Polymer Stabilization and Degradation - ACS Publications - American

20 Degradation of Poly(vinyl chloride) According to Non-Steady-State Kinetics J O S E P H D. D A N F O R T H

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Downloaded by UNIV LAVAL on July 13, 2016 | http://pubs.acs.org Publication Date: June 14, 1985 | doi: 10.1021/bk-1985-0280.ch020

Grinnell College, Grinnell, IA 50112

Poly(vinyl chloride) has been shown to degrade thermally by a chain mechanism that is best represented by nonsteady-state kinetics (NSSK). Degradations are initiated at a very few sites within a chain, and the subsequent zip reaction which accounts for substantially a l l of the evolved hydrogen chloride is confined to a single chain. The initiation reaction is temperamental. It is influenced by surfaces, impurities, and hydrogen chloride pressure. The number of initiations that result in a zip chain influences the average length of a zip chain, which in turn establishes the time at which the maximum degradation rate is attained. Although the uncertainty of the initiation reaction can significantly alter degradation patterns and make reproducibility under presumably identical conditions difficult to achieve, the NSSK model gives excellent agreement of observed and calculated data over the entire range of a degradation. The degradation of PVC has been described in terms of non-steadystate kinetics (NSSK) which were developed on the basis of the zipper mechanism (1,2). Observed degradation patterns were altered significantly by the presence of hydrogen chloride, inert surfaces, and intentionally added impurities (3). These degradation patterns were reproduced by NSSK using the best fit values of three parameters (previously named less descriptively) : k-^, the fraction of chains starting degradation per sec; k , the rate of unzipping of degrading chains expressed as the fraction of a chain unzipping per sec; and kx, a chain terminating constant that was based on certain assumptions about the way that impurities prevented the initiation of degradation chains. The initiation and zip constants were primarily responsible for degradation patterns. The terminating constant, kp, reduced the values of a, the fraction dehydrochlorinated, as a function of time. Its primary function was to obtain best f i t parameters when degradations did not go to completion. A l l degradation reactions for a l l samples were acceleratory. That is, the evolution z

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Deceased. 0097-6156/85/0280-0285$06.00/0 © 1985 American Chemical Society Klemchuk; Polymer Stabilization and Degradation ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

286

POLYMER STABILIZATION AND DEGRADATION


of hydrogen c h l o r i d e was slow a t t h e b e g i n n i n g , i n c r e a s e d t h r o u g h a maximum and t h e n d e c r e a s e d . The i n i t i a t i o n r e a c t i o n a c c o u n t e d f o r o n l y n e g l i g i b l e amounts o f hydrogen c h l o r i d e . The z i p r e a c t i o n a c c o u n t e d f o r g r e a t e r t h a n 99% o f t h e e v o l v e d hydrogen c h l o r i d e ( 3 ) . A l p h a - t i m e c u r v e s c a l c u l a t e d from b e s t f i t v a l u e s o f t h e parameters c o u l d be superimposed upon t h e d a t a c u r v e s . E x c e l l e n t agreement o f t h e o r y and d a t a was a l s o o b t a i n e d i n t h e more c r i t i c a l comparison i n which d e g r a d a t i o n r a t e s were p l o t t e d as a f u n c t i o n o f t i m e . I n d i v i d u a l d e g r a d a t i o n c u r v e s f o r n i n e samples o f PVC from t h r e e d i f f e r e n t s u p p l i e r s have been o b s e r v e d a t many temperatures i n t h e range 210-240°C. Each d e g r a d a t i o n was e f f e c t i v e l y r e p r o d u c e d by t h e p r o p e r assignment o f b e s t f i t parameters, b u t t h e d u p l i c a t i o n o f d e g r a d a t i o n c u r v e s under presumably i d e n t i c a l r u n c o n d i t i o n s was uncertain. D u p l i c a t i o n was o f t e n a t t a i n e d f o r r u n s made i n sequence, but a r u n made a t a n o t h e r time under presumably i d e n t i c a l c o n d i t i o n s would o c c a s i o n a l l y g i v e an a l t e r e d d e g r a d a t i o n p a t t e r n and s i g n i f i c a n t l y d i f f e r e n t v a l u e s o f t h e parameters a t best f i t . I t i s now a p p a r e n t t h a t d i f f i c u l t r e p r o d u c i b i l i t y i s a b u i l t - i n c h a r a c t e r i s t i c of zipper k i n e t i c s . Even though r e p r o d u c i b i l i t y i s a r e c o g n i z e d problem, t h e v a l u e s o f t h e parameters k i and k have t h e o r e t i c a l and p r a c t i c a l s i g n i f i c a n c e and c a n be d i r e c t l y r e l a t e d to t h e p r o c e s s e s t h a t o c c u r i n any s p e c i f i c d e g r a d a t i o n . K i n e t i c models o f polymer d e g r a d a t i o n based on c h a i n p r o c e s s e s have been s u g g e s t e d ( 4 - 8 ) . These models and o t h e r models f o r p o l y mer d e g r a d a t i o n have n o r m a l l y i n v o k e d t h e s t e a d y - s t a t e h y p o t h e s i s (9). B a r r o n and Boucher (10) d e s c r i b e a k i n e t i c model f o r z i p k i n e t i c s b u t assume an apparent f i r s t o r d e r b e h a v i o r and do n o t a c c o u n t e f f e c t i v e l y f o r t h e a c c e l e r a t o r y phase o f t h e d e g r a d a t i o n . MacCallum has q u e s t i o n e d t h e v a l i d i t y o f t h e s t e a d y - s t a t e h y p o t h e s i s (11) b u t d i d n o t d e v e l o p a p r a c t i c a l k i n e t i c model f o r NSSK. I t i s the non-steady-state f e a t u r e that i s r e s p o n s i b l e f o r the s u c c e s s f u l a p p l i c a t i o n o f t h i s model t o t h e z i p d e g r a d a t i o n o f PVC. z

Experimental The a p p a r a t u s w h i c h measures p r e c i s e l y t h e r a t e s o f gas e v o l u t i o n a s a f u n c t i o n o f time has been d e s c r i b e d (2, 12-14). PVC samples from G o o d r i c h and S c i e n t i f i c Polymer P r o d u c t s have been c h a r a c t e r i z e d by the name o f t h e s u p p l i e r and t h e average degree o f p o l y m e r i z a t i o n . C u r v e f i t t i n g t e c h n i q u e s and t h e computer g e n e r a t i o n of d e g r a d a t i o n c u r v e s f o r s i n g l e and mixed parameters have been d e s c r i b e d (15). The e q u a t i o n s r e p r e s e n t i n g NSSK when i n i t i a t i o n i s f i r s t o r d e r have been d e r i v e d f o r c h a i n t e r m i n a t i o n t h a t i s f i r s t o r d e r i n i m p u r i t i e s (16). Other i n i t i a t i o n and z i p o r d e r s have been e v a l u a t e d . A l l nons t e a d y - s t a t e models appear t o be markedly s u p e r i o r t o models t h a t i n v o k e t h e s t e a d y - s t a t e h y p o t h e s i s , b u t none i s a p p r e c i a b l y b e t t e r than t h e s i m p l e assumption o f f i r s t o r d e r i n i t i a t i o n and z e r o o r d e r zip. The d e r i v a t i o n and e v a l u a t i o n o f o t h e r n o n - s t e a d y - s t a t e models w i l l be t h e s u b j e c t o f a l a t e r p u b l i c a t i o n . R e s u l t s and D i s c u s s i o n The

equations

representing the behavior of a c c e l e r a t o r y degradations

Klemchuk; Polymer Stabilization and Degradation ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

20.

Degradation of Polyvinyl chloride)

DANFORTH

287

w h i c h have been p r e v i o u s l y d e s c r i b e d ( 1 , 2 , 1 6 ) a r e summarized i n Table I. Though complex i n a p p e a r a n c e , n o n - s t e a d y - s t a t e equations a r e based on v e r y s i m p l e assumptions about i n i t i a t i o n and p r o p a g a tion. W i t h computer f a c i l i t i e s a v a i l a b l e i t i s no l o n g e r n e c e s s a r y to i n v o k e s t e a d y - s t a t e assumptions i n o r d e r t o s o l v e t h e p r o b l e m s . The i d e a l e q u a t i o n r e p r e s e n t s e x p e c t e d b e h a v i o r s when t h e r e i s no c h a i n t e r m i n a t i o n by s u r f a c e s and i m p u r i t i e s . When c h a i n t e r m i n a t i o n o c c u r s d u r i n g the i n i t i a l s t a t e s o f a d e g r a d a t i o n , o n l y a p o r t i o n o f the c h a i n s t h a t a r e t h e r m a l l y i n i t i a t e d a c t u a l l y p r o d u c e s a zip reaction. R e a c t i o n o f an i n i t i a t e d c h a i n w i t h s u r f a c e o r i m p u r i t i e s p r e v e n t s the z i p r e a c t i o n f o r t h a t i n i t i a t i o n . The n o n i d e a l e q u a t i o n p r o p e r l y a c c o u n t s f o r i n i t i a t i o n s t h a t do not r e s u l t in a zip reaction.


Table I.

Equations for Non-Steady-State

Kinetics

I d e a l E q u a t i o n - No C h a i n T e r m i n a t i o n A c c e l e r a t o r y Phase,

t = o to t =

^/^

a = k t

exp

k /k.

+

z

(k /k.) z

D e c e l e r a t o r y Phase, (Wk.)

a = 1 +

(-k.t)

t = l/k

exp

(-

-

z

to t =

z

k.t)

z

[(1

-

0 0

exp

(k /k )] ±

z

Equation with Chain Termination A c c e l e r a t o r y Phase, a = k t

+

k /k.

t = o to t =

exp

z

D e c e l e r a t o r y Phase,

(-

k.t

t = 1/k

1/k z (k k /k.)

+

z

to t =

T

exp

(-k.t)

0 0

z a = (k /k.) z

exp

(-

-

(k^ly^k.)

exp

-

(k k /2k.)

(1 -

z

T

k.t)

(-

(1 -

2k.t)

exp

(-

exp

(1 -

(k./k ))

exp

z

(k./k )) z

+ 1

k./k )) z

The a v s . time c u r v e s o f F i g u r e 1 have been g e n e r a t e d from a s s i g n e d v a l u e s o f k ^ , k , and k to i l l u s t r a t e how t h e v a l u e s o f the parameters i n f l u e n c e d e g r a d a t i o n p a t t e r n s . For a z i p r a t e , k = 0.0005 s e c " " * , t h e i n f l e c t i o n p o i n t o f the r e s u l t i n g a - t c u r v e s w i l l f a l l at 2000 sec because the maximum r a t e w i l l appear a t t = l/k . A t c o n s t a n t k the d e g r a d a t i o n p a t t e r n s a r e s i g n i f i c a n t l y a l t e r e d by the v a l u e s o f k^ and t o a l e s s e r e x t e n t by t h e v a l u e s assigned to kp. F i g u r e 2 p r e s e n t s g e n e r a t e d r a t e d a t a as Aa/100 s e c v s . t . The m i d d l e c u r v e o f F i g u r e 2 r e p r e s e n t s t h e r a t e d a t a f o r t h e c a s e where k . = k = 0.0005 and K j , = 0. The maximum r a t e appears a t 2000 s e c , wfeich i s the i n f l e c t i o n p o i n t o f the c o r r e s p o n d i n g a - t c u r v e o f z

T

z

z

z

z



288


1000

2000

3000

SECONDS Figure 1. Calculated alpha-time curves for assigned values of sec - 1 . sec"" ; and k . ( A ) ki = 0.0005, kp - 0; 0.00010, (A) i = 0.0005, k = 0.0005, k = 0.2; (•) k 0.0005, 0; i - 0.0001, k = 0.0010, kr = 0.

ki,

1

k

?

z

±

x

k

z

2000 SECONDS

Figure 2. Calculated rate curves for changing k±, sec and k , sec . (0) k = 0.0005, k = 0.0010; ( Q ) k = k = 0.0005; (A) i 0.0001, k = 0.0010. 1

- 1

±

k

=

z

±

z

z


z

20.


DANFORTH

289

F i g u r e 1. The two upper c u r v e s o f F i g u r e 2 r e p r e s e n t d e g r a d a t i o n b e h a v i o r s a t c o n s t a n t i n i t i a t i o n ( k i = 0.0005 s e c " ) f o r k z v a l u e s of 0.001 sec"" (upper c u r v e ) and 0.0005 s e c " ( m i d d l e c u r v e ) . The lower r a t e c u r v e has t h e same kg v a l u e as the upper c u r v e b u t t h e v a l u e o f k i has been reduced t e n - f o l d t o 0.0001 s e c " . These gene r a t e d r a t e c u r v e s i l l u s t r a t e t h e d r a s t i c changes i n d e g r a d a t i o n p a t t e r n s t h a t c a n be e x p e c t e d from changes i n t h e i n i t i a t i o n and z i p constants. A t v a l u e s w i t h i n t h e range n o r m a l l y e n c o u n t e r e d t h e c h a i n t e r m i n a t i n g c o n s t a n t l o w e r s somewhat t h e i n i t i a l p o r t i o n s o f a d e g r a d a t i o n c u r v e b u t does n o t s i g n i f i c a n t l y change d e g r a d a t i o n p a t t e r n s a t l o n g e r times and h i g h e r c o n v e r s i o n s . 1

1

1

1

I n a d d i t i o n t o t h e t h r e e p a r a m e t e r s , k i , k , and kp, t h e r e i s a time s h i f t , t . The time s h i f t i s n e c e s s a r y t o a c c o u n t f o r i n d u c t i o n periods. When c h a i n s a r e immediately t e r m i n a t e d d u r i n g an i n d u c t i o n p e r i o d , the k i n e t i c model based on z i p k i n e t i c s o b v i o u s l y does n o t apply. The time s h i f t g i v e s an i n i t i a l t i m e t h a t depends on t h e b e h a v i o r o f t h e d e g r a d a t i o n c u r v e a f t e r c h a i n t e r m i n a t i o n h a s become almost n e g l i g i b l e . I t e l i m i n a t e s t h e i n d u c t i o n p e r i o d f o r purposes of c u r v e f i t t i n g b u t does n o t a l t e r t h e g e n e r a l shape o f t h e d e g r a d a t i o n curve. I t has been shown i n e a r l i e r work t h a t z i p k i n e t i c s g i v e b e s t f i t p a r a m e t e r s t h a t w i l l r e p r o d u c e a - t and r a t e - t i m e c u r v e s o v e r t h e e n t i r e range o f a d e g r a d a t i o n (3,16). The q u a n t i t a t i v e s i g n i f i c a n c e of t h e i n i t i a t i o n and z i p c o n s t a n t s was i m p l i e d b u t n o t emphasized because d i f f e r e n t d e g r a d a t i o n p a t t e r n s and c o r r e s p o n d i n g l y d i f f e r e n t parameter v a l u e s were o f t e n o b t a i n e d f o r t h e same sample under p r e sumably t h e same c o n d i t i o n s . I t i s now a p p a r e n t t h a t d i f f i c u l t r e p r o d u c i b i l i t y i s an e x p e c t e d c h a r a c t e r i s t i c of z i p k i n e t i c s . The n a t u r e o f z i p k i n e t i c s t h a t makes r e p r o d u c t i o n o f d a t a d i f f i c u l t w i l l be d e s c r i b e d and t h e quant i t a t i v e c h a r a c t e r i z a t i o n o f sample b e h a v i o r i n terms o f i n i t i a t i o n and z i p parameters w i l l be demonstrated. I t i s u s e f u l f o r the b e t t e r u n d e r s t a n d i n g o f z i p k i n e t i c s t o i l l u s t r a t e how a p p r o x i m a t e d e g r a d a t i o n d a t a c o r r e s p o n d i n g t o o b s e r v e d d a t a c a n be c a l c u l a t e d f o r two h y p o t h e t i c a l samples. E a c h i s 100 mg; t h e i r c h a i n l e n g t h s a r e 500 and 1000 v i n y l c h l o r i d e u n i t s . The term, " a p p r o x i m a t e , i s a p p r o p r i a t e because o f t h e way Aa/A more c l o s e l y approaches d a / d t , and t h e term, " a p p r o x i m a t e " , would be u n n e c e s s a r y for the c a l c u l a t e d data. These c a l c u l a t e d d a t a r e p r e s e n t an i d e a l s i t u a t i o n i n w h i c h t h e r e i s no m i x t u r e o f c h a i n l e n g t h s and i n which no premature t e r m i n a t i o n o f z i p c h a i n s o c c u r s . A c t u a l samples w i l l always have some v a r i a t i o n s i n c h a i n l e n g t h , and s t a r t i n g c h a r a c t e r i s t i c s may a l s o show v a r i a t i o n s due t o premature c h a i n t e r m i n a t i o n . A l t h o u g h i t has been shown t h a t s i n g l e v a l u e d p a r a m e t e r s g i v e good r e p r e s e n t a t i o n o f d a t a g e n e r a t e d from samples i n w h i c h c h a i n l e n g t h s and s t a r t i n g c h a r a c t e r i s t i c s have been p u r p o s e l y mixed (3,15), t h e term " a p p r o x i m a t e " w i l l always be a p p r o p r i a t e when s i n g l e v a l u e d p a r a m e t e r s a r e used t o r e p r e s e n t a c t u a l d e g r a d a t i o n i n w h i c h t h e r e must be c h a i n s o f d i f f e r e n t l e n g t h s . z


g

11

C a l c u l a t i o n o f D e g r a d a t i o n Data f o r H y p o t h e t i c a l Samples o f D i f f e r e n t Degrees o f P o l y m e r i z a t i o n . One hundred m i l l i g r a m s o f PVC, r e g a r d l e s s o f c h a i n l e n g t h , w i l l c o n t a i n 0.100 • DP moles hydrogen MW



290

c h l o r i d e where DP i s the v i n y l c h l o r i d e u n i t s per c h a i n , and MW i s the number a v e r a g e m o l e c u l a r w e i g h t . I f t h e weight o f t h e sample i s doubled the r a t e of hydrogen c h l o r i d e e v o l u t i o n e x p r e s s e d as moles hydrogen c h l o r i d e • sec"" w i l l d o u b l e , but the r a t e e x p r e s s e d as Aasec"" w i l l n o t change w i t h the sample s i z e . The r a t e e x p r e s s e d as moles HC1 • sec"" w i l l depend upon the number o f c h a i n s t h a t a r e unz i p p i n g and the i n t r i n s i c r a t e o f u n z i p p i n g e x p r e s s e d as moles HC1 • chain • sec" . I n the z i p p e r mechanism t h e i n t r i n s i c r a t e o f unz i p p i n g i s assumed t o be t h e same f o r a l l samples r e g a r d l e s s o f c h a i n l e n g t h . However k , t h e f r a c t i o n o f a c h a i n u n z i p p i n g p e r s e c , w i l l depend upon the c h a i n l e n g t h . D u r i n g the a c c e l e r a t o r y phase o f a d e g r a d a t i o n the moles hydrogen c h l o r i d e e v o l v e d p e r s e c a t any time w i l l be the moles o f d e g r a d i n g c h a i n s m u l t i p l i e d by the i n t r i n s i c rate. The moles of d e g r a d i n g c h a i n s d u r i n g a c c e l e r a t i o n can be e s t i mated a t any time as the c u m u l a t i v e sum o f c h a i n s t h a t have s t a r t e d during preceding i n t e r v a l s . 1

1

- 1

-1


z

The c h a i n s t h a t s t a r t d u r i n g an i n t e r v a l can be e s t i m a t e d from t h e sample w e i g h t , t h e degree of p o l y m e r i z a t i o n , t h e f i r s t o r d e r i n i t i a t i o n c o n s t a n t , k^, and the l e n g t h o f the i n t e r v a l . Thus, 0.10 | samples w i l l c o n t a i n i n i t i a l l y 1.60 • I O " (DP 1000) and 3.2 x 10~ (DP 500) moles o f polymer c h a i n s . I f k^ i s a s s i g n e d t h e r e a s o n a b l e v a l u e , 0.0005 s e c " , t h e moles o f polymer c h a i n s u n z i p p i n g a f t e r 100 s e c w i l l be (moles o f i n i t i a l polymer) • 0.0005 sec"" • 100 s e c . The moles o f polymer c h a i n s s t a r t i n g d u r i n g the f i r s t 100 s e c can be s u b t r a c t e d from t h e number of polymer c h a i n s p r e s e n t i n i t i a l l y t o g i v e the number o f u n s t a r t e d c h a i n s p r e s e n t a t the s t a r t of the i n t e r v a l , 100-200 s e c . The number o f c h a i n s s t a r t i n g d u r i n g t h e 100-200 s e c i n t e r v a l can t h e n be c a l c u l a t e d . D u r i n g the a c c e l e r a t i n g p e r i o d the c u m u l a t i v e sum o f t h e average number of c h a i n s s t a r t i n g p e r i n t e r v a l m u l t i p l i e d by the i n t r i n s i c ^ i p r a t e w i l l g i v e t h e moles HC1 p e r i n t e r v a l . When t = l / k the f i r s t s t a r t e d c h a i n s a r e c o m p l e t e l y decomposed. A t t = l / k + 1 0 0 the number of p r o d u c i n g c h a i n s c a l c u l a t e d as t h e c u m u l a t i v e sum must be c o r r e c t e d by s u b t r a c t i n g t h e c h a i n s t h a t have t e r m i n a t e d . The s u b t r a c t e d number w i l l be the a v e r a g e number o f c h a i n s p r o d u c i n g from 0-100 s e c , and so on f o r subsequent i n t e r v a l s . The a v e r a g e number o f p r o d u c i n g c h a i n s m u l t i p l i e d by the i n t r i n s i c r a t e (DP • k ) g i v e s the r a t e o f hydrogen c h l o r i d e e v o l u t i o n as moles HC1 p e r i n t e r v a l . This value d i v i d e d by the moles h y d r o g e n c h l o r i d e i n the o r i g i n a l samples g i v e s Aa/interval. The c a l c u l a t e d moles hydrogen c h l o r i d e e v o l v e d p e r i n t e r v a l can be e n t e r e d i n the same way t h a t o b s e r v e d peak a r e a s of an a c t u a l r u n a r e e n t e r e d and the b e s t f i t v a l u e s of t h e parameters obtained. The b e s t f i t v a l u e s of the parameters from the c a l c u l a t e d d a t a , as would be e x p e c t e d , a r e e s s e n t i a l l y the same as t h o s e v a l u e s t h a t were used i n making the c a l c u l a t i o n s . The i d e a l e q u a t i o n shown i n T a b l e 1 d e s c r i b e s more s i m p l y the k i n e t i c b e h a v i o r t h a t has been e s t i m a t e d by the p r e c e d i n g s t e p w i s e c a l c u l a t i o n s . The s t e p w i s e c a l c u l a t i o n i s s i m i l a r t o the way r u n d a t a a r e o b t a i n e d s i n c e i n a r u n the peak a r e a r e c o r d e d r e p r e s e n t s A a / i n t e r v a l . 6

6

1

1

z

z

z

T h e r e i s one c r i t i c a l p o i n t t h a t r e q u i r e s a d d i t i o n a l comment. When the i n t r i n s i c r a t e i s a s s i g n e d a v a l u e , DP • k , the unwarranted assumption t h a t a z i p c h a i n l e n g t h i s the same as t h e l e n g t h o f a polymer c h a i n has been made. T h i s a s s u m p t i o n would be t r u e i f t h e r e were one i n i t i a t i o n s i t e p e r polymer c h a i n . I f t h e r e were two i n i z


20. DANFORTH


291

t i a t i o n s i t e s p e r polymer c h a i n t h e z i p c h a i n would be o n e - h a l f as l o n g but the f r a c t i o n u n z i p p i n g per sec would be d o u b l e d . The i n t r i n s i c z i p r a t e as i n i t i a l l y assumed f o r z i p k i n e t i c s would not depend upon c h a i n l e n g t h . However, the number of s t a r t s p e r c h a i n w i l l c e r t a i n l y i n f l u e n c e b o t h k^ and k . The s t a r t s p e r c h a i n must be a s m a l l number i f the z i p p e r mechanism i s t o a p p l y . A reasonable model f o r PVC would assume t h a t each sample c o n t a i n e d an a v e r a g e number o f p o t e n t i a l s t a r t i n g p o s i t i o n s p e r c h a i n c h a r a c t e r i s t i c of t h a t sample. The a c t u a l number of s t a r t s t h a t l e d t o a z i p r e a c t i o n would depend upon the i m p u r i t i e s p r e s e n t and the number o f s u r f a c e c o n t a c t s t h a t were c h a i n t e r m i n a t i n g . The p a r t i a l p r e s s u r e of h y d r o gen c h l o r i d e , which has been shown t o i n f l u e n c e the i n i t i a l r e a c t i o n , would a l s o i n f l u e n c e not o n l y the r a t e of i n i t i a t i o n but a l s o the f r a c t i o n of p o t e n t i a l s t a r t i n g p o s i t i o n s t h a t a c t u a l l y i n i t i a t e s a z i p r e a c t i o n . S i n c e the b u i l d u p of hydrogen c h l o r i d e a t the b e g i n n i n g of a d e g r a d a t i o n depends on z i p c h a i n s a l r e a d y p r e s e n t and weak l i n k a g e s t h a t s l o w l y decompose t h e r m a l l y , an e r r a t i c b u i l d u p of hydrogen c h l o r i d e c o n t r i b u t e s t o d i f f i c u l t r e p r o d u c i b i l i t y i n the same way t h a t c h a i n t e r m i n a t i n g i m p u r i t i e s and s u r f a c e s c o n t r i b u t e . Thus, i n i t i a t i o n comprises o n l y an i n s i g n i f i c a n t p a r t o f d e g r a d a t i o n but i n f l u e n c e s s i g n i f i c a n t l y the number of c h a i n s t h a t w i l l be p r o d u c i n g a t any time and the avergage c h a i n l e n g t h t h a t t h o s e c h a i n s w i l l have. The a v e r a g e c h a i n l e n g t h i s d i r e c t l y r e l a t e d t o the time a t w h i c h the maximum r a t e i s a t t a i n e d ( t a x - l / k ) so t h o s e substances or run c o n d i t i o n s that a l t e r s t a r t i n g c h a r a c t e r i s t i c s w i l l a l s o a l t e r somewhat the v a l u e of k . Changes i n k^ and k , as i l l u s t r a t e d i n F i g u r e s 1 and 2, s i g n i f i c a n t l y i n f l u e n c e d e g r a d a t i o n p a t terns. Thus, the p r e s e n c e of Chromsorb o r a p i e c e of a p a p e r c l i p , p r e h e a t i n g a sample, the sample s i z e w h i c h i n f l u e n c e s the r a t i o of sample t o s u r f a c e c o n t a c t s , the p a r t i a l p r e s s u r e of hydrogen c h l o r i d e , the r a t e a t w h i c h hydrogen c h l o r i d e forms i n the sample, and c h a i n t e r m i n a t i n g i m p u r i t i e s a l r e a d y p r e s e n t (3) w i l l a l t e r the i n i t i a t i o n c h a r a c t e r i s t i c s and t h e s e i n t u r n w i l l i n f l u e n c e the a v e r a g e c h a i n length.


z

m

z

z

z

S i n c e i t has a l r e a d y been e s t a b l i s h e d t h a t PVC d a t a from the b e g i n n i n g t o t h e end o f a t h e r m a l d e g r a d a t i o n can be r e p r o d u c e d from NSSK, (2,3,16) t h e r e seems t o be no r e a s o n t o b u r d e n t h e l i t e r a t u r e w i t h the many d e g r a d a t i o n c u r v e s and b e s t f i t p a r a m e t e r s t h a t have been o b t a i n e d f o r o v e r 600 i n d i v i d u a l r u n s u s i n g n i n e d i f f e r e n t samples and a v a r i e t y of r u n c o n d i t i o n s . I t does seem a p p r o p r i a t e t o i l l u s t r a t e how d a t a can be r e p r o d u c e d under v e r y c a r e f u l l y c o n t r o l l e d c o n d i t i o n s and t o show how o c c a s i o n a l samples d e v i a t e from t h e i r expected behavior. I t w i l l a l s o be s u g g e s t e d t h a t f o r e i g h t of the n i n e samples s t u d i e d the c h a i n l e n g t h of the polymer has an o v e r r i d i n g i n f l u e n c e on d e g r a d a t i o n p a t t e r n s . The b e h a v i o r of one sample t h a t d i d not f o l l o w t h e d e g r a d a t i o n p a t t e r n t h a t was e x p e c t e d on the b a s i s o f i t s c h a i n l e n g t h w i l l be c o n s i d e r e d . The i n f l u e n c e of p r e h e a t i n g on d e g r a d a t i o n p a t t e r n s w i l l a l s o be d e s c r i b e d . The C h a r a c t e r i z a t i o n of PVC Samples i n Terms of T h e i r K i n e t i c P a r a m e t e r s . Under c a r e f u l l y c o n t r o l l e d c o n d i t i o n s runs t h a t a r e made i n sequence may g i v e r e p r o d u c i b l e d a t a and i l l u s t r a t e t h a t d i f f i c u l t i e s o f r e p r o d u c i b i l i t y a r e n o t caused by s h o r t c o m i n g s o f the t e c h n i q u e s and a p p a r a t u s used i n the measurements. The sample G o o d r i c h


292


684 has been chosen t o i l l u s t r a t e t h e r e p r o d u c i b i l i t y o f d a t a and a l s o t o i l l u s t r a t e t h a t o c c a s i o n a l runs do not d u p l i c a t e the e x p e c t e d d e g r a d a t i o n p a t t e r n . F i g u r e 3 shows a - t c u r v e s f o r i d e n t i c a l runs a t 225°C u s i n g samples o f G o o d r i c h 684 i n t h e 70-80 mg range. Three samples d e m o n s t r a t e r e p r o d u c i b i l i t y . The o t h e r sample i s s i g n i f i cantly different. Rate c u r v e s f o r t h e s e samples a r e r e p r o d u c e d i n F i g u r e 4. T a b l e I I g i v e s t h e v a l u e s o f t h e b e s t f i t parameters o b t a i n e d by m i n i m i z i n g t h e d i f f e r e n c e s between t h e o b s e r v e d and c a l c u l a t e d v a l u e s of a o v e r t h e e n t i r e range of t h e d e g r a d a t i o n . In t h e s e runs t h e sample was removed s h o r t l y a f t e r t h e d e g r a d a t i o n r e a c h e d t h e d e c e l e r a t o r y phase.


Table I I .

B e s t F i t Parameters f o r G o o d r i c h

i 1 1 (sec-i-lO^) 1.37 2.24 2.15 2.13

684

k

Run 2D46A 2D25A 2D24A 2D49A

- 1

J

(sec -10 ) 0.65 0.82 0.83 0.76

t

0.36 0.78 0.59 0.48

s,sec 189 131 197 211

a t 225°C

A,% d i f per p o i n t 0.73 0.97 0.94 1.17

U s i n g t h e n o n - i d e a l e q u a t i o n o f T a b l e I and t h e b e s t f i t v a l u e s o f t h e parameters, c a l c u l a t e d a - t and r a t e d a t a a g r e e w i t h . o b s e r v e d d a t a , and the c a l c u l a t e d time o f t h e maximum r a t e f a l l s v e r y c l o s e t o t h e time of t h e o b s e r v e d maximum r a t e . Each s e t o f d e g r a d a t i o n d a t a i s e f f e c t i v e l y r e p r e s e n t e d by t h e b e s t f i t parameters, y e t t h e r e i s a s i g n i f i c a n t v a r i a t i o n o f parameter v a l u e s f o r r u n 2D46A which was presumably r u n under c o n d i t i o n s i d e n t i c a l w i t h t h e o t h e r r u n s . Run 2D46A d i s p l a y s the c h a r a c t e r i s t i c s t h a t a r e always e n c o u n t e r e d i n runs t h a t misbehave. The v a l u e s o f and k a r e lower than t h o s e o f t h e "good" runs w h i c h i n v a r i a b l y show more r a p i d a c c e l e r a t i o n . The j u s t i f i c a t i o n f o r d i f f i c u l t r e p r o d u c i b i l i t y and d e c r e a s e i n k^ and k f o r runs t h a t misbehave i s of c o u r s e i n h e r e n t i n t h e mechanism. The i n i t i a t i o n r e a c t i o n r e p r e s e n t s o n l y an i n s i g n i f i c a n t p a r t of t h e o v e r a l l reaction. I t i s extremely s e n s i t i v e to i m p u r i t i e s , to s u r f a c e c o n t a c t s , and t o t h e p a r t i a l p r e s s u r e of hydrogen c h l o r i d e . The d a t a o f F i g u r e s 1 and 2 i l l u s t r a t e t h e d r a m a t i c changes i n d e g r a d a t i o n p a t t e r n s t h a t a r e t o be e x p e c t e d f o r changes i n t h e f r a c t i o n o f c h a i n s s t a r t i n g p e r s e c even i f t h e c h a i n l e n g t h remained unchanged. However, when t h e f r a c t i o n i n i t i a t e d p e r sec i s d e c r e a s e d the f r a c t i o n o f a c t u a l s t a r t s p e r c h a i n i s a l s o somewhat d e c r e a s e d . Even though t h e p o t e n t i a l s t a r t s p e r c h a i n a r e i n i t i a l l y i d e n t i c a l f o r a g i v e n sample, the a c t u a l number of z i p c h a i n s s t a r t e d p e r polymer c h a i n i s l e s s than n o r m a l under poor s t a r t i n g c o n d i t i o n s . The fewer the number s t a r t s p e r c h a i n the l o n g e r w i l l be t h e average l e n g t h o f a z i p c h a i n , and t h i s i s r e f l e c t e d i n a lower v a l u e of k and a l o n g e r time t o a c h i e v e t h e maximum r a t e . z

z

z

B e f o r e the i m p l i c a t i o n s o f t h e z i p p e r mechanism i n terms o f r e p r o d u c i b l e d a t a were f u l l y a p p r e c i a t e d , e f f o r t s t o a t t a i n r e p r o d u c i b i l i t y commensurate w i t h t h e q u a l i t y of the a p p a r a t u s and the method o f o p e r a t i o n l e d t o hundreds of d e g r a d a t i o n r u n s . Some of t h e s e runs



20.

DANFORTH


293

1000 SECONDS F i g u r e 3. F r a c t i o n degraded v s time f o r i d e n t i c a l r u n c o n d i t i o n s G o o d r i c h 684 a t 225°C. ( A ) 2D46A, ( Q ) 2D25A, ( A ) 2D24A, (Q) 2D49A.

1000 SECONDS F i g u r e 4. R a t e - t i m e c u r v e s f o r G o o d r i c h 684 a t 225°C, ( A ) (Q) 2D25A, ( A ) 2D24A, ( Q ) 2D49 A.


2D46A,


294


gave good i n i t i a l a c c e l e r a t i o n and were i n t u i t i v e l y c o n s i d e r e d t o be "good r u n s " . O t h e r s d i d n o t " t a k e o f f " and a l t h o u g h t h e y gave b e s t f i t parameters t h a t would d u p l i c a t e the d a t a f o r t h a t r u n , the p a r a meter v a l u e s d i f f e r e d somewhat from t h o s e o b t a i n e d f o r o t h e r runs under presumably t h e same c o n d i t i o n s . From many hundreds of runs on a v a r i e t y of samples t h e r e a r e a number of d e g r a d a t i o n b e h a v i o r s t h a t can be q u a n t i t a t i v e l y e x p r e s s e d i n terms of parameter v a l u e s . From t h e v e r y l a r g e amounts of d a t a a v a i l a b l e some of t h e sample c h a r a c t e r i s t i c s and r u n v a r i a b l e s t h a t a r e r e f l e c t e d i n the v a l u e s of the parameters w i l l be d e s c r i b e d . Changes i n t h e Number of P o t e n t i a l S t a r t s Per C h a i n Can I n f l u e n c e t h e D e g r a d a t i o n P a t t e r n . The sample SP 917 has p r e v i o u s l y been shown t o a c c e l e r a t e more r a p i d l y and t o a t t a i n i t s maximum r a t e i n l e s s time t h a n SP 634 and SP 1381 ( 3 ) . Samples SP 634 and SP 1381 f o l l o w a p p r o x i m a t e l y the p a t t e r n of a l l G o o d r i c h samples i n w h i c h a t compara b l e c o n d i t i o n s l o n g c h a i n samples a c c e l e r a t e d s l o w l y and r e q u i r e d a l o n g e r time t o a c h i e v e t h e i r maximum r a t e s ( 1 6 ) . F i g u r e 5 shows r e p r e s e n t a t i v e p l o t s o f Aa/60 sec as a f u n c t i o n o f time f o r SP 634, SP 917 and SP 1381. A l l runs were made by t h e d i r e c t i n t r o d u c t i o n o f t h e sample i n t o the r e a c t i o n chamber a f t e r t h e temperature of t h e r u n had been a t t a i n e d . B e s t f i t v a l u e s o f t h e p a r a m e t e r s f o r each o f the t h r e e runs and t h e i n t e r p o l a t e d v a l u e s e x p e c t e d f o r SP 917 on t h e b a s i s of the l e n g t h of t h e c h a i n a r e r e c o r d e d i n T a b l e I I I .

T a b l e I I I . B e s t F i t V a l u e s o f Parameters f o r t h e o f SP 634, SP 917 and SP 1381 a t 225°C Comparable C o n d i t i o n s

k

Sample SP 634 SP 917 SP 1381 Interp. 917

Run C110 C109 C108 _

i - l (sec «10 ) 1.12 1.73 0.58 3 J

Degradations

k

i - l 3 fsec -10 ) 0.68 0.85 0.32 J

s sec 171 46 164 r

0.6 1.0 1.0 _

0.52

0.88

t

A,% d i f per p o i n t

0.53 0.39 0.44

_

_

The parameter v a l u e s o f SP 634 and SP 1381 a r e i n t h e range o f v a l u e s e x p e c t e d from d e g r a d a t i o n s t u d i e s on f i v e G o o d r i c h samples i n w h i c h the time t o a c h i e v e t h e maximum r a t e ( l / k ) i n c r e a s e d w i t h i n c r e a s i n g c h a i n l e n g t h o f t h e sample. Sample SP 917 i s c o m p l e t e l y out o f l i n e , g i v i n g k^, 1.73 x 10~ s e c " and k , 0.85 x 10" sec vs e x p e c t e d v a l u e s o f 0.88 x 10"" s e c " and 0.52 x 10~ sec" , respectively. On t h e b a s i s o f t h e p r e v i o u s d i s c u s s i o n s o f mechanism, t h e anomalous b e h a v i o r o f SP 917 can be u n d e r s t o o d i f t h a t sample, e i t h e r i n p r e p a r a t i o n o r i n subsequent h a n d l i n g , had s i g n i f i c a n t l y more p o t e n t i a l s t a r t i n g p o s i t i o n s p e r c h a i n . The f r a c t i o n s t a r t i n g p e r sec and t h e number of a c t u a l z i p s p e r c h a i n a r e s i g n i f i c a n t l y g r e a t e r than would be e x p e c t e d f o r t h a t c h a i n l e n g t h . A l t h o u g h no t e c h n i c a l i n f o r m a t i o n i s a v a i l a b l e concerning the s t a b i l i t y characz

3

1

3

- 1

z

3

1

3

1


20.

DANFORTH

295


t e r i s t i c s o f SP 917, i t would be e x p e c t e d t h a t t h e sample would be l e s s s t a b l e t h a n t h e o t h e r samples t h a t have been s t u d i e d . Thermal P r e t r e a t m e n t I n f l u e n c e s t h e S t a r t i n g C h a r a c t e r i s t i c s and t h e Degradation Pattern. Even though a l l PVC samples e x c e p t SP 917 demonstrate t h a t t h e r e i s a u n i f o r m dependence o f t h e d e g r a d a t i o n p a t t e r n on t h e c h a i n l e n g t h o f t h e sample, t h e r e i s a s i g n i f i c a n t i n f l u e n c e o f t h e t h e r m a l p r e t r e a t m e n t o f t h e sample on t h e d e g r a d a tion pattern. F i g u r e 6 shows a c o m p a r i s o n o f d e g r a d a t i o n p a t t e r n s f o r SP 1381 a f t e r t h e r m a l p r e t r e a t m e n t s a t 235°C o f 0, 2, and 3 minutes. Thermal p r e t r e a t m e n t seems d e f i n i t e l y t o i n c r e a s e t h e number of p o t e n t i a l s t a r t s p e r c h a i n and t h e number o f z i p c h a i n s a c t u a l l y started. Because t h e number o f z i p c h a i n s s t a r t e d i s i n c r e a s e d , t h e a v e r a g e l e n g t h o f a z i p c h a i n i s r e d u c e d , so k , t h e f r a c t i o n o f a chain unzipping per sec, i s increased.


z

The b e h a v i o r o f samples a f t e r p r e h e a t i n g a t 235°C i l l u s t r a t e s the problem t h a t one e n c o u n t e r s when r u n s a t d i f f e r e n t t e m p e r a t u r e s a r e compared. D u r i n g t h e i n i t i a l p e r i o d o f a r u n t h e b u l k o f t h e sample i s p r e h e a t e d a t t h e r u n t e m p e r a t u r e . As has been shown, t h e time, and presumably t h e t e m p e r a t u r e a t which t h e p r e h e a t i n g o c c u r s , i n f l u e n c e t h e d e g r a d a t i o n p a t t e r n o f t h e sample. Thus, even though r u n s a t d i f f e r e n t t e m p e r a t u r e s g i v e d e g r a d a t i o n p a t t e r n s t h a t c a n be p r e c i s e l y a c c o u n t e d f o r by t h e b e s t f i t parameters o f NSSK, t h e r e i s no a s s u r a n c e t h a t t h e p a r a m e t e r s a t t h e two d i f f e r e n t t e m p e r a t u r e s a r e d i r e c t l y comparable. T h i s problem was r e c o g n i z e d and has been more f u l l y d i s c u s s e d i n a p u b l i c a t i o n t h a t d e s c r i b e s t h e s p e c i a l p r e c a u t i o n s t h a t a r e neces

Polymer Stabilization and Degradation - ACS Publications - American

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