Thermal Runaway in Chain-Addition Polymerizations and

2

Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 31, 2018 | https://pubs.acs.org Publication Date: July 31, 1979 | doi: 10.1021/bk-1979-0104.ch002

Thermal Runaway in Chain-Addition Polymerizations and Copolymerizations JOSEPH A. BIESENBERGER Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030 The objectives of this presentation are to discuss the general behavior of nonisothermal chain-addition polymerizations and copolymerizations and to propose dimensionless c r i t e r i a for e s t i mating nonisothermal reactor performance, in particular thermal runaway and instability, and its effect upon polymer properties. Most of the results presented are based upon work (1-8), both theoretical and experimental, conducted in the author's laboratories at Stevens Institute of Technology. Analytical methods i n clude a Semenov-type theoretical approach (1,2,9) as well as computer simulations similar to those used by Barkelew (3,4,6,7,10). Analyses of reactor performance are limited to rate functions

and thermal energy balances

of the forms shown in equations 1 and 2. Polymer property analyses are limited to chain-addition polymerizations

and copolymerizations

0-8412-0506-x/79/47-104-015$07.00/0 © 1979 American Chemical Society Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

16

POLYMERIZATION REACTORS AND PROCESSES


with termination, whose general characteristics are shown in equations 3,4,5 and 6. It should be noted that equations 3 and 5 are written in general form to encompass many different chain mechanisms and therefore do not necessarily represent elementary reactions steps. Experimental results quoted herein are limited to polymerizations and copolymerizations of styrene (S) and acrylonitrile (AN) monomers via free-radical intermediates for which the following specific reactions obtain. For homopolymerizations we have

Termination scheme 11 applies to the geometric mean and phi factor models and scheme 12 is required for the penultimate effect model. All the above reaction models were used in attempts to simulate kinetic data. Parameters and Variables Reaction rate functions expressing rate of polymerization R generally depend upon the molar concentrations of monomer and initiator, and temperature. R -

R([m], [m ],T) Q

Henderson and Bouton; Polymerization Reactors and Processes ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

(13)

2.

BIESENBERGER

Thermal

17

Runaway

D u r i n g p o l y m e r i z a t i o n , when i n i t i a t o r i s i n t r o d u c e d c o n t i n u o u s l y f o l l o w i n g a p r e d e t e r m i n e d f e e d s c h e d u l e , o r when h e a t removal i s c o m p l e t e l y c o n t r o l l a b l e so t h a t t e m p e r a t u r e c a n be programmed w i t h a p r e d e t e r m i n e d t e m p e r a t u r e p o l i c y , we may r e g a r d f u n c t i o n s [ r o o ( t ; ] , or T ( t ) , as r e a c t i o n parameters. A common s p e c i a l case of T ( t ) i s t h e i s o t h e r m a l mode, T = c o n s t a n t . In t h e p r e s ent a n a l y s i s , h o w e v e r , we t r e a t o n l y u n c o n t r o l l e d , b a t c h p o l y m e r i z a t i o n s i n which [ m ( t ) ] and T(t) are reaction variables, s u b j e c t t o v a r i a t i o n i n a c c o r d a n c e w i t h t h e c o n s e r v a t i o n laws (balances). Thus, o n l y t h e i r i n i t i a l (feed) v a l u e s , [ m ] andT , are t r u e parameters. In a d d i t i o n t o t h e s e , we have r e a c t o r d e s i g n p a r a m e t e r s : o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t U, r a t i o o f r e a c t i o n v o l u m e t o heat t r a n s f e r area I = V/A and h e a t e x c h a n g e r e s e r v o i r t e m p e r a t u r e TR . W h i l e t h e r m o d y n a m i c p r o p e r t i e s (-AH, p C ) and k i netic properties (r,Ap,E ,A ,Et) a r e d e t e r m i n e d f o r t h e most p a r t by t h e monomers b e i n g p o l y m e r i z e d , i n i t i a t o r c h o i c e (Ad,Ed) i s v i e w e d a s a p a r a m e t e r a s w e l l a s i n i t i a l monomer c o n c e n t r a t i o n [ m ] , w h i c h c a n be a d j u s t e d t h r o u g h t h e u s e o f d i l u e n t s . I twill be shown t h a t runaway (R-A) and i g n i t i o n (IG) phenomena a r e d e t e r mined by t h e v a l u e s o f c e r t a i n d i m e n s i o n l e s s g r o u p i n g s , w h i c h a r e made up o f t h e a f o r e m e n t i o n e d p a r a m e t e r s . T h u s , i f R-A i s s e n s i t i v e t o o n e o f t h e s e g r o u p i n g s , f o r i n s t a n c e , i t w i l l a l s o be s e n s i t i v e t o a l l o t h e r parameters i n t h a t grouping. Frequently function R c a n be w r i t t e n a s a s i n g l e t e r m having t h e s i m p l e f o r m o f e q u a t i o n 1. For i n s t a n c e , w i t h the a i d o f t h e l o n g c h a i n a p p r o x i m a t i o n (LCA) and t h e q u a s i - s t e a d y s t a t e a p p r o x i m a t i o n (QSSA), t h e r a t e o f monomer c o n v e r s i o n , i . e . , t h e r a t e o f p o l y m e r i z a t i o n , f o r many c h a i n - a d d i t i o n p o l y m e r i z a t i o n s c a n be w r i t t e n a s 0


0

0

Q

p

p

t

Q

R

where

k

=

a p

k

a

p

[ / [ , /

=

A

a

p

[ ]P[ m

m

o

]

q

exp(-E R T) a p

i s a lumped o r c o m p o s i t e r a t e c o n s t a n t .

homopolymerization

i s an e x a m p l e

(p = 1, q = 1/2)

g

(14)

Free-radical a s seen i n

T a b l e I . F r e e - r a d i c a l c o p o l y m e r i z a t i o n , on t h e o t h e r h a n d , l e a d s t o a sum o f t e r m s , e a c h o f w h i c h i s more c o m p l e x t h a n e q u a t i o n \k, a s seen i n T a b l e II ( N o t e t h e p r e s e n c e o f f u n c t i o n H , g i v e n i n T a b l e I I I f o r v a r i o u s t e r m i n a t i o n m o d e s ) . To remedy t h i s s i t u a t i o n , approximate rate functions f o r copolymerization of the form o f e q u a t i o n 1 a r e used i n s t e a d . In s u c h c a s e s t h e d i m e n s i o n l e s s r a t e f u n c t i o n R' = R/(R)

o

(15)

c a n be v i e w e d a s a p r o d u c t o f s e p a r a t e f u n c t i o n s R' = f ( t ) g ( T ' ) where


(16)

18

POLYMERIZATION REACTORS AND PROCESSES TABLE I RATE FUNCTIONS FOR FREE-RADICAL

R. - k.[m ] = 2 f . l c . I l ] i i o d d

HOMOPOLYMERIZATIONS

k. = f k . i d

QSSA 1/2 R - k [P][ra] = k [ m ] [ l ] P P ap 1

/

k

0

ap

= k

[ m l= 2[l] o

(2fk,/kJ p d' V

1 / 2

x

n

2

k


V

k

•

P

t

[

m

]

2

k

s

p*

k

/

p

k

t

LCA w R

R = R. + R i p

p

QSSA

R. « i

R„ t

LCA

R » P

R. i

TABLE I I RATE FUNCTIONS FOR FREE-RADICAL COPOLYMERIZATIONS R.. = k f . [ m ] = 2 f k . f . [ l ] IJ iJ o d J

j = 1,2

L

R

=

R

E

=

ij

k

\

[ m

o

=

]

2

f

k

d

[

,

]

E

f

J R

pjk

= k .. [ P . ] [ m J pjk j k

J

= k [m.][m.][l] apjk j k ]

0

pk

R p

"

1

j

/

k ., = k k . ( 2 f k . / k ..k ) apjk p j k p&j d t j j til

R

=

j

X) J

R

1

H

k = 1,2

I = 1,2

0

I * j

PJk

= R » ( Y Y \ pk ^f^f

R = R. + R « i p Symmetry

Q

1 / 2

k

R p a p j k

a

PJ

k

[m.][m,])[l] J

1 / 2

H

k

f r o m LCA = k^.

R

p j |

Factor

k

H = L

p21

[ m

]

l

k

+

2

(

, / 2

(k 22)

k

p21 p12 k

[ m

l

] [ m

2

k

]

[ m

)'/2

k

t

]

2 1/2

k

V K

Penultimate

pl2

< t11>

K

t22 tir

effect

,1/2 r , [m

k

[ m

1

(k ) t22'

,

H =

p21

]

/

z

til/ r j Lm J + l m J 1

2

2

V K

/k

\

1 / 2

r [m ] + 2

.

k

p12

[ m

2

2

]

r [m J o T T V K

where

7

2

2

"

2

+ [mj]

tir

k ^ -

k t

n

l

2

>

k

k

t

2r t2112

;

k

tl2

k

tl221

;

k

k

t22~ t2222


20


n j

(k

(R ) = (k ) ir [ C . ] o ap o . J o

(17) '

) = IK exp(-E; ) ap o ap ap

(18)

N

E ' = E /R T ap ap g o

(19)

n


f ( t ) = ir C j J

(20)

and g(T') Frequently

= e x p E ' T V ( 1 + T') ap

(21)

i t i s convenient t o w r i t e g ( 6 ) = e x p 0/(1 + e6)

(22)

i n l i e u o f e q u a t i o n 21 where e = 1/E' ap

(23)

We n o t e t h a t u n d e r f e e d c o n d i t i o n s g(o) = l .

(R') = 1 0

since

f(0) = 1

C h a r a c t e r i s t i c Times B a l a n c e e q u a t i o n s f o r b a t c h r e a c t o r s may a l l be v i e w e d a s special cases o f the f o l l o w i n g general equation

j where p i s a n i n t e n s i v e p r o p e r t y ( m o l a r c o n c e n t r a t i o n o r temp e r a t u r e ) and p j i s t h e r a t e w i t h w h i c h p r o c e s s j c a u s e s p t o i n c r e a s e i n v a l u e . When q u a n t i t i e s p and p j a r e made d i m e n s i o n l e s s t h r o u g h d i v i s i o n by t h e i r c o r r e s p o n d i n g f e e d v a l u e s V'

=

p/(p)

Pj

~

W

Q

o

(25)

U

6

)

t h e a f o r e m e n t i o n e d b a l a n c e e q u a t i o n s become p a r t l y d i m e n s i o n l e s s , h a v i n g d i m e n s i o n s o f r e c i p r o c a l t i m e o n l y , and t a k e on t h e f o l lowing g e n e r a l form

3f • E»J' »i


(27)

2.

BIESENBERGER

Thermal

in which a c h a r a c t e r i s t i c f i n e d as

time

Xj


21

Runaway

s

(CT)

f o r e a c h p r o c e s s may

(P> /(Pj) 0

be

de-

(28)

0

We n o t e t h a t e q u a t i o n 15 i s an e x a m p l e o f e q u a t i o n 26. I t c a n be shown t h a t a l l d i m e n s i o n l e s s p a r a m e t e r s , a r r i v e d a t i n t h e c o n v e n t i o n a l manner by w r i t i n g e q u a t i o n s o f t y p e 24 i n c o m p l e t e l y d i m e n s i o n l e s s f o r m , c a n be e x p r e s s e d a s q u o t i e n t s o f CT's. T a b l e s IV and V c o n t a i n a p p r o p r i a t e b a l a n c e e q u a t i o n s f o r n o n i s o t h e r m a l f r e e - r a d i c a l p o l y m e r i z a t i o n s and c o p o l y m e r i z a t i o n s , w h i c h a r e seen t o c o n f o r m t o e q u a t i o n 24. Following the proced u r e o u t l i n e d a b o v e , we o b t a i n t h e CT's f o r h o m o p o 1 y m e r i z a t i o n s l i s t e d i n T a b l e V I . C o r r e s p o n d i n g CT's f o r c o p o l y m e r i z a t i o n s c a n be. o b t a i n e d i n a s i m i l a r way, and i n d e e d t h e f i r s t and f o u r t h l i s t e d i n T a b l e V I I w e r e . The r e m a i n i n g o n e s , h o w e v e r , were d e r i v e d v i a an a l t e r n a t e r o u t e based upon t h e d e f i n i t i o n s i n T a b l e VI l a b e l e d " e q u i v a l e n t " t o g e t h e r w i t h a p p r o x i m a t e f o r m s f o r p j , w h i c h w e r e n e c e s s i t a t e d by a p p l i c a t i o n o f t h e Semenov-type r u n away a n a l y s i s t o c o p o l y m e r i z a t i o n s , and w h i c h w i l l s u b s e q u e n t l y be d e s c r i b e d . Some u s e f u l d i m e n s i o n 1 e s s p a r a m e t e r s d e f i n e d i n terms o f t h e s e CT's a p p e a r i n T a b l e s V I I I , IX and X. Reactor

Performance

The c o n d i t i o n o f t h e r m a l runaway (R-A) i n p o l y m e r i z a t i o n and c o p o l y m e r i z a t i o n r e a c t o r s has been c h a r a c t e r i z e d (1,7) by a r a p i d l y r i s i n g temperature dT/dt » 0 t o g e t h e r w i t h an a c c e l e r a t i o n of the r i s e d T/dt > 0 . When R-A a d d i t i o n a l l y e x h i b i t s p a r a m e t r i c s e n s i t i v i t y i t i s termed i g n i t i o n ( I G ) . Beyond i t s r o l e as a p o t e n t i a l c a u s e o f i n s t a b i l i t y , R-A c a n a l s o a f f e c t conversion e f f i c i e n c y . S p e c i f i c a l l y , t h e w e l l - k n o w n phenomenon o f d e a d - e n d i n g ( D - E ) , i n w h i c h c o n v e r s i o n o f monomer t o p o l y m e r i s a b o r t e d by p r e m a t u r e d e p l e t i o n o f i n i t i a t o r , i s e x a c e r b a t e d by r i s i n g t e m p e r a t u r e s . T h i s i s so b e c a u s e h i g h t e m p e r a t u r e s a c c e l e r a t e i n i t i a t o r d e p l e t i o n r a t e s much more t h a n monomer c o n v e r sion rates. The phenomenon c a n o b v i o u s l y be m i t i g a t e d by i n c r e a s i n g i n i t i a t o r c o n c e n t r a t i o n , but t h i s has an a d v e r s e e f f e c t on d e g r e e o f p o l y m e r i z a t i o n ( D P ) . The c r i t e r i o n f o r D-E, shown i n T a b l e X I , was f o r m u l a t e d i n t e r m s o f d i m e n s i o n l e s s p a r a m e t e r , shown i n T a b l e V I I I , w h i c h c o r r e c t l y r e f l e c t s t h e e f f e c t s o f feed parameter T as w e l l a s [l] , since k has a n e g a t i v e temperature c o e f f i c i e n t . C r i t e r i a f o r R-A and IG, a l s o shown i n T a b l e X I , w e r e f o r m u l a t e d i n terms o f d i m e n s i o n l e s s p a r a m e t e r s e, a , B and b. They a p p l y t o b o t h h o m o p o l y m e r i z a t i o n s and c o p o l y m e r i z a t i o n s f o r v a r i ous i n i t i a t o r s y s t e m s a t o r n e a r t h e c o n d i t i o n TR = T , and w e r e d e v e l o p e d t h r o u g h m o d i f i e d Semenov-type a n a l y s e s (1,JL>Z) a n c * numerous c o m p u t e r s i m u l a t i o n s ( 3 j 4 ^ 6 ) . Owing t o t h e f a c t t h a t the dimensionless r a t e f u n c t i o n f o r homopolymerization c o n t a i n s 2

Q

2

Q

a x

Q


22

POLYMERIZATION REACTORS AND PROCESSES TABLE IV BATCH MATERIAL BALANCE EQUATIONS FOR FREE-RADICAL POLYMERIZATIONS AND COPOLYMERIZATIONS

In 1 1 I a t o r _ d[ml

. 2

dt

m

dt

f

v


Monomer d[m.]

LCA R

-TT-- !k -

+

R

pk

= R = R. i

dt

+

w

V

R p

~

p

Moment

4lip-=

dt

" -

[(2 - r)/2]R.

R

(1 + r ) R . + (3 + 2 r ) R

p

+ (2 +

r)R

p t

TABLE V BATCH ENERGY BALANCE EQUATIONS FOR FREE-RADICAL POLYMERIZATIONS AND COPOLYMERIZATIONS Homo po 1 y me r i z a t i o n s LCA pC

Q

p

*

-AHR

- (UA/V)(T - T )

p

R

C o p o l y m e r i z a t i ons P C

p

£

L

"

(-AH j

j k

)R

p l k

- (UA/VMT - T ) R

k


2.

BIESENBERGER

Thermal

23

Runaway

TABLE VI CHARACTERISTIC TIMES FOR HOMOPOLYMERIZATIONS


Definitions CT

Original

X.

2f[l] /(R,) o

initiator

o

n

heat g e n e r a t i o n

PC T / ( - A H ) ( R ) p o o

o 3G

ad

X

R

C

T

P p o

pC

/ (

-

consumption

monomer c o n v e r s i o n

W„/(R) o p o

A

Process

Equ i v a l e n t v-1

A H ) ( R )

VI adiabatic

E

o ap

heat

£/U

induction

removal

P

TABLE VI I CHARACTERISTIC TIMES FOR CT

Original

COPOLYMERIZATIONS Equivalent

X. o

PJ

k

o

1

(-£) X

Gjk (G ) e o 3G \~1 ad

P

I


-1 Gjk

24


TABLE V I I I DIMENSIONLESS PARAMETERS FOR HOMOPOLYMERIZATIONS Defini tion Parameter


a

x

k V

For I n t e r p r e t a t i o n

N

ap

B

b

a d

V

A

/X

R

ad

x,/X

" Vo o

/ a

f I , ]

a d

J

/ 2

k _

X ,/X. ad G X

B/b

X

"

e E

=

V i

For Evaluation

1

(E' ) ap' E /R T ap g o (^)V(-AH)(k

(-

A H

E

) ;

^H)(k

a x

[ m ]

o

P

a p

/ p C

) E; [m] [l] o

p

p

T

o

/ 2 o

/pC T

TABLE IX DIMENSIONAL PARAMETERS FOR COPOLYMERIZATIONS Pa r a m e t e r ak \

Def i n i t i on A /X. m A

( x

o

x

Q

< 2Vl

+ ( x

+

x

2

+

P

+

£l

x

T

r

E'T' •

x

r

x

2

0

2

o

2

2

)

2

0

2

( r

r

X

2m

2

E

)

o

+

T

_

«* >o< 2'o 2> 2

_ ( x

+

2

e

x

2

p

0

J>

2

o

2

2?TirT

£1

E

2

T

1

Q

2

0

2

o

2

I

T

)

2

E

n

+ ( x ^

l

T

' P2 ' nx ) A m exp- Tr (x ) (r ) m exp ^ r

T W )

; Dtl2 ' (x ) (r ) m exp (x ) (r ) X m exp^Hfn

X

2 1

Jjl

< 2>o< 2»o 2

x

^£1

lVl' 2»Q' 2^ 2 lV P 2(m')

0

* » ( » i > ( r i V i ( » 2 > o < 2 > o 2 + » 2>o< 2>o 2>

"< l>cAl>o

( r

2

IFFTT

p ( i t r i 2^iy PuTr) E' T' (x ) (r ) m ex r + (x ) m

r

t iW i>o i

X

*' l'o

( l>o< l>o l

x

X

E X P

» l'o''-l'o l'

t*zWo fr

x

^ o ^ o ^

iWrj*

2 1

p

£.

fery

r

( l>o< lVl

o< l'o l> l

x

P enultimate Effect

H'

=

Phi Factor

Q

( i»o« i»o*i"i

Geometric Mean

H'

Dimensionless Termination Function

TABLE X EXPRESSIONS FOR H"


§

5*

to

^

|

H

JSCS

§

2

g

§

B S S

w



TABLE XI DIMENSIONLESS CRITERIA FOR REACTOR PERFORMANCE ( p o l y m e r i z a t i o n s and C o p o l y m e r i z a t i o n s ) Phenomena

Criteria

D-E

a

R-A

e « 1 a < 2

IG/ERA

B > 20 b > 100

k

> 1


2.

BIESENBERGER

Thermal

Runaway

27

only one simple term R' H

=

n

1

1 / 2

exp

E'T'/O dp

+ T-)

and t h u s c o n f o r m s t o e q u a t i o n 16, i t c a n be shown by t h e p r o c e d u r e l e a d i n g t o e q u a t i o n 27 t h a t t h e p a r t l y monomer b a l a n c e e q u a t i o n


-3?

"

dt

(29) following dimensionless

(30)

X

'JK m

p

c o n t a i n s o n l y a s i n g l e f u n c t i o n on t h e RHS and t h e p a r t l y s i o n l e s s e n e r g y b a l a n c e e q u a t i o n t a k e s on a f o r m

G

R

e

dimen-

e

w h i c h i s a m e n a b l e t o Semenov-type a n a l y s i s ( 1 ) . P e r t i n e n t d i m e n s i o n l e s s p a r a m e t e r s w e r e d e f i n e d i n t e r m s o f r e s u l t i n g CT's and are l i s t e d in Table V I I I . D u r i n g t h e d e v e l o p m e n t o f t h e s e c r i t e r i a t h e Semenov a n a l y s i s was e x t e n d e d t o s y s t e m s w i t h h e a t - e x c h a n g e r r e s e r v o i r t e m p e r a t u r e s d i f f e r e n t from feed temperatures (TR < T ) and w i t h d e l a y e d runaway ( l a r g e r v a l u e o f e ) , w h i c h r e s u l t e d i n s i g n i f i c a n t c o n c e n t r a t i o n d r i f t p r i o r t o runaway. S i n c e v a l u e s o f e for c h a i n - a d d i t i o n p o l y m e r i z a t i o n s a r e n o t n e a r l y a s s m a l l as t h o s e f o r t h e g a s e o u s e x p l o s i o n s i n v e s t i g a t e d by Semenov, R-A i s n o t as s e n s i t i v e nor i s i t as e a r l y i n terrrs o f e x t e n t o f r e a c t i o n . T h u s , t h e c r i t i c a l v a l u e o f R-A p a r a m e t e r 'a' i s n o t t h e same n o r i s i t as c l e a r l y d e f i n e d . M o r e o v e r , i t i s p o s s i b l e t o e x p e r i e n c e i n s e n s i t i v e ( p o t e n t i a l l y s t a b l e ) R-A. Sample e x p e r i m e n t a l r e s u l t s s h o w i n g s e n s i t i v e and i n s e n s i t i v e R-A have been p l o t t e d i n F i g u r e s 1 and 2, r e s p e c t i v e l y . In t h e c o m p u t e r s i m u l a t i o n s i t was n e c e s s a r y t o s t u d y r e a c t i o n s e q u e n c e s more c o m p l e x t h a n t h o s e s t u d i e d by B a r k e l e w , which consequently led to r a t e f u n c t i o n s having double r a t h e r than s i n g l e c o n c e n t r a t i o n dependence. Numerous r e s u l t s f r o m b o t h t h e o r e t i c a l and c o m p u t a t i o n a l a n a l y s e s , i n c l u d i n g t h e e f f e c t s o f e and TR , have been d e s c r i b e d e l s e w h e r e ( s e e e s p e c i a l l y F i g u r e 8 of reference 1). C r i t e r i a f o r s e n s i t i v i t y , B and b , are also c r i t e r i a f o r v a l i d i t y o f t h e e a r l y R-A a p p r o x i m a t i o n (ERA), w h i c h s a y s t h a t R-A o c c u r s v i r t u a l l y when m = 1 = I . W h i l e B f o r most f r e e r a d i c a l p o l y m e r i z a t i o n s l i e s w i t h i n a narrow range, which exceeds the c r i t i c a l v a l u e , b v a r i e s w i d e l y from s u b c r i t i c a l t o c r i t i c a l v a l u e s , d e p e n d i n g s t r o n g l y u p o n c h o i c e o f i n i t i a t o r and f e e d p a r a meters [ l ] and T . Decreasing values of b generally depress the c r i t i c a l v a l u e of 'a' slightly. Computed R-A Q

0

Q



Figure

T

R

\}/jt

a

1.

A A

Experimental

O R A O

O D

O

o

o •

0

A

•

o

0

A

LJ

o •

o

A

o LJ n

o

o

o 0

0

A A A A A A A A A &

o •

o °

•

o

•

•

o o a

o°

6

o

8

d

o

o

o

show-

Polymer Engineering and Science

°

O

A A ^ A A A A A A A

data from styrene polymerization initiated with benzoyl peroxide ing R-A sensitivity to parameter U/l (5)

0

A 0

u n O • o •

44 0 43 A 42 • 34 O

RUN

on o g °

07 975 -0035 0032 0029 .0027

•o

ofia



Figure

& o

6°

•

2.

120

Experimental

•

• •

A

A

360

\

m

*

A

m m

m

•

TIME

SEC.

0

0

3

initiated [I] (5)

• ft a M ^ A A a

A

m

data from styrene polymerization R-A sensitivity to parameter

m

A 5

l 0

R

5

T

*

with

0

4

0

[)/£ 5 1

0

2

6

*

5

4

56

•

"

•

A

O

O

55

53

52

RUN

1080

peroxide

less


* *

0

0027

.0028

.0029

.0035

0

benzoyl

840

l 0 2


30


b o u n d a r i e s f o r h o m o p o l y m e r i z a t i o n s a r e shown i n F i g u r e 3 From T a b l e s V I I I and XI we f i n d t h a t R-A may be i n d u c e d ('a r e d u c e d b e l o w c r i t i c a l v a l u e ) by r a i s i n g T , [ l ] o r E ( v i a Ed) a s w e l l a s by l o w e r i n g U/£ . We a l s o f i n d t h a t IG may be i n d u c e d (b i n c r e a s e d a b o v e c r i t i c a l v a l u e ) by r a i s i n g [l] , lowering T o r l o w e r i n g kd ( v i a l o w e r Ad o r h i g h e r Ed). Consequently, we must c o n c l u d e t h a t w h i l e a h i g h v a l u e o f T contributes to t h e o n s e t o f R-A, i t s i m u l t a n e o u s l y m i t i g a t e s i t s s e n s i t i v i t y . F u r t h e r m o r e , w h i l e i n i t i a t o r s a z o - b i s - i s o b u t y r o n i t r i l e (Ad ^ 1 0 ^ 5 s e c - 1 , Ed ^ 3 0 K c a l ) , b e n z o y l p e r o x i d e (Ad * loH sec" , Ed ^ 3 0 K c a l ) and d i - t e r t - b u t y l p e r o x i d e (Ad * 1 0 ^ 5 s e c " , Ed ^ 3 7 K c a l ) a r e g e n e r a l l y r e g a r d e d a s i n c r e a s i n g i n " s l o w n e s s " i n t h e d i r e c t i o n 1 i s t e d , b e c a u s e Ad d e c r e a s e s o r Ed i n creases, o r both, t h e i r value o f b increases i n the order shown, a l l o t h e r f a c t o r s r e m a i n i n g e q u a l . C o n s e q u e n t l y , we must c o n c l u d e t h a t ' s l o w ' i n i t i a t o r s a r e more l i k e l y t o p r o d u c e u n s t a b l e R-A's t h a n f a s t o n e s . The a b o v e c o n c l u s i o n s i n v o l v i n g T and i n i t i a t o r c h o i c e have been o b s e r v e d e x p e r i m e n t a l l y . 1

0

0

a p

0

0

Q


1

1

0

The r a t e f u n c t i o n f o r c o p o l y m e r i z a t i o n c o n t a i n s a summation o f t e r m s , each o f which R

pjk

=

» A

'

,

/

2

H- « p

E ;

p

J

k

T V ( l

i s more c o m p l e x t h a n e q u a t i o n 1 6 , and t h e r e s u l t i n g balance equation i s . dm

=

dt

y y L^tL-j

j The c o r r e s p o n d i n g e n e r g y

J

k

x

T

l

(

j k

} N

R

(32)

+T-) monomer

(33)

.

k'o p j k

k balance

G

R

e

e

i s c o n s e q u e n t l y n o t a m e n a b l e t o Semenov-type a n a l y s i s . The f u n c t i o n a l form o f f o r each o f t h e t h r e e t e r m i n a t i o n models c i t e d i s g i v e n i n T a b l e X. In o r d e r t o remedy t h i s s i t u a t i o n , e q u a t i o n s 3 2 , 3 3 and 3k w e r e f o r c e d t o c o n f o r m t o 2 9 , 3 0 and 31 by r e c o g n i z i n g a l t e r n a t i v e , e q u i v a l e n t d e f i n i t i o n s ( t h i r d column i n T a b l e V I ) o f CT's f o r homopolymer b a l a n c e s and s u b s e q u e n t l y a p p l y i n g them t o c o p o l y m e r b a l a n c e s . In t h i s way, a p p r o x i m a t e c o polymer b a l a n c e s

|S

-

1

A" m l m

1 / 2

e x p E ' T V O + T*)


(35)


-

2 10

2.1

1

1

1

1 1

Figure

NON RUNAWAY

3.

Computed

3 10

1 1 1 1

RUNAWAY

IG boundaries

1

32

41

b

I I I

i

I

1

1

e=o.04

(4)

r=i.o

s

(/^n)o 3000

R

e «=o.O

I

I

1

I


I

6 E - * 1.467

4 10

I

for homopolymerizations

B = fiO


32


m I


G

1/2

exp

E ' T V O + T') - X ^ ( T - T*)

(36)

R

e

e

w e r e d e v e l o p e d i n w h i c h CT's w e r e o b t a i n e d u s i n g e q u i v a l e n t d e f i n i t i o n s (second c o l u m n i n T a b l e VI l) and a l l i m p o r t a n t dimensionl e s s p a r a m e t e r s f o r c o p o l y m e r s ( T a b l e I X ) , i n c l u d i n g an o v e r a l l a c t i v a t i o n energy E', w e r e d e f i n e d i n a c c o r d a n c e w i t h t h e i r homopolymer c o u n t e r p a r t s ( T a b l e V I I I ) . I t was f o u n d t h a t n o t o n l y d i d p a r a m e t e r s a , B and b so d e f i n e d c h a r a c t e r i z e R-A and IG b e h a v i o r o f c o p o l y m e r i z a t i o n s , but a p p r o x i m a t e e q u a t i o n s 3 5 and 36 c l o s e l y t r a c k the exact balance equations over wide conversion and t e m p e r a t u r e r a n g e s , e x c e p t when one comonomer i s e x h a u s t e d o r when t h e s y s t e m i s n e a r IG ( 7 ) . V e r i f i c a t i o n of the a p p l i c a b i l i t y o f R-A b o u n d a r i e s t o c o p o l y m e r i z a t i o n s i s e v i d e n t i n F i g u r e 4 . C o m p a r i s o n s between " e x a c t " c o m p u t e r m o d e l s and c o p o l y m e r a p p r o x i mate f o r m s (CPAF) a p p e a r i n F i g u r e 5 . P o l y m e r and

Copolymer P r o p e r t i e s

Owing t o t h e c h a i n n a t u r e o f c h a i n - a d d i t i o n p o l y m e r i z a t i o n s and c o p o l y m e r i z a t i o n s w i t h t e r m i n a t i o n , o n l y a s m a l l f r a c t i o n o f t h e u l t i m a t e p r o d u c t m o l e c u l e s grow a t any i n s t a n t , but t h e y grow t o t h e i r f i n a l s i z e so r a p i d l y t h a t t h e y may be r e g a r d e d a s i n stantaneous product without a p p r e c i a b l e e r r o r . The f i n a l product i s an a c c u m u l a t i o n o f a l l i n s t a n t a n e o u s p r o d u c t s formed d u r i n g t h e c o u r s e o f p o l y m e r i z a t i o n , and i t s c u m u l a t i v e p r o p e r t i e s a r e c o m p o s i t e s o f t h e i n s t a n t a n e o u s p r o p e r t i e s . Examples a r e d e g r e e o f p o l y m e r i z a t i o n d i s t r i b u t i o n , DPD, c o p o l y m e r c o m p o s i t i o n d i s t r i b u t i o n , CCD, and t h e i r r e s p e c t i v e a v e r a g e v a l u e s , DP and CC (see T a b l e X I I ) . D i s p e r s i o n o f t h e s e d i s t r i b u t i o n s i s c o n s e quently the r e s u l t of the inherent d i s p e r s i o n of the molecular p r o c e s s e s a t e a c h i n s t a n t , termed s t a t i s t i c a l d i s p e r s i o n , t o g e t h e r w i t h t h e e f f e c t o f t i m e d r i f t s u p e r i m p o s e d upon i t , termed d r i f t d i s p e r s i o n , w h i c h i s a c h a r a c t e r i s t i c o f b a t c h r e a c t o r s and w h i c h can o n l y r e s u l t i n g r e a t e r d i s p e r s i o n i f a l l o w e d t o o c c u r . Thus, the response o f these p o l y m e r i z a t i o n s t o changes i n a p a r a m e t e r , s u c h a s t e m p e r a t u r e o r c o m p o s i t i o n , may be v i e w e d a s m a n i f e s t i n g i t s e l f i n two w a y s , i n s t a n t a n e o u s and d e l a y e d (3). I t i s w e l l known t h a t low v a l u e s o f T and [ l ] lead to h i g h DPs. T h i s i s a c c u r a t e l y r e f l e c t e d by p a r a m e t e r (v^) , the i n i t i a l k i n e t i c c h a i n length (Table X I l l ) , which i s a q u o t i e n t of feed composition r a t i o x and d i m e n s i o n l e s s p a r a m e t e r a ^ . T h u s , given x , a small v a l u e of w o u l d seem t o f a v o r h i g h i n i t i a l DP. On t h e o t h e r hand, c r i t e r i o n ak < 1 s i g n a l s a downward d r i f t o f i n s t a n t a n e o u s DP d u r i n g i s o t h e r m a l p o l y m e r i z a t i o n (3) w h i c h has the o p p o s i t e e f f e c t . F u r t h e r m o r e , u n d e r non i s o t h e r m a l c o n d i t i o n s , r i s i n g t e m p e r a t u r e s e x a c e r b a t e t h i s downward d r i f t . Consequently, we c o n c l u d e t h a t d r i f t r e s p o n s e and i n s t a n t a n e o u s r e s p o n s e may be Q

Q

Q

Q

Q



BIESENBERGER

Thermal

4

Runaway

Hoiflopolymer

A

Boundary

• •

8^41 €=0.025 • .26 S AN • .38 AN MMA

10

10

2

Figure 4.

Computed

3

b IG boundaries

™ for

4

1

copolymerizations


°

5



34

8 Ο

Ι ο ο

% V.

•a

•8 Ο V.

I I

ο 1 i t d r i f t s upward. We t h e r e f o r e c o n c l u d e t h a t t o a c h i e v e a t a r g e t c c h i g h i n comonomer 1, s a y , i n s t a n t a n e o u s r e s p o n s e c o n s i d e r a t i o n s ( T a b l e IX) s u g g e s t t h a t , g i v e n ( x j ) a l o w v a l u e f o r 3k »s r e q u i r e d , w h e r e a s e q u a t i o n 37 i n d i c a t e s t h a t 3^ < 1 w o u l d c a u s e t h e c o m p o s i t i o n t o d r i f t downward, o p p o s i t e t o t h e t a r g e t d i r e c t i o n . O b v i o u s l y , when 3k 1 > no d r i f t o c c u r s . I t c a n be shown t h a t h i g h t e m p e r a t u r e l e v e l s and R-A have v i r t u a l l y no b r o a d e n i n g e f f e c t on CCD d i s p e r s i o n b e c a u s e 3k has a s m a l l t e m p e r a t u r e c o e f f i c i e n t , w h i c h f r e q u e n t l y e v e n t a k e s on negative values causing d r i f t dispersion to a c t u a l l y lessen a t high temperatures. F i g u r e s 7 and 8 show t h e s m a l l n e s s and d i r e c t i o n ( i m p r o v e m e n t ) o f t e m p e r a t u r e e f f e c t on d r i f t , and t h e a b i l i t y o f 3k t o c h a r a c t e r i z e d i r e c t i o n ( s e e c r o s s o v e r i n F i g u r e 7 and c o r r e s p o n d i n g d r i f t s i n F i g * 8) a s w e l l a s m a g n i t u d e o f d r i f t * As a f i n a l n o t e i t s h o u l d be p o i n t e d o u t t h a t R-A p a r a m e t e r s f o r h o m o p o l y m e r i z a t i o n and c o p o l y m e r i z a t i o n c a n be e v a l u a t e d f r o m i n i t i a l k i n e t i c rate data using the i n t e r p r e t a t i o n s given to c h a r a c t e r i s t i c t i m e s i n T a b l e s VI and V I I . C o u p l i n g between c h a n g i n g r e a c t i o n v i s c o s i t y and k i n e t i c c o n s t a n t s and o t h e r t r a n s p o r t p r o p e r t i e s was n e g l e c t e d b e c a u s e runaway g e n e r a l l y o c c u r s e a r l y d u r i n g r e a c t i o n , and s u c h e f f e c t s a r e c o n s e q u e n t l y o f m i n o r importance. n s

0 >

=



400


-(XN)inst - C U M . XN C A S E S 7,8,9 300

TABLE REF.

17 3

/

ix

ISOTHERMAL

200

100 NON-ISOTHERMAL, ADIABATIC

0.05

0.10

0.15

0.20

0.25

Polymer Engineering and Science Figure

6.

Computed

drift curves for instantaneous

and cumulative

DPs (3)


Thermal

Runaway


BIESENBERGER



Figure

5*

O

CO

N

y

Nst

Computed

8.19

A Adiabatic

R Runaway

1 0.38

_

!

J 0.40

____

1

1 0.58

)

PHI

1 0.60

1

J 01.79

I QI

drift curves for instantaneous and cumulative CCs of styrene-methyl acrylate polymers initiated with AIBN

0.20

QiQuasi-Isothermal

0 = .598

8.

y

i Isothermal

&*.820

9

K

6 995

—-R

IQI


meth-

3

O

2

o

2.

BIESENBERGER

Thermal

41

Runaway

SYMBOLS NOT DEFINED IN TEXT pre-exponential c o e f f i c i e n t i n rate constant expressions w i t h a p p r o p r i a t e s u b s c r i p t s o r heat t r a n s f e r s u r f a c e area. Cj = g e n e r a l r e a c t i o n component j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f component j . E = a c t i v a t i o n energy i n r a t e constant e x p r e s s i o n s w i t h appropriate subscripts. E^ =s d i m e n s i o n l e s s a c t i v a t i o n e n e r g y f o r c o p o l y m e r i z a t i o n d e f i n e d i n T a b l e IX.


A

E

=

=

rk

E

E

Dk f = fj = I = k =

rk

/ R

T

g o

E

E

/ R

T

( tjkkj " tkkkk) g o initiator efficiency factor i n i t i a t o r e f f i c i e n c y f a c t o r f o r comonomer j i n i t i a t o r o r dimensionless i n i t i a t o r concentration rate constant with appropriate subscript

kap " M

2 f k

/ k

d t>!£

kax - k p / ( 2 f k k ) l / 2 a p j k = kpjk k j ( 2 f k d / k j j k ) t = k + k m = monomer o r d i m e n s i o n l e s s monomer c o n c e n t r a t i o n mj = comonomer j o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f comonomer j o generalized i n i t i a t o r o r dimensionless concentration of generalized i n i t i a t o r m = x-mer o r d i m e n s i o n l e s s c o n c e n t r a t i o n o f x-mer P = a c t i v e i n t e r m e d i a t e s o f a l l l e n g t h s and t y p e s P j = a c t i v e j - m e r i n t e r m e d i a t e s o f a l l l e n g t h s w i t h comonomer j as t e r m i n a l u n i t P = a c t i v e i n t e r m e d i a t e s o f a l l l e n g t h s and t y p e s x,j a c t i v e i n t e r m e d i a t e o f l e n g t h x w i t h comonomer j a s terminal u n i t P j = a c t i v e i n t e r m e d i a t e o f a n y l e n g t h w i t h comonomer j a s terminal u n i t P j P k = a c t i v e i n t e r m e d i a t e o f a n y l e n g t h w i t h comonomer j and k a s p e n u l t i m a t e and u l t i m a t e u n i t s , r e s p e c t i v e l y R = r a t e f u n c t i o n f o r t o t a l monomer c o n v e r s i o n ( r a t e o f p o l y m e r i z a t i o n ) o r any r a t e f u n c t i o n w i t h a p p r o p r i a t e s u b s c r i p t Rp = rate function defined i nTable I Rg = gas constant r = ktc/kt or reactivity ratio with appropriate subscript T - (T - T ) / T U = o v e r a l l heat t r a n s f e r c o e f f i c i e n t V = r e a c t o r volume xj^j = number a v e r a g e DP x = w e i g h t a v e r a g e DP x - [m]Q/[m ] Xj = [ m j j / [ m ] y = m o l e f r a c t i o n o f comonomer 1 i n c o p o l y m e r d

t

k

p A

t

M

]

/

Z

k

t c

m

t D

=

x

x

p

=

t

0

0

w

Q

0

0


42 A


k

k

-( tjkkj k

/ k

tkkkk)o k

+ = k / tl11 t22 $ = 1 - m = f r a c t i o n monomer c o n v e r t e d 6 = E ' T" X.A = c h a r a c t e r i s t i c t i m e s w i t h a p p r o p r i a t e s u b s c r i p t s y k - |

Thermal Runaway in Chain-Addition Polymerizations and

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