Advantages of Interfacing a Viscoelastic Device with a High-Speed...
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8 Advantages of Interfacing a Viscoelastic Device with a High-Speed and -Capacity Computer Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
and an Advanced Statistical-Graphics Software Package Stephen Havriliak, Jr. Bristol Research Laboratories, Rohm and Haas Company, Bristol, PA 19007
There are many advantages to the polymer scientist for constructing such interfaces. First of a l l , a high storage computer allows one to store large amounts of data in a form that makes data storage and retrieval, as well as comparisons, quite simple and efficient. Secondly, complicated calculations, involving experimental design, error estimation or conventional polymer science theories of one form or another can readily be carried out. For example, a replication study could be carried out and variance or standard deviations be represented in terms of measured quantities. Viscoelastic data could then be presented in a form of experimental quantities along with confidence limits. When polymer systems are compared, one can estimate the differences in behavior relative to the estimated error (signal/noise ratio) and select the optimum conditions for comparison.
We have f o u n d s i t u a t i o n s where c o m p a r i s o n s c a n be made i n r e g i o n s where t h e e x p e r i m e n t a l e r r o r may be
0097-6156/86/0313-0076$06.00/0 © 1986 American Chemical Society
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
8. HAVRILIAK
Interfacing a Viscoelastic Device
h i g h b u t t h e d i f f e r e n c e s i n o b s e r v e d b e h a v i o r more t h a n compensate f o r t h e e r r o r . Smoothing functions that r e d u c e t h e n o i s e i n t h e s y s t e m c a n a l s o be used s o t h a t the u s e f u l range o f t h e i n s t r u m e n t c a n be e x t e n d e d several fold. B l e n d c a l c u l a t i o n s u s i n g any o f t h e w e l l known e x p r e s s i o n s c a n be used t o e s t i m a t e t h e p r o p e r t i e s o f b l e n d s f r o m t h e p r o p e r t i e s o f t h e p u r e compon e n t s and t h e i r volume f r a c t i o n . The r e s u l t s o f s u c h calculations c a n t h e n be compared to experimental v a l u e s and t h e m a g n i t u d e o f t h e e x p e r i m e n t a l e r r o r t o d e t e r m i n e whether the d i f f e r e n c e s are meaningful or not. T h i s paper r e v i e w s t h e advantages t o t h e polymer s c i e n t i s t when such an i n t e r f a c e i s u s e d .
EXPERIMENTAL A l l t h e v i s c o e l a s t i c measurements were c a r r i e d o u t i n t h e R h e o m e t r i e s Dynamic S p e c t r o m e t e r RDS-770 a t a f r e q u e n c y o f 1Hz, a s t r a i n o f 0.1%, and a t e m p e r a t u r e range o f -140 t o 140 C i n c r e m e n t e d e v e r y 2 d e g r e e s . The T e x a s I n s t r u m e n t T e r m i n a l S i l e n t 700 was t a p p e d t o p r o v i d e a hookup t o an IBM 308X main frame computer l o c a t e d some m i l e s away. The o u t p u t o f t h e R h e o m e t r i e s u n i t was c o n v e r t e d t o a d a t a f i l e t o be used i n c o n j u c t i o n w i t h SAS ( 1 ) . A l l s t a t i s t i c a l m a n i p u l a t i o n s , s o f t w a r e d e v e l o p m e n t s , and t h e n e c e s s a r y g r a p h i c s t h a t are r e p o r t e d h e r e were c a r r i e d o u t w i t h t h e a i d o f SAS• S e t t i n g t h e i n c r e m e n t a l t e m p e r a t u r e change t o 2°C r e s u l t e d i n an a v e r a g e 2°C change b u t t h e r e were many p l a c e s where t h e change was 1 o r 3 d e g r e e s . S i n c e t h e s e c h a n g e s o c c u r r e d randomly and v a r i a n c e c a l c u l a t i o n s o r o t h e r c o m p a r i s o n s must be p e r f o r m e d a t the same t e m p e r a t u r e f o r each m a t e r i a l , a s m a l l p r o g r a m was w r i t t e n t o i n t e r p o l a t e t h e d a t a t o 1 d e g r e e i n c r e ments. The SAS d a t a f i l e s c o n s i s t e d o f r e a l (6SP) and i m a g i n a r y (GDP) p a r t s o f t h e m o d u l u s , t h e l o s s t a n g e n t ( t a n d e l ) , t e m p e r a t u r e (T) and t h e sample i d e n t i f i c a t i o n (sampno)• The t h r e e p o l y m e r s t h a t were c h o s e n f o r s t u d y , e.g. PNNA ( 2 ) , EPDM ( 3 ) , and H y t r e l ( 4 ) , were s e l e c t e d because t h e y r e p r e s e n t a wide range o f v i s c o e l a s t i c materials. These materials were processed into plaques. The p l a q u e s were a n n e a l e d a t 125 C between h i g h l y p o l i s h e d chrome p l a t e d f l a t p l a t e s and c o o l e d slowly to minimize the e f f e c t s of r e s i d u a l s t r e s s e s . V i s c o e l a s t i c measurements were made under conditions c i t e d above on two t e s t s p e c i m e n s t h a t were c u t f r o m
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
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COMPUTER APPLICATIONS IN THE POLYMER LABORATORY
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adjacent l o c a t i o n s i n the plaque t o minimize p o s s i b l e preparation variations. The t e s t s p e c i m e n s i z e i n a l l c a s e s was 2 x 0.5 x 0.125 i n . B l e n d s o f PMMA/Hytrel = 3/1 were a l s o p r e p a r e d by e x t r u s i o n b l e n d i n g i n a 1 i n . K i l l i o n e x t r u d e r . The p e l l e t s were i n j e c t i o n m o l d ed i n t o p l a q u e s . These p l a q u e s were a n n e a l e d a t 125 C for 3 minutes, and t h e n c o o l e d t o room temperature slowly to minimize r e s i d u a l s t r e s s e s . RESULTS A*
ESTIMATES OF EXPERIMENTAL ERROR
Variance (5,6), related to the scatter i n r e p l i cated experiments, was c a l c u l a t e d u s i n g SAS'S PROC MEANS f o r s t o r a g e m o d u l u s , l o s s modulus and l o s s t a n g e n t f o r each t e m p e r a t u r e and m a t e r i a l , e . g . , PMMA, EPDM AND HYTREL. V a r i o u s r e l a t i o n s h i p s were examined to s e l e c t t h e p r o p e r meter f o r r e l a t i n g v a r i a n c e t o t h e m a g n i t u d e o f measurement, e.g. l i n e a r , s e m i - l o g and log-log. The most s a t i s f a c t o r y meter t h a t was f o u n d was t h e l o g - l o g r e l a t i o n s h i p . SAS's PROC STEPWISE was used t o c o n s t r u c t a model f o r r e p r e s e n t i n g t h e v a r i a n c e i n terms o f t h e e x p e r i m e n t a l v a r i a b l e s , such a s t h e m a g n i t u d e o f t h e measurements, t h e i r c r o s s - t e r m s and temperature. T e m p e r a t u r e was f o u n d t o c o n t r i b u t e o n l y s l i g h t l y i n these r e l a t i o n s h i p s . SAS's PROC GLM was used t o e s t i m a t e t h e c o n t r i b u t i o n o f p o l y m e r type. T h i s was found t o be o n l y a weak c o r r e l a t i o n and need n o t be i n c l u d e d . T a b l e I s u m m a r i z e s t h e r e s u l t s and a n a l y s i s and t h e a s s u m p t i o n s t h a t were used t o c o n s t r u c t the f i n a l a l g e b r a i c equation to represent the variance. 95% c o n f i d e n c e l i m i t s were t h e n c a l c u l a t e d f r o m t h e e x p r e s s i o n s i n Table I I , w h i c h were d e r i v e d f r o m SAS's PROC GLM, t h e s i m p l i f i e d model and an e s t i mate o f t h e r e s i d u a l s . I t s h o u l d be p o i n t e d o u t t h a t the n u m e r i c a l v a l u e s c a l c u l a t e d from these e x p r e s s i o n s s h o u l d be used c a r e f u l l y ( s e e D i s c u s s i o n ) s i n c e t h e y include important assumptions i n t h e i r d e r i v a t i o n . I t i s e x p e c t e d t h a t o t h e r l a b o r a t o r i e s may d e r i v e s i m i l a r r e l a t i o n s h i p s b u t w i t h somewhat d i f f e r e n t numerical values• An example o f t h e u t i l i t y o f t h e s e e x p r e s s i o n s i s g i v e n i n F i g u r e 1 where t h e l o g ( r e a l modulus) i s p l o t t e d a g a i n s t temperature f o r two t e s t s p e c i m e n s o f EPDM. The f i r s t t e s t s p e c i m e n i s r e p r e s e n t e d by o ' s , w h i l e t h e s e c o n d s p e c i m e n i s r e p r e s e n t e d by t h e d a s h e d l i n e s , w h i c h a r e 95% c o n f i d e n c e l i m i t s c a l c u l a t e d f r o m t h e e x p r e s s i o n s i n T a b l e I I and i t v i s c o e l a s t i c p r o p e r ties. The measurements were made t h r e e weeks a p a r t .
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
8.
HAVRILIAK
Interfacing a Viscoelastic Device
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Table I . Summary of R-Square Values for the Various Variance Models
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MODEL TYPE
TANDEL*
GSP*
GDP*
1. SAS'S PROC STEPWISE, no polymer type
.45
.90
.75
2. SAS's PROC GLM, p o l y m e r t y p e is a class variable
.41
.93
.82
3. S i m p l i f i e d m o d e l , s e e T a b l e I I
.41
.88
.74
•TANDEL i s t h e l o s s t a n g e n t , GSP and GDP i s t h e l o s s m o d u l u s .
i s t h e s t o r a g e modulus
Table I I . Numerical Expressions Used to Represent the 957. Confidence Limits of the V i s c o e l a s t i c Quantities 1.
Log(VDT)=-3.13902+2.1813 L o g ( T D ) 0.144921 Log(GSP)+0.01117 PROD S
SDTD (VTD/0.41)and
VTD»10*EXP(Log(VTD))
2. Log(VGSP)*-2.0235+0.02906 Log(TD)+ 2.4905 Log(GSP)+0.6803 PROD SDGSP«(VGSP/0.88)
1/2
and
VGSP*10EXP(Log(VGSP))
3. Log(VGDP)=2.40928+2.6814 L o g ( G D P ) 0.6744 Log(GSP)-O.38506 PRODI SDGDP-(VGDP/0.74)
1/2
and
VGDP-10EXP(Log(VGDP))
Note t h a t GSP and GDP have been r e d u c e d by 10exp9 w i t h PROD=Log(TANDEL) Log(GSP) and PRODl*Log(GSP) Log(GDP) Note t h a t V T D = v a r i a n c e o f L o s s T a n g e n t , and t h a t SDTD i s the s t a n d a r d d e v i a t i o n o f Loss Tangent w i t h s i m i l a r d e f i n i t i o n s f o r GSP (G* o r r e a l modulus) and GDP (G" o r l o s s modulus)•
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
COMPUTER APPLICATIONS IN THE POLYMER LABORATORY
-150
-100
-50
0
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100
Temperature (°C) F i g u r e 1* A p l o t o f t h e l o g ( s t o r a g e modulus) f o r EPDM w i t h t e m p e r a t u r e . The o's r e p r e s e n t t h e f i r s t run while the confidence l i m i t s o f the s e c o n d r u n a r e r e p r e s e n t e d by t h e dashed l i n e s .
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
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8.
HAVRILIAK
Interfacing a Viscoelastic Device
81
N o t e how t h e c o n f i d e n c e band c h a n g e s w i t h c h a n g i n g temperature* A s an a s i d e , i t g h o u l d be p o i n t e d o u t t h a t a t a t e m p e r a t u r e o f a b o u t 0 C, t h e machine t o r q u e i s below t h e recommended range b u t t h e t r a n s d u c e r i s s t i l l responding to the s i g n a l .
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B.
SIGNAL/NOISE RATIO
Suppose one wanted t o compare t h e b e h a v i o r o f two p o l y m e r s and t h e i r b l e n d s . L e t us d e f i n e t h e s i g n a l as t h e d i f f e r e n c e between t h e l o g a r i t h i m s o f t h e v i s c o e l a s t i c q u a n t i t i e s and t h e n o i s e as t h e e r r o r calculated f o r a s p e c i f i c s e t of v i s c o e l a s t i c properties associated with a s p e c i f i c composition. The s i g n a l t o n o i s e r a t i o w o u l d have t h e a p p e a r a n c e o f t h e t h r e e c u r v e s shown i n F i g u r e 2 f o r a P M M A / H y t r e l b l e n d »3/l. S e l e c t i o n o f t h e optimum c o n d i t i o n s f o r c o m p a r i son i s a p p a r e n t i n t h a t f i g u r e . E m p h a s i s s h o u l d be placed a t those temperatures with high s i g n a l / n o i s e ratios. C.
SMOOTHING FUNCTIONS
The p r o p e r t i e s o f v a r i a n c e n o t e d e a r l i e r a l l o w us t o t r e a t t h e s c a t t e r i n t h e r e s u l t s a s n o i s e . A number o f s m o o t h i n g f u n c t i o n s e x i s t f o r t h i s p u r p o s e . One s u c h method t h a t i s p a r t i c u l a r l y s u i t e d s i n c e t h e i n c r e m e n t a l t e m p e r a t u r e change h a s been k e p t c o n s t a n t i s t h a t due t o S a v i t s k y and G o l a y ( 7 ) . T h i s method i s a r i g o r o u s a p p l i c a t i o n o f t h e method o f l e a s t s q u a r e s t o t h o s e r e l a t i o n s h i p s t h a t c a n be r e p r e s e n t e d by p o l y n o m i a l s and f o r e x p e r i m e n t s t h a t a r e u n i f o r m l y s p a c e d i n the independent v a r i a b l e . I n the p r e s e n t case the t e m p e r a t u r e range was u n i f o r m l y s p a c e d a t 1 d e g r e e i n t e r v a l s and t h e v i s c o e l a s t i c f u n c t i o n s c a n be r e p r e s e n t e d by p o l y n o m i a l s no g r e a t e r t h a n d e g r e e 3. The r e s u l t s o f smoothing t h e H y t r e l modulus t e m p e r a t u r e c u r v e i s shown i n F i g u r e 3. A n o t h e r a d v a n t a g e o f t h e S a v i t s k y - G o l a y method i s t h a t d e r i v a t i v e s o f t h e s e f u n c t i o n s c a n a l s o be d e t e r m i n e d f r o m t h e method o f l e a s t s q u a r e s . This method c a n be used t o d e t e r m i n e a l p h a - p e a k t e m p e r a t u r e s a u t o m a t i c a l l y s i n c e t h e f i r s t d e r i v a t i v e changes s i g n a t t h e peak t e m p e r a t u r e . The a d v a n t a g e o f s m o o t h i n g i s t h a t t h e number o f e x t r a n e o u s p e a k s due t o n o i s e h a s been m i n i m i z e d .
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
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COMPUTER APPLICATIONS IN THE POLYMER LABORATORY
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
20
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0
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Temperature (°C) F i g u r e 2. P l o t o f t h e s i g n a l / n o i s e r a t i o a s defined i n the t e x t with temperature f o r a p o l y b l e n d o f PMMA and HYTREL•
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
8. HAVRILIAK
Interfacing a Viscoelastic Device
r
-20
-10
T
"T 10
T
•"•I"
20
30
40
83
""I " " I " SO
60
TTTT
TT
T 70
TTrrpr
80
90
Temperature ( C) F i g u r e 3. P l o t o f t h e l o s s t a n g e n t w i t h t e m p e r a t u r e f o r H y t r e l i n t h e t e m p e r a t u r e range o f 0 t o 140 Deg. The x ' s r e p r e s e n t t h e e x p e r i m e n t a l values, while the s o l i d l i n e represents the r e s u l t s o f smoothing using the S a v i t z k y - G o l a y technique•
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
100
84
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D.
COMPUTER APPLICATIONS IN THE POLYMER LABORATORY
VISCOELASTIC PROPERTIES OF BLENDS
The SAS d a t a files t h a t were c r e a t e d a s a r e s u l t s o f t h e o p e r a t i o n s n o t e d e a r l i e r have t h e i m p o r tant property that a l l three v i s c o e l a t i c p r o p e r t i e s have e i t h e r been measured o r i n t e r p o l a t e d t o t h e same temperature. T h e r e f o r e one c a n merge d a t a s e t s f o r d i f f e r e n t p o l y m e r s by t e m p e r a t u r e (a SAS d a t a s e t m a n i p u l a t i o n ) and t h e n p e r f o r m b l e n d c a l c u l a t i o n s on t h e d a t a q u i t e s i m p l y i n SAS• F o r e x a m p l e , one c a n c a l c u l a t e the expected viscoelastic properties of a b l e n d f r o m t h e p u r e components and t h e i r volume f r a c t i o n u s i n g t h e e q u a t i o n s o f Uemura and T a k a y n a g i ( 8 ) • These r e s u l t s c a n t h e n be compared t o e x p e r i m e n t a l v a l u e s ( a t t h e same t e m p e r a t u r e ) i n a number o f i n f o r m a t i v e ways. F i r s t we c a n p l o t t h e c a l c u l a t e d values as a f u n c t i o n o f temperature and r e p r e s e n t r e s u l t s as a l i n e , see F i g u r e 4. The e x p e r i m e n t a l r e s u l t s c a n be r e p r e s e n t e d a s an e r r o r band v s t e m p e r a ture p l o t . Real d i f f e r e n c e s are r e a d i l y apparent s i n c e they must l i e o u t s i d e t h e 95% c o n f i d e n c e limits. A n o t h e r way t o r e p r e s e n t t h e d i f f e r e n c e i s t o p l o t t h e d i f f e r e n c e between c a l c u l a t e d and e x p e r i m e n t a l v a l u 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 . I n t h e same g r a p h an e s t i m a t e and p l o t o f t h e e x p e r i m e n t a l e r r o r s c a n a l s o be made, s e e F i g u r e 5 . DISCUSSION The e x a m p l e s d e s c r i b e d h e r e , a s w e l l a s o t h e r s , have been combined i n t o a s o f t w a r e p a c k a g e w h i c h we c a l l POLYREOM. The u s e r o f t h i s r o u t i n e h a s a t h i s d i s p o s a l a Menu s o t h a t he c a n s e l e c t any o f t h e comp a r i s o n s d e s c r i b e d a b o v e . I n t h i s way, q u i t e c o m p l i c a ted c a l c u l a t i o n s c a n be c a r r i e d o u t s i m p l y by anyone w i t h m i n i m a l computer e x p e r i e n c e . In fact the entire p r o c e d u r e c a n be r u n on a r o u t i n e b a s i s f r o m t h e t i m e t h a t a measurement i s made. Some i m p o r t a n t c o n d i t i o n s c o n c e r n i n g t h e e s t i m a t i o n o f e r r o r s h o u l d be p o i n t e d o u t . F i r s t , modulus measurements o f r e c t a n g u l a r b a r s a r e made i n t o r s i o n and the calculations c o n t a i n assumptions t h a t may depend on g e o m e t r y . How t h i s i n f l u e n c e s e r r o r , p a r t i c u l a r l y a t l o w t o r q u e l e v e l s i s n o t known. S e c o n d , t h e s t r a i n s were k e p t c o n s t a n t a t 0.1%; o t h e r s t r a i n s m i g h t n o t y i e l d t h e same r e s u l t s . On t h e o t h e r hand one w o u l d e x p e c t an i n v e r s e p r o p o r t i o n a l i t y t o e x i s t b e tween t h e m a g n i t u d e s o f e r r o r and s t r a i n . Thirdly, t h e s e e r r o r s were e s t i m a t e d f o r a f r e q u e n c y o f 1Hz.
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Interfacing a Viscoelastic Device
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HAVRILIAK
F i g u r e 4. P l o t o f t h e l o s s t a n g e n t w i t h t e m p e r a t u r e f o r PMMA/HYTREL blend»3/l. The s o l i d l i n e represents the c a l c u l a t e d values while the dashed l i n e s r e p r e s e n t t h e 95% c o n f i d e n c e l i m i t s for the experimental v a l u e s .
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
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F i n a l l y , thecontribution to error, that i s s p e c i f i c to t h i s l a b o r a t o r y , e s p e c i a l l y when compared t o o t h e r l a b o r a t o r i e s , i s n o t known. On t h e o t h e r hand, t h e r e a r e some v e r y i n t e r e s t i n g and n o t e w o r t h y o b s e r v a t i o n s t o be made f r o m t h e e r r o r s t u d y . F i r s t , repeated a t t e m p t s t o i n c l u d e p o l y m e r t y p e and t e m p e r a t u r e i n t o t h e e r r o r model f a i l e d . This observation implies that temperature c o n t r o l o f the d e v i c e i s independent o f temperature and t h a t any f l u c t u a t i o n i s t h e same t h r o u g h o u t t h e i n t e r v a l t h a t was used i n t h i s s t u d y . S e c o n d l y , r e p e a t e d a t t e m p t s t o i n c l u d e sample t y p e i n t o the a n a l y s i s a l s o f a i l e d , i m p l y i n g t h a t t h e e s t i m a t e d v a r i a n c e s were i n d e p e n d e n t n o t o n l y o f t e m p e r a t u r e b u t of m a t e r i a l . This r e s u l t suggests very s t r o n g l y that t h e v a r i a n c e s a r e due t o t h e magnitude o f t h e m e a s u r e ment, t h e d e v i c e t h a t was u s e d , and o u r own s e t o f laboratory circumstances. There a r e many p o l y m e r s c i e n c e t h e o r i e s ( 9 , 10 and 11) t h a t a t t e m p t t o r e l a t e v i s c o e l a s t i c p r o p e r t i e s to polymer s t r u c t u r e o r , i n t h e case o f b l e n d s , t o t h e p r o p e r t i e s o f t h e p u r e components and t h e i r volume fraction. Implicit i n these t h e o r i e s i s that the v i s c o e l a s t i c p r o p e r t i e s were o b t a i n e d under c o n t r o l l e d c o n d i t i o n s and i n t h e l i n e a r r e g i o n . Linearity i n p o l y m e r s i s an i d e a l i z a t i o n t h a t may n e v e r be r e a l i z e d , and may o n l y be a p p r o x i m a t e d by making v i s c o e l a s t i c measurements a t l o w and c o n s t a n t s t r a i n . T h i s cons t r a i n t p l a c e s s e r i o u s r e s t r i c t i o n s on e x p e r i m e n t a l e q u i p m e n t as t h e f o l l o w i n g example w i l l demonstrate. Consider t h e t e m p e r a t u r e dependence o f t h e s t o r a g e modulus a s a f u n c t i o n o f t e m p e r a t u r e f o r two m a t e r i a l s , where a t room t e m p e r a t u r e one i s g l a s s y (PMMA), and t h e o t h e r i s l e a t h e r y (EPDM), s e e F i g u r e 6. A t l o w tempera t u r e s , the moduli are not o n l y s i m i l a r but q u i t e high. As a r e s u l t o f e x p e r i m e n t a l c o n d i t i o n s , t h e t o r q u e , a machine q u a n t i t y , i s near i t s upper limit. However a s t h e t e m p e r a t u r e i s r a i s e d , t h e c u r v e s b e have quite d i f f e r e n t l y . A t 0 C the torque f o r the EPDM s y s t e m i s near i t s l o w e r l i m i t , w h i l e f o r PMMA i t i s s t i l l near t h e i n s t r u m e n t s upper l i m i t . Eventually t h e t o r q u e goes o u t o f t h e recommended range f o r EPDM. A s i m i l a r b e h a v i o r i s o b s e r v e d f o r PMMA b u t a t higher temperatures. I f one s h o u l d w i s h t o e s t i m a t e t h e p r o p e r t i e s o f a b l e n d o f t h e s e two m a t e r i a l s and stay w i t h i n the manufacturer's torque recommendations, t h e n t h e t e m p e r a t u r e range i s s e v e r e l y l i m i t e d b e c a u s e any i n t e r a c t i o n s w i t h t h e a l p h a and b e t a p r o c e s s e s o f PMMA c a n n o t be s t u d i e d . Changing t h e dimensions o f t h e specimens, the t r a n s d u c e r , or t h e l e v e l o f s t r a i n a r e not a c c e p t a b l e a l t e r n a t i v e s t o m i n i m i z e t h e e f f e c t s o f a l i m i t e d torque range. One way t o m i n i m i z e t h e s e e f f e c t s i s d e r i v e d f r o m t h e r e s u l t s o f t h i s work. F o r example, t h e
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
8. HAVRILIAK
Interfacing a Viscoelastic Device
87
Temperature (°C)
F i g u r e 5. P l o t o f t h e l o s s t a n g e n t d i f f e r e n c e w i t h t e m p e r a t u r e f o r d a t a i n F i g u r e 4* The c i r c l e s represent the experimental values, while t h e l i n e r e p r e s e n t s t h e 95% c o n f i d e n c e l i m i t s f o r the e x p e r i m e n t a l v a l u e s * TORQUE-1321
6~ ^1
-150
i '
-100
|......... |
-59
0
'i
58
1
i
180
" " I
150
Temperature (°C)
F i g u r e 6* Dependence o f s t o r a g e modulus f o r PMMA and EPDM on t e m p e r a t u r e a t a f r e q u e n c y o f 1Hz and a s t r a i n o f 0*1%.
Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on March 27, 2018 | https://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch008
88
C O M P U T E R APPLICATIONS IN THE POLYMER LABORATORY
i n c r e a s e i n e x p e r i m e n t a l e r r o r i s n o t as i m p o r t a n t as is the signal/noise r a t i o . A knowledge o f t h i s r a t i o i s important because o p t i m a l c o n d i t i o n s ( i n t h i s case t e m p e r a t u r e ) c a n be s e l e c t e d f o r c o m p a r i s o n * In addit i o n , use o f t h e S a v i t z k y - G o l a y t e c h n i q u e t o reduce e r r o r i s j u s t i f i e d b e c a u s e t h e e r r o r was f o u n d t o be e s s e n t i a l l y n o i s e , and n o t a l o w v a l u e machine c u t off. The p r o b l e m becomes one o f s e a r c h i n g f o r t h e s i g n a l i n t h e p r e s e n c e o f n o i s e . U s i n g 26 e x p e r i m e n t a l q u a n t i t i e s , w h i c h r e p r e s e n t s 26 d e g r e e s o f measurement, i s not unreasonable. One w o u l d e x p e c t an e r r o r r e d u c t i o n o f 5, t h u s l e a d i n g t o , o r an e x t e n s i o n o f , t h e i n s t r u m e n t s r a n g e by 5 f o l d . Acknowledgments
T h i s w r i t e r wishes t o express h i s a p p r e c i a t i o n t o Dr. E. P. D o u g h e r t y and Mr. P. M i l l e r f o r many h e l p f u l d i s c u s s i o n s i n p r e p a r i n g t h e s u b r o u t i n e s used i n t h i s work.
Literature Cited 1. SAS Institute, SAS Circle, Box 8000, Carry, North Carolina 27511. 2.
The PMMA used in this work is Plexiglas product of the Rohm and Haas Co.
V(811), a
3.
The EPDM used in this work is Nordel 2722, manufactured by the Du Pont Co.
4.
The Hytrel used in this work is Hytrel-4056, product of the DuPont Co.
5.
Box G.E.P., Hunter W.G., and Hunter J . S . , Statistics for Experimenters, John Wiley and Sons (1978).
6.
Draper N. and Smith H., Applied Regression Analysis, Second Edition, John Wiley and Sons (1981).
7.
Savitzky A. and Golay M.J.E., Analytical Chemistry, Vol. 36, No. 8, pp. 1622-1639 (1964).
8.
Bucknall C.B., Toughened Plastics, Applied Science Publishers (1977).
9.
McCrum N. G., Read B. E . , and Williams G., Anelastic and Dielectric Effects in Polymer Solids, John Wiley and Sons (1967).
Chapter
a
5,
10. Ferry J . D., Viscoelastic Properties of Polymers, Second Edition, John Wiley and Sons (1982). 11. Mansfield M. L . , J of Poly. Div., Vol 21, 787-806 (1983).
Sci.,
Polymer Phys
Received December 24, 1985 Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
