Generalized Intrinsic Viscosity Relations for Copolymers and Higher

Chapter 15 Generalized Intrinsic Viscosity Relations for Copolymers and Higher Multispecies Polymers for Size Exclusion C h r o m a t o g r a p h i c Universal C a l i b r a t i o n

Downloaded by MONASH UNIV on December 7, 2016 | http://pubs.acs.org Publication Date: October 2, 1987 | doi: 10.1021/bk-1987-0352.ch015

Robert A. Mendelson Monsanto Company, 730 Worcester Street, Springfield, MA 01151 An appropriate formalism for Mark-HouwinkSakurada (M-H-S) equations for copolymers and higher multispecies polymers has been developed, with specific equations for copolymers and terpolymers created by addition across single double bonds in the respective monomers. These relate i n t r i n sic viscosity to both polymer MW and composition. Experimentally determined i n t r i n s i c viscosities were obtained for poly(styrene-acrylonitrile) in three solvents, DMF, THF, and MEK, and for poly(styrene-maleic anhydride-methyl methacrylate) in MEK as a function of MW and composition, where SEC/LALLS was used for MW characterization. Results demonstrate both the v a l i d i t y of the generalized equations for these systems and the limitations of the specific (numerical) expressions in particular solvents. Determination of the dilute solution i n t r i n s i c v i s c o s i ties of homopolymers and the relating of these quantities to molecular weight was the f i r s t method of polymer molecular weight characterization and remains a principal method. The relationship used is generally called the Mark-Houwink-Sakurada (M-H-S) equation, and the constants of the equation are specific to each polymer-solvent system. These M-H-S equations have extensive usefulness throughout fundamental and applied polymer research. Definition of appropriate equations has become even more important with the advent of size exclusion chromatography (SEC) as a means of completely characterizing the molecular weight distributions (MWD) of polymers because 0097-6156/87/0352-0263$06.00/0 © 1987 American Chemical Society

Provder; Detection and Data Analysis in Size Exclusion Chromatography ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


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DETECTION AND DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

o f t h e r e c o g n i t i o n t h a t S E C s y s t e m s may b e c a l i b r a t e d b y the s o - c a l l e d method o f " u n i v e r s a l c a l i b r a t i o n " { 1 ) . This m e t h o d i s b a s e d o n t h e o b s e r v a t i o n 2) t h a t t h e p r o d u c t o f the i n t r i n s i c v i s c o s i t y times molecular weight (hydrodynamic volume) i sa unique f u n c t i o n o f t h e e l u t i o n volume o f a n SEC c o l u m n s e t f o r a w i d e v a r i e t y o f p o l y m e r s i n a given solvent. Thus, t h e f a c t t h a t w e l l c h a r a c t e r i z e d n a r r o w MWD s t a n d a r d s f o r c a l i b r a t i o n a r e a v a i l a b l e f o r only a few polymeric species (e.g., p o l y s t y r e n e , p o l y methyl methacrylate) no l o n g e r l i m i t s t h e c a l i b r a t i o n o f SEC s y s t e m s . T h e s e s t a n d a r d s may b e u s e d t o c r e a t e a universal calibration function applicable to essentially a l l p o l y m e r s w h i c h t a k e on a random c o i l c o n f i g u r a t i o n i n solution. While a p p l i c a t i o n of t h i s u n i v e r s a l c a l i b r a t i o n f o r a p a r t i c u l a r polymer r e q u i r e s knowledge o f t h e M-H-S e q u a t i o n f o r t h a t p o l y m e r i n t h e c h r o m a t o g r a p h i c s o l v e n t , t h i s h a s i n g e n e r a l p r e s e n t e d no m a j o r p r o b l e m f o r homopolymer c h a r a c t e r i z a t i o n . However, t h e case o f copolymers and higher m u l t i s p e c i e s polymers i s more c o m p l e x . Here i t i se x p e c t e d t h a t t h e i n t r i n s i c v i s c o s i t y i sa f u n c t i o n of both molecular weight and polymer composition, and g e n e r a l i z e d M-H-S e q u a t i o n s t o r e p r e s e n t t h i s complex f u n c t i o n a l i t y have n o t been used e x t e n s i v e l y . Rather, t h e p r a c t i c e i n t h e case o f copolymers h a s been t o e v a l u a t e t h e m o l e c u l a r w e i g h t dependence o f i n t r i n s i c v i s c o s i t y a t some f i x e d c o p o l y m e r c o m p o s i t i o n and t o use t h i s r e l a t i o n s h i p , per s e . In t h i s paper a g e n e r a l i z e d approach i spresented t o t h e d e r i v a t i o n o f M-H-S e q u a t i o n s f o r m u l t i s p e c i e s p o l y mers c r e a t e d by a d d i t i o n p o l y m e r i z a t i o n a c r o s s s i n g l e d o u b l e bonds i n t h e monomers. The s p e c i a l c a s e s o f copolymers and terpolymers a r ed e r i v e d . This development i s combined w i t h experimental results to evaluate the numerical parameters i n the equations f o r p o l y ( s t y r e n e a c r y l o n i t r i l e ) (SAN) i n t h r e e s e p a r a t e s o l v e n t s a n d f o r poly(styrene-maleic anhydride-methyl methacrylate) (S/MA/MM) i n a s i n g l e s o l v e n t . The t h r e e s o l v e n t s i n t h e c a s e o f SAN a r e d i m e t h y l f o r m a m i d e ( D M F ) , t e t r a h y d r o f u r a n (THF), a n d m e t h y l e t h y l ketone (MEK); and t h e s o l v e n t f o r S/MA/MM i s MEK. Theoretical

Treatment

We a t t e m p t h e r e t o d e v e l o p a m a t h e m a t i c a l e x p r e s s i o n f o r the dependence o f t h e d i l u t e s o l u t i o n i n t r i n s i c viscosity of m u l t i s p e c i e s p o l y m e r s on b o t h m o l e c u l a r w e i g h t a n d p o l y m e r c o m p o s i t i o n w i t h some b r o a d d e g r e e o f g e n e r a l i t y and t o p a r t i c u l a r i z e t h e r e s u l t f o r t h e s p e c i f i c c a s e s o f c o p o l y m e r s a n d t e r p o l y m e r s s u c h a s SAN a n d S/MA/MM. T h e d e t a i l s of t h ed e r i v a t i o n a r e s p e c i f i c t o polymers r e s u l t i n g from a d d i t i o n p o l y m e r i z a t i o n across a s i n g l e double b o n d i n e a c h monomer u n i t . I n p r i n c i p l e t h e a p p r o a c h may be e x p a n d e d t o o t h e r s c h e m e s o f p o l y m e r i z a t i o n s o l o n g a s



15.

MENDELSON

Generalized Intrinsic Viscosity Relations

265

the number o f c a r b o n atoms i n the backbone c h a i n can be r e l a t e d t o a s i m p l e measure o f c o m p o s i t i o n . Indeed, K r u s e and Padwa(_3) have t r e a t e d the s p e c i f i c c a s e o f s t y r e n e - b u t a d i e n e c o p o l y m e r s , where t h e r e a r e two p o l y m e r i z a b l e d o u b l e bonds i n the b u t a d i e n e monomer ( t h e y assume a l l 1 , 4 - a d d i t i o n ) . A s e c o n d r e s t r i c t i o n on t h e c u r r e n t work i s t h a t o f a p p l i c a b i l i t y t o l i n e a r p o l y m e r s , only. The p r o b l e m t o be a d d r e s s e d i s t h a t o f d e v e l o p i n g a c o n t i n u o u s r e l a t i o n between i n t r i n s i c v i s c o s i t y and m o l e c u l a r w e i g h t and c o m p o s i t i o n , w h i l e r e t a i n i n g s u f f i c i e n t s i m p l i c i t y to a l l o w experimental d e f i n i t i o n of the e q u a t i o n ' s p a r a m e t e r s f o r s p e c i f i c p o l y m e r - s o l v e n t systems. Three f a c t o r s , which are consequences of p o l y m e r c o m p o s i t i o n a l change must be a d d r e s s e d . First, s i n c e the d i f f e r e n t monomer s p e c i e s ' m o l e c u l a r w e i g h t s a r e g e n e r a l l y d i f f e r e n t , the r e l a t i o n s h i p between p o l y m e r m o l e c u l a r w e i g h t and c h a i n s i z e i s a f u n c t i o n o f c o m p o s i tion. Second, i n t r o d u c t i o n o f d i f f e r e n t monomer s p e c i e s i n t o the backbone may a l t e r the u n p e r t u r b e d c o i l d i m e n s i o n s ; and, t h i r d , the s o l v e n t - p o l y m e r i n t e r a c t i o n may v a r y w i t h polymer c o m p o s i t i o n . I t s h o u l d be n o t e d t h a t t h e s e i s s u e s have been a d d r e s s e d i n a v e r y d i f f e r e n t manner by G o l d w a s s e r and Rudin( Γ7 ). The s t a r t i n g p o i n t i s the h y p o t h e s i s t h a t t h e i n t r i n s i c v i s c o s i t y i s a d i r e c t f u n c t i o n o f the number o f c a r b o n atoms i n the backbone c h a i n . T h i s a d d r e s s e s the f i r s t o f the above c o n s i d e r a t i o n s and i s c o n s i s t e n t w i t h the homopolymer c a s e and w i t h the a p p r o a c h o f K r u s e and Padwa(_3) . The s p e c i f i c form o f the f u n c t i o n a l d e p e n d e n c e o f i n t r i n s i c v i s c o s i t y on the number o f backbone c a r b o n atoms i s g i v e n by [ΠΙ

= JZ

(1)

1 3

where Ζ i s the number o f c a r b o n atoms i n the b a c k b o n e , and J and β i n c l u d e the a v e r a g e d c o n f o r m a t i o n a l and e x c l u d e d volume t e r m s . Thus, J and β a r e a n a l o g o u s t o the c l a s s i c a l Κ and α terms i n the homopolymer M-H-S equation. In t h i s d e r i v a t i o n i t i s assumed t h a t J and β a r e c o n s t a n t o v e r some i m p o r t a n t l y wide range o f compo s i t i o n a l change. Thus, the s e c o n d and t h i r d c o n c e r n s s t a t e d e a r l i e r a r e i n i t i a l l y a d d r e s s e d by a s s u m i n g t h a t the b a l a n c e o f segment-segment and s o l v e n t - s e g m e n t i n t e r a c t i o n s i s e s s e n t i a l l y i n v a r i a n t o v e r some wide c o m p o s i t i o n range. As w i l l become a p p a r e n t , t h i s a s s u m p t i o n i s r e a d i l y t e s t a b l e e x p e r i m e n t a l l y f o r s p e c i f i c systems. For t h e c a s e o f p o l y m e r i z a t i o n by a d d i t i o n a c r o s s s i n g l e d o u b l e bonds i n e a c h monomer, Ζ may be w r i t t e n as Ζ = 2M

ρ

Zw./M. 1 1

where M i s t h e polymer are the^weight f r a c t i o n

(i = 1 —

n)

m o l e c u l a r w e i g h t and and m o l e c u l a r w e i g h t

(2) w. oè

and M. the i ^ t h


266

DETECTION A N D DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

monomer t y p e i n t h e p o l y m e r o f η monomer t y p e s . Thus, t h e g e n e r a l e q u a t i o n f o r t h e i n t r i n s i c v i s c o s i t y o f an η - s p e c i e s p o l y m e r f o l l o w s i m m e d i a t e l y as β

[Π] = 2 3

Μ

β

(Zw./M )

ρ

P

( i= 1 —

i

n)

(3)

where t h e M^'s a r e known, M and w a r e a n a l y t i c a l l y d e t e r m i n a b l e , and J and β nuust be e x p e r i m e n t a l l y d e t e r m i n e d f o r any s p e c i f i c p o l y m e r i n a s p e c i f i c solvent. F o r t h e c a s e o f c o p o l y m e r s , i = 1,2 and i

β


[ri] = 2 ϋ

Μ

β

(w /M

ρ

1

+ [1^ ]/Μ )

1

1

β

(4)

2

E q u a t i o n (4) may be r e a r r a n g e d i n a number o f ways. p a r t i c u l a r form l e n d i n g s i m p l i c i t y t o t h e f i n a l expression i s [Π]

β

- {2 3[(Μ -Μ )/Μ Μ ] } β

2

1

1

β

Μ

2

ρ

{w

1

+ Μ /(Μ -Μ )} 1

2

A

β

(5)

1

where t h e term i n t h e f i r s t b r a c k e t s i s e x p e c t e d t o be a c o n s t a n t i n v o l v i n g J and β and t h e two monomer m o l e c u l a r w e i g h t s , and t h e c o m p o s i t i o n term, {w^ + M-^/i M -M- ) , i n c l u d e s a c o n s t a n t w h i c h i s u n i q u e l y d e t e r m i n e d èy t h e monomer m o l e c u l a r w e i g h t s . I n t h e s p e c i f i c c a s e o f SAN, t a k i n g AN a s monomer-1, M = 53.1 and M = 104.1, e q . ( 5 ) yields 2

1

2

2

β

[Π] = ( 1 . 8 4 5 χ 1 0 " ) α Μ

β

(w

ρ

+ 1.041)

A N

β

(6)

where J and β must be d e t e r m i n e d e x p e r i m e n t a l l y i n p a r t i c u l a r s o l v e n t s . The t e r p o l y m e r c a s e f o l l o w s r e a d i l y from e q . ( 3 ) : β

[Π] = 2 ^ J Μ

ρ

(w /M 1

1

+ w /M 2

+ w /M )

2

3

P

(7)

3

A g a i n , t h e terms may be r e a r r a n g e d i n a number o f ways; t h e p a r t i c u l a r form c h o s e n h e r e i s [11]-

P

P

(2/M ) JM {w (M -M )/M 3

p

1

3

1

+ w (M -M )/M

1

2

3

2

+ 1}

2

β

(8)

In t h e s p e c i f i c c a s e o f S/MA/MM, l e t t i n g MA be monomer-1, MM be monomer-2, and s t y r e n e be monomer-3, M^ = 98, M = 100, and M = 104. I n t r o d u c i n g t h e s e v a l u e s i n t o e q . ( 8 ) yields 2

3

2

[ri] = ( 1 . 9 2 3 x l O " ) ^ J M

β

2

2

β

( 6 .122xlO~ w +4 . 0 0 0 x l 0 ~ w + l ) Ma

M M

MA

ρ

run

^ ^ j

S i n c e M and M a r e v e r y s i m i l a r , t h e S/MA/MM t e r p o l y m e r m i g h t be t r e a t e d a s a c o p o l y m e r (S/MA), l u m p i n g methyl m e t h a c r y l a t e and s t y r e n e t o g e t h e r , and r e w r i t i n g e q . ( 5 ) as 2

3

3

[ri] = ( 1 . 1 7 7 χ 1 0 ~ )

β

J Μ

β ρ

(w

M A

+ 16.33)

β


(10)

15.

MENDELSON

267


A g a i n , J and β must be d e t e r m i n e d e x p e r i m e n t a l l y f o r s p e c i f i c s o l v e n t s . These p r e d i c t i o n s w i l l be examined i n the R e s u l t s s e c t i o n o f t h i s p a p e r . Experimental The p o l y m e r samples s t u d i e d h e r e f a l l i n t o t h r e e d i s t i n c t categories. Data from two sample p o p u l a t i o n s have been combined i n the SAN c o p o l y m e r s t u d y . A g r o u p o f SAN m a t e r i a l s h a v i n g c o m p o s i t i o n s r a n g i n g from 42 ( w t ) % AN t o 82% AN were p o l y m e r i z e d and c h a r a c t e r i z e d q u i t e some t i m e ago ( 1 9 7 2 ) , w i t h i n t r i n s i c v i s c o s i t i e s d e t e r m i n e d o n l y i n DMF. V e r y r e c e n t l y , a s e c o n d group o f SAN s w i t h compo s i t i o n s from 5 ( w t ) % t o 48% AN, as w e l l as one sample o f p o l y s t y r e n e ( 0 % AN), were p o l y m e r i z e d and c h a r a c t e r i z e d , w i t h i n t r i n s i c v i s c o s i t i e s d e t e r m i n e d i n DMF, THF, and MEK. These two p o p u l a t i o n s a r e d i f f e r e n t i a t e d i n t h e R e s u l t s s e c t i o n by the d e s i g n a t i o n s " o l d d a t a " and "new data". The t h i r d c a t e g o r y o f samples i s t h a t o f S/MA c o p o l y m e r s and S/MA/MM t e r p o l y m e r s , w i t h i n t r i n s i c v i s c o s i t i e s measured o n l y i n MEK. In a l l c a s e s , i n t r i n s i c v i s c o s i t i e s were measured a t 25°C i n c o n s t a n t t e m p e r a t u r e b a t h s c o n t r o l l e d t o + 0 . 1 ° C or b e t t e r , u s i n g s u s p e n d e d l e v e l U b b e l o h d e d i l u t i o n v i s c o m e t e r s w i t h s o l v e n t f l o w t i m e s o f a t l e a s t 100 s e c . No k i n e t i c e n e r g y c o r r e c t i o n s were made. S o l u t i o n flow t i m e s were measured a t f o u r c o n c e n t r a t i o n s f o r e a c h sample, and i n t r i n s i c v i s c o s i t i e s were o b t a i n e d from t h e c l a s s i c a l double e x t r a p o l a t i o n of * ! / ^ (In f i ) / c v s . c to a s i n g l e i n t e r c e p t v a l u e . C o n c e n t r a t i o n r a n g e s were v a r i e d somewhat w i t h the m o l e c u l a r w e i g h t s o f the samples, but were c h o s e n s u c h t h a t b o t h f u n c t i o n s were s t r a i g h t l i n e s i n a l l c a s e s . The c h a r a c t e r i z e d m o l e c u l a r w e i g h t s u s e d i n t h i s i n v e s t i g a t i o n were i n a l l c a s e s w e i g h t a v e r a g e v a l u e s , M, o b t a i n e d by SEC. However, the SEC method v a r i e d , as m i g h t be e x p e c t e d , b o t h w i t h the n a t u r e o f t h e p o l y m e r c h a r a c t e r i z e d and w i t h the time a t w h i c h the measurements were made. Thus, the "new" p o l y s t y r e n e and SAN samples were c h a r a c t e r i z e d u s i n g a d u a l d e t e c t i o n SEC/LALLS (Waters 150C S E C / L D C - M i l t o n Roy KMX-6 low a n g l e l a s e r l i g h t s c a t t e r i n g d e t e c t o r ) system(_4,5) . T h i s system uses a 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 (DRI) d e t e c t o r as t h e c o n c e n t r a t i o n d e t e c t o r and LALLS t o measure e x c e s s s c a t t e r i n g i n t e n s i t y ( p r o p o r t i o n a l to molecular w e i g h t ) . As i s w e l l known by now, the use o f the l i g h t s c a t t e r i n g d e t e c t o r p e r m i t s the d i r e c t measurement o f m o l e c u l a r w e i g h t as a f u n c t i o n o f r e t e n t i o n volume, w i t h o u t r e c o u r s e t o t h e n e c e s s i t y o f any form o f column c a l i bration. For a l l c h a r a c t e r i z a t i o n s i n , . t h i s s y s t e m the column s e t c o n s i s t e d o f a 10 , 10 , 10 , 10 A assembly ( e i t h e r W a t e r s μ - S t y r a g e l or ASI U l t r a g e l c r o s s l i n k e d polystyrene). The c h r o m a t o g r a p h i c s o l v e n t was THF c o n t a i n i n g 250ppm a n t i o x i d a n t (BHT). R e f r a c t i v e index


r

C

v s

c

a n

S D

r

w

f i



268

DETECTION AND DATA ANALYSIS IN SIZE EXCLUSION CHROMATOGRAPHY

i n c r e m e n t (dn/dc) v a l u e s were i n d e p e n d e n t l y determined using a precision d i f f e r e n t i a l refractometer (LDC/Milton Roy KMX-16). Although thedata a r enotdiscussed here, d n / d c was f o u n d t o be l i n e a r w i t h AN c o n t e n t , a s m i g h t be expected. From t h e s e d a t a i t was r e l a t i v e l y s t r a i g h t forward t o assess t h e expected e r r o r o f u s i n g a sample average dn/dc t o c a l c u l a t e t h e i n d i v i d u a l MWs o f t h e e l u a n t s from l i g h t s c a t t e r i n g , assuming t h eworst case o f combined c o m p o s i t i o n a l h e t e r o g e n e i t y and c o m p o s i t i o n a l c o r r e l a t i o n w i t h molecular s i z e i n a given sample. Thus, a v a r i a t i o n o f +5% A N c o n t e n t ( a b s o l u t e ) a b o u t t h e m e a n of t h e sample, i f c o r r e l a t e d w i t h e l u t i o n volume, would be e x p e c t e d t o r e s u l t i n a p p r o x i m a t e l y +5% e r r o r i n t h e s a m p l e Mw; n o c o r r e l a t i o n o f c o m p o s i t i o n a l h e t e r o g e n e i t y w i t h e l u t i o n volume, o f course, e l i m i n a t e s t h e e r r o r . S i m i l a r l y , e r r o r s i n t h e DRI m e a s u r e m e n t o f c o n c e n t r a t i o n due t o c o m p o s i t i o n a l h e t e r o g e n e i t y c o r r e l a t e d w i t h e l u t i o n volume were viewed as p o t e n t i a l l y r e l a t i v e l y s m a l l . Of c o u r s e , a d d i t i o n a l d e t e c t o r s t o f o l l o w p o s s i b l e c o m p o s i t i o n a l d r i f t i ^ e ) would e l i m i n a t e these p o t e n t i a l s o u r c e s o f e r r o r , b u t t h e y were n o t used i n t h i s work. The l i g h t s o u r c e s f o r b o t h L A L L S a n d t h e KMX-16 w e r e He-Ne l a s e r s w i t h 6 3 2 8 A i n c i d e n t w a v e l e n g t h . The a c c u r a c y o f t h e SEC/LALLS was c h e c k e d b y d e t e r m i n i n g t h e m o l e c u l a r w e i g h t s o f a n u m b e r o f n a r r o w MWD s t a n d a r d s , with excellent results. By c o n t r a s t , t h e " o l d " SAN's h a v i n g compositions f r o m 4 2 % t o 8 2 % AN w e r e c h a r a c t e r i z e d ( 6 ) i n 1 9 7 2 u s i n g a s i n g l e d e t e c t o r SEC s y s t e m w i t h a c o l u m n s e t c o n s i s t i n g of f o u r porous g l a s s bead columns ( P o r a s i l ) c a l i b r a t e d against osmometrically determined M values f o r s e v e r a l of t h e samples s t u d i e d . That i s , tRe " Q - f a c t o r " c a l i b r a t i o n o b t a i n e d from p o l y s t y r e n e s t a n d a r d s was m o d i f i e d t o f o r c e c o r r e c t SEC e v a l u a t i o n o f M for a n u m b e r o f h i g h A N SAN s a m p l e s o f k n o w n M . I n t h e c a s e of t h i s group o f samples, t h e chromatographic s o l v e n t was DMF c o n t a i n i n g 0.05M L i B r a s a n e l e c t r o l y t e . I n t h e c a s e o f t h e t h i r d c a t e g o r y o f s a m p l e s , S/MA a n d S/MA/MM, t h e M v a l u e s w e r e d e t e r m i n e d b y A . S. Kenyon(7) u s i n g a ^EC/LALLS system s i m i l a r t o t h a t d e g c r i b ^ d e a g l i e r , w i t h μ - S t y r a g e l c o l u m n s ( a g a i n , 10 , 1 0 , 1 0 , 10 A ) . T h e c h r o m a t o g r a p h i c solvent i n this c a s e w a s DMF c o n t a i n i n g m a l e i c a c i d a s a n e l e c t r o l y t e , and v a l u e s o f dn/dc were measured a s d e s c r i b e d above f o r t h e "new" SAN w o r k . I n some c a s e s t h e S E C / L A L L S - d e r i v e d M^'s were checked a g a i n s t those o b t a i n e d by " s t a t i c " l i g h t s c a t t e r i n g measurement a t a s e r i e s o f c o n c e n t r a t i o n s , w i t h good agreement. A v e r a g e c o p o l y m e r c o m p o s i t i o n s o f SAN s a m p l e s w e r e determined by e l e m e n t a l a n a l y s i s , y i e l d i n g weight percent a c r y l o n i t r i l e i n t h e polymer. C o m p o s i t i o n s o f S/MA a n d S/MA/MM w e r e d e t e r m i n e d b y s e q u e n t i a l h y d r o l y s i s a n d pyridine t i t r a t i o n t o obtain maleic anhydride content and by i n f r a r e d a n a l y s i s f o r m e t h y l m e t h a c r y l a t e c o n t e n t . n

3


15.

MENDELSON

Results

and


269

Discussion

The c o m b i n e d c h a r a c t e r i z a t i o n r e s u l t s f o r a l l o f t h e SAN s a m p l e s ( i n c l u d i n g t h e one p o l y s t y r e n e s a m p l e ) , i . e . , w e i g h t f r a c t i o n o f AN mer u n i t s ( ) , Μ , a n d [η] i n each s o l v e n t , are summarized i n Taole I . Where b l a n k s e x i s t i n t h e [η] c o l u m n s , t h e i n t r i n s i c v i s c o s i t y was not measured f o r t h a t p a r t i c u l a r sample i n t h a t p a r t i c u l a r solvent. E q u a t i o n (6) p r e d i c t s t h a t a p l o t or r e g r e s s i o n of log[r)] vs. l o g [ M ( w + 1.041)] should t e s t the v a l i d i t y o f the r e l a t i o n s h i p and, i f v a l i d , s h o u l d y i e l d β and J f r o m t h e s l o p e and i n t e r c e p t , r e s p e c t i v e l y . Therefore, the f i n a l column of Table I g i v e s the c a l c u l a t e d v a l u e s of ( M ( w + 1.041)]. To t e s t t h e v a l i d i t y o f e q . ( 6 ) , t h e l a r g e b o d y o f SAN [Y]] d a t a f o r DMF a s t h e s o l v e n t was i n i t i a l l y p l o t t e d as i n d i c a t e d above w i t h c e r t a i n omissions. B e c a u s e DMF i s k n o w n t o be a p o o r s o l v e n t f o r p o l y s t y r e n e r e l a t i v e t o i t s s o l v e n t power f o r SAN s o f r e a s o n a b l y h i g h l e v e l o f AN, t h e p o l y s t y r e n e s a m p l e a n d t h o s e SAN s a m p l e s c o n t a i n i n g 1 0 % AN o r l e s s w e r e o m i t t e d . T h i s p l o t , i n c l u d i n g b o t h " o l d " a n d "new" d a t a , i s shown h e r e a s F i g u r e 1, d e m o n s t r a t i n g a good s t r a i g h t l i n e f i t t o t h e d a t a ( o v e r t h e c o m p o s i t i o n a l r a n g e , 1 5 - 8 2 % AN, and the M r a n g e , 4 5 , 0 0 0 - 8 0 0 , 0 0 0 ) , and c o n f i r m i n g t h e v a l i d i t y of eq.(6) f o r t h i s copolymer-solvent system. It a l s o i n d i c a t e s no s y s t e m a t i c b e h a v i o r d i f f e r e n c e b e t w e e n t h e o l d a n d new d a t a s e t s . L i n e a r l e a s t s q u a r e s f i t t i n g of the data y i e l d s W

A

w


w

N

A N

A N

f

w

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^25°C,DMF

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1-86X10-

4

(w

0

A N

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6 9 0

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0

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6

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( 11)

w h e r e t h e u n i t s o f [η] a n d M h e r e and throughout^ this p a p e r a r e d l / g a n d d a l t o n s , r e s p e c t i v e l y . The R c o r r e l a t i o n c o e f f i c i e n t f o r the l o g a r i t h m i c form of e q . ( l l ) i s 0 . 9 6 7 , w h i c h m u s t be c o n s i d e r e d q u i t e g o o d c o n s i d e r i n g the d i f f e r e n t time f r a m e s o f t h e d a t a and the accumulated i n h e r e n t e r r o r s of a l l of the measurements involvedT h u s , f r o m e q s . ( 6 ) a n d ( 1 1 ) , β = 0.690 a n d J = 2.93x10 . R e t u r n i n g t o t h e o m i t t e d AN

Generalized Intrinsic Viscosity Relations for Copolymers and Higher

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