£ = 1.505. These may be compared w i t h t h e c o r r e s p o n d i n g c o n s t a n t s V £ = 0.763 m l / g and n2 = 1.495 r e p o r t e d b y T a n n e r and B e r r y f o r s o l u t i o n o f C ( 2 . 4 5 ) A . I n s p e c t i o n o f F i g u r e 2 r e v e a l s t h a t w i t h s i n g l e component s o l v e n t s f o r C ( 3 . 0 0 ) A , Bn/cc3 I s g e n e r a l l y s m a l l , e.g. l o W c ^ l < 0.05. T h i s i s i n a c c o r d w i t h the l i m i t e d range o f s o l v e n t s f o r CTA and t h e g e n e r a l p r i n c i p l e t h a t " l i k e d i s s o l v e s l i k e . " F o r example, a n approximate c o r r e l a t i o n o f t e n o b t a i n s between the s o l u b i l i t y p a r a m e t e r $ o f t h e s o l v e n t a n d | £n/^2 U w i t h l o W d ^ l b e i n g l a r g e s t f o r s o l v e n t s w i t h $ most d i f f e r e n t f r o m t h e s o l u b i l i t y p a r a m e t e r 62 °f p o l y m e r a n d | 0*1/cC21 b e i n g n e a r l y z e r o f o r s o l v e n t s w i t h 6 « 62* E v i d e n t l y , w i t h CTA, t h e s o l v e n t p o l y m e r c o n t a c t s must be c o m p a r a b l e t o t h e p o l y m e r - p o l y m e r contacts for d i s s o l u t i o n t o occur. D e s p i t e repeated a t t e m p t s , the d a t a f o r the mixed s o l v e n t s a r e n o t a s p r e c i s e a s s h o u l d be e x p e c t e d . See, f o r e x a m p l e , t h e d a t a f o r (£n/dC2) 3 shown i n F i g u r e 2. R e p r e s e n t a t i v e d a t a o f A n v e r s u s Cn a r e g i v e n i n F i g u r e 3. S i n c e c o m p a r a b l e m e a s u r e ments o n C ( 2 . 4 3 ) A were more r e a d i l y c o m p l e t e d , we a r e a t a l o s s f o r a d e f i n i t i v e e x p l a n a t i o n f o r the d i f f i c u l t y e x p e r i e n c e d w i t h s o l u t i o n s o f C(3.00)A i n mixed s o l v e n t s . P o s s i b l e e x p l a n a t i o n s i n c l u d e the e f f e c t s o f s o l v e n t e v a p o r a t i o n , incomplete d i s s o l u t i o n o f the polymer o r ( p a r t i a l ) a b s o r p t i o n o f the polymer on v e s s e l w a l l s d u r i n g p r e p a r a t i o n and/or A n measurement. I n the o n l y d i r e c t c o m p a r i s o n w i t h p u b l i s h e d d a t a , we f i n d ( e n / ' c * ^ ^ 0.178 m l / g f o r C ( 2 . 9 6 ) A i n a 1:1 (by v o l u m e ) m i x t u r e o f m e t h y l e n e c h l o r i d e and m e t h a n o l , i n c o m p a r i s o n w i t h 0.130 m l / g f o r C ( 2 . 9 6 ) A r e p o r t e d b y P a t e l and c o w o r k e r s . The d i s p a r i t y i s l a r g e r t h a n s h o u l d be e x p e c t e d . V a l u e s o f ( c n / c * ^ ) found here are e n t e r e d i n Table I I , together w i t h ( c W & ^ a r t ^ " l a t e d w i t h Eqn. ( 1 ) , u s i n g (£n/dc ) = -0.0982 m l / g r e p o r t e d b y T a n n e r and B e r r y . A c c o r d i n g t o Cas^issa ( 1 3 ) , f o r some s y s t e m s f o r w h i c h \ e x h i b i t s no r e v e r s a l o f s i g n w i t h cp t h e q u a n t i t y c p ^ / x i s n e a r l y a l i n e a r f u n c t i o n o f 9 3 . P l o t s o f \ and cp-^/x v e r s u s 9 3 f o r t h e d a t a on C ( 3 . 0 0 ) A i n m i x t u r e o f m e t h y l e n e c h l o r i d e and m e t h a n o l a r e g i v e n i n F i g u r e 4 a and 4b, r e s p e c t i v e l y . The l i n e a r r e l a t i o n a p p l i e s w i t h i n the e x p e r i m e n t a l e r r o r o f o u r data g i v i n g the c o r r e l a t i o n


g

g

t

n

e

g

c

=

f

o

m T

a

b

l

e

1

a

n

d

c

a

l

c

u

3

3

cp (i_cp ) —2——3A

=

A(1+B

cp.) J


(13)

68

SOLUTION PROPERTIES OF POLYSACCHARIDES


An

C

2

Figure 3. Representative plots of An vs. C for CTA in solutions of CTA in the mixed-solvent methylene chloride (1) and methanol (3) with cp = 0.20. Data are for undialyzed (O) and dialyzed (•) solutions. 2

3

I

1

O.I

i

i

i

0.2

0.3

0.4

1

1

0.5

Figure 4. (a) The parameter \ = (dC /dC )M vs. the volume fraction cp of methanol for solutions of CTA in mixtures of methylene chloride and methanol; (b) The function op/Opa/A vs. qp for the data in Figure 4a (O), and for polystyrene in benzene (1) and methanol (3) and in carbontetrachloride (1) and methanol (3), according to Cassassa. 3

2

3

3


6.

BERRY A N D

LEECH

Cellulose

69

Triacetate

Table I I R e f r a c t i v e Index Increments o f C e l l u l o s e T r i a c e t a t e i n Mixed Solvent Component 1

Component

3 9^

x 2

Methylene Methylene Methylene


a

Methanol Methanol Methanol

Chloride Chloride Chloride

0,20 0.25 0.50

0.099 0.160 0.178

a

C

^ 2 ^ c

3

0.069 0.112 0.108

-0.30 -0.49 -0.71

( 1 ) and ( 2 ) f o r a d e f i n i t i o n o f X-

S e e Eqn.

a

f o r X s a f u n c t i o n o f ^3 w i t h A = -0.67 and B = - 1 . 1 . S i m i l a r d a t a f o r p o l y s t y r e n e i n b e n z e n e ( 1 ) and m e t h a n o l ( 3 ) , a n d i n c a r b o n t e t r a c h l o r i d e ( 1 ) and m e t h a n o l ( 3 ) d i s c u s s e d b y C a s a s s a a r e i n c l u d e d i n F i g u r e 4b f o r c o m p a r i s o n . I t was r e m a r k e d b y C a s a s s a t h a t a c r u d e m o d e l f o r p r e f e r e n t i a l s o l v a t i o n i n v o l v i n g " s p e c i f i c b i n d i n g s i t e s " on the polymer w i t h c o m p e t i t i v e b i n d i n g o f t h e two s o l v e n t s t o t h i s s i t e g o v e r n e d by a n i s o t h e r m d e p e n d e n t o n 93/cpi w i l l l e a d t o Eqn. ( 1 3 ) . I n t h i s m o d e l , t h e r e a r e presumed t o b e v b i n d i n g s i t e s p e r gram o f p o l y m e r , e a c h c a p a b l e o f b i n d i n g e i t h e r g ^ grams o f component 1 o r g3 grams o f component 3 s o t h a t t h e m a s s e s ^1 and 5 3 o f t h e two components bound t o 1 gram o f p o l y m e r a t e q u i l i b r i u m a r e r e l a t e d b y t h e mass b a l a n c e

h

h

•r g

g

l

and b y t h e ?

-~

+

=

1

4

)

3

isotherm

1

/ S

1 =

k 5 p

The m o d e l p r o v i d e s Eqn. ( 1 3 ) , w i t h A

(

v

1

3

V

w

h=0 d(Kc/R ) n

l l m

M

l i m

h=0

w

M m W

as)

= r

2-

w

c=0

2

d (^c Kc/RJ _H_ h

[

U

2

=

±1

l

s

t

t

;

( 1 9 )

0

2 W i t h t y p i c a l p o l y m e r s , i t i s found t h a t p l o t s of Kc/R v e r s u s h have s l o p e s t h a t a r e i n d e p e n d e n t o f c o n c e n t r a t i o n , as r e q u i r e d by Eqn. ( 1 ) . D e v i a t i o n s f r o m t h i s b e h a v i o r u s u a l l y d e n o t e e f f e c t s o f i n t e r m o l e c u l a r a s s o c i a t i o n . F o r e x a m p l e , T a n n e r and B e r r y reported that ^(KC/RQ)/^h i n c r e a s e d w i t h i n c r e a s i n g c f o r some s o l u t i o n s o f C ( 2 . 4 3 ) A . The l a t t e r a u t h o r s a l s o r e p o r t e d e x p e r i ments f o r w h i c h d ( K c / R Q ) / h was i n d e p e n d e n t o f c, b u t w h i c h Q

2

0



6.

Cellulose

71

Triacetate

revealed e f f e c t s o fa s s o c i a t i o n i n large values o f M ^ . The l i g h t s c a t t e r i n g d a t a o n s o l u t i o n s o f a C ( 3 . 0 0 ) A p o l y mer ( C M U - D T 7 5 ) s t u d i e d i n s e v e n d i f f e r e n t s o l v e n t s a r e summari z e d i n T a b l e I I I . D a t a o n K C / R Q v e r s u s h a r e shown i n F i g u r e s 5-8 f o r f o u r s y s t e m s , and d a t a o n K C / R Q v e r s u s c f o r two s y s t e m s ( t h e same m i x e d s o l v e n t s , w i t h 9 3 = 0.25 a n d 0.20) a r e shown i n F i g u r e 9. V a l u e s o f dn/dC2> o r ( d n / c ^ ) ^ f o r t h e m i x e d s o l v e n t s , g i v e n i n T a b l e I I , were u s e d t o compute M ^ . I t may be n o t e d t h a t e n t r i e s f o r T2 * ( ^)LS l i knowledge o f dn/ C2. I n s p e c t i o n o f t h e e n t r i e s i n T a b l e I I I shows t h a t t h e estimate f o r M i s n o t independent o f s o l v e n t w i t h values o f ^ i n t h e range 5.7 x 1 0 ^ t o 2.2 x 10^ ( d e l e t i n g a v e r y l a r g e e s t i m a t e i n £-tetrachloroethane, f o r w h i c h dn/dc2 i s v e r y s m a l l ) . I n a d d i t i o n , v a l u e s o f ( S ) L S v a r i e d c o n s i d e r a b l y among t h e s o l v e n t s s t u d i e d , a n d f o r most o f t h e d a t a t h e s l o p e ? \ ( K C / R Q ) / d h i s not independent o f c o n c e n t r a t i o n . I n obtaining the estimates o f M and ( s 2 ) given i n Table I I I , t h e data a t small s c a t t e r i n g a n g l e were n e g l e c t e d i n c a s e s f o r w h i c h K C / R Q v e r s u s s i n 9 / 2 was sharply curved. I t s h o u l d a l s o be r e m a r k e d t h a t p h a s e s e p a r a t i o n o c c u r r e d w i t h t h e s o l u t i o n i n t h e m i x e d s o l v e n t w i t h cp3 = 0.50 ( m e t h y l e n e c h l o r i d e / m e t h a n o l ) when t h e s o l u t i o n was a l l o w e d t o s t a n d a t 25°C. The v a r i a b i l i t y o f d ( K c / R Q ) d h w i t h c o n c e n t r a t i o n seen e s p e c i a l l y i n F i g u r e s 6 a n d 8, a n d t o some e x t e n t , i n F i g u r e 7 i n d i c a t e s t h a t the degree o f aggregation f o r C ( 3 . 0 0 ) A i n those s o l v e n t systems i n c r e a s e s w i t h i n c r e a s i n g polymer c o n c e n t r a t i o n . S i m i l a r r e s u l t s were r e p o r t e d f o r s o l u t i o n s o f C ( 2 . 4 5 ) A b y Tanner and B e r r y . The d a t a o b t a i n e d h e r e i n d i c a t e t h a t C ( 3 . 0 0 ) A i s a g g r e g a t e d t o v a r y i n g d e g r e e i n most ( o r p e r h a p s a l l . ) o f t h e solvents studied. The l o w e s t M i s o b t a i n e d i n t h e m e t h y l e n e c h l o r i d e / m e t h a n o l m i x e d s o l v e n t w i t h cp = 0.25 ( w i t h n e g l e c t o f t h e d a t a f o r s c a t t e r i n g angle l e s s than about 60 degrees as t h e l a t t e r a r e much a f f e c t e d b y t h e p r e s e n c e o f t h e a g g r e g a t e d s p e c i e s ) . The second v i r i a l c o e f f i c i e n t i s s m a l l e s t i n t h e system w i t h t h e l e a s t a g g r e g a t i o n , s i m i l a r t o b e h a v i o r r e p o r t e d b y Tanner and Berry for C(2.45)A. Since the r e f r a c t i v e index data suggest that C ( 3 . 0 0 ) A i s c o m p l e t e l y s o l v a t e d b y m e t h y l e n e c h l o r i d e when d i s s o l v e d i n m i x t u r e s o f m e t h y l e n e c h l o r i d e and m e t h a n o l , i t appears t h a t the mixed s o l v e n t o f the a p p r o p r i a t e composition ( e . g . n e a r l y 9 3 = 0.25) a c t s t o d i s s o l v e t h e m e t h y l e n e c h l o r i d e solvated C(3.00)A. The v a l u e s o f 10 ( s ) L S ^ W e n t e r e d i n T a b l e I I I v a r y f r o m 16 t o 5 9 , w i t h t h e l a r g e s t v a l u e c o r r e s p o n d i n g t o t h e m i x e d s o l v e n t f o r w h i c h M was s m a l l e s t . I t i s i n s t r u c t i v e t o compare (s )-| g/M w i t h the value expected f o r a worm-like chain according t o Eqns. ( 4 ) - ( 6 ) ( u s i n g M L = 4 9 0 n m " l ) . W i t h M = 5.7 x 1CA Eqns. ( 4 ) - ( 6 ) g i v e 1 0 S ( S 2 ) / M = 590 c m w i t h p = 5 0 nm, o r 2

A N C

d

S

o

n

o

t

r

e

c

u

r

e

0


W

2

2

W

L S

2

2

1

W

3

1

2

M

W

2

j

W

W

1

2


72


SOLUTION PROPERTIES O F POLYSACCHARIDES

2

Figure 6. Plots of Kc/Re vs. h for solutions of CTA in a mixture of methylene chloride (1) and methanol (3) with cp = 0.25 for four concentrations: (O-) 0.297 g/dL; (0)0.194 g/dL; (-O) 0.132 g/dL; and (Q) 0.091 g/dL. s




Cellulose

Triacetate

Figure 7. Light-scattering data for a dilute solution of cellulose triacetate in a mixture of methylene chloride (1) and methanol (3) with qp == 0.20. K ' = K(dn/ dc)»~ . The symbols O , —O, O—, and O designate solutions with concentrations of 3.80, 5.04, 6.67, and 8.39 g/L, respectively. 3

2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 8. Light-scattering data for a dilute solution of cellulose triacetate in tetrachloroethane, K ' = K(dn/dc)' . The symbols 0,0, O—, and O designate solutions with concentrations of 4.10, 6.22, 7.99, 8.93 g/L, respectively. 2



0.25

0.20

0

0

0

0

MeCl

MeCl

MeCl

Chloroform

s-TCE

m-cresol

25

25

25

25

20

17

35

T (°C)

6

2

0.174

(0.26)

0.031

0.28, 6 0.07

0.14

2.37

4

a

10~ (dn) M 1 2

2

620

a

2

a

M

T O

280

--

160

420

280

590

300

w

#^

10l8(

Solvents:

marked^ effect

--

precip. a t 25°C

Remarks

V a l u e s i n p a r e n t h e s e s a r e f o r systems w i t h low ( d n / d C ) . b 2 The q u a n t i t y d ( K c / R ) / o h d e c r e a s e d w i t h d e c r e a s i n g c o n c e n t r a t i o n ; t h e v a l u e o f (s ) / M e n t e r e d 2 L.b w was c a l c u l a t e d f r o m t h e v a l u e o f * ( K c / R ) / d h extrapolated to i n f i n i t e dilution.

22

1.9

1600

1060

30

2.4

(300 )

160

100

2.9

--

350

0.57

10

w

7.5

5

10" M

i n Mixed

300

2 (ml/g)

r

80

34

225

9

IS

(cm )

K>

f o r a C e l l u l o s e T r i a c e t a t e Polymer Component 1 + M e t h a n o l

M e C l = M e t h y l e n e C h l o r i d e ; js-TCE = s - T e t r a c h l o r o e t h a n e

0.50

*3

MeCl

Component 1

L i g h t S c a t t e r i n g Parameters

Table I I I


b


6.

Cellulose

75

Triacetate

1 0 ( s ) / M = 380 c m w i t h = 3 7 . 5 nm. The l a t t e r p r o b a b l y p r o v i d e s a r e a s o n a b l e e s t i m a t e f o r C ( 3 . 0 0 ) A b a s e d on t h e d a t a i n t h e m i x e d s o l v e n t w i t h 9 3 = 0.25, t a k i n g a p p r o x i m a t e a c c o u n t o f t h e p o l y d i s p e r s i t y o f t h e s a m p l e u s e d by a p p r o x i m a t i o n o f ( s 2 ) / M by ( s ) 5 / 1 . 5 M . T h i s e s t i m a t e o f p i s somewhat l a r g e r t h a n t h e v a l u e 11 nm r e p o r t e d f o r C ( 2 . 4 5 ) A b y T a n n e r and B e r r y , b u t s m a l l e r t h a n p found f o r C ( 2 . 9 6 ) A b y P a t e l and c o w o r k e r s i n s t u d i e s u s i n g t h e m e t h y l e n e c h l o r i d e / m e t h a n o l m i x e d s o l v e n t w i t h 9 3 = 0.5. The e x p e r i m e n t a l e s t i m a t e o f 37.5 nm f o r p may be compared w i t h t h e p r e d i c t i o n s o f t h e r o t a t i o n a l i s o m e r i c s t a t e model u s i n g t h e r e s u l t f o r C«, o f Y a t h i n d r a and Rao m e n t i o n e d a b o v e , f o r w h i c h p l i e s i n t h e r a n g e 13 t o 22 nm. The d i f f e r e n c e i s s m a l l enough to be a t t r i b u t e d t o e r r o r i n e x p e r i m e n t a l l i g h t s c a t t e r i n g , t h e e f f e c t s of r e s i d u a l intermolecular a s s o c i a t i o n , the e f f e c t s o f molecular weight d i s p e r s i t y , o r s o l v a t i o n e f f e c t s , which are n e g l e c t e d i n t h e t h e o r e t i c a l e s t i m a t e o f p. S u m m a r i z i n g t h e l i g h t s c a t t e r i n g d a t a , we f i n d e v i d e n c e f o r s u b s t a n t i a l a s s o c i a t i o n o f C ( 3 . 0 0 ) A i n most ( i f not a l l ) o f the s o l v e n t s s t u d i e d . The a s s o c i a t i o n i s most p r o n o u n c e d i n j n - c r e s o l and _ s - t e t r a c h l o r e t h a n e , a n d l e a s t i n t h e m i x e d s o l v e n t m e t h y l e n e c h l o r i d e ( 1 ) and m e t h a n o l ( 3 ) , w i t h 9 3 = 0.25. I n t h e l a t t e r , we f i n d a p e r s i s t e n c e l e n g t h o f a b o u t 37.5 nm, compared w i t h a c o n t o u r l e n g t h L^, o f 116 nm; t h e s y s t e m i s n e a r l y a t h e t a s o l v e n t a t 17°C, as shown b y t h e s m a l l v a l u e o f ^2* l 8

2

p

2


L

w

Intrinsic Viscosity. V i s c o s i t i e s of d i l u t e solutions determ i n e d w i t h c a p i l l a r y v i s c o m e t e r s were a n a l y z e d b y t h e u s u a l relations

\ sp J °

U

n

= W

+

)/c

k ,

tT]]

=

\el

1

a

n

d

2

(

c + ...

k

" 2 " ' ) t ^ =

w

i

t

h

(20)

2

c

+

a

n

••• d

< t

h

e

2 1 )

w h e r e T|sp = \ - e l ~ ^ r e l VjlO^ T\ f]0 viscosities o f s o l u t i o n and s o l v e n t , r e s p e c t i v e l y . Values o f the i n t r i n s i c v i s c o s i t y [T|] and t h e H u g g i n s c o n s t a n t k' d e t e r m i n e d w i t h f i v e d i f f e r e n t s o l v e n t s a r e g i v e n i n T a b l e 4. The v a l u e s o f [T]] and k a r e r e m a r k a b l y s i m i l a r t o e a c h o t h e r i n v i e w o f t h e a s s o c i a t i o n found i n t h e l i g h t s c a t t e r i n g results. S i m i l a r i n s e n s i t i v i t y o f [T]] t o t h e e f f e c t s o f a s s o c i a t i o n w e r e r e p o r t e d b y T a n n e r and B e r r y i n s t u d i e s o n C ( 2 . 4 3 ) A . Presumably, t h i s r e s u l t s from t h e i n s e n s i t i v i t y o f the hydrod y n a m i c volume t o a s s o c i a t i o n a t t h e l e v e l p r e s e n t i n c e l l u l o s e acetate solutions. I n an approximate treatment o f t h i s e f f e c t T a n n e r and B e r r y e s t i m a t e d t h e e f f e c t s o f a s s o c i a t i o n b y a model w i t h random c r o s s l i n k i n g o f c h a i n s o f p r i m a r y m o l e c u l e s , c a l c u l a t i n g t h e number, w e i g h t and z - a v e r a g e s o f t h e d e g r e e o f 1


76

SOLUTION

PROPERTIES

O F POLYSACCHARIDES

T a b l e IV I n t r i n s i c V i s c o s i t y o f CTA i n S e v e r a l S o l v e n t s Component

Component 3

3


Methylene C h l o r i d e Methylene C h l o r i d e Methylene C h l o r i d e Chloroform m-cresol

Methanol Methanol

25.0 24.7 24.9 25.0 25.0

0.25 0.20 0 0 0

----

k»

T (°c)

) o n i r r a d i a t e d p o l y d i m e t h y l s i l o x a n e a r e shown i n F i g u r e 10. I t c a n be s e e n t h a t s u b s t a n t i a l c r o s s l i n k i n g g i v e s r i s e t o o n l y modest i n c r e a s e i n [T|], s i m i l a r to the e f f e c t s o f a s s o c i a t i o n observed w i t h C(3.00)A. I f i t i s a c c e p t e d t h a t t h e v a l u e o f [T|] i s n e a r l y u n a f f e c t e d b y t h e l e v e l o f a s s o c i a t i o n p r e s e n t w i t h C ( 3 . 0 0 ) A , t h e n Eqn. ( 8 ) may be u s e d t o e s t i m a t e p f r o m d a t a on [T|] and L u s i n g , f o r examp l e , t h e f u n c t i o n f ( L / d , p / d ) c a l c u l a t e d by Yamakawa and F u j i i ( 1 1 ) , o r b y E i z n e r and P t i t s y n ( 1 0 ) . S i n c e we do n o t have [T|] as a f u n c t i o n o f L ( o r M ) , we a r e u n a b l e t o make a d e f i n i t i v e comp a r i s o n b e t w e e n d a t a o n C ( 3 . 0 0 ) A and Eqn. ( 8 ) . We c a n , h o w e v e r , use t h e e x p e r i m e n t a l v a l u e s o f [T|] and 1^ t o c a l c u l a t e p w i t h Eqn. ( 8 ) , u s i n g a r a n g e o f p l a u s i b l e v a l u e s f o r d. F o r e x a m p l e , w i t h 1 ^ = 116 nm and d = 1.2 nm, we f i n d p = 6nm. W i t h d = 0.5 nm, t h e e s t i m a t e f o r p i n c r e a s e s t o 8 nm. The e s t i m a t e o f p g i v e n by t h e l i g h t s c a t t e r i n g d a t a i s not reached even w i t h d as s m a l l a s 0.1 nm. The d i s p a r i t y b e t w e e n e s t i m a t e s o f p b a s e d o n t h e l i g h t s c a t t e r i n g and t h e v i s c o m e t r i c d a t a may i n d i c a t e t h a t t h e l i g h t s c a t t e r i n g data a r e a f f e c t e d by r e s i d u a l a s s o c i a t i o n , even w i t h t h e m e t h y l e n e c h l o r i d e / m e t h a n o l m i x e d s o l v e n t w i t h CD3 = 0.25. F o r example, i f M o f t h e C(3.00)A s t u d i e d i s l e s s than the e s t i m a t e 5.7 x 1 0 g i v e n by l i g h t s c a t t e r i n g s t u d i e s on t h e f o r m e r m i x e d s o l v e n t , r e v i s i o n w o u l d d e c r e a s e p^g b a s e d on t h e l i g h t s c a t t e r i n g d a t a s l i g h t l y ( o w i n g t o t h e c o m p e n s a t o r y e f f e c t s on (s^-)^/^ n o t e d a b o v e ) b u t w o u l d augment p^ d e d u c e d f r o m t h e v i s c o m e t r i c data. F o r e x a m p l e , 50 p e r c e n t r e d u c t i o n i n M w o u l d be e x p e c t e d t o h a v e l i t t l e e f f e c t on PLS* h u t p^ w o u l d be i n c r e a s e d t o a b o u t 17 nm. n

w

2


w

w

4

w

1

Summary The l i g h t s c a t t e r i n g d a t a o n d i l u t e s o l u t i o n s o f show e f f e c t s o f i n t e r m o l e c u l a r a s s o c i a t i o n i n a l l t h e component s o l v e n t s s t u d i e d , a n d i n two o f t h r e e m i x e d examined. I t i s p o s s i b l e that a s s o c i a t i o n i s minimal

C(3.00)A singlesolvents i n mixtures


6.


Cellulose

Triacetate

79


o f m e t h y l e n e c h l o r i d e ( 1 ) and m e t h a n o l ( 3 ) w i t h cp = 0.25, b u t t h i s i s a t e n t a t i v e conclusion a t present. A n a l y s i s o f the data w i t h t h e l e t t e r m i x e d s o l v e n t g i v e a p e r s i s t e n c e l e n g t h cp o f 4 0 nm f o r C ( 3 . 0 0 ) A . Data o n t h e r e f r a c t i v e i n d e x i n c r e m e n t o f C ( 3 . 0 0 ) A show t h a t a n / C 2 i s s m a l l f o r t h e a v a i l a b l e s i n g l e component s o l v e n t s f o r C ( 3 . 0 0 ) A , i n d i c a t i n g t h a t p o l y m e r - p o l y m e r i n t e r a c t i o n s l o s t on d i s s o l u t i o n must be r e p l a c e d b y s i m i l a r polymer-solvent interactions to effect s o l u b i l i t y . I n the mixed s o l v e n t m e t h y l e n e c h l o r i d e and m e t h a n o l , C ( 3 . 0 0 ) A i s a p p a r e n t l y n e a r l y completely s o l v a t e d by methylene c h l o r i d e . Viscometric data on d i l u t e s o l u t i o n s a r e r e l a t i v e l y i n s e n s i t i v e t o a s s o c i a t i o n i n t h e range e n c o u n t e r e d h e r e . A n a l y s i s o f t h e d a t a g i v e s a somewhat s m a l l e r v a l u e o f p t h a n t h a t o b t a i n e d f r o m t h e l i g h t s c a t t e r i n g data. Acknowledgment P a r t i a l s u p p o r t f o r t h i s study from the O f f i c e o f Water R e s e a r c h a n d T e c h n o l o g y , G r a n t No. 14-34-0001-7528, i s g r a t e f u l l y acknowledged.

Abstract Properties of cellulose triacetate, CTA, in dilute solution have been investigated using light scattering, refractometry, and viscometry with moderately concentrated solutions. The weight average molecular weight M was determined with solutions in seven different solvent systems, including four mixed solvents (different ratios of methylene chloride and methanol). Values of M varied over a wide range, revealing the presence of severe intermolecular association of CTA in dilute solution. The most reliable M was obtained in a mixed solvent with 0.75 methylene chloride: 0.25 methanol. The best estimate for the radius of gyration based on the light scattering data results in a persistence length p of 37 nm for CTA. The relative insensitivity of [η] to interchain association observed with CTA is similar to the effects reported on [η] for linear chains undergoing radiation induced crosslinking. The sort of randomly branched structure produced in the radiation crosslinked polymer may also be dominant with intermolecularly associated CTA. w

w

w

Literature 1. 2. 3.

Cited

Nair, P. R. M.; Gohel, P. M.; Patel, K. C.; Patel, R. D. Europ. Polym. J., 1977, 13, 273. Tanner, D. W.; Berry, G. C. J. Polym. Sci., Polym Phys. Ed., 1974, 12, 941. Eisenberg, H., "Biological Macromolecules and Polyelectrolytes in Solution", London, Oxford Univ. Press, 1976.


80

SOLUTION PROPERTIES

4. 5. 6. 7. 8. 9.


10. 11. 12. 13. 14. 15. 16.

O F POLYSACCHARIDES

Shakhparonov, M. J.; Zakwedazeva, N. F.; Podgorodetskii, Ye. K. Polym. Sci. USSR, 1967, 19, 1349. Yamakawa, H., "Modern Theory of Polymer Solution", New York, 1971. Yathindra, N.; Rao, V. S. R. Biopolymers, 1970, 9, 783. Moore, W. R.; Russel, J. J. Colloid Sci., 1954, 9, 338. Flory, P. J.; Spurr, O. K. Jr.; Carpenter, D. K. J. Polym. Sci., 1958, 27, 231. Helminiak, T. E.; Berry, G. C. J. Polym. Sci., Polymer Symp., 1978, 65, 107. Eizner, Y. E.; Ptitsyn, O. B. Vysokonol Soedin, 1962, 4, 1725. Yamakawa, H.; Fujii, M. Macromolecules, 1974, 7, 128. Sharpies, A.; Swinton, T. L. J. Polym. Sci., 1961, 50, 53. Casassa, E. F. Polym. J., 1972, 3, 517. Spiro, J. G.; Goring, D. A. I.; Winkler, C. A. J. Phys. Chem., 1964, 68, 323. Shultz, A. R.; Roth, P. I.; Rathmann, G. B. J. Polym. Sci., 1956, 22, 495. Kilb, R. W. J. Phys. Chem., 1959, 63, 1838.

R E C E I V E D September 22,

1980.


Properties of Cellulose Acetate in Solution - ACS Symposium Series

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