Differential Scanning Calorimetry of Flexible, Linear Macromolecules

11 Differential Scanning Calorimetry of Flexible, Linear Macromolecules B E R N H A R D W U N D E R L I C H and U M E S H G A U R

Downloaded by UNIV OF CINCINNATI on February 18, 2015 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch011

Rensselaer Polytechnic Institute, Department of Chemistry, Troy, NY 12181

A summary of instrument and application news for dif ferential scanning calorimetry (DSC) and a study of low temperature DSC are presented. From 140 to 300 K, a reasonably critical application range, DSC is shown to be capable of up to 2% precision. This is less than clas sical calorimetry can provide, but many applications may be served by these measurements. Heat capacities of poly(acrylate) and poly(methacrylate) are presented for the temperature range 220—500 Κ (specifically, methyl, ethyl, n-butyl, isobutyl, and octadecyl acrylates, and methyl, ethyl, n - b u t y l , isobutyl, dodecyl, and octadecyl methacrylates). These heat capacities are an alyzed in terms of the side-chain heat capacity by comparison with the heat capacities of polyethylene, poly propylene, polybutene-1, polyisobutylene, and polypentene. The latter are taken from our data bank, which contains heat capacities on over 100 different mac romolecules and will be the basis of a general addition scheme on heat capacities.

D

IFFERENTIAL SCANNING CALORIMETRY (DSC)

has

become a

signifi

c a n t a n a l y t i c a l t e c h n i q u e o v e r t h e l a s t 10 y e a r s . B e c a u s e a l m o s t a n y p h y s i c a l or c h e m i c a l changes o c c u r w i t h a change i n e n t h a l p y , a l l c a n b e f o l l o w e d b y c a l o r i m e t r y . S i m i l a r l y , t h e r m a l p r o p e r t i e s t h a t are e x p r e s s e d t h r o u g h e n t h a l p y , e n t r o p y , a n d G i b b s e n e r g y (free e n t h a l p y ) can be evaluated b y calorimetry u s i n g heat capacity a n d heat of tran s i t i o n m e a s u r e m e n t f r o m 0 Κ to the t e m p e r a t u r e i n q u e s t i o n . A l t h o u g h c a l o r i m e t r y p l a y s a m a j o r r o l e a m o n g a n a l y t i c a l t e c h n i q u e s , i t has s t i l l not r e a c h e d its l i m i t . T h e i n i t i a l s e c t i o n o f t h i s c h a p t e r d i s c u s s e s t h e history of the d e v e l o p m e n t of calorimetry a n d includes a listing of m o d e r n D S C apparatus. 0065-2393/83/0203-0195$06.00/0 © 1983 A m e r i c a n C h e m i c a l Society

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


196

POLYMER CHARACTERIZATION

T h e m a i n portion of this chapter concentrates o n the a p p l i c a t i o n o f D S C to heat capacity m e a s u r e m e n t s o f flexible linear mac r o m o l e c u l e s , o u r m a i n r e s e a r c h i n t e r e s t . U l t i m a t e l y , w e h o p e to d e r i v e a n a d d i t i o n s c h e m e that permits the p r e d i c t i o n of heat capacities of m a c r o m o l e c u l e s w i t h the h e l p of a series of tables of group c o n t r i b u t i o n s . D i f f e r e n t i a l s c a n n i n g c a l o r i m e t r y i n s t r u m e n t a t i o n is d e s c r i b e d b y u s i n g a c o m p a r i s o n o f d i f f e r e n t D S C e q u i p m e n t a p p l i e d to l o w temperature heat capacity measurements. I n a d d i t i o n , heat capacities of poly(acrylate)s a n d p o l y (methacrylate) s i n the t e m p e r a ture range 2 2 0 - 5 0 0 Κ ( m e t h y l , e t h y l , η-butyl, i s o b u t y l , a n d o c t a d e c y l acrylates a n d m e t h y l , e t h y l , η-butyl, i s o b u t y l , d o d e c y l , a n d o c t a d e c y l m e t h a c r y l a t e s ) a r e p r e s e n t e d . T h e s e d a t a are u s e d a l o n g w i t h l i t e r a ture data o n polyacrylates, polymethacrylates, a n d polyalkenes [poly ethylene (PE), polypropylene (PP), polybutene-1 (PBu), polypentene-1 (PPe), polyhexene-1 ( P H e ) , poly(4-methyl-l-pentene) ( P 4 M 1 P ) , a n d p o l y i s o b u t y l e n e (PIB)] to study the heat capacity c o n t r i b u t i o n s d u e to t h e s i d e g r o u p s . T h i s p r e s e n t s a n o v e r v i e w o f t h e u t i l i t y o f D S C u s i n g the e x a m p l e of heat capacity of l i n e a r m a c r o m o l e c u l e s cover i n g history, instrumentation, data, a n d data treatment.

History

and

List

of

Instruments

C a l o r i m e t r y has t w o h a n d i c a p s that h a v e i m p e d e d its a p p l i c a t i o n . T h e f i r s t is t h e l a c k o f p e r f e c t i n s u l a t o r s . T h e h e a t t o b e m e a s u r e d c a n n o t b e c o n t a i n e d ; i t i s a l w a y s i n flux, so t h a t l o s s c o n t a i n m e n t a n d l o s s c a l c u l a t i o n s a r e b a s i c t o c a l o r i m e t r y . T h e s e c o n d h a n d i c a p is t h e lack o f a d i r e c t heat m e t e r . A l l c a l o r i m e t r y is d o n e i n d i r e c t l y , e i t h e r b y c o m p e n s a t i o n (e.g., b y e l e c t r i c a l h e a t i n g o r c o o l i n g i n c a s e o f e n d o t h e r m s o r e x o t h e r m s ) , o r b y d e t e r m i n a t i o n o f s e c o n d a r y e f f e c t s (e.g., the m e a s u r e m e n t of temperature rise). D i f f e r e n t i a l s c a n n i n g c a l o r i m e t r y has its roots i n t w i n c a l o r i m e t r y ( 1 , 2 ) w h i c h w a s d e v e l o p e d to m i n i m i z e the heat loss p r o b l e m . N e x t was the d e v e l o p m e n t of c o n s t a n t h e a t i n g r a t e c a l o r i m e t e r s (3) t h a t a l l o w e d r a p i d m e a s u r e m e n t over a large temperature range w i t h o u t the n e e d of frequent e q u i l i b r a t i o n a n d l o s s c a l i b r a t i o n . T h e f i r s t t w i n c a l o r i m e t e r o p e r a t i n g at c o n s t a n t h e a t i n g r a t e w a s d e s c r i b e d i n 1 9 6 0 (4). T h e n e x t s t e p i n t h e development i n v o l v e d invention and commercialization of a modern d i f f e r e n t i a l s c a n n i n g c a l o r i m e t e r for m i l l i g r a m - s i z e d s a m p l e s b a s e d on temperature sensing a n d electronically regulated heating of the r e f e r e n c e a n d s a m p l e ( P e r k i n - E l m e r ) (5). C u r r e n t l y a v a r i e t y o f a d d i t i o n a l D S C i n s t r u m e n t s are a v a i l a b l e c o m m e r c i a l l y . A n u m b e r o f D S C s i n v o l v e h e a t i n g b y flux t h r o u g h a c o n t r o l l e d l e a k . T h e t e m p e r ature m e a s u r e m e n t c a n be d o n e b y t h e r m o c o u p l e (du Pont) b y thermopile (temperature difference) (Mettler), a n d b y resistance


11.

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197

t h e r m o m e t e r (Heraeus*). A d d i t i o n a l variations i n v o l v e t h e c a p a b i l i t y to a d d e l e c t r i c a l c a l i b r a t i o n h e a t p u l s e s ( N e t z s c h ) . F i n a l l y , t h e r e i s a D S C based o n measurement o f heat flux u s i n g m u l t i p l e thermocouple arrangements (Setaram ). 2


A l l these i n s t r u m e n t s o f D S C are c a p a b l e o f m e a s u r e m e n t rates o f u p to 5 0 K / m i n a n d m a y r e a c h a p r e c i s i o n i n h e a t c a p a c i t y as h i g h as 0 . 5 % . B e c a u s e o f fast h e a t i n g r a t e s , i t i s n o t o n l y p o s s i b l e t o m e a s u r e e q u i l i b r i u m f u n c t i o n s o f state, b u t i t i s a l s o p o s s i b l e t o s t u d y m e t a s t a b l e a n d u n s t a b l e states. T h e l a t t e r i s o f k e y i m p o r t a n c e t o e s t a b l i s h information o n t h e r m a l , m e c h a n i c a l , a n d perhaps also electrical his t o r y (6).

Instrumentation W e have m e a s u r e d the heat capacity of m o l t e n s e l e n i u m from 500—700 Κ u s i n g the three c o m m e r c i a l , w i d e l y available D S C s ( M e t t l e r T A 2 0 0 0 , d u P o n t 9 9 0 , P e r k i n - E l m e r D S C - 2 ) (7). A l l t h r e e D S C s r e p r o d u c e d adiabatic calorimetry data to w i t h i n 3%. U s i n g a c o m p u t e r c o u p l e d D S C , t h e accuracy o f the heat capacity c o u l d b e i m p r o v e d f u r t h e r t o b e t t e r t h a n 1 % (8). Continuing our comparison of commercial instruments, the suba m b i e n t accessories for M e t t l e r T A 2000, d u P o n t 990, a n d P e r k i n E l m e r D S C - 2 w e r e u s e d for heat capacity measurements o f p o l y m e r s , extending the temperature range o f measurements d o w n to l i q u i d nitrogen temperatures. T h e d u P o n t 9 9 0 l i q u i d n i t r o g e n a c c e s s o r y i s l i m i t e d i n its d e s i g n . It c o n s i s t s o f a s m a l l c o o l e r (~ 1 5 0 m L ) t h a t i s p l a c e d o v e r t h e D S C c e l l assembly a n d f i l l e d w i t h l i q u i d nitrogen to cool the c e l l assembly. T h e cooling of t h e c e l l is slow a n d uncontrolled, p r e c l u d i n g p r e c i s i o n m e a s u r e m e n t s o n c o o l i n g . A l s o , t h e i s o t h e r m at l i q u i d n i t r o g e n t e m perature is not f u l l y stable. T h e P e r k i n - E l m e r l i q u i d nitrogen accessory consists o f a tank (—4.5 L ) t h a t i s f i l l e d w i t h l i q u i d n i t r o g e n . T h i s a l l o w s f o r fast, c o n t r o l l e d c o o l i n g o f t h e s a m p l e h o l d e r s . C o o l i n g rates o f as m u c h as 8 0 K / m i n are possible. T h e baseline is quite good. H o w e v e r , isotherms are u n s t a b l e a n d s h o w s i g n i f i c a n t drifts, c a u s e d b y t h e c o n t i n u o u s change of the l i q u i d nitrogen l e v e l . T h e M e t t l e r T A 2000 is e q u i p p e d w i t h a sophisticated c o o l i n g system for the c e l l . T h e furnace is fitted w i t h a heat exchanger for c o o l i n g . T h e l i q u i d n i t r o g e n coolant is stored i n a separate tank. A n e v a p o r a t o r ( h e a t i n g e l e m e n t ) i n t h e l i q u i d n i t r o g e n c o n t r o l s t h e flow Heraeus, W. C , G m b H , Postfach 169, 6450 Hanau 1, Federal Republic of Ger many. 1

2

Setaram, 101-103 rue de Sexe, 69451 Lyon, Cedex 3, France.


198



o f c o o l a n t to t h e heat e x c h a n g e r . T h e e l e c t r i c h e a t i n g a n d t h e c o o l i n g w i t h l i q u i d n i t r o g e n are separately c o n t r o l l e d . T h e r e f e r e n c e a n d the s a m p l e pans are p l a c e d o n the t h i n - f i l m sensors. S o m e d i f f i c u l t i e s w e r e e n c o u n t e r e d d u e to p o o r c o n t a c t s b e t w e e n t h e p a n s a n d t h e s e n s o r s . A g i v e n s c a n w a s f o u n d to b e r e p r o d u c i b l e t o w i t h i n ± 1 / x V i f the p a n was kept i n place. H o w e v e r , i f the pans w e r e r e m o v e d a n d r e p l a c e d r a n d o m l y on the sensor, the signal r e p r o d u c i b i l i t y was m u c h p o o r e r ( ± 1 2 μ,ν). T h i s p r o b l e m w a s a v o i d e d b y u s i n g g o l d p a n s t h a t are m a d e u p o f h e a v i e r m e t a l sheet, w h i c h r e s u l t e d i n m o r e u n i f o r m contact b e t w e e n the pans a n d the sensor. T h e e r r o r i n h e a t c a p a c i t y m e a s u r e m e n t s at l i q u i d n i t r o g e n t e m peratures u s i n g the P e r k i n - E l m e r a n d the M e t t l e r instruments on A 1 0 a n d P M M A ( u s i n g b e n z o i c a c i d as s t a n d a r d a r e s u m m a r i z e d below: 2

3

Perkin-Elmer Temp (K) 150 200 250

A1 0 2

±7

PMMA (%) ±5

±3 ±1

±2 ±2

3

(%)

Mettler Al O 2

(%)

s

PMMA

(%)

+3

±2

±2 ±2

±2 ±2

T h e s e data a n d the general d e s c r i p t i o n indicate that l o w temperature heat c a p a c i t y m e a s u r e m e n t s are p o s s i b l e w i t h a l l t h r e e i n s t r u m e n t s w i t h o n l y s l i g h t l y r e d u c e d a c c u r a c y , b u t i t i s n e c e s s a r y to u s e c o n s i d erably more care i n a v o i d i n g spurious temperature gradients. Heat capacity measurements were made w i t h a computer c o u p l e d P e r k i n - E l m e r D S C - 2 , fitted w i t h t h e m o r e r e p r o d u c i b l e i n t r a c o o l e r at a p p r o x i m a t e l y 2 0 0 Κ t o r e a c h t h e p r e c i s i o n n e e d e d f o r o u r data bank. T h i s use of m e c h a n i c a l refrigeration limits the l o w temper ature. D e t a i l s of the instrumentation, calibration, a n d computations a r e g i v e n i n R e f e r e n c e 8.

Results T h e acrylic polymers u s e d i n this study were secondary standards obtained from Scientific Polymer Products, Inc. T h e molecular w e i g h t s p r o v i d e d b y t h e m a n u f a c t u r e r s are l i s t e d i n T a b l e I . T h e manufacturers provided P M - 1 , P M - 2 , P M - 4 i , and P M - 1 8 i n granular form. A l l the other acrylic polymers have T values b e l o w room t e m p e r a t u r e . F o r e a s e o f h a n d l i n g t h e s e s a m p l e s w e r e p r o v i d e d as 4 0 % s o l u t i o n i n t o l u e n e a n d w e r e l a t e r d r i e d i n v a c u u m at 3 3 0 — 3 5 0 Κ f o r 24—48 h . E a c h s a m p l e (10—25 mg) was transferred i n t o a h e r m e t i c a l l y s e a l e d p a n for heat c a p a c i t y m e a s u r e m e n t s . A l l t h e m e a s u r e m e n t s w e r e d o n e o n h e a t i n g at 1 0 - 2 0 K / m i n a n d A 1 0 w a s u s e d as r e f e r e n c e g

2

3


11.

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WUNDERLICH AND GAUR

Scanning

199

Calorimetry

T a b l e I, Characterization of P o l y m e r s


Polymer

Abbreviation

P o l y ( m e t h y l acrylate) P o l y ( e t h y l acrylate) P o l y ( n - b u t y l acrylate) P o l y ( i s o b u t y l acrylate) Poly(octadecyl acrylate) Poly(methyl methacrylate) Poly(ethyl methacrylate) Poly(n-butyl methacrylate) Poly(isobutyl methacrylate) Poly(dodecyl methacrylate) Poly(octadecyl methacrylate)

PA-1 PA-2 PA-4 PA-4i PA-18 PM-1 PM-2 PM-4 PM-4i PM-12 PM-18

M

w

M /M w

n

3.2 3.2 3.6 3.7 1.8 1.82 2.7 4.4 2.14 1.5 6.9

200,000 125,000 119,000 116,000 23,300 60,000 340,000 320,000 300,000 113,000 671,000

m a t e r i a l . T h e a v e r a g e d a t a o f t w o to f i v e m e a s u r e m e n t s ( w i t h i n ± 1 % ) are l i s t e d i n T a b l e s I I a n d I I I .

Discussion T h e n e w l y measured heat capacities of acrylic polymers s h o w n i n T a b l e s II a n d III have b e e n c o m b i n e d w i t h the literature data ( m a i n l y at l o w t e m p e r a t u r e s ) o n t h e s a m e a c r y l i c p o l y m e r s to d e r i v e a set o f r e c o m m e n d e d d a t a f o r e a c h a c r y l i c p o l y m e r (9). T h e s e r e c o m m e n d e d data, w h i c h n o w c o v e r a w i d e r range t h a n the data r e p o r t e d here, have b e e n u s e d to d e r i v e t h e h e a t c a p a c i t y c o n t r i b u t i o n o f t h e C H g r o u p o n the C - C backbone a n d the contribution of a C H group i n the side c h a i n [ ( C H ) C H to ( C H ) C H ] b e l o w a n d a b o v e t h e g l a s s t r a n s i t i o n . D a t a are g i v e n i n T a b l e s I V — V I I . T h e s e c o n t r i b u t i o n s h a v e a l s o b e e n d e r i v e d for p o l y p r o p y l e n e (10), p o l y b u t e n e (11), p o l y p e n t e n e (11), p o l y h e x e n e (11), a n d p o l y i s o b u t y l e n e ( I I ) . A l s o l i s t e d i n t h e s e t a b l e s a r e t h e c o r r e s p o n d i n g d a t a o n p o l y e t h y l e n e (12). H e a t c a p a c i t y c o n t r i butions of the C O O - group i n polyacrylates a n d polymethacrylates have also b e e n d e r i v e d b y t a k i n g the difference i n heat capacity c o n tribution b e t w e e n the acrylic p o l y m e r a n d the corresponding p o l y a l k e n e . T h e s e d a t a b e l o w a n d a b o v e t h e g l a s s t r a n s i t i o n are l i s t e d i n Tables VIII and IX. 3

2

2

3

2

1 7

3

T h e d i s c u s s i o n o f these g r o u p c o n t r i b u t i o n s is d o n e i n stages. F i r s t , w e l o o k at t h e t h e o r e t i c a l f e a s i b i l i t y o f a n a d d i t i o n s c h e m e f o r l i n e a r m a c r o m o l e c u l e s a n d t h e n , the p o s s i b l e e m p i r i c a l extensions are analyzed. A detailed d i s c u s s i o n of the heat capacities of l i n e a r macr o m o l e c u l e s has r e v e a l e d t h a t , b e c a u s e o f t h e c h e m i c a l n a t u r e o f t h e molecules, the vibrational spectrum c a n be separated into group a n d s k e l e t a l v i b r a t i o n s (13). F u r t h e r m o r e , t h e s k e l e t a l v i b r a t i o n s are largely intramolecular i n nature because of the strong b o n d i n g along


200



T a b l e I I . H e a t Capacity of Poly(acrylate)s T(K)

PA-1

PA-2

PA-4

PA-4i

PA-18

220 230 240 250 260 270

90.4 93.3 96.0 98.9 102.1 105.5

114.3 119.0 123.6 130.2 153.7 173.9

174.7 217.6 221.5 221.1 223.5 224.9

156.0 163.0 171.5 197.2 223.9 223.2

449.6 476.7 505.0 535.6 570.0

280 290 300 310 320 330

110.5 124.2 153.6 153.6 155.1 156.3

175.2 177.1 178.9 180.7 182.4 184.5

227.5 230.2 232.7 235.5 238.3 241.7

226.0 229.0 232.1 235.1 238.1 241.5

579.7

340 350 360 370 380 390

158.3 160.2 161.3 162.7 163.9 165.1

187.7 190.2 191.9 193.9 195.8 197.7

246.0 249.3 252.1 255.6 258.4 261.8

245.0 248.3 251.6 255.2 258.5 261.2

694.3 703.5 708.5 718.3 728.4 738.4

400

168.3

200.1

265.4

410 420 430 440 450

170.4 172.6 174.8 175.3 175.6

202.3 204.5 206.2 208.6 211.6

270.1 273.4 275.7 277.3

265.8 273.1 275.1 276.2 277.4 284.4

758.9 769.8 771.9 792.8 802.4

460 470 480 490 500

178.5 179.8 181.1 182.9 183.8

213.5 215.9 219.1 220.8 222.5

278.6 287.0 293.0 295.8 300.3

804.5 814.7 824.4 830.9 843.2

— — — — —

747.1

Note: Heat capacity measurements are given in J m o l K . - 1

_ 1

t h e b a c k b o n e c h a i n o f t h e m o l e c u l e . O n l y at t e m p e r a t u r e s b e l o w about 40 Κ is the i n f l u e n c e of the i n t e r m o l e c u l a r skeletal v i b r a t i o n s o n the heat capacity dominant. T h u s , a m o d e l of l i n e a r m a c r o m o l e c u l e s b a s e d o n this analysis is that of a string o f b e a d s . E a c h b e a d has the mass o f the r e p e a t i n g u n i t (or s i n g l e b a c k b o n e c h a i n a t o m u n i t ) a n d i s c o u p l e d s t r o n g l y i n t h e chain direction. E a c h string of beads is, however, only w e a k l y c o u p l e d w i t h its n e i g h b o r s t r i n g s . S u b t r a c t i n g t h e c o n t r i b u t i o n o f t h e group vibrations leaves the heat capacity of an assembly of structure l e s s b e a d s . B e c a u s e at l e a s t a l l c a r b o n b a c k b o n e m a c r o m o l e c u l e s h a v e


11.

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201

the same b o n d i n g b e t w e e n beads a n d have also similar

geometry,

Differential

Scanning

their intramolecular heat capacities must be related. T h i s relationship was established (13) u s i n g a one-dimensional D e b y e function D

x

with

a ^ - t e m p e r a t u r e p r o p o r t i o n a l to t h e i n v e r s e o f t h e mass o f t h e o n e carbon backbone b e a d ( M ) . B y taking the ratio of M

c

c

to the p o l y e t h y l

ene mass ( 1 4 g/mol) the u n i v e r s a l e q u a t i o n is w r i t t e n b y u s i n g the polyethylene ^-temperature 5 4 0 Κ C

= D

x

[540 (14/Me) ' } 1

(1)

2


for t h e i n t r a m o l e c u l a r s k e l e t a l h e a t c a p a c i t y . Table I I I . H e a t Capacity of Poly(methacrylate)s T(K)

PM-1

PM-2

PM-4

PM-12

PM-4i

220

PM-18

398.1

455.2

230

108.9

132.5

182.7

173.6

467.5

482.9

240

112.8

137.5

192.5

181.5

574.4

514.0

250

116.5

142.3

200.5

188.6

740.0

554.0

260

120.2

147.0

208.8

195.0

525.8

608.2

270

124.5

151.5

218.1

201.6

498.0

280

128.3

157.7

231.7

207.6

499.3

290

132.2

162.0

246.3

217.8

504.5

300

135.9

167.5

259.1

228.5

509.9

310

140.1

172.9

267.5

240.0

516.2

320

143.8

179.9

273.6

255.1

523.2

330

147.7

189.1

277.5

267.4

532.5

340

151.1

201.8

282.8

278.2

541.7

730.5

350

156.3

215.2

288.1

286.9

549.4

741.1

360

161.4

226.1

294.2

290.4

556.7

749.1

370

167.8

230.0

300.5

293.5

565.2

759.0

233.5

720.1

380

180.4

306.1

293.8

572.6

766.8

390

204.3

304.9

295.4

578.1

775.5

400

207.5

311.4

302.5

582.5

410

209.2

313.7

801.9 813.3

789.7

420

212.2

318.5

430

214.8

323.2

825.4

440

217.9

329.1

831.2

450

220.9

337.7

839.5

460

223.6

470

226.2

873.3

480

228.9

890.1

490

231.4

903.0

500

234.4

857.0

913.7

Note: Heat capacity measurements are in J m o l K . - 1

- 1


202


Table IV. Heat Capacity Contribution of C H Group on C - C Backbone Polymers B e l o w the Glass Transition Polyacrylates Polyalkenes 3


T(K)

I

II»

a

40 80 120 160 200 240 280 320 360 400 440

2.0 3.2 5.7 8.6 13.0 18.2

7.1 10.6 14.6 18.8

III

e

6.1 8.9 11.9 15.2

IV

d

9.7

V

VI

e

VII

f

s

0.6 2.8 7.1 12.2 16.7

3.8 5.3 9.2 12.7 16.5 19.4 22.0 27.9 32.8 30.6 27.1

2.2 4.0 8.2 12.5 16.6

CH

2

3.2 7.8 10.2 13.5 15.6 17.9 20.6 23.0 26.5 34.1 42.7

Note: Heat capacity measurements are in J m o l K . C (PM-1) - C (PA-1); error ± 0.4-2.6 J m o ^ K " . C (PM-2) - C (PA-3); error ± 1.2-2.8 I m o ^ K " . C (PM-4) - C (PA-4); error ± 0.6-3.8 I m o l " ^ . C (PM-4i) - C (PA-4i) error ± 3.6 J m o l ^ K " . C (PP) - 2C (PE); error ± 0.2-2.2 I m o ^ K " . ' C (PIB) - C (PE); error ± 0.2-1.2 I m o ^ K " . [C (PIB) - 2C (ΡΕ)] - 2; error ± 0.2-0.6 I m o ^ K " . - 1

a b

c

p

p

p

p

p

d e

9

1

1

1

1

p

p

p

p

P

p

p

p

;

1

1

1

1

P

1

T h e intermolecular skeletal contribution is not additive, b u t has to b e d e t e r m i n e d b y m e a s u r e m e n t at l o w t e m p e r a t u r e ( t h r e e - d i m e n sional D e b y e function). T h e development of a reliable technique of l o w t e m p e r a t u r e h e a t c a p a c i t y m e a s u r e m e n t , p r e f e r a b l y t o at l e a s t 10 Κ as d i s c u s s e d p r e v i o u s l y , is thus o f k e y importance. A u s e f u l c o m b i n a t i o n of the i n t r a m o l e c u l a r a n d i n t e r m o l e c u l a r skeletal heat capacities is p o s s i b l e u s i n g t h e T a r a s o v e q u a t i o n (13). B a s e d o n this analysis i t s h o u l d b e p o s s i b l e to d e v e l o p a n a d d i t i o n s c h e m e o f heat capacities that covers t h e i n t r a m o l e c u l a r skeletal v i brations a n d the group vibrations based o n a single atom backbone chain bead. A n initial attempt of such a n addition scheme s h o w e d p r o m i s i n g r e s u l t s (14). T h e t e m p e r a t u r e r a n g e o f s u c h s i m p l e a n a l y s i s is e s t i m a t e d to r e a c h f r o m 4 0 Κ to t h e glass t r a n s i t i o n o r t h e m e l t i n g transition. Strict correlation b e t w e e n vibrational frequencies a n d heat c a p a c i t i e s e x i s t s o n l y f o r t h e h e a t c a p a c i t i e s at c o n s t a n t v o l u m e . H e a t c a p a c i t i e s at c o n s t a n t p r e s s u r e d e v i a t e a b o v e 1 5 0 - 2 0 0 Κ i n c r e a s i n g l y f r o m t h e h e a t c a p a c i t y at c o n s t a n t v o l u m e . W i t h i n a r e a s o n a b l e t e m perature range the d e v i a t i o n is, however, proportional to the square o f t h e h e a t c a p a c i t y i t s e l f w i t h a n a l m o s t u n i v e r s a l c o n s t a n t (15). T h e r e fore, t h e a d d i t i o n s c h e m e s h o u l d also a p p l y t o heat capacities at c o n stant p r e s s u r e u p t o a p p r o x i m a t e l y 4 0 0 — 5 0 0 K . T h e e a r l y a d d i t i o n


11.

wuNDERLicH A N D G A U R

S Ο


•a

Differential

Scanning

Calorimetry

d d © q ^ d i > d ' - H c o oqcocococococo^^

S

0 ( M CO l p

^

oq oq oq co

^

ο oo i n oq

*

ce

OCOCCOŒ>iO'-jl> ^ d d «-H d d ci oqoqoqcocococo^^

© i n σ> co oo co d t> i n oq CO ^ ΙΟ CD

00 0 5 οο ιή CO CO ."o S

1

1ι

Η Ι Ο QO Η d d oq d CO CO ^

•Ξ I I I Φ ^ ^ ς ο

Ο ft* cS+l+l+lggS^g oq

^

^

η

λ

η

H tî I f

®

CO CO

oq oq oq oq co

^

Î

Y'' ^

M ft ^oo" I g^cq^^rn I

~

te S S S S ^ prS E

>

o o o o o o o o o c o o ^ o o o q c D O ^ o o o q c o c o c o ^ ^ i o i o m

^

a

&

&

a, a

a

a

Η


203


p

19.4

23.2

240

280

p

23.3

18.7

14.1

10.6

IP

21.6

16.7

12.4

9.2

IIP

- 1

1

1

1

31.6

27.8

24.0

20.2

16.1

12.0

11.6

IV

1

of - C H

1

2

h

9

f

e

d

c

b

1

1

1

1

Note: Heat capacity measurements are in J m o l ^ K . « C (PM-1) - Cp (PM Acid); error ± 0.4-3,2 J m o l ^ K " . Cp (PA-2) - Cp (PA-1); error ± 1.4-1.8 J πιοΗΚ" . [Cp (PA-4) - C (PA-1)] - 3; error ± 1.4-3.0 J m o l ^ K ' . Cp (PM-2) - Cp (PM-1); error ± 1.2-3.6 J m o l ^ K r . [Cp (PM-4) - Cp (PM-1)] Η- 3; error ± 1.6-4.4 J m o l ^ K . Cp (PBu) - Cp (PP); error ± 0.2-1.6 J m o l ^ K " . [Cp (PPe) - Cp (PP)] - 2; error + 1.0 J m o ^ K " . [Cp (PHe) - Cp (PP)] - 3; error ± 0.2-0.8 J m o l " * ^ .

320

13.8

16.1

160

200

10.8

13.0

80

120

5.0

P

Polyacrylates

Heat Capacity Contribution

40

Τ (Κ)

Table VI.

31.0

26.6

17.9 22.3

13.4

10.2

e

V

26.4

20.8

16.6

13.3

9.8

4.7

VP

20.1

VIP

21.5

16.7

12.9

9.1

4.6

VHP

Polyalkenes

G r o u p i n the S i d e C h a i n B e l o w the G l a s s


2

23.0

20.6

17.9

15.6

13.5

10.9

7.8

3.2

CH

Transition


/

a

p

p

35.5

37.7

460

500

p

p

p

p

p

p

33.8

31.6

29.3

27.1

IP

38.8

36.9

35.1

33.2

31.4

IIP

30.4

IV

_ 1

1

_ 1

1

1

36.4

33.1

e

V

1

1

1

1

1

1

1

33.7

31.8

k

j

1

h

9

e

d

c

b

p

p

p

p

p

p

p

p

p

p

p

p

p

p

1

1

1

1

33.5

VIP

39.7

37.6

35.5

33.8

VHP 1

2

41.3 43.0

37.9

37.8

36.1

34.5

32.6

30.9

20.2

CH

36.6

27.2

XP

39.5

39.4

36.6

33.7

30.9

28.0

25.1

s

X

35.3

33.9

32.6

31.3

30.0

28.7

27.3

ÎX

Polyalkenes

G r o u p i n the Side C h a i n A b o v e the Glass Transition

VP

2

Note: Heat capacity measurements are in J m o l K . C (PA-2) - C (PA-1); error ± 3.6-4.4 J m o l ^ K " . [C (PA-4) - C (PA-1)] + 3; error ± 1.6-1.8 J m o ^ K " . [C (PA-18) - C (PA-1)] -f- 17; error ± 0.4-1.0 J m o l ^ K r . C (PM-2) - C (PM-1); error ± 4.5 J m o ^ K " . [C (PM-4) - C (PM-1)] + 3; error ± 2.0-2.2 J m o l " ^ . [C (PM-6) - C (PM-1)] - 5; error ± 1.4-1.6 J m o l " ^ . [C (PM-12) - C (PM-1)] - 11; error ± 1.0 J m o ^ K " . [C (PM-18) - C (PM-1)] 17; error ± 1.0 J m o l ^ K r . C (PBu) - C (PP); error ± 2.2-2.4 J m o ^ K " . [C (PPe) - C (PP)] 4- 2; error ± 1.4-2.0 J m o ^ K " . [C (PHe) - C (PP)] -h 3; error ± 1.0 J m o l " ^ .

580

540

31.2

33.4

380

29.1

340

420

26.9

300

260

T(K)

ja

Table V I I . Heat Capacity Contribution of - C H Polyacrylates


206


Table VIII. Heat Capacity Contribution of C O O - i n the Side C h a i n B e l o w the Glass Transition VIP VP V T(K) Ρ IV IIP IP e

40 80 120 160 200 240 280

6.2 15.6 22.2 28.3 33.8 39.0 44.3

23.2 29.5 33.6 36.9 40.2

17.6 25.1 31.8 38.9

23.4 28.0 33.7 37.1

26.7 31.1 34.7 37.2

54.2

Note: Heat capacity measurements are in J mol *K *. C (PM-Acid) - C (PP); error ± 0.2-2.2 J m o ^ K " . C (PM-1) - C (PIB); error ± 0.4-2.0 J m o l " ^ . C (PA-1) - C (PP); error ± 0.8-2.0 J m o ^ K " . C (PA-2) - C (PBu); error ± 1.4-2.4 J m o ^ K " . C (PA-4) - C (PHe); error ± 1.4-3.0 J m o ^ K " . ' C (PA-4Ï) - C (P4M1P); error ± 3.4 J m o l " ^ . Heat capacity of main chain C O O — from Reference 21. a

p

6


10.6 23.6 28.0 29.9 33.2

c

d e

1

p

p

1

p

1

p

p

p

p

p

p

p

1

1

1

1

p

1

9

s c h e m e has b o r n e o u t t h i s a n a l y s i s (14). A s t h e a n a l y s i s o f t h e c u r r e n t l y d e v e l o p e d s e t o f r e c o m m e n d e d d a t a i s c o m p l e t e d (9-12), a n exp a n d e d a n d i m p r o v e d set o f tables w i l l b e presented. I n the meantime, two e m p i r i c a l extensions of the addition scheme are a t t e m p t e d . T h e f i r s t d e a l s w i t h l i q u i d s (16) i n s t e a d o f s o l i d s . I n t h e l i q u i d state, h e a t c a p a c i t i e s a r e n o t o n l y c a u s e d b y v i b r a t i o n s , b u t h a v e considerable potential energy contributions. Reasonable additivity c a n b e e s t a b l i s h e d as l o n g as t h e i n c r e a s e i n h e a t c a p a c i t y at t h e g l a s s transition temperature was normal. T h e data o f Tables V , V I I , a n d I X reaffirm this finding. T h e second extension o f the addition scheme is tested i n Tables I V — I X . H e r e w e try e m p i r i c a l l y to establish t h e heat capacity c o n t r i butions of side-chain groups (disregarding the changes i n the nonadditive contributions to the i n t r a m o l e c u l a r skeletal heat capacity). S u c h Table IX. Heat Capacity Contribution of C O O - i n the Side C h a i n Above the Glass Transition IIP T(K) Ρ IP 260 300 340 380 420 460 500

73.5

Note: Heat capacity C (PM-1) - C C (PA-1) - C C (PA-2) - C C (PA-4) - C α b

c

d

p

p

p

p

p

p

p

p

60.6 61.9 63.2 64.4 65.7 67.0 68.3

64.6 65.0 65.4 65.9

measurements are in J mol *K . (PIB); error ± 4.0 J m o l ^ K " . (PP) error ± 3.2-3.6 J m o H K " . (PBu); error ± 3.4-4.4 J m o l ^ K " . (PHe); error ± 4.4 J m o l ^ K " . 1

1

1

;

1

1


11.

wuNDERLicH A N D G A U R

Differential

Scanning

Calorimetry

207

a n a p p r o a c h s h o u l d b e s u c c e s s f u l for l o n g s i d e c h a i n s , w h i c h a g a i n a p p r o a c h the case o f i s o l a t e d c h a i n s , b u t is less s u c c e s s f u l for short side chains w h e r e the b a c k b o n e b e a d change i n mass on substitution o f a s i d e c h a i n is i m p r o p e r l y a c c o u n t e d for. Before d i s c u s s i n g T a b l e s I V - I X it m u s t be r e m a r k e d that the e r r o r l i m i t s o f t h e v a r i o u s t a b l e e n t r i e s v a r y as g i v e n i n t h e f o o t n o t e s to the tables. T h e error l i m i t s are e s t i m a t e d u s i n g a 2 % error i n the heat capacities of the parent data. T h u s , the error b e c o m e s m u c h larger i f the d i f f e r e n c e i n heat c a p a c i t y n e e d e d for t h e g i v e n g r o u p is m u c h smaller than the m e a s u r e d heat capacities of the parent polymers. T a k i n g these error l i m i t s into account, one finds that the C H g r o u p c o n n e c t e d to the c a r b o n b a c k b o n e s u b s t i t u t e d for a h y d r o g e n (i.e., i n s e r t i n g a C H b e t w e e n a C - H b o n d ) s h o w s c o n t r i b u t i o n s t o t h e h e a t c a p a c i t y t h a t a r e n o t far f r o m t h o s e o f C H g r o u p s , i n c l u d i n g s k e l e t a l v i b r a t i o n s . T h e c a u s e o f t h e v a r i o u s d e v i a t i o n s is n o t o b v i o u s at p r e s e n t a n d n e e d s m o r e s t u d y i n l i g h t o f t h e f u l l y d e v e l o p e d a d d i t i o n s c h e m e . T h e l i q u i d C H g r o u p data fit a g e n e r a l a d d i t i o n s c h e m e better t h a n the data for the glass. I n t h i s case a l l s k e l e t a l v i b r a t i o n s c a n b e a s s u m e d to b e e x c i t e d g i v i n g t h e r e a s o n for the b e t t e r a g r e e m e n t . T h e change i n heat capacity, u p o n introduction of additional C H groups into the side c h a i n , is l i s t e d i n T a b l e s V I a n d V I I a n d s h o w s e v e n c l o s e r a d h e r e n c e to a d d i t i v i t y w i t h t h e l i q u i d d a t a a p p r o a c h i n g e x p e r i m e n t a l a c c u r a c y . A g a i n , a g r e e m e n t i n t h e l i q u i d state i s b e t t e r t h a n i n t h e g l a s s y state. T h e h e a t c a p a c i t y c o n t r i b u t i o n s d u e to C O O l i s t e d i n T a b l e s V I I I a n d I X also s h o w that the data are a d d i t i v e w i t h i n the e x p e r i m e n t a l error limits. T h e i r d e v i a t i o n from the heat capacity c o n t r i b u t i n g ester groups i n the m a i n c h a i n also seems small.


3

2

2

3

2

Conclusions D i f f e r e n t i a l s c a n n i n g c a l o r i m e t r y is one of the b a s i c a n a l y s i s t e c h n i q u e s . W i t h m o d e r n i n s t r u m e n t a t i o n , a c c u r a c i e s c l o s e to c l a s s i c a l c a l o r i m e t r y c a n b e r e a c h e d . L o w t e m p e r a t u r e o p e r a t i o n to a b o u t 150 Κ i s p o s s i b l e w i t h o n l y s l i g h t l y r e d u c e d p r e c i s i o n . T h e n e w d a t a o n polyacrylate a n d p o l y m e t h a c r y l a t e heat capacities s h o w that the prior established heat capacity a d d i t i o n scheme of m a c r o m o l e c u l a r s o l i d s , w h i c h is b a s e d o n a n a n a l y s i s o f the v i b r a t i o n a l s p e c t r u m , c a n p r o b a b l y b e e m p i r i c a l l y e x t e n d e d to s i d e g r o u p c o n t r i b u t i o n s a n d a l s o to t h e l i q u i d state. O n t h e b a s i c e x a m p l e o f h e a t c a p a c i t i e s , t h e u s e f u l ness a n d i m p o r t a n c e of D S C is thus i l l u s t r a t e d . Acknowledgments T h i s is a p u b l i c a t i o n f r o m o u r A d v a n c e d T h e r m a l A n a l y s i s L a b o ratory. M a j o r f i n a n c i a l s u p p o r t for t h i s w o r k w a s g i v e n b y t h e N a t i o n a l Science F o u n d a t i o n , P o l y m e r s P r o g r a m D M R 78-15279. T h e l o w


208


temperature data w e r e d e r i v e d w i t h the h e l p of a n instrument loan b y the M e t t l e r Instrument C o r p o r a t i o n (Princeton, N J ) .


Literature Cited 1. Joule, J. P. Mem. ManchesterLit.Phil. Soc. 1845, 2, 559. 2. Pfaundler, L. Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 1 1896, 59, 145. 3. Sykes, C. Proc. R. Soc. London, Ser. A 1935, 148, 422. 4. Mueller, F. H.; Martin, H. Kolloid Z. 1960, 172, 97. 5. Watson, E. S.; O'Neill, M. J.; Justin, J.; Brenner, N. Anal. Chem. 1964, 36, 1233. 6. Wunderlich, B. In "Thermal Analysis in Polymer Characterization"; Turi, E., Ed.; Heyden: New York, 1981. 7. Mehta, Α.; Bopp, R. C.; Gaur, U.; Wunderlich,Β.J.Therm. Anal. 1978, 13, 197. 8. Gaur, U.; Mehta, Α.; Wunderlich, B. J. Therm. Anal. 1978, 13, 71. 9. Gaur, U.; Wunderlich, Β. B.; Wunderlich, B. J. Phys. Chem. Ref. Data, to be published. 10. Gaur, U.; Wunderlich, B. J. Phys. Chem. Ref. Data, to be published. 11. Gaur, U.; Wunderlich, Β. B.; Wunderlich, B. J. Phys. Chem. Ref. Data, to be published. 12. Gaur, U.; Wunderlich, B. J. Phys. Chem. Ref. Data 1981, 10. 13. Wunderlich, B.; Baur, H. Adv. Polym. Sci. 1970, 7, 151. 14. Wunderlich, B.; Jones, L. J. Macromol. Sci., Phys. 1969, 3, 67. 15. Nernst, W.; Lindemann, F. A. Z. Electrochem. 1911, 17, 817. 16. Gaur, U.; Wunderlich, B. Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem. 1979, 20, 429. RECEIVED for review October 14, 1981. ACCEPTED July 28, 1982.


Differential Scanning Calorimetry of Flexible, Linear Macromolecules

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