Pram~.na- J. Phys., Vol. 34, No. 6, June 1990, pp. 565-573. © Printed in India.

A study of absorption characteristics in polyimide and polyimide fluorocarbon-2 polymer film

M M HOSSAIN Department of Applied Physics and Electronics, Rajshahi University, Rajshahi, Bangladesh. Present address: Department of Physics, College of Science, University of Salahuddin, Arbil, Iraq

MS received 14 August 1989; revised 18 January 1990

Abstract. The absorption characteristics of polyimide (PM) and p61yimide fluorocarbon (PMF-2) polymer film were studied at temperatures ranging from 20 to 230°C. The glass transition or critical temperature of PMF-2 was found at 160°C. Conduction of PMF-2 was observed due to the upper fluorocarbon layer below the transition temperature while the middle PM layer is important above this temperature. The time-dependent absorption/ resorption current does not satisfy the traditional Cude-Von Schweidler law. The experi- mental results of the absorption characteristics are analysed using a simple R-C circuit.

Keywords. Absorption/resorption current; residual/discharge voltage; Curie-Von Schweidler low; conduction; R-C circuit.

PACS No. 72-20

1. Introduction

Synthetic polymers are extensively used as electrical insulators because of their good electrical and mechanical properties. They have wide applications ranging from power apparatus and cables to microelectronics. Among the possible synthetic polymers, polyimide and polyimide fluorocarbon (abbreviated hereafter as PM and PMF-2 respectively) seems quite promising.

The present paper reports the comparative study of the absorption characteristics of both these films at different temperatures. Sample films have been used for measuring the absorption/resorption currents and the residual/discharge voltages.

The applications of step voltage to dielectric causes a flow of current which decays with time before reaching a steady-state value. The time-dependent part of the current (absorption current) is due to dielectric polarization under the applied electric field. The polarization of polymeric dielectrics may be due to dipolar orientation, accumulation of charge carriers near the electrodes or trapping in the bulk (Van der Schueren and Linkens 1976; Nakumara etal 1976). Under certain conditions, additional charge carriers may be provided by injection from the electrodes, which also contribute to space charge polarization (Wintle 1977). A systematic study of the absorption currents can reveal the carrier injection, trapping and polarization processes which may be present in a dielectric. An understanding of the absorption currents is therefore necessary to discover the true conductivity of the material.

The resorption current usually decays with time in the direction opposite to the absorption current. This has been explained as the result of dipolar depolarization

565

566 M M Hossain

or redistribution of charge carriers due to interracial polarization or space charge polarization (Das Gupta et al 1980).

Considerable high voltage sometimes appears on the inner-conductor of a power transmission cable and condenser after opening a circuit which was previously electrically stressed and short-circuited for a short time. This voltage gives an electric shock when touched and is termed the residual voltage. Recently, measurement of the residual voltage was proposed as a method for detecting degradation of the cable insulation (Kalsumi et al 1982).

In the present study the absorption/resorption currents and lhe residual/discharge voltages at different temperatures were measured in PM and PMF-2 and the results analysed using simple R-C circuits.

2. Experimental

Commercial-grade polyimide (Yslovia 1972) and polyimide fluorocarbon film [(10/~m fluorocarbon- 30/~m polyimide- 10/~m fluorocarbon sandwich film commercially known as PMF-2 (Yslovia 1983)-I of thickness 40/~m and 50/~m respectively were used. Aftar washing with alcohol, aluminium electrodes of 28 mm diameter were deposited on both surfaces of the films by vacuum evaporation. The sample was then mounted in a measuring cell and the absorption/resorption currents and the residual/discharge voltages at different temperatures were measured using a BK2-16 electrometer (USSR), an x-y recorder provided with a time base, and a stabilized d.c. power supply.

The absorption/resorption currents were measured according to standard proce- dures, of applying a step voltage, measuring the absorption current decay for some polarization time tp, short circuiting the sample and measuring the resorption current.

The measurement procedure of residual voltage was as follows. A voltage Vp was applied to a sample for a time tp and the circuit shorted for a time ts. After the circuit was opened, a voltage VR appeared on an electrode after t. Also for measuring discharge voltage, Vp was applied to a sample for tp, the circuit opened and the discharge voltage Vd recorded.

3. Results and discussion

Variation of the absorption and resorption current with time for PM and PMF-2 is shown in figures 1 and 2 respectively at various temperatures. No time-dependent part of the currents was soon above 180°C for PM (figure 1) while the PMF-2 film showed time-dependent currents at higher temperatures (figure 2). Figure 2 shows that absorption and resorption current for PMF-2 above and below 160°C is sharply divided into two characters and so this temperature of 160°C may be the glass transition or critical temperature for PMF-2.

Atkinson and Fleming (1980) showed that absorption currents in non-polar materials were largely due to currents flowing on fhe surface of the polymer from the edges of the electrode. We may therefore conclude that the time-dependent parts of the currents for PMF-2 up to 120°C is due only to the outside fluorocarbon layers of the film.

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568 M M Hossain

Above 160°C, the upper thin fluorocarbon layer (10 gm) strates to soft and becomes non-continuous, while the time-dependent parts of the currents may arise due to the contribution of the middle polyimide layer. As is evident from figures 1 and 2, at high temperatures (above 160°C) the time-dependent current of PMF-2 film is similar to the low temperature (below 160°C) time-dependent current of PM film i.e the actual temperature of the middle layer polyimide of PMF-2 may be much smaller than the upper fluorocarbon layer. In practice, the upper fluorocarbon layer is used as a heat-resistive layer of PMF-2 film.

Variation of the residual voltage with time for PM and PMF-2 films at various temperatures is shown in figures 3 and 4. The residual voltage increases with increase of temperature. The origin of residual voltage can then be explained qualitatively from experimental results as follows. Under a constant voltage and rise of temperature, the carriers pre-existing in the film or injected from the electrode, migrate within the film and establish a space charge distribution. During short-circuiting, the charge redistributes in the sample and some of the changes will be swept out of the electrode. After the circuit is opened, charge distribution is rearranged by migration of carriers in the film because of the space charge field, resulting in the appearance of residual voltage which is due to charge imbalance on the electrode and the sample.

Figures 3 and 4 show that the residual voltage increases sharply with increase of temperature but above 160°C, the PMF-2 film (figure 4) does not follow the same nature as seen in PM film (figure 3). The residual voltage for PMF-2 film takes about 1/4th time less than the simple PM film. The residual voltage for PMF-2 film at 180°C does not fall to zero at the time of measurement which agrees with the time-dependent residual voltage characteristics of PM film.

The above results indicate that there are two charge storage mechanisms in the PMF-2 film which is also seen in figure 2 in the case of time-dependent current.

VR~VolTs ~ 180" C

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), calculated

Absorption characteristics in P M and PMF-2 polymer film

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180"C

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Time Time-dependent residual voltage for PMF-2 film. Details same as in figure 3.

Variation of discharge voltage with time for PM and PMF-2 films at different temperatures is shown in figures 5 and 6 respectively. The magnitude of the discharge voltages decreases with increasing temperature. It is also clear from the figures that the process of depolarization in the PMF-2 film is slower than the simple PM film.

It is seen from figures 1 and 2 that the logarithmic plots of absorption and resorption currents are not linear, i.e. the observed time dependence of the current transients does not satisfy the Curie-Von Schweidler law (Van der Schueren and Linkens 1976);

l(t) = A(T)t-", (1)

where I is the absorption/resorption current, t the time and A(T) the temperature- dependent factor.

The analysis of the absorption/resorption current curves (figures I, 2) shows that it is the time-dependent summation of exponents, i.e

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where Ti is the relaxation time for currents. The analysis of the time-dependent curves i.e. log Vo =f(t) and log VR =f(t) for PM and PMF-2 films also shows time-dependent summation of exponents, i.e.

VD,R = ~ Vo~ 'R exp ( - t/O,), (3) i=1

where 0i is the relaxation time for voltage. Since the absorption/resorption currents and the residual/discharge voltages are

time-dependent summation of exponents, we may conclude that the PM and PMF-2

570 M M Hossain

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films consist of some layers (Hossain 1988). We can therefore consider an R-C circuit to represent each layer as shown in figure 7.

The expressions for charge storage and relaxation process of this circuit (figure 7) can be written as follows;

l(t) = Ci dEi(t)/dt + Ei(t)/Ri,

qi(t) = Ci + l Ei + 1(0 - CiEi(t),

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(5)

(6)

Absorption characteristics in P M and PMF-2 polymer film 571

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During the process of charging V = Vcharg ¢ and V = 0 we have to consider the former for the discharging voltage and the latter for the residual voltage. During charging, qO = V. C z and at the end of charging i.e. when the process is saturated,

where q~= Vzi/Rz, I~= V/Rz,

Rz= ~ Ri and Cz= ~ (l/C,) -1 i = 1 i = 1

It was observed that the absorption/resorption current curve i.e. logla, R =f(t) at 160°C consists of two exponents for the PM and three exponents for the PMF-2 film; on the other hand the discharge/residual voltage curve log Vo.e =f(t) at that temperature is of three and four exponents for the respective film. These results indicate that the PM film consists of three layers and the PMF-2 film consists of four layers.

After solving equations (4), (5) and (6) and considering the initial and final conditions of charge storage, the following expressions can be obtained for variations of discharge/residual voltage and absorption/resorption current with time for the three-layer PM film

Here

VD(t ) = V/Rr[R 1 cxp( - t/O1) + R 2 exp ( - t / 02 ) + R3exp(- t /Oa)] , (7)

VR(t) = V/Rz[R,(1-0203~exp(-t /O1)ztr2 /

+ R 3 ( 1 0t02"~ - t l r2 ) exp(-t/O3)], (8)

la = - le = V/Rz [ (T1 - 0t)(--~t-(z2 ------Zl)T 202)(--Zt -- 03) exp (--t/zt)

(T2 -- 01)(T2 -- 02)(~z -- 03) exp(--t/~2) ] + J

+ I~. (9)

+ R2(1-0103~exp(-t/O2)zlz2 ]

I , = V/R z, 0 I = R1C 1, 0 2=R2C 2, 0 3=R3C 3

572 M M Hossain

Table 1. Values of E~, 0~, R~ and C~ for different circuits.

i Ei (Volts) 0i (s) gi (ohm) Ci (10- t l F) zi (s)

1 1,0 9090 1'2 x 1011 7985 5880 2 10,9 1820 10"2 x 10 n 174 330 3 22"2 1110 20'9 x 1011 52

and

where

Y_.R,(Oj + Ok) ( Ri(Oa_ +___Ok) 2 ERiOjOk'~I/2 ~t,2 = 2gz + \ 2gz ~ x J (10)

i4:j~k.

From the exponents of the curve log Yo =f(t), we can find out the conductivity 7~ of each layer as follows;

~ = eoe/0~, (11)

where e is the dielectric constant of the sample. If the charging process is saturated, i.e. (EI71 = E2"~2.. .E.rn), then the thickness of

the layers may be obtained as follows.

hffhi+l = EiyffE~+Ni+I; h= ~ h~, (12) k-'- I

where h is the thickness of the whole polymer film and Ei the potential across the ith layer shown in figure 7 as a potential across the ith condensor.

From the exponent of the curve log Vo =f(t) and also from equations (11) and (12) one can easily evaluate the values of E i, Oi, Ri and Ci (see table 1). The above values were used for computing the variation of absorption/resorption current and the residual/discharge voltage with time. It is clear from figures 1, 3 and 5 that the calculated and experimental results are quite compatible.

If the total exponents of the discharge voltage curve are unchanged over a wide range of temperatures, then the high temperature parameters can be used to calculate the absorption characteristics at different temperatures for accelerating the process of measurements.

4. Conclusion

It is clear that charge storage mechanism in PMF-2 film above and below 160°C is sharply divided into two. The logarithmic plots of absorption and resorption currents do not satisfy the Curie-Von Schweidler law and are the time dependent summation of exponents. The charge storage and relaxation process of the polymer film have been analysed with the help of a parallel R-C circuit. The theoretical and experimental results of the absorption characteristics are quite compatible.

Absorption characteristics in PM and PMF-2 polymer film 573

Acknowledgements

The author is grateful to Professor S N Koikov and Professor M E Baricova of the Leningrad polytechnical Institute, Leningrad, USSR for stimulating discussions.

References

Atkinson P J and Fleming R J 1980 J. Phys. D13 625 Das-Gupta D K, Doughty K and Brocklay R S 1980 J. Phys. DI3 2101 Hossain M M 1988 Indian J. Phys. A62 944 Kalsumi Y, Jun K, Munsoo Y, Ken-lchi N, Yoshio I and Nobuharu K 1982 Jpn. J. Appl. Phys. 21 1333 Nakumara S, Sawa G and Idea M 1976 Jpn. J. Appl. Phys. 18 995 Vander Schueren J and Linkens A 1976 J. Appl. Phys. 49 4195 Yslovia T (TY) 6-05-1491-1972 (U.S.S.R) Yslovia T (TY) 6-19-226-1983 (U.S.S.R) Wintle H J 1977 IEEE Trans. Electr. Insul. El-12 424