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Charging of polypropylene foils in corona triode system
Journal of Electrostatics, 30 (1993) 57-64 Elsevier
57
C h a r g i n g of p o l y p r o p y l e n e foils in corona triode system E. M o t y l I n s t i t u t e o f E l e c t r i c a l E n g i n e e r i n g and T e c h n o l o g y , T e c h n i c a l U n i v e r s i t y o f W r o c t a w , W y b r z e z e W y s p i a f i s k i e g o 27, 5 0 - 3 7 0 W r o c t a w , Poland
Abstract
T h e t r a n s i e n t c h a r g i n g c u r r e n t s I - t and the v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s I - U o f o n e - s i d e m e t a t l i z e d PP f o i l s w e r e m e a s u r e d in c o r o n a t r i o d e s y s t e m . T h e t i m e d e p e n d e n c e o f c h a r g i n g c u r r e n t s was f o u n d as I ~ t -m. T h e I - U c h a r a c t e r i s t i c s p e c u l i a r to the SCL c o n d u c t i o n w e r e found for negative corona, A sublinear behaviour of I-U dependence in low e l e c t r i c f i e l d f o r p o s i t i v e c o r o n a w a s f o u n d . T h e d e e p s u r f a c e t r a p s f o r c o r o n a c h a r g e s w e r e o b t a i n e d f r o m the T S D e x p e r i m e n t s . T h e p a r t i a l d i s c h a r g e s a g i n g a f f e c t s I - U as well I - t c h a r a c t e r i s t i c s . A g r e a t e r i n c r e a s e o f the c u r r e n t was o b s e r v e d f o r n e g a t i v e t h a n p o s i tive charged samples.
1. I N T R O D U C T I O N T h e c o r o n a c h a r g i n g m e t h o d has w i d e s p r e a d a p p l i c a t i o n in the preparation o f the p o l y m e r foil e l e c t r e t s . The surface charge d i s t r i b u t i o n o f s a m p l e s c h a r g e d d i r e c t l y by the p o i n t e l e c t r o d e is u s u a l l y n o n u n i f o r m . A p p l i c a t i o n o f the g r i d e l e c t r o d e r e s u l t s us the g r e a t e r u n i f o r m i t y o f the s u r f a c e c h a r g e . P r a c t i c a l l y p a r a l l e l - p l a t e g e o m e t r y can be u s e d f o r t h e o r e t i c a l a n a l y s i s . C o r o n a t r i o d e s y s t e m m a k e s it p o s s i b l e to d e t e r m i n e the e q u i v a l e n t s u r f a c e c h a r g e s , c u r r e n t s and p o t e n t i a l s d u r i n g the c h a r g i n g p r o c e s s [ l ] . One - side m e t a l l i z e d s a m p l e s can be m e a s u r e d and the e l e c t r o d e e f f e c t s can be i n v e s t i g a t e d in the s y s t e m [2]. I n t e r f a c i a l p h e n o m e n a p l a y an i m p o r t a n t r o l e in e l e c t r i c a l t r a n s p o r t in p o l y m e r f o i l s [ 3 , 4 ] . T h e m e c h a n i s m o f the c h a r g e b u i l d - u p and dec a y is not yet a d e q u a t e l y u n d e r s t o o d [ 3 , 5 ] . It has b e e n s h o w n t h a t the c h a r g i n g c u r r e n t s and c o n d u c t i v i t y in p o l y m e r i c i n s u l a t o r s are dep e n d e n t on the s a m p l e t r e a t m e n t and the c h a r g i n g m e d i u m [ 6 , 7 ] . T h i s p a p e r p r e s e n t s r e s u l t s o f the e x p e r i m e n t s u n d e r t a k e n to i n v e s t i g a t e the i n f l u e n c e o f the h i g h c o r o n a f i e l d s on o n e - s i d e m e t a l l i z e d PP foils. T h e t r a n s i e n t c h a r g i n g c u r r e n t s and the v o l t a g e - c u r r e n t 0304-3886/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
58 c h a r a c t e r i s t i c s w e r e m e a s u r e d in c o r o n a t r i o d e s y s t e m . 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 s w e r e m e a s u r e d in the o p e n c i r c u i t a f t e r c o r o n a c h a r g i n g . The e f f e c t s o f the s u r f a c e t r e a t m e n t by p a r t i a l d i s c h a r g e s and i m p r e g n a t i o n o f s a m p l e s with oil on c h a r g i n g c h a r a c t e r i s t i c s w e r e also i n v e s t i g a t e d .
2.
EXPERIMENTAL
The c h a r g i n g s y s t e m as s h o w n b e l o w in F i g u r e 1 c o n s i s t s o f the c o r o n a p o i n t e l e c t r o d e P c o n n e c t e d to a v a r i a b l e high - v o l t a g e s o u r c e U c. 13 n e e d l e s w e r e used as the p o i n t e l e c t r o d e . The grid G has a d i a m e t e r o f 58 mm and is made o f c o p p e r wire 50 ~tm in d i a m e ter with a mesh w i d t h o f 120 gm. The s a m p l e S is m o u n t e d on a m e t a l e l e c t r o d e E and a g u a r d ring R. One s u r f a c e o f the s a m p l e is unc o a t e d ; the o t h e r is c o v e r e d by e v a p o r a t e d a l u m i n i u m . The area o f m e a s u r i n g e l e c t r o d e is 8 cm 2. The d i s t a n c e b e t w e e n the g u a r d ring and the m e a s u r i n g e l e c t r o d e is 1 mm. The d i s t a n c e b e t w e e n the p o i n t e l e c t r o d e and the grid is 35 mm and the d i s t a n c e grid to metal e l e c t r o d e E is 4 mm.
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F i g u r e 1. S c h e m a t i c d i a g r a m o f the c o r o n a t r i o d e s y s t e m . P, p o i n t e l e c t r o d e ; G, g r i d ; E, m e a s u r i n g e l e c t r o d e ; R, g u a r d ring; U c and U~, c o n t r o l l e d p o w e r s u p p l i e s ; pA, p i c o a m m e t e r .
S a m p l e s o f 12 ~tm and 26 gm p o l y p r o p y l e n e c o m m e r c i a l film EK500 f r o m H e r c u l e s w e r e k e p t s t r e t c h e d with the help o f a m e t a l l i c
59 h o l d e r d u r i n g the c h a r g i n g p r o c e s s . The v o l t a g e U a c r o s s the s a m p l e was c a l c u l a t e d by U = Ug
- Usg(I),
w h e r e the v o l t a g e b e t w e e n the grid and the s a m p l e U s g ( I ) was d e t e r m i n e d e m p i r i c a l l y f r o m the c a l i b r a t i o n c u r v e . The s u r f a c e p o t e n t i a l o f the s a m p l e was a l m o s t the same as the grid p o t e n t i a l . T h u s , the grid e l e c t r o d e G p l a y s a role o f a c o n t a c t l e s s e l e c t r o d e for c u r r e n t m e a s urements. The TSD s p e c t r a o f s a m p l e films w e r e o b s e r v e d u n d e r the o p e n - c i r cuit c o n d i t i o n f r o m r o o m t e m p e r a t u r e to a b o u t 460 K at a h e a t i n g rate o f a b o u t 3 K / m i n . The d i s t a n c e f r o m the p r o b e to the n o n m e t a l l i z e d s u r f a c e o f the p o l y m e r was 4 mm.
3. R E S U L T S
AND
DISCUSSION
M e a s u r e m e n t s o f the time d e p e n d e n c e o f the c h a r g i n g c u r r e n t s w e r e m a d e at c o n s t a n t c o r o n a c u r r e n t I = 2 ~tA. A grid v o l t a g e Ug was a p p l i e d for 30 min and I ( t ) was m e a s u r e d , then the v o l t a g e was inc r e a s e d to h i g h e r v a l u e for a n o t h e r 30 min and the new c u r v e l ( t ) was m e a s u r e d and so f o r t h . The fixed grid v o l t a g e w e r e 20, 50, 100, 200, 500, 1000, 2 0 0 0 and 4 0 0 0 V. Time d e p e n d e n c i e s o f the c h a r g i n g c u r r e n t s for p o s i t i v e c o r o n a are s h o w n in F i g u r e 2. On a d o u b l e l o g a r i t h m i c scale, d e c a y c u r r e n t s can be a p p r o x i m a t e d by the s t r a i g h t lines g i v i n g I~t -m. As it is s h o w n in the F i g u r e 2 w h e n the v o l t a g e b e l o w 1000 V is a p p l i e d to the grid the c u r r e n t d e c r e a s e s r a p i d l y for m o r e than 1000 s and n e v e r a p p r o a c h e s a s t e a d y value. U n d e r the h i g h e r v o l t a g e s a quasi s t e a d y s t a t e is acc o m p l i s h e d in a b o u t 1000 s. The c h a r g i n g c u r r e n t s for n e g a t i v e c o r o n a are s l i g h t l y l o w e r t h a n for positive corona. The quasi s t a t i o n a r y c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s w e r e o b t a i n e d f r o m the t r a n s i e n t c h a r g i n g c u r r e n t s . The i s o c h r o n a l I - U c h a r a c t e r i s tics at t = 1000 s are s h o w n in F i g u r e 3. The l i n e a r o h m i c I - U dep e n d e n c e in low v o l t a g e s and the I~U n d e p e n d e n c e for h i g h e r than 800 V was o b s e r v e d for n e g a t i v e c o r o n a . A s u b l i n e a r b e h a v i o u r o f I - U d e p e n d e n c e in low v o l t a g e s for p o s i t i v e c o r o n a was f o u n d . The c u r rent d e p e n d s u p o n the p o l a r i t y o f the c o r o n a e l e c t r o d e . The p o s i t i v e c o r o n a e l e c t r o d e s h o w s a l a r g e r c u r r e n t than the n e g a t i v e ones. The i s o c h r o n a l I - U c h a r a c t e r i s t i c s at t = 1000 s o f a s p e c i m e n with e v a p o r a t e d Al e l e c t r o d e s on b o t h s u r f a c e s was also m e a s u r e d . The AI e l e c t r o d e s h o w s n e a r l y the same c u r r e n t as the n e g a t i v e c o r o n a e l e c t r o d e in low v o l t a g e r a n g e as s h o w n in F i g u r e 3. The s t u d y o f the s u r f a c e c h a r g e d e c a y has s h o w n that the s u r f a c e p o t e n t i a l r e m a i n s c o n s t a n t with time f o r the initial s u r f a c e p o t e n t i a l s - 5 0 0 V and d e c r e a s e s v e r y s l o w l y for _+2 kV. S a m p l e s c h a r g e d
60 t h r o u g h the g r i d e x h i b i t e d a u n i f o r m c h a r g e d i s t r i b u t i o n o v e r the ent i r e s u r f a c e . T h e r e was no n o t i c e a b l e e v i d e n c e o f the l a t e r a l c h a r g e s p r e a d i n g on t h e film s u r f a c e . T h e w i d t h o f the c h a r g e p r o f i l e was k e p t c o n s t a n t f o r 120 h a f t e r c h a r g i n g at _+2 kV in the air f o r 200 s.
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102 03 t [s]
F i g u r e 2. T r a n s i e n t c h a r g i n g c u r rents for increased values of grid v o l t a g e s Ug f r o m 20 to 2 0 0 0 V f o r 12 ]am p o l y p r o p y l e n e foils. P o s i t i v e c o r o n a . I c = 2 gA.
//
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16131 10
102 103 U IV]
10~"
F i g u r e 3. C u r r e n t - v o l t a g e c h a r acteristics for positive (C+/PP/ A1) and n e g a t i v e (C'/PP/AI) c o r o n a in c o m p a r i s o n w i t h A1/PP/A1 structure.
TSD r e s u l t s o f PP s a m p l e s c h a r g e d with v a r i o u s g r i d v o l t a g e s f r o m - 3 kV to 3 kV at t = 200 s are s h o w n in F i g u r e 4. T h e p e a k s at t e m p e r a t u r e s a b o u t 330, 380 and 410 K w e r e o b s e r v e d f o r n e g a t i v e c o r o n a c h a r g i n g . O n e p e a k at 350 K and a n o t h e r a p p e a r i n g b e t w e e n 390-400 K were observed for positive corona charging. The activation e n e r g i e s w e r e d e t e r m i n a t e d by the initial rise m e t h o d u s i n g p a r t i a l h e a t i n g t e c h n i q u e for s a m p l e s c h a r g e d at _+3 kV. W i d e d i s t r i b u t i o n o f the a c t i v a t i o n e n e r g i e s 0,9 - 2,0 eV c o r r e s p o n d s w i t h the p e a k at 330 K f o r n e g a t i v e c h a r g e d s a m p l e s . T h e a c t i v a t i o n e n e r g y f o r p e a k at 350 K f o r p o s i t i v e c h a r g e d s a m p l e s is a b o u t 1,7 eV.
61
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._. 0
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300
350
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T[K] F i g u r e 4. TSD m e a s u r e m e n t s in open c i r c u i t for d i f f e r e n t grid v o l t a g e s Uo, H e a t i n g rate b=3 K/min, c o r o n a c u r r e n t Ic=2 p,A, c h a r g i n g time tc= 200 s.
lC~ 1
10
102 f [s]
03
Fi gur e 5. E f f e c t o f s u r f a c e t r e a t ment on t r a n s i e n t c h a r g i n g currents. 1, u n t r e a t e d sample; 2, vacuum i m p r e g n a t e d sample with c o n d e n s e r oil; 3, PD aged sample by 5 h; 4, PD aged sample by 10 h. N e g a t i v e c o r o n a , U g = - I kV.
The c h a r g e s d e p o s i t e d on the p o l y m e r s u r f a c e aft er c o r o n a c h a r g i n g may be easily r e m o v e d by o u t g a s s i n g in vacuum. The TSD c u r r e n t s w e r e d e c r e a s e d 4 times for n e g a t i v e c h a r g e d samples, and 20 times for p o s i t i v e ones af t er 30 min hol di ng u n d e r vacuum o f 10 -5 t orr. Thus, the n e g a t i v e c h a r g e is bound more s t r o n g l y with the p o l y m e r than the p o s i t i v e ch ar g e. C ha r ges d e p o s i t e d on the p o l y m e r s u r f a c e are t r a p p e d in deep traps and i m m o b i l i z e d , t h e r e f o r e the TSD c u r r e n t s are small for T < 340 K and U < 1 kV. U n d e r hi gh er v o l t a g e s (+3 kV) a negative c h a r g e t r a n s f e r from s u r f a c e to bulk traps and i n j e c t i o n o f elect r o n s from metallic e l e c t r o d e can be possible. The c h a r g e t r a n s f e r from the s u r f a c e to the bulk will depend on the p r o p e r t i e s o f the g a s e o u s ions, s u r f a c e states and the bulk p r o p e r t i e s [7,8]. We obt a i n ed the a c t i v a t i o n e n e r g y 0,94 eV from the t e m p e r a t u r e d e p e n d e n c e o f the c o n d u c t i v i t y in t e m p e r a t u r e range 3 4 0 - 3 9 0 K. This value con-
62 f o r m s to the a c t i v a t i o n e n e r g y o f T S D p e a k at 380 K f o r the n e g a t i v e c o r o n a . T h u s , it can be c o n c l u d e d t h a t the d e c a y o f the c h a r g e c o r r e s p o n d i n g to the n e g a t i v e p e a k at 380 K r e s u l t s f r o m d i s s i p a t i o n o f c h a r g e s by o h m i c c o n d u c t i v i t y . S p a c e c h a r g e d e c a y at this t e m p e r a t u r e is c o n n e c t e d to the r e l a x a t i o n in the a m o r p h o u s p h a s e o f the p o l y p r o p y l e n e [9]. T h e p e a k s at t e m p e r a t u r e s f r o m 410 to 420 K can be a t t r i b u t e d to e l e c t r o n i c t r a p s in the bulk. The o p e n c i r c u i t T S D p e a k s a f t e r c h a r g i n g with on e l e c t r o n b e a m w e r e also o b t a i n e d at the s a m e t e m p e r a t u r e range~ The r e l a x a t i o n p r o c e s s at this t e m p e r a t u r e r a n g e can be e x p l a i n e d as a s e p a r a t i o n o f the c h a r g e c a r r i e r s f r o m the h e l i x m o l e c u l e s in the c r y s t a l l i n e s t r u c t u r e o f the p o l y m e r [10]. T h e T S D r e s u l t s s u g g e s t t h a t d e c a y o f the c h a r g e t r a p p e d in the d e e p s u r f a c e t r a p s o f the p o l y p r o p y l e n e s a m p l e m a y o r i g i n a t e f r o m the b u l k p r o c e s s such as t h e r m a l b o p p i n g c o n d u c t i v i t y . The c o n d u c t i v i t y p r o c e s s is c o n n e c t e d with an a m o r p h o u s p a r t o f the p o l y m e r . D e e p t r a p s in the c o m m e r c i a l l y p r o d u c e d p o l y m e r m a y be c a u s e d by i m p u r i ties such as a n t i o x i d a n t s and a n t i s t a t i c a g e n t s . C h a n g e s in the s u r f a c e l a y e r and a m o r p h o u s p a r t o f the p o l y m e r s h o u l d lead to g r e a t c h a n g e s in c h a r g e t r a n s p o r t in the p o l y m e r . G r e a t c h a n g e s in t h e s e a r e a s may be c a u s e d by the e x p o s u r e to ext e r n a l p a r t i a l d i s c h a r g e s ( P D ) and i m p r e g n a t i o n the s a m p l e s in oil [ 1 1 , 1 2 ] . V a c u u m i m p r e g n a t e d PP s a m p l e s with c o n d e n s e r oil and s a m p l e s a g e d by PD in the air with g l a s s i n s e r t (10 kV, 50 H z ) by 5 and 10 h w e r e e x a m i n e d . F i g u r e 5 p r e s e n t s the t r a n s i e n t c h a r g i n g c u r r e n t s o f a g i n g s a m p l e s f o r n e g a t i v e c o r o n a . It is seen f r o m F i g u r e 5 t h a t g r e a t i n c r e a s e o f the c u r r e n t is o b s e r v e d due to a g i n g or i m p r e g n a t i o n . T h e s a m e e f f e c t is s e e n in I - U i s o c h r o n a l c h a r a c t e r i s t i c s as s h o w n in F i g u r e 6. The p o w e r d e p e n d e n c e I ~ U n is o b s e r v e d for v o l t a g e s g r e a t e r t h a n 40 V in c a s e o f the s a m p l e s a g e d f o r 10 h o u r s . T h e d i f f e r e n c e in c u r r e n t s b e t w e e n n o n - a g e d and 10 h a g e d s a m p l e s is a b o u t 3 o r d e r s o f m a g n i t u d e . The a g e d s a m p l e s e x p o s e d to p o s i t i v e c o r o n a b e h a v e d i f f e r e n t l y as s h o w n in F i g u r e 7. The i n c r e a s e o f the c u r r e n t f o r a g e d s a m p l e s is a b o u t 0,5 o r d e r o f m a g n i t u d e . A s u b l i n e a r b e h a v i o u r o f I - U d e p e n d e n c e in low v o l t a g e s is o b s e r v e d . T h e m o d e l o r i g i n a l l y p r o p o s e d by P o p e s c u and H e n i s c h [13] f o r r e l a x a t i o n s e m i c o n d u c t o r s s e e m s to be a d e q u a t e to e x p l a i n s u b l i n e a r d e p e n d e n c e o f I - U c h a r a c t e r i s t i c s in low v o l t a g e a r e a . T h e i n j e c t i o n o f m i n o r i t y c a r r i e r s or the e l e c t r o d e e f f e c t s w e r e s u p p o s e d to be the d o m i n a n t m e c h a n i s m t h e r e . T r a p p i n g o f the p o s i t i v e c h a r g e , t h e i r rec o m b i n a t i o n with e l e c t r o n s c a u s e s m a j o r i t y - c a r r i e r d e p l e t i o n and inc r e a s e o f e l e c t r i c a l r e s i s t a n c e in the n e a r s u r f a c e a r e a . T h e m e c h a n i s m s i n v o l v e d in t r a n s p o r t o f e l e c t r i c a l c h a r g e s a c r o s s p o l y p r o p y l e n e f i l m s d u r i n g c o r o n a c h a r g i n g are not well u n d e r s t o o d . C o m m e r c i a l l y p r o d u c e d p o l y m e r s c o n t a i n m a n y d o p a n t s such as a n t i s t a t i c a g e n t s and a n t i o x i d a n t s . E l e c t r i c a l p r o p e r t i e s o f the p o l y m e r s u r f a c e s are l i k e l y to be a f f e c t e d by a b s o r b e d i m p u r i t i e s and p r o d u c t s o f the a g i n g p r o c e s s . A t a c t i c a m o r p h o u s m a t e r i a l is p o s s i b l y a c c u m u -
63 l a t e d in the s u r f a c e l a y e r o f the p o l y m e r [14]. T h u s , the s u r f a c e p r o p e r t i e s o f t h e p o l y m e r can d i f f e r g r e a t l y f r o m t h e b u l k p r o p e r t i e s . S p e c t r o s c o p i c s t u d i e s o f the s u r f a c e o f the p o l y m e r a f t e r c o r o n a c h a r g i n g and i n f o r m a t i o n on s p a c e c h a r g e d i s t r i b u t i o n is n e c e s s a r y to o b t a i n a r e a l i s t i c m o d e l f o r the m e c h a n i s m o f the c o r o n a c h a r g i n g and charge decay.
10 8 '
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F i g u r e 6. E f f e c t o f s u r f a c e t r e a t m e n t on I - U c h a r a c t e r i s t i c s . C o n d i t i o n s as f o r Fig. 5.
10
10 2
103
U IV] F i g u r e 7. E f f e c t o f s u r f a c e t r e a t m e n t on I - U c h a r a c t e r i s t i c s f o r p o s i t i v e c o r o n a , U g = l kV. C o n d i t i o n s o f t r e a t m e n t as f o r Fig. 5.
4. C O N C L U S I O N S T h e c h a r g i n g t r a n s i e n t c u r r e n t s I - t and I - U c h a r a c t e r i s t i c s d e p e n d on the c o r o n a p o l a r i t y and s u r f a c e p r o p e r t i e s o f the p o l y p r o p y l e n e foils. T h e c o r o n a d e p o s i t e d c h a r g e s are t r a p p e d in the d e e p s u r f a c e t r a p s o f 2.0 eV f o r n e g a t i v e and 1,7 eV f o r p o s i t i v e c a r r i e r s . T h e p o s i t i v e s u r f a c e c h a r g e s a r e a n o t p r o b a b l y i n j e c t e d i n t o the bulk. E l e c t r o n s are p r o b a b l y r e s p o n s i b l e f o r the c o n d u c t i o n and c h a r g e d e c a y in p o l y p r o p y l e n e .
64 T h e c h a n g e s o f the s u r f a c e p r o p e r t i e s due to PD a g i n g h a v e g r e a t e r i n f l u e n c e in I - U f o r n e g a t i v e c o r o n a t h a n p o s i t i v e o n e s . It is p r o b a b l y b e c a u s e o f the c h a n g e s in i n j e c t i n g e f f i c i e n c y for n e g a t i v e c h a r g e s w h i c h can be i n j e c t e d .
5. A C K N O W L E D G E M E N T S T h i s w o r k was f i n a n c e d by a g r a n t f r o m the C o m m i t t e e o f the Scie n t i f i c R e s e a r c h u n d e r c o n t r a c t No 3 0721 91 01, w h i c h is g r a t e f u l l y acknowledged.
6. R E F E R E N C E S
1 2 3 4 5 6 7 8 9 10 11 12 13 14
R.A. M o r e n o and B. G r o s s , J. A p p l . P h y s . , 47 ( 1 9 7 6 ) 3 3 9 7 . M. I e d a , T. M i z u t a n i and S. I k e d a , I E E E T r a n s . E l e c t r . I n s . , 21 ( 1 9 8 6 ) 301. M. I e d a , I E E E T r a n s . E l e c t r . I n s . , 19 ( 1 9 8 4 ) 162. T.J. L e w i s , I E E E T r a n s . E l e c t r . I n s . , 21 ( 1 9 8 6 ) 289. J. K y o k a n e , K. Y o s h i n o , Y. I n u i s h i and R. C o e l h o , T r a n s . I E E Japan, 102 ( 1 9 8 2 ) 25. D . K . D a s - G u p t a and K. D o u g h t y , I E E E T r a n s . E l e c t r . I n s . , 23 ( 1 9 8 8 ) 47. D . K . D a s - G u p t a , M a t e r i a l s S c i e n c e , 16 ( 1 9 9 0 ) 131. T.J. L e w i s , J. P h y s . D: A p p l . P h y s . , 23 ( 1 9 9 0 ) , 1469. G. K r a u s e , K. M o i l e r , I E E E T r a n s . E l e c t r . I n s u l . , 24 ( 1 9 8 9 ) 215. G. K r a u s e , D. M e u r e r , D. K l e e , P r o c . 6th Int. S y m p . on E l e c t r e t s ( e d s D . K . D a s - G u p t a and A.W. P a t t u l l o ) , O x f o r d ( 1 9 8 8 ) 92. C. M a y o u x , G. G a r c i a and J. S a r l a b o u x , I E E E T r a n s . E l e c t r . I n sul., 17 ( 1 9 8 2 ) 156. T. T a n a k a , I E E E T r a n s . E l e c t r . I n s u l . , 21 ( 1 9 8 6 ) 881. C. P o p e s c u and H . K . H e n i s c h , P h y s . R e v . B 14 ( 1 9 7 6 ) 517. C. R o d e h e d , A. G u s t a f s s o n and U . W . G e d d e I E E E T r a n s . E l e c t r . I n s u l . , 25 ( 1 9 9 0 ) 1066.
57
C h a r g i n g of p o l y p r o p y l e n e foils in corona triode system E. M o t y l I n s t i t u t e o f E l e c t r i c a l E n g i n e e r i n g and T e c h n o l o g y , T e c h n i c a l U n i v e r s i t y o f W r o c t a w , W y b r z e z e W y s p i a f i s k i e g o 27, 5 0 - 3 7 0 W r o c t a w , Poland
Abstract
T h e t r a n s i e n t c h a r g i n g c u r r e n t s I - t and the v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s I - U o f o n e - s i d e m e t a t l i z e d PP f o i l s w e r e m e a s u r e d in c o r o n a t r i o d e s y s t e m . T h e t i m e d e p e n d e n c e o f c h a r g i n g c u r r e n t s was f o u n d as I ~ t -m. T h e I - U c h a r a c t e r i s t i c s p e c u l i a r to the SCL c o n d u c t i o n w e r e found for negative corona, A sublinear behaviour of I-U dependence in low e l e c t r i c f i e l d f o r p o s i t i v e c o r o n a w a s f o u n d . T h e d e e p s u r f a c e t r a p s f o r c o r o n a c h a r g e s w e r e o b t a i n e d f r o m the T S D e x p e r i m e n t s . T h e p a r t i a l d i s c h a r g e s a g i n g a f f e c t s I - U as well I - t c h a r a c t e r i s t i c s . A g r e a t e r i n c r e a s e o f the c u r r e n t was o b s e r v e d f o r n e g a t i v e t h a n p o s i tive charged samples.
1. I N T R O D U C T I O N T h e c o r o n a c h a r g i n g m e t h o d has w i d e s p r e a d a p p l i c a t i o n in the preparation o f the p o l y m e r foil e l e c t r e t s . The surface charge d i s t r i b u t i o n o f s a m p l e s c h a r g e d d i r e c t l y by the p o i n t e l e c t r o d e is u s u a l l y n o n u n i f o r m . A p p l i c a t i o n o f the g r i d e l e c t r o d e r e s u l t s us the g r e a t e r u n i f o r m i t y o f the s u r f a c e c h a r g e . P r a c t i c a l l y p a r a l l e l - p l a t e g e o m e t r y can be u s e d f o r t h e o r e t i c a l a n a l y s i s . C o r o n a t r i o d e s y s t e m m a k e s it p o s s i b l e to d e t e r m i n e the e q u i v a l e n t s u r f a c e c h a r g e s , c u r r e n t s and p o t e n t i a l s d u r i n g the c h a r g i n g p r o c e s s [ l ] . One - side m e t a l l i z e d s a m p l e s can be m e a s u r e d and the e l e c t r o d e e f f e c t s can be i n v e s t i g a t e d in the s y s t e m [2]. I n t e r f a c i a l p h e n o m e n a p l a y an i m p o r t a n t r o l e in e l e c t r i c a l t r a n s p o r t in p o l y m e r f o i l s [ 3 , 4 ] . T h e m e c h a n i s m o f the c h a r g e b u i l d - u p and dec a y is not yet a d e q u a t e l y u n d e r s t o o d [ 3 , 5 ] . It has b e e n s h o w n t h a t the c h a r g i n g c u r r e n t s and c o n d u c t i v i t y in p o l y m e r i c i n s u l a t o r s are dep e n d e n t on the s a m p l e t r e a t m e n t and the c h a r g i n g m e d i u m [ 6 , 7 ] . T h i s p a p e r p r e s e n t s r e s u l t s o f the e x p e r i m e n t s u n d e r t a k e n to i n v e s t i g a t e the i n f l u e n c e o f the h i g h c o r o n a f i e l d s on o n e - s i d e m e t a l l i z e d PP foils. T h e t r a n s i e n t c h a r g i n g c u r r e n t s and the v o l t a g e - c u r r e n t 0304-3886/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
58 c h a r a c t e r i s t i c s w e r e m e a s u r e d in c o r o n a t r i o d e s y s t e m . 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 s w e r e m e a s u r e d in the o p e n c i r c u i t a f t e r c o r o n a c h a r g i n g . The e f f e c t s o f the s u r f a c e t r e a t m e n t by p a r t i a l d i s c h a r g e s and i m p r e g n a t i o n o f s a m p l e s with oil on c h a r g i n g c h a r a c t e r i s t i c s w e r e also i n v e s t i g a t e d .
2.
EXPERIMENTAL
The c h a r g i n g s y s t e m as s h o w n b e l o w in F i g u r e 1 c o n s i s t s o f the c o r o n a p o i n t e l e c t r o d e P c o n n e c t e d to a v a r i a b l e high - v o l t a g e s o u r c e U c. 13 n e e d l e s w e r e used as the p o i n t e l e c t r o d e . The grid G has a d i a m e t e r o f 58 mm and is made o f c o p p e r wire 50 ~tm in d i a m e ter with a mesh w i d t h o f 120 gm. The s a m p l e S is m o u n t e d on a m e t a l e l e c t r o d e E and a g u a r d ring R. One s u r f a c e o f the s a m p l e is unc o a t e d ; the o t h e r is c o v e r e d by e v a p o r a t e d a l u m i n i u m . The area o f m e a s u r i n g e l e c t r o d e is 8 cm 2. The d i s t a n c e b e t w e e n the g u a r d ring and the m e a s u r i n g e l e c t r o d e is 1 mm. The d i s t a n c e b e t w e e n the p o i n t e l e c t r o d e and the grid is 35 mm and the d i s t a n c e grid to metal e l e c t r o d e E is 4 mm.
II
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R
Uc
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e
--
e
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E
I
57 u
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,) ) L--
F i g u r e 1. S c h e m a t i c d i a g r a m o f the c o r o n a t r i o d e s y s t e m . P, p o i n t e l e c t r o d e ; G, g r i d ; E, m e a s u r i n g e l e c t r o d e ; R, g u a r d ring; U c and U~, c o n t r o l l e d p o w e r s u p p l i e s ; pA, p i c o a m m e t e r .
S a m p l e s o f 12 ~tm and 26 gm p o l y p r o p y l e n e c o m m e r c i a l film EK500 f r o m H e r c u l e s w e r e k e p t s t r e t c h e d with the help o f a m e t a l l i c
59 h o l d e r d u r i n g the c h a r g i n g p r o c e s s . The v o l t a g e U a c r o s s the s a m p l e was c a l c u l a t e d by U = Ug
- Usg(I),
w h e r e the v o l t a g e b e t w e e n the grid and the s a m p l e U s g ( I ) was d e t e r m i n e d e m p i r i c a l l y f r o m the c a l i b r a t i o n c u r v e . The s u r f a c e p o t e n t i a l o f the s a m p l e was a l m o s t the same as the grid p o t e n t i a l . T h u s , the grid e l e c t r o d e G p l a y s a role o f a c o n t a c t l e s s e l e c t r o d e for c u r r e n t m e a s urements. The TSD s p e c t r a o f s a m p l e films w e r e o b s e r v e d u n d e r the o p e n - c i r cuit c o n d i t i o n f r o m r o o m t e m p e r a t u r e to a b o u t 460 K at a h e a t i n g rate o f a b o u t 3 K / m i n . The d i s t a n c e f r o m the p r o b e to the n o n m e t a l l i z e d s u r f a c e o f the p o l y m e r was 4 mm.
3. R E S U L T S
AND
DISCUSSION
M e a s u r e m e n t s o f the time d e p e n d e n c e o f the c h a r g i n g c u r r e n t s w e r e m a d e at c o n s t a n t c o r o n a c u r r e n t I = 2 ~tA. A grid v o l t a g e Ug was a p p l i e d for 30 min and I ( t ) was m e a s u r e d , then the v o l t a g e was inc r e a s e d to h i g h e r v a l u e for a n o t h e r 30 min and the new c u r v e l ( t ) was m e a s u r e d and so f o r t h . The fixed grid v o l t a g e w e r e 20, 50, 100, 200, 500, 1000, 2 0 0 0 and 4 0 0 0 V. Time d e p e n d e n c i e s o f the c h a r g i n g c u r r e n t s for p o s i t i v e c o r o n a are s h o w n in F i g u r e 2. On a d o u b l e l o g a r i t h m i c scale, d e c a y c u r r e n t s can be a p p r o x i m a t e d by the s t r a i g h t lines g i v i n g I~t -m. As it is s h o w n in the F i g u r e 2 w h e n the v o l t a g e b e l o w 1000 V is a p p l i e d to the grid the c u r r e n t d e c r e a s e s r a p i d l y for m o r e than 1000 s and n e v e r a p p r o a c h e s a s t e a d y value. U n d e r the h i g h e r v o l t a g e s a quasi s t e a d y s t a t e is acc o m p l i s h e d in a b o u t 1000 s. The c h a r g i n g c u r r e n t s for n e g a t i v e c o r o n a are s l i g h t l y l o w e r t h a n for positive corona. The quasi s t a t i o n a r y c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s w e r e o b t a i n e d f r o m the t r a n s i e n t c h a r g i n g c u r r e n t s . The i s o c h r o n a l I - U c h a r a c t e r i s tics at t = 1000 s are s h o w n in F i g u r e 3. The l i n e a r o h m i c I - U dep e n d e n c e in low v o l t a g e s and the I~U n d e p e n d e n c e for h i g h e r than 800 V was o b s e r v e d for n e g a t i v e c o r o n a . A s u b l i n e a r b e h a v i o u r o f I - U d e p e n d e n c e in low v o l t a g e s for p o s i t i v e c o r o n a was f o u n d . The c u r rent d e p e n d s u p o n the p o l a r i t y o f the c o r o n a e l e c t r o d e . The p o s i t i v e c o r o n a e l e c t r o d e s h o w s a l a r g e r c u r r e n t than the n e g a t i v e ones. The i s o c h r o n a l I - U c h a r a c t e r i s t i c s at t = 1000 s o f a s p e c i m e n with e v a p o r a t e d Al e l e c t r o d e s on b o t h s u r f a c e s was also m e a s u r e d . The AI e l e c t r o d e s h o w s n e a r l y the same c u r r e n t as the n e g a t i v e c o r o n a e l e c t r o d e in low v o l t a g e r a n g e as s h o w n in F i g u r e 3. The s t u d y o f the s u r f a c e c h a r g e d e c a y has s h o w n that the s u r f a c e p o t e n t i a l r e m a i n s c o n s t a n t with time f o r the initial s u r f a c e p o t e n t i a l s - 5 0 0 V and d e c r e a s e s v e r y s l o w l y for _+2 kV. S a m p l e s c h a r g e d
60 t h r o u g h the g r i d e x h i b i t e d a u n i f o r m c h a r g e d i s t r i b u t i o n o v e r the ent i r e s u r f a c e . T h e r e was no n o t i c e a b l e e v i d e n c e o f the l a t e r a l c h a r g e s p r e a d i n g on t h e film s u r f a c e . T h e w i d t h o f the c h a r g e p r o f i l e was k e p t c o n s t a n t f o r 120 h a f t e r c h a r g i n g at _+2 kV in the air f o r 200 s.
10-7
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F i g u r e 2. T r a n s i e n t c h a r g i n g c u r rents for increased values of grid v o l t a g e s Ug f r o m 20 to 2 0 0 0 V f o r 12 ]am p o l y p r o p y l e n e foils. P o s i t i v e c o r o n a . I c = 2 gA.
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F i g u r e 3. C u r r e n t - v o l t a g e c h a r acteristics for positive (C+/PP/ A1) and n e g a t i v e (C'/PP/AI) c o r o n a in c o m p a r i s o n w i t h A1/PP/A1 structure.
TSD r e s u l t s o f PP s a m p l e s c h a r g e d with v a r i o u s g r i d v o l t a g e s f r o m - 3 kV to 3 kV at t = 200 s are s h o w n in F i g u r e 4. T h e p e a k s at t e m p e r a t u r e s a b o u t 330, 380 and 410 K w e r e o b s e r v e d f o r n e g a t i v e c o r o n a c h a r g i n g . O n e p e a k at 350 K and a n o t h e r a p p e a r i n g b e t w e e n 390-400 K were observed for positive corona charging. The activation e n e r g i e s w e r e d e t e r m i n a t e d by the initial rise m e t h o d u s i n g p a r t i a l h e a t i n g t e c h n i q u e for s a m p l e s c h a r g e d at _+3 kV. W i d e d i s t r i b u t i o n o f the a c t i v a t i o n e n e r g i e s 0,9 - 2,0 eV c o r r e s p o n d s w i t h the p e a k at 330 K f o r n e g a t i v e c h a r g e d s a m p l e s . T h e a c t i v a t i o n e n e r g y f o r p e a k at 350 K f o r p o s i t i v e c h a r g e d s a m p l e s is a b o u t 1,7 eV.
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T[K] F i g u r e 4. TSD m e a s u r e m e n t s in open c i r c u i t for d i f f e r e n t grid v o l t a g e s Uo, H e a t i n g rate b=3 K/min, c o r o n a c u r r e n t Ic=2 p,A, c h a r g i n g time tc= 200 s.
lC~ 1
10
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Fi gur e 5. E f f e c t o f s u r f a c e t r e a t ment on t r a n s i e n t c h a r g i n g currents. 1, u n t r e a t e d sample; 2, vacuum i m p r e g n a t e d sample with c o n d e n s e r oil; 3, PD aged sample by 5 h; 4, PD aged sample by 10 h. N e g a t i v e c o r o n a , U g = - I kV.
The c h a r g e s d e p o s i t e d on the p o l y m e r s u r f a c e aft er c o r o n a c h a r g i n g may be easily r e m o v e d by o u t g a s s i n g in vacuum. The TSD c u r r e n t s w e r e d e c r e a s e d 4 times for n e g a t i v e c h a r g e d samples, and 20 times for p o s i t i v e ones af t er 30 min hol di ng u n d e r vacuum o f 10 -5 t orr. Thus, the n e g a t i v e c h a r g e is bound more s t r o n g l y with the p o l y m e r than the p o s i t i v e ch ar g e. C ha r ges d e p o s i t e d on the p o l y m e r s u r f a c e are t r a p p e d in deep traps and i m m o b i l i z e d , t h e r e f o r e the TSD c u r r e n t s are small for T < 340 K and U < 1 kV. U n d e r hi gh er v o l t a g e s (+3 kV) a negative c h a r g e t r a n s f e r from s u r f a c e to bulk traps and i n j e c t i o n o f elect r o n s from metallic e l e c t r o d e can be possible. The c h a r g e t r a n s f e r from the s u r f a c e to the bulk will depend on the p r o p e r t i e s o f the g a s e o u s ions, s u r f a c e states and the bulk p r o p e r t i e s [7,8]. We obt a i n ed the a c t i v a t i o n e n e r g y 0,94 eV from the t e m p e r a t u r e d e p e n d e n c e o f the c o n d u c t i v i t y in t e m p e r a t u r e range 3 4 0 - 3 9 0 K. This value con-
62 f o r m s to the a c t i v a t i o n e n e r g y o f T S D p e a k at 380 K f o r the n e g a t i v e c o r o n a . T h u s , it can be c o n c l u d e d t h a t the d e c a y o f the c h a r g e c o r r e s p o n d i n g to the n e g a t i v e p e a k at 380 K r e s u l t s f r o m d i s s i p a t i o n o f c h a r g e s by o h m i c c o n d u c t i v i t y . S p a c e c h a r g e d e c a y at this t e m p e r a t u r e is c o n n e c t e d to the r e l a x a t i o n in the a m o r p h o u s p h a s e o f the p o l y p r o p y l e n e [9]. T h e p e a k s at t e m p e r a t u r e s f r o m 410 to 420 K can be a t t r i b u t e d to e l e c t r o n i c t r a p s in the bulk. The o p e n c i r c u i t T S D p e a k s a f t e r c h a r g i n g with on e l e c t r o n b e a m w e r e also o b t a i n e d at the s a m e t e m p e r a t u r e range~ The r e l a x a t i o n p r o c e s s at this t e m p e r a t u r e r a n g e can be e x p l a i n e d as a s e p a r a t i o n o f the c h a r g e c a r r i e r s f r o m the h e l i x m o l e c u l e s in the c r y s t a l l i n e s t r u c t u r e o f the p o l y m e r [10]. T h e T S D r e s u l t s s u g g e s t t h a t d e c a y o f the c h a r g e t r a p p e d in the d e e p s u r f a c e t r a p s o f the p o l y p r o p y l e n e s a m p l e m a y o r i g i n a t e f r o m the b u l k p r o c e s s such as t h e r m a l b o p p i n g c o n d u c t i v i t y . The c o n d u c t i v i t y p r o c e s s is c o n n e c t e d with an a m o r p h o u s p a r t o f the p o l y m e r . D e e p t r a p s in the c o m m e r c i a l l y p r o d u c e d p o l y m e r m a y be c a u s e d by i m p u r i ties such as a n t i o x i d a n t s and a n t i s t a t i c a g e n t s . C h a n g e s in the s u r f a c e l a y e r and a m o r p h o u s p a r t o f the p o l y m e r s h o u l d lead to g r e a t c h a n g e s in c h a r g e t r a n s p o r t in the p o l y m e r . G r e a t c h a n g e s in t h e s e a r e a s may be c a u s e d by the e x p o s u r e to ext e r n a l p a r t i a l d i s c h a r g e s ( P D ) and i m p r e g n a t i o n the s a m p l e s in oil [ 1 1 , 1 2 ] . V a c u u m i m p r e g n a t e d PP s a m p l e s with c o n d e n s e r oil and s a m p l e s a g e d by PD in the air with g l a s s i n s e r t (10 kV, 50 H z ) by 5 and 10 h w e r e e x a m i n e d . F i g u r e 5 p r e s e n t s the t r a n s i e n t c h a r g i n g c u r r e n t s o f a g i n g s a m p l e s f o r n e g a t i v e c o r o n a . It is seen f r o m F i g u r e 5 t h a t g r e a t i n c r e a s e o f the c u r r e n t is o b s e r v e d due to a g i n g or i m p r e g n a t i o n . T h e s a m e e f f e c t is s e e n in I - U i s o c h r o n a l c h a r a c t e r i s t i c s as s h o w n in F i g u r e 6. The p o w e r d e p e n d e n c e I ~ U n is o b s e r v e d for v o l t a g e s g r e a t e r t h a n 40 V in c a s e o f the s a m p l e s a g e d f o r 10 h o u r s . T h e d i f f e r e n c e in c u r r e n t s b e t w e e n n o n - a g e d and 10 h a g e d s a m p l e s is a b o u t 3 o r d e r s o f m a g n i t u d e . The a g e d s a m p l e s e x p o s e d to p o s i t i v e c o r o n a b e h a v e d i f f e r e n t l y as s h o w n in F i g u r e 7. The i n c r e a s e o f the c u r r e n t f o r a g e d s a m p l e s is a b o u t 0,5 o r d e r o f m a g n i t u d e . A s u b l i n e a r b e h a v i o u r o f I - U d e p e n d e n c e in low v o l t a g e s is o b s e r v e d . T h e m o d e l o r i g i n a l l y p r o p o s e d by P o p e s c u and H e n i s c h [13] f o r r e l a x a t i o n s e m i c o n d u c t o r s s e e m s to be a d e q u a t e to e x p l a i n s u b l i n e a r d e p e n d e n c e o f I - U c h a r a c t e r i s t i c s in low v o l t a g e a r e a . T h e i n j e c t i o n o f m i n o r i t y c a r r i e r s or the e l e c t r o d e e f f e c t s w e r e s u p p o s e d to be the d o m i n a n t m e c h a n i s m t h e r e . T r a p p i n g o f the p o s i t i v e c h a r g e , t h e i r rec o m b i n a t i o n with e l e c t r o n s c a u s e s m a j o r i t y - c a r r i e r d e p l e t i o n and inc r e a s e o f e l e c t r i c a l r e s i s t a n c e in the n e a r s u r f a c e a r e a . T h e m e c h a n i s m s i n v o l v e d in t r a n s p o r t o f e l e c t r i c a l c h a r g e s a c r o s s p o l y p r o p y l e n e f i l m s d u r i n g c o r o n a c h a r g i n g are not well u n d e r s t o o d . C o m m e r c i a l l y p r o d u c e d p o l y m e r s c o n t a i n m a n y d o p a n t s such as a n t i s t a t i c a g e n t s and a n t i o x i d a n t s . E l e c t r i c a l p r o p e r t i e s o f the p o l y m e r s u r f a c e s are l i k e l y to be a f f e c t e d by a b s o r b e d i m p u r i t i e s and p r o d u c t s o f the a g i n g p r o c e s s . A t a c t i c a m o r p h o u s m a t e r i a l is p o s s i b l y a c c u m u -
63 l a t e d in the s u r f a c e l a y e r o f the p o l y m e r [14]. T h u s , the s u r f a c e p r o p e r t i e s o f t h e p o l y m e r can d i f f e r g r e a t l y f r o m t h e b u l k p r o p e r t i e s . S p e c t r o s c o p i c s t u d i e s o f the s u r f a c e o f the p o l y m e r a f t e r c o r o n a c h a r g i n g and i n f o r m a t i o n on s p a c e c h a r g e d i s t r i b u t i o n is n e c e s s a r y to o b t a i n a r e a l i s t i c m o d e l f o r the m e c h a n i s m o f the c o r o n a c h a r g i n g and charge decay.
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F i g u r e 6. E f f e c t o f s u r f a c e t r e a t m e n t on I - U c h a r a c t e r i s t i c s . C o n d i t i o n s as f o r Fig. 5.
10
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103
U IV] F i g u r e 7. E f f e c t o f s u r f a c e t r e a t m e n t on I - U c h a r a c t e r i s t i c s f o r p o s i t i v e c o r o n a , U g = l kV. C o n d i t i o n s o f t r e a t m e n t as f o r Fig. 5.
4. C O N C L U S I O N S T h e c h a r g i n g t r a n s i e n t c u r r e n t s I - t and I - U c h a r a c t e r i s t i c s d e p e n d on the c o r o n a p o l a r i t y and s u r f a c e p r o p e r t i e s o f the p o l y p r o p y l e n e foils. T h e c o r o n a d e p o s i t e d c h a r g e s are t r a p p e d in the d e e p s u r f a c e t r a p s o f 2.0 eV f o r n e g a t i v e and 1,7 eV f o r p o s i t i v e c a r r i e r s . T h e p o s i t i v e s u r f a c e c h a r g e s a r e a n o t p r o b a b l y i n j e c t e d i n t o the bulk. E l e c t r o n s are p r o b a b l y r e s p o n s i b l e f o r the c o n d u c t i o n and c h a r g e d e c a y in p o l y p r o p y l e n e .
64 T h e c h a n g e s o f the s u r f a c e p r o p e r t i e s due to PD a g i n g h a v e g r e a t e r i n f l u e n c e in I - U f o r n e g a t i v e c o r o n a t h a n p o s i t i v e o n e s . It is p r o b a b l y b e c a u s e o f the c h a n g e s in i n j e c t i n g e f f i c i e n c y for n e g a t i v e c h a r g e s w h i c h can be i n j e c t e d .
5. A C K N O W L E D G E M E N T S T h i s w o r k was f i n a n c e d by a g r a n t f r o m the C o m m i t t e e o f the Scie n t i f i c R e s e a r c h u n d e r c o n t r a c t No 3 0721 91 01, w h i c h is g r a t e f u l l y acknowledged.
6. R E F E R E N C E S
1 2 3 4 5 6 7 8 9 10 11 12 13 14
R.A. M o r e n o and B. G r o s s , J. A p p l . P h y s . , 47 ( 1 9 7 6 ) 3 3 9 7 . M. I e d a , T. M i z u t a n i and S. I k e d a , I E E E T r a n s . E l e c t r . I n s . , 21 ( 1 9 8 6 ) 301. M. I e d a , I E E E T r a n s . E l e c t r . I n s . , 19 ( 1 9 8 4 ) 162. T.J. L e w i s , I E E E T r a n s . E l e c t r . I n s . , 21 ( 1 9 8 6 ) 289. J. K y o k a n e , K. Y o s h i n o , Y. I n u i s h i and R. C o e l h o , T r a n s . I E E Japan, 102 ( 1 9 8 2 ) 25. D . K . D a s - G u p t a and K. D o u g h t y , I E E E T r a n s . E l e c t r . I n s . , 23 ( 1 9 8 8 ) 47. D . K . D a s - G u p t a , M a t e r i a l s S c i e n c e , 16 ( 1 9 9 0 ) 131. T.J. L e w i s , J. P h y s . D: A p p l . P h y s . , 23 ( 1 9 9 0 ) , 1469. G. K r a u s e , K. M o i l e r , I E E E T r a n s . E l e c t r . I n s u l . , 24 ( 1 9 8 9 ) 215. G. K r a u s e , D. M e u r e r , D. K l e e , P r o c . 6th Int. S y m p . on E l e c t r e t s ( e d s D . K . D a s - G u p t a and A.W. P a t t u l l o ) , O x f o r d ( 1 9 8 8 ) 92. C. M a y o u x , G. G a r c i a and J. S a r l a b o u x , I E E E T r a n s . E l e c t r . I n sul., 17 ( 1 9 8 2 ) 156. T. T a n a k a , I E E E T r a n s . E l e c t r . I n s u l . , 21 ( 1 9 8 6 ) 881. C. P o p e s c u and H . K . H e n i s c h , P h y s . R e v . B 14 ( 1 9 7 6 ) 517. C. R o d e h e d , A. G u s t a f s s o n and U . W . G e d d e I E E E T r a n s . E l e c t r . I n s u l . , 25 ( 1 9 9 0 ) 1066.