STUDIES OF DISCHARGE DELAY TIME IN POLYMERS UNDER NANOSECOND VOLTAGE EXPOSURE

V. S. KOROLEV, N. M. TORBIN

(Presented by the scientific seminar of the Research Institute of High Voltages)

Only a few works have been devoted to experimental studies of the electrical strength of solid dielectrics in the nanosecond voltage range [1, 2, 3].

The study of the electrical properties of organic electrical-insulating materials under short voltage exposures is of interest both for the physics of breakdown and for practical questions concerning the behavior of insulation in constructions of high-voltage nanosecond technology.

In work [1], the electrical strength of certain polymers and mica was investigated in a uniform field at voltage exposures of \(5 \cdot 10^{-9}\)–\(10^{-6}\) sec. The thickness of the specimens was \(0.002\)–\(0.008\) cm. An increase in breakdown voltage was found at an exposure of about \(5 \cdot 10^{-9}\) sec.

In a uniform field, for fluoroplastic, getinax, organic glass, and vinyl plastic, the discharge delay during breakdown on the crest of a rectangular pulse was measured [2]. The pulse length was varied from 3 to 100 nsec. An increase in electrical strength in these dielectrics was observed in the interval from 2 to 20 nsec; the average discharge velocity was about \(3 \cdot 10^{6}\) cm/sec. The specimen thickness in this work was \(0.01\) cm.

Ditmer’s studies [3] in a nonuniform field established that the delay time in organic glass and epoxy resin of thickness \(0.3\) cm is of the order of 20 nsec. Breakdown was likewise produced on the flat portion of a rectangular pulse with a front length of about 10 nsec.

In this work, very high velocities of discharge development were obtained, reaching \(10^{8}\) cm/sec, which have been questioned by some investigators [4].

Dittert [5] investigated the dependence of the electrical strength of ebonite and bakelized paper, of thickness on the order of tenths of a millimeter, in a uniform field. He likewise found no discharge delay down to \(10^{-8}\) sec.

From the cited works it follows that the discharge delay time in high-strength dielectrics is small and amounts to \(3 \cdot 10^{-9}\) sec, while the velocities of discharge development may reach \(10^{8}\) cm/sec. We have carried out studies of discharge delay in a nonuniform field for polystyrene, high-pressure polyethylene, organic glass, fluoroplastic-4, and plasticized polyvinyl chloride, with the aim of establishing the connection between electrical strength and discharge delay time and the physicochemical properties of the indicated polymers. For alkali-halide crys-

a dependence has long been found between their physical constants and the magnitude of the electric strength [6].

For some polymers and hydrocarbon liquids, attempts have been made to establish a relationship between electric strength and the magnitude of intermolecular bonding (cohesion) [7—10]. We have also made an attempt to trace a similar relationship in the region of nanosecond voltage exposures in a nonuniform field for the polymers listed above.

The dielectrics were selected according to the type of intramolecular bonds in the structure.

The work was carried out on a generator of nanosecond voltage pulses constructed at the Tomsk Polytechnic Institute [11].

The voltage pulses were approximately rectangular in shape, with a front of 3 nsec and a flat-top duration of about 30 nsec. The voltage drop over 30 nsec is 7%. An oscillogram of breakdown is shown in Fig. 1.

Fig. 1. Oscillogram of a pulse with breakdown on the flat portion. Frequency of calibration oscillations 100 MHz.

Breakdown of the specimens was carried out in a point—plane field for both polarities of the point. In the work, specimens measuring \(30 \times 30 \times 8\) mm with a conical recess were used, the radius of curvature of which was 60 μm. Graphite powder was pressed into the recess and clamped by the electrode.

The plane, 40 mm in diameter, was made of brass. The thickness of the specimens at the breakdown site was 1.5 mm for polyethylene and polystyrene, and 3 mm for the other dielectrics. The static breakdown voltage of the specimens was determined by breakdown on the front of a pulse with length \(\tau_{\phi} = 6 \cdot 10^{-6}\) sec. The pulses were recorded with an OK-19 oscillograph.

The experimental results are given in Figs. 2a, b in the form of dependences of the average breakdown gradients on the time of voltage application. Each curve was constructed from 4–5 points. For each point, a batch of 35 specimens was broken down; statistical processing was carried out by Laue’s method.

The dashed lines in Fig. 2b indicate the average breakdown gradients for polystyrene and organic glass at a voltage exposure of \(6 \cdot 10^{-6}\) sec.

From the curves presented it is seen that the impulse coefficient in a nonuniform field reaches \(2.2 \div 2.4\) when the exposures decrease from \(6 \cdot 10^{-6}\) to \(3 \cdot 10^{-9}\) sec, which can be explained by discharge delay.

In the breakdown of fluoroplastic-4 and plasticized polyvinyl chloride, the difference in breakdown voltages for different point polarities is weakly expressed over the entire time interval from 30 to 3 nsec, whereas at a voltage exposure of \(6 \cdot 10^{-6}\) sec it amounts to about 20% for both dielectrics.

For polystyrene and organic glass at an exposure of \(6 \cdot 10^{-6}\) sec, the breakdown voltage for a negative point is 30% higher, and for polyethylene 36% higher, than for a positive point. These

Fig. 2a, b. Dependence of the average breakdown field strength on the time of voltage application for polystyrene 1, polyethylene 2, organic glass 3, fluoroplastic-4 (4), and polyvinylidene chloride 5; 6 and 7 are the average breakdown field strengths for polystyrene and organic glass at a voltage exposure of \(6 \cdot 10^{-6}\) sec.
a) with negative polarity of the point,
b) with positive polarity of the point.

data agree with the data of works [3, 7, 8]. During breakdown in the interval of voltage exposure time \(3 \div 30 \cdot 10^{-9}\) sec, for organic glass a considerable decrease in the effect of point polarity is observed, while for polyethylene and polystyrene, on the contrary, there is a considerable increase in the difference in breakdown voltages depending on electrode polarity, as compared with a voltage exposure of \(10^{-6}\) sec (Fig. 2 a, b). In view of the absence of literature data on studies of solid dielectrics in a nonuniform field under the action of nanosecond high-voltage pulses, comparison of our results with other data does not appear possible. It can only be noted that in work [12], for organic glass, an increase in the effect of point polarity with decreasing voltage exposure was noted.

The author puts forward the supposition that, at short voltage exposure times, the positive space charge does not have time to dissipate under the action of the high field strength at the charge boundary; therefore, with decreasing voltage exposure, the influence of the space charge during breakdown of the dielectric should increase. This explanation does not address the question of the influence of the dielectric structure on discharge formation.

Böer [13] showed that the structure of a solid dielectric significantly affects the occurrence and quantitative distribution of space charge in the interelectrode gap. Therefore there is reason to believe that the course of the dependences \(E_{\mathrm{av}} = f(t_{\mathrm{lag}})\) at different point polarities in strong fields is determined not only by the value of the electric field and the time of voltage application, but also by the structure of the dielectric.

When very short voltage pulses are applied, a very high local field strength is created at the point. In this case, the source of free electrons, in addition to ionization by collision, may be a Zener-type tunneling effect, the probability of which increases sharply at a field strength \(E = 10^7\) V/cm.

Under the conditions of our experiments, the maximum field strength at the point, when determined by the formula [15]:

\[ E_{\max} = \frac{2V}{r \cdot \ln\left(1 + \frac{4d}{r}\right)}, \]

where \(V\) is the breakdown voltage,
\(r\) is the radius of curvature of the point,
\(d\) is the specimen thickness,

in the time interval from 30 to 4 nsec in the region of the point was \(1.0 \cdot 10^7 \div 2.2 \cdot 10^7\) V/cm.

At high field strengths and short exposures of the applied voltage, a somewhat different redistribution of space charges at the electrodes is possible, in contrast to the microsecond range of voltage application.

With a negative point, owing to the simultaneous development of numerous avalanches from the cathode, the positive space charge can reach a large magnitude, which will lead to sharp retardation of the developing avalanches. A considerable increase in the voltage at the electrodes will be required for further development of the discharge. In the case of a positive point, there will be observed, on the one hand, some compensation of the positive space charge by the tunneling effect, but, on the other hand, owing to the intensification of impact ionization because of the large number of elect-

the positive charge near the tip will increase.

In addition, the development of a space charge into the depth of the gap may be limited by the short exposure of the voltage. It follows from this that the accumulation of space charge, which plays the decisive role in the formation of the discharge, will depend on the magnitude of the ionization potential of the dielectric molecules.

Table 1 shows that fluoroplast-4 and plasticized polyvinyl chloride (polyvinylidene chloride) [16] are characterized by the highest ionization potential and, consequently, by the smallest value of the space charge.

Table 1

Then the effect of the polarity of the tip during breakdown of fluoroplast-4 and polyvinylidene chloride in the interval \(4 \div 30\) nsec should be weakly expressed, whereas for polyethylene and polystyrene it should have a considerable magnitude.

With a further decrease in the voltage exposure, the influence of the polarity of the tip during breakdown of dielectrics should decrease.

In our studies it was also established that the discharge delay time for positive tip polarity in organic glass and polystyrene is \(24 \div 30 \cdot 10^{-9}\) sec, which is consistent with the data of [3].

The small values of the delay time and the large overvoltages make it possible to neglect the static delay time and to regard the discharge delay as the formation time. Then the average discharge velocity is determined as

\[ V_{\mathrm{cp}}=\frac{d}{t_{\mathrm{del}}}, \]

where \(d\) is the thickness of the dielectric,
\(t_{\mathrm{del}}\) is the discharge delay time.

For organic glass, at \(E_{\mathrm{cp}} = 16\) mV/cm and a formation time of \(4 \cdot 10^{-9}\) sec, \(V_{\mathrm{cp}} = 7 \cdot 10^{7}\) cm/sec, which confirms the data of [3]. This value of the discharge-development velocity exceeds by an order of magnitude the velocity of discharge propagation in this dielectric in a uniform field [2] and corresponds to the velocity of discharge in air.

Evidently, in a very strong field, electrons, possessing very high velocities, experience less braking in collisions with atoms of the solid substance.

From the results of the work the following conclusions can be drawn:

1. During breakdown of solid dielectrics in the nanosecond range of voltage exposures, the structure of the dielectric has a large influence on the development of space charge.

1. The discharge delay time in organic glass and polystyrene in a nonuniform field is \(2.4 \div 3 \cdot 10^{-8}\) sec.

2. The average rate of discharge development in polymers in the voltage-exposure interval \(4 \div 30 \cdot 10^{-9}\) sec is \(10^7 \div 7 \cdot 10^7\) cm/sec.

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