PolystyreneâPolydimethylsiloxane Multiblock Copolymers

15

Polystyrene—Polydimethylsiloxane Multiblock Copolymers

J O H N C. SAAM, A N D R E W H. W A R D and F. W. G O R D O N F E A R O N

Downloaded by FUDAN UNIV on February 22, 2017 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0129.ch015

Dow Corning Corp., Midland, Mich., 48640

The

title block copolymers

with characteristics

ranging

from thermoplastic elastomers to polyethylene-like thermo plastics are obtained from ring opening polymerization of hexamethylcyclotrisiloxane

with "living" α,ω-dilithiopoly-

styrene.

and

Chain

scissions

oligomerizations

which

usually complicate siloxane polymerization are avoided, and molecular parameters regulating physical and mechanical properties are conveniently controlled to provide a unique family of thermoplastic materials.

j D l o c k c o p o l y m e r s of p o l y d i m e t h y l s i l o x a n e a n d v a r i o u s

thermoplastics

offer c o m b i n a t i o n s of properties w h i c h h a v e i n t r i g u e d n u m e r o u s i n vestigators.

T h e interest generated b y the earlier c o p o l y m e r systems as

w e l l as those of t h e present i n v e s t i g a t i o n stems i n large part f r o m t h e u n i q u e features i m p a r t e d b y t h e p o l y d i m e t h y l s i l o x a n e b l o c k s . these a r e retention of

flexibility

properties, ozone resistance,

at l o w t e m p e r a t u r e , excellent

durability towards weathering, a n d a h i g h

degree of p e r m e a b i l i t y t o w a r d s gases. to

be incorporated

i n such

Among electrical

Thermoplastic blocks

thermoplastic

reported

elastomers

so f a r i n c l u d e

silphenylene-siloxane ( I ) , poly(bisphenol-A-carbonate)

( 2 ) , polystyrene

(3, 4), a n d p o l y a r y l s u l f o n e s ( 5 ) . block

copolymer

I n each case t h e r u b b e r y p a r t o f t h e

is p o l y d i m e t h y l s i l o x a n e .

A l l show

interesting a n d

u n i q u e p r o p e r t y profiles, b u t t h e o n l y b l o c k c o p o l y m e r s w h i c h seem economically

suited

for volume

manufacture

are those

where the

" h a r d " b l o c k s a r e c o m p o s e d of p o l y s t y r e n e o r its d e r i v a t i v e s . T h e most p r o m i s i n g a p p r o a c h f o r p r e p a r i n g b l o c k c o p o l y m e r s of p o l y s t y r e n e ( A ) a n d p o l y d i m e t h y l s i l o x a n e ( B ) involves p o l y m e r i z a t i o n of

cyclosiloxane

monomers

with

" l i v i n g " «,ω-polystyrene

anions

(6).

T h e o r i g i n a l a p p r o a c h , h o w e v e r , gives materials c o n t a m i n a t e d w i t h t h e 239 Platzer; Polymerization Reactions and New Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

240

P O L Y M E R I Z A T I O N

R E A C T I O N S

A N D N E W

c o m p o n e n t h o m o p o l y m e r s w h i c h are r u i n o u s to m e c h a n i c a l

P O L Y M E R S

properties.

T h e present effort shows that v a r i a t i o n of the o r i g i n a l a n i o n i c p o l y m e r i z a t i o n of cyclosiloxanes w i t h l i v i n g p o l y s t y r e n e ( 7 )

c i r c u m v e n t s these

difficulties a n d p r o v i d e s a n effective route to a range of u s e f u l materials. Synthesis T h e k e y to s y n t h e s i z i n g w e l l d e f i n e d b l o c k c o p o l y m e r s successfully is the a n i o n i c r i n g - o p e n i n g p o l y m e r i z a t i o n of h e x a m e t h y l c y c l o t r i s i l o x a n e , D , f r o m the " l i v i n g " ends of «,ω-dilithiopolystyrene.

T h i s gives a B A B

s

b l o c k c o p o l y m e r t e r m i n a t e d w i t h l i t h i u m silanolate ends.

T h e ends are


t h e n c o u p l e d w i t h d i a l k y l d i c h l o r o s i l a n e to g i v e ( B A B ) * m u l t i b l o c k co p o l y m e r s essentially free of h o m o p o l y m e r s a n d b y - p r o d u c t cyclosiloxanes. T h e siloxane p o l y m e r i z a t i o n is r u n i n s o l u t i o n i n the presence of p r o m o t i n g solvents s u c h as T H F or the g l y m e s . cyclosiloxane employed,

l i t t l e or n o c o n c o m i t a n t

m o d e l experiments

where

Ά

gave

T h i s has b e e n

butyllithium

styrene was u s e d to p o l y m e r i z e Ό

are u s u a l l y

c h a i n scission or e q u i l i b r a t i o n is

o b s e r v e d w h e n l i t h i u m is the c o u n t e r i o n . in

C o n t r a r y to t y p i c a l a n i o n i c

p o l y m e r i z a t i o n s w h e r e p o t a s s i u m silanolates

rather

than

demonstrated "living"

poly

under comparable conditions.

These

l i t t l e of the b y - p r o d u c t c y c l o d i m e t h y l s i l o x a n e s u s u a l l y f o u n d i n

a n i o n i c siloxane r i n g - o p e n i n g p o l y m e r i z a t i o n s d o n e i n s o l u t i o n .

High

conversions to p o l y d i m e t h y l s i l o x a n e w i t h n a r r o w m o l e c u l a r w e i g h t dis t r i b u t i o n w e r e also o b t a i n e d .

T h e m o l e c u l a r w e i g h t c o r r e s p o n d e d closely

to that c a l c u l a t e d f r o m the a m o u n t of catalyst a n d the w e i g h t of D

3

p r o v i d e d the system was s c r u p u l o u s l y p u r g e d of moisture a n d protic

impurities.

Thus,

as

in "living"

styrene

polymerizations

m o l e c u l a r w e i g h t of the siloxane b l o c k s c a n be closely r e g u l a t e d .

used other the This

p r o c e d u r e a l l o w s c o n t r o l of b l o c k size a n d relative a m o u n t of the b l o c k s i n the c o p o l y m e r system.

T h e precise n a t u r e of the p o l y m e r i z a t i o n a n d

the a b i l i t y to c o n t r o l m o l e c u l a r variables w e r e t h e n u s e d to synthesize polystyrene-polydimethylsiloxane A B block copolymers

(8).

Reaction

1 outlines the synthesis of the m u l t i b l o c k c o p o l y m e r s . Li[CH CH(C H )]nLi + 2/3M(Me SiO) 2

6

5

2

3

+

(polar solvent) ->

Li(OMe Si) [CH CH(C H )]n(SiMe 0) Li 2

|R SiX 2

m

2

6

5

2

w

(1)

2

[(OMe Si) (CH —CH(C H )) (SiMe,0)J, 2

m

2

e

e

n

T h e e x p e r i m e n t a l c o n d i t i o n s w e r e essentially those a l r e a d y r e p o r t e d for the synthesis of the c o r r e s p o n d i n g A B b l o c k c o p o l y m e r s . T h e o n l y differences w e r e the d i f u n c t i o n a l i n i t i a t o r ( 9 ) a n d the use of a d i f u n c t i o n a l rather t h a n m o n o f u n c t i o n a l c h l o r o s i l a n e for r e a c t i o n w i t h the

Platzer; Polymerization Reactions and New Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

15.

S A A M

E T

Polysty

A L .

241

rene-Polydimethylsïloxane

l i t h i u m siloxanolate t e r m i n a t e d p o l y m e r .

A t least 18 hours w e r e a l l o w e d

for t h e latter step to ensure c o m p l e t e r e a c t i o n .

Absence of homopoly-

m e r w a s assessed b y t h e p r e v i o u s l y d e s c r i b e d p r o c e d u r e of d e t e r m i n i n g s o l u b i l i t y i n selective solvents

a n d i n t w o examples b y f r a c t i o n a l

(8)

p r e c i p i t a t i o n of 1% toluene solutions of b l o c k c o p o l y m e r u s i n g m e t h a n o l as a p r e c i p i t a n t .

T h e c o m p o s i t i o n s of each f r a c t i o n as d e t e r m i n e d b y

s i l i c o n analysis w e r e constant w i t h i n e x p e r i m e n t a l error over t h e r a n g e of m o l e c u l a r w e i g h t s

obtained

(given

i n Figures

1 a n d 2.)

Gross

variations i n s i l i c o n content f r o m o n e f r a c t i o n t o another w o u l d b e expected

f o r either t h e c o p o l y m e r r i c h i n p o l y d i m e t h y l s i l o x a n e o r t h e


c o p o l y m e r r i c h i n p o l y s t y r e n e i f significant amounts

of either

homo-

p o l y m e r w e r e present. Table I. Effect of Free P o l y d i m e t h y l s i l o x a n e on Mechanical Properties of a Compression Molded (BAB)^ Block Copolymer with 50 wt % P o l y s t y r e n e a

6

{MeiSiO)n Added, wt %

Tensile at Break, psi, (Break)

0 5 10 15 20

2200 1600 1400 440 150

Elongation at Break, (Break)

%,

350 280 340 40 20

° Molecular weight 22,800. Molecular weight of polystyrene blocks, 23,500; overall molecular weight 107,000. 6

M o i s t u r e a n d o x y g e n m u s t b e r i g o r o u s l y e x c l u d e d f r o m t h e system if t h e synthesis is to b e successful.

I n a d v e r t a n t i n t r o d u c t i o n of t r a c e

p r o t i c i m p u r i t i e s o f m e t a l oxides d u r i n g t h e synthesis leads t o the f o r m a t i o n of p o l y d i m e t h y l s i l i o x a n e h o m o p o l y m e r .

T h i s m a t e r i a l , present i n

even s m a l l amounts, is d e t r i m e n t a l to t h e m e c h a n i c a l properties of t h e final

block copolymer.

T h i s effect c a n b e i l l u s t r a t e d b y d e l i b e r a t e l y

i n c l u d i n g k n o w n amounts of p o l y d i m e t h y l s i l o x a n e i n a b l o c k c o p o l y m e r of d e m o n s t r a t e d m e c h a n i c a l strength.

T h e s e effects are s u m m a r i z e d i n

Table I. Structure-Property

Relationships

T h e characteristics of t h e c o p o l y m e r s , w h i c h range f r o m elastomers to l o w m o d u l u s thermoplastics

of v a r y i n g mechanical a n d rheological

properties, d e p e n d o n m o l e c u l a r parameters that c a n b e p r e d e t e r m i n e d i n t h e synthesis

b y t h e relative amounts

c o u p l i n g reagent ( R S i X ) 2

2

used.

of m o n o m e r s , i n i t i a t o r , a n d

T h e s e parameters a r e o v e r a l l m o l e c -

u l a r w e i g h t , t h e relative a n d absolute sizes of t h e c o m p o n e n t


blocks,

242


R E A C T I O N S

A N D N E W

a n d the glass t r a n s i t i o n t e m p e r a t u r e of the " h a r d " b l o c k s .

P O L Y M E R S

T h e influence

of e a c h of these o n properties is c o n s i d e r e d separately. T h e effect of o v e r a l l m o l e c u l a r w e i g h t o n m e c h a n i c a l a n d r h e o l o g i c a l properties was d e t e r m i n e d b y m e a s u r i n g properties o n samples o b t a i n e d b y f r a c t i o n a l p r e c i p i t a t i o n of t w o different ( B A B ) * b l o c k c o p o l y m e r s . O n e c o p o l y m e r c o n t a i n i n g 30 w t % p o l y s t y r e n e g a v e seven w h e r e χ v a r i e d f r o m 1.6 to 60. c a l b e t w e e n fractions.

fractions

T h e s i l i c o n e content was n e a r l y i d e n t i

A s e c o n d c o p o l y m e r c o n t a i n i n g 50 w t % p o l y

styrene gave five fractions.

T e n s i l e properties w e r e m e a s u r e d o n solu

t i o n cast films f r o m the first series.

T h e d a t a s h o w e d that χ m u s t b e

greater t h a n 2 f o r the films to s h o w a n y significant m e c h a n i c a l strength. Downloaded by FUDAN UNIV on February 22, 2017 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0129.ch015

T e n s i l e strength increases s h a r p l y w i t h m o l e c u l a r w e i g h t u n t i l χ reaches 8 to 10, after w h i c h l i t t l e f u r t h e r increase is seen.

T h e general

of the stress-strain c u r v e is essentially the same f o r e a c h f r a c t i o n .

shape The

e n v e l o p e of the stress-strain curves a n d points of f a i l u r e are s h o w n i n F i g u r e 1. TENSILE STRENGTH

(PSI)

2500

2000 KEY

1500

—

M

Ο

€ 1000

Q Φ

—

©

•

500

N

Χ

10*5

30.9 25.8 19.3 12.9 4.0 1.6 0.71

ι ι

5

15

10

EXTENTION RATIO

Figure 1. Effect of molecular weight on tensile properties of fractionaly precipitated samples of (BAB) which contain 30 wt % polystyrene and M = 13,500 X

A

T h e effect of o v e r a l l m o l e c u l a r w e i g h t or the n u m b e r of

blocks

o n r h e o l o g i c a l properties f o r the samples f r o m the s e c o n d f r a c t i o n a t i o n c a n b e i l l u s t r a t e d as a p l o t of r e d u c e d viscosity vs. a f u n c t i o n p r o p o r tional

to the

principal molecular

relaxation

time

(Figure

2).

This

f u n c t i o n i n c l u d e s the variables of z e r o shear viscosity, shear rate, γ, a n d absolute temperature, T, i n a d d i t i o n to m o l e c u l a r w e i g h t , a n d a l l o w s the d a t a to b e expressed as a single master c u r v e (10). fractions

A l l b u t one of the

f r o m the c o p o l y m e r c o n t a i n i n g 50% p o l y s t y r e n e f a l l o n this


15.

sA A M E T A L .

243

Poly sty rene-Polydimethyhiloxane

5 + LOG τ?Α?

0


5.0 Κ—

Figure 2. Effect of molecular weight on reduced bulk viscosity ex pressed as a master curve for fractionally precipitated samples of (BAB) which contain 50 wt % polystyrene and M = 13,500. T = 463°K. X

A

curve.

T h e e x c e p t i o n is t h e f r a c t i o n of l o w e s t m o l e c u l a r w e i g h t w h i c h

contains a h i g h p r o p o r t i o n of the species ( B A B ) ^ w h e r e χ = 1.

The

v a l u e of —0.99 f o r t h e l i m i t i n g slope of the master c u r v e i n F i g u r e 2 is u n u s u a l . dicted

T h i s is s u b s t a n t i a l l y h i g h e r t h a n t h e v a l u e of —0.82 p r e

f r o m theoretical

considerations

polystyrene a n d polydimethylsiloxane

a n d t h e values

observed

for

(11).

T h e m o l e c u l a r w e i g h t of the p o l y s t y r e n e b l o c k s is d e t e r m i n e d b y the r a t i o of m o n o m e r to i n i t i a t o r u s e d i n t h e synthesis a n d is c r i t i c a l i n d e t e r m i n i n g m e c h a n i c a l a n d r h e o l o g i c a l properties.

T h e data i n Table

I I i n d i c a t e that a b l o c k size of a b o u t 8000 is r e q u i r e d to o b t a i n u s e f u l

T a b l e I I . E f f e c t of P o l y s t y r e n e B l o c k Size o n M e c h a n i c a l P r o p e r t i e s of C o m p r e s s i o n M o l d e d P o l y s t y r e n e - P o l y d i m e t h y l s i l o x a n e B l o c k Copolymers C o n t a i n i n g 30% Polystyrene M

n

Polystyrene Block 4,000 7,700 11,100 12,300 13,550

Degree of Condensation, 3.3 3.6 3.9 3.5 3.3

χ

Ultimate Stress, psi 240 700 950 1,020 1,030

Ultimate Strain, % 120 260 550 350 480


244


R E A C T I O N S

A N D N E W

P O L Y M E R S

m e c h a n i c a l properties a n d that a m o l e c u l a r w e i g h t greater t h a n 12,000 gives l i t t l e f u r t h e r i m p r o v e m e n t . M e l t viscosity increases as the m o l e c u l a r w e i g h t of the p o l y s t y r e n e b l o c k s is increased, b u t the effect tends t o d i m i n i s h as the rate of shear is increased.

T h e influence of b l o c k size is expressed as a f a m i l y of

c o n v e r g i n g v i s c o s i t y — s h e a r rate curves f o r three c o p o l y m e r s of d i f f e r i n g b l o c k size, ( F i g u r e 3 ) . character

T h e s e curves also illustrate the n o n - N e w t o n i a n

of t h e p o l y s t y r e n e - p o l y d i m e t h y l s i l o x a n e b l o c k

copolymers.

T h e effect of c h a n g i n g b l o c k size cannot b e expressed as a single master c u r v e as i n t h e case of o v e r a l l m o l e c u l a r w e i g h t .

S u c h master

curves


m u s t b e b a s e d o n p o l y m e r s of constant b l o c k size. τ? (POISE) ν

(SEC-1)

Figure 3. Effect of size of polystyrene blocks on true ap parent viscosity at 190°C for a multiblock copolymer con taining 40 wt % polystyrene; overall molecular weight= 130 ± 10 X 10"; M = 9.5 X 10*. A

T h e r e l a t i v e amounts of t h e t w o m o n o m e r s u s e d i n the synthesis d e t e r m i n e the r e l a t i v e size o f the t w o b l o c k s o r the c o m p o s i t i o n of ( B A B ) . T h i s i n t u r n determines w h e t h e r m e c h a n i c a l b e h a v i o r re sembles that of thermoplastics o r t h e r m o p l a s t i c elastomers. T h e greater the p o l y s t y r e n e content, t h e greater the i n i t i a l m o d u l u s a n d y i e l d p o i n t of t h e b l o c k c o p o l y m e r . O v e r a l l c o m p o s i t i o n thus tends t o d o m i n a t e the parameters discussed above. A t a g i v e n l e v e l of p o l y s t y r e n e t h e X


15.

S A A M

E T

245

Polystyrene-Polydimethylsiloxane

A L .


STRESS (PSI)

EXTENTION RATIO

Figure 4. Effect of polystyrene content on tensile properties of polystyrene-polydimethylsiloxane multiblock copolymers other parameters c h a n g e u l t i m a t e m e c h a n i c a l properties b u t effect o n l y m i n o r alterations i n t h e g e n e r a l shape o f t h e stress-strain

curve. E n

velopes of stress-strain curves w h e r e o v e r a l l m o l e c u l a r w e i g h t s a n d t h e size of p o l y s t y r e n e b l o c k s c h a n g e

b r o a d l y at three g i v e n contents o f

p o l y s t y r e n e a r e i l l u s t r a t e d i n F i g u r e 4. T h e a m o u n t o f p o l y s t y r e n e also influences t h e p e r m e a b i l i t y of t h e b l o c k c o p o l y m e r s t o gases.

T h u s , a c o m p r e s s i o n m o l d e d f i l m of t h e r m o

p l a s t i c elastomer c o n t a i n i n g 2 0 w t % p o l y s t y r e n e shows a p e r m e a b i l i t y t o w a r d s o x y g e n t y p i c a l o f a s i l i c a - f i l l e d silicone elastomer, 49.2 Χ 10" cm -cm/cm -sec, 3

2

c m H g at 2 5 ° C .

9

T h e p e r m e a b i l i t y of films w i t h i n

c r e a s i n g amounts of p o l y s t y r e n e r a p i d l y decreases l i n e a r l y to a n inflec t i o n p o i n t at 50 w t % p o l y s t y r e n e w h e r e t h e p e r m e a b i l i t y is 3.6 X 10r

9

cm -cm/cm -sec, 3

2

C0 .

cm Hg.

A s i m i l a r t r e n d is n o t e d w i t h n i t r o g e n a n d

T h e i n f l e c t i o n p o i n t at 50 w t % m i g h t b e a c o n s e q u e n c e of t h e

2

m u c h less p e r m e a b l e p o l y s t y r e n e p r e d o m i n a t i n g i n t h e c o n t i n u o u s phase of t h e m i c r o d i s p e r s e t w o - p h a s e system ( 3 ) .

T h e m e t h o d of f a b r i c a t i o n

c a n also b e a n b e a n i m p o r t a n t factor i n d e t e r m i n i n g p e r m e a b i l i t y . B l o c k c o p o l y m e r s c o n s t i t u t e d so that t h e h a r d A b l o c k s s h o w i n creased glass temperatures

m i g h t b e e x p e c t e d to s h o w better u l t i m a t e

tensile properties t h a n c o m p a r a b l e b l o c k c o p o l y m e r s o f a l o w e r T i n t h e g

glassy

phase

(12).

This

is d e m o n s t r a t e d

i n t h e present

system b y

s u b s t i t u t i n g t h e m a j o r p o r t i o n of t h e p o l y s t y r e n e i n t h e present for p o l y ( « - m e t h y l s t y r e n e ) .

system

A short l e n g t h of p o l y s t y r e n e is i n c l u d e d

at e a c h c h a i n e n d of t h e h a r d b l o c k to f a c i l i t a t e the s e c o n d step of t h e synthesis a n d to g i v e a m o r e stable p o l y m e r .

T h e effect of r e p l a c i n g


246


R E A C T I O N S

A N DN E W

P O L Y M E R S

DYNAMIC STORAGE


MODULUS DYNES/CM'

TEMPERATURE ° C

Figure 5. Effect of T in the glassy block on thermomechanical properties of (BAB) containing 40 wt % "Α'; curve A , " A " block is poly(a-methylstyrene); curve B, "A" block is polystyrene. 0

X

Table III.

Effect of T of the H a r d " A " Block on Tensile Properties of (BAB), Containing 40 wt % of A 9

A = Polystyrene Temperature, °C

Tensile at Break, psi

25 50 100 130 150

1550 1080 90 — —

polystyrene w i t h

A =

Elongation at Break, % 800 1000 300 — —

poly(«-methylstyrene)

Poly(a-methylstyrene)

Tensile at Break, psi

Elongation at Break, %

2400 — 870 300 90

700 — 800 1160 1100

i n the A b l o c k s o n t h e r m o -

m e c h a n i c a l properties is s u m m a r i z e d i n F i g u r e 5 a n d T a b l e III.

Figure

5 shows that t h e m o d u l u s of t h e m a t e r i a l b a s e d o n p o l y ( α-methylstyrene ) is r e t a i n e d to temperatures based on polystyrene. strength

at a

7 0 ° greater t h a n a c o r r e s p o n d i n g m a t e r i a l

T a b l e III shows a s i g n i f i c a n t l y greater

g i v e n . temperature

for copolymers

based

on

methylstyrene).


tensile poly(a-

15.

S A A M

E T

A L .

Polysty

247

rene-Polydimethylsïloxane

M u l t i b l o c k copolymers based on poly(a-methylstyrene)

also s h o w

s i g n i f i c a n t l y better o x i d a t i v e t h e r m a l s t a b i l i t y t h a n the b l o c k c o p o l y m e r s based o n p o l y s t y r e n e .

Thus, polystyrene-polydimethyldisiloxane multi-

b l o c k c o p o l y m e r s lose h a l f of t h e i r tensile strength after 80 hours w i t h considerable

yellowing

at

150 ° C

i n air, b u t c o r r e s p o n d i n g

materials

b a s e d o n p o l y ( a - m e t h y l s t y r e n e ) s h o w n o d i s c o l o r a t i o n or loss i n tensile properties u n d e r the same c o n d i t i o n s .


Literature

Cited

1. Merker, R. L., Scott, M. M., J. Polymer Sci. (1964) 2, 15. 2. Vaughn, Η. Α.,J.Polymer Sci., Pt. Β (1969) 7, 569. 3. Saam, J. C., Fearon, F. W. G., Ind. Eng. Chem., Prod. Res. Develop. (1971) 10, 10; Polymer Preprints (1970) 11, (2), 455. 4. Dean, J. W., J. PolymerSci.,Pt. Β (1970) 8, 677. 5. Noshay, Α., Matzner, M., Merriam, C. N., Polymer Preprints (1971) 12 (1) 247. 6. Greber,G.,Metzinger, L., Makromol. Chem. (1960) 39, 167. 7. Morton, M., Rembaum, Α. Α., Bostick, Ε. E., J. Appl. Polymer Sci., (1964) 8, 2707. 8. Saam, J. C., Gordon, D. J., Lindsey, S. L., Macromolecules (1970) 3, 1. 9. Gilman, H., Carteledge, F. K., J. Organometal Chem. (1964) 2, 447. 10. Graessly, W. N., J. Chem. Phys. (1967) 47, 1942. 11. Lee, C. L., Polmanteer, Κ. E., King, E. G., J. Polymer Sci., Pt. A-2 (1970) 8, 1909. 12. Fetters, T. J., Morton, M., Macromolecules (1969) 2, (5), 453. R E C E I V E D May

1,

1972.


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