experimental investigation into the heat capacity measurement using a modulated dsc

7/28/2019 EXPERIMENTAL INVESTIGATION INTO THE HEAT CAPACITY MEASUREMENT USING A MODULATED DSC

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Journal o f Thermal Analysis, Vol. 50 (1997) 365-373

E X P E R I M E N T A L I N V E S T I G A T I O N I N T O T H E H E A TC A P A C I T Y M E A S U R E M E N T U S IN G A N M O D U L A T E DD S C

J i n a n C a o ~, Y u L o n g 2. a n d R . A . S h a n k s 2~CSIRO Division of Wool Technology, P.O. Box 21, Belmont, Victoria 32162CRC for Polymer Blends and Applied Chemistry, Royal Melbourne Institute of TechnologyP.O. Box 2476V Melbourne 3001, Australia(Received November 26, 1995, in revised form November 18, 1996)

A b s t r a c tExperiments using a commercial modulated DSC (MDSC) for the measurement of specific

heat capacity o f a sample have been carried out. It is found that because the ampl itude of heatflow of MDSC is a complicated non-line ar function of various experimental conditions suchas the modula tion frequency and the heat capacities of a sample and pan, the methodology ofheat capacity de termination using an MDSC in a single run has not been justified. The experi-mental results, on the other hand, agree with the theoretical equation of one of the authors. It istherefore conc luded that the capabilities of MDSC should be further examined.Keywords: DSC, heat capacity, indium, linearity, modulated DSC

I n t r o d u c t i o nR e c e n t l y , a n e w D S C t e c h n iq u e t e r m e d M o d u l a t e d D i f fe r e n ti a l S c a n n i n gC a l o r i m e t r y ( M D S C ) [ 1 - 8 ] h a s b e e n d e v e l o p e d to p e r m i t a s m a l l s i n u s o id a lm o d u l a t io n o f t e m p e r a t u re s u p e r i m p o s e d o n th e l i n ea r ly p r o g r a m m e d t e m p e r a -

t u re c h a n g e s t h a t a r e u s e d in a c o n v e n t i o n a l D S C . T h i s n e w M D S C t e c h n i q u e isd r a w i n g c o n s i d e r a b l e a t t e n ti o n f r o m r e s e a r c h e r s i n t h e f ie l d s o f t h e r m a l a n a l y s i sa n d p o l y m e r s c i e n c e s i nc e D S C is t he m o s t p o w e r f u l a n d p o p u l a r t e c h n i q u e u s e di n t h e s e f i e l d s [ 1 - 8 ] .T h e m o d u l a t i o n p e r i o d , p , a m p l i tu d e o f m o d u l a t i o n t e m p e r a t u r e , A b , a n d u n -d e r l y i n g h e a t i n g r a te , q , o f an M D S C e x p e r i m e n t a r e d e f i n e d in F ig . l a a n dF i g . 1b i ll u s tr a te s a n e x a m p l e o f a r a w o u t p u t c u r v e . U n l i k e a c o n v e n t i o n a l D S C ,t h e c u r v e o f M D S C c o n s i s ts o f a s i n u s o i d a l h e a t f lu x c u r v e w i t h th e s a m e p e r i o d* Current address: CSIRO Division of Materials Science and Technology, Private Bag 33, RosebankMDC, Clayton, Victoria 3q68, Australia

0368-4466/97/$ 5.00 John Wiley & Sons Limited9 1997 AkadOmiai Kiad6, Budapest Chichester


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366 C A O e t a l.: M O D U LA T ED D S C

- - T b = T . + q t + A b s i n ( 2 7 r t / p ) (M D S C)- - Tb = To+ q t ( DS C ) F " ~

J

T i m e

u p p 7 envelop

r a w o u t p u t t h e m o g r a m o f ~D SC

b

TemperatureF i g . 1 S c h e m a t i c i l l u s t r a t i o n o f a h e a t i n g p r o g r a m ( a ) a n d h e a t f l o w o u t p u t ( b ) o f M D S C

as the modulation period. It has been believed that the upper and lower envelopsof the curve represent the D SC curves of a conventional DSC corresponding to(or related to in a simple form) the highest and lowest heating rates; the formerequals the sum of the under lying heating rate and the amplitude of modulationtemperature (q+Au); and the latter is obtained by subtracting the amplitude ofmodulation temperature from theund er lying heating rate (q-Ab). This under-standing invites one to believe that the heat capacity of a sample can be obtainedin a single MDSC experiment [7]. In particular, it is believed that because eachperiod of modulation in MDSC represents one measurement for the heat capac-ity of a sample, one can further separate "reversing" and "non-reversing" com-ponents of a thermal event. This has been achieved by subtracting the heat ca-pacity component, determined by the amplitude of heat flow, from the total av-eraged or under lying heat flow [ 1-5]. According to this proposal, the crystal-lization of a quenched PET is a non-reversing thermal event, and the melting ofPET is found to be a reversing thermal event under the experimental conditionsadopted in those studies.

J . Thermal Anal . , 50, 1997


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C A O e t a l.: M O D U L A T E D D S C 3 67

C l e a r l y , a l l t h e s e u n d e r s t a n d i n g s a s s u m e t h a t a n M D S C p e r m i t s a r e l i a b l ea n d a c c u r a t e d e t e r m i n a t i o n o f t h e h e a t c a p a c i t y o f a s a m p l e t h r o u g h i t s a m p l i -t u d e o f h e a t f l ow . T h e r e f o r e a s y s t e m a t i c e x p e r i m e n t a l s t u d y o n t h e h e a t c a p a c -i ty m e a s u r e m e n t u s i n g a n M D S C b e c o m e s e s s e n t i a l. T h e a i m o f t h is a r ti c le i s t op r o v i d e s o m e f u n d a m e n t a l e x p e r i m e n t a l e v i d e n c e to d e e p e n o u r u n d e r s t a n d i n gt o w a r d s t h e c a p a c i t i e s o f M D S C .Theore t i ca l backgrou nd

I n a c o n v e n t i o n a l D S C , t w o e x p e r i m e n t s w i t h d if f e r e n t h e a t i n g r a t e s f o r t h es a m e s a m p l e n e e d t o b e c a r r ie d o u t [ 9 , 1 0]. A s s u m i n g t h a t id e n t i c a l p a n s a r eu s e d f o r t h e s a m p l e a n d r e f e r e n c e , a n d t h a t th e r e f e r e n c e is t h e e m p t y p a n o n l y ,o n e o b t a i n s t h e s p e c i f i c h e a t c a p a c i t y o f th e s a m p l e , Cps ( J ( g K ) ~ ) , u s i n g E q . ( 1 );

C p s - C p r H fl - Hf2 ( 1 )Cps ~ m m(ql - q2)w h e r e C ps a n d C pr ( J K -1 ) d e n o t e t h e h e a t c a p a c i t i e s o f t h e s a m p l e a n d t h e r e f e r -e n c e , m ( g ) t h e m a s s o f t h e s a m p l e ; H r ( m W ) a n d q ( K m i n -1) r e p r e s e n t t h e m e a s -u r e d h e a t f l o w a n d t h e h e a t i n g ra t e, r e s p e c t i v e l y . T h e s u b s c r i p t s 1 a n d 2 i n d i c a t et h e e x p e r i m e n t 1 a n d e x p e r i m e n t 2 .A n a l te r n a ti v e D S C m e t h o d i s a l so a v a i la b le , i n w h i c h t w o e x p e r i m e n t s w i t ht h e s a m e h e a t i n g r a te f o r t w o i d e n t ic a l s a m p l e s w i t h d i ff e r e n t m a s s e s a r e c a r r i e do u t. T h e s p e c i f i c h e a t c a p a c i t y o f th e s a m p l e i s c a l c u l a t e d a s f o l lo w s ;

H f l - H f 2 ( 2 )Cps - q ( m l - m 2 )

T h e m a j o r s o u r c e o f e r ro r o f t h e c o n v e n t i o n a l D S C t e c h n i q u e i s , p e r h a p s , t h el o n g te r m s t a b il it y o f a n i n s t ru m e n t a n d th e s l o w p h y s i c o - c h e m i c a l c h a n g e s o ft h e s a m p l e d u r i n g t w o r u n s . T h e b a s e l in e c o u l d h a v e s l ig h t l y s h i f t e d d u r i n g t w or u n s d u e t o l o w f r e q u e n c y d r i f t in g o f e l e c t r o n i c s o f t h e i n s tr u m e n t . H o w e v e r ,m o s t c o m m e r c i a l D S C i n s tr u m e n t s h a v e s o l v e d th is p r o b l e m s a t i s f a c to r i l y . O nt h e o t h e r h a n d , w h e t h e r t h e re a re s l o w c h a n g e s f o r a s a m p l e d u r i n g t w o D S Cr u n s i s a n o t h e r m a t t e r , w h i c h m u s t b e a d d r e s s e d c a s e b y c a s e a c c o r d i n g t o th ep h y s i c o - c h e m i c a l n a t u re o f t h e s a m p l e .

I n M D S C , t h e a m p l i t u d e o f h e a t f l o w o f a s in g l e ru n i s e m p l o y e d t o d e t e r m i n et h e h e a t c a p a c i t y o f a s a m p l e t o m i n i m i s e t h e e x p e r i m e n t a l e r r o r s r e s u l t i n g f r o ml o w f r e q u e n c y d r i f t in g o f b a s e l in e a n d s l o w c h a n g e s o f th e s a m p l e d u r i n g t w or u n s . W u n d e r l i c h , J i n a n d B o l l e r h a v e p r o p o s e d t h a t t h e h e a t c a p a c i t y c a n b e o b -t a i n e d b y d i v i d i n g t h e a m p l i t u d e o f h e a t f l o w , Ahr ( m W ) , b y t h e p r o d u c t o f t h ea m p l i t u d e o f m o d u l a t i o n te m p e r a t u r e , Ab (K) a n d t h e m o d u l a t i o n a n g u l a r f r e -q u e n c y , o ~(r = 2 To /p , w h e r e p i s t h e m o d u l a t i o n p e r i o d ) [ 5, 6] .

J . T h e r m a l A n a l . , 5 0 , 1 9 9 7


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3 6 8 C A O e t a l . : M O D U L A T E D D S C

A h fC p s = C p r + r n C p s = K C P A b ----- ( 3 )

w h e r e , C p a n d Cp r e p r e s e n t t h e h e a t c a p a c i t y a n d s p e c i f i c h e a t c a p a c i t y , r e s p e c -t i v e ly . T h e s u b s c r i p t r o r s d e n o t e s t h e r e f e r e n c e o r s a m p l e , a n d t h e s y m b o l Kcpr e p r e s e n t s a c o n s t a n t f o r i n s t r u m e n t a l c a l i b r a ti o n .M o r e o v e r , t h e h e a t c a p a c i t y d e t e r m i n e d a c c o r d i n g t o E q . ( 3 ) h a s b e e n m u l t i-p l i e d w i t h t h e u n d e r l y i n g h e a t i n g r a te t o o b ta i n s o c a l l e d " h e a t c a p a c i t y c o m p o -n e n t " o r " r e v e r s i n g " c o m p o n e n t . B y s u b t r a c ti n g th e " r e v e r s i n g " h e a t f l o w f r o mt h e t o ta l u n d e r l y i n g h e a t f l o w , o n e o b ta i n s so c a l l e d " n o n - r e v e r s i n g " c o m p o -n e n t s [ 5 - 7 ] . T h i s c a p a b i l i t y o f s e p a r a t i n g th e r e v e r s i n g a n d n o n - r e v e r s i n g c o m -p o n e n t s f r o m t h e to t a l u n d e r l y i n g h e a t f l o w h as b e e n c o n s i d e r e d t o be t h e u n i q u ef e a t u r e o f M D S C . I t is t h e r e f o r e p a r t ic u l a r l y i m p o r t a n t to i n v e s t i g a t e th e p h y s i -c a l m e a n i n g o f t h e a m p l i tu d e o f h e a t f l o w f o r a n M D S C e x p e r im e n t .R e c e n t l y , o n e o f t h e a u t h o r s h a s u s in g m a t h e m a t i c a l a n a l y s i s f o r m u l i s e d ad i f f e r e n t t h e o r e t i c a l e x p r e s s i o n o f t h e a m p l i tu d e o f h e a t f l o w o f a n M D S C , Ah,-,as fo l low s [ 10 , 11 ]

A h f = A b ( C p s C p r )~ 2 f . o q ~ z f 'D 2 ( C p s + C p r ) 2 + ( C p s C p r (D 2 - - ~ 2 ) 2_ ( 4 )( C 2 S ( O 2 -t - ~ 2 ) ( C ~ r 0 , )2 4 . ~ 2 )w h e r e , t h e s y m b o l 2~ ( J s q K q ) d e n o t e s t h e c o e f f i c i e n t o f N e w t o n ' s c o o l i n g l a wf o r a n M D S C e x p e r i m e n t , w h i c h is a n i n d i c a t i o n o f t h e i n t e n s it y o f t h e r m a lt r a n s f e r f r o m t h e h e a t i n g b l o c k t o a s a m p l e .

I t is c l e a r f r o m E q . ( 4 ) th a t th e a m p l i t u d e o f h e a t f l o w o f a n M D S C is a c o m -p l i c a t e d n o n l i n e a r f u n c t i o n o f m , Cps a n d Cpr a n d ~ , a l t h o u g h t h e r e l a t io n s h i p b e -t w e e n t h e a m p l i t u d e o f h e a t f l o w , A hf, a n d t h e a m p l i t u d e o f m o d u l a t i o n t e m p e r a -t u r e , Ab, is l in e a r , a n d t h e a m p l i t u d e i s in d e p e n d e n t o f t h e u n d e r l y i n g h e a t i n gra t e , q .O b v i o u s l y E q s ( 3 ) a n d ( 4 ) a r e c o n t r a d i c t o r y e a c h o t h e r . F o r t h is r e a s o n , a s y s -t e m a t i c e x p e r i m e n t a l s t u d y o n th e h e a t c a p a c i t y m e a s u r e m e n t u si n g a n M D S Cb e c o m e s d e s i r a b l e .E x p e r i m e n t a l

P u r e i n d i u m w a s c u t i n to t h i n s h e e t s a n d w e i g h e d i n a P e r k i n - E l m e r m i c r ob a l a n c e w i t h a c c u r a c y 0 . 0 0 1 m g . T h e t h i n i n d i u m s h e e t s w e r e t h e n u n i f o r m l yp a c k e d i nt o a n a l u m i n i u m p a n a n d t h e p a n w a s s u b s e q u e n t l y s e a l e d. T h e s a m -p l e s w e r e h e a t e d t o a b o v e t h e i r m e l t i n g te m p e r a t u r e s a n d k e p t i s o t h e r m a l l y f o ra r o u n d 2 m i n , c o o l e d to r o o m t e m p e r a t u r e a t a c o o l i n g ra t e o f 2 0 ~ r a in ~ o p e r -m i t t h e s a m p l e s t o f o r m c a k e s i n t i m a t e l y c o n t a c t i n g t h e p a n s . M D S C c u r v e sw e r e r e c o r d e d a s t h e s a m p l e s w e r e h e a t e d u s i ng a s e r i es o f t e m p e r a t u r e p r o-g r a m s .

. s T h e r m a l A n a l . , 5 0 , 1 9 9 7


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C AO e t a l .: M O DULA TED DS C 369

A l l t h e M D S C e x p e r i m e n t s w e r e c a r r i ed o u t u s i n g a T A I n s tr u m e n t s I n c.D S C - 2 9 2 0 . H e l i u m g a s p u r ge w a s u s e d a t a f l o w r a te o f 25 m l m i n -~. S a m p l et e m p e r a t u r e a n d h e a t f l o w w e r e r e c o r d e d a s a f u n c t i o n o f ti m e . D S C c u r v e s w e r eo b t a i n e d b y p l o t t in g t h e h e a t f l o w a g a i n st t h e s a m p l e t e m p e r a tu r e .R e s u l t s a n d d i s c u s s io n

F i g u r e 2 s h o w s s o m e e x a m p l e s o f t h e h e a t f l o w o u t p u t o f a n id e n t i c a l i n d iu ms a m p l e a n d an id e n t i c al r e f e r e n c e p a n f o r v a r i o u s m o d u l a t i o n p e r i o d s w h i l e a l lo t h e r e x p e r i m e n t a l c o n d i t i o n s , s h o w n i n T a b l e 1, w e r e k e p t e x a c t l y t h e s a m e .T h e a b s c i s s a o f th e p lo t i s th e s a m p l e t e m p e r a tu r e , a n d t h e o r d in a t e d e n o t e s t h eh e a t f l o w o u t p u t. E i g h t c u r v e s c o r r e s p o n d i n g t o th e e x p e r i m e n t s w i t h t h e m o d u -l a t i o n p e r i o d 1 0 , 1 5 , 2 0 , 3 0 , 4 0 , 6 0 , 8 0 a n d 1 0 0 s e c o n d s h a v e b e e n p l o t t e d i n o n eg r a p h i n o r d e r t o r e d u c e t h e s i z e o f t h is p a p e r , a l s o i n o r d e r t o a v o i d t o o m a n y

2

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20 30 40 50 60 70 80 90Temperature ~

F i g . 2 T h e a m p l i tu d e o f h e a t fl o w v a r i es w i t h t h e m o d u l a t io n p e r i o d ( s a m p l e m a s s 3 7 . 9 2 m g )

T a b l e 1 E x p e r i m e n t a l c o n d i t io n s e m p l o y e d in F i g s 2 , 3 a , 3 b a n d 4U n d e r l y i n g h e a t i n g r a t eM o d u l a t i o n t e m p e r a t u r eM a s s o f a l u m i n i u m p an( H e a t c a p a c i t y o f r e f e r e n c e , CprM a s s o f i n d iu m( H e a t c a p a c i ty o f s a m p l e , Cp~)

T e m p e r a t u r e r an g e o f m e a s u r e m e n t s

5 ( ~ m i n - t )_+ l~2 5 .1 m g ( e m p t y p a n f o r r e f e r e n c e )( 0 . 0 2 5 1 x 0 . 9 0 0 = 0 . 0 2 2 6 J K ~ [ 1 3 ] )3 7 . 9 2 m g o r 1 2 . 5 3 m g( 0 . 0 3 7 9 2 x 0 . 2 3 4 + 0 . 0 2 2 6 = 0 . 0 3 1 5 [ 1 3 ])( 0 . 0 1 2 5 3 [ 1 3 ] )0 - 1 0 0 ~

J . The r ma l Ana l . , 50 , 1997


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370 CA O e t a l. : MOD ULATED DSC

c u r v e s o v e r l a p p i n g e a c h o t h e r , o n e p a r t o f t h e c u r v e o n l y f o r e a c h c u r v e s w a sp l o t t e d i n t h e f i g u re . S i n u s o i d a l - l ik e h e a t f l o w c u r v e s w e r e o b s e r v e d w h e n t h eh e a t f l o w o u t p u t w e r e p l o t t e d a g a i n s t t im e ( n o t p r e s e n t e d i n t h e a r ti c le ) . C l e a r lyt h e a m p l i tu d e o f h e a t f l o w i s n o t a s i m p l e l i ne a r f u n c t i o n o f t h e m o d u l a t i o n f r e-q u e n c y .I n F i g . 3 th e a m p l i t u d e o f h e a t f l o w is p l o t t e d a g a i n s t t h e m o d u l a t i o n p e r i o df o r t h e t w o i n d i u m s a m p l e s w i t h d i f f e r e n t w e i g h t s . It c a n b e s e e n f r o m t h e f i g -u r e s t h a t th e a m p l i t u d e i n c re a s e s i n i ti a ll y w i t h d e c r e a s i n g t h e m o d u l a t i o n p e -r io d , r e a c h e s a m a x i m u m a t a m o d u l a t i o n p e r i o d o f a r o u n d 2 0 s e c o n d a n d t h e nd e c r e a s e s o n f u r t h e r d e c r e a s i n g t h e m o d u l a t i o n p e r io d . T h i s r e s u lt is i n c o n t r a s tw i t h E q . ( 3 ) , w h i c h e s s e n t i a l ly a s s u m e s t h a t t h e a m p l i t u d e o f h e a t f l o w s h o u l di n c r e a s e l i n e a r ly w i t h t h e m o d u l a t i o n p e r io d .

T h e m o d u l a t i o n p e r i o d d e p e n d e n c e o f t h e a m p l i t u d e o f h e a t f l ow , h o w e v e r ,c a n b e w e l l i n te r p r e t e d u s i n g E q. ( 4 ). B y c h o o s i n g d i f fe r e n t N e w t o n ' s c o o l i n gc o e f f i c i e n t s , )~, w h i c h i s m a i n l y d e t e r m i n e d b y t h e d e s i g n a n d c o n s t r u c t i o n o f a nM D S C i n s t r u m e n t [5 , 1 0 ], a n d b y p l a c i n g th e h e a t c a p a c i t ie s o f th e r e f e r e n c e a n ds a m p l e i n t o E q . ( 4 ), o n e o b t a i n s t h e o r e t i c a l c u r v e s , a l s o s h o w n i n F i g . 3 ( s o l id

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0 . . . , . . . , - . . ,4 0 8 0 1 2 0Modul a t i on pe r i od ( s )F i g . 3 C o m p a r i s o n b e t w e e n e x p e r i m e n t a l r e s u l t s a n d t h e o r e t i c a l c a l c u l a t io n s o f E q . ( 4 )a ) s a m p l e m a s s 3 7 . 9 2 m g ; b ) s a m p l e m a s s 1 2 . 5 3 m g .

J . Thermal Anal . , 50, 1997


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CAO et al.: MODULATED DSC 37t

l i n e s ) . T h e e x p e r i m e n t a l r e s u l t s a n d t h e t h e o r e t i c a l c u r v e s a r e i n r e a s o n a b l ea g r e e m e n t a t t h e h i g h m o d u l a t i o n p e r i o d r e g i o n ( > 2 0 s ). T h e d e v i a t i o n o f th e e x -p e r i m e n t a l r e s u l ts f r o m t h e t h e o r e ti c a l c u r v e s o f E q . ( 4 ) a t th e l o w m o d u l a t i o np e r i o d r e g i o n ( < 2 0 s ) c o u l d b e c a u s e d b y t h e e f f e c t o f t e m p e r a t u r e g r a d i e n t int h e s a m p l e s a t s u c h h i g h m o d u l a t i o n f r e q u e n c i e s . A n o t h e r p o ss i b le r e a s o n c o u l db e t h e d e v i a t io n o f te m p e r a t u r e w a v e f o r m o f h e a ti n g b l o c k f r o m a t r ue s in u s o i-d a l f u n c t i o n at s u c h h i g h m o d u l a t i o n f r e q u e n c i e s .

T h e D S C c u r v e s w e r e u s e d to o b t a i n th e s p e c i f ic h e a t c a p a c i t y o f t h e s a m p l eu s i n g t h e s o f t w a r e p r o v i d e d b y T A I n s t r u m e n t s I n c ( n o f o r m u l a a b o u t h o w i t w a sc a l c u l a t e d w a s p r o v i d e d i n th e m a n u a l ) . T h e r e s u l t s f o r t h e s a m p l e o f m a s s3 7 .9 2 m g w e r e u s e d a s a n e x a m p l e to p l o t v s . t em p e ra t u re i n F ig . 4 . It is s een t h a tt h e o b t a i n e d f i g u re i n c r e a s e s w i t h t h e m o d u l a t i o n p e r i o d . O b v i o u s l y , t h e se r e -s u l ts a r e i n c o n s i s t e n t w i t h e a c h o t h e r a n d c o n t r a d i c t o r y w i t h t h e l i te r a t u r e v a l u eo f 0 .2 3 4 J ( g K ) - I [ 1 3], i n d i c a t i n g t h a t t h e m e t h o d o l o g y u s e d f o r t h e i n s t r u m e n t tod e t e r m i n e t h e s p e c i f ic h e a t c a p a c i t y o f a s a m p l e h a s n o t b e e n j u s t if i e d a n d n e e d st o b e r e v i s e d .

T h e p h y s i c a l m e a n i n g o f th e m a x i m u m a m p l i tu d e o f h e a t f lo w a t c e r ta inm o d u l a t i o n p e r i o d i s o b v i o u s . A t a lo w e r m o d u l a t i o n p e r i o d , t h e r e is n o s u f f i c i e n tt i m e f o r th e r m a l t r a n s f e r f r o m t h e h e a t i n g b l o c k t o b o t h th e s a m p l e a n d r e f e r e n c e ,a s m a l l e r a m p l i tu d e o f h e a t f l o w w i l l b e e x p e c t e d . A t a h i g h e r m o d u l a t i o n p e r i o d ,o n t h e o t h e r h a n d , b o t h t h e s a m p l e a n d r e f e r e n c e c a n c a t c h u p th e t e m p e r a t u r ec h a n g e s o f h e a t i n g b l o c k , r e s u lt i n g in a m i n i m u m t e m p e r a t u r e d i f f e r e n c e b e -t w e e n t h e s a m p l e a n d r e f e r e n c e , t h e r e f o r e a s m a l l e r a m p l i t u d e o f h e a t f lo w .A s c a n b e s e e n f r o m E q . ( 4 ) , n o t o n l y t h e m o d u l a t i o n p e r i o d b u t a l so t h e h e a tc a p a c i t y o f a D S C p a n w o u l d a f f e c t t h e a m p l it u d e o f h e a t f lo w . E x p e r i m e n t s u s -i n g d i f f e r e n t D S C p a n s t h a t a re t h o u g h t t o h e s u it a b le f o r M D S C e x p e r i m e n t s f o r

0.3

0 . 2 50~ 0.2v

0 . 1 5Q.

~ 0.1-I-

1O0 sec BO sec 60 sec

40 sec

20 sec

I S sec

10 sec

0 . 0 5 I I I I I I I4 0 4 5 5 0 S S 6 0 6 5 7 0 7 5 8 0

Tempaerature ~Fig. 4 Specific heat capacity of the pu re indium samp le calculated by u sing the software ofthe instrument for various m odulationfrequencies (samp le mass 37.92)

J . Th e r ma l An a l . , 5 0 , 1 9 9 7


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372 CAO et al.: MO DULA TED DSC

T a b l e 2 E x p e r i m e n t a l c o n d i t i o n s e m p l o y e d i n Fi g . 5U n d e r l y i n g h e a t i n g r a teM a s s o f a l u m i n i u m p a n( H e a t c a p a c i t y o f r e f e r e n c e , C prM a s s o f i n d iu mc p ,T e m p e r a t u r e r a n g e o f m e a s u r em e n t s

5 ( ~ m i n 1 )2 5 .1 m g o r 3 5 .6 0 m g(0 .0226 J K ] o r 0 .0320 J K - I )10.05 m g (mXC ps=0.00235 J K - ] )0 .0 250 J K -1 , 0 .03 44 J K -1O - I O 0 ~

3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 00.2

Pen mass 35 .6mgo. 1

v

o,, c

~ - o . 1

Pan m ass 25.1mg- 0 . 2

Temperature *CF i g . 5 A n e x a m p l e s h o w i n g th e d e p e n d e n c e o f th e a m p l i t u d e o f h e a t f l o w o n D S C c e l l u s e d

f o r e x p e r i m e n t s ( m o d u l a t i o n p e r i o d 8 0 s )

t w o i n d i u m s a m p l e s w i t h t h e s a m e m a s s w e r e t h e n c a r r i e d o ut , w h i l e a ll o t h e r e x -p e r i m e n t a l c o n d i t i o n s , s h o w n i n T a b l e 2 , w e r e m a i n t a i n e d c o n s t a n t . F i g u r e 5s h o w s t h e h e a t f l o w o u t p u t o f t h e s e e x p e r i m e n t s . S i g n i f i c a n t d i f f e r e n c e h a s b e e no b s e r v e d . T h i s h a s l e d a n i n c o n s i s t e n t s p e c i f ic h e a t c a p a c i t y v a l u e f o r i n d i u m o b -t a i n e d f r o m t h e t w o m e a s u r e m e n t s w i t h d i f f e r e n t p a n s ( n o t s h o w n i n f i g u re ) . T h el i g h te r p a n ( s m a l l e r Cpr a n d C os) h a s l e d t o a g r e a t e r a m p l i t u d e o f h e a t f l o w , w h i l s tE q . ( 3 ) i n d i c a t e s th a t t h e a m p l i t u d e s h o u l d i n c r e a s e w i t h th e h e a t c a p a c i t y o f ap an . T h e ex p e r i m en t a l r e s u l t in F ig . 5 i s co n s i s t en t w i t h t h e t h eo re t i ca l r e s u l t s o fE q . ( 4) , w h i c h s u g g e s t s t h a t t h e a m p l i t u d e o f h e a t f l o w d e c r e a s e s m o n o t o n i c a l l yw i t h i n c r e a s i n g th e h e a t c a p a c i t y o f p a n s u s e d f o r s a m p l e a n d r e f e r e n c e [ 10 , 1 1].C o n c l u s i o n

E x p e r i m e n t s u si n g a c o m m e r c ia l m o d u l a te d D S C ( M D S C ) h a s b e e n c a r r ie do u t t o i n v e s t i g a te t h e r e l a t io n s h i p b e t w e e n t h e a m p l i tu d e o f h e a t f l o w a n d t h e

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modulation frequency as well as the heat capacity of a pan used for a sample andreference. Agreement is observed between the experimental results and theo-retical curves of Eq. (4) for the modulation frequency dependence of the ampli-tude of heat flow at low frequency region. The deviation of the experimental re-sults from the theoretical prediction at the high frequency region, however, isconsidered to be caused by the temperature gradient within the sample etc. Theamplitude dependence on the heat capacity of pan was also observed. Indeed,further work is required in order to fully understand the use of, and the capabili-ties of MDSC.R e f e r e n c e s

1 M. Reading, D. Elliot and V. L. Hill, Proc. 9th ICTA Meeting, Hatfield, UK, August1992: J. Thermal Anal., 40 (1993) 949.2 P. S. Gill, S. R. Saurbrunn and M. Reading, Proc. 9th ICTA Meeting, Hatfield, UK, Au-gust 1992: J. Thermal Anal. , 40 (1993) 931.

3 M. Reading, Trends Potym. Sci., 8 (1993) 248.4 M. Reading, A. Luget and R. Wilson, Thermochim. Acta, 238 (1994) 295.5 B. Wunderlich, Y. Jin and A. Botler, Thermochim. Acta, 238 (1994) 277.6 A. Boller, Y. Jin and B. Wunderlich, J. Thermal Anal. 42 (1994) 307.7 TA Instruments, "Modulated DSC Workshop 10/94," Melbourne, Oct. 1994.8 L. H~irlldahl and B. Olofsson, Thermochim. Acta, 256 (1995) 137.9 For example V. A. Bershten and V. M. Egorov, "Differential Scanning Calorimetry ofPolymers", Ellis Horwood, New York 1994.

10 J. Cao, Thermochim. Acta, (submitted).11 J. Cao, Thermochim. Acta, (submitted).12 T. Ozawa and K. Kanari , Thermochim. Acta, 253 (1995) 183.13 D. R. Lide, CRC Handbook of Chemistry and Physics, 71st Ed., 1990-1991, CRC press,Boca Raton.

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experimental investigation into the heat capacity measurement using a modulated dsc

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