Dissolution Mechanism of Water-Soluble Polymers (Partially

Extra pure grade KCl, NaCl, CaCl 2 , Na-SO,, KSCN, n-butanol, ethyl ... KCl was further purified by re- crystallization .... polymer phase is large (9...
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20 Dissolution Mechanism of Water-Soluble Polymers (Partially Saponified Polyvinyl Acetates) Downloaded by UNIV OF MASSACHUSETTS AMHERST on June 1, 2018 | https://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/bk-1975-0009.ch020

HIRONOBU KUNIEDA and KŌZO SHINŌDA Department of Chemistry, Yokohama National University, Ooka-2, Minamiku, Yokohama, Japan

Introduction R e g u l a r s o l u t i o n s ( i n c l u d i n g i d e a l s o l u t i o n s and athermal s o l u t i o n s ) , electrolyte s o l u t i o n s and r e g u l a r polymer s o l u t i o n s were a l r e a d y fairly w e l l explored (1, 2, 3). The types o f s o l v e n t s and intermolecular f o r c e s i n v o l v e d i n these s o l u t i o n s c o v e r s wide v a r i e ties, namely, from water to h y d r o c a r b o n and from London d i s p e r s i o n f o r c e s to i o n - i o n i n t e r a c t i o n s . N e v e r t h e l e s s , s o l v e n t and s o l u t e mix randomly i n all o f t h e s e s o l u t i o n s and the t h e o r i e s a l s o assume random m i x i n g o f components. Such an idealization seems adequate i n t h e s e s o l u t i o n s , but it is the most simple and n a i v e idealization. These s o l u t i o n s , however, are r a t h e r e x c e p t i o n a l s o l u t i o n s among so many s o l u t i o n s t h a t we encounter i n n a t u r e , i n biological systems, i n the p r o c e s s o f manuf a c t u r i n g or i n e n v i r o m e n t a l problems. Hence, i n our o p i n i o n , the study on s o l u t i o n s o f more s o p h i s t i c a t e d , delicate and realistic systems i s c r a v e d f o r . Most striking f e a t u r e o f these s o l u t i o n s may be the d i s s o lution due to the o r i e n t a t i o n , arrangement and s t r u c t u r e f o r m a t i o n o f s o l u t e m o l e c u l e s , which are o t h e r wise practically i n s o l u b l e by random m i x i n g . One typical example i s a m i c e l l a r s o l u t i o n o f s u r f a c t a n t , i n which s u r f a c t a n t m o l e c u l e s o r i e n t , a r r a n g e and form micelles. The s o l u t i o n which i s e x p l o r e d i n r e c e n t two decades a p p l y i n g s o l u t i o n t h e o r y (4). The s a t u r a tion c o n c e n t r a t i o n o f m o l e c u l a r ( ionic) d i s p e r s i o n i s v e r y s m a l l , y e t the solubility i s u n e x p e c t e d l y l a r g e . Because, it d i s s o l v e s forming m i c e l l e s . Polymer which c o n s i s t s o f h y d r o p h i l i c groups and lypophilic groups may d i s s o l v e by o r i e n t a t i o n , rearrangement and s t r u c ture formation of molecules. T h i s type o f dissolution seems v e r y i m p o r t a n t , y e t not w e l l e x p l o r e d . 278

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

20.

KUNiEDA A N D SHiNODA

279

Water-Soluble Polymers

It i s with t h i s

image t h a t we began t h i s

study.

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Experimental Materials. P a r t i a l l y saponified polyvinyl acetate (PVA-Ac) were o b t a i n e d from Nihon G o s e i Kagaku Kogyo Co.. D i l u t e aqueous s o l u t i o n s o f PVA-Ac (2-5 w t l ) were heated and s e p a r a t e d i n t o two phases above the c l o u d point. I m p u r i t i e s which i s more w a t e r - s o l u b l e , such as s a l t s , were e l i m i n a t e d by r e p e a t e d décantation o f water phase. Then the samples were d r i e d by f r e e z e - d r y i n g , so t h a t they w i l l more e a s i l y mix w i t h water. PVA-Ac f r a c t i o n a t e d by adding water to acetone s o l u t i o n d i d not show a p p r e c i a b l e change i n the phase diagram. E x t r a pure grade K C l , N a C l , C a C l , Na-SO,, KSCN, n - b u t a n o l , e t h y l a c e t a t e , D - s o r b i t o l o f WaKo Pure Chem­ i c a l s Co. were used. KCl was f u r t h e r p u r i f i e d by r e c r y s t a l l i z a t i o n t h r e e times from water, s i n c e i t was used as s t a n d a r d s o l u t i o n f o r i s o p i e s t i c vapor p r e s s u r e measurements. 2

Procedures » Phase diagram. V a r i o u s amounts o f PVA-Ac, water, ( s a l t o r o r g a n i c compound) were s e a l e d i n ampoules. C l o u d p o i n t were determined by r a i s i n g and l o w e r i n g temperature at a r a t e o f 0.5°C per minute. In the case o f v e r y d i l u t e s o l u t i o n s , say l e s s than 1 w t l , the am­ p o u l e s were l e f t a t c o n s t a n t temperature from s e v e r a l hours t o 3 days t i l l the p r e c i p i t a t i o n o c c u r r e d , be­ cause i t was d i f f i c u l t to p e r c e i v e t h a t the s o l u t i o n became c l o u d y . Otherwise the apparent c l o u d p o i n t would have d e c r e a s e d w i t h c o n c e n t r a t i o n i n i t i a l l y . V a p o r - p r e s s u r e measurements. The vapor p r e s s u r e o f water i n aqueous s o l u t i o n s o f PVA-Ac was d e t e r m i n e d by the i s o p i e s t i c method (5») . A c y l i n d r i c a l g l a s s d i s h c o n t a i n i n g PVA-Ac s o l u t i o n was put on a glass-made sup­ porter placed i n a c y l i n d r i c a l , separable glass v e s s e l and r e f e r e n c e s o l u t i o n was added a t the bottom o f g l a s s vessel. A s e r i e s o f such samples was kept i n an a i r t h e r m o s t a t i n reduced p r e s s u r e f o r two to s i x months and the e q u i l i b r i u m c o n c e n t r a t i o n was determined by weight. KCl s o l u t i o n s were used as r e f e r e n c e s o l u t i o n s The water a c t i v i t i e s were i n t e r p o l a t e d from the ac­ t i v i t y - c o n c e n t r a t i o n r e l a t i o n g i v e n by Robinson and Stokes a p p l y i n g Debye-HUckel s f o r m u l a (2). 1

R e s u l t s and

Discussion

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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280

COLLOIDAL DISPERSIONS AND MICELLAR BEHAVIOR

Phase Diagram o f PVA-Ac-H-Q System. PVA-Ac was p r e p a r e d by a l k a l i s a p o n i f i c a t i o n o f p o l y v i n y l a c e t a t e i n aqueous acetone s o l u t i o n . It i s considered that PVA-Ac resembles the b l o c k copolymers o f v i n y l a c e t a t e v i n y l a l c o h o l (6, 7). In o r d e r t o be s o l u b l e i n water, s a p o n i f i c a t i o n cTegree o f PVA-Ac has to be more than 72 I o r so. I f the s a p o n i f i c a t i o n degree i s optimum, PVAAc d i s s o l v e s i n water a t lower temperature over a l l c o m p o s i t i o n but s p l i t s i n t o two phases a t h i g h e r tem­ perature. The phase diagram o f PVA-Ac-r^O as a f u n c ­ t i o n o f temperature i s shown i n F i g u r e 1. The c u r v e ABCD r e p r e s e n t s the mutual s o l u b i l i t y o f water and PVAAc. The shape o f the c u r v e as w e l l as the lower c r i t i ­ c a l s o l u t i o n temperature i m p l i e s t h a t the s o l u t i o n i s quite nonregular. I t i s c l e a r from F i g u r e 1 t h a t the l i q u i d - l i q u i d s o l u b i l i t y curve i s a f f e c t e d s e n s i t i v e l y to the s a p o n i f i c a t i o n degree, but not to the p o l y m e r i ­ z a t i o n degree. A l t h o u g h the s o l u t i o n i s so v i s c o u s and d i f f i c u l t to d i s s o l v e above 20-25 w t l (without the a i d o f added a l c o h o l ) , i t i s s o l u b l e i n water over a l l com­ p o s i t i o n below the c l o u d p o i n t , ( r e g i o n BC). The s o l u ­ t i o n becomes c l o u d y and s p l i t s i n t o two phases a t tem­ p e r a t u r e above the c l o u d p o i n t c u r v e . The one i s a po­ lymer phase c o n t a i n i n g a l a r g e amount o f water, and the o t h e r i s the water phase c o n t a i n i n g p r a c t i c a l l y no p o l ­ ymer. The water a c t i v i t y o f t h i s phase i s c l o s e to u n i t y as shown l a t e r . The s t e e p s l o p e o f BC c u r v e may be r e s u l t e d from the d i s t r i b u t i o n o f the s a p o n i f i c a t i o n degree o f polymers. The s o l u b i l i t y o f polymer i n water phase i s con­ v e n t i o n a l l y shown by In a

2

= In Φ

+ Φ (1

2

χ

- ν /ν ) 2

χ

+ V^B'/RT

(1)

On the o t h e r hand, the s o l u b i l i t y o f water i n polymer phase i s c o n v e n t i o n a l l y shown by In a

x

= In Φ

+ Φ (1

χ

2

- V /V ) + V^B'/RT 1

2

(2)

where a i s the r e l a t i v e a c t i v i t y , V. the m o l e c u l a r v o l ­ ume o f r e s p e c t i v e component i n s o l u t i o n , Φ- the volume f r a c t i o n and B the e n t h a l p y o f s o l u t i o n p e r u n i t v o l ­ ume ( 3 ) . I t i s e x p e c t e d from E q u a t i o n (1) t h a t the s o l u b i l i t y o f polymer may be v e r y s m a l l , because the m o l e c u l a r volume V and t h e r e f o r e the h e a t o f s o l u t i o n o f polymer i s v e r y l a r g e . I n v e r s e l y , the molar volume o f s o l v e n t V-, i s so s m a l l t h a t water d i s s o l v e i n f i n i t e ­ l y i n polymer, p r o v i d e d the heat o f s o l u t i o n p e r mole i s s m a l l e r than *RT. The c l o u d p o i n t c u r v e BC i n t e r s e c t s to the s o l u f

2

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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20.

KUNiEDA A N D SHiNODA

Water-Soluble Polymers

281

b i l i t y curve A B . S i m i l a r d i s c o n t i n u i t y i n s o l u b i l i t y curve i s observed i n n o n i o n i c s u r f a c t a n t - w a t e r system (8, 11). In the case o f p o l y m e r , curve AB approaches to tEe water a x i s much c l o s e r than n o n i o n i c s u r f a c t a n t s o l u t i o n , because polymer does not d i s s o c i a t e i n t o small molecules. Whereas the s a t u r a t i o n c o n c e n t r a t i o n of s u r f a c t a n t phase i s equal to the s a t u r a t i o n c o n c e n t ­ r a t i o n of single molecules. The s o l u b i l i t y of water i n polymer phase i s l a r g e (99.99 m o l e ! or 76 w t l ) a l r e a d y at p o i n t C . The d i s s o l u t i o n o f water i n t o polymer p r o ­ ceeds w i t h temperature d e p r e s s i o n due to the i n c r e a s e of i c e - b e r g f o r m a t i o n and h y d r a t i o n o f water s u r r o u n d ­ ing s o l u t e m o l e c u l e , and f i n a l l y water and polymer mix each o t h e r c o m p l e t e l y below the temperature a t B. The schematic diagram o f the d i s s o l u t i o n p r o c e s s o f polymer which c o n s i s t s o f h y d r o p h i l i c and l y p o p h i l i c g r o u p s , i n water i s shown i n F i g u r e 2. I t i s c o n s i d e r e d t h a t wa­ t e r d i s s o l v e s i n f i n i t e l y i n t o polymer phase and pseudophase i n v e r s i o n o c c u r s i n polymer phase. I f i t hap­ pens, water becomes c o n t i n u o u s phase. Polymer mole­ c u l e s w i l l o r i e n t , r e a r r a n g e so as to decrease the f r e e energy o f m i x i n g . T h i s phenomena i s a k i n to the m i c e l l a r d i s s o l u t i o n o f s u r f a c t a n t due to the i n c r e a s e o f water s o l u b i l i t y i n t o n o n i o n i c s u r f a c t a n t phase at low temperature (11). I f the s a p o n i f i c a t i o n degree o f PVAAc i s s m a l l e r , i . e . , l e s s h y d r o p h i l i c , the curve BC w i l l s h i f t to lower temperature and CD c u r v e w i l l s h i f t to h i g h e r c o n c e n t r a t i o n , because the h y d r a t i o n o f water per u n i t weight o f polymer w i l l d e c r e a s e . Only s w e l l ­ ing o f water i n polymer may occur below a c e r t a i n s a ­ p o n i f i c a t i o n degree (y70 I ) , and i n s o l u b l e i n w a t e r . A l t h o u g h molecules are aggregated to m i c e l l e s by p h y s ­ i c a l bond i n the case o f s u r f a c t a n t , and monomers are connected by c o v a l e n t bond i n p o l y m e r , the mechanism of d i s s o l u t i o n i n water i s s i m i l a r . Important c o n d i ­ t i o n s f o r complete d i s s o l u t i o n o f these substances are 1) the f i n i t e a g g r e g a t i o n o f these molecules i n water and 2) i n f i n i t e m i x i n g w i t h w a t e r . R e l a t i v e A c t i v i t y o f Water i n PVA-Ac-H^O System. The r e l a t i v e a c t i v i t y o f water i n aqueous s o l u t i o n o f PVA-Ac ( s a p o n i f i c a t i o n degree 75.6 %, p o l y m e r i z a t i o n degree 2200) at 25 °C i s p l o t t e d i n F i g u r e 3. Because of the l a r g e m o l e c u l a r w e i g h t , polymer s o l u t i o n whose weight per cent ranges from 0 to 50 w t l c o r r e s p o n d s to 0 - 0.00015 i n mole f r a c t i o n u n i t . The d o t t e d l i n e ex­ p r e s s e s the r e l a t i v e a c t i v i t y o f water i n i d e a l d i l u t e solution. The curve r e p r e s e n t s the r e l a t i v e a c t i v i t y of water determined by i s o p i e s t i c method. The r e l a t i v e a c t i v i t y o f water i s p r a c t i c a l l y equal to 1 up to 40

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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282

C O L L O I D A L DISPERSIONS A N D M I C E L L A R

20' 0 HzO

0.2 weight

' 0.4 fraction

BEHAVIOR

'—ι 06 PVA-Ac

Figure 1. Phase diagram of PVA-Ac-H 0 as functions of temperature, saponification degree (D.S.), and polymerization degree (D.P.). Ç): O.P. 2200, 80% saponified. Φ: O.P. 2200, 75.6% saponified. Q: O.P. 1200, 75.1% saponified. O: D.P. 550, 74.1% saponified. 2

HzO

Polymer

tfU

^

Figure 2. Schematic of dissolution process of polymer in water consisting of hydrophilic and lypophilic groups

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

20.

K U N i E D A AND

WaterSoluble Polymers

SHiNODA

283

w t l s o l u t i o n , i . e . , d e v i a t e to p o s i t i v e s i d e from t h a t o f i d e a l s o l u t i o n . A p p l y i n g Gibbs-Duhem e q u a t i o n ,

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^ ί

1

^

1

)

+

χ

2

2 ( τ ΐ τ )

=

0

( 3 )

we know t h a t the a c t i v i t y o f polymer a l s o does not change w i t h c o n c e n t r a t i o n . The r e l a t i v e a c t i v i t y of water d e c r e a s e s r a p i d l y above 40 wt% s o l u t i o n . I t can be c o n c l u d e d from t h i s r e s u l t t h a t the s o l u t i o n i s a k i n to two phase m i x t u r e o f pure water and water s w o l l e n polymer phase. Hence, we know one phase s o l u t i o n below the c l o u d p o i n t (25 C) and two phase s o l u t i o n above the c l o u d p o i n t (60 °C) i n F i g u r e 1 resemble each o t h e r t h e r m o d y n a m i c a l l y , but not o p t i c a l l y . The d i f f e r e n c e between two s t a t e s i s t h a t the h y d r a t e d polymer aggre­ gates i n f i n i t e l y above the c l o u d p o i n t , whereas the a g g r e g a t i o n i s f i n i t e below the c l o u d p o i n t . The mutu­ a l s o l u b i l i t y o f l i q u i d s i n o r d i n a r y s o l u t i o n changes, g r a d u a l l y w i t h temperature. On the c o n t r a r y , polymer (PVA-Ac) i s p r a c t i c a l l y i n s o l u b l e i n w a t e r above the c l o u d p o i n t , but i t mixes w i t h water over a l l composi­ t i o n s l i g h t l y below the c l o u d p o i n t . I t i s concluded t h a t the change from the complete s o l u b i l i t y to i n s o l ­ u b i l i t y w i t h the s m a l l change o f temperature i s charac­ t e r i s t i c to polymers. S i m i l a r phenomenon can be ob­ s e r v e d a l s o to the minute change i n h y d r o p h i l i c - l y p o p h i l i c b a l a n c e o f polymer m o l e c u l e s , because the c l o u d p o i n t o f PVA-Ac i s moved to h i g h e r or lower temperature depending on the s a p o n i f i c a t i o n degree. I t i s a l s o de­ p r e s s e d or r a i s e d i n the p r e s e n c e o f t h i r d s u b s t a n c e s . The e f f e c t o f added i n o r g a n i c s a l t s and o r g a n i c a d d i ­ t i v e s on the c l o u d p o i n t o f 2 w t l aqueous s o l u t i o n o f PVA-Ac ( s a p o n i f i c a t i o n degree 75.6 % and p o l y m e r i z a t i o n degree 2200) i s shown i n F i g u r e s 4 and 5. The t r e n d s o f the change o f c l o u d p o i n t i n PVA-Ac s o l u t i o n i s s i m i l a r to those i n aqueous s o l u t i o n o f n o n i o n i c s u r ­ f a c t a n t (12). I t i s then c o n c l u d e d t h a t the change from complete s o l u b i l i t y to i n s o l u b i l i t y o f polymer w i t h water may occur by the a d d i t i o n of t h i r d sub­ stances at a c o n s t a n t temperature. Complete i n s o l u b i l ­ i t y and s o l u b i l i t y are i m p o r t a n t , because b i o l o g i c a l t i s s u e has to be f a i r l y h y d r o p h i l i c and y e t c o m p l e t e l y insoluble. C o n d i t i o n s o f the Complete D i s s o l u t i o n o f WaterS o l u b l e PolymefsT In the p r o c e s s o f the d i s s o l u t i o n o f a w a t e r - s o l u b l e polymer, many f a c t o r s come i n t o play. 1. L i q u i d s t a t e o f polymer i n the p r e s e n c e o f s o l v e n t . D i s s o l u t i o n o f polymer w i t h s o l v e n t i s , i n r e a l i -

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

C O L L O I D A L DISPERSIONS A N D M I C E L L A R

1

~W \

0

025

i.oooor^-^ '

weight 0.40

fraction 0.50

0.60

~

1

0.9998

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0.9994 μ

o.oooi

0

H2O

0.2

0.4 mole

0.6

0.8

1.0 PVA-Ac

fraction

Figure 3. Relative activity of water in aqueous solu­ tion of PVA-Ac (saponification degree, 75.69c; polym­ erization degree, 2200) at25°C

0

1.0

0.5 lomc

S'rength

Figure 4. Effect of added inorganic salts on the cloud point of 2 wt % aqueous solution of PVA-Ac (saponification degree, 75.6%; polymerization degree,

2m)

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

BEHAVIOR

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20.

K U N i E D A AND SHiNODA

Wat er-Soluble Polymers

Figure 5. Effect of organic additives on the cloud point of 2 wt % aqueous solution of PVA-Ac (saponi­ fication degree, 75.6%; polymerization degree, 2200)

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

285

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286

C O L L O I D A L DISPERSIONS A N D M I C E L L A R

BEHAVIOR

ty the d i s s o l u t i o n o f s o l v e n t i n t o polymer, because the s o l u b i l i t y o f polymer i n s o l v e n t i s n e g l i g i b l y s m a l l . I t i s n e c e s s a r y t h a t a polymer i s i n a l i q u i d s t a t e i n the p r e s e n c e o f s o l v e n t , so t h a t s o l v e n t can mix w i t h polymer. 2. Linear molecule. I f a polymer i s t h r e e d i m e n s i o n a l i t w i l l s w e l l s o l v e n t , but the s w e l l i n g does not proceeds i n f i n i t e l y . 3. F l e x i b l e molecular structure. Polymers which p o s s e s s both h y d r o p h i l i c and l y p o p h i l i c groups have t o o r i e n t and r e a r r a n g e so as to de­ c r e a s e the energy o f m i x i n g w i t h water. In t h i s con­ t e x t b l o c k polymer may be p r e f e r a b l e . . E n t h a l p y o f m i x i n g , V,B , has to be s m a l l e r than *RT. 4. H y d r o p h i l e - L i p o p h i l e B a l a n c e (HLBJ and Pseudo-Phase Inversion. The most i m p o r t a n t f a c t o r i n the p r o c e s s o f d i s s o ­ l u t i o n o f w a t e r - s o l u b l e polymer seems t o be 1) the s w e l l i n g o f s o l v e n t i n polymer and 2) i n v e r s i o n o f the c o n t i n u o u s medium from polymer to water. T h i s means t h a t i n the f i r s t i n s t a n c e the polymer i s the c o n t i n u ­ ous medium, but i n the next s t e p the w a t e r - s o l u b l e p o l ­ ymer m o l e c u l e s o r i e n t themselves so as to d e c r e a s e the energy o f m i x i n g , h y d r o p h i l i c groups b e i n g o r i e n t e d o u t s i d e and h y d r o p h o b i c groups i n s i d e and f i n a l l y water becomes the c o n t i n u o u s medium due t o the i n c r e a s e o f d i s s o l v e d water. Once t h i s pseudo-phase i n v e r s i o n oc­ c u r s i n the polymer phase, b o t h phase may e a s i l y mix. f

Literature

Cited

1. H i l d e b r a n d , J . H., e t al., "Regular S o l u t i o n s " P r e n t i c e - H a l l , Englewood Cliffs. N.J. 1962, "Regular and R e l a t e d S o l u t i o n s " Van Nostrand R e i n h o l d Co., New York, N.Y. 1970. 2. Robinson, R. Α., and S t o k e s , R. Η., "Electrolyte S o l u t i o n s " B u t t e r w o r t h s , London, 1959. 3. F l o r y , P. J . , "Principles of Polymer C h e m i s t r y " C o r n e l l U n i v . P r e s s , I t h a c a , N.Y. 1953. 4. Shinoda, Κ., e t al., "Colloidal Surfactants" Academic P r e s s , New York, 1963. 5. Robinson, R. Α., and Sinclair, D. Α., J . Am. Chem. Soc., (1934) 56 1830. 6. N a g a i , Ε., Kobunshi Kagaku, (1955) 12 195. 7. Sakurada, I . , Kobunshi, (1968) 17 21. 8. Balmbra, P. R., C l u n i e , J . S., Corkill, J . Μ., and Goodman, J. F., T r a n s . Faraday Soc., (1962) 58 1661. 9. Corkill, J . Μ., Goodman, J . F., and H a r r o l d , S. P., ibid. (1964) 60 202. 10. C a r l e s s , J . E., Challis, R. Α., and M u l l e y , Β. Α.,

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

KUNiEDA AND SHiNODA

Water-Soluble Polymers

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J. Colloid I n t e r f a c e Sci., (1964) 19 201. 11. Shinoda, Κ., ibid. (1970) 34 278. 12. M a c l a y , W. Ν., ibid. (1956) 11 272.

Mittal; Colloidal Dispersions and Micellar Behavior ACS Symposium Series; American Chemical Society: Washington, DC, 1975.