Foam Fractionation of Polymer Mixtures in a Nonaqueous Solvent

toward exclusion of high molecular weight PS from the ... case 2, separation was selective to high molecular weight ... in the foam breaker is called ...
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15 Foam Fractionation of Polymer Mixtures in a Nonaqueous Solvent System R. P. CHARTOFF and L. T. C H E N

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University of Dayton, The Center for Basic and Applied Polymer Research, Dayton, OH 45469 R. J. ROE University of Cincinnati, Department of Metallurgy and Materials Science, Cincinnati, OH 45221

The selectivity obtained in the foam fractionation of polymer mixtures in a nonaqueous solvent system was studied and related to a multilayer theory of adsorption of polymers. Two mixtures of polymethyl methacrylate (PMMA) and polystyrene (PS) in xylene were fractionated using a batch foaming technique with and without addition of a surfactant. The two mixtures consisted of (1) two commercial samples with broad molecular weight distributions (MWD) with PS having the higher weight-average molecular weight (Mw), and (2) two narrow-distribution polymers differing greatly in Mw with PS again having the higher value. In case 1, although little separation occurred without surfactant, the trend was toward exclusion of high molecular weight PS from the foamate. This trend was more pronounced and the amount of separation was improved by adding surfactant. In case 2, separation was selective to high molecular weight PS when fractionation was carried out without surfactant. With surfactant added, the foamate was enriched in low molecular weight PMMA. No conclusive results were obtained on the effect of bubble size on separation efficiency, although the data pointed toward an improvement with decreasing bubble size. These observations were consistent with the trends predicted by a multilayer theory of adsorption of polymers from solution. 0065-2393/83/0203-0271$06.00/0 © 1983 A m e r i c a n C h e m i c a l Society

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

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F O A M F R A C T I O N A T I O N is a t e c h n i q u e t h a t u s e s a d s o r p t i o n o f a c o m p o n e n t o r s o l u t e at b u b b l e s u r f a c e s to s e p a r a t e t h e c o m p o n e n t f r o m a s o l u t i o n . B u b b l e s a r e p r o d u c e d b y s u p p l y i n g gas at t h e b o t t o m o f t h e l i q u i d p o o l . T h e b u b b l e s f o r m a f o a m , r i s e to t h e t o p o f t h e l i q u i d , a n d then overflow into a foam breaker. T h e concentrated l i q u i d collected i n the foam b r e a k e r is c a l l e d foamate. B y c a r r y i n g out the f o a m i n g process i n v e r t i c a l glass tubes or c o l u m n s , the d y n a m i c s o f b u b b l e formation, foam generation, a n d foamate c o l l e c t i o n m a y be o b s e r v e d conveniently. B e c a u s e t h e s o l u t e i s c o n c e n t r a t e d at t h e s u r f a c e o f t h e b u b b l e s , the size a n d d y n a m i c s o f the b u b b l e s are i m p o r t a n t i n f o a m f r a c t i o n a t i o n . T h u s , b u b b l e s i z e , gas f l o w r a t e , a n d c o l u m n d i a m e t e r w e r e a m o n g the process parameters s t u d i e d . I n a d d i t i o n , solution paramet e r s s u c h as s o l u t e c o n c e n t r a t i o n a n d m o l e c u l a r s i z e , c h o i c e o f s o l v e n t , a n d a d d i t i o n of a surfactant w e r e c o n s i d e r e d . T h i s chapter r e v i e w s the m o r e s i g n i f i c a n t o f t h e s e factors i n t e r m s o f t h e e x p e r i m e n t a l t r e n d s o b s e r v e d a n d t h e i r r e l a t i o n to a m u l t i l a y e r t h e o r y of a d s o r p t i o n of p o l y m e r s f r o m s o l u t i o n a d v a n c e d b y R o e (1—3).

Background

Information

F o a m f r a c t i o n a t i o n o f p o l y m e r s h a s r e c e i v e d r e l a t i v e l y l i t t l e att e n t i o n from researchers, p r o b a b l y b e c a u s e the process of foam fract i o n a t i o n is c o m p l e x , a n d o n l y l i m i t e d s u c c e s s h a s b e e n a c h i e v e d i n t h e s t u d i e s p u b l i s h e d p r e v i o u s l y . A s u m m a r y o f r e l e v a n t l i t e r a t u r e is p r o v i d e d i n T a b l e I. A m o n g the v a r i o u s types of separations a t t e m p t e d b y foam fract i o n a t i o n are those b y m o l e c u l a r size variants i n c l u d i n g m o l e c u l a r w e i g h t , b r a n c h i n g , a n d s t e r e o r e g u l a r i t y as w e l l as t h o s e b y c o p o l y m e r c o m p o s i t i o n a n d f u n c t i o n a l i t y . T h e w o r k r e p o r t e d h e r e is u n i q u e i n that it considers the s e l e c t i v i t y i n separation of m i x t u r e s of a polar a n d nonpolar p o l y m e r i n a nonaqueous system. M o s t of the studies p u b l i s h e d p r e v i o u s l y w e r e o n aqueous systems a n d the separation of m i x t u r e s of t w o d i s t i n c t p o l y m e r s b y foam fractionation has not b e e n reported previously.

Theoretical O n e u s e f u l p r o p e r t y o f p o l y m e r s is that p o l y m e r m o l e c u l e s r e a d i l y b e c o m e a d s o r b e d to s o l i d s u r f a c e s f r o m s o l u t i o n . T h i s t e n d e n c y for adsorption is b o t h m o l e c u l a r w e i g h t d e p e n d e n t a n d c o m p o s i t i o n dep e n d e n t so t h a t u n d e r d i f f e r e n t c o n d i t i o n s d i f f e r e n t t y p e s o f s e l e c t i v ity may be observed. E x a m p l e s of selective adsorption occur a m o n g polymers differing s i m p l y i n molecular weight, h a v i n g different c h e m i c a l compositions, or a m o n g p o l y m e r s of the same type b u t dif-

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983. Foam

polydimethylsiloxane (benzene) polymethyl methacrylate ( P M M A ) (benzene) P M M A , polystyrene (xylene)

1973

1974 1976 1979

1968, 1969

1977

1981

10

11 12 13

14 15 16

17

Nonaqueous

Foam

Studied

molecular weight, composition

stereoregularity

molecular weight

chain branching chain branching, molecular weight molecular weight

copolymer composition, functional groups

Fractionation

PVA poly(methacrylie acid— co-methyl methacrylate) poly(methyl methacrylateco-n,n ' - d i m e t h y l a m i n o e t h y l methacrylate) PVA PVA alkyd resin

1972 1970

Effect

molecular weight stereoregularity molecular weight, stereoregularity, functional groups stereoregularity, chain branching copolymer composition, functional groups

Fractionation

8 9

polyvinyl alcohol (PVA) PVA PVA

Aqueous

1958 1961, 1963 1962

Date

4 5,6 7

References

Polymer

T a b l e I. Relevant Literature on F o a m Fractionation of Polymers

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00

to

8*

2 ο 2". ο

ο

H >

w

ο

X >

η

274

POLYMER CHARACTERIZATION

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fering i n stereoregularity. Selective adsorption also occurs copolymers differing i n comonomer composition.

among

I n a l l o f these cases, a d s o r p t i o n t e n d s to b e h i g h l y c o m p e t i t i v e w i t h o n e t y p e o f m o l e c u l e b e i n g a d s o r b e d a l m o s t e x c l u s i v e l y at t h e expense of another e v e n though only m i n o r differences exist i n the adsorption affinity of the species. Q u a l i t a t i v e l y , the selectivity exp e c t e d for a d s o r p t i o n o f p o l y m e r m o l e c u l e s f r o m s o l u t i o n onto a s o l i d s u b s t r a t e c a n b e d e s c r i b e d b y t h e o r i e s s u c h as t h e m u l t i l a y e r t h e o r y o f a d s o r p t i o n a d v a n c e d b y R o e (I - 3 ) . R o e ' s t h e o r y d e s c r i b e s a d s o r p t i o n at s u r f a c e s i n t e r m s o f t h e s o l v e n t p o w e r , t h e 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 solute, the solution composition, the thickness of the ads o r b e d layer, the shape of the a d s o r b e d p o l y m e r c h a i n s , etc. T h e theory confirms the b e l i e f that e v e n small differences i n segmental a d s o r p t i o n a f f i n i t i e s are m a g n i f i e d g r e a t l y b e c a u s e o f t h e s h e e r n u m b e r o f a n c h o r i n g segments p e r m o l e c u l e . T h i s factor leads to t h e extreme selectivity observed d u r i n g adsorption. T h e s a m e t h e o r e t i c a l c o n s i d e r a t i o n s s h o u l d a p p l y to a d s o r p t i o n o f p o l y m e r m o l e c u l e s at t h e g a s — l i q u i d i n t e r f a c e f o r m e d b y t h e b u b b l e s i n a f o a m . A c c o r d i n g to t h e t h e o r y , the f o l l o w i n g t r e n d s are p r e d i c t e d : 1. F o r a s i n g l e s o l u t e w i t h a m i x t u r e o f m o l e c u l a r w e i g h t s , h i g h e r m o l e c u l a r w e i g h t p o l y m e r w i l l h a v e a g r e a t e r aff i n i t y f o r t h e i n t e r f a c e at l o w - s o l u t e c o n c e n t r a t i o n s . 2. F o r m u l t i p l e s o l u t e s , t h e p o l y m e r h a v i n g s t r o n g e r i n teraction w i t h the interface w i l l be adsorbed w h i l e the other w i l l b e e x c l u d e d , e v e n i f its a d s o r p t i o n affinity is only slightly less. 3. A l s o f o r m u l t i p l e s o l u t e s , a p o l y m e r h a v i n g n o o r l i t t l e interaction w i t h the interface w i l l be excluded, the h i g h e r its m o l e c u l a r w e i g h t the greater the e x c l u s i o n . 4. P o o r s o l v e n t s p r o m o t e a d s o r p t i o n . T h e theory represents the e q u i l i b r i u m l i m i t i n g case. I n practice, a l t h o u g h t h e s e p r e d i c t i o n s s h o u l d i n d i c a t e t h e t r e n d s to b e e x p e c t e d i n terms of selectivity, 100% efficiency cannot be achieved i n the l a b o r a t o r y . T h e p u r p o s e o f t h i s s t u d y , h o w e v e r , w a s to t e s t o u r o r i g i n a l hypothesis by d e t e r m i n i n g i f the trends observed i n foam fractionation e x p e r i m e n t s w e r e consistent w i t h the theory, a n d w h a t effect various process parameters h a d on the separation efficiencies observed.

Experimental A schematic d r a w i n g of the foam fractionation apparatus u s e d is s h o w n i n F i g u r e 1. It is a closed-loop system i n w h i c h dry nitrogen is saturated w i t h solvent a n d t h e n c i r c u l a t e d . T w o glass c o l u m n s , one w i t h a 2 5 - m m i n s i d e diameter (ID) a n d one w i t h a 2 0 - m m I D are connected to the gas source a n d a single central foamate collector. B o t h c o l u m n s are 65—70 c m l o n g . F o a m is

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

Figure

2

1. Foam fractionation apparatus. Key: A, N gas; B, desiccant; C, manometer; D, pump; saturator; F, saturation monitor; G, rotameter; and H, fractionation column(s).

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E,

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POLYMER CHARACTERIZATION

Table I I . Separation of Broad-Distribution Polymers W i t h o u t Surfactant Fraction O r i g i n a l solution* 1 2 3 Residual solution

Time

M

(h) 42,500 39,900 42,300 32,200 42,300

1

2 4 6 —

M

w

203,000 197,000 199,000 156,000 197,000

z

662,000 654,000 651,000 572,000 643,000

N O T E : Values given are the average molecular weights of polymer in foamate. Polymer concentration by weight: 2% P S - 1 and 2% P M M A - 1 ; column diameter 20 mm, orifice size 30 jum.

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α

generated by b u b b l i n g the saturated N through i n d i v i d u a l spinarette disks containing precisely formed holes of 15, 30, a n d 50 μιη. F o a m fractionation i n this type of apparatus is a batch or intermittent process. L i q u i d is charged, foam is generated, a n d fractions are c o l l e c t e d at selected t i m e intervals. T h e c o m p o s i t i o n of the l i q u i d p o o l thus changes w i t h t i m e . T h e t i m e intervals referred to subsequently i n T a b l e s I I a n d I I I are the times e l a p s e d from the b e g i n n i n g of foaming. T h e successive fractions l i s t e d i n T a b l e s I V a n d V w e r e c o l l e c t e d at 10-min intervals. T h e polymers u s e d w e r e c o m m e r c i a l , broad 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 samples of P S a n d P M M A w i t h M values of 70,000 ( P S - 1 ) a n d 51,000 ( P M M A - 1 ) a n d narrow d i s t r i b u t i o n samples w i t h M values of 670,000 ( P S - 2 ) a n d 19,400 ( P M M A - 2 ) . T h e solvent selected was xylene. T h e surfac­ tant used i n certain foam fractionations was F C — 4 3 1 , a fluorocarbon c o m ­ p o u n d manufactured b y the 3 M C o m p a n y . Analyses of the foamates w e r e performed b y size e x c l u s i o n chromatography ( S E C ) u s i n g a Spectra P h y s i c s 8000 h i g h pressure l i q u i d chromatography ( H P L C ) system e q u i p p e d w i t h a variable U V detector a n d a d u P o n t Zorbax b i m o d a l c o l u m n set rated at 1000 and 60 À. T h e S E C analyses of various fractions c o l l e c t e d d u r i n g each foaming experiment were c a r r i e d out b y isolating the solute i n each sample from the xylene solvent a n d r e d i s s o l v i n g it i n tetrahydrofuran ( T H F ) for m o b i l e phase compatibility. M o l e c u l a r weights a n d concentrations were measured b y the appropriate use of e l u t i o n v o l u m e s , peak heights, a n d peak areas. F o r the S E C 2

w

w

Table III. Separation of Broad-Distribution Polymers w i t h Surfactant Fraction Original solution 1 2 3

Time 6

(min)

a

— 10 20 30

M

n

36,700 16,700 38,100 32,800

M

M

w

192,000 43,000 188,000 167,000

z

655,000 92,900 636,000 587,000

N O T E : Values given are the average molecular weights of polymer in foamate. Fresh surfactant was injected after each fraction was taken at 10-min intervals. Polymer concentration by weight: 2% P S - 1 and 2% P M M A - 1 with 0.1% F C surfactant; column diameter 20 mm, orifice size 30 μτη. a

6

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

15.

CHARTOFF ET AL.

Foam

277

Fractionation

T a b l e I V . Separation of Narrow-Distribution P o l y m e r s — Effect of Orifice D i a m e t e r on Fractionation Orifice Fraction

Size

(μτη)

15

30

50

29 28 23 29 27

29 29 25 25 —

30 29 24 25 —

Original solution" 1 2 3 4

N O T E : Values given are percent of P S - 2 in foamate based on total solute. Polymer concentration by weight: 0.6% P S - 2 and 1.4% P M M A - 2 with 0.1% surfactant; column diameter 20 mm; fractions were collected at 10-min intervals.

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α

FC

s o l v e n t - p o l y m e r c o m b i n a t i o n , T H F w i t h P S a n d P M M A , the U V detector was set at 235 n m .

Results and

Discussion

F r a c t i o n a t i o n d a t a w e r e c o l l e c t e d for m i x t u r e s o f P S a n d P M M A at v a r i o u s c o n c e n t r a t i o n s a n d f o r d i f f e r e n t f o a m i n g c o n d i t i o n s . T h e r e s u l t s for s o m e o f t h e s e tests are p r e s e n t e d i n T a b l e s I I - V a l o n g w i t h descriptions of the e x p e r i m e n t a l variables. T h e data on the mixtures of the commercial broad distribution samples i n Tables II a n d III w e r e a n a l y z e d b y a s s u m i n g a s i n g l e M W D p e a k for t h e t o t a l m i x t u r e . T h e d a t a for t h e m i x t u r e s o f n a r r o w M W D s a m p l e s i n T a b l e s I V a n d V w e r e a n a l y z e d for c o n c e n t r a t i o n s i n t e r m s o f i n d i v i d u a l p e a k areas a n d peak intensities. T h e data of T a b l e s II a n d I I I i n d i c a t e that fractionation occurs, b u t e f f i c i e n c y is l o w w i t h o u t a d d i n g a surfactant. A d d i t i o n o f a surfac­ t a n t ( T a b l e I I I ) i m p r o v e s f r a c t i o n a t i o n at s h o r t e r f o a m i n g i n t e r v a l s . I n b o t h c a s e s , t h e h i g h m o l e c u l a r w e i g h t P S t e n d s to b e e x c l u d e d f r o m the foamate. T h e i m p r o v e m e n t i n fractionation efficiency w i t h sur­ factant p r o b a b l y arises because o f i n c r e a s e d foam stability. F i g u r e 2 contains t y p i c a l photographs of a foam generated from a T a b l e V . Effect of Surfactant on Selectivity Fraction Original solution" 1 2 3

With

Surfactant 29 29 25 25

Without

Surfactant 28 30 32 38

N O T E : Values given are percent of P S - 2 in foamate based on total solute. Solute concentration 2% with surfactant; and 4% without surfactant; column diameter 20 mm; orifice size 30 μ,ιη; fractions were collected at 10-min intervals. a

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

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POLYMER CHARACTERIZATION

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a

b

c

Figure 2. Foam generated during foam fractionation of a polymer solution without added surfactant: early stage of foam buildup (a), steady state foam structure (b), and upper surface of foam column showing bubble coalescence (c).

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

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15.

CHARTOFF ET AL.

Foam

Fractionation

279

p o l y m e r s o l u t i o n c o n t a i n i n g no surfactant: F i g u r e 2a depicts the early stages o f f o a m g e n e r a t i o n ; F i g u r e 2 b d e p i c t s t h e c e l l u l a r s t r u c t u r e o f a f u l l y d e v e l o p e d f o a m ; a n d F i g u r e 2c is the u p p e r surface o f the foam. T h e u p p e r s u r f a c e a p p e a r s to b e w e t a n d i n p r a c t i c e b r e a k s u p r e a d i l y . W h e n the foams are u n s t a b l e i n t h i s f a s h i o n , b u b b l e s c o a l e s c e r a p i d l y a n d c o l l a p s e so t h a t e q u i l i b r i u m c a n n o t b e a p p r o a c h e d . T h e l o w eff i c i e n c i e s a c h i e v e d i n t h i s m o d e r e s u l t i n l i t t l e s e p a r a t i o n as n o t e d earlier. A d d i t i o n of surfactant promotes foam stability a n d results i n dryer, more u n i f o r m foams. T h e more stable a n d d r y the foams are, the c l o s e r w e c a n a p p r o a c h e q u i l i b r i u m . T h i s b e h a v i o r is the r e s u l t of b o t h the m i n i m i z a t i o n of foam collapse a n d the a c h i e v e m e n t of better e n r i c h m e n t d u e to i m p r o v e d foam d r a i n a g e . T h e latter effect is s i m i l a r to r e f l u x i n a d i s t i l l a t i o n p r o c e s s . B o t h factors c o n t r i b u t e to t h e i m p r o v e d efficiency o f separation o b s e r v e d w h e n surfactant is u s e d . T h e data also i n d i c a t e a great difference i n s e l e c t i v i t y w h e n a surfactant is u s e d . W i t h the t w o p o l y m e r s , P S - 2 a n d P M M A - 2 , h a v i n g extremely different molecular weights, the h i g h m o l e c u l a r w e i g h t P S - 2 n o r m a l l y has the greatest a d s o r p t i v i t y . W h e n surfactant is a d d e d , h o w e v e r , s e l e c t i v i t y reverses a n d the P M M A is a d s o r b e d preferentially. T h e data of T a b l e s III a n d I V do not indicate any particular a d vantage i n fractionation b y c h a n g i n g b u b b l e d i a m e t e r (orifice size), although the lowest concentration of P S — 2 i n any fraction was obtained w i t h the smallest orifice diameter. I n s u m m a r y , i n the m i x t u r e that consisted of t w o c o m m e r c i a l samples w i t h b r o a d M W D w i t h P S h a v i n g the h i g h e r weight-average m o l e c u l a r w e i g h t , little separation o c c u r r e d w i t h o u t surfactant a n d the trend was toward exclusion of h i g h molecular w e i g h t P S from the foamate. T h i s t r e n d was m o r e p r o n o u n c e d b y a d d i n g surfactant, a n d the a m o u n t o f separation i m p r o v e d . I n the m i x t u r e that consisted of two narrow distribution polymers differing greatly i n M with PS h a v i n g t h e h i g h e r v a l u e , s e p a r a t i o n w a s s e l e c t i v e to h i g h m o l e c u l a r w e i g h t P S w h e n fractionation was c a r r i e d out w i t h o u t surfactant. W i t h surfactant a d d e d , the foamate was e n r i c h e d i n l o w m o l e c u l a r w e i g h t P M M A . N o c o n c l u s i v e results w e r e o b t a i n e d o n the effect of b u b b l e size on separation efficiency, although one w o u l d expect an i m p r o v e ment w i t h decreasing b u b b l e size. w

A l l o f t h e t r e n d s o b s e r v e d are c o n s i s t e n t w i t h t h e m u l t i l a y e r a d sorption theory discussed earlier. I n particular, the reversal of selectivity b e t w e e n P S a n d P M M A w h e n the p e r f l u o r i n a t e d surfactant was p r e s e n t is a g r a p h i c i l l u s t r a t i o n o f the n o t i o n that the p o l y m e r w i t h the strongest i n t e r a c t i o n w i t h the interface w i l l be adsorbed.

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

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Acknowledgments T h e authors are p l e a s e d to h a v e r e c e i v e d f u n d i n g for this r e s e a r c h from the National Science Foundation. W e thank P a u l Karichoff of the C e l a n e s e F i b e r s C o m p a n y for p r o v i d i n g t h e spinarette disks u s e d to

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generate foam.

Literature Cited 1. Roe, R.J.J.Chem. Phys. 1974, 60, 4192. 2. Roe, R. J., presented at the American Physical Society Meeting, Atlanta, GA, March 1976. 3. Roe, R. J. In "Adhesion and Adsorption of Polymers," Part B; Lee, L.-H., Ed.; Plenum: New York, 1980; pp. 629-41. 4. Al-Madfai, S.; Frisch, H. L. J. Am. Chem. Soc. 1958, 80, 5613. 5. Imai, K.; Matsumoto, M. J. Polym. Sci. 1961, 55, 355. 6. Imai, K.; Matsumoto, M. Bull. Chem. Soc. Jpn. 1963, 36, 455. 7. Devin, C.; Minfray, M. Compt. Rend. 1962, 255, 116. 8. Kikukawa, K.; Nozakura, S.; Murahashi, S. Polym. J. 1972, 3(1), 52. 9. Bolewski, K.; Tomaskiewicz, T.; Olbracht, M. Polimery (Warsaw) 1970, 15, 15. 10. Bolewski, K.; Nalewajko, H.; Maruzewski, I. Ann. Pharm. (Poznan) 1973, 10, 73. 11. Schildknecht, C. E., Tannebring, J. Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem. 1974, 15(2), 439. 12. Morishima, Y.; Irie, Y.; Iimuro, H.; Nozakura, S. J. Polym. Sci., Polym. Chem. 1976, 14, 1267. 13. Bierwagen, G. P.; Rehfeldt, T. K.; Schewing, D. R., presented at The Water-Borne and Higher Solids Coatings Symposium, New Orleans, LA, February 1979. 14. Gaines, G. L.; LeGrand, D. G. Polym. Lett. 1968, 6, 625. 15. Gaines, G. L.; LeGrand, D. G. J. Colloid Interface Sci. 1969, 31, 162. 16. Schröeder, E . ; Giesau, Κ. E. Germ. Patent 125 807, 1977. 17. Chartoff, R. P.; Chen, L. T.; Roe, R. J. Org. Coat. Plast. Chem. 1981, 44, 607. RECEIVED for review October 14, 1981. ACCEPTED February 3, 1982.

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.