The Molecular Weight Distributions of Emulsion Polymers - American

5 The Molecular Weight Distributions of Emulsion Polymers

Downloaded by COLUMBIA UNIV on October 14, 2014 | http://pubs.acs.org Publication Date: October 7, 1981 | doi: 10.1021/bk-1981-0165.ch005

DONALD H. NAPPER, GOTTFRIED LICHTI, and ROBERT G. GILBERT Departments of Physical and Theoretical Chemistry, The University of Sydney, N.S.W. 2006 Australia The object of this paper is to review a general procedure (1) that allows the molecular weight distribution (MWD) of the polymer produced in an emulsion polymerization to be predicted with considerable generality. The theory to be presented permits the following microscopic kinetic processes to be comprehended: (i) the entry of free radicals into the latex particles from the continuous phase; (ii) the exit (or desorption) of free radicals from the particles; (iv) chain transfer, whether to monomer or added chain transfer agent; (v) bimolecular termination, whether by combination and/or disproportionation. The procedure allows all of these kinetic events to be acting simultaneously. It could be readily extended to encompass the effects of retarders. Chain transfer to polymer, which may be important in some industrial emulsion polymerizations and which results in long chain branching, is specifically excluded from the present treatment, although an extension of the theory should permit this kinetic process to be incorporated. The prediction of the MWD of emulsion polymers proved to be a relatively intractable problem even after the advent of the Harkins-Smith-Ewart theory. Perhaps the most successful early attack on the problem was that of Katz, Shinnar and Saidel (2). They considered only two microscopic events: entry and bimolecular termination by combination. Their theory resulted in a set of partial integrodifferential equations, whose numerical solution provided the lower moments of the molecular weight distribution function. Other attempts to predict the MWD of emulsion polymers include those of Parts and Watterson (3), Sundberg and Eliassen (4), Min and Ray (5) and Gardon (6). Overall Strategy The overall strategy to be described in detail below is straightforward (1). We consider first a set of chains, all of which began growing at the same instant. We shall refer to these chains as being 'distinguished': they are distinguished from all 0097-6156/81/0165-0105$05.00/0 © 1981 American Chemical Society

In Emulsion Polymers and Emulsion Polymerization; Bassett, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

106

EMULSION POLYMERS AND EMULSION POLYMERIZATION

o t h e r c h a i n s g e n e r a t e d i n t h e l a t e x b y h a v i n g commenced g r o w t h a t t h e same i n s t a n t . P a r t i c l e s c o n t a i n i n g d i s t i n g u i s h e d f r e e r a d i c a l s w i l l themselves be r e f e r r e d t o as b e i n g ' d i s t i n g u i s h e d . N e x t , we f o l l o w t h e g r o w t h h i s t o r i e s o f e a c h d i s t i n g u i s h e d c h a i n by f o l l o w i n g t h e time e v o l u t i o n o f t h e d i s t i n g u i s h e d particles. T h i s p e r m i t s u s t o s p e c i f y t h e number c o n c e n t r a t i o n o f t h e d i f f e r e n t t y p e s o f d i s t i n g u i s h e d p a r t i c l e s a t any t i m e . F i n a l l y , t h e time o f growth o f each c h a i n i s found by d e t e r m i n i n g how many d i s t i n g u i s h e d l a t e x p a r t i c l e s s t o p p e d g r o w i n g a t any p a r t i c u l a r i n s t a n t . T h i s i s o b t a i n e d r e a d i l y f r o m t h e p r o d u c t o f t h e number c o n c e n t r a t i o n o f t h e d i f f e r e n t t y p e s o f d i s t i n g u i s h e d p a r t i c l e s and t h e (known) r a t e c o e f f i c i e n t f o r t h e a p p r o p r i a t e k i n e t i c e v e n t . Of c o u r s e , t h e g r o w t h time o f each c h a i n determines t h e m o l e c u l a r weight o f t h e p o l y m e r p r o d u c e d on t e r m i n a t i o n . The f o r e g o i n g p r o c e d u r e i s t h a t a p p l i c a b l e t o c h a i n s t o p p a g e by a f i r s t o r d e r p r o c e s s ( e . g . , t r a n s f e r , e x i t ) b u t an e x t e n s i o n p e r m i t s b i m o l e c u l a r t e r m i n a t i o n , whether by c o m b i n a t i o n o r d i s p r o p o r t i o n a t i o n , t o be encompassed. F o r b i m o l e c u l a r t e r m i n a t i o n , two f r e e r a d i c a l s a r e i n v o l v e d i n t h e p r o d u c t i o n o f t h e dead p o l y m e r . I t i s t h e r e f o r e n e c e s s a r y t o know t h e g r o w t h h i s t o r i e s of both free r a d i c a l s involved i n the bimolecular event. This gives r i s e t o the concept of doubly d i s t i n g u i s h e d p a r t i c l e s , i . e . , p a r t i c l e s t h a t c o n t a i n two f r e e r a d i c a l s , t h e f i r s t o f w h i c h b e g a n g r o w i n g a t one a r b i t r a r i l y c h o s e n i n s t a n t and t h e s e c o n d o f w h i c h commenced g r o w i n g a t a n o t h e r a r b i t r a r i l y c h o s e n i n s t a n t . I n t h i s way t h e g r o w t h h i s t o r i e s o f b o t h d i s t i n g u i s h e d f r e e r a d i c a l s c a n be f o l l o w e d and p r o p e r a l l o w a n c e made f o r t h e t e r m i n a t i o n mechanism. A g a i n , t h e g r o w t h t i m e s d e t e r m i n e t h e m o l e c u l a r w e i g h t o f t h e polymer produced by t h e emulsion polymerization process. I t i s n e c e s s a r y i n a c o m p a r t m e n t a l i z e d r e a c t i o n t o keep track of not only the distinguished free r a d i c a l s i n a l a t e x p a r t i c l e but also the other free r a d i c a l s i n the p a r t i c l e ( i . e . , t h e n o n d i s t i n g u i s h e d r a d i c a l s ) . T h i s s u g g e s t s t h e n o t a t i o n N.' and N.'', w h e r e N = r e l a t i v e number o f l a t e x p a r t i c l e s , i d e n o t e s t h e t o t a l number o f f r e e r a d i c a l s i n t h e l a t e x p a r t i c l e and t h e number o f p r i m e s u p e r s c r i p t s s p e c i f i e s t h e number o f d i s t i n guished chains s t i l l growing i n the p a r t i c l e . The n o n d i s t i n guished f r e e r a d i c a l s determine the range of microscopic k i n e t i c p r o c e s s e s t h a t t h e d i s t i n g u i s h e d c h a i n can undergo. F o r example, the d i s t i n g u i s h e d c h a i n i n an N^'-type p a r t i c l e cannot undergo b i m o l e c u l a r t e r m i n a t i o n whereas t h a t i n an N^'-type p a r t i c l e can. F o r t h e p u r p o s e s o f t h i s a r t i c l e , we s h a l l make two s i m p l i f y i n g assumptions i n t h a t t h e d i s c u s s i o n w i l l be c o n f i n e d t o t h e p o l y m e r p r o d u c e d i n t h e s t e a d y s t a t e domain ( i . e . , I n t e r v a l I I ) o f a '0-1-2' s y s t e m . By a '0-1-2' s y s t e m , we i m p l y one i n w h i c h p a r t i c l e s c a n c o n t a i n o n l y 0, 1 o r 2 f r e e r a d i c a l s , t h e p o p u l a t i o n s o f p a r t i c l e s c o n t a i n i n g more t h a n two f r e e


1


5.

NAPPER ET AL.

Molecular

Weight

107

Distributions

r a d i c a l s being considered too s m a l l t o i n f l u e n c e the o v e r a l l behaviour. I t i s s t r e s s e d that n e i t h e r o f the foregoing s i m p l i f y i n g a s s u m p t i o n s i s n e c e s s a r y i n t h e g e n e r a l t h e o r y (_1), a l t h o u g h t h e i n c l u s i o n o f p a r t i c l e s c o n t a i n i n g more t h a n two f r e e r a d i c a l s u s u a l l y precludes a n a l y t i c a l formulae being obtained. N o t e t h a t I n t e r v a l I , where n u c l e a t i o n o c c u r s , i s n o t comprehended by t h i s a n a l y s i s . The

Smith-Ewart Equations

tion,

L i k e most t h e o r e t i c a l d i s c u s s i o n s o f e m u l s i o n p o l y m e r i z a t h a t o f t h e MWD b e g i n s w i t h t h e S m i t h - E w a r t e q u a t i o n s ( 7 ) :


dN. d t

= pCN.^ - N.) + k ( [ i + l ] N . + c([i+2][i+l]N.

+ 2

+ 1

- iN.)

- i[i-l]N.)

(1)

w h e r e N. = r e l a t i v e number o f l a t e x p a r t i c l e s c o n t a i n i n g i (=0,1, 2,3, ... ) f r e e r a d i c a l s , p = r a d i c a l e n t r y r a t e c o e f f i c i e n t ( i . e . , t h e a v e r a g e number o f f r e e r a d i c a l s t h a t e n t e r a p a r t i c l e i n u n i t t i m e ) , k = e x i t r a t e c o e f f i c i e n t and 2c = b i m o l e c u l a r termination rate coefficient. N o t e t h a t t h e n o r m a l i z a t i o n adopt e d i s ? N = 1; m o r e o v e r , o n l y i f i > 2 w i l l b i m o l e c u l a r e v e n t s i

c o n t r i b u t e terms t o e q u a t i o n s ( 1 ) . Any term i n v o l v i n g a n e g a t i v e subscript i s ignored. The S m i t h - E w a r t e q u a t i o n s c a n b e s o l v e d u s i n g a s i n g l e n u m e r i c a l e i g e n v a l u e d e t e r m i n a t i o n under a l l c o n d i t i o n s . A n a l y t i c a l s o l u t i o n s can a l s o b e o b t a i n e d i f n i s n o t t o o l a r g e ( n < 0 . 7 ) ( 8 , 9 , 1 0 ) . These s o l u t i o n s encompass b o t h t h e s t e a d y s t a t e and t h e a p p r o a c h t o t h e s t e a d y s t a t e . Thus t h e p a r t i c l e number c o n c e n t r a t i o n s N^, N^, N , . . . a r e known o n c e P, k and c have been determined e x p e r i m e n t a l l y . As w i l l be seen, these p o p u l a t i o n s a r e t h e s t a r t i n g p o i n t f o r t h e MWD a n a l y s i s . 2

The

Distinguished

Particle

Equations

The Number o f D i s t i n g u i s h e d P a r t i c l e s P r o d u c e d . We w i l l assume t h a t t h e s t e a d y s t a t e has b e e n e s t a b l i s h e d and t h a t a t some t i m e , d e n o t e d b y t = 0, a s t o p w a t c h (numbered 1) i s s t a r t e d . The t i m e o n s t o p w a t c h 1, d e n o t e d b y t , t h u s s p e c i f i e s t h e p e r i o d t h a t t h e e x p e r i m e n t has b e e n u n d e r way. A f t e r an a r b i t r a r y p e r i o d , a s e c o n d s t o p w a t c h (number 2) i s s t a r t e d t o s i g n a l t h e commencement o f g r o w t h o f t h e d i s t i n g u i s h e d s e t o f f r e e r a d i c a l s . S t o p w a t c h 2 a c c o r d i n g l y s p e c i f i e s how l o n g t h e d i s t i n g u i s h e d c h a i n s h a v e b e e n g r o w i n g ; t h i s s e c o n d t i m e we d e n o t e b y t . I n a n 0-1-2 system, the N^ -type p a r t i c l e s are produced a t any i n s t a n t b y t h e e n t r y o f f r e e r a d i c a l s i n t o p a r t i c l e s c o n t a i n i n g no f r e e r a d i c a l s o r b y c h a i n t r a n s f e r i n p a r t i c l e s c o n t a i n i n g one f r e e r a d i c a l . The number c o n c e n t r a t i o n g e n e r a t e d a t any i n s t a n t i s r e a d i l y f o u n d f r o m t h e p r o d u c t o f t h e r e s p e c f

f


108


t i v e number c o n c e n t r a t i o n o f t h e d i f f e r e n t t y p e s o f p a r t i c l e s the a p p r o p r i a t e r a t e c o e f f i c i e n t . Thus

Y

= pN

+ k

Q

N

t r

and

(2)

x

where k = ( p s e u d o - f i r s t - o r d e r ) t r a n s f e r r a t e c o e f f i c i e n t (=k E , where k = (second o r d e r ) r a t e constant f o r t r a n s f e r tr,m m' tr,m t o monomer and C = monomer c o n c e n t r a t i o n i n t h e l a t e x p a r t i c l e s ) . For s t y r e n e , and are o f t e n comparable i n magnitude whereas t


k

( o f o r d e r 0.1s "*") may be l a r g e r t h a n p ( o f o r d e r , s a y , -2 -1

f f

where M = a t . The u p p e r l i m i t t o t h e g r o w t h t i m e o f t h e l o n g e r chain i s c l e a r l y the time of t h e experiment t * . The t o t a l d i s t r i b u t i o n f u n c t i o n f o r t h e c h a i n s p r o d u c e d by d i s p r o p o r t i o n a t i o n i s o b t a i n e d by summing t h e number d i s t r i b u t i o n s o f t h e l o n g e r and s h o r t e r c h a i n s : .bd

The

„ bd . „ bd Sf + S„ S a

T o t a l Chain

D a

(19)

Production

The f o r e g o i n g a n a l y s i s was e x p r e s s l y e l a b o r a t e d t o t r e a t a d i v e r s e range of m i c r o s c o p i c k i n e t i c processes. Each t e r m i n a t i o n p r o c e s s , h o w e v e r , was r e g a r d e d a s a c t i n g a l o n e . I t i s possible t o h a n d l e any c o m b i n a t i o n o f t e r m i n a t i o n mechanisms b y s i m p l e a d d i t i o n o f t h e number d i s t r i b u t i o n f u n c t i o n s f o r t h e f i r s t o r d e r and s e c o n d o r d e r e v e n t s : S = Polydispersity

S

"

+ S

b c

+ S

b d

(20)

Index

One a d v a n t a g e o f t h e p r o c e d u r e d e l i n e a t e d above i s t h a t i t p e r m i t s t h e c o m p l e t e 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 f u n c t i o n t o be c a l c u l a t e d , sometimes a n a l y t i c a l l y , w h a t e v e r t h e t e r m i n a t i o n mechanism. Of c o u r s e , t h e l o w e r moments o f t h e d i s t r i b u t i o n f u n c t i o n c a n a l s o be r e a d i l y c a l c u l a t e d :


5. NAPPER ET AL,

Molecular oo

= w

=

a l l o w i n g t h e commonly u s e d p o l y d i s p e r s i t y i n d e x / n w found.

to be


Results F i r s t Order Stoppage A l o n e . I f stoppage i s determined s o l e l y by a f i r s t o r d e r p r o c e s s , s u c h a s t r a n s f e r , t h e f o r e g o i n g a n a l y s i s p r e d i c t s a n e a r l y e x p o n e n t i a l d i s t r i b u t i o n f u n c t i o n . The p o l y d i s p e r s i t y i n d e x must t h e n b e v e r y c l o s e t o 2.00. The same r e s u l t i s o b t a i n e d f o r b u l k and s o l u t i o n p o l y m e r i z a t i o n s d o m i n a t e d b y c h a i n transfer. C o m p a r t m e n t a l i z a t i o n t h u s has no m a j o r e f f e c t o n t h e p o l y d i s p e r s i t y o f t h e p o l y m e r p r o d u c e d , a s was r e c o g n i z e d b y G e r r e n s (11), i f t h e s t o p p a g e p r o c e s s i s d o m i n a t e d b y c h a i n transfer. T h i s c o n t r a s t s w i t h t h e s i g n i f i c a n t e f f e c t s o f compartm e n t a l i z a t i o n i f b i m o l e c u l a r events dominate t e r m i n a t i o n . Bimolecular Termination Alone. The e f f e c t o f c o m p a r t m e n t a l i z a t i o n i n an emulsion p o l y m e r i z a t i o n i s to broaden s i g n i f i c a n t l y t h e MWD o f t h e p o l y m e r p r o d u c e d i f t e r m i n a t i o n i s d o m i n a t e d b y bimolecular events. T h i s was c l e a r l y e s t a b l i s h e d b y K a t z , S h i n n a r and S a i d e l (2) f o r t e r m i n a t i o n b y c o m b i n a t i o n b u t a l s o h o l d s f o r d i s p r o p o r t i o n a t i o n . We n o t e i n p a s s i n g t h a t o n e t h e o r y (6) o f e m u l s i o n p o l y m e r i z a t i o n c l a i m s t h a t c o m p a r t m e n t a l i z a t i o n d e c r e a s e s t h e p o l y d i s p e r s i t y o f t h e p o l y m e r p r o d u c e d a t any i n s t a n t ; t h e r e i s , h o w e v e r , no sound t h e o r e t i c a l b a s i s f o r t h i s claim. The o r i g i n o f t h e b r o a d e n i n g o f t h e MWD b y c o m p a r t m e n t a l i z a t i o n i s r e a d i l y l o c a t e d . The w i d t h o f t h e MWD r e f l e c t s t h e d i f f e r e n t environments i n which the polymer chains are c r e a t e d , grow and c e a s e g r o w t h . I f t h e a v e r a g e number o f f r e e r a d i c a l s p e r p a r t i c l e (n) i s l a r g e , t h e e n v i r o n m e n t s o f t h e c h a i n s i n t h e compartmentalized s y s t e m w i l l b e s i m i l a r t o t h o s e i n t h e b u l k and the p o l y d i s p e r s i t y index w i l l be c l o s e t o the b u l k v a l u e . As n d e c r e a s e s , h o w e v e r , t h e e n v i r o n m e n t s d i f f e r more w i d e l y f r o m t h o s e i n t h e b u l k s y s t e m . Of p a r t i c u l a r i m p o r t a n c e a r e t h e g r o w i n g c h a i n s i n p a r t i c l e s c o n t a i n i n g o n l y one f r e e r a d i c a l . These c h a i n s c a n n o t u n d e r g o b i m o l e c u l a r t e r m i n a t i o n and s o grow unhindered u n t i l a second f r e e r a d i c a l e n t e r s the l a t e x p a r t i c l e . This environment i s m a n i f e s t l y d i f f e r e n t from t h a t i n other g r o w i n g l a t e x p a r t i c l e s and f r o m t h a t i n t h e b u l k s y s t e m . This argument a l s o e x p l a i n s why c o m p a r t m e n t a l i z a t i o n has no e f f e c t o n t h e MWD i f t e r m i n a t i o n i s b y c h a i n t r a n s f e r b e c a u s e t h e c h a i n s c o n t a i n i n g one f r e e r a d i c a l c a n s t i l l u n d e r g o t h e t r a n s f e r p r o c e s s , j u s t a s t h e y do i n t h e b u l k s y s t e m .


114


The l i m i t i n g b e h a v i o u r i n t h e s t e a d y s t a t e f o r b i m o l e c u l a r t e r m i n a t i o n o f e m u l s i o n p o l y m e r i z a t i o n s i s s u m m a r i z e d as f o l l o w s : Combination 1.5 /

n

n

= I 2,0 =

^ 4.0 oo

/ n =

h

Disproportionation Combination Alone. F i g u r e 1 d i s p l a y s the dependence o f t h e p o l y d i s p e r s i t y i n d e x on n i f t e r m i n a t i o n i s s o l e l y by combination. Note t h a t these r e s u l t s have been c a l c u l a t e d u s i n g the f u l l a n a l y s i s (1), n o t j u s t t h e 0-1-2 system. Other t h e o r i e s g i v e n i n the l i t e r a t u r e i m p l y d i f f e r e n t v a l u e s f o r /^M > i f n = %: t h e s e r a n g e f r o m 1.0(6) t o 2.5 ( 5 ) . The l i m i t i n g v a l u e o f 2.00 was a l s o o b t a i n e d by K a t z , S h i n n a r and S a i d e l (2) by an e n t i r e l y d i f f e r e n t method f r o m t h a t e l a b o r a t e d a b o v e and i s u n q u e s t i o n a b l y c o r r e c t . I t c a n be e s t a b l i s h e d by t h e f o l l o w i n g r e a s o n i n g . I f n = h, e a c h p a r t i c l e c o n t a i n s a t most one f r e e r a d i c a l . Growing chains i n the l a t e x p a r t i c l e s c a n t h u s e i t h e r grow o r be t e r m i n a t e d i n s t a n t a n e o u s l y by e n t r a n t f r e e r a d i c a l s . These m u t u a l l y e x c l u s i v e k i n e t i c e v e n t s i m m e d i a t e l y p r e s c r i b e t h e F l o r y 'most p r o b a b l e ' d i s t r i b u t i o n f u n c t i o n f o r t h e g r o w i n g c h a i n s ( 1 2 ) ; t h i s i s an e x p o n e n t i a l d i s t r i b u t i o n f u n c t i o n w i t h a p o l y d i s p e r s i t y i n d e x o f 2.00 ( 1 3 ) . The t e r m i n a t i o n p r o c e s s o c c u r s i n s t a n t a n e o u s l y v i a e n t r a n t f r e e r a d i c a l s o f ( n e a r ) z e r o m o l e c u l a r w e i g h t . These r a d i c a l s do n o t p e r t u r b s i g n i f i c a n t l y the d i s t r i b u t i o n of c h a i n l e n g t h s i n convert i n g g r o w i n g c h a i n s t o dead p o l y m e r . Indeed, t e r m i n a t i o n i n t h i s i n s t a n c e i s e q u i v a l e n t t o c h a i n t r a n s f e r , w h i c h g i v e s an i d e n t i c a l v a l u e f o r the p o l y d i s p e r s i t y index. D i s p r o p o r t i o n a t i o n Alone. Figure 2 d i s p l a y s the p o l y d i s p e r s i t y i n d e x as a f u n c t i o n o f n f o r t e r m i n a t i o n by d i s p r o p o r t i o n a tion. A g a i n , t h e s e h a v e b e e n c a l c u l a t e d by a f u l l a n a l y s i s ( 1 ) . As w i t h t e r m i n a t i o n by c o m b i n a t i o n , t h e p o l y d i s p e r s i t y shows a r a p i d decrease i n the n r a n g e o f 0.5 - 1.0. The r e a s o n f o r t h e u p p e r l i m i t o f < M >/=4.00 follows i m m e d i a t e l y f r o m t h e d i s c u s s i o n g i v e n i n ¥he p r e c e d i n g s e c t i o n f o r t e r m i n a t i o n by c o m b i n a t i o n . A g a i n , the growing c h a i n s have a F l o r y 'most p r o b a b l e ' d i s t r i b u t i o n w i t h /= 2.00.



5. NAPPER ET AL.

Molecular

Weight

Distributions

115

Figure 1. Polydispersity index of the polymer produced in Interval II of an emulsion polymerization terminated solely by combination as a function of the average number of free radicals per particle

Figure 2. Polydispersity index of the polymer produced in Interval II of an emulsion polymerization terminated solely by disproportionation as a function of the average number of free radicals per particle.


116


T e r m i n a t i o n i n t h i s c a s e p r o d u c e s a number, e q u a l t o t h e number o f g r o w i n g c h a i n s , o f l o w m o l e c u l a r w e i g h t dead c h a i n s . T h i s does n o t a f f e c t b u t h a l v e s . Hence / i s doubled to

A Combination of Termination

Mechanisms

Displayed i n F i g u r e 3 are the r e s u l t s f o r the p o l y d i s p e r s i t y i n d e x f o r an e m u l s i o n p o l y m e r i z a t i o n s y s t e m i n w h i c h c h a i n s t o p page o c c u r s by a c o m b i n a t i o n o f c h a i n t r a n s f e r 0^ r 1 r e c i p r o c a l t i m e u n i t ) and d i s p r o p o r t i o n a t i o n ( c ^ = 100 r e c i p r o c a l t i m e u n i t s ) . These r e s u l t s w e r e o b t a i n e d by v a r y i n g p and t h u s n. The results s u g g e s t how i t m i g h t be p o s s i b l e t o t a i l o r a d i s t r i b u t i o n t o some desired p o l y d i s p e r s i t y index. Downloaded by COLUMBIA UNIV on October 14, 2014 | http://pubs.acs.org Publication Date: October 7, 1981 | doi: 10.1021/bk-1981-0165.ch005

tJ

Comparison w i t h

Experiment

The e x p e r i m e n t a l r e s u l t s on t h e p o l y m e r p r o d u c e d i n e m u l s i o n p o l y m e r i z a t i o n s p u b l i s h e d t h u s f a r a r e b o t h c o n f u s i n g and c o n t r a dictory. S e v e r a l f a c t o r s may be r e s p o n s i b l e f o r t h i s : f i r s t , many s u r f a c t a n t s b e h a v e a s c h a i n t r a n s f e r a g e n t s , w h i c h has o f t e n n o t b e e n r e c o g n i z e d ; s e c o n d , measurements h a v e o f t e n b e e n made on samp l e s t h a t c o n t a i n p o l y m e r f r o m I n t e r v a l s I , I I and I I I , w h i c h leads to a s i g n i f i c a n t i n c r e a s e i n the p o l y d i s p e r s i t y index because < M > i s s e n s i t i v e t o the presence of lower m o l e c u l a r weight s p e c i e s ; t R i r d . d i r e c t measurements o f t h e MWD h a v e o n l y r e c e n t l y become p o s s i b l e w i t h t h e a d v e n t o f g e l p e r m e a t i o n c h r o m a t o g r a p h y . F o r many monomers ( e . g . , s t y r e n e , m e t h y l m e t h a c r y l a t e , v i n y l a c e t a t e ) , i t seems l i k e l y t h a t 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 p r o d u c e d by e m u l s i o n p o l y m e r i z a t i o n i s i n many i n s t a n c e s d o m i n a t e d n o t by b i m o l e c u l a r t e r m i n a t i o n as i n t h e b u l k b u t r a t h e r by c h a i n t r a n s f e r t o monomer. T h i s i s most c o n v i n c i n g l y d e m o n s t r a t e d by t h e a v e r a g 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 p r o d u c e d ( 4 ) . w o u l d be o f o r d e r t e n s o f m i l l i o n s i f c h a i n s t o p p a g e w e r e d o m i n a t e d by b i m o l e c u l a r t e r m i n a t i o n b u t o n l y s e v e r a l m i l l i o n s o r l e s s i f c h a i n t r a n s f e r t o monomer i s o p e r a t i v e . E x p e r i m e n t a l r e s u l t s u s u a l l y c o n f i r m t h e l a t t e r o r d e r o f m a g n i t u d e , w h i c h i s i t s e l f an order of magnitude l a r g e r than t h a t f o r polymer produced i n b u l k or i n s o l u t i o n . The k i n e t i c r e s u l t s o f H a w k e t t e t a l . (8) a l l o w t h e p r o c e s s o f c h a i n t r a n s f e r t o monomer t o be p l a c e d i n p e r s p e c tive. The e x p e r i m e n t a l r e s u l t s show t h a t i n t h e s e s y s t e m s a f r e e r a d i c a l e n t r y e v e n t o c c u r s o n l y once e v e r y few m i n u t e s , e v e n a t t h e h i g h e s t i n i t i a t o r c o n c e n t r a t i o n . An e x i t e v e n t t a k e s p l a c e e v e r y f i f t e e n m i n u t e s . C h a i n t r a n s f e r t o monomer, h o w e v e r , o c c u r s every t e n seconds. T h i s i s c l e a r l y the dominant c h a i n stoppage e v e n t and s h o u l d r e s u l t i n p o l y m e r w i t h a p o l y d i s p e r s i t y i n d e x o f 2.00. T h i s r e s u l t d e m o n s t r a t e s t h a t c o m p a r t m e n t a l i z a t i o n c a n cause a f u n d a m e n t a l c h a n g e i n t h e c h a i n s t o p p i n g mechanism. P i i r m a and c o - w o r k e r s ( 1 4 , 15) h a v e p e r f o r m e d c a r e f u l s t u d i e s on t h e p o l y s t y r e n e p r o d u c e d by e m u l s i o n p o l y m e r i z a t i o n u s i n g g e l



NAPPER ET AL.

' 0

0.5

Molecular

_ 1 . 0 n

Weight

1.5

117

Distributions

Figure 3. Polydispersity index of the polymer produced in Interval II of an emulsion polymerization as a function of the average number of free radicals per particle. Chain stoppage occurs by chain transfer (k = 1 reciprocal time unit) and disproportionation (c /k = 100). tr

d



118


permeation chromatography. T h e i r r e s u l t s b r o a d l y support t h e c o n t e n t i o n t h a t c h a i n t r a n s f e r t o monomer c o n t r o l s t h e MWD. Note that i fn = t h e p o l y d i s p e r s i t y i n d e x h a s a v a l u e o f 2.00 i r r e s p e c t i v e o f w h e t h e r t e r m i n a t i o n i s d o m i n a t e d b y t r a n s f e r t o monomer or by c o m b i n a t i o n , which i s t h e dominant b i m o l e c u l a r t e r m i n a t i o n event f o r styrene i n b u l k o r s o l u t i o n p o l y m e r i z a t i o n s . T h i s ambig u i t y c a n u s u a l l y be removed b y c o n s i d e r a t i o n o f t h e ( w e i g h t ) average m o l e c u l a r weight o f t h e polymer produced, as noted above. Note t h a t i f i t i s p o s s i b l e t o cause f r e e r a d i c a l e n t r y events t o o c c u r much more f r e q u e n t l y t h a n c h a i n t r a n s f e r t o monomer e v e n t s (e.g., f o r styrene, a t a r a t e greater than 1 p e r second), then the p o l y m e r w i l l be c o n t r o l l e d p r i m a r i l y b y b i m o l e c u l a r t e r m i n a t i o n . Note, t o o , t h a t i f c h a i n stoppage i s dominated by c h a i n t r a n s f 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 p r o d u c e d w o u l d be i n d e p e n d e n t o f p a r t i c l e v o l u m e . M o r t o n et_ a l . ( 1 6 ) h a v e o b t a i n e d d a t a f o r styrene that support t h i s c o n c l u s i o n . Conclusions I t i s p o s s i b l e t o p r e d i c t t h e MWD o f p o l y m e r p r o d u c e d b y a n e m u l s i o n p o l y m e r i z a t i o n w i t h s i g n i f i c a n t g e n e r a l i t y . The r e s u l t s show t h a t n o t o n l y i s t h e i n s t a n t a n e o u s a v e r a g e m o l e c u l a r w e i g h t s i g n i f i c a n t l y l a r g e r b u t a l s o t h a t t h e MWD o f t h e p o l y m e r p r o d u c e d i n compartmentalized r e a c t i o n s i s r e l a t i v e l y broader than the corresponding polymer produced i n a b u l k o r s o l u t i o n p o l y m e r i z a t i o n p r o v i d e d b i m o l e c u l a r t e r m i n a t i o n i s dominant. I f , however, c h a i n t r a n s f e r t o monomer i s t h e d o m i n a n t c h a i n s t o p p i n g mechanism, c o m p a r t m e n t a l i z a t i o n h a s no e f f e c t o n t h e MWD o f t h e p o l y m e r p r o d u c e d . The l a t t e r a p p e a r s t o be t h e c a s e f o r some common monomers ( e . g . , s t y r e n e ) i n many e m u l s i o n p o l y m e r i z a t i o n s . Thus c o m p a r t m e n t a l i z a t i o n c a n c a u s e a f u n d a m e n t a l change i n t h e dominant c h a i n s t o p p a g e mechanism. L e g e n d o f Symbols a c c Cd C k kp k-tr M n N-L N^

= = = = = = =

c

Q

f

Ni

f f

=

molecular weight i n c r e a s e per u n i t time o f a growing c h a i n . pseudo-first-order bimolecular termination rate coefficient. r a t e c o e f f i c i e n t f o r t e r m i n a t i o n by c o m b i n a t i o n . r a t e c o e f f i c i e n t f o r t e r m i n a t i o n by d i s p r o p o r t i o n a t i o n . monomer c o n c e n t r a t i o n i n l a t e x p a r t i c l e s . rate coefficient f o r exit. propagation rate c o e f f i c i e n t . p s e u d o - f i r s t order r a t e c o e f f i c i e n t f o r chain t r a n s f e r . = m o l e c u l a r w e i g h t o f monomer. = a v e r a g e number o f f r e e r a d i c a l s p e r p a r t i c l e . = r e l a t i v e number o f l a t e x p a r t i c l e s c o n t a i n i n g i f r e e r a d i c a l s . = r e l a t i v e number o f l a t e x p a r t i c l e s c o n t a i n i n g one d i s t i n g u i s h e d f r e e r a d i c a l and ( i - 1 ) n o n d i s t i n g u i s h e d r a d i c a l s . = r e l a t i v e number o f l a t e x p a r t i c l e s c o n t a i n i n g two d i s t i n g u i s h e d f r e e r a d i c a l s and ( i - 2 ) n o n d i s t i n g u i s h e d r a d i c a l s .


NAPPER ET AL.

5.

Molecular

Weight Distributions

119

S£

= distribution of singly distinguished particles i n state i whose d i s t i n g u i s h i n g c h a i n c e a s e d g r o w t h a t t i m e t a f t e r k i t s c r e a t i o n due t o f i r s t o r d e r s t o p p a g e e v e n t s . S 2 = d i s t r i b u t i o n o f d o u b l y d i s t i n g u i s h e d p a r t i c l e s whose d i s t i n g u i s h i n g c h a i n s ceased growth a t time t after the c r e a t i o n o f t h e s e c o n d c h a i n due t o m u t u a l t e r m i n a t i o n . S = d i s t r i b u t i o n o f nongrowing c h a i n s produced by stoppage , events. T

t

f

l

DC

S = d i s t r i b u t i o n o f nongrowing c h a i n s produced by combination, gbd = d i s t r i b u t i o n o f n o n g r o w i n g c h a i n s p r o d u c e d b y d i s p r o p o r t i onation. ^ S = contribution to S by l o n g e r c h a i n s . bH bd S = contribution to S by s h o r t e r c h a i n s . t* = time the experiment has r u n . t = growth time o f d i s t i n g u i s h e d c h a i n s i n s i n g l y d i s t i n g u i s h e d particles. t = simultaneous growth times o f d i s t i n g u i s h e d c h a i n s i n doubly distinguished particles, ρ = entry rate c o e f f i c i e n t .


0

s

f

f f

Acknowledgement s We t h a n k t h e A u s t r a l i a n R e s e a r c h G r a n t s C o m m i t t e e f o r t h e i r support o f these s t u d i e s .

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Lichti, G.; Gilbert, R.G.; Napper, D.H. J. Polym. Sci. Polm. Chem. 1980, 18, 1297. Katz, S.; Shinnar, R.; Saidel, G.M. Adv. Chem. Ser. 1969, 91, 145. Watterson, J.G.; Parts, A.G. Makromol. Chem. 1971, 146, 1. Sundberg, D.C.; Eliassen, J.D. in "Polymer Colloids", Fitch, R.M., Ed.: Plenum: New York, 1971; p.153. Min, K.W.; Ray, W.H. J. Macromol. Sci. Rev. Macromol. Chem. 1974, C11, 177. Gardon, J.L. J. Polym. Sci. A-I, 1968, 6, 665. Smith, W.V.; Ewart, R.H. J. Chem. Phys. 1943, 16, 592. Hawkett, B.S.; Napper, D.H.: Gilbert, R.G. J. Chem. Soc. Faraday Trans. I 1980, 76, 1323. Hawkett, B.S.; Napper, D.H.; Gilbert, R.G. J. Chem. Soc. Faraday Trans. I 1977, 73, 690. Brooks, B.W. J. Chem. Soc. Faraday Trans. I 1980, 76, 1599. Gerrens, H. Fortschr. Hochpolymer-Forsch. 1959, 1, 234. Flory, P.J. "Principles of Polymer Chemistry"; Cornell University: Ithaca, 1953; chap. 8. Peebles, L.H. "Molecular Weight Distributions in Polymers"; Interscience: New York, 1971; p.10. Piirma, I.; Kamath, V.R.; Morton, M. J.Polym. Sci. Chem. Ed. 1975, 13, 2087.


120 15. 16.


James, H.L.; Piirma, I. in "Emulsion Polymerization", Piirma, I. and Gardon, J.L., eds., ACS Symp. Series 24, American Chemical Society: Washington, D.C.; 1976; p. 197. Morton, M.S.; Kaizerman, S.; Altier, M.W. J. Colloid Sci. 1954, 9, 300. April 6, 1981.


RECEIVED


The Molecular Weight Distributions of Emulsion Polymers - American

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