Nonisothermal Behavior and Thermal Runaway Phenomena in Chain

15 Nonisothermal Behavior and Thermal Runaway

Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 31, 2018 | https://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch015

Phenomena in Chain Addition Copolymerization D O N A L D H . S E B A S T I A N and J O S E P H A. B I E S E N B E R G E R Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030

The condition of thermal runaway (RA) in polymerization re actors has been characterized (1,2) by rapidly increasing tempera tures (dT/dt » 0) and an upward concavity in the temperature profile (d T/dt > 0 ) . When runaway additionally exhibits para metric s e n s i t i v i t y i t is termed thermal ignition (IG). Beyond the obvious consequence of large temperature rises and possible i n s t a b i l i t y , RA could cause a sharp reduction in polymer molecu lar weight and an increased spread in molecular weight d i s t r i b u tion. 2

2

Runaway Analysis of Polymerizations and Copolymerizations A study of RA in chain polymerizations was undertaken in our laboratories with the aim of developing quantitative c r i t e r i a for predicting the onset of both RA and IG. A modification of Semenov-type dimensional analysis, together with computer simula tion and experimentation, have shown (1,2) that 5 independent parameter groupings characterize the thermal behavior of chain homopolymerizations: a,Β,b,ε,εΕ' . The approach of Semenov deals with the thermal energy balance. Putting temperature and concen tration in dimensionless form the thermal energy balance for homopolymerization appears as (1) : ι mm 1/2 . = expÎEV/l+T'ï-iiT'-T;) (0 d

The f i r s t term of the RHS of Eq. 1 can be interpreted as the rate of heat generation function while the second term as heat removal. The Semenov technique locates the c r i t i c a l temperature for RA at the point where heat generation and removal are not only equal, but their change with temperature ( i . e . , derivative with respect to Τ ) is also equal. Applying these steps to the generation and removal terms of Eq.l eliminates T',with resulting c r î t e r i a formed as functions of ' a and ε. The effect of the remaining para meters was investigated through numerical simulation. The impor tant c r i t e r i a for RA is a < 2, and for parametrically sensitive RA, Β > 20 and b > 100. Parameters Β and b are dimensionless 1

©

0-8412-0401-2/78/47-065-173$05.00/0

Weekman and Luss; Chemical Reaction Engineering—Houston ACS Symposium Series; American Chemical Society: Washington, DC, 1978.

CHEMICAL REACTION ENGINEERING—HOUSTON

174

groupings appearing i n the monomer and i n i t i a t o r component b a l ances r e s p e c t i v e l y . The a n a l y t i c a l methods employed i n the R A a n a l y s i s o f homop o l y m e r i z a t i o n a r e not immediately a p p l i c a b l e to chain a d d i t i o n c o p o l y m e r i z a t i o n . The e q u i v a l e n t expression to Eq. 1 i s λ


6

+

ηΠ»] exp Ε ^ τ ' / l + Τ

XQ22

M

2

Β

Χ

Ρ

Ε

2 2

Τ

,

/

1

+

T

'

J

1

+

m

o

/ 2

( Q|2 X

H

'

"

+ X

X

G21 ^

R

1

(

T

m

l

'

M

"

2

T

E

X

R

P

1 2

E

]

T

'

(

+

2

T

'

)

The b a s i c k i n e t i c equations f o r chain a d d i t i o n copolymeriza t i o n are given i n Table I f o r three t e r m i n a t i o n models: geometric mean (GM), phi f a c t o r (PF) and penultimate e f f e c t (PE). I t i s important to note the symmetry i n form created by c o n f i n i n g the e f f e c t o f choice o f t e r m i n a t i o n model to a s i n g l e f a c t o r a b l e f u n c t i o n H. A Semenov-type a n a l y s i s cannot be a p p l i e d to Eq. 2 . The presence of four exponential terms w i t h d i f f e r e n t a c t i v a t i o n en e r g i e s , and the complicated f u n c t i o n a l form o f H = H/H preclude e x p l i c i t s o l u t i o n f o r a c r i t i c a l T . A more general technique based upon p h y s i c a l i n t e r p r e t a t i o n o f R A parameters has led to c o p o l y m e r i z a t i o n analogs f o r the groupings a,B,b,e and εΕ^. Each such parameter can be expressed as the r a t i o o f a p p r o p r i a t e time constants. While appearing as c o e f f i c i e n t s i n the balances, time constants serve a l s o as i n i t i a l values f o r the balance. For ex ample i n E q . l , note that the r e c i p r o c a l of XG» the c h a r a c t e r i s t i c time f o r heat g e n e r a t i o n , i s a l s o the value o f the heat genera t i o n f u n c t i o n when dimensionless c o n c e n t r a t i o n s and temperature take on t h e i r i n i t i a l values o f one. The second i n t e r p r e t a t i o n , when a p p l i e d to the generation p o r t i o n o f Eq. 2 , d e f i n e s an over a l l AQ f o r c o p o l y m e r i z a t i o n . S i m i l a r a t t a c k on the t o t a l monomer balance y i e l d s an expression f o r A , the c h a r a c t e r i s t i c time f o r monomer decay. In homopolymerization a n a l y s i s ( J j the time constant X j = ελβ i s c r u c i a l to the f o r m u l a t i o n o f runaway parameters a, B,b, ε and εΕ^. I t does not appear e x p l i c i t y i n any o f the d i mensionless balances, but rather i s a consequence of a Semenovtype a n a l y s i s . In the process of t a k i n g the temperature d e r i v a t i v e o f the heat generation f u n c t i o n of Eq. 1 the product E'/XQ 1/eXG a r i s e s . Because t h i s a n a l y s i s could not be a p p l i e c to c o p o l y m e r i z a t i o n , an a l t e r n a t e means was r e q u i r e d . The R A parameter 'a' i s more than a mere by-product o f a Semenov ap proach. I t i s the r a t i o of i n i t i a l values o f the temperature de r i v a t i v e o f the heat removal and generation f u n c t i o n s o f Eq. 1 . Expressed i n terms o f time constants t h i s r a t i o i s X j/XR, and thus the i n t e r p r e t a t i o n o f X | as the i n i t i a l temperature d e r i v a t i v e o f the heat generation f u n c t i o n serves t o d e f i n e an analog, ^ad f o r copolymer i z a t ion. By making use o f A j i n combination w i t h other o v e r a l l time c o n s t a n t s , a s e t o f R A parameters f o r c o p o l y m e r i z a t i o n corresponding to i t s homopolymerization 1

Q

1

M

ac

=

ac

ac

a c



15.

SEBASTIAN AND

BiESENBERGER

Chain Addition Copolymerization

175

counterpart ( 0 , was d e f i n e d . The parameters are given i n Table I I . I t i s important t o note that the homopolymerization c r i t e r i a evolved from combined s e n i - a n a l y t i c a l and numerical s o l u t i o n s t o s p e c i f i c k i n e t i c equations. In t h i s work, p h y s i c a l s i g n i f i c a n c e has been attached t o each parameter i n a manner that permits ex tension o f the RA a n a l y s i s , independently o f the k i n e t i c form. The u t i l i t y o f the runaway and s e n s i t i v i t y parameters a,B, and b has been demonstrated through both numerical s i m u l a t i o n and experimentation (3,^0· Numerical s i m u l a t i o n s employed l i t e r a t u r e values f o r the k i n e t i c constants f o r the monomer p a i r s o f StyreneMethyl Methacrylate (SMMA), S t y r e n e - A c r y l o n i t r i l e (SAN) and, Acrylonîtrile-Methyl Methacrylate (ANMMA). P h i - f a c t o r k i n e t i c s were g e n e r a l l y used, however both geometric mean and r e c e n t l y advanced penultimate e f f e c t k i n e t i c s (6) were tested as w e l l . Ex periments were confined t o the S t y r e n e - A c r y l o n i t r i l e comonomer system, however, the f u l l range o f compositions was s t u d i e d . An e x t e n s i v e i n i t i a l r a t e study was performed on t h i s system to de velop the k i n e t i c constants needed t o evaluate the runaway para meters ( 4 , 5 ) . A convenient way t o i l l u s t r a t e the e f f e c t o f the RA para meters i s through the use o f RA boundaries. K i n e t i c constants as s o c i a t e d w i t h real polymer systems l i m i t the values o f Β t o a narrow range ( g e n e r a l l y 30 - 60) and t h i s i s above the region where monomer s e n s i t i v i t y e f f e c t s become important. Furthermore, i n i t i a t o r consumption w i t h i t s stronger temperature dependence plays a f a r greater r o l e i n reducing s e n s i t i v i t y than monomer con sumption does. T o t a l l y u n r e a l i s t i c values o f i n i t i a t o r concentra t i o n (on the order o f 100 m/1) are needed i f monomer s e n s i t i v i t y l i m i t a t i o n s are t o be e x h i b i t e d in the absence o f i n i t i a t o r l i m i t a t i o n s . Thus the most meaningful way t o represent runaway bound a r i e s i s t o show acr vs b w i t h other dimensionless groups as con stant parameters. D e t a i l e d s t u d i e s o f homopolymerization have i l l u s t r a t e d t h i s dependence (2). What i s noteworthy i s that the copolymer systems f o l l o w the same q u a n t i t a t i v e behavior. Figure 1 shows dimensionless runaway boundaries f o r several copolymer sys tems shown along w i t h the a s s o c i a t e d homopolymerization boundary. A l l boundaries are not p e r f e c t l y c o i n c i d e n t due t o the e f f e c t s o f composition d r i f t in the c o p o l y m e r i z a t i o n s . The d e v i a t i o n s are rather small although the d r i f t a s s o c i a t e d w i t h SAN and ANMMA sys tems f o r Β = 41 i s s i g n i f i c a n t . In Table III values f o r RA parameters a t the t r a n s i t i o n p o i n t are presented f o r v a r i o u s comonomer-initiator systems. Note that RA parameter 'a c o n s i s t e n t l y takes on values near the expected value o f two when RA occurs. As i n homopolymerizations, the c r i t i c a l value o f 'a' becomes depressed as 'b decreases. This e f f e c t i s a by-product o f the decreasing s e n s i t i v i t y o f the cop o l y m e r i z a t i o n c o r r e c t l y c h a r a c t e r i z e d by the d e c l i n i n g value o f 'b'. Figures 2 and 3 i l l u s t r a t e i n i t i a t o r - l i m i t e d s e n s i t i v i t y more c l e a r l y . At a value o f b = 195 there i s a s h a r p l y defined t r a n s i t i o n from non-runaway t o runaway behavior, and t h i s i s 1

1


CHEMICAL REACTION

176

TABLE

ENGINEERING—HOUSTO

I

RATE FUNCTIONS AND BALANCES FOR COPOLYMER IZATI ON


Balance Ini

equations

tiator

dim ] 7^

=

dt

Κ >L

d

ο

J

Co-monorners

dim J —dt

-

R

dt

pH

p!2

pl2

p22

d

d M dt

Thermal

P

C

m

i

]

d

[

m

2 dt

dt

]

energy

P£

= Σ Σ

(

i

j

"

[ -

"

where

C

I

a

H

Û H

n

k

-

Δ

p n

k

k

22 p22

( u / t ) ( T

ν ν ι -

l

p Z l h

k

2

"

(

H

' .2

+

4

2

p l

-

ν

H

21

t

2t'"2l ]

m

)

k

k

p 2 p21

[

I

o

]

'»" /2

m

,

H

m

2

)

(U/t)(T

"V

= y/A w

Rate

functions for

propagation 1/2

Rp-11 ii =

R

pl2

"

k

ii

k

pll

o» U ^

p21 \

k

t

2

k

n

t

2

I K ] [ m J°

^ 1 2 ^ 2 l / r ^ til

1 / 2

1

2 /

[m^tm^tmj

H

1

/

2

H

-

R

p 2 1

t22^ 1/2

V 2

-

%n^2k-T-) ^ tl! k

WV » 2

k

t22j

and H is :


SÉBASTIAN

for

Copolymerization

g e o m e t r i c mean (GM) model

k

[ m

p21 l

(k for

Chain Addition

BiESENBERGER

AND

phi f a c t o r

t22

3

p!2

)T72

l

J

2 ΓΪ72

~tir

(PF) model


_,2 (k )

2\-1/2 k

2φ

Ï72

p2^Pl2

penultimate

(k

effect

m

l

]

[

m

2

k

] +

172

t M

for

[

k

t22 tl1

[m

p12 2

]

(kt l T J / 2

]

(PE) model

[m ] 2

k

[

p21 "l

(k

(22

]

) 1/2

J

k

[m

r

3

pl2 2 T72

1/2

2 U [m

fei « [m

+

r [m J 2

2

]

+ [m^

TABLE II

E

(E

Bi

i l T l l 12T12 Y

+

E

*J_ ad A

VT21 * 2 2 W ~ i f j

E

+

E

-1 -1 -1 -1 3H -1 îl GU + 12G12 * 12621 + 22622* * W G -1 < mll ml2 m21 m22 > X

E

j -1 r il Gll E

X

X

+

E

+

X

+

X

E

X

+

X

A

X

-1 -1 -1 12G12 * 12G21 22G22

E

X

E

X

+

E

X

)

3H +

-1 -1 * h 6U * J2G12 * 12G21 * 22G22 H -1 -1 -1 -1 G11 G12 G21 G22 E

"ad

+

Y

X

bi

-1

DIMENSIONLESS RUNAWAY PARAMETERS

ad

X

E

A

X

E

X

X

E

A

X

X

~

Λ

-1 ) Gj1 X

m

3Τ·




178

Δ "

Δ 5

ο

ο

ο Br 41 e=0.025 Δ .26 S A N Ο .38

10

2

10

3

10

AN MMA

4

10

5

b Figure 1.

Simulated RA boundary for two copolymer systems

TABLE

πι

SIMULATION RESULTS Τ

System

ο

Β

u/t

Wo

Ε'

b

a

RA

c a l / c e s e c °K

mol/1

°K 1.57 x Ι Ο " 1.55

5

45

28.6

300

2.025 1.998

No Yes

1.61 χ Ι Ο " 1.60

2

45

23.5

300

1.998 1.985

No Yes

8.99 χ Ι Ο " 8.88

6

45

31.3

300

2.075 2.05

No Yes

ϊ.54 χ ΙΟ" 1.52

6

45

33.5

300

2.05 2.026

No Yes

.05

1.04 χ ί ο " 1.03

2

36

30

400

1.985 1.975

No Yes

.025

4.86 χ Ι Ο " 4.82

3

136

1.915 1.90

No Yes

.01

3.01 χ Ι Ο 2.97

86

1.875 1.85

No Yes

.10

3.55 χ ί ο " 3.49

2

42

1.77 1.74

No Yes

.05

2.37 χ Ι Ο " 2.34

2

30

1.67 1.65

No Yes

1

.2

322

.8

378

.2

318

1.21 χ 10"

.8

306

7.44 χ ίο"**

S/AN/DTBP

.7

403

S/AN/BP

.7

373

AN/MMA/BP

S/MMA/BP

S/AN/AIBN

.7

373

1.33 x ίο" »

• 119

3

1

3

36.0

28.0



SÉBASTIAN A N D

1

BiESENBERGER

3

Figure 2.


5 •Med

7

9

RA transition, b = 195


180


c a u s e d by a 0 . 3 % change i n ' a . When b i s d e c r e a s e d t o 30 t h e RA p o i n t i s not c l e a r l y d e f i n e d . A continuous spectrum of p r o f i l e s f i l l s the t r a n s i t i o n r e g i o n . Changes i n p a r a m e t e r ' a a r e an o r d e r o f magnitude g r e a t e r than i n the p r e v i o u s case t o b r i n g a b o u t s i m i l a r changes i n t h e t h e r m a l h i s t o r i e s . In a d d i t i o n , t h e v a l u e o f 'a' i n t h e r e g i o n o f t r a n s i t i o n has been s i g n i f i c a n t l y d e c r e a s e d f r o m t h e n o m i n a l v a l u e o f two. 1


1

The

Copolymer

Approximate

Form

(CPAF)

The f a c t t h a t c o p o l y m e r and homopolymer runaway e n v e l o p s a g r e e d b o t h q u a l i t a t i v e l y and q u a n t i t a t i v e l y s u g g e s t s t h a t perhaps c o m p l e x c o p o l y m e r i z a t i o n k i n e t i c s m i g h t be s u c c e s s f u l l y a p p r o x i mated by s i m p l e r k i n e t i c s , s i m i l a r t o t h e homopolymer f o r m . I t is p r o p o s e d t h a t be r e p l a c i n g p a r a m e t e r s i n t h e homopolymer b a l a n c e s by t h e i r c o p o l y m e r a n a l o g s , i . e . , X , XQ and ε = X j / X Q by A , AQ, and ε = A J / A Q r e s p e c t i v e l y , and s u b s e q u e n t l y i n t e g r a t i n g them we w i l l o b t a i n c o n v e r s i o n and t h e r m a l h i s t o r i e s t h a t match the h i s t o r i e s o f t h e e x a c t k i n e t i c f o r m . I n d e e d , t h i s was t h e case. Thus Eq. 2 w o u l d be a p p r o x i m a t e d by t h e f a r s i m p l e r f o r m : M

ac

M

3C

dT« ^

-1 = A

G

Ε'

1/2

Λ

mm

o

Τ'

exp

1 -

^

, , (Τ τ

τ

,ν

T ) R

(3)

I n d e e d , i t c a n be shown t h a t i f c o n c e n t r a t i o n changes a r e n o t con s i d e r e d , the r e m a i n i n g t e m p e r a t u r e dependent p o r t i o n o f Eqs. 2 and 3 a r e n u m e r i c a l l y e q u i v a l e n t . Under i s o t h e r m a l c o n d i t i o n s th< c o n v e r s i o n h i s t o r i e s match p r o v i d e d t h a t one o f t h e comonomers i s not exhausted p r i o r t o the c o m p l e t i o n o f the r e a c t i o n . Under noni s o t h e r m a l c o n d i t i o n s , c o m p o s i t i o n d r i f t i n f l u e n c e s the agreement between t h e two f o r m s . When d r i f t i s t o w a r d s t h e more r e a c t i v e comonomer, t h e a p p r o x i m a t e f o r m u n d e r e s t i m a t e s t h e t h e r m a l t r a j e c t o r y (See F i g . 4 ) . C o n v e r s e l y , when d r i f t i s t o w a r d s t h e l e s s re a c t i v e o f the p a i r , the approximate form o v e r e s t i m a t e s the t r a j e c tory. S i m i l a r b e h a v i o r i s n o t e d i n t h e RA b o u n d a r i e s o f F i g . 1. P o i n t s f o r t h e SAN s y s t e m l i e a b o v e t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s h i g h AN c o n t e n t c o m p o s i t i o n s . P o i n t s f o r t h e ANMMA b o u n d a r y l i e b e l o w t h e homopolymer b o u n d a r y , and d r i f t i s t o w a r d s t h e l e s s r e a c t i v e o f t h e p a i r , MMA. As c o n d i t i o n s become e i t h e r more a d i a b a t i c o r more i s o t h e r m , s p r e a d between t h e forms narrows. The p o o r e s t a g r e e m e n t o f t h e forms o c c u r s a t t h e p a r a m e t r i c a l l y s e n s i t i v e p o i n t o f t h e RA t r a n s i t i o n . E x p e r i m e n t a l T e s t s o f t h e Runaway

Parameters

The SAN c o p o l y m e r s y s t e m was c h o s e n f o r e x p e r i m e n t a l s t u d y due t o i t s g r o w i n g i n d u s t r i a l i m p o r t a n c e . T h e r e i s a l a c k o f pub l i s h e d r a t e d a t a f o r t h i s s y s t e m , as w e l l as b r o a d d i s a g r e e m e n t among t h e d a t a r e p o r t e d f o r h o m o p o l y m e r i z a t i o n o f AN. Without k i n e t i c d a t a t h e r e w o u l d be no way t o e v a l u a t e t h e d i m e n s i o n l e s s parameters a s s o c i a t e d w i t h experimental runs. T h e r e f o r e c o p o l y m e r i z a t i o n k i n e t i c s t u d i e s were conducted v i a the t e c h n i q u e o f D i f f e r e n t i a l S c a n n i n g C a l o r i m e t r y , w h i c h had p r e v i o u s l y been used



15.

SEBASTIAN A N D

BiESENBERGER


181

by o t h e r s f o r homopolymerîzation s t u d i e s . The c o p o l y m e r a p p r o x i mate k i n e t i c f o r m (CPAF) p r o v i d e d t h e means f o r s e p a r a t i n g r e a c t i o n r a t e f r o m h e a t o f r e a c t i o n r e q u i r e d by t h e u s e o f t h i s technique. I t s h o u l d be n o t e d t h a t under i n i t i a l c o n d i t i o n s t h e e x a c t and a p p r o x i m a t e k i n e t i c forms a r e n u m e r i c a l l y e q u i v a l e n t , t h u s t h e r e i s no e r r o r i n v o l v e d i n a p p l y i n g t h e a p p r o x i m a t e f o r m to i n i t i a l r a t e s t u d i e s . The i n i t i a l r a t e s f o r SAN s y s t e m s w i t h s t y r e n e c o n t e n t o f t e n to n i n e t y mole p e r c e n t were d e t e r m i n e d w i t h b o t h b e n z o y l p e r o x i d e and azo-bîs-îsobutyronîtrîle i n i t i a t o r s . T h e s e r a t e s were used t o c a l c u l a t e t h e t e r m i n a t i o n p a r a m e t e r s f o r b o t h PF and PE models o f c o p o l y m e r t e r m i n a t i o n . No s i n g l e , c o m p o s i t i o n - i n d e p e n d e n t value of t h e PF a d e q u a t e l y f i t t h e i n i t i a l r a t e d a t a . The PE model p r o v i d e d f a i r a g r e e m e n t . H i g h s t y r e n e c o n t e n t c o p o l y m e r s showed t h e w i d e s t s c a t t e r i n t h e c o r r e l a t i o n o f t h e model p a r a m e t e r s . If the a v e r a g e v a l u e o f t h e PF i s c h o s e n (φ - 25), t h i s model p r e d i c t s q u a l i t a t i v e l y h i g h e r r a t e s t h a n t h e PE m o d e l . E x p e r i m e n t a l s t u d i e s o f t h e r m a l runaway i n t h e homopolymerîz a t i o n o f s t y r e n e have been c o n d u c t e d i n t h e s e l a b o r a t o r i e s . The Thermal I g n i t i o n P o i n t A p p a r a t u s (TIPA) d e v e l o p e d f o r t h i s work (7) was u s e d f o r t h e e x p e r i m e n t a l s t u d y o f runaway i n SAN c o p o l y merization. The c o m p o s i t i o n s o f 90, 80, 70, 60, 40, and 20% s t y r e n e were p r o v o k e d f r o m non-runaway t o runaway c o n d i t i o n s a t t h e f e e d t e m p e r a t u r e o f 373°K by m a n i p u l a t i n g t h e i n i t i a l c o n c e n t r a t i o n o f i n i t i a t o r a z o - b i s . The 90, 80, and 70% c o m p o s i t i o n s were a l s o t e s t e d a t 363°K and t h e 70% c o m p o s i t i o n was t e s t e d w i t h benzoyl peroxide as i n i t i a t o r . ( F u r t h e r m o r e , an i g n i t i o n e n v e b p e o f T v s [ l ] was c o n s t r u c t e d f o r t h e 70% SAN s y s t e m i n i t i a t e d by b e n z o y l p e r o x i d e ) (k). V a l u e s o f t h e runaway p a r a m e t e r s a,B, and b f o r t h e e x p e r i m e n t a l RA t r a n s i t i o n s u s i n g e a c h o f t h e t h r e e p o p u l a r t e r m i n a t i o n mechanisms, a r e p r e s e n t e d i n T a b l e IV. They r e f l e c t t h e t r e n d s ob s e r v e d i n t h e b e h a v i o r o f t h e e x p e r i m e n t a l r u n s . A l l RA's were o f t h e t y p e c l a s s i f i e d a s n o n - s e n s i t i v e . The v a l u e s o f p a r a m e t e r b c l e a r l y a r e i n agreement w i t h t h i s o b s e r v a t i o n . L o w e r i n g f e e d t e m p e r a t u r e r e s u l t e d i n h e i g h t e n e d s e n s i t i v i t y , and a g a i n an i n c r e a s e d v a l u e o f b i s i n agreement w i t h t h i s o b s e r v a t i o n . Figjres 5 and 6 i l l u s t r a t e t h i s b e h a v i o r f o r 80% SAN a t 363°K and 373°K respectively. They a r e c o m p u t e r g r a p h s o f e x p e r i m e n t a l d a t a w h i c h are not c u r v e - f i t t e d , but r a t h e r a r e p o i n t - t o - p o i n t connect ions o f t h e d a t a . The c u r v e s i n b o t h f i g u r e s a p p e a r v e r y s i m i l a r t o t h e n o n - s e n s i t i v e t r a n s i t i o n i n F i g . 3 o b t a i n e d from n u m e r i c a l s i m u lation. The p a r a m e t e r s i n T a b l e IV r e f l e c t t h e d e c r e a s e i n s e n s i t i v i t y c a u s e d by i n c r e a s e d t e m p e r a t u r e . As c h a r a c t e r i z e d by *b' t h e e f f e c t o f t e m p e r a t u r e on t h e r a t e o f i n i t i a t i o n îs r e s p o n s i b l e f o r t h e d e c r e a s e d s e n s i t i v i t y a s i n i t i a l t e m p e r a t u r e r i s e s (4). A t a c o n s t a n t i n i t i a t o r l e v e l , runaway c a n be c a u s e d by m a n i p u l a t i n g t h e i n i t i a l s t y r e n e c o n t e n t . With i n i t i a l i n i t i a t o r con c e n t r a t i o n f i x e d a t 0.03 m/1 and i n i t i a l t e m p e r a t u r e T = 373°K, r u n n i n g t h e r a n g e o f c o m p o s i t i o n s from 90 t o 20% c a u s e s t h e o n s e t 0

0

Q


182

CHEMICAL

REACTION

ENGINEERING—HOUSTON

S A N BP (*,)o

[ilç τ .0734 383 β* 35.6 26.7 β

0.60 b

195


exact —

1

5

3

Figure 4.

7

TABLE

IV

PARAMETERS FOR EXPERIMENTAL RUNS

GM Τ ο .9

SAN/AIBN

363 373

.8

SAN/AIBN

363 373

.7

SAN/AIBN

363 373

.6 .4 .2

SAN/AIBN

SAN/A IBN

SAN/AIBN

373 373 373

9

Exact and Cpaf nonisothermal histories, 60% SAN

DIMENSI0NLESS

System

approx

PF

PE

a

Β

b

a

B

b

a

B

b

Typ

0.87 0.79

35 35

34

0.94 0.86

36 36

31 32

0 98 0 89

34 34

30

N R

0.71 0,58

33 33

16

.05

0.75 0.62

34 34

15 16

0 79 0 65

32 32

.05 .06

0.80 0.76

36 36

30 34

0.94

38 38

26 29

0 99 0 94

34 34

24

0.89

27

N R

.015 .02

0.80 0.64

35 35

12

0.91 0.73

36 36

10 11

1 00 0 80

33 33

9 10

N R

.0425 .05

1.03 0.87

39 39

44

1.37 1.Ί4

42 42

33 35

1 41

N

1 19

36 36

32

45

33

R

.015 .0175

0.95 0.57

36 36

11 16

0.85 0.71

38 38

12

33 33

10 11

N

13

0 95 0 78

.0075 .01

0.72

12 14

0.98

42 42

9 11

1 .12 0 .97

34 34

8

0.63

39 39

N R

.0035 .005

0.71 0.69

44 44

12 16

1.19 1.18

49

7 9

1 .44 1 .39

34 34

6 8

N

49

.0035 .005

0.55 0.39

51 51

17 19

1.32 0.92

57 57

7 8

1 .99 1 .44

27 27

4

N

5

R

Mo .09

.04

35 17

13

0.85


31 14 15

9

N R

R

R

BiESENBERGER



SÉBASTIAN A N D


184


o f RA a t t h e 80% l e v e l . I t s h o u l d be n o t e d t h a t t h e v a l u e s o f 'a' a s s o c i a t e d w i t h e x p e r i m e n t a l RA t r a n s i t i o n s a r e somewhat l o w . The e x t r e m e l y i n s e n s i t i v e n a t u r e o f t h e r e a c t i o n s would depress t h e v a l u e o f a consîderably. S c a t t e r i n t h e d a t a used t o d e t e r m i n e t h e p a r a m e t e r s f o r t e r m i n a t i o n was s u f f i c i e n t t h a t i n o r d e r t o f i t t h e e n t i r e r a n g e o f c o m p o s i t i o n s w i t h a s i n g l e m o d e l , e r r o r was i n troduced i n the r a t e s . The c r i t i c a l v a l u e s o f ' a ' s h o u l d l i e more i n t h e v i c i n i t y o f 1.4 t h a n 1.0. A l t h o u g h t h e r e i s an o f f s e t i t i s important t o note t h a t t h e e x p e r i m e n t a l systems respond i n t h e same manner as t h e p a r a m e t e r s p r e d i c t . When e x p e r i m e n t s i n d i c a t e d e c r e a s i n g s e n s i t i v i t y t h e p a r a m e t e r s change i n t h e same direction. When t h e e x p e r i m e n t s show t h e r m a l t r a j e c t o r i e s be coming i n c r e a s i n g l y more non-îsothermal, t h e p a r a m e t e r ' a ' d e creases accordingly. The p a r a m e t e r s seem t o d e s c r i b e a more r e a c t i v e s y s t e m t h a n i s o b s e r v e d , and t h u s RA t r a n s i t i o n w o u l d be p r e d i c t e d a t l o w e r values of T f o r a given [ l ] . C e r t a i n l y , the results using the k i n e t i c constants developed s a t i s f y t h e engineering accuracy ex p e c t e d o f them. The s t r o n g q u a l i t a t i v e agreement s u g g e s t s t h a t more p r e c i s e d e t e r m i n a t i o n s w o u l d c a u s e p r e d i c t i o n s and e x p e r i m e n t a t i o n t o merge. F u r t h e r m o r e , t h e c r i t e r i a w e r e f o r m u l a t e d i n such a way t h a t s h o u l d a more a p p r o p r i a t e t e r m i n a t i o n mechanism be d e t e r m i n e d o r s h o u l d t h e h e t e r o g e n e o u s k i n e t i c mechanism o f a c r y l o n i t r i l e p o l y m e r i z a t i o n and acrylonitrîle - r i c h c o p o l y m e r i z a t i o n be s u c c e s s f u l l y m o d e l l e d , t h e r e s u l t i n g p a r a m e t e r s c o u l d be e a s i l y adapted.


c

Q

r

Q

Symbol s a

=

b,B

=

Cp Ε E

= = =

ε jk

= =

f H AHjk

= = =

I k I

= = =

1

E

m. J

=

R-A p a r a m e t e r d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r c o p o l y m e r î z a t i o n s IG p a r a m e t e r s d e f i n e d i n r e f e r e n c e 1 f o r h o m o p o l y m e r i z a t i o n s and T a b l e M l f o r copolymerîzatîons s p e c i f i c heat a c t i v a t i o n energy (with a p p r o p r i a t e s u b s c r i p t ) E/RgT = 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 ( w i t h a p p r o priate subscript) Ι/Ε' ( p j k ' Epiu) 1/2 ( E " E - j - E ) = Ekj f o r copoly mer ιzation initiator efficiency factor a f u n c t i o n defined i n Table I h e a t o f r e a c t i o n between f r e e r a d i c a l w i t h end u n i t j and monomer k free-radical initiator reaction rate constant heat t r a n s f e r l e n g t h = V/A , r e a c t o r volume/wetted heat t r a n s f e r area 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 , [mj]/[mj] Q

E

+

d

tJ

TN

w

0


15.

SEBASTIAN A N D

m

=


BiESENBERGER

185

I n i t i a t i n g species or dimensionless concentration of i n i t i a t i n g s p e c i e s , [ m ] / [ m ] ; for i n i t i a t o r s used i n t h i s s t u d y , I -*· 2m r e a c t i o n r a t e p o i n t f u n c t i o n w i t h u n i t s moles/volume/time (and 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 ) u n i v e r s a l gas c o n s t a n t t e m p e r a t u r e (K) ( Τ - To)/To time 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 mole f r a c t i o n o f comonomer j time c o n s t a n t s o r c h a r a c t e r i s t i c times ( w i t h a p p r o p r i a t e subscr i pts) 2 2 ^ ^ Εj / X j ^ + g j T f° copolymerization 0

0

0


Q

R

=

Rg Τ Τ* t U xj λ,Λ

= = = = = =

A

=

ad

k

r

G

G

j = l k=l λ

1II pC Τ /(-ΔΗ)(k ) [m] [m ] f o r homopolymerization p o a p o o o o pC Τ / ( - A H . , ) ( R .. ) f o r c o p o l y m e r i z a t i o n ρ ο jk pjk ο

=

0

G λ... Gjk

=

2

^G

=

^2 ^2 ^ ^ G j k ^ j = l k=l

λ. J X

l/(k

mjk

ρ [ Y

-1

2

=

Κ

]

=

o r

c

°P°Wmer izat ion 1 / 2

..) [ f ( k . ) / ( k , . . ) pjj ο d o / t j jο ο /

(

Κ

1

[m ] ο ο

/

2

ρ ] ^ ο

j = l k=l density molar c o n c e n t r a t i o n

= ] =

Tyk

^

X

A

Gjk R

Subscr i pts ap d G i j,k

= = = = =

£

=

m ο ρ R t

= = = = =

a p p a r e n t o r lumped decomposition o f i n i t i a t o r g e n e r a t i o n o f heat initiator depletion or initiation comonomer o r r e p e a t u n i t o f t y p e j o r k, where j = 1 , 2 and k = 1,2 i n d e x w h i c h t a k e s on v a l u e s I = 1,2 b u t a l w a y s such that £ = j monomer d e p l e t i o n feed c o n d i t i o n s (except i n m ) propagation r e s e r v o i r ( t h e r m a l ) o r removal o f h e a t termination Q



186 Acknowledgment

T h i s work was s u p p o r t e d i n p a r t by a G r a n t f r o m t h e N a t i o n a l S c i e n c e F o u n d a t i o n (ENG-7605053). The a u t h o r s a l s o w i s h t o t h a n k U n i o n C a r b i d e f o r s u p p l y i n g t h e s t y r e n e monomer a t no c o s t .

Literature Cited Downloaded by UNIV OF MASSACHUSETTS AMHERST on May 31, 2018 | https://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0065.ch015

1. 2. 3. 4. 5. 6. 7.

Biesenberger, J . Α., Capinpin, R . , and Sebastian, D . , Appl. Polymer Symp. (1975), 26, 211. Biesenberger, J. Α., Capinpin, R., and Yang, J., Polymer Eng. Sci., (1976), 16, 101. Sebastian, D. H. and Biesenberger, J. Α., submitted to J. Appl. Polym. Sci. Sebastian, D. H., Ph.D. Thesis, Stevens Institute of Tech nology (1977). Sebastian, D. H. and Biesenberger, J. Α., submitted to J. Polymer S c i . Russo, S., Munari, S., J. Macromol. Sci-Chem., (1967), A-1,5, 2159. Sebastian, D. H. and Biesenberger, J. Α., Polymer Eng. Sci., (1976), 16, 117.


Nonisothermal Behavior and Thermal Runaway Phenomena in Chain

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