Polymer Characterization - ACS Publications - American Chemical

1 Automated Dynamic Mechanical Testing RAYMOND F. BOYER

Downloaded by 95.85.80.246 on June 28, 2016 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch001

Michigan Molecular Institute, Midland, MI 48640

During the past 10 years a number of fully automated instruments for the dynamic mechanical testing of polymers became commercially available. Our purpose is to provide an introductory survey that covers key references, the goals of such test methods, general but not specific differences between the several types of instruments, and factors to consider in choosing an instrument. These latter topics include fixed vs. variable (resonant) frequency, frequency range, resolving power, types of specimens that can be handled, and maintenance costs. We also emphasize that all suppliers and users of such instruments are striving to improve and/or extend the range of capabilities of their respective instruments. A special section discusses the problem of determining activation enthalpies for any loss process. Finally, we point out that parallel developments are occurring in dielectric testing via new techniques: automated self-balancing dielectric bridges, and new methods of treating dielectric data. Thermally stimulated creep and thermally stimulated current are relatively new methods. We consider these alternate techniques as both competitive with, and complementary to, dynamic mechanical methods. Possible artifacts introduced by the use of porous substrates to support fluid polymers are discussed and dismissed.

^JENERAL

ASPECTS O F D Y N A M I C M E C H A N I C A L a n d dielectric testing, automated or not, are d i s c u s s e d i n this chapter. B a c k g r o u n d material is g i v e n i n R e f e r e n c e s 1 - 1 0 . F o r m a n y years I c o l l e c t e d transition a n d relaxation temperature data from the literature, w h e t h e r obtained b y static m e t h o d s s u c h as t h e r m a l e x p a n s i o n o r b y d y n a m i c m e t h o d s i n c l u d i n g b o t h m e c h a n i c a l a n d d i e l e c t r i c loss. T h i s e n d e a v o r p r o -

0065-2393/83/0203-0003$06.75/0 © 1983 A m e r i c a n C h e m i c a l Society

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

4

POLYMER

CHARACTERIZATION


v i d e d a n o p p o r t u n i t y to c o m p a r e n u m e r o u s test m e t h o d s a n d i n s t r u m e n t s w h i l e b e i n g r e l a t i v e l y n e u t r a l as r e g a r d s a n y o n e m e t h o d (J - 9 ) . I have b e e n closely associated w i t h J . K . G i l l h a m i n the preparat i o n o f p u b l i c a t i o n s (see, f o r e x a m p l e , R e f e r e n c e 11) i n v o l v i n g d a t a o b t a i n e d b y t h e t o r s i o n a l b r a i d m e t h o d d e s c r i b e d i n R e f e r e n c e 12. I n 1979, w e a c q u i r e d a d u P o n t 981 d y n a m i c m e c h a n i c a l a n a l y z e r ( D M A ) (13). S e v e r a l j o i n t p u b l i c a t i o n s w i t h K . V a r a d a r a j a n r e s u l t e d f r o m s t u d i e s w i t h t h i s i n s t r u m e n t (14—16). T h e s e p e r s o n a l e x p e r i e n c e s w i l l not detract from m y goal of objectivity i n preparation of this i n t r o d u c tory c h a p t e r . I p l a n to e m p h a s i z e c e r t a i n p r i n c i p l e s a n d features o f d y n a m i c test m e t h o d s that s h o u l d b e c o n s i d e r e d b y those w h o are i n t e r e s t e d i n a c q u i r i n g a n i n s t r u m e n t for a s p e c i f i c r e s e a r c h p r o g r a m . I w i l l c o m m e n t o n t w o o f m y p r e v i o u s p u b l i c a t i o n s (17, 18) t o emphasize rapid developments i n this field. I n 1972,1 compared general features of the R h e o v i b r o n a n d the torsion p e n d u l u m , b o t h of w h i c h were c o m m e r c i a l a n d neither of w h i c h was automated; a n d also the n e w l y e m e r g i n g torsional b r a i d analysis ( T B A ) i n v e n t e d b y L e w i s a n d G i l l h a m a n d p e r f e c t e d b y G i l l h a m (12). R e f e r e n c e 19 g i v e s a historical r e v i e w a n d comparison of both the torsion p e n d u l u m a n d t h e T B A (19). I n 1 9 7 6 (18) I p r o j e c t e d a c o m p l e t e s w i n g to t h e a u t o m a t i o n o f dynamic mechanical testing. T h i s v i e w p o i n t hardly required a crystal b a l l . G i l l h a m ' s a p p a r a t u s n o w i s p e r f e c t e d , m u c h as h e h a s s u m m a r i z e d i t (12). K e n y o n e t a l . h a d a l r e a d y p r e s e n t e d a l e c t u r e o n t h e i r s u c c e s s i n a u t o m a t i n g t h e R h e o v i b r o n (20). A u t o m a t i o n o f d y n a m i c t e s t i n g e q u i p m e n t i n d e e d w a s at h a n d , e v i d e n c e d b y t h e D y n o s t a t i n s t r u m e n t d e v e l o p e d b y S t e r n s t e i n (22); t h e m e c h a n i c a l s p e c t r o m e ter d e v e l o p e d b y S t a r i t a (23); a n d l a t e r t h e P L d y n a m i c m e c h a n i c a l t h e r m a l a n a l y z e r d e v e l o p e d b y W e t t o n (24). S t i l l a n o t h e r a u t o m a t e d d y n a m i c m e c h a n i c a l t e s t e r d e v e l o p e d i n c o n n e c t i o n w i t h H e d v i g is the U n i r e l a x (Tetrahedron Associates). A l t h o u g h i n c o m m e r c i a l use, it temporarily was w i t h d r a w n from the market p e n d i n g d e v e l o p m e n t of a n e w m o d e l . H e n c e , t h i s i n s t r u m e n t is not d i s c u s s e d i n this v o l u m e . T h i s proliferation i n instrumentation thus includes automation of o l d e r i n s t r u m e n t s s u c h as t h e R h e o v i b r o n , t h e i n t r o d u c t i o n o f t o t a l l y n e w t y p e s , a n d e x t e n s i v e u s e o f c o m p u t e r d a t a p l o t t e r s to p e r m i t r e p resentation of a n y d e s i r e d m e c h a n i c a l loss f u n c t i o n i n a n y d e s i r e d f o r m a t . [See also t h e r e c e n t p a p e r b y I k e d a a n d S t a r k w e a t h e r (25).] T w o net c o n s e q u e n c e s o f the p a t t e r n just m e n t i o n e d are the f o l l o w i n g : (1) A t r e m e n d o u s a d v a n c e i n t h e state o f t h e art i n a c q u i r i n g p r e c i s i o n test results o n d y n a m i c m e c h a n i c a l a n d r e l a t e d r h e o l o g i c a l d a t a b y a v a r i e t y o f s o p h i s t i c a t e d c o m p e t i t i v e m e t h o d s ; a n d (2) b e w i l d e r m e n t a n d c o n f u s i o n for t h e r e s e a r c h p e r s o n f a c e d w i t h a c h o i c e o f p u r c h a s i n g o n e o f t h e s e n e w u n i t s to p e r f o r m t h e t a s k s h e has i n m i n d , while generally working within a prescribed budget limitation.


1.

BOYER

Automated

Mechanical

Testing

5

P e r h a p s t h e most u s e f u l f u n c t i o n I c a n p e r f o r m is to suggest a series o f considerations that m i g h t b e h e l p f u l i n s e l e c t i n g a n i n s t r u ment.


Meaning

of Dynamic

Mechanical

and Dielectric

Loss

Peaks

W h e n a n y m a t e r i a l i s s u b j e c t t o a s m a l l m e c h a n i c a l stress a n d h e n c e l o w strain, the s t r e s s - s t r a i n curve is linear. I f the substance is truly elastic, a l l o f the stored elastic energy, n a m e l y the area u n d e r the s t r e s s — s t r a i n l i n e , i s r e c o v e r e d o n r e m o v i n g t h e l o a d , as at t h e l e f t o f F i g u r e 1. H o w e v e r , m o s t m a t e r i a l s a r e n o t t r u l y e l a s t i c a n d w i l l e x h i b i t a h y s t e r e s i s l o o p , as at t h e r i g h t o f F i g u r e 1, o n r e m o v i n g t h e load. Z e n e r c a l l e d this latter b e h a v i o r anelastic. Some o f the stored e n e r g y is d i s s i p a t e d i n t h e f o r m o f heat. T h e area o f the hysteresis loop, w h i c h is a measure o f heat generation p e r deformation cycle, varies w i t h temperature. O v e r a short temperature r e g i o n near a m o l e c u l a r r e l a x a t i o n p r o c e s s , t h e l o o p m a y b e e x c e e d i n g l y s m a l l at t e m peratures above a n d b e l o w the relaxation process w i t h a m a x i m u m i n a r e a at t h e t e m p e r a t u r e o f t h e r e l a x a t i o n . O v e r a b r o a d t e m p e r a t u r e region i n a polymer w i t h m u l t i p l e transitions, several m a x i m a i n the area o f the hysteresis loops, o n e for each relaxation process, w i l l b e evident. F o r a d i e l e c t r i c stress a p p l i e d t o a p o l a r p o l y m e r , o n e o r m o r e h y s t e r e s i s l o o p s a l s o a r i s e as f r e q u e n c y o r t e m p e r a t u r e i s i n c r e a s e d . D i e l e c t r i c h e a t i n g t a k e s a d v a n t a g e o f t h i s fact. I n d y n a m i c m e c h a n i c a l t e s t i n g , h e a t i n g effects are u s u a l l y s m a l l b u t n o n e t h e l e s s r e a l . A n e x a m p l e o f s u c h h e a t i n g e f f e c t s w a s g i v e n b y T ô r m à l â e t a l . (26). A c y l i n d e r o f polycarbonate ( P C ) is s a n d w i c h e d b e t w e e n t w o steel r o d s — a n elastic i n p u t bar a n d a n elastic output bar. I m p a c t i n g t h e i n p u t b a r w i t h a s t r i k e r g e n e r a t e s a stress p u l s e t h a t i s t r a n s m i t t e d t h r o u g h t h e s p e c i m e n to t h e output bar. H e a t generated b y this d y n a m i c l o a d i n g o f t h e p o l y m e r b a r is m e a s u r e d w i t h a t h e r m o c o u p l e for a series o f s t a r t i n g t e m p e r a t u r e s . T h e s e t e m p e r a t u r e i n c r e a s e s c a n

PERFECT ELASTICITY STRESS

0

0

Figure 1. Schematic stress—strain plots: left, a perfectly elastic material; and right, a material that is not perfectly elastic. Area of hysteresis loop represents energy dissipated in the form of heat.


6

POLYMER CHARACTERIZATION

b e c o n v e r t e d to d y n a m i c loss m o d u l i b y the f o l l o w i n g a p p r o x i m a t e equation: G" =

4mC AT/ne p

2

max

w h e r e m i s t h e m a s s o f t h e s a m p l e , C i s its s p e c i f i c h e a t , Δ Γ i s t h e temperature rise, and e is t h e c o m p r e s s i v e strain. L o s s p e a k s for T ( 2 3 0 Κ), Τ ( 3 5 0 Κ ) , a n d T ( a b o v e 4 3 0 K ) a r e d e p i c t e d . W e h a v e f o u n d (27) t h e s e t h r e e l o s s p e a k s (at l o w e r t e m p e r a t u r e s b e c a u s e o f l o w e r f r e q u e n c i e s ) u s i n g t h e 9 8 1 D M A u n i t d e s c r i b e d i n R e f e r e n c e 13. T h e e x i s t e n c e o f a t r u e /^-relaxation n e a r 350 Κ has c r e a t e d s o m e c o n t r o v e r s y , w h i c h w a s s u m m a r i z e d r e c e n t l y (16). T h e t e m p e r a t u r e i n c r e a s e m e a s u r e d b y T ô r m â l â e t a l . (26) a p p r e n t l y offers a d d i t i o n a l e v i d e n c e for a β-loss p r o c e s s i n P C . p

m a x


β

y

g

T h e various dynamic mechanical testing units currently available a r e s i m p l y v e r y s e n s i t i v e , s o p h i s t i c a t e d i n s t r u m e n t s u s e d to m e a s u r e e n e r g y loss p e r c y c l e (and h e n c e heat generation) b y a v a r i e t y of n o n t h e r m a l s e n s i n g d e v i c e s , s u c h as d a m p i n g p e r c y c l e o r p h a s e angle. T h e various instruments measure a n d report the following quantities, d e p e n d i n g o n their mode(s) of operation: real, G ' , a n d i m aginary, G " , shear m o d u l i ; the corresponding c o m p l i a n c e s , / ' a n d / " ; r e a l , Ε ', a n d i m a g i n a r y , E " , t e n s i l e m o d u l i . T h e l o s s a n g l e , δ, u s u a l l y is r e p o r t e d as t a n δ = G 7 G ' = Ε'ΊΕ'; t h e d y n a m i c m e l t v i s c o s i t y , η, i s r e p o r t e d as η=&'/ω w h e r e ω r e p r e s e n t s t h e a n g u l a r f r e q u e n c y , n a m e l y , ω = 2 Π / w h e r e / i s the f r e q u e n c y i n h e r t z . Q u a n t i t i e s p r o p o r t i o n a l to some of these parameters also m a y be g i v e n . Instruments i n w h i c h the frequency varies also m a y d i s p l a y the frequency d i r e c t l y or m a y p r o v i d e information from w h i c h i t can be calculated. T a b l e I lists units a n d relations b e t w e e n units. A l t h o u g h a n a p p l i e d a l t e r n a t i n g v o l t a g e stress g i v e s r i s e to h e a t g e n e r a t i o n , e s p e c i a l l y at h i g h f r e q u e n c i e s a n d v o l t a g e s , t e m p e r a t u r e r i s e i s n o t u s e d n o r m a l l y to m e a s u r e d i e l e c t r i c l o s s ( b u t m a y b e as d i s c u s s e d i n R e f e r e n c e 5). D i e l e c t r i c q u a n t i t i e s c o m m o n l y r e p o r t e d i n c l u d e d i e l e c t r i c c o n s t a n t , β ' ; d i e l e c t r i c l o s s , e"; a n d t a n g e n t o f t h e l o s s a n g l e , t a n δ = e'Ve'. O t h e r r e l a t e d q u a n t i t i e s m a y b e g i v e n . Competitive

Techniques

A n y o n e contemplating the purchase of d y n a m i c m e c h a n i c a l e q u i p m e n t m u s t b e a w a r e o f s e v e r a l t e c h n i q u e s that are c o m p e t i t i v e w i t h and/or c o m p l e m e n t a r y to the m e c h a n i c a l m e t h o d s . S o m e o f these t e c h n i q u e s are r e l a t i v e l y n e w ; a l l h a v e b e e n or are c a p a b l e o f b e i n g automated. T h e r m a l l y Stimulated C r e e p . T h i s m e c h a n i c a l t e c h n i q u e w a s d e v e l o p e d b y L a c a b a n n e e t a l . (27-29). T h e s p e c i m e n i s s u b j e c t e d to


1.

BOYER

Automated

Mechanical

7

Testing

T a b l e I. C o m m o n T e r m s , Symbols, and Units for D y n a m i c M e c h a n i c a l and D y n a m i c M e l t Viscosity Data Units Term Shear modulus

New

Old

Symbol

dynes/cm kg/cm lb/in. lb/in. lb/in. lb/in. degrees

G'

2

N/m " 2

2


2

S h e a r loss Tensile modulus T e n s i l e loss L o s s angle Loss tangent Decrement Frequency Angular frequency D y n a m i c melt viscosity

G" E' E' δ tan δ Δ° 1

N/m N/m N/m same 2

2

2

6

c y c l e s/s radians/s Ps

ω

e

Note: Conversion factors are approximately as follows: 1 kg force/cm = 14.2 PSI = 0.968 arm = 0.981 bar = 9.81 xl0 N/m

Hz same same

2

4

(Because E' and G ' may be of the order of 10 N / m gigapascals is being used with symbol gP.) 9

a

6 c

d e

2

2

= 10 Pascals, the term 9

Newtons per meter squared, also called Pascals.

Tan δ = G 7 G ' = E"/E'.

Δ = π tan δ. Log Δ is plotted directly by some instruments.

7]' = G''/ω.

Pascal seconds.

a t o r s i o n a l l o a d at a n e l e v a t e d t e m p e r a t u r e a n d c o o l e d r a p i d l y w i t h the l o a d s t i l l a p p l i e d . O n w a r m i n g , b o t h strain a n d its t i m e d e r i v a t i v e a r e r e c o r d e d as a f u n c t i o n o f t e m p e r a t u r e . T h e m e t h o d is c a p a b l e o f h i g h r e s o l v i n g p o w e r for d e t e c t i n g m u l t i p l e transitions. It uses a tor s i o n p e n d u l u m w i t h the s p e c i m e n s u p p o r t e d o n a glass b r a i d i f the m e l t state is to b e s t u d i e d . Dielectric Methods. T h e s e m e t h o d s a r e o f t w o t y p e s : (a) d i r e c t r e a d i n g b r i d g e s that p r o v i d e e i t h e r r e c o r d i n g or d i g i t a l r e a d o u t o f d i e l e c t r i c c o n s t a n t , d i e l e c t r i c l o s s , t a n δ, a n d o t h e r q u a n t i t i e s as a function of temperature; some instruments provide a choice of several f r e q u e n c i e s ; a n d (b) t h e r m a l l y s t i m u l a t e d c u r r e n t d i s c h a r g e ( T S C ) . T h i s m e t h o d is t h e e l e c t r i c a l a n a l o g o f t h e r m a l l y s t i m u l a t e d c r e e p . A h i g h v o l t a g e i s a p p l i e d to a p o l y m e r f i l m at e l e v a t e d t e m p e r a t u r e a n d t h e s a m p l e is c o o l e d r a p i d l y w i t h t h e v o l t a g e o n . A f t e r r e m o v a l o f t h e a p p l i e d v o l t a g e , t h e s p e c i m e n is h e a t e d at a s l o w r a t e w h i l e c u r r e n t flow t h r o u g h t h e s p e c i m e n i s m e a s u r e d . A c u r r e n t p e a k o c c u r s at e a c h t r a n s i t i o n (see R e f e r e n c e s 8 a n d 9 for d e t a i l s ) . F i g u r e 2 s h o w s a c u r r e n t t r a c e for a t a c t i c p o l y m e t h y l m e t h a c r y l a t e ( P M M A ) (30). A n a u t o -


8


_I(1(T A) 1 1

τ>τ

3

6

-


2

P=180°C

\

[/T(°C> I'

I

-200 J 0 0

I

0

I

100

200

Figure 2. TSC trace on atactic polymethyl methacrylate that was polarized at 180 °C for 2 min by an applied field of 1Œ Vim, rapidly cooled under voltage, and heated at about 1 Klmin. Effective frequency was ~10~ Hz. Vertical axis is electric current in amperes generated by the polarized specimen because of reorientation of dipoles and/or motion of charge carriers. See Ref. 28 for details. 4

m a t e d i n s t r u m e n t for o b t a i n i n g s u c h d a t a is t h e E l e c t r e t T h e r m a l A n a l y z e r ( A t l a s E l e c t r i c D e v i c e s ) . R e s o l v i n g p o w e r is v e r y h i g h a n d m a n y s m a l l current peaks, e a c h i n d i c a t i v e of some transition or relaxa t i o n , m a y b e s e e n i n a d d i t i o n to m a j o r t r a n s i t i o n s o b s e r v e d i n d y n a m i c t e s t i n g . T S C has s e v e r a l advantages

besides high

resolv-

i n g p o w e r a n d s i m p l i c i t y . F i r s t , i t c a n w o r k i n t h e m o l t e n state w h e r e p o l y m e r s are m e c h a n i c a l l y w e a k , v e r y s t i c k y , a n d s u b j e c t to flow.

viscous

L a c a b a n n e et a l . u s e d T S C to o b s e r v e t h e l i q u i d — l i q u i d

t r a n s i t i o n i n P S (31) a n d P M M A (30).

(T ) H

Second, having scanned a speci-

m e n f r o m l o w to h i g h t e m p e r a t u r e a n d l o c a t e d a l l o f t h e c u r r e n t p e a k s , one can do a n e w experiment c o m b i n i n g selection of the p o l a r i z i n g t e m p e r a t u r e f o l l o w e d b y s h o r t - c i r c u i t i n g at s o m e l o w e r

temperature

to i s o l a t e a n y d e s i r e d t r a n s i t i o n r e g i o n . E x a m p l e s a p p e a r i n R e f e r e n c e 3 1 f o r P S a n d R e f e r e n c e 3 0 for P M M A . A p p l i c a t i o n o f t h e T S C t e c h n i q u e to o t h e r s p e c i f i c p o l y m e r s m a y b e c i t e d as f o l l o w s : s e v e r a l p o l y s t y r e n e s (32);

p o l y a c r y l o n i t r i l e (33);

p o l y c a r b o n a t e ( P C ) (34);

crystalline polymers [polyethylene (PE), Teflon, p o l y v i n y l i d e n e


several fluoride

1.

BOYER

Automated

Mechanical

Testing


( P V D F ) ] (35, 36); p o l y b l e n d s (37); e p o x i e s (38); a n d n y l o n s (39). c o u r s e , n u m e r o u s e x a m p l e s a p p e a r i n R e f e r e n c e s 8 a n d 9.

9 Of

A (qualitative) comparison b e t w e e n d y n a m i c m e c h a n i c a l a n d d i e l e c t r i c test results m a y b e i n s t r u c t i v e . E x c e p t i n s p e c i a l cases, r e l a t i n g a d y n a m i c m e c h a n i c a l l o s s p e a k to a s p e c i f i c t y p e o f m e c h a n i c a l motion may be difficult. O f course, J . Heijboer's torsion p e n d u l u m s t u d y (40) o f c y c l o h e x y l a n d o t h e r c y c l o a l k y l r i n g m o t i o n s is a n o t e d exception i n w h i c h the type of m o t i o n is k n o w n i n detail. I f a p o l y m e r c o n t a i n s a p o l a r g r o u p ( i n c l u d i n g m i l d l y o x i d i z e d P E ) so t h a t t h e r e i s direct c o u p l i n g b e t w e e n the d i e l e c t r i c f i e l d a n d that p o l a r group, the nature of the m o t i o n may be k n o w n w i t h precision. F o r a c o m p l i c a t e d p o l y m e r l i k e P C , a c o m b i n a t i o n o f m a n y t e c h n i q u e s w a s n e e d e d to u n r a v e l the l o w temperature loss peaks: d y n a m i c m e c h a n i c a l , d i e l e c tric, IR, T S C , a n d N M R . W e r e v i e w e d the pertinent literature on this p o l y m e r (14, 16). D i e l e c t r i c t e s t i n g a l w a y s has f a c e d a d i l e m m a b e t w e e n d i r e c t c u r r e n t c o n d u c t i o n l o s s at l o w f r e q u e n c y a n d p o o r r e s o l v i n g p o w e r at high frequency. A technique recently reported by Klaase and V a n T u r n h o u t (41) a l l o w s for c i r c u m v e n t i o n o f t h e p r o b l e m s a s s o c i a t e d w i t h c o n d u c t i o n c u r r e n t s at r e l a t i v e l y l o w f r e q u e n c y . T r a d i t i o n a l l y , e" loss peaks m a y be b u r i e d c o m p l e t e l y b y c o n d u c t i o n currents, u s u a l l y at h i g h fluidity, w h e t h e r t h e r e s u l t o f h i g h t e m p e r a t u r e , t h e p r e s e n c e of d i l u e n t s , or b o t h . C l a s s i c a l methods c a n correct this p r o b l e m . H o w e v e r , R e f e r e n c e 4 1 p o i n t s o u t t h a t t h e d i e l e c t r i c c o n s t a n t , e', i s n o t a f f e c t e d b y c o n d u c t i o n c u r r e n t s . H e n c e , t h e d e r i v a t i v e , de'ldT o r de'ld l o g / , w i l l e x h i b i t a m a x i m u m at a n e" l o s s p e a k b u r i e d u n d e r t h e conduction current. T h i s technique can greatly extend the utilization o f d i e l e c t r i c t e s t i n g . A p p l i c a t i o n o f t h i s m e t h o d to d i e l e c t r i c l o s s at 1 H z as a p p l i e d t o P V D F h a s b e e n d e m o n s t r a t e d (41). I predict a resurgence of interest i n dielectric testing sparked b y the electronic applications of electrets a n d other piezoelectric devices p r e p a r e d f r o m p o l y m e r s a n d c o p o l y m e r s o f v i n y l i d e n e fluoride. T h i s resurgence w i l l be a i d e d both b y the self-balancing bridges a n d b y the i m p r o v e d data treatment methods just m e n t i o n e d . M o r e o v e r , a d i e l e c t r i c b r i d g e is a c o n v e n i e n t m e t h o d f o r e x t e n d i n g t h e f r e q u e n c y range o f d y n a m i c m e c h a n i c a l loss e q u i p m e n t , thus p e r m i t t i n g c a l c u l a t i o n o f m o r e a c c u r a t e a c t i v a t i o n e n e r g i e s . (See s e c t i o n e n t i t l e d " T e s t Frequency.") H e d v i g (4) d e s c r i b e d t h e p r i n c i p l e s o f v a r i o u s s e l f - b a l a n c i n g a n d / o r d i r e c t r e c o r d i n g b r i d g e s . Y a l o f a n d W r a s i d l o (42) d i s c u s s e d a specific direct b a l a n c i n g - r e c o r d i n g unit n o w commercially availa b l e as A u d r e y ( a u t o m a t i c d i e l e c t r o m e t e r ) f r o m T e t r a h e d r o n . T h i s g r o u p (42) s t r o n g l y r e c o m m e n d s t h e c o m b i n e d u s e o f d i e l e c t r i c


10


testing w i t h one other m e t h o d , for e x a m p l e , differential s c a n n i n g calorimetry ( D S C ) , i n production quality control. W e use a H e w l e t t - P a c k a r d automatic b a l a n c i n g b r i d g e that pro v i d e s d i g i t a l r e a d o u t s o f c a p a c i t a n c e , r e s i s t a n c e , i n d u c t a n c e , t a n 8, a n d Q at a n y o f t h r e e p r e s e l e c t e d f r e q u e n c i e s , Ι Ο , 1 0 , a n d 1 0 H z (42). D e s i g n e d for p r o d u c t i o n l i n e q u a l i t y c o n t r o l t e s t i n g o f e l e c t r i c a l c o m p o n e n t s , i t h a s p r o v e n to b e a u s e f u l r e s e a r c h t o o l . Its l o w e r l i m i t o f tan δ is 0.001. T h i s a u t o m a t i c b a l a n c i n g b r i d g e c a n b e i n t e r f a c e d w i t h r e c o r d i n g e q u i p m e n t . Its u s e i n d e t e c t i n g T i n p o l y c h l o r o s t y r e n e is d i s c u s s e d e l s e w h e r e (43). T h e l i q u i d - l i q u i d t r a n s i t i o n ( T ) i n p o l y p r o p y l e n e g l y c o l 4000 also was detected w i t h this same instru m e n t (44). 2

3

4

tt

H


Choosing

an

Instrument

T h i s task is f o r m i d a b l e , i n part b e c a u s e o f t h e v a r i e t y o f h i g h c a l i b e r i n s t r u m e n t s a v a i l a b l e f r o m w h i c h to m a k e a c h o i c e ; i n p a r t because usually more than one n e e d and/or more than one group must be satisfied; a n d finally because there may be m o n e y restrictions. Some compromises frequently must be made i n o p t i m i z i n g the choice i n i n s t r u m e n t a t i o n . I a t t e m p t o n l y to p o i n t o u t s o m e f a c t o r s f o r c o n s i d eration. I s h a l l n o t a t t e m p t to m a k e a p o i n t - t o - p o i n t c o m p a r i s o n o f a l l c o m m e r c i a l instruments. I do speak of specific b n m d names i n rela t i o n to a s i t u a t i o n o r p r o b l e m u n d e r d i s c u s s i o n ; h o w e v e r , t h e c i t i n g o f a s p e c i f i c b r a n d n a m e s h o u l d n o t b e c o n s t r u e d as e n d o r s i n g t h a t i n s t r u m e n t o v e r c o m p e t i t i v e b r a n d s . T h e m a i n factors that I w i s h to c o v e r as g u i d e l i n e s o f c h o i c e a r e t h e f o l l o w i n g : 1. D e f i n i n g t h e task(s) being chosen. T h i s possible future needs. can best be solved by areas.

or problem(s) of the i n s t r u m e n t i n c l u d e s i m m e d i a t e as w e l l as T h i s is a n i n d i v i d u a l p r o b l e m a n d c o n s i d e r i n g the f o l l o w i n g specific

2. T y p e s o f s p e c i m e n s , t e m p e r a t u r e r a n g e , f r e q u e n c y r a n g e , a n d d e f o r m a t i o n m o d e . (See T a b l e II.) 3. F i x e d v s . v a r i a b l e f r e q u e n c y . (See Frequency.")

the section o n " T e s t

4. P r o p e r t i e s ( d y n a m i c l o s s , s t o r a g e m o d u l u s , etc.) as a f u n c t i o n o f f r e q u e n c y v s . s u c h p r o p e r t i e s as a f u n c t i o n o f t e m p e r a t u r e , o r as a f u n c t i o n o f b o t h . 5. R e s o l v i n g p o w e r , a c c u r a c y , a n d r e p r o d u c i b i l i t y . (See section on " R e s o l v i n g Power.")

the

6. T o t a l c a p a b i l i t y o f a g i v e n i n s t r u m e n t ; a o n e - l i n e characterization of any instrument can be misleading. (See t h e s e c t i o n o n " O v e r C a t e g o r i z a t i o n . " )


1.

BOYER

Automated

Mechanical

11

Testing

T a b l e II. T y p e s of Specimens and Temperature Ranges Specimen

Comment

Type

1. F i x e d l i q u i d s s u c h as plasticizers that m a y have t r a n s i t i o n s s u c h as m e l t i n g and T 2. E l a s t o m e r s

A s u b s t r a t e to c a r r y t h e s p e c i m e n is n e e d e d w i t h m o s t instruments α

g

3. A m o r p h o u s t h e r m o p l a s t i c s m e a s u r e d u p to or j u s t above T 4. S a m e as 3 b u t m e a s u r e d above T 5. S e m i c r y s t a l l i n e p o l y m e r s u p to T 6. S a m e as 5 b u t g o i n g above T 7. T h e r m o s e t s ( a l r e a d y c u r e d ) u p to t h e r m a l d e c o m p o s i tion temperatures 8. C u r a b l e l o w m o l . w t . l i q u i d s or s o l i d s that c h a n g e to t h e r m o p l a s t i c s or thermosets on cure 9. C o m p o s i t e s c o n s i s t i n g o f a thermoplastic polymer b l e n d e d w i t h particulate or fibrous filler 10. C o m p o s i t e t h e r m o s e t s

M a y require vulcanization and special sample clamping device Usually no problem unless s p e c i m e n is v e r y b r i t t l e b

g

M e c h a n i c a l support needed

a


g

U s u a l l y no problems

m

Mechanical support needed

a

m

Usually no problems

Support system needed

a

Filler may provide internal s u p p o r t i n t o t h e Τ >T tem perature region g

Usually no problems

Substrate may be a porous system impregnated with the polymer; or a solid such as a metal strip coated with the polymer. See section on " T h e Braid Controversy." Low molecular weight polymers tend to have low strength and may be quite brittle. α

6

Temperature vs. F r e q u e n c y as an Independent Plotting V a r i able. D y n a m i c m e c h a n i c a l f u n c t i o n s s u c h as E ' , G ' , E", G " , a n d t a n δ m a y b e p l o t t e d as a f u n c t i o n o f t e m p e r a t u r e at a s i n g l e f i x e d f r e q u e n c y ( i s o c h r o n a l p l o t ) ; a g a i n s t f r e q u e n c y , / , at a s i n g l e f i x e d t e m p e r a t u r e ( i s o t h e r m a l p l o t ) ; c o m b i n a t i o n s i n w h i c h Τ o r / is t h e i n d e p e n d e n t variable a n d different isochrones or isotherms appear o n the same plot as a f u n c t i o n o f Τ o r / , r e s p e c t i v e l y ; o r f i n a l l y , o n a r e d u c e d f r e q u e n c y p l o t a g a i n s t l o g fa w h e r e a is t h e r e d u c t i o n f a c t o r . S u c h p l o t s c o m b i n e d i f f e r e n t sets o f t e m p e r a t u r e a n d f r e q u e n c y d a t a i n t o a s i n g l e c u r v e c o m m o n l y g i v e n at a r e f e r e n c e t e m p e r a t u r e o f 2 5 ° C , a l t h o u g h T

T


12


any reference temperature may be selected. E x a m p l e s of these vario u s t y p e s o f p l o t s m a y b e i n s p e c t e d i n s t a n d a r d r e f e r e n c e w o r k s (J - 5 ) .


S o m e instruments m a y c o m e w i t h accessories that i n c l u d e a selfc o n t a i n e d c o m p u t e r - p l o t t e r for p l o t t i n g a n y d e p e n d e n t v a r i a b l e against one or m o r e i n d e p e n d e n t v a r i a b l e s . M o r e s i m p l y , data f r o m the instrument m a y be tape p u n c h e d a n d u s e d i n a standard c o m p u t e r - d a t a p l o t t i n g system. O n e s o p h i s t i c a t e d d e v i c e of great v e r s a t i l i t y w a s d e s c r i b e d e l s e w h e r e (25). A n y d y n a m i c m e c h a n i c a l u n i t c a p a b l e o f b e i n g p r e s e t to a f i x e d f r e q u e n c y (see t h e s e c t i o n e n t i t l e d " T e s t F r e q u e n c y " ) w i l l h a v e a r e l a t i v e l y s m a l l n u m b e r o f t h e s e f i x e d f r e q u e n c i e s t o s e l e c t as w e l l as a s m a l l t o t a l r a n g e . T e m p e r a t u r e i n c r e m e n t s at a f i x e d f r e q u e n c y c a n b e as s m a l l as t h e e x p e r i m e n t e r d e s i r e s , s u c h as 1, 5, 10, a n d 2 0 ° C , o r , w i t h some instruments, they can increase continuously. Plots against t e m p e r a t u r e s h o w l o c a t i o n s o f t r a n s i t i o n s at t e m p e r a t u r e s t h a t c a n b e c o r r e l a t e d w i t h d a t a f r o m q u a s i - s t a t i c d e v i c e s s u c h as D S C , t h e r m a l expansion, and other devices. F i n a l l y , t w o p r a c t i c a l s u g g e s t i o n s are b a s e d o n t h e a s s u m p t i o n t h a t a n i n d i v i d u a l o r g r o u p h a s a r r i v e d at a c h o i c e b e t w e e n t w o c o m p e t i t i v e i n s t r u m e n t s or e v e n a s i n g l e i n s t r u m e n t . O n e s u g g e s t i o n is to t a l k to o n e o r s e v e r a l i n d i v i d u a l s a l r e a d y u s i n g o n e o r t h e o t h e r o f t h e two instruments i n question. Subtle points about mechanical d e p e n d a b i l i t y , s p e e d o f s e r v i c e , r e p l a c e m e n t c o s t s , etc., m a y e m e r g e . T h e o t h e r p o i n t is to r e q u e s t f r o m t h e i n s t r u m e n t m a n u f a c t u r e r a t e s t r u n o n o n e o r s e v e r a l t y p i c a l s p e c i m e n s t h a t are o f c u r r e n t i n t e r e s t to t h e e v e n t u a l user. T h e r e are, of course, m a n y other practical c o n s i d erations. F o r example, i f the i n t e n d e d use of an instrument covers a study of elastomers, b l o c k p o l y m e r s , or any system w i t h T w e l l b e l o w r o o m t e m p e r a t u r e , one s h o u l d c o m p a r e alternate i n s t r u m e n t s i n costs for l i q u i d n i t r o g e n a n d / o r m e c h a n i c a l r e f r i g e r a t i o n systems. g

Over

Categorization

I t is r e l a t i v e l y e a s y t o a t t a c h to a n y g i v e n i n s t r u m e n t a l a b e l t h a t i m p l i e s l i m i t e d u s e for t h a t i n s t r u m e n t . S u c h l a b e l s are r e s t r i c t i v e a n d m i s l e a d i n g . I n a n early r e v i e w w e stated that the R h e o v i b r o n was l i m i t e d t o t h e t e n s i o n m o d e at t e m p e r a t u r e s u p t o T , W e l e a r n e d (see f o o t n o t e s t o T a b l e I o f R e f e r e n c e 17) t h a t i t h a d i n d e e d b e e n u s e d i n s h e a r a b o v e T . M a n u f a c t u r e r s are a w a r e o f t h e d i v e r s e , e v e n t h o u g h s e l d o m u s e d , c a p a b i l i t i e s o f t h e i r o w n i n s t r u m e n t s as d e v e l o p e d b y t h e m s e l v e s or d e s c r i b e d i n the literature. g

g

G i l l h a m e m p h a s i z e s t h a t a T B A u n i t c a n b e u s e d as a t o r s i o n p e n d u l u m b y s u b s t i t u t i n g a p o l y m e r f i l m for t h e l o a d e d b r a i d ; a n d , conversely, that any torsional p e n d u l u m c a n f u n c t i o n i n the T B A m o d e by u s i n g a l o a d e d b r a i d i n place of the film. T h e only substan-


1.

BOYER

Automated

Mechanical

Testing

13

t i v e d i f f e r e n c e s are t h a t (a) t h e b r a i d p l u s p o l y m e r s y s t e m is a c o m p o s i t e t h a t d o e s n o t y i e l d a n a b s o l u t e v a l u e o f G ' ; a n d (b) o n e c a n n o t operate a p p r e c i a b l y above T or T i n the p e n d u l u m m o d e .


g

m

W e e x p e c t the t r e n d to g r o w s u c h that a n y g i v e n i n s t r u m e n t w i l l have one or s e v e r a l p r i n c i p a l m o d e s of o p e r a t i o n b u t it n e e d not be c o n f i n e d to t h o s e m o d e s . C o m p e t i t i o n b e t w e e n s u p p l i e r s o f i n s t r u m e n t s a n d / o r i n g e n u i t y o n t h e p a r t o f u s e r s w i l l l e a d to a c o n s t a n t stream of innovations. T h e m o d e of o p e r a t i o n o f the d u P o n t D M A 981 u n i t has p u z z l e d m a n y p e r s o n s . L e a r (45) c l a r i f i e d t h i s s i t u a t i o n b y s h o w i n g t h a t at a l o w Lit ( l e n g t h / t h i c k n e s s ) r a t i o t h e d e f o r m a t i o n is p r i m a r i l y s h e a r ; at h i g h Lit, t h e d e f o r m a t i o n i s i n b e n d i n g , h e n c e t e n s i o n . O f course, before the development of T B A , techniques h a d b e e n d e v e l o p e d a n d t h e o r y p r o v i d e d as e a r l y as 1 9 5 1 f o r p o l y m e r - c o a t e d m e t a l s t r i p s to b e m e a s u r e d b y t h e t o r s i o n p e n d u l u m m e t h o d , t h u s permitting study of l o w molecular weight polymers and/or polymers a b o v e T (see f o o t n o t e to T a b l e I i n R e f e r e n c e 17 a n d A p p e n d i x C ) . g

Subsequently, numerous techniques have b e e n described: use of p o r o u s s u p p o r t s f o r t o r s i o n p e n d u l u m (46) a n d R h e o v i b r o n (47); polymer-coated c o i l e d springs i n the R h e o v i b r o n , a m e t h o d c a l l e d d y n a m i c s p r i n g a n a l y s i s ( D S A ) (48); u s e o f a g l a s s m o n o f i l a m e n t c o a t e d w i t h a u n i f o r m t h i c k n e s s o f p o l y m e r as t h e s p e c i m e n i n a T B A u n i t (49). A l t h o u g h t h e s p e c i m e n i s a c o m p o s i t e , s i m p l e g e o m e t r y permits calculation of p o l y m e r constants. P r o b l e m s c o n c e r n initial uniformity of coating a n d vertical flow of p o l y m e r d u r i n g the e x p e r i ment. O b v i o u s l y , the same e x p e r i m e n t can be c o n d u c t e d i n a c o n v e n tional torsion p e n d u l u m . Test

Frequency

A v a i l a b l e d y n a m i c m e c h a n i c a l test e q u i p m e n t is o f s e v e r a l t y p e s : (a) a s m a l l n u m b e r o f f i x e d , p r e s e l e c t e d f r e q u e n c i e s , w i t h t e m p e r a t u r e as t h e v a r i a b l e ; (b) a f r e q u e n c y s w e e p a g a i n s t a l i n e a r o r l o g a r i t h m i c f r e q u e n c y s c a l e ; a n d (c) r e s o n a n t s y s t e m s i n w h i c h t h e f r e q u e n c y d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e as t h e m o d u l u s o f t h e s p e c i m e n decreases. T h e t o r s i o n p e n d u l u m a n d D M A 981 u n i t s are o f this type. T h e i n t e n d e d e n d use for a d y n a m i c m e c h a n i c a l tester w i l l b e a major factor i n d e c i d i n g w h i c h o f three types of u n i t s to c h o o s e . O n e m a y w i s h to correlate w i t h i m p a c t t e s t i n g w h e r e the effective freq u e n c y is about 1000 H z ; or w i t h acoustic e n e r g y a b s o r p t i o n w h e r e a r a n g e f r o m a b o u t 100 to a b o u t 1 0 , 0 0 0 H z m a y b e o f i n t e r e s t . A l t e r n a t i v e l y , t h e i n v e s t i g a t o r m a y w i s h to c o n s t r u c t r e l a x a t i o n m a p s , n a m e l y , plots o f l o g f r e q u e n c y against r e c i p r o c a l t e m p e r a t u r e for e a c h o f the several loss peaks i n a s p e c i m e n , f r o m w h i c h a p p a r e n t e n t h a l p i e s of


14

POLYMER

CHARACTERIZATION

a c t i v a t i o n , Δ Η , c a n b e c a l c u l a t e d . I n t h i s c a s e , a f r e q u e n c y r a n g e o f at l e a s t t w o a n d p r e f e r a b l y a m i n i m u m o f t h r e e d e c a d e s is d e s i r a b l e to g e t m e a n i n g f u l v a l u e s o f Δ Η . I f e x t r e m e p r e c i s i o n i n ΔΗ i s d e s i r e d , s e v e r a l d y n a m i c m e c h a n i c a l test i n s t r u m e n t s m a y b e n e e d e d . F o r e x a m p l e , o n e g r o u p advocates t h e u s e o f f i v e d i f f e r e n t i n s t r u m e n t s to c o v e r t h e f r e q u e n c y r a n g e f r o m 1 0 ~ H z ( c r e e p ) to 1 0 H z (50). C o n v e r s e l y , l o w f r e q u e n c y m e c h a n i c a l loss results m a y b e s u p plemented w i t h dielectric measurements i n w h i c h a single dielec t r i c b r i d g e m a y c o v e r t h e r a n g e f r o m 6 0 t o 1 0 H z . If, h o w e v e r , o n e ' s i n t e r e s t is p r i m a r i l y i n l o c a t i n g m e c h a n i c a l l o s s p e a k s a l o n g t h e t e m p e r a t u r e s c a l e as a f u n c t i o n o f c h e m i c a l s t r u c t u r e , p o l y m e r b l e n d s , block copolymers, percent crystallinity, cross-linking, additive con t e n t s u c h as f i l l e r s o r p l a s t i c i z e r s , a r e s o n a n t - t y p e a p p a r a t u s i s g e n e r a l l y a d e q u a t e . 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 for m o s t c o m m o n t h e r m o p l a s t i c s a n d t h e r m o s e t s is r e l a t i v e l y i n v a r i a n t w i t h f r e q u e n c y over a range of 1 0 0 - 1 0 0 0 H z . α

α

α

4

6


5

W i t h resonant systems, the initial frequency can be v a r i e d w i t h i n limits b y c h a n g i n g the geometry of the instrument and/or the speci m e n dimensions. A torsion p e n d u l u m may choose any of several iner t i a d i s k s to alter i n i t i a l f r e q u e n c y , a l t h o u g h t h i s a p p r o a c h is not c o m m o n . T h e d u P o n t D M A 981 u n i t c a n e m p l o y specimens of different l e n g t h s a n d / o r t h i c k n e s s e s to a l t e r t h e s t a r t i n g f r e q u e n c y . O u r p h i l o s o p h y a b o u t f r e q u e n c y v a r i a t i o n for c a l c u l a t i n g Δ Η v a l u e s is n o w b e s t d e s c r i b e d as c a u t i o u s t h o u g h n o t c a l l o u s . T h i s a t t i t u d e is b a s e d o n t h e f o l l o w i n g o b s e r v a t i o n s a n d c o n s i d e r a t i o n s : α

1. M a n y r e l a x a t i o n m a p s h a v e b e e n d e t e r m i n e d a n d p u b l i s h e d , g e n e r a l l y i n c o n v e n i e n t c o l l e c t i o n s (I —7). 2. I n f o r m a t i o n g a i n e d f r o m t h e s e r e p o r t s s h o w s t h a t Δ Η for T increases m o n o t o n i c a l l y (actually, e x p o n e n t i a l l y ) w i t h i n c r e a s i n g T so t h a t k n o w i n g T b y a n y l o w f r e q u e n c y m e t h o d s u c h as D S C o r t o r s i o n p e n d u l u m a l l o w s a r e a s o n a b l y accurate estimate o f Δ Η for T to b e m a d e . (See R e f e r e n c e 10 a n d a l s o A p p e n d i x B.) α

g

g

g

α

g

3. I n s i m i l a r f a s h i o n , ΔΗ for t h e ^ - r e l a x a t i o n [Τ (Κ) T (K) f o r m a n y p o l y m e r s ] i n c r e a s e s l i n e a r l y w i t h (51). α

β

g

0.75 Τ (Κ) β

4. K n o w i n g t h e s e v e r a l t r a n s i t i o n s i n o r d e r o f d e c r e a s i n g t e m p e r a t u r e at a l o w f r e q u e n c y s u c h as a b o u t 1 H z , namely, melting, T , Τ , T, T , a n d other transitions, the relaxation m a p most l i k e l y w i l l consist of a series of straight l i n e s d r a w n from these 1-Hz values a n d intersect at o r n e a r 1 0 / T ( K ) o n t h e v e r t i c a l s c a l e at a t e m p e r a t u r e v e r y near to T (52). g

β

y

b

1 2

m

5. N u m e r i c a l a n a l y t i c a l p r o c e d u r e s f o r d e t e r m i n i n g a c t i v a -


1.

BOYER

Automated

Mechanical

15

Testing

tion energies from a single frequency have been pro p o s e d (53). T h e t r e a t m e n t o f r e s o n a n t m o d e s is a s p e c i a l case. 6. O c c a s i o n a l l y , w e c o l l e c t e d s c a t t e r e d m e c h a n i c a l l o s s data from the literature a n d constructed a relaxation m a p , u s u a l l y of l i m i t e d scope. I n one instance, w e m e r g e d our l o w frequency D M A data on a β-loss peak w i t h h i g h e r f r e q u e n c y literature data to estimate a r e l i a b l e v a l u e o f ΔΗ (16). α

T h e s e r e m a r k s s h o u l d not b e c o n s t r u e d to i m p l y a n e g a t i v e atti t u d e o n o u r p a r t a b o u t r e l a x a t i o n m a p s a n d v a l u e s o f ΔΗ . S u c h n u m e r i c a l v a l u e s a n d plots c l e a r l y assist i n the o v e r a l l u n d e r s t a n d i n g of r e l a x a t i o n a n d t r a n s i t i o n p h e n o m e n a . R a t h e r , w e are m a k i n g t w o p o i n t s : (1) I f a n i n d i v i d u a l o r g r o u p is f o r c e d , f o r w h a t e v e r r e a s o n , to purchase an i n s t r u m e n t l a c k i n g c o n t r o l l e d frequency settings, various a l t e r n a t i v e s are a v a i l a b l e f o r e s t i m a t i n g ΔΗ v a l u e s , as j u s t e n u m e r a t e d ; a n d (2) o n e m a y g e t c a r r i e d a w a y b y t h e s e e m i n g l u x u r y o f twisting knobs w i t h o u t r e a l i z i n g some of the attendant problems i n a n a l y z i n g the data.


α

α

Resolving

Power

R e s o l v i n g p o w e r denotes h e r e i n the a b i l i t y of a t e c h n i q u e or a n i n s t r u m e n t to s e p a r a t e t w o a d j a c e n t l o s s p e a k s . T h i s a b i l i t y w i l l d e p e n d o n s e v e r a l f a c t o r s : (1) a c t u a l s e p a r a t i o n o f t h e t r a n s i t i o n s i n K e l v i n s f o r a l o w f r e q u e n c y t e s t s u c h as t h e r m a l e x p a n s i o n o r D S C ; (2) s t r e n g t h s o f t h e t w o t r a n s i t i o n s ; (3) f r e q u e n c y o f t h e t e s t m e t h o d ; (4) i n h e r e n t s e n s i t i v i t y o f t h e t e s t i n s t r u m e n t ; (5) a c t i v a t i o n e n t h a l p i e s for t h e t w o l o s s p r o c e s s e s ; a n d (6) m o d e o f d e f o r m a t i o n , n a m e l y s h e a r , t e n s i o n , or b e n d i n g . A g o o d p o l y m e r w i t h w h i c h to c h e c k r e s o l v i n g p o w e r i s P V D F at l o w t e m p e r a t u r e . A c c o r d i n g to u n p u b l i s h e d t o r s i o n p e n d u l u m d a t a o f H e i j b o e r at 1 H z , a T l o s s p e a k at - 4 0 ° C a n d a s t i l l l o w e r t e m p e r a t u r e p e a k at —100 ° C a r e w e l l r e s o l v e d . O u r e x p e r i e n c e i n e x a m i n i n g l i t e r ature data from different researchers o n different specimens, b u t a l l u s i n g a R h e o v i b r o n , has b e e n t h a t t h e s e t w o p e a k s are n o t r e s o l v a b l e at a f r e q u e n c y o f 1 1 0 H z , a r e j u s t r e s o l v e d at a b o u t 3 5 H z , a n d a r e r e s o l v e d c l e a r l y at 11 H z a n d l o w e r . g

T o check this observation further, w e conducted experiments on a s i n g l e s p e c i m e n o f P V D F u s i n g t h e d u P o n t 9 8 1 D M A u n i t at t h r e e starting frequencies d e t e r m i n e d b y v a r y i n g the sample l e n g t h a n d t h i c k n e s s . T h e r e s u l t s at a b o u t 10 H z a r e s h o w n i n F i g u r e s 3 a n d 4. T h e p a t t e r n w a s m u c h t h e s a m e : n o t r e s o l v e d at 5 0 H z ; p a r t l y r e s o l v e d


16


Ο CO

LO CM

Ο CM


LO

Ο Ο

Ο

Ο

ο •120.0

-80.0

•40.0

0.0

TEMPERATURE

40.0 (C)

Figure 3. DMA 981 dynamic mechanical loss data in millivolts for PVDF, showing the resolved β-loss peak at -84 °C for {=10 Hz, as well as the lower (L) and upper (U) glass transition loss peaks, T ( L ) = -38 °C, and T (U) = 14 °C. g

g

at 2 5 H z ; a n d w e l l r e s o l v e d at 10 H z . V a r i o u s t e c h n i q u e s s u c h as u s e of a c u r v e r e s o l v e r or c o m p u t e r s i m u l a t i o n c a n h e l p i n d o u b t f u l cases, b u t use of f r e q u e n c i e s b e l o w 20—25 H z are g e n e r a l l y most r e l i a b l e . D a t a on other pairs of transitions and/or other polymers m a y give d i f f e r e n t results. A l s o , t h e a u t o m a t e d R h e o v i b r o n is s a i d to h a v e b e t t e r r e s o l v i n g p o w e r t h a n t h e o l d e r m o d e l s (20). T h e b a s i c p r o b l e m at i s s u e is s h o w n s c h e m a t i c a l l y i n F i g u r e 5, w h i c h represents a r e l a x a t i o n m a p for a p o l y m e r h a v i n g t w o l o w t e m p e r a t u r e t r a n s i t i o n s w i t h f r e q u e n c y d e p e n d e n c e as i n d i c a t e d . T h e t w o l i n e s u l t i m a t e l y c o n v e r g e at h i g h e r f r e q u e n c i e s . R e s o l u t i o n o f t h e t w o p r o c e s s e s is o b v i o u s l y b e s t at l o w e r f r e q u e n c i e s a n d w i l l u l t i m a t e l y


1.

BOYER

Automated

Mechanical

17

Testing

f a i l at t h e h i g h e r f r e q u e n c i e s , r e g a r d l e s s o f t h e c a p a b i l i t y o f a g i v e n instrument. E v e n at l o w f r e q u e n c y ( ~ 1 H z ) w i t h t h e m o s t s e n s i t i v e o f t h e d y n a m i c m e c h a n i c a l i n s t r u m e n t s , there are s t i l l loss p e a k s w h o s e d e t a i l s c a n n o t b e r e s o l v e d . Y e t o t h e r m e t h o d s c a n a c h i e v e a f a c t o r o f 3 to 10 i n g r e a t e r d e t a i l . A c a s e i n v o l v i n g T S C (see s e c t i o n e n t i t l e d " C o m petitive T e c h n i q u e s " ) a n d the γ-peak i n P C recently was r e v i e w e d (14,16).


A n o t h e r s t r i k i n g c a s e i s a f f o r d e d b y a s t u d y (29) o n a t a c t i c P M M A using both thermally stimulated current and thermally stimulated creep whose results were c o m b i n e d w i t h literature data on phos-

TEMPERATURE

(°C)

Figure 4. Data of Figure 3 converted to E ' and E", both in units of Pascals. Logarithmic scale for Έ" enhances apparent strength of β-peak compared to T ( L ) peak. T(°C): T ( U ) , 14; T ( L ) , -38; and Ύ , -84. g

g

g

β



18


1000/T Figure 5. Schematic plot of log frequency against 1/Ύ for a polymer with two close lying transitions. The ability to resolve these two pro cesses must decrease as frequency increases.

phorescence. T h e s e several t e c h n i q u e s e s t a b l i s h e d that the k n o w n /3-peak o f P M M A c o n t a i n s at l e a s t f o u r s u b m o d e s .

long-

A t a c t i c P M M A w a s o b s e r v e d i n t h e b u l k state w i t h C N M R at r o o m t e m p e r a t u r e (p. 1 0 3 f f o f R e f e r e n c e 3). T h e m o t i o n o f e a c h o f t h e s e v e r a l types o f c a r b o n atoms present, —C H - C H — , C = 0 , etc., w a s resolved and their respective motional frequencies were determined. P o s s i b l y , one or m o r e o f these types o f m o t i o n m a y c o n t r i b u t e to t h e s e v e r a l sub-jS p r o c e s s e s i n P M M A . 1 3

2

?

3

T h e q u e s t i o n o f r e s o l v i n g p o w e r m a y s e e m to b e p r i m a r i l y o f a c a d e m i c i n t e r e s t ; h o w e v e r , i t has m a n y p r a c t i c a l a s p e c t s . F o r e x a m p l e , a b s o r b e d w a t e r c a n affect t h e m e c h a n i c a l l o s s s p e c t r a o f m a n y p o l y m e r s s u c h as t h e n y l o n s (see F i g u r e 12.9 o f R e f e r e n c e 1); t h e m e t h a c r y l a t e s ( F i g u r e 8.9 o f R e f e r e n c e 1); t h e e p o x i e s (54), a n d o t h e r systems i n some m a n n e r that c a n be subtle or major. U s u a l l y , this effect is most p r e v a l e n t i n p o l y m e r s c o n t a i n i n g p o l a r groups that c a n interact strongly w i t h water. A n o t h e r p r a c t i c a l case i n v o l v e s p o l y m e r b l e n d s , for e x a m p l e , blends of two incompatible polymers w i t h similar values of T: the b l e n d w i l l e x h i b i t e i t h e r a b r o a d , s i n g l e glass p e a k or a r e s o l v a b l e d o u b l e loss peak. g

T h e general f i e l d of additives presents m a n y possible problems. A r m e n i a d e s e t a l . (55) d e s c r i b e d a s i t u a t i o n i n w h i c h m i n e r a l o i l , w h i c h is c o m p a t i b l e w i t h g e n e r a l p u r p o s e P S at a m b i e n t t e m p e r a t u r e s , p h a s e s e p a r a t e s a n d g i v e s a n a r r o w d i s t i n c t l o s s p e a k at l o w temperature. C o n c e r n i n g a l l three p r o b l e m s that w e r e l u m p e d together (re solving power, r e p r o d u c i b i l i t y , a n d accuracy), w e t h i n k the ultimate


1.

BOYER

Automated

Mechanical

19

Testing

answer lies i n h a v i n g duplicate (possibly multiple) runs on a specific material o n the instrument^s) b e i n g c o n s i d e r e d for a c q u i s i t i o n . The

Braid

Controversy

T h r e e papers appeared recently u s i n g rheological data and/or r h e o l o g i c a l arguments to c l a i m that a t r a n s i t i o n (relaxation) o b s e r v e d b y T B A above T i n P S is a n artifact c a u s e d b y a n i n t e r a c t i o n b e t w e e n g l a s s b r a i d a n d m o l t e n p o l y m e r (56—58). G i l l h a m a n d I a s s e m b l e d v a r i o u s facts t o c o u n t e r t h e s e c l a i m s (11, 59, 60). W e u s e b o t h rheological data obtained b y methods not e m p l o y i n g a b r a i d a n d n o n rheological types of data i n w h i c h no net transport of m o l t e n p o l y m e r o c c u r s s u c h as t h e r m a l e x p a n s i o n , s p e c i f i c h e a t , a n d s e v e r a l t y p e s o f spectroscopic evidence. T h e interested reader can consult the three r e f e r e n c e s j u s t c i t e d , a p a p e r b y C o w i e (61 ), a n d t h e s t u d y o f N g u y e n a n d M a x w e l l o n m e l t - e l a s t i c i t y o f P S (62).


g

A specific p r o b l e m involves the T B A b r a i d a n d T . G i l l h a m a n d S c h w a r t z r e p o r t e d (63) t h a t t h e T o f P S d e p e n d s o n t h e b r a i d material. T h e y a s c r i b e d this p h e n o m e n o n to a n interfacial t e n s i o n p r o b l e m . H o w e v e r , H e d v a t s u b s e q u e n t l y demonstrated that these effects a r i s e b e c a u s e o f t h e c o m p o s i t e s y s t e m , s u c h t h a t m o d u l i o f b r a i d a n d p o l y m e r p l a y a r o l e b o t h at T a n d T (64, 65). u

tl

g

a

A m o r e i m p o r t a n t area concerns the use o f T B A to f o l l o w t h e c u r i n g o f t h e r m o s e t s (66). H e r e , G i l l h a m o b s e r v e s a p r e g e l a t i o n l o s s peak. M y belief, b a s e d o n the studies just n o t e d i n the T r e g i o n , is that this a n d other aspects o f t h e c u r i n g process o b s e r v e d b y T B A are genuine. A c t u a l l y , t h e basic p r o b l e m goes b e y o n d that o f a specific t e c h nique, namely, T B A . A n y dynamic mechanical technique involving a s u p p o r t s y s t e m f o r a p o l y m e r t h a t is w e a k o r f l u i d m a y r a i s e t h e s a m e issues. O t h e r supports reportedly used i n c l u d e blotting paper, filter p a p e r , m e t a l w i r e m e s h , glass c l o t h , i n c o m p a t i b l e p o l y m e r s , c o m p a t i b l e p o l y m e r s , m e t a l s t r i p s , e t c . V a r a d a r a j a n a n d I (67) r e v i e w e d t h i s subject e l s e w h e r e . K o l e s k e a n d F a u c h e r also r e v i e w e d the use o f p o r o u s s u b s t r a t e s (68). u

O n e m a y i g n o r e a n y g e n e r a l a n d / o r t h e o r e t i c a l a r g u m e n t s as t o w h e t h e r t h e b r a i d i n T B A (or, f o r t h a t m a t t e r , t h e p o r o u s s u b s t r a t e i n a n y d y n a m i c m e c h a n i c a l test) i n t r o d u c e s o n e o r m o r e f a l s e t r a n s i t i o n s , i.e., artifacts. T h e r e a l issue is w h e t h e r or n o t loss peaks o b s e r v e d b y any of these porous support methods correlate i n a m e a n i n g f u l w a y w i t h end-use properties. Summary T h i s c h a p t e r p r e s e n t e d (1) a t u t o r i a l i n t r o d u c t i o n for i n d i v i d u a l s n e w to t h e f i e l d b u t i n t e r e s t e d i n t h e n a t u r e a n d p o t e n t i a l o f d y n a m i c m e c h a n i c a l t e s t i n g a n d (2) a n o v e r v i e w o f t h e t y p e s o f a u t o m a t e d


20


e q u i p m e n t c u r r e n t l y a v a i l a b l e . F a c t o r s to c o n s i d e r b e f o r e p u r c h a s i n g a n i n s t r u m e n t w e r e l i s t e d . A t the same t i m e , it is e m p h a s i z e d that v a r i o u s n e w t e c h n i q u e s s u c h as t h e r m a l l y s t i m u l a t e d c u r r e n t a n d t h e r m a l l y s t i m u l a t e d c r e e p , as w e l l as i m p r o v e m e n t s i n d i e l e c t r i c l o s s m e a s u r e m e n t s , c a n y i e l d i n f o r m a t i o n that m a y b e s u p e r i o r to, or m o r e g e n e r a l l y c o m p l e m e n t a r y to, that o b t a i n e d b y d y n a m i c m e c h a n i c a l testing. R e s o l v i n g p o w e r , o r t h e a b i l i t y to o b s e r v e d e t a i l b e t w e e n a n d / o r i n m e c h a n i c a l l o s s p e a k s , a p p e a r s to h a v e t w o a s p e c t s : 1. R e s o l u t i o n o f t h e jS-peak (at 0.75 T ) f r o m T w i t h m o d e r n i n s t r u m e n t s a p p e a r s to r e q u i r e u s e o f a f r e q u e n c y i n t h e r a n g e o f 1 - 1 0 H z , as i s i l l u s t r a t e d w i t h P V D F (see F i g u r e s 3 a n d 4). 2. F i n e s t r u c t u r e w i t h i n t h e j8-peak o f P M M A o r w i t h i n t h e γ - p e a k ( c i r c a - 1 2 0 °C) o f P C r e q u i r e s t h e u s e o f t e c h n i q u e s s u c h as t h e r m a l l y s t i m u l a t e d c u r r e n t o r t h e r m a l l y stimulated creep, w i t h effective frequencies i n the range of 10~ H z , a n d h e n c e m u c h h i g h e r r e s o l v i n g p o w e r .


g

g

4

F i n a l l y , the use of porous substrates (braids, filter paper, a n d w i r e m e s h ) as s u p p o r t s f o r f l u i d s y s t e m s ( o l i g o m e r s , c u r a b l e m o n o m e r s , o r m o l t e n polymers) was d i s c u s s e d from the v i e w p o i n t of possible ar tifacts a r i s i n g f r o m the c o m p o s i t e nature o f the s p e c i m e n . I b e l i e v e that, b e c a u s e t r a n s i t i o n s o b s e r v e d w i t h s u p p o r t e d systems are g e n e r ally observable b y a variety of methods not i n v o l v i n g supports, the artifact p r o b l e m has b e e n exaggerated.

Appendix

A.

Additional

Automated

Instruments

S u b s e q u e n t to t h e p r e p a r a t i o n o f t h e f o r e g o i n g m a t e r i a l , w e l e a r n e d of t w o a d d i t i o n a l a u t o m a t e d i n s t r u m e n t s that r e c e n t l y b e c a m e c o m m e r c i a l l y a v a i l a b l e . O n e s u c h i n s t r u m e n t is t h e T o r s i o n a u t o m a t s u p p l i e d b y B r a b e n d e r . A s t h e n a m e i m p l i e s , t h i s i n s t r u m e n t is a f u l l y a u t o m a t e d t o r s i o n a l p e n d u l u m . A f o u r - c o l o r p l o t t e r is e m p l o y e d to r e c o r d q u a n t i t i e s s u c h as G ' , G " , l o g d e c r e m e n t , a n d f r e q u e n c y as a function of temperature or t i m e . A d y n a m i c v i s c o s i m e t e r w a s offered b y R o d e m . It consists o f os cillating concentric cylinders driven mechanically with continuously v a r i a b l e f r e q u e n c y o v e r a range o f 100 to 5 x 10~ H z . T h e p a r a m e t e r s G ' , G " , a n d loss angle c a n b e o b t a i n e d o n s o l u t i o n s , gels, a n d m o l t e n p o l y m e r s . D i g i t a l r e a d o u t i s s t a n d a r d for a c o m p u t e r w i t h d a t a h a n dling being optional. 5

M o s t l i k e l y , o t h e r a u t o m a t e d i n s t r u m e n t s are u n d e r d e v e l o p m e n t o r are e v e n a l r e a d y a n n o u n c e d ; a s u r v e y w a s n o t c o n d u c t e d .


1.

BOYER

Automated

Appendix

B.

Mechanical

Activation

21

Testing

Energies

for

T

Τ,

Q9

β

and

Tu

A s m e n t i o n e d e a r l i e r , Δ Η v a l u e s t e n d t o i n c r e a s e as t h e t r a n s i t i o n temperature i n q u e s t i o n increases. F i g u r e 6 is a s e m i l o g a r i t h m i c p l o t o f AH f o r T as a f u n c t i o n o f T . α

a

g

g

F i g u r e 7 is a s i m i l a r p l o t f o r Τ . W e f i n d t h e l a t t e r p l o t to b e s l i g h t l y m o r e l i n e a r t h a n t h e l i n e a r f i t p r o p o s e d b y H e i j b o e r (32). Values of Δ Η on w h i c h Figures 6 and 7 were based can be found i n T a b l e s I I I a n d I V o f R e f e r e n c e 10. β

α

P l o t s o f l o g / - 1/T f o r T a r e c u r v e d d e c i d e d l y , b e i n g c o n c a v e d o w n w a r d . T h e y do not follow an A r r h e n i u s equation but rather a V o g e l - W L F t y p e o f r e l a t i o n s h i p , w i t h e x p - [B/(T - T ) ] w h e r e T is a r e f e r e n c e t e m p e r a t u r e , a n d Β is a c o n s t a n t . E x a m p l e s o f c u r v e d p l o t s for T m a y b e f o u n d i n R e f e r e n c e s 30 a n d 31 a n d i n F i g u r e s 2 0 a n d 22 o f R e f e r e n c e 60. H e n c e , Δ Η for T decreases w i t h i n c r e a s i n g fre q u e n c y . C o w i e (61 ) s u g g e s t s t h a t Δ Η f o r T i s a b o u t h a l f o f t h a t f o r T , b u t t h i s statement m u s t refer to f r e q u e n c i e s of t h e o r d e r o f 100 H z . tl

Q

0


a

tl

α

tl

α

Appendix

C.

Polymer-Coated

Metal

g

Strips

Used

with

DMA

P o l y m e r - c o a t e d m e t a l s t r i p s h a v e b e e n u s e d as s p e c i m e n s i n t h e t o r s i o n p e n d u l u m f o r m a n y y e a r s (69—71), b u t t h i s p r a c t i c e is n o t w i d e s p r e a d . S t a r k w e a t h e r a n d G i r i (72) d e v e l o p e d a v a r i a t i o n o f t h i s

ιοί I 100

I

I

I

1 I 200

1

I

I

» ι 300

ι

ι

*

I I 400

»

ι

ι

I 500

GLASS TEMP., Κ Figure 6. Apparent activation energy, Δ Η ^ in kilocalories per mole, as a function of quasistatic value of T . The rectangle in upper right corner indicates literature range o / T and Δ Η for poly(2,6-dimethylphenylene oxide). g

g

Η



22


BETA TEMP., Κ Figure 7. Same as Figure 6 but for β-transition

(Ύ < T ) . (See Ref β

g

29.)

o l d c o n c e p t i n w h i c h a l o w m e c h a n i c a l l o s s m e t a l s t r i p (e.g., b r a s s s h i m stock) is u s e d as a s u p p o r t for p o l y m e r s to b e s t u d i e d i n t h e d u P o n t 981 D M A u n i t . S e v e r a l advantages are f o u n d , e s p e c i a l l y w h e n t h e m e t a l is c o a t e d u n i f o r m l y o n b o t h s i d e s w i t h t h e p o l y m e r t o b e studied. 1. A b s o l u t e m o d u l u s o f t h e p o l y m e r i n b e n d i n g c a n b e c a l culated. 2. L o s s p e a k s c a n b e l o c a t e d a l t h o u g h a b s o l u t e v a l u e s o f the loss m a y not a l w a y s b e o b s e r v e d . 3. M e a s u r e m e n t o f t h e d y n a m i c p r o p e r t i e s is p o s s i b l e at least 100 Κ a b o v e T p r o v i d e d that a d h e s i o n b e t w e e n p o l y m e r a n d s u p p o r t is m a i n t a i n e d . 4. R e s o n a n t f r e q u e n c y v a r i a t i o n i s r e d u c e d g r e a t l y b e c a u s e the m o d u l u s of the metal changes little over the tempera ture range of interest. g

F i g u r e 8 s h o w s loss e x p r e s s e d i n m i l l i v o l t s a n d resonant fre q u e n c y i n h e r t z as a f u n c t i o n o f t e m p e r a t u r e for 1 0 - m i l c o p p e r s h i m s t o c k c o a t e d o n b o t h s i d e s w i t h a b o u t 10 m i l s o f a h i g h m o l e c u l a r w e i g h t (ca. M = 5 x 1 0 , w h e r e M r e p r e s e n t s t h e n u m b e r - a v e r a g e m o l e c u l a r w e i g h t ) p o l y i s o b u t y l e n e ( P I B ) . T h e T , Τ > T , o r Tu t r a n s i t i o n s a n d a w e a k ^ - r e l a x a t i o n a r e e v i d e n t . T h e r a t i o T (K)/T (K) i s 1.22. T h e Τ p e a k i s n o t w e l l r e s o l v e d b u t a p p e a r s to b e c l o s e t o 0 . 7 5 T (K) = - 1 0 7 ° C . M o r g a n e t a l . (.73) w e r e u n a b l e t o l o c a t e a β - p e a k i n P I B u s i n g the vibrating r e e d t e c h n i q u e but a β-peak was observed b y W e i (74) i n t h e r e g i o n o f - 9 0 ° C o n s i x d i f f e r e n t s p e c i m e n s o f P I B v a r y i n g i n M from 7 6 0 - 8 . 6 Χ 10 , u s i n g T B A . R e s o l u t i o n was best i n the n

5

n

g

g

a

g

β

n

g

5


1.

BOYER

Automated

Mechanical

23

Testing


ο

- 1 2 0 . 0

- 8 0 . 0

- 4 0 . 0

0 . 0

TEMPERATURE

4 0 . 0

8 0 . 0

(C)

Figure 8. DMA 981 loss curve for PIB coated on both sides of 10-mil copper shim stock, which permits loss measurements to be extended to about 100 Κ above T at a relatively constant frequency. g

specimen of lowest M F i g u r e 8.

n

b u t not a p p r e c i a b l y better t h a n that s h o w n i n

Acknowledgments I a m i n d e b t e d t o K . V a r a d a r a j a n , a f o r m e r p o s t d o c t o r a l f e l l o w at M i c h i g a n M o l e c u l a r Institute, for the D M A results p r e s e n t e d i n F i g u r e s 3, 4, a n d 8. I a l s o a m i n d e b t e d t o H o w a r d S t a r k w e a t h e r o f Ε . I . d u P o n t de N e m o u r s & C o . , I n c . E x p e r i m e n t a l Station, for d i s c u s s i n g the advantages o f p o l y m e r - c o a t e d s h i m stock i n D M A p r i o r to p u b l i cation. C . L a c a b a n n e p r o v i d e d us, p r i o r to p u b l i c a t i o n , w i t h the manuscript from w h i c h F i g u r e 2 was prepared. H e l p f u l comments w e r e r e c e i v e d f r o m J o h n G i l l h a m , P r i n c e t o n U n i v e r s i t y a n d P h i l i p S. G i l l , d u Pont Instrument Products Department, Wilmington, D E . T h i s chapter is d e d i c a t e d to D a l e J . M e i e r , M i c h i g a n M o l e c u l a r Institute, o n the occasion of his 60th birthday.



24

POLYMER

CHARACTERIZATION

Literature Cited 1. McCrum, N. G.; Read, Β. E.; Williams, G. "Anelastic and Dielectric Ef fects in Polymer Solids"; Wiley: New York, 1967. 2. Read, B. E.; Dean, G. D. "The Determination of Dynamic Properties of Polymers and Composites"; Halsted Press: New York, 1979. 3. "Molecular Basis of Transitions and Relaxations", Midland Macromolecular Monograph No. 4; Meier, D. J., Ed.; Gordon: New York, 1978. 1978. 4. Hedvig, P. "Dielectric Spectroscopy of Polymers"; Halsted Press: New York, 1977. 5. Hedvig, P. Macromol. Rev. 1980, 15, 375. 6. McCall, D. W. NBS Spec. Publ. U.S. 1967, 301. 7. Törmälä, P. J. Macromol. Sci. Rev. Macromol. Chem. 1979, 17, 297. 8. Van Turnhout, J. "Thermally Stimulated Discharge of Polymer Electrets"; Elsevier: Amsterdam, 1975. 9. "Thermally Stimulated Processes in Solids: New Prospects", Proc. Int. Workshop, Montpelier, VT, June 1976; Fillard, J. P.; van Turnhout, J., Eds.; Elsevier: New York, 1978. 10. Boyer, R. F. "Transitions and Relaxations"; In "Encyclopedia of Polymer Science and Technology Supplement" Vol. 2; Bikales, N., Ed.; Wiley: New York, 1977. 11. Gillham, J. K.; Boyer, R. F. J. Macromol. Sci. Phys. 1977, 13, 497. 12. Gillham, J. K. AIChE J. 1974, 20, 1066. 13. Blaine, R. L.; Gill, P. S.; Hassel, R. L . Woo, L. J. Appl. Polym. Sci. Appl. Polym. Symp. 1978, 34, 157. 14. Varadarajan, K.; Boyer, R. F. Org. Coat. Plast. Chem. 1980, 42, 689. 15. Varadarajan, K.; Boyer, R. F. Org. Coat. Plast. Chem. 1981, 44, 409. 16. Varadarajan, K.; Boyer, R. F. J. Polym. Sci., Polym. Phys. Ed. 1981, 19, 141. 17. Boyer, R. F. J. Macromol. Sci. Phys. 1974, 9, 187. 18. Boyer, R. F. Polymer 1976, 17, 996. 19. Boyer, R. F. (Guest Ed.) Polym. Eng. Sci. 1979, 19, 661-759. 20. Kenyon, A. S.; Grote, W. Α.; Wallace, D. Α.; Rayford, M. C. J. Macromol. Sci. Phys. 1977, 13, 553. 21. Technical product bulletin, Rheovibron, Imass, Inc., Hingham, MA. 22. Technical product bulletin, Dynastat, Imass, Inc., Hingham, MA. 23. Technical bulletin, The Mechanical Spectrometer, Rheometrics, Inc., Union, NJ. 24. Technical bulletin, PL Dynamic Mechanical Analyzer, Stow, OH. 25. Ikeda, R. M.; Starkweather, H. W. Polym. Eng. Sci. 1980, 20, 322. 26. Törmälä, P.; Paakonen, E.; Kemppainen, P. J. Mater. Sci. 1981, 16, 275. 27. Chatain, D.; Lacabanne, C.; Monpagens, J.-C. Makromol. Chem. 1977, 178, 583. 28. Lacabanne, C. et al. Org. Coat. Plast. Chem. 1980, 43, 550. 29. Lamarre, L.; Schreiber, H. P.; Wertheimer, M. R.; Chatain, D.; Lacabanne, C. J. Macromol. Sci., Phys. 1980, 18, 195. 30. Lacabanne, C.; Chatain, D. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 2315. 31. Lacabanne, C.; Goyaud, P.; Boyer, R. F. J. Polym. Sci., Polym. Phys. Ed. 1980, 18, 277. 32. Marchal, E.; Benoit, H.; Vogl, O. J. Polym. Sci., Polym. Phys. Ed. 1978, 16, 949. 33. Stupp, S. I.; Carr, S. H. J. Polym. Sci., Polym. Phys. Ed. 1978, 16, 13. 34. Aoki, Y.; Brittain, J. O. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 199. 35. Takamatsu, T.; Fukada, E . Polym. J. 1970, 1, 101. 36. Fukada, E.; Sakurai, T. Polym. J. 1971, 2, 656. 37. Carr, S. H. Proc. 10th North Am. Therm. Anal. Soc., Boston, MA, Oct. 26-29, 1980, 1-4. ;



1.

BOYER

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Mechanical

Testing

25

38. Ibid., 161-166. 39. Chatain, D.; Gautier, P.; Lacabanne, C. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 1631. 40. Heijboer, J., Ph.D. Thesis, Leiden Univ., Delft, Netherlands, 1972. 41. Klaase, P. Τ. Α.; van Turnhout, J. IEE Conf. Publ. 177 1979, Delft, Netherlands. 42. Yalof, S.; Wrasidlo, W. J. Appl. Polym. Sci. 1972, 16, 2159. 43. Varadarajan, K.; Boyer, R. F. Org. Coat. Plast. Chem. 1981, 44, 402. 44. Varadarajan, K.; Boyer, R. F. Polymer 1982, 23, 314. 45. Personal communication, Lear, J., Ε. I. du Pont de Nemours & Co., Inc., Instrument Products, Wilmington, D E . 46. Boyer, R. F. (Guest Ed.) Polym. Eng. Sci. 1979, 19, 716. 47. Boyer, R. F. (Guest Ed.) Polym. Eng. Sci. 1979, 19, 709. 48. Senich, G. Α.; MacKnight, W. J. J. Appl. Polym. Sci. 1978, 22, 2633. 49. Gillham, J. K.; Manzione, L. T.; Tu, C. F.; Poek, V. C. Org. Coat. Plast. Chem. 1979, 41, 357. 50. Struik, L. C. E.; Bree, H. W.; Tak, A. G. M., private publ., 75-61, Central Laboratory, TNO Delft, Netherlands. 51. Heijboer, J. Int. J. Polym. Mater. 1977, 6, 11. 52. Starkweather, H. W.,Jr.J.Macromol. Sci., Phys. 1968, 2, 781. 53. Schatzki, T. In "Molecular Basis of Transitions and Relaxations", Mid land Macromolecular Monographs No. 4; Meier, D. J., Ed.; Gordon: New York, 1978; 263-75. 54. Gillham, J. K.; Glandt, C.; McPherson, C. A. "Chemistry and Properties of Cross-linked Polymers"; Labana, S. S., Ed.; Academic: New York, 1977. 55. Armendiades, C. D.; Baer, E.; Rieke, J. K. J. Appl. Polym. Sci. 1970, 14, 2635. 56. Nielsen, L. E. Polym. Eng. Sci. 1977, 17, 713. 57. Neumann, R. M.; Senich, G. Α.; MacKnight,W.J.Polym. Eng. Sci. 1978, 18, 624. 58. Heijboer, J. Polym. Eng. Sci. 1979, 19, 670. 59. Boyer, R. F. Polym. Eng. Sci. 1979, 19, 732. 60. Boyer, R. F. J. Macromol. Sci., Phys. 1980, 18, 461. 61. Cowie, J. M. G. Polym. Eng. Sci. 1979, 19, 709. 62. Maxwell, B.; Nguyen, M. Polym. Eng. Sci. 1979, 19, 1140. 63. Schwartz, B. G.; Gillham, J. K. Org. Coat. Plast. Chem. 1979, 41, 442, 447. 64. Hedvat, S. Org. Coat. Plast. Chem. 1980, 42, 667. 65. Polym. Eng. Sci. 1981, 21, 129. 66. Gillham, J. K. Polym. Eng. Sci. 1979, 19, 676. 67. Varadarajan, K.; Boyer, R. F. Org. Coat. Plast. Chem. 1981, 44, 409. 68. Koleske, J. V.; Faucher, J. A . Polym. Eng. Sci. 1979, 19, 716. 69. Oberst, H.; Frankenveld, K. Acoustica 1951, 2, 4. 70. Van Oort, W. P. Mikroteknik 1952, 7, 246. 71. Schwarzl, F. Acoustica 1958, 8, 164. 72. Personal communication, Starkweather, H. W.; Giri, M. R., Ε. I. du Pont de Nemours & Co., Inc., du Pont Experimental Station, Wilmington, DE; see J. Appl. Polym. Sci. 1982, 27, 1243. 73. Morgan, R. J.; Nielsen, L. E.; Buchdahl,R.J.Appl. Phys. 1971, 42, 4683. 74. Wei, L. M., B.S. Thesis, Princeton Univ., Princeton, NJ, 1979. RECEIVED for review October 14, 1981. ACCEPTED February 12, 1982.


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