Experimental investigation of the relationship between generation and decay of charges on dielectrics

Journal of Electrostatics, 2 (1976) 151--173

151

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

EXPERIMENTAL INVESTIGATION OF THE RELATIONSHIP BETWEEN GENERATION AND DECAY OF CHARGES ON DIELECTRICS

H.T.M. HAENEN

Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, Eindhoven (The Netherlands) (Received October 7, 1975; in revised form December 12, 1975)

Summary Decay characteristics of corona-charged crystals (NaCI, CaF2), sintered AI20~, bakelized paper and epoxy resin are presented. The crystals are of scientific interest and could serve as reference material, as they show very good reproducibility. At the end of the decay, most charges are conserved in the crystal at the grounded electrode side and by turning the crystal over again a further decay can be initiated. Epoxy resin showed a strong dependence on the water content. The mobilities of several dielectrics are summarized. A relationship between relative decay rates of positive and negative charges and triboelectric charge is found.

1. Introduction Nowadays, decay characteristics belong to just one of the experimental techniques frequently used to study electronic transport processes in dielectrics. Other experimental techniques are: the study of d.c., a.c. and transient conductivity, photoconductivity, thermally stimulated current and voltage (TSC, TSV), dielectric loss and contact potential. Most of these techniques have been applied to polymers. The behaviour of polymers varies widely because of the use of a range of additives, surface treatments and environments. Considerable "decay-work" has already been done on polyethylene [1,2,3]. Here the results depended on crystallinity [4] and ambient atmosphere [5]. From a scientific point of view, it is interesting to study the decay in dielectrics with a simple structure. The following experiments cover a wide range of dielectrics from crystals to a quite amorphous and anisotropic material like bakelized paper. The first two important features to compare are decayrate and the dependence of decay-rate on polarity.

2. Experimental results The experimental set-up was similar to that described previously [6]. Generally, the probe-to-dielectric distance was 0.5 cm. Hence, an electrometer

152 reading of I mV corresponded to 35 V across the dielectric. All dielectrics were corona-charged, with charging times of 15 s and 1 min. Experiments were carried out at room temperature. 2.1 D e c a y w i t h s o d i u m c h l o r i d e

The polished and unpolished NaC1 single crystals (infra-red window material) were 6 cm X 6 cm X 0.5 cm. The initial surface voltage ranged from 3 kV to 9 kV, both positive and negative. Relative h u m i d i t y was smaller than 15%, and no disturbing surface effects were observed. Generally, charge decayed within two hours. Thereafter, the crystal kept residual charge with a half-life of a week or more. Residual voltage a m o u n t e d to 5%--10% of its initial value. This a m o u n t had been found earlier in a breakdown experiment [7]. By changing polarity, residual charge could be almost completely removed (Fig. 1). Experimental results (Fig. 1) fitted well into a

Fig. 1. Typical decay curve of sodium chloride.

model which t o o k account of surface deep trapping [8], given by: V / V o = 1 -- p0(2 -- P o ) ½ t / t T

0 < t < tT

(1)

V / V o = ½ t T / t + ( 1 - - po)2 ½ t / t T

tT < t <

(2)

V / V o = 1 - - Po

t ~" t F

tF

(3)

where p 0 is the ratio of injected charge to total surface charge, V is the surface voltage, V0 is the initial voltage, t is the time, t T is the transit time, and t~ the final time. t F and t T are related by tT

tv - - I --Po

(4)

153 The mobility p can be calculated from: L2 -

VotT

(5)

where L is the thickness of the crystal. The calculated mobility range for polished as well as unpolished crystals, for experiments repeated over months, was found to be 0.9 -- 1.1 × 1 0 - " m2/ (V.s). This is exactly equal to the mobility derived from a photoconductivity experiment with a similar crystal. For KC1 a mobility of 1 0 - " m2/(V.s) was found [9]. This low mobility must be an effective one resulting from shallow trapping. An interesting experiment in which this crystal is turned during the decay proved to be reproducible. The crystal is lifted from a grounded polished copper electrode, turned over, and put back on the electrode. In this way, the decay is "restarted". Figure 2(a) demonstrates the decay of the probe scanning curves after negative corona-charging. After 110 min the crystal is turned and probe potential is raised more than 10 times (Figs. 2(b), 3). At the second turn (Figs. 2(c), 3), the same effect is established. The third turn (Figs. 2(d}, 3) is made when the decay has reached half its initial value. No surface potential increase is detected. At the fourth turn (Figs. 2(e), 3) the usual increase is found. Sometimes a disturbance occurs from breakdown between crystal surface and grounded electrode. This causes some change in the charge profile, as may be seen in Figs. 2(a)-2(e). The voltages on the cross-sections AB and BA in Figs. 2(a)--2(e) (always negative) are plotted in Fig. 3 as functions of time. Neglecting the deeplytrapped charge (p 0 = 1), eqns. (1), (2) and (3) convert into a simpler wellknown model [10], from which mobility is easily calculated by: A(1/V) L 2 u = At 2

(6)

After corona-charging, mobility calculated from eqns. (1), (2) and (3) yields 1.1 × 10 -l' m2/(V.s), while eqn. (6) yields 1.9 × 1 0 - " m2/(V.s). After the first and third turn (Fig. 3) the mobilities calculated from eqn. (6) are 3.6 X 1 0 - " m2/(V.s) and 7.3 X 1 0 - " m2/(V.s}respectively. This increase in mobility with turning may be explained by injected charge of reverse polarity. This experiment demonstrates that the electrode contact must be blocking. During the decay, charge is collected at the undersurface and, by turning, this charge is on the upper surface, thus raising surface potential. If the turn is made at the m o m e n t when surface potential is half its initial value, surface potential does not change. So the charge distribution inside the crystal must be symmetrical with respect to its thickness.

154

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Figs. 2(a)--2(e). Probe scanning curves with sodium chloride, initiallycorona-charged (a) and then turned over (b); (c) after second turn over, (d) after third turn over and (e) after fourth turn over. All voltages shown are negative.

155

Fig.

2(d)

fo::

~

Fig. 3

!

~

2,0

_tV Imv)~

20o

i '

I '

I

I /

,

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t

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[

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00

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hoo

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~

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,

]

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t,

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,

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,

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:.J

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i~ ,/4o irwerse val.ues

40

0 50

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10

;

'

~ ],

I /

observedvaiues

~--theory

i. °

i-'-1 -~-Z,0

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i [-~

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30

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~q'/V v%

/t

......I,,

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.I

//'0

50

60

110 0

~ I ~ 10

20

30

~-~-=~ 20

30

40

50

0 65

10

Fig. 3. Repeated decay of sodium chloride corresponding to cross-sections AB, BA in Figs. 2(a)--2(e). All voltages shown are negative.

2.2 Decay with calcium fluoride Polished CaF2 single crystals 5 cm in d i a m e t e r and 1-mm thick were used. Initial d e c a y was so rapid t h a t t h e initial voltage could n o t be recorded b u t was estimated to be a b o u t 3 kV. For m o d e l fitting, advantage can be t a k e n of the fact t h a t , in m o s t models, the voltage versus time characteristic is i n d e p e n d e n t of initial voltage after transit time. As with NaC1, there was residual charge after the decay. The following'expression, resulting f r o m a

156

model accounting for deep trapping [ 11 ], was successfully applied to the experimental results: v(t)

=

(7)

1 -- exp(--t/r)

where r = e/tzq, q is the residual charge density and e the total dielectric constant. If the residual voltage is V~, the following expression for the mobility U can be derived from eqn. (7): L 2 Aln(1-- V~/V) =

-

-

-

(8)

2V~

at

In Fig. 4 typical plots of (1 -- V ~ / V ) versus t on a logarithmic-linear scale are

Z,

8

12

16

Fig. 4. Modified decay curves of calcium fluoride.

given. The slopes of the straight lines yield a mobility range of ~ = 0.6 × 10 -11. = 0 . 9 × 10 -1~ m~/(V.s) (1, 2, 3, 4 correspond to different residual voltages). 2.3 Decay with sintered a l u m i n i u m o x i d e

The samples, which had an A1203 percentage higher than 99.5%, were 7.5 cm in diameter and 8 mm thick. Before being used, they were heated to glowing point at approx. 1000°(3. Modified decay curves are presented in Fig. 5. As the inverse probe voltage is linear with time, it can be concluded that the decay is a space-charge-limited one. Mobilities ranged from 0.5 X 10 -~° to 2 X 1 0 -1° m 2 / ( V . s ) .

Experiments carried o u t with sapphire and electrolytic A1203 did n o t yield any results. The crystals were t o o small and, owing to the presence of little leakage channels in the layer, the electrolytic A1203 did n o t charge.

157

150, i ' V (m~V) 1IV (v-1) .

.

.

.

.

100

.......

0

5

10

1 .................. :

; ::',°o=[v:':o

15

20

.............

2b

Fig. 5. Inverse d e c a y curves and n o r m a l d e c a y curve o f s i n t e r e d a l u m i n i u m oxide.

Thin oxide layers on metals are of interest because of troublesome surface charging in vacuum systems [12]. 2.4 Decay with bakelized paper Sample sizes were 15 cm X 9 cm X 1 cm. The initial charging level varied from 350 V to 3500 V, while a Perspex sample in an equivalent situation charged to a minimum of 7000 V. Although each sample had its individual initial voltage, the decay curves were similar. Conditioning at a certain relative humidity was done during a period of 3 days. The decay at t w o relative humidities is given in Fig. 6(a). When a sample which t o o k on a relatively low charge was coated with an insulating paint, the charging level increased considerably (Fig. 6(b)). Samples that had a silver-painted electrode at the ioniser side showed an extremely low charge (7 V on the surface electrode). As the apparatus t o o k some seconds to reach a stage at which a measurement could be made, an experiment with electrode charging was carried o u t to study fast decay. The experimental set-up is given in Fig. 7 (bandwidth of system 40 kHz), and Fig. 8 presents some typical decay curves. The decay t o o k only a b o u t 0.5 s, was independent of initial field strength and became " o h m i c " after a certain time. From this phase, a specific resistance of 3 × 10 9 ~2.m was derived, taking for the relative dielectric constant a value of 7.0, obtained from bridge measurements. Until now the influence of intrinsic conduction on decay has been neglected. The decay with a two-electrode, coated sample of bakelized paper seems, however, to be principally determined b y its intrinsic conduction, as values derived from d.c. measurements also yield 3 × 10 9 ~2.m at low field strengths (see the appendix). The discrepancy in the decay of corona-charged samples, Figs. 6(a), 6(b)

158

0.1

1

10

i B

100

Fig. 6(a) and 6(b). Decay curves of corona-charged bakelized paper.

7 J I

H V" °'~7

I I

r'el.ectro L ..... l em0ry --] meter oscil[oscol~ ~e[ectro:t:tic- probe

$'

~ Isampte

~

Fig. 7. Experimental set-up to study fast decay.

and electrode-charged samples, Fig. 8, can be explained either by a surface retention effect of ions or by relatively low ion conductivity in the corona-charging case. 2. 5 Decay with e p o x y resin Araldite D (CY 230) with hardener HY 950 in a mixture 5:1, sizes

159

1.0

_-t ~ q r ~ 2 / V . ~ c 7 - _ _

/xlO-,

oE0=5 kV/cm ~ +E0ffilOkV/cm xE0=20 kV/cm

/

----k

o~o VO VOvO "--10 +10 " kV kV"sam kV~~amPle - - -2/' 1:--, r e~ 0:1

---- ~ V,, u : - 10 kV /

-//

~

0.2

0.4

0.6

0.1

....

/-/

I

0.01 0

~

G(g )

61.8

62.0

62.2

62.4

-

Fig. 8. Decay curves of electrode-charged bakelized paper. Fig. 9. Mobility v e r s u s

weight after water absorption with Araldite D (CY 230).

14 cm X 12 cm × 0.3 cm was used. The samples were weighed on a high precision balance (accuracy -+ 0.002 g). Assuming carrier injection and constant mobility, the decay could then be interpreted in a well-known way, [10]. Recently, it has been shown that the decay of deposited epoxy layers increases with relative humidity [13]. In our experiments we found that carrier mobility did not correlate with relative humidity but with water content. Polymers, like epoxy resin and Perspex, can acquire considerable amounts of water [14] because of the OH-group in their structures and water strongly influences electrical conduction in epoxy resin [15]. The mobilities derived from the decay characteristics are plotted in Fig. 9. It was found that mobility increased exponentially with water content. Mobility of positive charge increased somewhat faster with water content than did the mobility of negative charge. Some scatter in the points of Fig. 9 is caused by weight change during the experiment. Water content was varied by putting samples for weeks either in a dry or in a saturated atmosphere. 3. Discussion of charge decay Results of charge decay in air are summarised in Table 1. With respect to mobility and its polarity preference, mobility here also represents decay rate. The crystals NaC1 and CaF2 show relatively high mobility (10 -11 m2/V.s) compared to most polymers. Elsewhere, the conductivity (as the product of mobility and intrinsic carrier density) at low field strengths of NaCI was found to be

Charging

2.5 × 10 -'s 3.6 x 1 0 - ' 5 3.5 × 10 -'3

corona

corona

breakdown method

P E T (polyethylene terephthalate, 12.7 # m [22]

PS (polystyrene), 15urn PMMA, 16 u m Perspex, Lucite [21]

breakdown method

corona

corona

corona

corona

corona corona

method

F E P (polyfluoroe t h y l e n e propylene, 12.7 u m [ 22 ]

1.4 × 10-'5

depending

10-,2

E p o x y resin, 3 ram, Araldite D*

on w a t e r content

/,t+ > p_

10 -'°

U- > > > > > > u+

u+ > > > u_ ~÷ > > > u -

Preference polarity

A1203 (sintered) 8 ram*

[6]*

Pyrex, 1--10 ram,

1 0 - " - - 1 0 - '°

10-'3--10 -'2

P M M A , 1 mm,

[6]*

10-'5

I0-'8--I0-'~

PTFE, 1 m m ,

0.1ram [6]*

Mobility u (m2/V.s)

Material thickness (references)

Charge dissipation in air

Charge dissipation with p o l y m e r s and cr ys t als

TABLE 1

107

10 ~

10 7

107

3 × 106

• 106

5 × 10 ~'

5 X 106

5 X 10 ~

5 × 10 6

(V/m)

Initial field s t r e n g t h

25

25

25

25

21

21

21

21

21 21

(°c)

Temp. R.H..

<10

<10

<15

55

55

55 --

(%)

var.

1.0

<0.007 <0.007

Water content** ( w e i g h t ) (%)

o n l y negative charged accu r acy 30%

positive charge, n o t reproducible

h e a t e d to glowing p o i n t at ap p r o x . 1000°C

storage for m o n t h s u n d e r room conditions initial charge d e n s i t y : ± 300 p C / r a m 2

initial charge d e n s i t y : -+ 160 p C / r a m 2

Comment

O

10 -'s

10 - ' '

10-"

10- ' '

54~m [23]

PE, [ 5 ] , [ 3 ] , [ 4 ]

P V K (poly, N-vinyl carbazole), 20 ~ m [17]

NaCI (single crystal)*

CaF, (single crystal)*

*present w o r k **[51]

I 0 -'s

1.5 ~ + = 3.3 u_ = 3.3

~÷

~+

=/~_

10 -'s

10 - ' s

1 O - 's

1.4

#_ =

~+ =

Polystyrene

(stun, o n ) ,

Preference polarity

Mobility u (m2lV.s)

(continued)

Material thickness (references)

TABLE 1

corona

<15 <15

21

3 x 10 6

68

24

(%)

R.H.

21

(°C)

Temp.

2 × I0 ~

10 7

photoconductive layer corona

>3 x I0 ~

10 ~

10'

Initial field s t r e n g t h (V/m)

corona

corona

corona

Charging method

m

Water content** (weight) (%)

hole injection

polarity effect d e p e n d i n g o n a m b i e n t gas, density, a n d agent-doping

Comment

b~ O~

162

high in comparison to polymers [16]. Higher mobility than 10 -~1 m2/V.s is found only with Pyrex which has a high ionic conductivity, and with sintered aluminium oxide. The mobility of the crystals equals that of PVK [17]. Here, the holes were injected. It is known that most polymers are more or less crystalline, and from our results, it would seem that mobility of injected holes or electrons decreases with decreasing crystaUinity. However, if a material is more amorphous, there is the possibility of higher ionic mobility. Certainly, in the presence of pure water and water contaminated with salts, conduction can increase considerably [18]. Although it is rarely reported, even a polymer like PE acquires some water [14] and a strong influence of humid air on electrical conduction in PE is shown [19]. While crystals show no polarity effect, most polymers do. PTFE, FEP, PS and sintered aluminium oxide show relatively low decay rates for negative charges, while PMMA and Pyrex show a low decay rate for positive charges. This is associated with a low water content with PTFE and FEP and a relatively high water content with PMMA. In experiment, PE showed a higher decay rate for negative charges at room temperature [4]. This may be explained b y the results of another experiment which showed that while coronacharging, negative charge penetrated into the bulk b u t positive charge rested at the surface [20]. Until now, the nature of the injected charges has not been completely clear and has only been discussed in any depth in ref. 21. 4. Charge generation in air 4.1 Introduction When two solids make contact, charge is transferred from the one to the other. This basic p h e n o m e n o n has given rise to many electrostatic problems in industry and found various applications. Now, it has become the subject of many investigations. Contact electrification between metals is well understood [24]. With contact electrification at metal--dielectric interfaces, the situation is much more complex. Many contact situations under ideal, welldefined circumstances (vacuum) could be explained by extrapolating Fermi level theory to this type of contact [2,25]; however, some recent investigations showed more complex results [26,27] and more parameters were taken into consideration [28]. The influence of the presence of air on electrical conduction [19], charge storage [29], and also on contact electrification has been shown [30,31]. From a mechanical viewpoint, there are three types of contact. First of all the pure, steady contact, with or without force acting on it. Secondly, the sliding contact and last the rolling contact.Until now, it has n o t been clear whether t h e y differ essentially or in only minor points [32,33].

163

4.2 Experimental* A schematic view of the experimental set-up is given in Fig. 10 and this is a modification o f apparatus described earlier [34]. The metal part in the contact consists of a wire suspended between a support and a pulley. A tension G in the wire is created b y a weight. The wires, 0.3 mm in diameter, were prepared b y cleaning with alcohol only. The shape of the polymer samples at

L_

l

earthed grid ['~

,

•

•

!o

i~ :tire ellmln; ~tor

.

.

.

.

.

.

.

.

/

! I

1

i ,' I t,

.

Fig. 10. Experimental set-up for sliding electrification measurement.

*Carried out, during a two months' stay, at the Laboratoire d'Electrostatique, CNRS, Grenoble, France.

164 the contact side was a half cylinder, 4 mm in diameter. The rub was made over 2.5 cm, t y p e 45~--45 ° (in Fig. 1 0 : 7 = 45°). If d < < l, it can be derived that the charge density o is related to the electrometer voltage Ve by: Cl o =- Ve 2LDd

(9)

where D is the polymer sample diameter, d the wire bending depth, I the wire length between support and pulley, L the track length and C the capacitance of the electrometer system. With D = 4 mm, d = 2 mm, l = 105 mm, L = 25 mm and C = 96 pF, it can be derived that a 1 V electrometer reading corresponds to 25.2 p C / m m ~ (1 pC/ram 2 equals 1 uCm-2). The force F acting on the contact is given by: F =

4d l

V

(10)

With masses of 7.5 g to 100 g, the range of F is 0.0056 N--0.075 N on an effective contact area of 0.046 mm 2. Hence, maximum contact pressure is a b o u t 1.5 N / m m 2 (1 N / m m 2 equals 106 Nm-2).

4.3 E x p e r i m e n t a l results

All dielectrics used (PTFE, PE, PMMA, bakelized paper and an e p o x y resin (Araldite}) were rubbed a minimum of 50 times against a metal at a certain contact force. The average voltage determined is plotted in Fig. 11 for PTFE, PE and PMMA. For these dielectrics, the voltage generated after each rub was independent of time and velocity (1.9--3.5 cm/s). The voltage generated after each rub increased significantly with bakelized paper and Araldite. This may be explained b y the charge-elimination m e t h o d used. A radioactive device ionizes the air surrounding the sample. Ions, with a sign opposite to the surface charge, then drift towards the surface charge. These ions neutralize the surface charge and, generally, charge exchange between ions and surface charge will occur [35]. If this charge exchange does not occuri which may be the case with Araldite and bakelized paper (a surface retention effect, among others, was supposed to explain the corona charge decay), these trapped ions may give rise to further growth of generated charge, when rubbing is continued [36,37]. The sign and level of the charge generated are given in Table 2 (average values for PTFE, PE, PMMA; for bakelized paper and Araldite the value given is that after the first rub of a virgin sample). Sign and level are in agreement with the well-known triboelectric series [34, p. 1 6 2 ] , [38] and another experimental result [39l. When the molar fraction of MMA increased from 0 to 1 in a copolymer with Styrene, sign reversal occurred from negative to positive in sliding electrification [40]. Positive charging may be established

165

~l°('

'°I

/ .....

xperspex o polyethylene +'°'+

.

.

.

.

.

I p°wer °~ [-

.

O2

Ir

0

I ]

I

'1

'V (vott) -5

I

-4

I I I

PTFE

I

100 g -2

I

0,~--.-_.~ -d'V(vott )

-5 -4

309 7.5 g

~

,.

'1

I

I

I I I I

I I

I

PE

I

lOOg

-2q

30 9 7.5 9 I

V (volt)

I

I

I

I

PMMA 100 g

+4

~

Ii

.!

'30g 7.59

0

I

n

At Cu Au Pt Fig. 11. P o w e r ~ a n d g e n e r a t e d voltages as a f u n c t i o n o f t h e m e t a l used.

166

by the removal of an electron from a double bond [41]. This is situated in PMMA as follows: H I --C

0 = COCH3 I -C--

H

CH3

An earlier laborious study pointed out that in metal--insulator contact, polymers with high water content charged positive, while those with low water c o n t e n t charged negative [42]. The relation between generated charge Q and contact force F is well expressed by (see Fig. 12) Q~F a

(11)

The power a is plotted in Fig. 11 as a function of the metal used. It is seen that it is determined in the main by the metal and to a lesser extent by the polymer. Theoretical consideration limits a to the range 1/3--1. For a = 1/3, there is complete elastic deformation and for a = 1, the number of asperities making contact increases proportionally to force [34]. The determined forcedependence demonstrates a well-established contact between metal and insulator. Friction, in itself, seems to have no or only little influence on charge transfer. While the coefficient of friction for PMMA and PE is 0.4--0.5 and 0.6--0.8, respectively, and for PTFE is 0.05--0.1 [43], the charge levels for all polymers are of the same order.

-10

1 •"I'V (volt)

PTFE -Au J

-1 /

m a s s (9_) ,, I

1 Fig. 12. Generated voltage

10 versus mass

100 with Teflon gold contact.

*Present work.

NaCI (single crystal [48] AI203 (single crystal) [48]

Copolymer M M A / St, [40], molar fraction M M A : 0 MMA: 1

Bakelized paper* Epoxy Resin*

radioactive radioactive

sliding

--19

radioactive radioactive radioactive radioactive radioactive

Elimination

sliding

sliding

sliding sliding sliding sliding sliding

Type contact

+19

+

--73 +124 --43 +10 +26

PTFE* PMMA*

PE*

Charge density (pC/mm 2)

Material, Reference

Charge generation in air

Charge generation with polymers and crystals

TABLE 2

2--3 2--3

1.5 1.5

22

21

21 21 21 21 21

2--3 2--3 2--3 2--3 2--3

1.5 1.5 1.5 1.5 1.5

30 30 30 30 30

Velocity R.H. Temp. (cm/s) (%) (°C)

Force (N/mm ~)

rubbing against tantalum wire

rubbing against gold wire

Comment

O~

168 From Fig. 11 it is seen that generated charge is not sharply dependent on the metal used. Gold (Au) and platinum (Pt) generally generate the same amount. Copper (Cu) and aluminium (A1) yield a lower amount possibly because of lower work functions (oxide layers present). 5. Related charge decay and charge generation Comparing Table 1 and Table 2, one finds that polarity effects and charge generated are related in the following way. If the charge generated is positive, then the decay for the positively charged dielectric is slower, while in the case of negatively generated charge, the decay of negative charge is slower. The higher the charge generated, the stronger the polarity effect. In the tables, the effects are strongest with PTFE and PMMA. The effect may be explained by an effective charge trapping which is selective for carrier sign. This explanation may be of relevance to the recent discussions on charge generation and whether bulk traps are involved with it [44,45,46,47]. 6. Conclusions (1) From the charge decay technique as well as from a photoconductivity technique, a mobility of 10 -11 m2/(V.s) is determined for alkali metal salt crystals. Using crystals, the first step may be to relate results of several measuring techniques. (2) Charge injected can be conserved to a great extent and kept moving by turning over the samples. This may lead to more insight in momental charge distribution in the bulk. (3) Crystals without impurities yield the same mobility when their structures are similar. (4) Evident polarity effects in the decay characteristics of polymers are related in the following way to the charge acquired upon rubbing: when a sample takes on a positive charge upon rubbing, surface charge decay will be slower for the positive charge, while negatively generated charge will show a relatively slower decay for negative charge. (5) The polymers used here obey the rule that, in air, positive charging upon rubbing is associated with high water content, while negative charging is generally found with dielectrics having a low water content. Acknowledgements The author wishes to thank Professor Dr. D.Th.J. ter Horst, Dr. L.M.L.F. Hosselet and all members of the EHO group. He is grateful also to Professor N.J. Felici for allowing him to work in his laboratory and to Dr. R.F. Challande for his kind advice during that period. He would also like to thank the British Council for the opportunity to participate in the "Younger Research Workers Interchange Scheme 1975" and all those who received him so kindly in Britain.

169

References 1 H.J. Wintle, Decay of surface electric charge in insulators, Jpn. J. Appl. Phys., 10 (1971) 659. 2 D.K. Davies, The generation and dissipation of static charge on dielectrics in a vacuum, Static Electrification Conf., London, May 1967, Inst. Phys. and Phys. Soc. Conf. Ser. No. 4, p. 29. 3 M. Ieda, G. Sawa and U. Shinchara, Decay of electric charges on polymeric films, Electr. Eng. in Jpn, 88 (1968) 67. 4 M. Ieda, R. Takeuchi and G. Sawa, Effects of temperature, 7-ray irradiation and crystallinity on decay process of surface electric charges across polyethylene film, Jpn. J. Appl. Phys., 9 (1970) 727. 5 M. Ieda, G. Sawa and R. Takeuchi, Decay processes of different kinds of surface electric charges across polyethylene film, Jpn. J. Appl. Phys., 8 (1969) 809. 6 H.T.M. Haenen, The characteristic decay with time of surface charges on dielectrics, J. Electrostatics, 1 (1975) 173. 7 A. yon Hippel, Electronic conduction in insulating crystals under very high field strength, Phys. Rev., 54 (1938) 1096. 8 I.P. Batra, K.K. Kanazawa, B.H. Schehtman and H. Seki, Charge carrier dynamics following pulsed photoinjection, J. Appl. Phys., 42 (1971) 1124. 9 F.H. Chapple, G. Lehmann and A.B. Scott, Photoconductivity in colored potassium chloride, Phys. Rev., 174 (1968) 1012. 10 H.J. Wintle, Decay of Static Electrification by conduction processes in polyethylene, J. Appl. Phys., 41 (1970) 4004. 11 H.J. Wintle, Surface charge decay in insulators with nonconstant mobility and with deep trapping, J. Appl. Phys., 43 (1972) 2927. 12 R. Dobrozemsky and E. Haltau, Electrical surface charges on metals, Ned. Tijdschr. Vacuumtech., 8 (1970) 133. 13 J. Booij, P.H. Ong, J. van Turnhout and G.H. Douma, A study of the electrostatic powder coating process b y charge and current measurements, Static Electrification Conf., London, May 1975, Inst. Phys. and Phys. Soc. Conf. Ser. No. 27, p. 188--201. 14 W. Kienast and W. Burkhardt, Die mathematische Behandlung der Feuchtedurchdringung yon Plastwerkstoffen, Wiss. Z. Tech. Hochsch. Ilmenau, 99 (1974) 87. 15 R. Lovell, Decaying and steady currents in an e p o x y polymer at high electric fields, J. Phys. D., 7 (1974) 1518. 16 V. Adamec and J.H. Calderwood, Electrical conduction in dielectrics at high fields, J. Phys. D., 8 (1975) 551. 17 J. Mort, Transient space charge perturbed current in films of poly (N-vinyl) carbazole, 1971 Annual Report, Conf. on Electr. Insulation and Dielectric Phenomena, N.A.S. 1972, p. 17--23. 18 T. Kawamura and K. Isaka, Humidity dependence of moisture absorption, leakage current and fiashover voltage on contaminated insulator surfaces, Electr. Eng. in Jpn., 93 (1973) 62. 19 K. Yahagi and K. Shinohara, Electrical conductivity of polyethylene in vacuum and air at room temperature, Electr. Eng. in Jpn., 90 (1970) 191. 20 T. Takada, T. Saki and Y. Toriyama, Evaluation of electric charge distribution in polymeric films, Electr. Eng. in Jpn., 92 (1972) 28. 21 A. Reiser, N.W.B. Lock and J. Knight, Migration and trapping of extrinsic charge carriers in polymer films, Trans. Faraday Soc., 65 (1969) 2168. 22 G.M. Sessler and J.E. West, Charge decay characteristics of polymer foils, 1970 Annual Report, Conf. on Electr. Insulation and Dielectric Phenomena, N.A.S., 1971, p. 8--15. 23 R.E. Mc. Curry and R.M. Schaffert, Space charge limited currents in resin films, IBM J. Res, Dev., 4 (1960) 359.

170

24 J. Lowell, Contact electrification of metals, J. Phys. D., 8 (1975) 53. 25 D.K. Davies, Charge generation on dielectric surfaces, J. Phys. D., 2 (1969) 1533. 26 R.G. Cunningham and H.P. Hood, The relation between contact charging and surface potential differences, J. Colloid Interface Sci., 32 (1970) 373. 27 B.C. O'Neill and T.R. Foord, Contact and tribo charging of polymer surfaces, Static Electrification Conf., London, May 1975, Inst. Phys. and Phys. Soc. Conf. Ser. No. 27, p. 104--114. 28 R.G. Cunningham, Electrification of insulating belts passing over grounded rollers, J. Colloid Interface Sci., 32 (1970) 401. 29 B. Gross, G.M. Sessler and J.E. West, Radiation hardening and pressure-actuated charge release of electron-irradiated Teflon electrets, Appl. Phys. Lett., 24 (1974) 351. 30 D.E. Debeau, The effect of adsorbed gases on contact electrification, Phys. Rev., 66 (1944) 9. 31 D.A. Hays and D.K. Donals, Effect of an electric field on the contact electrification of polymer by mercury, 1971 Annual Report, Conf. on Electr. Insulation and Dielectric Phenomena, N.A.S., 1972, p. 74. 32 W.R. Harper, How do solid surfaces become charged?, Static Electrification Conf., London, May 1967, Inst. Phys. and Phys. Soc., Conf. Ser. No. 4, p. 3. 33 A. W~/hlin and G. B/ickstrSm, Sliding electrification of teflon by metals, J. Appl. Phys., 45 (1974) 2058. 34 D.J. Montgomery, Static electrification of solids, Adv. Solid State Phys., 9 (1959) 139. 35 D.W. Vance, The surface charging of insulators by ion irradiation, 1970 Annual Report, Conf. on Electr. Insulation and Dielectric Phenomena, N.A.S., 1971, p. 1--7. 36 H. Bauser, Static electrification of organic solids, Elektrostatische Aufladung, 2nd International Conf. on Static Electricity, Frankfurt, April 1973, DECHEMAMonogr. Vol. 72, No. 1370--1409, p. 11 37 E.S, Robins, A.C. Rose-Innes and J. Lowell, Are adsorbed ions involved in the contact charging of insulators by metals, Static Electrification Conf., London, May 1975, Inst. Phys. and Phys. Soc. Conf. Set. No. 27, p. 115--121. 38 J. Henniker, Triboelectricity in polymers, Nature, 196 (1962) 474. 39 R.A. Coffee, Electrostatic charging of insulators after contact with metals, Jpn. J. Appl. Phys., 11 (1972) 1391. 40 N. Murasaki, N. Kono, M. Matsui and H. Mada, The generation and decay of charge produced by frictional rubbing of polymers, Static Electrification Conf., London, May 1971, Inst. Phys. and Phys. Soc. Conf. Ser. No. 11, p. 44. 41 E. Zimmer, Die elektrostatische Aufladung yon Hochpolymeren Isolierstoffen, Kunststoffe, 60 (1970) 465. 42 W. Schumann, Untersuchungen zur elektrostatischen Aufladung fester KSrper, Piaste Kautsch., 10 (1963) 526, 590, 654. 43 F.P. Bowden and D. Tabor, Friction and Lubrication, Methuen, London, 1960, pp. 37, 66. 44 C.G. Garton, Charge transfer from metal to dielectric by contact potential, J. Phys. D., 7 (1974) 1814. 45 A. Chowdry and C.R. Westgate, The role of bulk traps in metal-insulator contact charging, J. Phys. D., 7 (1974) 713. 46 H.J. Wintle, Contact charging of polymers, J. Phys. D., 7 (1974) L128. 47 A. Chowdry and C.R. Westgate, Comments on "Contact charging of polymers", J. Phys. D., 7 (1974) L149. 48 R.F. Challande, Studies on the nature of charges acquired by crystals upon rubbing with metals, Static Electrification Conf., London, May 1967, Inst. Phys. and Phys. Soc., Conf. Set. No. 4, p. 18. 49 W.G. Lawson, High field conduction in impregnated paper dielectric, IEE Conf. Publ., No. 67, 1970, p. 202.

171 50 D.K. Davies, Carrier transport in polythene, J. Phys. D., 5 (1972) 162. 51 J. Crank and G.S. Park, Diffusion in polymers, Academic Press, London/New York, 1968, Chap. 8, p. 259.

Appendix The d.c. conductivity o f b a k e l i z e d paper In this experiment, one side of a sample was covered with a silver painted electrode, the other supported b y a copper electrode with a guard ring. By connecting b o t h electrodes to a variable d.c. source, an electric field E and a current density J were created. Figure 13 represents a series of observed values in a logarithmic-linear scale. Maximum variation between t w o series was 20% while the curves were of similar shape. Variation in time was a b o u t 5% over 5 minutes. Generally, bakelized paper consists of sheets of paper which are pressed together with a binding agent. This was confirmed b y SEM (Scanning Electron Microscope) photographs. Figure 14 shows a picture of bulk material, prepared by breaking a little sample. It shows layers, lying parallel to the surface. Photographs showed also that the surface itself was quite smooth. For this structure a hopping model like the one used earlier for oil-filled paper insulation is proposed [ 49]. Cellulose layers form potential barriers for the charge carriers. To by-pass a potential barrier of width d, the carrier has to travel a distance c in the binding agent, an " o h m i c " medium with specific conductivity 1 / p . When the condition c > > d is valid, the following relationship can be derived for the current density J: J = A'exp(-(p/kT)sinh(ec(E

-- pJ)/2kT}

(12)

where A' is a constant and e x p ( - - O / k T ) the Boltzmann factor. By substituting and B = e c / 2 k T , eqn. (12) is simplified to

A = A'exp(--O/kT)

J = A sinhB(E -- p J)

(13)

Expressing explicitly the field strength from eqn. (13) one obtains 1

E = p J + - - l n [ J / A + ~ / ( ( J / A ) 2 + 1)] B

(14)

To determine A, B and p at least three observed values, (E,, J,), (E2, J2) and (E3, J3) are needed. Next, t w o expressions can be made for p using eqn. (14). p, is expressed explicitly with (E,, J,), (E2, J2), and P2 with (E2, J2), (E3, J3). Choosing A as the independent variable, we seek the intersection of the functions p l = f , ( A ) a n d P2 = f2(A). After carrying o u t this procedure on a c o m p u t e r the constants are calculated to b e : p , = p 2 = p = 3 . 5 × 1 0 s ~ 2 . m , A = 3 . 6 × 1 0 -TA/m 2 , B = 2 . 8 × 1 0 -s m/V. The distance between the potential barriers is now calculated from

172

I~ 2

- J(A/m !

]

-

l°-3

i

1

o observed vatues

/ i+

--theory 10-~

,

i~s 0

J

H,V s,lvlrp;Hnted electr~dt'

I

,

I0

Fig. 13. Current density

20 versus

i

E (kVlcm)

-,

30

field strength plot for bakelized paper.

Fig. 14. SEM photograph of bakelized paper (bulk), preparation breaking and coating with carbon-gold, enlargement 110 times.

173 ~.idS

i

I(A)

3.~6s

/

2j6 s

u5 s

/

/

/ 20cm

H.V, ' ' '25cm ' . ' ~

v(~'- !

*r-~~ -T-

E (kV/cm)

0

0.5

1

1.5

Fig. 15. Current v e r s u s field strength for bakelized paper, parallel electrodes (silver painted) on surface.

= 1.5/~m. This distance is of the same order as the distance between impurity centres in semiconductors and has been found for some polymers [50]. Measuring the conductivity along the surface, it was found that the conduction current is proportional to field strength at low values (Fig. 15). Thus, the conduction current is mainly flowing through the ohmic medium, as the cellulose layers are lying parallel to each other and to the surface.

B: C = 2kT/e