Polymer Characterization - American Chemical Society

13 Use of the Single Dynamic Temperature Scan Method in Differential Scanning Calorimetry for Quantitative Reaction Kinetics

Downloaded by UNIV LAVAL on July 12, 2014 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch013

THEODORE PROVDER, RICHARD M. HOLSWORTH, THOMAS H. GRENTZER, and SALLY A. KLINE Glidden Coatings and Resins, Division of SCM Corporation, Strongsville, OH 44136

Various reaction kinetics methodologies for differential scanning calorimetry (DSC) are reported and compared experimentally, utilizing the thermal decomposition of calcium oxalate monohydrate and of 2,2'-azobis(isobutyronitrile) (AIBN) as model systems, to demonstrate the reliability, efficiency, analysis speed, and simplicity of the single dynamic temperature scan method of Borchardt and Daniels. The DSC results for the activation energy of decomposition of AIBN by the Kissinger, Ozawa, and ASTM-E698 methods (all of which utilize numerous thermograms generated at various heating rates) were found to be more than 25% lower than the kinetic results reported by classical techniques (volumetric titration, UV spectroscopy, etc.), yet the single dynamic temperature scan method results were within 2% of the classical results. A comparison of isothermal reaction kinetics with single dynamic temperature scan reaction kinetics for the reaction of phenylglycidyl ether with 2-ethyl-4-methylimidazole indicated that the isothermal method grossly underestimated the total heat of reaction while providing lower values of activation energy and Arrhenius frequency factor than the single dynamic temperature scan method. The single dynamic temperature scan method also was used to provide quantitative reaction kinetics information for some chemical coatings systems (e.g., powder coatings, gel coat resins, and casket varnish). 0065-2393/83/0203-0233$06.25/0 © 1983 American Chemical Society

In Polymer Characterization; Craver, C.; Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

234

V

POLYMER CHARACTERIZATION

ARIOUS

METHODS

HAVE BEEN

REPORTED

for

determining

reaction


kinetics b y differential scanning colorimetry ( D S C ) . Isothermal re action kinetics require numerous thermograms over a range of r e a c t i o n t e m p e r a t u r e s . T h e O z a w a (J) a n d K i s s i n g e r (2) m e t h o d s u t i l i z e a n u m b e r of thermograms generated b y the use of different h e a t i n g rates. M e t h o d s for o b t a i n i n g r e a c t i o n k i n e t i c s i n f o r m a t i o n from a single differential scanning calorimetry/differential thermal analysis ( D S C / D T A ) temperature scan greatly decrease the t i m e nec e s s a r y for a n a l y s i s a n d h a v e b e e n r e p o r t e d p r e v i o u s l y ( 3 - 2 0 ) . I n t h i s study, w e c o m p a r e d some of these methodologies a n d a p p l i e d one of t h e m to t h e c h a r a c t e r i z a t i o n o f t h e r e a c t i o n k i n e t i c s o f m o d e l s y s t e m s and some coatings systems.

Methodologies M u l t i p l e D y n a m i c T e m p e r a t u r e Scans. A n equation was re p o r t e d (2) f o r o b t a i n i n g r e a c t i o n k i n e t i c s f r o m D T A b y s c a n n i n g a c h e m i c a l r e a c t i o n at d i f f e r e n t f i x e d h e a t i n g r a t e s . B y p l o t t i n g I n (φ/Τ ) v s . ( 1 / T p ) , w h e r e φ i s t h e h e a t i n g rate (K/s) a n d T i s t h e t e m p e r a t u r e at t h e p e a k o f t h e e x o t h e r m ( K ) , t h e a c t i v a t i o n e n e r g y ( E ) a n d A r r h e n i u s f r e q u e n c y f a c t o r (A) are d e t e r m i n e d f r o m t h e s l o p e a n d intercept, respectively. R e e d e t a l . (4) c o m p a r e d r e a c t i o n k i n e t i c s r e s u l t s for t h e d e c o m position of benzenediazonium chloride by conventional methods re p o r t e d p r e v i o u s l y [the D T A ( B o r c h a r d t - D a n i e l s ) m e t h o d (3) a n d t h e K i s s i n g e r a p p r o a c h (2)]. T h e r e s u l t s i n d i c a t e d t h a t t h e K i s s i n g e r a p p r o a c h p r o d u c e d k i n e t i c s results that w e r e 4 2 % l o w e r t h a n those o b t a i n e d b y o t h e r m e t h o d o l o g i e s . T h e u n d e r l y i n g e r r o r s t h a t a r e as sociated w i t h the K i s s i n g e r m e t h o d u s i n g D T A analysis also w e r e d e s c r i b e d (4). P r i m e (8) s h o w e d t h a t t h e a p p l i c a t i o n o f K i s s i n g e r ' s m e t h o d to t h e D S C c u r e o f e p o x y r e s i n s w a s i n b e t t e r a g r e e m e n t w i t h other results (isothermal D S C kinetics a n d dc conductivity) than the D T A a p p l i c a t i o n r e p o r t e d b y R e e d et a l . 2

ρ

p

A n o t h e r e q u a t i o n to d e t e r m i n e reaction k i n e t i c s parameters b y m u l t i p l e d y n a m i c D S C scans was r e p o r t e d b y O z a w a (I). B y s c a n n i n g t h e c h e m i c a l r e a c t i o n at d i f f e r e n t f i x e d h e a t i n g r a t e s a n d p l o t t i n g l o g φ v s . (1/T ), t h e e n e r g y o f a c t i v a t i o n a n d t h e A r r h e n i u s f r e q u e n c y f a c t o r can be d e t e r m i n e d from the slope a n d intercept, respectively. C o r r e c t i o n s for t h e m e a s u r e d p e a k t e m p e r a t u r e a n d t h e c a l c u l a t e d e n e r g y o f a c t i v a t i o n h a v e b e e n a p p l i e d to t h i s m e t h o d b y t h e A m e r i c a n S o c i e t y for T e s t i n g a n d M a t e r i a l s ( A S T M ) . T h e d e s c r i p t i o n o f this m e t h o d a n d its u s e c a n b e f o u n d i n A S T M E 6 9 8 - 7 9 (17). Single D y n a m i c Temperature Scan Approach IPrime (7,8)]. Be c a u s e t h e f r a c t i o n r e a c t e d [F(t,T)] i s a f u n c t i o n o f t i m e a n d t e m p e r a P


13.

PROVDER ET A L .

Quantitative

Reaction

235

Kinetics

t u r e i n a d y n a m i c D S C e x p e r i m e n t , t h e t o t a l d e r i v a t i v e dF(t,T)

must

b e e x p r e s s e d as a f u n c t i o n o f t i m e a n d t e m p e r a t u r e . dt T h e n t h e rate e x p r e s s i o n dF(t,T)/dt


dF(t,T)

(1)

is g i v e n b y

(dF(t,T)\

( dF(t,T)\

m

w h e r e t = t i m e (s); Τ = a b s o l u t e t e m p e r a t u r e ( K ) ; a n d φ = dT/dt ( K / s ) . U t i l i z i n g E q u a t i o n 2 a n d the A r r h e n i u s r e l a t i o n s h i p for the rate c o n s t a n t , P r i m e (7, 8) s h o w e d t h a t t h e e n e r g y o f a c t i v a t i o n , t h e A r r h e n i u s f r e q u e n c y factor, a n d the order o f the r e a c t i o n c a n b e c a l c u l a t e d f r o m o n e d y n a m i c D S C t e m p e r a t u r e s c a n f r o m E q u a t i o n s 3—5. In

dH(t,T)/dt L

(ΔΗ )Ζ

= I n A + {-1/RT

+ c l n [ l - F(t,T)]}E

(3)

C!llc

0

Ζ = 1 +

(E AT\ est

\

RT RT

22

[l-F(t,T)] η

= C E caie —

(dH(t,T)/dt)

(4)

I E cale

(5)

w h e r e t h e s y m b o l s u s e d i n t h e e q u a t i o n s a r e d e f i n e d h e r e a n d are i l l u s t r a t e d i n F i g u r e 1: dH(t, T)ldt = h e a t flow v a l u e (cal/g-s); Δ Η = total heat of r e a c t i o n (cal/g); A = A r r h e n i u s f r e q u e n c y factor ( s ) ; R = 0

- 1

TEMPERATURE Figure

1. Schematic

of an exothermic peak observed Prime's calculation.

by DSC


for

236


gas c o n s t a n t ( k c a l / m o l - d e g ) ; F(t,T) = fractional extent of reaction ( H / Δ Η ο ) ; ^caic c a l c u l a t e d e n e r g y of a c t i v a t i o n ( k c a l / m o l ) ; E t — e s t i mated energy of activation (kcal/mol); ΔΤ = difference b e t w e e n the i n s t a n t a n e o u s t e m p e r a t u r e a n d t h e i n i t i a l t e m p e r a t u r e ; F(t,T) = frac t i o n a l e x t e n t o f r e a c t i o n at t h e p e a k ; T = t e m p e r a t u r e at t h e p e a k ( K ) ; η = r e a c t i o n o r d e r ; a n d (dH(t,T)/dt) = h e a t f l o w v a l u e (cal/g-s) at t h e peak. I n P r i m e ' s m e t h o d , a v a l u e of E t is selected. T h e left side of E q u a t i o n 3 i s p l o t t e d v s . { - 1 / R T + c I n [1 - F ( t , T ) ] } , w h e r e E i i s t h e s l o p e a n d In A is the i n t e r c e p t . T h e v a l u e of E i c t h e n is u s e d i n E q u a t i o n s 3 a n d 4 for E . T h i s p r o c e d u r e is c o n t i n u e d u n t i l n o d i f f e r e n c e exists b e t w e e n E and E . Then E is u s e d to d e t e r m i n e η f r o m E q u a t i o n 5. —

e s

p

p

p

e s

c a

c

c a

est


c a l c

e s t

c a l c

P r i m e (8) s h o w e d t h a t t h i s m e t h o d p r o v i d e s c l o s e r a g r e e m e n t b e t w e e n i s o t h e r m a l a n d d y n a m i c scan D S C data for e p o x y r e s i n / aromatic amine reaction systems. Single D y n a m i c Temperature Scan A p p r o a c h [Borchardt and D a n i e l s (3)]. K i s s i n g e r (19), H i l l (20), a n d S i m m o n s a n d W e n d l a n d t (21 ) s h o w e d t h a t t h e t e r m [dF(t,T)/dT] i n E q u a t i o n 2 is a l w a y s zero. K i s s i n g e r argues that " F i x i n g t i m e fixes the p o s i t i o n o f a l l the p a r t i c l e s i n the s y s t e m . " T h u s , i f t i m e is h e l d constant t h e n F also m u s t b e c o n s t a n t . T h e rate e x p r e s s i o n t h e n b e c o m e s t

(6) T h e rate e x p r e s s i o n f o r t h e s i n g l e d y n a m i c t e m p e r a t u r e s c a n a p p r o a c h thus is d e s c r i b e d b y the i s o t h e r m a l k i n e t i c s e q u a t i o n s . T h e w o r k i n g equations consist of the general n o r d e r rate e q u a t i o n a n d t h e A r r h e n i u s e q u a t i o n a n d are a n a l o g o u s to t h e e q u a t i o n s p r o p o s e d b y B o r c h a r d t a n d D a n i e l s (3) f o r s t u d y i n g r e a c t i o n k i n e t i c s b y D T A . I n t h e p r e s e n t w o r k , a u t o c a t a l y t i c r e a c t i o n k i n e t i c s are not c o n s i d e r e d . T h e g e n e r a l rate e x p r e s s i o n i s t h

dF(t,T) dt

= Jfe(T) [l -

F(t,T)]

n

(7)

w h e r e F(t,T) = f r a c t i o n a l e x t e n t o f c o n v e r s i o n ; k(T) = rate c o n s t a n t f o r the reaction ( s ) ; η = reaction order; a n d Τ = temperature (K). T h e f r a c t i o n a l e x t e n t o f c o n v e r s i o n [F(t,T)] i s d e f i n e d as t h e r a t i o o f t h e p a r t i a l h e a t o f r e a c t i o n , at a g i v e n t i m e a n d t e m p e r a t u r e , [H(t,T)] to t h e t o t a l h e a t o f r e a c t i o n ( Δ Η ) . - 1

0

F(t,T)

= Η(ί,Τ)/ΔΗ

0

(8)

T h e f r a c t i o n a l e x t e n t o f c o n v e r s i o n r a n g e s f r o m 0 to 1.0 a n d is r e p r e s e n t e d i n F i g u r e 1.


13.

Quantitative

PROVDER ET A L .

Reaction

237

Kinetics

T h e rate c o n s t a n t , fc(T), c a n b e e x p r e s s e d i n t e r m s o f o b s e r v a b l e parameters obtained from the D S C experiment and, subsequently, c a n b e r e l a t e d to t h e e n e r g y o f a c t i v a t i o n ( E ) a n d t h e f r e q u e n c y f a c t o r (A) o f t h e A r r h e n i u s e q u a t i o n . S u b s t i t u t i n g E q u a t i o n 8 i n t o E q u a t i o n 7 a n d s o l v i n g for t h e rate c o n s t a n t k(T) i n l o g a r i t h m i c f o r m y i e l d s t h e following expression:

w h e r e dH H(t,T)

(t,T)ldt

j

dH(t,T)\

In Jfc(T) = In

dt

[àH -H(t,T)]

n

0

//

ΔΗ

0

(9)

η _ 1

= heat f l o w i n t o a n d out of the s a m p l e (cal/g-s);

= p a r t i a l heat of r e a c t i o n (cal/g); Δ Η

0

= total heat of reaction


(cal/g); a n d η = r e a c t i o n order. A l l o f t h e q u a n t i t i e s o n t h e r i g h t s i d e o f E q u a t i o n 9 are o b s e r v a b l e p a r a m e t e r s e x c e p t for t h e r e a c t i o n o r d e r , n . S u b s t i t u t i n g t h e A r r h e n i u s e x p r e s s i o n s h o w n i n E q u a t i o n 10 i n t o E q u a t i o n 9 y i e l d s t h e w o r k i n g E q u a t i o n 11.

hi HT) = In A ~

(10)

w h e r e A = A r r h e n i u s f r e q u e n c y factor ( s ) ; Ε = a c t i v a t i o n e n e r g y - 1

( k c a l / m o l ) ; a n d R = gas c o n s t a n t ( k c a l / m o l - d e g ) . In A

RT

= In 7dH(t,T)\ j

[AHp -

H(t,T)] ] n

(Π)

Λ dt ) I A H T h e i s o t h e r m a l f r a c t i o n a l e x t e n t o f c o n v e r s i o n as a f u n c t i o n o f t i m e (t) o r t e m p e r a t u r e (T) i s o b t a i n e d b y i n t e g r a t i n g t h e rate e x p r e s s i o n to y i e l d the f o l l o w i n g expressions: W

0

= 1 - [(n -

F(t,T)

l)k(T)t

1

+ l] ' -" 1

1

(12)

F o r the case w h e r e η = 1 F(t,T)

= 1 - e~

k(T)t

(13)

I n this chapter the basic methodology of Borchardt a n d D a n i e l s , de scribed earlier, w i l l be used. Experimental T h e d u Pont 990 t h e r m a l analyzer programmer/recorder a n d the 910 D S C c e l l m o d u l e were used to obtain the e x p e r i m e n t a l results. T h e sample atmo sphere was either nitrogen or compressed air at a flow rate of 50 m L / m i n . T h e sample weight was restricted to the 0.5-m g range. H e r m e t i c a l l y sealed sample pans were used for reactions e x h i b i t i n g a w e i g h t loss. Data

Analysis

Methods

T w o data a n a l y s i s m e t h o d s w e r e u s e d i n t h i s w o r k to o b t a i n η, E , a n d A . I n the first m e t h o d , the t h e r m o g r a m s w e r e d i g i t i z e d m a n u a l l y



238


a n d t h e d a t a a n a l y s i s m e t h o d o f W i l l a r d (6) w a s u s e d . I n t h i s m e t h o d , a series of A r r h e n i u s plots is g e n e r a t e d b y v a r y i n g the o r d e r o f the r e a c t i o n , n , i n E q u a t i o n 9, f r o m 0.2 t h r o u g h 3.0 i n i n c r e m e n t s o f 0 . 0 5 . T h e best v a l u e of the r e a c t i o n order is o b t a i n e d b y s e l e c t i n g the reac tion order g i v i n g the highest correlation coefficient of the linear l e a s t - s q u a r e s fit o f t h e I n k(T) v s . 1/T c u r v e . T h e v a l u e for t h e r e a c t i o n o r d e r t h e n i s s u b s t i t u t e d i n t o E q u a t i o n 11 to o b t a i n t h e a c t i v a t i o n e n e r g y a n d t h e A r r h e n i u s f r e q u e n c y factor. D u r i n g the c o u r s e o f t h i s work, the data a c q u i s i t i o n of the D S C was automated b y interfacing the i n s t r u m e n t to a m i c r o c o m p u t e r . D a t a t h e n are t r a n s f e r r e d o v e r a s e r i a l l i n e to a m i n i c o m p u t e r s y s t e m f o r s t o r a g e , a n a l y s i s , r e p o r t g e n eration, a n d plotting. D e t a i l s of the m i n i c o m p u t e r - m i c r o c o m p u t e r s y s t e m a n d its o r g a n i z a t i o n a n d o p e r a t i o n w e r e r e p o r t e d e l s e w h e r e (22, 2 3 ) . A n a l t e r n a t e d a t a a n a l y s i s p r o c e d u r e w a s u s e d w i t h t h e a u t o m a t e d D S C s y s t e m . R e w r i t i n g E q u a t i o n 11 as In

1 iH \ 0

(dH(t,T)\ dt

J

= I n A --^7- + η In RT

AHp

H(t,T)

ΔΗ

(14)

0

w h i c h is o f the f o r m Ζ = a + bx + cy

(15)

e n a b l e s t h e p a r a m e t e r s η , E , a n d A to b e o b t a i n e d s i m u l t a n e o u s l y b y a m u l t i p l e regression t e c h n i q u e . D e t a i l s of the automated t h e r m a l a n a l y s i s s y s t e m w e r e r e p o r t e d e l s e w h e r e (24). B o t h o f t h e j u s t d e scribed data analysis methods p r o d u c e calculated results w i t h c o m p a r a b l e p r e c i s i o n a l l o w i n g for d i f f e r e n c e s i n the n u m b e r o f data p o i n t s u s e d b e t w e e n the m a n u a l a n d the automated data acquisition methods. Results Model

and Systems.

Discussion D E C O M P O S I T I O N OF

CALCIUM

OXALATE

MONOHY

DRATE. F i g u r e 2 s h o w s the D S C trace for the d e c o m p o s i t i o n of c a l c i u m oxalate m o n o h y d r a t e . T h e e n d o t h e r m i c peak, b e t w e e n 125 a n d 225 °C, represents the d e h y d r a t i o n of c a l c i u m oxalate m o n o h y d r a t e . T h e exothermic peak, b e t w e e n 425 a n d 525 °C, represents the d e c o m p o s i t i o n o f c a l c i u m oxalate to c a l c i u m carbonate. T h e d e c o m p o s i t i o n o f c a l c i u m oxalate to c a l c i u m carbonate w a s f o u n d to b e i n d e p e n d e n t o f h e a t i n g rate a n d s a m p l e m a s s b y N a i r a n d N i n a n (25). T h e r e a c t i o n k i n e t i c s data for the f o r m a t i o n o f c a l c i u m carbonate f r o m the s i n g l e d y n a m i c temperature scan D S C m e t h o d along w i t h the kinetics data o b t a i n e d b y t h e r m o g r a v i m e t r i c analysis u n d e r the same e x p e r i m e n t a l c o n d i t i o n s as t h a t o f N a i r a n d N i n a n (25) a r e s h o w n i n T a b l e I . T h e r e sults o b t a i n e d f r o m these t w o t e c h n i q u e s are i n g o o d a g r e e m e n t . DECOMPOSITION OF A I B N . T h e thermal decomposition kinetics of 2,2'-azobis(isobutyronitrile) ( A I B N ) i n di-n-butyl phthalate were de t e r m i n e d b y the single d y n a m i c D S C temperature scan m e t h o d . T h e


13.

PROVDER ET A L .

Quantitative

Reaction

Kinetics

239

ο CO CO Ο

Ε

Χ


100

200 300 TEMPERATURE

400 (°C)

500

Figure 2. DSC thermogram for the decomposition of calcium oxalate monohydrate. Operating conditions: atmosphere, air; flow rate, 50 mLI min SCFH; and scan rate, 15 °C/min. k i n e t i c p a r a m e t e r s E, A, a n d η a r e r e p o r t e d i n T a b l e I I at s e v e r a l h e a t i n g rates a l o n g w i t h t h e l i t e r a t u r e v a l u e d e t e r m i n e d b y V a n H o o k a n d T o b o l s k y (28), w h o u s e d rate c o n s t a n t d a t a d e t e r m i n e d b y v o l u m e t r i c t i t r a t i o n (29-34), U V s p e c t r o s c o p y (35), a n d o t h e r c l a s s i c a l t e c h n i q u e s to c o n s t r u c t a c o m p o s i t e A r r h e n i u s p l o t . V e r y g o o d a g r e e m e n t b e t w e e n the single d y n a m i c temperature scan D S C results a n d those o b t a i n e d b y c l a s s i c a l m e t h o d s is s h o w n i n T a b l e I I . T a b l e I I I s h o w s t h e r m a l d e c o m p o s i t i o n k i n e t i c s parameters for A I B N c a l c u lated b y the m u l t i p l e d y n a m i c scan approaches of O z a w a , K i s s i n g e r , a n d t h e m o d i f i e d O z a w a m e t h o d as d e s c r i b e d i n t h e A S T M m e t h o d E—698. F o r comparison purposes, the data of V a n H o o k a n d T o b o l s k y a n d the results from the single d y n a m i c temperature scan D S C m e t h o d also are s h o w n i n T a b l e I I I . T h e a c t i v a t i o n e n e r g y v a l u e s o b t a i n e d b y t h e m u l t i p l e d y n a m i c s c a n m e t h o d s are m o r e t h a n 2 5 % l o w e r t h a n that r e p o r t e d b y V a n H o o k a n d T o b o l s k y . O n the other T a b l e I. T h e r m a l D e c o m p o s i t i o n K i n e t i c s of C a l c i u m Oxalate Monohydrate in a Nitrogen Atmosphere TGA

a

Parameter E n e r g y of activation (kcal/mol) A r r h e n i u s f r e q u e n c y factor O r d e r of reaction Correlation coefficient a 6 c

0

b

56.4

56.6 1.76 x 1 0 0.60 0.997

Equation

Equation

DSC

1 4

1.68 x 1 0 0.50 0.996

57.9 1 4

5.42 x

10

0.996

Ref. 25. C o a t s — R e d f e r n e q u a t i o n u s e d to analyze the data, Ref. 26. M a c C a l l u m — T a n n e r e q u a t i o n u s e d to analyze the data, Ref. 27.


1 4

240



T a b l e I I . T h e r m a l D e c o m p o s i t i o n K i n e t i c s of A I B N b y the S i n g l e D y n a m i c Temperature Scan D S C M e t h o d Scan rate ("C/min)

η

50 20 15 10 5 Average value Tobolsky (Ref. 28)

0.95 1.05 1.00 0.90 0.85 0.95 1.00

In A (s- )

Ε (kcal/mol)

1

32.3 31.9 32.6 29.5 31.1 31.4 30.8

36.3 36.4 35.0 33.4 35.7 35.4 35.0

h a n d , the single d y n a m i c temperature scan D S C m e t h o d gave an acti v a t i o n e n e r g y v a l u e that a g r e e d to w i t h i n 2 % of t h e c l a s s i c a l data reported by V a n Hook and Tobolsky. Isothermal D S C K i n e t i c s vs. Single D y n a m i c Temperature Scan D S C K i n e t i c s . I s o t h e r m a l D S C k i n e t i c s w e r e s t u d i e d for t h e r e a c t i o n o f p h e n y l g l y c i d y l e t h e r a n d 2 - e t h y l - 4 - m e t h y l i m i d a z o l e at a m o l a r r a t i o of 2:1, respectively. F i g u r e s 3 through 5 s h o w the isothermal heat flow response of the e m p t y sample pans a n d the sample pans c o n t a i n i n g t h e r e a c t i o n m i x t u r e at t h r e e d i f f e r e n t i s o t h e r m a l t e m p e r a t u r e set tings. T h e f o l l o w i n g p r o c e d u r e m u s t b e u s e d for i s o t h e r m a l a n a l y s i s o n t h e d u P o n t 9 9 0 t h e r m a l a n a l y z e r . E m p t y s a m p l e p a n s are p l a c e d i n t h e D S C c e l l ; t h e h e a t f l o w r e s p o n s e i s r e c o r d e d as a f u n c t i o n o f t i m e . As s h o w n i n F i g u r e s 3 - 5 , the sample pans absorb energy a n d then, after a p p r o x i m a t e l y a 1 - m i n t i m e s p a n , e q u i l i b r a t e t o a c o n s t a n t h e a t flow [dH (t,T)/dT] v a l u e . T h e e m p t y s a m p l e p a n t h e n i s r e m o v e d f r o m the D S C c e l l a n d the reactants are p l a c e d i n the s a m p l e p a n . T h e D S C c e l l is a l l o w e d to e q u i l i b r a t e to t h e i s o t h e r m a l t e m p e r a t u r e s e t t i n g .

Table III. T h e r m a l Decomposition Kinetics of A I B N : C o m p a r i s o n of D S C M e t h o d s W i t h Classical D a t a Source Ozawa Kissinger ASTM-E698 Tobolsky

Ε (kcal/mol)

In A (s' ) 1

M u l t i p l e d y n a m i c scan D S C methods" 22.6 22.2 22.2 C l a s s i c a l data 30.8 S i n g l e d y n a m i c scan D S C m e t h o d 31.4

28.6 27.9 21.2 35.0

6

35.4

° The reaction order is assumed to be η = 1. The reaction order was found to be η = 0.95. b



13.

PROVDER E T A L .

Quantitative

Reaction

241

Kinetics

10 15 TIME (min) Figure 3. Isothermal DSC thermogram at 90 °C for the reaction of phenyl glycidyl ether with 2-ethyl-4-methylimidazole in a 2:1 molar ratio. Operating conditions: y sensitivity, 0.2 mcal/s-in.; hermetically sealed pan.

ο φ co RESPONSE OF REACTION

CO Ο

MIXTURE PLUS PANS

Ε

I T3

RESPONSE OF EMPTY

4-

5

PANS

4-

10 TIME (min)

15

20

Figure 4. Isothermal DSC thermogram at 100 °C for the reaction of phenyl glycidyl ether with 2-ethyl-4-methylimidazole in a 2:1 molar ratio. Operating conditions: same as in Figure 3.



242


TIME

(min)

Figure 5. Isothermal DSC thermogram at 110 °C for the reaction of phenyl glycidyl ether with 2-ethyl-4-methylimidazole in a 2:1 molar ratio. Operating conditions: same as in Figure 3. T h e s a m p l e p a n s c o n t a i n i n g t h e r e a c t a n t s are p l a c e d i n t o t h e D S C c e l l . T h e h e a t flow is m o n i t o r e d as a f u n c t i o n o f t i m e . A t t h e 9 0 ° C i s o t h e r m a l t e m p e r a t u r e s e t t i n g , as s h o w n i n F i g u r e 3, the sample pans absorb energy, e q u i l i b r a t e , the reaction goes t h r o u g h a n i n d u c t i o n p e r i o d , a n d t h e n the r e a c t i o n b e g i n s . F o r the 100 °C i s o t h e r m a l t e m p e r a t u r e s e t t i n g , as s h o w n i n F i g u r e 4, a g a i n t h e s a m p l e p a n s a b s o r b e n e r g y , e q u i l i b r a t e , b u t n o w t h e r e a c t i o n b e g i n s at t h e same t i m e that the s a m p l e pans are e q u i l i b r a t i n g . F o r t h e 110 °C i s o t h e r m a l t e m p e r a t u r e s e t t i n g , as s h o w n i n F i g u r e 5, t h e r e a c t i o n i s t a k i n g p l a c e b e f o r e t h e s a m p l e pans h a v e c o m e to t h e r m a l e q u i l i b r i u m . T h e s e results i n d i c a t e that part of the r e a c t i o n e x o t h e r m is not b e i n g m o n i t o r e d at t h e h i g h e r i s o t h e r m a l t e m p e r a t u r e s e t t i n g . T h i s c o n c l u s i o n i s c o n f i r m e d b y t h e c a l c u l a t e d h e a t s o f r e a c t i o n at t h r e e different isothermal temperature settings, s h o w n i n T a b l e I V . A s the i s o t h e r m a l t e m p e r a t u r e s e t t i n g is i n c r e a s e d f r o m 80 to 120 °C, t h e heat o f r e a c t i o n ( Δ Η ) d e c r e a s e s f r o m 105.5 to 69.4 c a l / g . T h e s a m p l e s that were a n a l y z e d isothermally on the D S C t h e n were m o n i t o r e d b y D S C at t h e f i x e d h e a t i n g rate o f 15 ° C / m i n f r o m 2 5 - 2 0 0 ° C as s h o w n i n F i g u r e 6. N e x t , t h e s a m p l e s w e r e c o o l e d q u i c k l y to 2 5 ° C a n d t h e n r e - s c a n n e d at 15 ° C / m i n t o 2 0 0 ° C as s h o w n i n F i g u r e 7. A n e x o t h e r m i c p e a k i s o b s e r v e d i n F i g u r e 6 i n t h e v i c i n i t y o f 150 ° C . T h i s p e a k b e c o m e s m o r e p r o n o u n c e d as t h e i s o t h e r m a l t e m p e r a t u r e s e t t i n g i s l o w e r e d ; i t p r o b a b l y i s d u e to t h e r e m a i n i n g u n r e a c t e d m a t e r i a l f r o m the i s o t h e r m a l b a k e s c h e d u l e . F i g u r e 7 i n d i c a t e s that the r e a c t i o n is t a k e n t o c o m p l e t i o n b y r e - s c a n n i n g t h e t e m p e r a t u r e r a n g e to 2 0 0 ° C . 0


13.

PROVDER ET AL.

Quantitative

Reaction

243

Kinetics

T a b l e I V . I s o t h e r m a l H e a t s of R e a c t i o n for the R e a c t i o n of Phenyl Glycidyl Ether with 2-Ethyl-4-methylimidazole i n a 2:1 M o l a r R a t i o ΔΗ (cal/g)

Temperature (°C)

0


80 100 120

105.5 99.1 69.4

T h e s e results indicate that i f the i s o t h e r m a l reaction temperature is t o o l o w , t h e r e a c t i o n v e r y p o s s i b l y w i l l n o t p r o c e e d to c o m p l e t i o n i n the time frame of the experiment because the reacting p o l y m e r w i l l v i t r i f y b e f o r e t h e r e a c t i o n i s c o m p l e t e d at i s o t h e r m a l r e a c t i o n t e m p e r atures b e l o w the glass t r a n s i t i o n t e m p e r a t u r e of the f u l l y c u r e d p o l y m e r . T h e r e f o r e , the o b s e r v e d heat of r e a c t i o n w i l l b e less t h a n that for t h e f u l l y c u r e d s y s t e m . I f t h e i s o t h e r m a l r e a c t i o n t e m p e r a t u r e is set t o o h i g h , t h e r e a c t i o n w i l l b e g i n b e f o r e t h e s a m p l e c o m e s to t e m p e r a t u r e e q u i l i b r i u m , a l t h o u g h t h e r e a c t i o n m a y go to c o m p l e t i o n . I n t h i s case, the observed heat of reaction w i l l be underestimated because the i n i t i a l part of the r e a c t i o n e x o t h e r m is not b e i n g m o n i t o r e d . W i d m a n (36) a n d S o u r o u r a n d K a m a l (37) p r o v i d e m e t h o d s to e s t i m a t e t h e amount of heat liberated d u r i n g the initial heat-up portion of the isothermal D S C experiment. H o w e v e r , these correction methods a d d c o m p l e x i t y , a n d c o n s i d e r a b l e a d d i t i o n a l e x p e r i m e n t a l t i m e is r e q u i r e d to d e t e r m i n e the total heat of r e a c t i o n . T h e s i n g l e d y n a m i c D S C scan

u 50

1

1

100 150 TEMPERATURE (°C)

1—ι 200

Figure 6. DSC thermograms at 15 °C/min scan rate of reaction tures of phenyl glycidyl ether with 2-ethyl-4-methylimidazole isothermal DSC scans.


mix after

244


Ο Ο CO

73

ο Ε

Χ "Ό


100 150 TEMPERATURE (°C) Figure 7. DSC thermograms of second consecutive dynamic scan at 15 °C/min of reaction mixtures of phenyl glycidyl ether with 2-ethyl-4methylimidazole after isothermal DSC scans. m e t h o d provides more accurate values of the total heat of reaction i n m u c h less t i m e than i s o t h e r m a l D S C methods. T a b l e V contains the results of the single a n d m u l t i p l e d y n a m i c t e m p e r a t u r e scan D S C m e t h o d s , a n d the i s o t h e r m a l m e t h o d for o u r w o r k a n d is c o m p a r e d to t h e i s o t h e r m a l a n d s i n g l e d y n a m i c t e m p e r a t u r e s c a n D S C m e t h o d s o f B a r t o n a n d S h e p h e r d (13). B a r t o n a n d S h e p h e r d a s s u m e d η = 1 t h r o u g h o u t t h e i r w o r k . I n t h i s w o r k for t h e isothermal calculations a n d m u l t i p l e d y n a m i c temperature scan D S C m e t h o d s , w e a l s o a s s u m e d t h a t η = 1. H o w e v e r , i n t h i s w o r k f o r t h e s i n g l e d y n a m i c t e m p e r a t u r e s c a n D S C m e t h o d , η w a s a l l o w e d to v a r y . T h e i s o t h e r m a l results o n t h i s s y s t e m are i n e x c e l l e n t a g r e e m e n t w i t h t h a t o f B a r t o n a n d S h e p h e r d (13). B o t h sets o f d a t a i n d i c a t e t h a t h i g h e r a c t i v a t i o n e n e r g i e s a n d h i g h e r A r r h e n i u s f r e q u e n c y factors a r e obtained from the single d y n a m i c temperature scan D S C m e t h o d than o b t a i n e d from i s o t h e r m a l or m u l t i p l e d y n a m i c temperature scan D S C m e t h o d s . T h e g o o d n e s s o f fit o f t h e data for B a r t o n a n d S h e p h e r d a n d for o u r d a t a to t h e r e s p e c t i v e m o d e l s is o n t h e s a m e o r d e r o f m a g n i t u d e , w i t h c o r r e l a t i o n coefficients greater t h a n 0.998 for the i s o thermal a n d single d y n a m i c temperature scan D S C methods. Barton a n d S h e p h e r d also r e c o g n i z e d that the reaction m a y be o c c u r r i n g b e f o r e t h e s a m p l e c o m e s to t e m p e r a t u r e e q u i l i b r i u m i n t h e i s o t h e r m a l m e t h o d . I n t h e d y n a m i c t e m p e r a t u r e s c a n m o d e , t h e s c a n i s s t a r t e d at r e l a t i v e l y l o w t e m p e r a t u r e s , c o m p a r e d to r e a c t i o n t e m p e r a t u r e s , so t h a t t h e i n s t r u m e n t i s i n t e m p e r a t u r e e q u i l i b r i u m at t h e start o f t h e reaction. W i t h i n the t i m e frame of the d y n a m i c temperature scan ex p e r i m e n t , t h e r e a c t i o n w i l l g o to c o m p l e t i o n . A s a l r e a d y d i s c u s s e d ,


13.

PROVDER ET A L .

Quantitative

Reaction

245

Kinetics


t h i s b e h a v i o r i s n o t t h e c a s e i n t h e i s o t h e r m a l m o d e at t e m p e r a t u r e s w e l l b e l o w the glass t r a n s i t i o n t e m p e r a t u r e of the f u l l y c u r e d p o l y m e r because of sample vitrification. B a r t o n a n d S h e p h e r d (13) a t t e m p t e d to r e c o n c i l e t h e d i s c r e p a n c y b e t w e e n t h e i s o t h e r m a l a n d d y n a m i c d a t a t h r o u g h P r i m e ' s (7, 8) m e t h o d of c o r r e c t i o n . H o w e v e r , P r i m e ' s c o r r e c t i o n p r o c e d u r e is of d o u b t f u l v a l i d i t y b a s e d o n t h e a r g u m e n t s o f K i s s i n g e r (19), H i l l ( 2 0 ) , a n d S i m m o n s a n d W e n d l a n t (21). T h e differences i n activation energy and A r r h e n i u s frequency factor o b t a i n e d b y B a r t o n a n d S h e p h e r d a n d b y o u r g r o u p u s i n g the s i n g l e d y n a m i c t e m p e r a t u r e s c a n D S C m e t h o d as s h o w n i n T a b l e V at first was q u i t e p u z z l i n g . H o w e v e r , D S C r e a c t i o n k i n e t i c s a n a l y s i s o f t h e r e a c t i o n m i x t u r e p r e p a r e d a n d r u n w i t h i n 0.5 t o 2 h y i e l d e d d i f f e r e n t v a l u e s o f E, A, a n d η c o m p a r e d to t h e r e a c t i o n m i x t u r e a g e d at r o o m t e m p e r a t u r e f o r 2 4 h . O u r r e s u l t s for t h e r e a c t i o n m i x t u r e a g e d at r o o m t e m p e r a t u r e for 2 4 h a g r e e d q u i t e w e l l w i t h t h o s e o f B a r t o n a n d S h e p h e r d . W e do not k n o w h o w soon B a r t o n a n d S h e p h e r d ran t h e i r D S C k i n e t i c s a n a l y s i s after t h e r e a c t i o n m i x t u r e w a s p r e p a r e d . H o w ever, our D S C results i n d i c a t e that the c h e m i c a l reaction was g r a d u a l l y a d v a n c i n g at r o o m t e m p e r a t u r e as a f u n c t i o n o f t i m e . T a b l e V . C o m p a r i s o n of Isothermal D S C K i n e t i c s w i t h Single D y n a m i c T e m p e r a t u r e S c a n D S C K i n e t i c s for the R e a c t i o n o f Phenyl Glycidyl Ether with 2-Ethyl-4-methylimidazole Scan Rate (°C/min)

Ε (kcal/mol)

In A (s~*)

η

Isothermal" This work 20.0 22.3 1.0 R e f . 13 19.6 21.7 1.0 M u l t i p l e D y n a m i c T e m p e r a t u r e S c a n D S C M e t h o d (this w o r k ) Ozawa 14.5 22.1 1.0 Kissinger 16.0 20.8 1.0 ASTM-E698 16.1 20.9 1.0 S i n g l e D y n a m i c T e m p e r a t u r e S c a n D S C M e t h o d (this w o r k ) F r e s h R e a c t i o n M i x t u r e (this w o r k ) 10 27.0 31.7 0.98 15 27.2 31.9 1.01 20 28.7 33.5 0.98 R e a c t i o n M i x t u r e A g e d 2 4 h at R o o m T e m p e r a t u r e (this w o r k ) 15 23.7 27.4 1.02 20 23.7 27.3 0.97 R e f . 13° 20 23.8 26.7 1.0 6

c

6

6

a 6 c

Reaction order η = 1.0 is assumed. Reaction order η is allowed to vary. Reaction mixture prepared and run on D S C within 0.5 to 2 h.


a



246

T h i s hypothesis was confirmed by h i g h performance gel permeation chromatography ( H P G P C ) analysis of the i n d i v i d u a l reactants, of t h e r e a c t i o n m i x t u r e w i t h i n 0.5 h o f p r e p a r a t i o n , o f t h e r e a c t i o n m i x t u r e a g e d at r o o m t e m p e r a t u r e f o r 2 4 h , a n d o f t h e r e a c t i o n m i x t u r e a g e d at r o o m t e m p e r a t u r e f o r 10 d a y s . D e t a i l s o f t h e H P G P C m e t h o d o l o g y w e r e d e s c r i b e d e l s e w h e r e (38). F i g u r e 8 c o n f i r m s t h a t t h e r e a c t i o n m i x t u r e s l o w l y r e a c t s at r o o m t e m p e r a t u r e as a f u n c t i o n o f t i m e b y the b u i l d u p o f h i g h e r m o l e c u l a r w e i g h t c o m p o n e n t s . E v e n for t h e r e a c t i o n m i x t u r e p r e p a r e d a n d a n a l y z e d w i t h i n 0.5 h o f p r e p a r a t i o n , t h e r e a c t i o n m i x t u r e i s a l r e a d y a d v a n c i n g , as e v i d e n c e d b y t h e s m a l l p e a k at 3 1 . 2 m L . A f t e r 2 4 h o f a g i n g at r o o m t e m p e r a t u r e , t h e intensity of this peak increased significantly a n d another peak app e a r e d at 2 9 . 5 m L . A f t e r 10 d a y s o f a g i n g at r o o m t e m p e r a t u r e , a d d i t i o n a l h i g h e r m o l e c u l a r w e i g h t p e a k s appear. T h u s , for the p h e n y l glycidyl ether/2-ethyl-4-methylimidazole reaction, sample prepara-

I

38

«

I 34

I 30

I 26

RETENTION VOLUME (ml) MOLECULAR WEIGHT

•

Figure 8. Molecular weight distribution changes occurring at room temperature as a function of time for the reaction mixture of phenyl glycidyl ether with 2-ethyl-4-meihy Imidazole in a 2:1 molar ratio.



13.

PROVDER ET A L .

Quantitative

110 Figure

9. Rate constant

Reaction

Kinetics

247

130 150 170 190 210 TEMPERATURE (°C) vs. temperature formulations.

profile

for powder

coating

t i o n t i m e must b e m i n i m i z e d to a v o i d i n a d v e r t e n t l y a d v a n c i n g the r e action m i x t u r e . I n this w o r k a n d i n that o f B a r t o n a n d S h e p h e r d ( 1 3 ) , t h e a c t i v a t i o n e n e r g i e s a n d A r r h e n i u s f r e q u e n c y factors o b t a i n e d f r o m the single d y n a m i c temperature scan D S C m e t h o d are h i g h e r t h a n those o b t a i n e d from the i s o t h e r m a l m e t h o d . T h i s result m a y b e d u e to a change i n reaction m e c h a n i s m i n going from a n isothermal to a d y namic heating mode. Coatings Systems. P O W D E R C O A T I N G S . T h e cure kinetics for e p o x y polyester p o w d e r coatings w e r e d e s i r e d to m e e t stringent customer bake-time/temperature specifications. T h e p o w d e r coating is a p p l i e d t o m e t a l t u b i n g t h a t i s h e a t e d i n d u c t i v e l y . T h e c o a t i n g i s c u r e d at h i g h t e m p e r a t u r e s f o r s h o r t t i m e p e r i o d s ( < 5 s). F o r m u l a t i o n m o d i f i c a t i o n s of catalyst type a n d l e v e l w e r e r e q u i r e d to m a t c h t h e reactivity o f a standard sample. T h e reactivity of the p o w d e r coatings c o u l d not b e d e t e r m i n e d b y t h e p e l l e t f l o w t e c h n i q u e ( 3 9 ) d u e to t h e e x t r e m e l y fast b a k e s c h e d u l e . T h e s i n g l e d y n a m i c t e m p e r a t u r e s c a n r e a c t i o n k i n e t i c s m e t h o d w a s u s e d to d e t e r m i n e cure k i n e t i c s for t h e p o w d e r c o a t i n g s a m p l e s . T h e rate c o n s t a n t v s . t e m p e r a t u r e p r o f i l e s a r e s h o w n in F i g u r e 9 . T h e percent c o n v e r s i o n profiles for a n u m b e r o f p o w d e r c o a t i n g f o r m u l a t i o n s w i t h i n t h e 5-s c u r e s p a n at a 2 2 0 ° C b a k e t e m perature are s h o w n i n F i g u r e 1 0 . B y c o m p a r i n g the c o n v e r s i o n c u r v e s , cost effective formulations w e r e a c h i e v e d w i t h regard to t h e type a n d

ι ^"iCilcnr. Chsrafcal fori t ; Library ms i8«i st if. % uteshii|toii 0 . C . 2 0 0 3 S In Polymer Characterization; Craver, C.; Advances in Chemistry; American Chemical Society: Washington, DC, 1983. t

248



100

l e v e l o f catalyst r e q u i r e d to generate t h e d e s i r e d c u r e rate r e s p o n s e . I n the case s h o w n i n F i g u r e 1 0 , S a m p l e 3 c a m e closest to m a t c h i n g the standard. G E L COAT SYSTEM. G e l coats are p r o t e c t i v e / d e c o r a t i v e c o a t i n g s u s e d i n sanitary a n d m a r i n e applications. T h e gel coat is a n i n - m o l d i n tegral part of the product. T h e g e l coat system a l o n g w i t h catalyst a n d p r o m o t e r is s p r a y e d i n t o a m o l d . T h e g e l coat u n d e r g o e s f r e e - r a d i c a l c u r e at a m b i e n t t e m p e r a t u r e u n t i l a t a c k - f r e e s u r f a c e is o b t a i n e d . T h e n , a fiberglass m a t is p l a c e d o n the g e l coat a n d the s y s t e m is r e i n f o r c e d b y a b a c k - u p r e s i n . I f t h e fiberglass m a t i s a p p l i e d b e f o r e t h e g e l c o a t r e a c h e s a t a c k - f r e e state, t h e g e l c o a t c o u l d p u l l a w a y f r o m t h e m o l d a n d p r o d u c e a n i r r e g u l a r s u r f a c e . T h e r e f o r e , i t i s d e s i r a b l e to k n o w t h e c u r e k i n e t i c s o f t h e g e l c o a t s y s t e m at a v a r i e t y o f a p p l i c a t i o n t e m p e r atures. T h e A r r h e n i u s plot o b t a i n e d from the single d y n a m i c t e m p e r ature scan m e t h o d for the c u r i n g o f t h e g e l coat s y s t e m is s h o w n i n F i g u r e 1 1 . T h e c u r i n g r e a c t i o n is g o v e r n e d b y three different regions. H o w e v e r , b e c a u s e t h e g e l c o a t s y s t e m i s a p p l i e d a n d c u r e d at r o o m t e m p e r a t u r e , the i n i t i a l k i n e t i c s o f the s y s t e m is d e s c r i b e d b y t h e l o w temperature region of the A r r h e n i u s plot. Therefore, the raw D S C t h e r m o g r a m w a s a n a l y z e d o n l y u p to 6 5 °C b y t h e s i n g l e d y n a m i c t e m p e r a t u r e s c a n r e a c t i o n k i n e t i c s m e t h o d . T h e c o n v e r s i o n c u r v e s at f o u r d i f f e r e n t a p p l i c a t i o n t e m p e r a t u r e s are s h o w n i n F i g u r e 1 2 . T h e t i m e r e q u i r e d to p r o d u c e a t a c k - f r e e g e l c o a t s u r f a c e at 2 2 . 5 ° C i s s h o w n i n T a b l e V I . T h e p e r c e n t c u r e c o r r e s p o n d i n g to a t a c k - f r e e g e l c o a t s u r f a c e w a s i d e n t i f i e d b y r e l a t i n g p h y s i c a l m e a s u r e m e n t s at 2 2 . 5


Quantitative

Reaction

Kinetics

249


PROVDER ET A L .

Figure 12. Conversion

curves for a gel coat system at a range of cation temperatures.


appli-

250


Table V I . Reaction Kinetics for G e l Coat System Temperature (°C)

Percent

Time for Tack-free (min)

Conversion

Point

From Physical Measurements 22.5

4 5

25.0

3 0


F r o m Single D y n a m i c Temperature Scan D S C M e t h o d 20.0

19.7

61

22.5

19.7

4 5

25.0

19.7

3 3

30.0

19.7

19

° C to the 2 2 . 5 ° C D S C c o n v e r s i o n curve i n F i g u r e 1 2 . T h e 2 2 . 5 ° C D S C p e r c e n t c o n v e r s i o n i s d e f i n e d as t h e t a c k - f r e e p o i n t for t h e c u r i n g g e l coat system. T h e p r e d i c t i o n o f the t i m e necessary to achieve a tackf r e e g e l c o a t s u r f a c e at o t h e r a p p l i c a t i o n t e m p e r a t u r e s i s o b t a i n e d f r o m F i g u r e 1 2 at 1 9 . 7 % c o n v e r s i o n . T h e c o r r e s p o n d i n g t i m e s r e q u i r e d t o r e a c h a t a c k - f r e e s u r f a c e at t h e s e v a r i o u s a p p l i c a t i o n t e m p e r a t u r e s are s h o w n i n T a b l e V I . T h e c a l c u l a t e d t a c k - f r e e t i m e at 2 5 ° C o f 3 3 m i n agrees w i t h the e x p e r i m e n t a l l y d e t e r m i n e d tack-free t i m e o f 3 0 m i n . CASKET

VARNISH

EXPLOSION.

The

single

dynamic

temperature

scan reaction k i n e t i c s m e t h o d o l o g y was u s e d to d e t e r m i n e differences i n c o m b u s t i b i l i t y b e t w e e n production batches o f a casket v a r n i s h coating. T h e coating was a n alkyd amino-based resin. A n explosion occurred d u r i n g the application o f this coating. Q u e s t i o n s arose r e g a r d i n g differences i n the relative reactivity t o w a r d combustion b e t w e e n production batches o f different formulations. T h e d e c o m p o s i t i o n d a t a f o r t h e t w o p r o d u c t i o n b a t c h e s are s h o w n i n T a b l e V I I . A d e c i s i o n as t o w h i c h p r o d u c t i o n b a t c h i s m o r e r e a c t i v e i s o b s c u r e d b y t h e fact t h a t t h e s a m p l e w i t h t h e l o w e r a c t i v a t i o n e n e r g y ( 6 0 k c a l / m o l ) b e g i n s to react at a h i g h e r t e m p e r a t u r e ( 3 2 5 ° C ) . T h i s energy o f activation vs. onset temperature conflict is resolved b y the calculated isothermal percent conversion profile shown i n F i g u r e 1 3 . T h e s a m p l e i n v o l v e d i n t h e e x p l o s i o n reacts faster at the i s o t h e r m a l temperature o f 3 5 0 ° C .

Table V I I . Kinetics of Casket Varnish Explosion ΔΗ (cal/g) 0

Sample Sample 1 Sample 2 (explosion)

3 2 31

Ε (kcal/mol) 9 2 60

Onset

Temperature (°C) 3 1 0 325


13.

PROVDER ET A L .

Quantitative

Reaction

Kinetics

100

251

SAMPLE 2 (EXPLOSION)


SAMPLE 1

10 Figure

20 30 40 TIME (sec)

50

13. Conversion curves for two production batches of varnish coatings at 350 °C bake temperature.

casket

Conclusions T h e single d y n a m i c temperature scan D S C m e t h o d of Borchardt a n d D a n i e l s w a s s h o w n to c h a r a c t e r i z e r e l i a b l y t h e r e a c t i o n k i n e t i c s for the t h e r m a l d e c o m p o s i t i o n of c a l c i u m oxalate m o n o h y d r a t e a n d A I B N . F o r the t h e r m a l d e c o m p o s i t i o n of A I B N , the single d y n a m i c t e m p e r a t u r e s c a n D S C m e t h o d is i n m u c h b e t t e r a g r e e m e n t w i t h t h e c l a s s i c a l data o f T o b o l s k y t h a n are the m u l t i p l e d y n a m i c t e m p e r a t u r e scan D S C methods. A comparison of the isothermal D S C kinetics m e t h o d w i t h the single d y n a m i c temperature scan D S C kinetics m e t h o d for the r e a c t i o n o f p h e n y l g l y c i d y l e t h e r a n d 2 - e t h y l - 4 - m e t h y l i m i d a z o l e at a 2:1 m o l a r r a t i o s h o w s t h a t t h e i s o t h e r m a l m e t h o d d o e s n o t observe the total reaction and, thereby, underestimates the total heat of reaction. T h e isothermal m e t h o d does indicate the presence of a s m a l l i n d u c t i o n p e r i o d (2.5 m i n ) at 9 0 ° C . A t t e m p e r a t u r e s b e l o w t h e glass t r a n s i t i o n t e m p e r a t u r e o f the f u l l y c u r e d p o l y m e r , the i s o t h e r m a l m e t h o d shows that the r e a c t i n g p o l y m e r is v i t r i f y i n g . T h e a c t i v a t i o n e n e r g y a n d the A r r h e n i u s factor o b t a i n e d b y the s i n g l e d y n a m i c t e m perature scan D S C m e t h o d is h i g h e r t h a n that o b t a i n e d from the isothermal m e t h o d a n d may indicate a change i n the reaction m e c h a n i s m i n g o i n g from a n i s o t h e r m a l to a d y n a m i c h e a t i n g m o d e . T h e single d y n a m i c temperature scan D S C m e t h o d provides useful quantitative reaction kinetics information regarding the c u r i n g o f c o a t i n g s s y s t e m s s u c h as p o w d e r c o a t i n g s , g e l c o a t s y s t e m s , a n d casket v a r n i s h a n d provides insights into the c h e m i c a l a n d p h y s i c a l


252


factors affecting t h e c u r i n g p r o c e s s . T h i s m e t h o d is p a r t i c u l a r l y u s e f u l for o b s e r v i n g t h e effects o f catalyst t y p e a n d l e v e l o n r e l a t i v e k i n e t i c s . T h e major advantages o f this m e t h o d c o m p a r e d to i s o t h e r m a l or m u l tiple d y n a m i c temperature scan D S C methods is the s p e e d w i t h w h i c h kinetics data c a n b e o b t a i n e d , t h e n u m b e r o f samples that c a n b e analyzed i n a given time, a n d the experimental simplicity of the method. T h e s e advantages make the single d y n a m i c temperature scan D S C m e t h o d a v a l u a b l e t e c h n i q u e for s o l v i n g p r o d u c t i o n p r o b l e m s , a i d i n g coatings complaints analysis, a n d establishing useful r e l a t i o n ships b e t w e e n end-use application/performance properties a n d fun damental kinetics parameters.


Literature

Cited

Ozawa, T. J. Therm. Anal. 1970, 2, 301. Kissinger, H. E. Anal. Chem. 1957, 29 (11), 1702. Borchardt, H. J.; Daniels, F. J. Am. Chem. Soc. 1957, 79, 41. Reed, R. L.; Weber, L.; Gottfried, B. S. Ind. Eng. Chem. Fundam. 1965, 4 (1), 38. 5. Abolafia, O. R. Soc. Plast. Eng. [Tech. Pap.], 27th 1969, 15, 610. 6. Willard, P. E. Polym. Eng. Sci. 1972, 12 (2), 120. 7. Prime, R. B. Anal. Calorim. 1970, 2, 201. 8. Prime, R. B. Polym. Eng. Sci. 1973, 13 (5), 365. 9. Willard, P. E. SPE J.1973,29,38. 10. Slysh, R.; Hettinger, A. C.; Guyler, K. E. Polym. Eng. Sci. 1974, 14 (4), 264. 11. Peyser, P.; Bascom, W. D. Anal. Calorim. 1974, 3, 537. 12. Kay, R.; Westwood, A. R. Eur. Polym. J. 1975, 11, 25. 13. Barton, J. M.; Shepherd, P. M. Makromol. Chem. 1975, 176, 919. 14. Swarin, S. J.; Wims, A. M., presented at the 172nd ACS National Meeting, Anal 061, San Francisco, CA, Aug. 29-Sept. 3, 1976. 15. Peyser, P.; Bascom, W. D. J. Appl. Polym. Sci. 1977, 21, 2359. 16. Hauser, H. M.; Field, J. E. Thermochim. Acta 1978, 27, 1. 17. "Standard Test Method for Arrhenius Kinetic Constants for Thermally Unstable Materials," Annu. Book ASTM Stand., Part 41, ASTM E698-79. 18. Draper, A. L. Proc. Toronto Symp. Therm. Anal., 3rd 1969, 63. 19. Kissinger, H. E. J. Res. Natl. Bur. Stand. (U.S.) 1956, 57, 217. 20. Hill, R. A. Nature (London) 1970, 227, 703. 21. Simmons, E . L.; Wendlant, W. W. Thermochim. Acta 1972, 3, 498. 22. Niemann, T. F.; Koehler, M. E . ; Provder, T. "Personal Computers in Chemistry"; Wiley: New York, 1981; Chap. 7, p. 85ff. 23. Kah, A. F.; Koehler, M. E.; Eley, R. R.; Niemann, T. F.; Provder, T. Org. Coat. Plast. Chem. 1981, 45, 400. 24. Kah, A. F.; Koehler, M. E . ; Grentzer, T. H.; Niemann, T. F.; Provder, T. Org. Coat. Plast. Chem. 1981, 45, 480. 25. Nair, C. G. R.; Ninan, Ν. N. Thermochim. Acta 1978, 23, 161. 26. Coats, A. W.; Redfern, J. P. Nature (London) 1964, 201, 68. 27. MacCallum, J. R.; Tanner, J. Eur. Polym. J. 1970, 6, 1033. 28. Van Hook, J. P.; Tobolsky, A. V. J. Am. Chem. Soc. 1958, 80, 781. 29. Lewis, F. M.; Matheson, M. S. J. Am. Chem. Soc. 1949, 71, 747. 30. Overberger, C. G.; O'Shaughnessy, M. T.; Shalet, H. J. Am. Chem. Soc. 1949, 71, 2661. 31. Breitanback, J. W.; Schindler, A. Monatsh. Chem. 1952, 83, 724. 32. Talat-Erben, M.; Bywater, S. J. Am. Chem. Soc. 1955, 77, 3712. 1. 2. 3. 4.


13.

PROVDER ET A L .

Quantitative

Reaction

Kinetics

33. 34. 35. 36. 37. 38.

253

Russell, R. E . ; Tobolsky, Α. V. J. Am. Chem. Soc. 1954, 76, 395. Chapiro, A. J. Chem. Phys. 1954, 51, 165. Overberger, C. G.; Biletch, H. J. Am. Chem. Soc. 1951, 73, 4880. Widmann, G. Thermochim. Acta 1975, 11, 331. Sourour, S.; Kamal, M. R. Thermochim. Acta 1976, 14, 41. Kuo, C.; Provder, T.; Holsworth, R. M.; Kah, A. F. In Chromatοgr. Sci. 19, "Liquid Chromatography of Polymers and Related Materials III," Cazes, J., Ed.; Dekker: New York, 1981; p. 169. 39. "Inclined Plate Flow Test," Annu. Book ASTM Stand. Part 27, 1980, 741-742, ASTM Test D3451.17.


RECEIVED for review October 14, 1981. ACCEPTED March 30, 1982.


Polymer Characterization - American Chemical Society

Recommend Documents