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THERMAL DIFFUSIVITY OF POLYMER FOILS - SEMICRYSTALLINE PETP AND PE - AS A
FUNCTION OF DRAWING
B. Merté, P. Korpiun, E. Lüscher, R. Tilgner
To cite this version:
B. Merté, P. Korpiun, E. Lüscher, R. Tilgner. THERMAL DIFFUSIVITY OF POLYMER FOILS
- SEMICRYSTALLINE PETP AND PE - AS A FUNCTION OF DRAWING. Journal de Physique
Colloques, 1983, 44 (C6), pp.C6-463-C6-467. �10.1051/jphyscol:1983674�. �jpa-00223233�
JOURNAL DE PHYSIQUE
Colloque C6, suppliment au nO1O, Tome 44,'octobre 1983 page C6- 463
T H E R M A L DIFFUSIVITY OF POLYMER FOILS - SEMICRYSTALLINE PETP A N D P E - AS A FUNCTION OF DRAWING
B. Mert6, P. Korpiun, E. LGscher and R. ~ i l ~ n e r *
T e c h i s c h e Universitet MZinchen, Physik-Department, 0-8046 Garching, F. R. G.
Siemens AG, ZFA, 0-80U0 Miinchen, F . R. G.
R'esum'e
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La d i f f u s i v i t ' e thermique a des polymPresdiipend 'etroitement de l ' o r i e n t a t i o n des chaPnes macromol'eculaires, qui peut e t r e chang'ee pard'eformation. Une augmentation du taux de d'eformation peut a u s s i bien entra9ner une diminution qu'une augmentation de l a d i f f u s i v i t ' e thermique.
Abstract
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The thermal d i f f u s i v i t y a o f polymers depends s t r o n g l y on t h e o r i e n t a t i o n of t h e molecules which can be changed by drawing. a may de- c r e a s e o r i n c r e a s e with drawing.I
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INTRODUCTIONThe PA e f f e c t can be considered a s a nonstationary method t o measure t h e thermal d i f f u s i v i t y of samples with thicknesses i n t h e o r d e r of a f e w thermal d i f f u s i o n l e n g t h s ( i .e. a t audiofrequencies several 1 0 micrometers) / I / . The experimental technique a p p r o p r i a t e f o r such i n v e s t i g a t i o n s i s t h e gas-microphone method. The q u a n t i t y t h a t i s measured, i s t h e phase angle Alpbetween t h e modulation of t h e l i g h t i n t e n s i t y and t h e p r e s s u r e v a r i a t i o n a s a f u n c t i o n of t h e modulation f r e - quency v.
An i n t e r e s t i n g a p p l i c a t i o n of t h i s method is t h e e v a l u a t i o n of thermal d i f f u s i v i t i e s of polymer f o i l s . The measurement of thermal c o n d u c t i v i t y o r d i f f u s i v i t y normal t o t h e plane of polymer f o i l s of several micrometers t h i c k n e s s with conventional methods i s problematic. The thermal r e s i s t a n c e s o r i g i n a t i n g from t h e imperfect bond-
ing of t h e h e a t e r and t h e thermometer t o t h e sample may be of t h e same o r d e r of mag- n i t u d e a s t h e thermal r e s i s t a n c e of t h e f o i l /2,3,4/.
I 1
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PRINCIPLE OF MEASUREMENTWhite l i g h t from a halogen lamp i s p e r i o d i c a l l y i n t e r r u p t e d by a mechanical chopper (with chopping frequency v ) and
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a f t e r t r a v e r s i n g t h e o p t i c a l window of t h e photo- a c o u s t i c c e l l , f i g . 1, impinges on a bismuth l a y e r of approximately 8008
t h i c k n e s s evaporated on t h e sample. Within this l a y e r t h e l i g h t i s "completely" absorbed and converted i n t o heat by n o n r a d i a t i v e d e e x c i t a t i o n processes. The Bi-layer i s t h e r - mally very t h i n . In t h e mathematical treatment i t i s s u f f i c i e n t t o t a k e i t i n t o account a s a boundary condition f o r temperature and heat f l u x . The temperature wave o r i g i n a t i n g from t h e absorbing l a y e r t r a v e r s e s t h e sample and g i v e s r i s e t o a temperature o s c i l l a t i o n a t t h e back s i d e of t h e l a t t e r ( a t z = 0 ) t h a t makes t h e a i r within t h e neighbouring enclosed volume warm up and cool down p e r i o d i c a l l y . The r e s u l t i n g pressure v a r i a t i o n is d e t e c t e d by conventional gas-microphone technique.We have measured t h e phase angle A f a s a function of t h e square r o o t of chopping frequency
A.
For thermally t h i c k gas columns t h e r e holds approximate1 ywith w = 2nv, and 1, t h e t h i c k n e s s and a t h e thermal d i f f u s i v i t y of t h e sample;
t h e l a t t e r is t h e q u a n t i t y t o be determined.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983674
JQURNAL DE PHYSIQUE
F i g . 1
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P h o t o a c o u s t i c c e l l , schematic.i: "0" = o p t i c a l window,
"I" = sample, "2" = gas,
"3" = backing.
I11
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THEORETICAL TREATMENTA c c o r d i n g t o t h e Rosencwaig-Gersho t h e o r y /5/ we s t a r t f r o m t h e one-dimensional e q u a t i o n o f h e a t t r a n s f e r
The t h e r m a l d i f f u s i v i t y o f medium "i" i s a i = Xi/(pi-cpi) w i t h t h e t h e r m a l con- d u c t i v i t y Xi, t h e d e n s i t y p i , and t h e i s o b a r i c s p e c ~ f i c h e a t c p i . The i n d e x i goes f r o m 0 t o 4 w i t h i = 0: window, i = 1: sample, i = 2: gas volume, and i = 3: b a c k i n g ( s e e F i g . 1 ) t o d e s c r i b e t h e d i f f e r e n t p a r t s o f t h e p h o t o a c o u s t i c c e l l .
The s o l u t i o n f o r each r e g i o n "i" o f t h e c e l l i s g i v e n by
The i n t e g r a t i o n c o n s t a n t s E i , F i , . U i , and V i a r e e v a l u a t e d by t h e boundary con- d i t i o n s . The mean t e m p e r a t u r e v a r ~ a t i o n i n t h e gas i s /6/
so t h a t t h e phase a n g l e i s g i v e n by
F o r t h e e x p l i c i t e x p r e s s i o n o f A Y w e r e f e r t o /7/.
F i g u r e s 2a and 2b show t h e c a l c u l a t e d A'pas a f u n c t i o n o f
J;
f o r v a r i o u s e x p e r i - mental c o n d i t i o n s . As one can e a s i l y r e c o g n i z e , f o r h i g h e r f r e q u e n c i e s t h e r e h o l d s t h e approximate e x p r e s s i o n (1).As t h e s i g n a l a m p l i t u d e i s much h i g h e r f o r l o w e r f r e q u e n c i e s we used chopping f r e - quencies f r o m 12 Hz up t o 400 Hz t o g e t b e t t e r r e s u l t s . Thus we were o b l i g e d t o f i t o u r e x p e r i m e n t a l d a t a w i t h t h e more e l a b o r a t e d f o r m u l a ( 5 ) t o e v a l u a t e t h e c o r r e c t thermal d i f f u s i v i t y a.
PETP a, = 6.93 10-8 m21s
180
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-20%
180 - a.
+20%
- 1 8 0 0 ~ t -~ 1 8~ O O~ ~ ~~ i ~t I ~~ ~ ~t t ~I r t~ ~ ~~ l c~ ~ ~~ ~ ~~ ~ ~
5 10 15 20 5 10 15 20
Fig. 2a G I H Z ~ ' ~ --- Fig. 2b V i i / ~ z
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~ / ~Fig. 2 - Theoretical s h i f t A q o f t h e phase angle f o r PETP f o i l s versus frequency;
a ) f o r various sample t h i c k n e s s e s , b) f o r various d i f f u s i v i t i e s .
IV
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THERMAL DIFFUSIVITY OF POLYMERS AND THE EFFECT OF DRAWINGThe microscopic process of t h e t r a n s p o r t o f heat i n amorphous and s e m i - c r y s t a l l i n e polymers i s not a s well understood a s i n c r y s t a l l i n e s o l i d s . Nevertheless, t h e d i f f u s i o n of heat can be explained a t l e a s t q u a l i t a t i v e l y f a i r l y well by t h e con- c e p t t h a t t h e t r a n s p o r t of energy depends on t h e type of t h e i n t r a - and i n t e r - molecular chemical bonds. As t h e intramolecular bonds along t h e chain of a mole- c u l e a r e much s t r o n g e r than t h e intermolecular f o r c e s between d i f f e r e n t molecules, t h e t r a n s p o r t of heat along t h e d i r e c t i o n of t h e chain of t h e molecule i s much l a r g e r than perpendicular t o i t . Drawing of a sample i n one d i r e c t i o n changes t h e dimension i n t h e d i r e c t i o n s perpendicular t o i t . The degree of drawing i n t h e d i r e c t i o n k i s q u a n t i t a t i v e l y c h a r a c t e r i s e d by t h e draw r a t i o E!.= (sample length i n d i r e c t i o n k a f t e r drawing / i n i t i a l sarnple length i n k-direc ion). The influence of drawing on t h e thermal d i f f u s i v i t y of a polymer f o i l can be i l l u s t r a t e d using a s i m p l i f i e d p i c t u r e . With i n c r e a s i n g draw r a t i o t h e molecules w i l l p r e f e r e n t i a l l y o r i e n t i n t o t h e d i r e c t i o n of drawing, x- o r y - d i r e c t i o n r e s p e c t i v e l y , i n f i g . 3.
i
Fig. 3-
Foil geometryFoil
I
The thermal d i f f u s i v i t y a perpendicular t o t h e f o i l plane ( z - d i r e c t i o n i s expected t o decrease with i n c r e a s i n g draw r a t i o . I f one measures h o r a along various d i - r e c t i o n s a s a function o f drawing, informations on t h e s t r u c t u r e of t h e molecular network of a polymer and of i t s v a r i a t i o n by d i f f e r e n t t r e a t m e n t s can be obtained 18-ll/.
JOURNAL DE PHYSIQUE
V
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EXPERIMENTAL RESULTS ( i ) PE (Polyethylene)We i n v e s t i g a t e d w e l l d e f i n e d h i g h d e n s i t y (HOPE) and low d e n s i t y p o l y e h t y l e n e (LDPE) f o i l s of zU ym and 46 yrn thickness as r e c e i v e d from t h e manufacturer and o f d i f f e r e n t draw r a t i o s up t o E % 6. Figures 4 and 5 show t h e thermal d i f f u s i v i t y a measured normal t o t h e f o i l plane ( z - d i r e c t i o n ) as a f u n c t i o n o f draw r a t i o
(drawing i n x - d i r e c t i o n ) . The draw r a t i o o f t h e f o i l s n o t a d d i t i o n a l l y drawn by us i s p u t equal t o one.
Fig. 4
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Thermal d i f f u s i v i t y o f LDPE F i g . 5-
Thermal d i f f u s i v i t y o f HOPEversus draw r a t i o . versus draw r a t i o .
0 : "3512"-PE, nominal thickness 40 ym X : "6016"-PE, nominal thickness 20 ym A : "3512"-PE, Nominal thickness 20 ym 0: "6042"-PE, nominal thickness 40 ym
a:
data measured by Choy e t a l ./ l o / .
A : "6042"-PE, nominal thickness 20 ym 0 : data measured by Choy e t a l ./ l o / .
The experimental r e s u l t s show t h e decrease i n d i f f u s i v i t y expected f o r an increas- i n g draw r a t i o . The e x c e l l e n t agreement o f t h e absolute values f o r a w i t h data measured by Choy
/ l o /
p o i n t t o t h e accuracy a v a i l a b l e w i t h t h e photoacoustic method, f i g . 4 and 5.( i i ) PETP (Polyethyleneterephthalate)
PETP-foils o f "19 pm" and "30 ym" nominal thickness have been i n v e s t i g a t e d . The f o i l s were a l r e a d y b i a x i a l l y p r e o r i e n t e d by t h e process o f manufacturing. The molecules are o r i e n t e d p r e f e r e n t i a l l y along t h e x - d i r e c t i o n . I n a d d i t i o n , we have drawn these f o i l s u n i a x i a l l y i n two d i f f e r e n t d i r e c t i o n s ( x and y ) . The d i f f u s i v i t y obtained from t h e measured data o f t h e phase s h i f t i s p l o t t e d over t h e draw r a t i o i n Fig. 6. The draw r a t i o o f t h e f o i l s as r e c e i v e d from t h e manufacturers i s p u t equal t o one. The d i f f u s i v i t y a ( € ) f o r the "19 y m " - f o i l s show q u a l i t a t i v e l y t h e u s u a l l y expected dependence on drawing along t h e y-axis; i t decreases w i t h i n - creasing draw r a t i o . Drawing along the d i r e c t i o n o f i n i t i a l p r e f e r e n t i a l o r i e n - t a t i o n o f the molecules, x - d i r e c t i o n , o b v i o u s l y does n o t change t h e d i f f u s i v i t y f u r t h e r . For t h e "30 ym" f o i l s one o b t a i n s t h e s u r p r i s i n g r e s u l t t h a t t h e d i f f u - s i v i t y increases w i t h drawing i n e i t h e r d i r e c t i o n s t a r t i n g from a value f o r a t h a t i s 33 percent lower than t h a t f o r t h e "19 yml' f o i l s . There are two models of a semicrystal 1 in e polymer a p p r o p r i a t e t o e x p l a i n t h e observed increase o f a w i t h draw r a t i o . One i s t h e aggregate model of K i l i a n and P i e t r a l l a /8/ t h e o t h e r i s t h e two phase model o f Choy and Young /9/. The experimental r e s u l t s can be i n t e r - p r e t e d w i t h these models i f t h e f o l l o w i n g assumptions a r e made:
1. The o r i e n t a t i o n o f t h e c r y s t a l l i n e s u b s t r u c t u r e /8/, o r t h e c r y s t a l l i t e s em- bedded i n t h e amorphous medium /9/ r e s p e c t i v e l y , o f i n i t i a l l y b i a x i a l l y drawn f o i l s e x h i b i t s no r o t a t i o n a l symmetry w i t h respect t o a p r e f e r e n t i a l d i r e c t i o n i n t h e f o i l plane.
2. The a d d i t i o n a l drawing changes t h e o r i e n t a t i o n o f t h e c l u s t e r s /8/ o r t h e c r y s t a l l i t e s 1 9 1 , r e s p e c t i v e l y , and reduces t h e i r c r y s t a l l i n i t y .
Fig. 6
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Thermal d i f f u s i v i t y o f PETP f o i l s i n z - d i r e c t i o n versus draw r a t i o ."19 pm" f o i l s drawn i n x - d i r e c t i o n ( 0 ) and y - d i r e c t i o n ( 0 ) ;
"30 pm" f o i l s drawn i n x - d i r e c t i o n ( 0 ) and y - d i r e c t i o n ( A ).
V I
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CONCLUSIONSWe have developed a method t o measure t h e thermal d i f f u s i v i t y o f polymer f o i l s o f 10 pm t o about 40 pm thickness w i t h a p r e c i s i o n b e t t e r than 10 % f o r absolute and about 1 % f o r r e l a t i v e values. The PAE seems t o be t h e base o f a powerful tech- nique t o determine w i t h h i g h accuracy thermal d i f f u s i v i t i e s o f samples w i t h thicknesses i n t h e order o f some d i f f u s i o n lengths. For t h i s a p p l i c a t i o n t h e PAE can be considered t o be a c o n t a c t l e s s phase s e n s i t i v e temperature measurement.This method m i g h t be o f s p e c i a l i n t e r e s t f o r polymer physicisizs w i t h i n two p o i n t s . F i r s t , t h e r e i s t h e l a r g e f i e l d o f polymer f o i l s , which i s v e r y important.
F o r t u n a t e l y t h e f o i l thicknesses a r e i n t h e order o f some thermal d i f f u s i o n lengths i n t h e r e g i o n o f lower audio frequencies. On t h e o t h e r hand t h e thermal d i f f u - s i v i t y i s very s e n s i t i v e t o t h e o r i e n t a t i o n o f substructures i n t h e polymer t h a t may v a r y e s s e n t i a l l y a p p l y i n g r e l a t i v e small stresses.
References
/ I / KORPIUN P., FRITSCH G., SCHAMBERGER M., BAUMANN J., TILGNEK R., and LUSCHER E.
Proceedings o f t h e S i x t e e n t h I n t . C o n d u c t i v i t y Conference 1979, D.L. Larsen ed., Plenum Press, New York 1983
/2/ KNAPPE W., Adv.Polymer Sci. 7 (1971) 477
/3/ CHEN F.C., POON Y.M., and CHDY C.L., Polymer 1 8 (1977) 129
/4/ NEWMAN P.R., EWBANK
M.D.,
and MAUTHE C.D., SoiTState Comm.40
(1981) 975 /5/ ROSENCWAIG A., and GERSHO A., J.Appl .Phys. 47 ( 1 976) 64/ 6 / KORPIUN P., and BUCHNER B., Appl .Phys. B g 1 9 8 3 ) 121;
Journ. de Physique ( t h i s issue)
/7/ KORPIUN P., MERTE B., FRITSCH G., TILGNER R., and LUSCHER E., C o l l o i d & Poly- mer Sci.
261
(1983) 313/8/ KILIAN H.G., and PIETRLLA M., Polymer 19 (1978) 664 /9/ CHOY C.L., YOUNG K., Polymer 1 8 ( 1 9 7 7 ) f 6 9
/ l o / CHOY C.L., CHEN F.C., and L U K ~ . H . , J.Polymer Sci., Phys.Ed.
