I
HAROLD BASSECHES and MARY W. BARNES Bell Telephone Laboratories, Inc., Murray Hill, N. J.
Gassing of Liquid Dielectrics under Electrical Stress Influence of Voltage
and
Pressure
Gassing has an important influence on the life of a capacitor and its elimination would materially reduce the degradation and possibility of failure of a capacitor T
IN A previous study (3) the processes involved in the evolution of gas from a U.S.P. mineral oil under alternating current electrical stress were investigated. O n the basis of a study of decomposition products and the effect of various additives on gassing, free radical mechanisms were proposed for the decomposition processes and the inhibiting effect of additives such as quinones, nitroaromatics, and sulfur. Throughout the previous study (3) the alternating current voltage was maintained constant at 10 kv. (130 kv. per cm.). I n the hope of characterizing the gassing process more quantitatively, some parameters in the present study were varied. The voltage stress was varied from 40 to 150 kv. per cm. The effect of external pressure was studied
from 0.01 to 100 mm. of mercury. Previous studies of capacitors (20) have shown that life and voltage stress are related by an inverse power law. I t was hoped to discover in what ways the gassing process might be related to capacitor life and to understand the mechanism by which gassing is initiated.
Apparatus and Techniques The apparatus was identical with that used in the previous study (3), except for the electrode system. The oil, a U.S.P. white mineral oil (Primol D oil, Esso Standard Oil Co.) used in the earlier study, is placed in the oil reservoir, where it is degassed and then forced over into the electrode compartment. After the system is evacuated to a low pressure
SECTION THROUGH CENTER SHOWING ELECTRODE POSITION
TOP SPACER (MYCALEX )
SPACER SCREW DEE (MYCALE
ELECTRODE (ALUM1NUM )
(10-6 mm. of mercury) the manifold and gassing cell are isolated from the pumps. Voltage is applied to the electrodes and the gaseous decomposition products rise as bubbles between the electrodes and collect in the space above the surface. The pressure of the accumulated gas ismeasured periodically using the appropriate gage. A new electrode system was used in the present study; this design gives more precise control over electrode geometry than the electrodes used previously. The procedure for making a run follows that used in the earlier study except for the lower voltage runs, below 8 kv. For runs a t 6 and 7 kv. it is necessary to start the gassing process by using a higher stress and gassing at these conditions for about half an hour. The stress is then removed, the system is pumped out and isolated, and the voltage raised to the desired level. The oil will then gas, and reproducible results can be obtained. For the lowest voltage runs, at 4>4.5, 5, and 5.5 kv.. it is necessary not only to start a t a higher voltage but to run a t least overnight at the chosen low voltage before pumping down and starting. This cycle is repeated for several days until reproducible gassing curves are obtained (Figure 9). Why such a conditioning process is required is not clear, but it is believed to involve the establishment of an equilibrium number of gas nuclei characteristic for a given stress.
Results SEPARATOR PLP;TE (GLASS) ELECTRODE-TO-CLIP CONNECTOR BOTTOM SPACER ( M Y C A L E X ) ~
w - S P A C E R
SCREW
Analytical Expression. Representative gassing curves for the voltage range covered are given in Figure 1. Runs at 10, 9, and 6 kv. are single runs. The following expression includes the factors that influence the gassing rate for Primol D oil at a given temperature and interelectrode distance. dP/dt = L(V
CLIP ( PHOSPHOR BRONZE )
Apparatus used was identical with that used in earlier study, except for this electrode assembly, which gives more precise control over electrode geometry
-
Vs).Pu
(1)
where
dP/dt = gassing rate, millimeters of mercury per hour VOL. 50, NO. 6
JUNE 1958
'
959
I-
b Figure 3. Reproducibility of gassing curves shows that pressure and not time is governing factor Runs from Figure 2 superimposed
0
1
2
3 4 T I M E (HOURS)
5
6
7
Figure 1. Effect of voltage on gassing of mineral oil
V V, k
P
= operating voltage, kilovolts = starting voltage, kilovolts = aconstant = pressure, millimeters of mercury in gas phase above the oil
The gassing rate, dP/dt, was approximated by measuring the ratio of Ap to At a t various pressures with the corresponding pressure a t the midpoint. The data indicate that there is some threshold voltage, Vg,below which the gassing process, as it is recognized in this study, does not occur. The criterion for gassing is a continuous evolution of gaseous decomposition products with which is associated an increase of pressure in the gas phase above the oil. I n the present study pressure changes co-
0
0
incided with a visibly continuous evolution of bubbles, and observation of the bubbles was used experimentally as a guide to the occurrence of gassing. Fundamentally V, may be related to the emission process of electrons into the dielectric. The gassing curves tapered off as both pressure and time increased so that both factors were considered. As shown later, however, time was not a n independent variable. Effect of Pressure. From a consideration of gassing curves at each voltage the following relation was found log K f B1 log t
log P
(2)
where P is the pressure, K is a constant a t a given voltage, and t is the time. B1 was found to be approximately 0.86. Rewriting in exponential form p
=
K
(3)
t0.86
and differentiating dP/dt = 0.86 K
t-0.14
(4)
Solving for t from Equation 3 and substituting in Equation 4 gives (5)
I
A1260
/-Y. BO
60
Figure 2. Gassing rate i s a function of pressure at constant voltage
960
Thus at constant voltage Equation 5 predicts that the rate is a function only of the pressure. Equation 4 could have been left in terms of t. The problem remained to prove experimentally which one is the independent variable. The pressure dependency of the rate was amply demonstrated by the following experiments. The oil was gassed for a given period of time and the gassing
INDUSTRIAL AND ENGINEERING CHEMISTRY
L
IO
15 20 TIME ( r i O U R S
25
30
I
curve obtained. The voltage was cut off and the system evacuated for half an hour. The voltage was again applied and another gassing curve obtained. This cycle was repeated four times. If the gassing rate is a function of pressure only, the slope of the curves in Figure 2 a t points XI, X,, X3: and X4 should all be the same and the slopes a t Xz,X3, and X , should all be greater than at Y I , Yz,and Ys,respectively. If the gassing rate is a function of time only, the slope at Y I should equal that at X ? , Ya at X3,and Y3 at Xd. Figure 2 and Figure 3 (the reproducibility curve), which includes the superposition of all the loops of the curves of Figure 2 show that pressure and not time is the governing factor. This lack of dependence of gassing rate on time indicates that composition changes occurring in the oil do not have a significant effect on the gassing process. This does not confirm a suggestion made in the previous study that the decrease in gassing tendency of oil might be due to interaction of gaseous products with unsaturated material that develops in the oil. That the composition of the oil does change because of formation of degradation products was proved. Percentagewise, the change in composition is small, and present tests show its influence is negligible. Further tests also showed the dependence of rate on pressure at a constant voltage. After degassing a sample of fresh oil in the usual way, the system was pressurized with hydrogen to a given pressure and allowed to come to equilibrium with the oil. A gassing curve was
LIQUID DIELECTRIC GASSING
Figure 5. Determination of V, with log-log plots of gassing rate vs.
I
1
v - v,
3.9 NON-1.INEAR 2.75 2 0 2 Y 2.6 0 NON-LINEAR
I
PRESSURE = O S MM.Hp
I
0.01' 0.1
I
IO
I
V- Vg IK V.)
Figure 4. Further tests again show that gassing rate is dependent only on pressure
then obtained. The slope of this curve was then compared with a separate run made a t the same voltage in which the pressure developed covered the same range of pressure. The slopes of these curves are the same (Figure 4). The system was then evacuated to a pressure of 2 to 3 mm. of mercury and again gassed for a time. The slopes of the curves again show that the rate is dependent only on pressure. , The effect of pressure was shown to be independent of the chemical nature of the gas phase. Tests with helium made in the same manner as with hydrogen are shown in Figure 4 compared with hydrogen. Only the magnitude of the pressure is important.
Table 1.
The pressure relationship found is valid only up to about 65 mm. of mercury pressure. This is an important factor. One run with the system pressurized to 100 mm. of hydrogen gassed a t a rate much less than that given by Equation 5 . An interesting dynamic experiment was performed. With the system gassing at 11 kv., the manifold was opened to both pumps and to a line connected with a helium tank. By proper adjustment of stopcocks and valves, the pressure in the gas phase could be controlled over a wide range quickly. As the pressure increased, the bubbles rising from the electrodes decreased in size, and finally at a pressure of 200 mm. of mercury they completely disappeared. Visible gassing stopped. As the flow of helium was decreased the gassing started again. The significance of these tests in regard
Coefficients and Statistics from Fitting Data to Proposed Equation
Voltage Range,
8,
62
Kv.
n
ZL
4-11 4-11 4-11 4-11 4-11 4-11 4-11
3.737 2.846 2.528 2.191 1.821 1.376 0.8062
-0.1657 -0.1676 -0.1672 -0.1653 -0.1597 -0.1426 -0.08052
0.0004152 0.005038 0.01143 0.02596 0.05982 0.1455 0.3608
0.0395 0.0278 0.0244 0.0216 0.0197 0.0189 0.0185
0.00732 0.00679 0.00671 0.00684 0.00742 0.00920 0.0139
0.01165 0,01001 0.009811 0.01021 0.01212 0.01898 0.04597
0.9590 0.9647 0.9654 0.9640 0.9573 0.9332 0.8381
4.5-11 4.5-11 4.5-11 4.5-11 4.5-11 4.5-11 4.5-11
3.780 2.974 2.693 2.399 2.089 1.747 1.335 3.583 2.901 2.667 2.426 2.176 1.912 1.621 1.270
-0.1701 -0.1746 -0.1763 -0.1778 -0.1787 -0.1781 -0.1713 -0.1735 -0.1771 -0.1786 -0.1803 -0.1822 -0.1841 -0.1857 -0.1847
0.000256 0.00262 0.008394 0.01792 0.03828 0.08292 0.1892 0.0005875 0.004553 0.008746 0.01710 0.03285 0.06316 0.1227 0.3915
0.0532 0.0373 0.0321 0.0272 0.02262 0.0189 0.0170 0.0681 0.0502 0.0441 0.0380 0.0318 0.0257 0.0200 0.0158
0.00829 0.00746 0.00712 0.00677 0.00649 0.00650 0.00754 0.00877 0.00807 0.00775 0.00738 0.00692 0.00642 0.00591 0.00596
0.01377 0.01111 0.01009 0.009153 0.008400 0.008430 0.01143 0.01446 0.01222 0.01124 0.01017 0.008955 0.007675 0.006515 0.006636
0.9323 0.9454 0.9503 0.9549 0.9587 0.9585 0.9438 0.8860 0.9037 0.9114 0.9198 0.9294 0.9395 0.9486 0.9477
3
3.5 3.9
,
8,
Va 0
1.5 2 2.5
0 1.5 2 2.5 3 3.5 4 0
1.5 2 2.5 3 3.5 4 4.5
5-11 5-11 5-11 5-11 5-11 5-11 5-11
5-11
to the initiation mechanism is discussed later. Effect of Voltage Stress and Determination of V,. Log-log plots of gassing rate us. V - V, are shown in Figure 5 for one pressure, using various assigned values of V,. The most nearly linear plot is the one where V, = 2.75, which is therefore assumed to approximate the most suitable value. The slope of the linear curve shows that n = 2. However, these plots are obtained using only part of the data (only the values for rates at pressure equal to 0.5 mm, of mercury were used), and when all of the data were treated statistically using an IBM 650 machine calculator, the selectivity concerning V, is not really as good as these curves would suggest. There is, however, general agreement between the graphical and statistical
k
R2
"'I
0.8
RATES TAKEN AT
6
8
IO
VOLTAGE IKV.)
Figure 6. Effect of voltage on gassing rate VOL. 5 0 , NO. 6
JUNE 1958
961
28-
-
u
1
1
I2 4 r
p
CURRENTS M E A S U R E D AFTER SHORT T I M E AT V O L T A G E ( M I N U T E S)
I
L
4 Figure 7. Relation between resistive componentof gassing current and voltage Meusurable resistive current appeurs b e tween 2 and 3 kv.
.
/
:VI
3
k
.
Vs.0
'
NON-LINEAR 4 A
e
Figure 8. Use of resistive currents to determine starting voltage, V,
VOLTAGE (KV.)
methods, The results from statistical analysis (Table I, 4- to 11-kv. data when V,=3.9) are in agreement with the curve for Vs=3.9 of Figure 5, as the former show that the straight line calculated using this V , has a poorer correlation coefficient and larger variance than when other values of V , are chosen. A plot of rate us. voltage is shown in Figure 6. The rather large spread in data at high voltage occurs because the measurements were made soon after the run began and stable conditions were not yet reached. All the methods discussed below for finding V , give values in good agreement considering the experimental uncertainties involved. For lack of further knowledge of what V, fundamentally involves, a value for it can be determined only from a phenomenological viewpoint. V, may be found experimentally as the voltage at which gassing first appears or disappears. Reasonable values for V, are not obtained in starting from zero
7
Figure 9. Cycle of gassing and pumping gives reproducible results a t low voltage
962
x
1 O O C I I ~ .- -01
and raising the voltage. To initiate gassing it is necessary to use stresses in excess of values which maintain gassing once started. However, good reproducibility is obtained if gassing is started at some high voltage which i s then decreased. The same processes, possibly involving initiating nuclei, discussed earlier may be important. In one experiment, gassing was established at 11 kv., then run for 0.5 hour each at 9, 8, and 7 kv., then for 1 hour each at 6, 5, 4, 3, 3.5, and 3.25 kv. Gassing was visible down to 4 kv. and not Lisible at 3 kv. Half an hour after the voltage was raised from 3 to 3.5 kv., faint gassing appeared and persisted for an hour at 3.25 kv. In another series of esperiments gassing was established at 8 kv., then the oil was run at a fixed low voltage for several days (the cell was cvacuated each morning without removing the voltage in order to get repeated pressuretime curves). At 4.5,4, and 3.5 kv. the voltage was on fbr 7, 12, and 4 days, respectively; in each case visible gassing occurred and the pressure ZS. time curves reproduced themselves on succeeding days at each voltage. At 3 kv. no further visible gassing was observed after the first half hour. Another experimental approach to determine V, was the use of corona detection methods. In a darkened room faint bluish discharges are observed between the electrodes and the glass plate when gassing is taking place. Thus ionization phenomena are occurring. It was not unreasonable to expect that the onset of discharges should coincide with the appearance of gas bubbles. The detection of radio-frequency noise resulting from ionization discharges is used as a measure of the onset of corona phenomena. Observations of the current pattern on an oscilloscope have shown high frequency noise when gassing occurs. Using a corona set capable of deter-
INDUSTRIAL AND ENGINEERING CHEMISTRY
10
I
V-V,
'
NON-LINEAR
3
16 2 19 I NON-LINEAR 0 NON-LINEAR
I
IO0
IKV.)
mining surges or continuous corona of 5 bv. or higher, corona measurements indicated a value of V, betweed 2 and 3 kv. As in the V, measurements described above, reproducible results were obtained only when the voltage was lowered after corona and gassing had once started. The v a h e so obtained is called the corona extinction voltage. Another indication of V, is obtained rom the resistive component of the gassing current, which is discussed in morc detail below. A measurable resistive current begins to appear between 2 and 3 kv., indicating a V, in this range (Figure 7). Thc resistive component should begin'to enter only when ionization phenomena begin in the gas bubbles. A plot of log resistive current us. log ( V - V,) in Figure 8 can be fitted well by a straight line for V,= 1 to 3. An estimate of V, is obtained froin consideration of variances and correlation coefficients obtained in the statistical analysis of rate data shown in Table I. There is a minimum in the range of V, = 2 to 4, though F tests are only borderline in indicating significant differences among the variances. Significance tests show that V, lies somewhere between 1.5 and 3.5 kv. Taking into account all the ways used to arrive at V,, a value of 3.0 k 0 . 5 kv. is considered best. Relation between Resistive Current and Voltage. Measurements over the voltage range were made of the current through the cell during gassing, I,, as \vel1 as when no gassing was taking place, IC. The scatter is somewhat large, especially at the lower voltages. From Iz and I,, the resistive component may be calculated by vector subtraction. A plot of this computed current I8 us. voltage is shown in Figure 7. A plot of log IE us. log V - V, is shown in Figure 8 with V, as a parameter. Although the data are not too precise, especially at low stresses, there is approxi-
L I Q U I D D I E L E C T R I C GASSING
___CALCULATED
_ _E X _ PER_ I M E N T. AL
TIME (HOURS1
Figure 10. Comparison of calculated and experimental gassing curves
mately a square relationship between current and voltage of the form In= k(V-VJ2 at about the same V, which gives best match for the rate data. When gassing rate (at p=O.4 mm. of mercury) is plotted us. IR, a straight line can be drawn through the points even though there is spread in the data. This would be in accord with the rate-voltage relation, as if dP/dt = k ( V
-
V,)z at V, = 3
(6)
and IR = k ' ( V
-
V,)z at V , =_3
(7)
then dP/dt = k " 1 ~
(8)
Such a relationship suggests that measurement of the extent of chemical change (moles of hydrogen produced) may be correlated with basic emission processes and may give information about these processes. This would require a knowledge of the relationship between I E and the electron-emission current, which is not known at present. Simple calculations of the electron current that might be expected to produce the rate of hydrogen formation observed, assuming an efficiency of electron impact of unity (one molecule of hydrogen produced for every electron), give physically reasonable numbers (9). However, there is an agreement of only one to two orders of magnitude between this value and the resistive currents measured in the present study, the latter being smaller. ReproducibiIity of Data. The procedures necessary to obtain reproducible data have been indicated under the discussion of techniques. I t is primarily at
low voltages that reproducible results are difficult to obtain. Because gassing rate is low, it takes a long time to build u p appreciable pressures. Initial pressures are difficult to interpret, as evolution of residual gas remaining after the degassing process may represent a more than negligible fraction of the pressure rise in the early part of a low-voltage run. As discussed above, it is necessary to use a high voltage to start gassing and then to lower to the desired operating voltage. A cycle of gassing and subsequent pumping as described gives reproducible results at the lowest voltages used. The results of such a cycle at 4.5 kv. are shown in Figure 9. Examples of the reproducibility of gassing curves obtained with higher voltages are shown in Figure 3 for 11 kv. Statistical Determination of Parameters of Rate Equation. Values for the parameters of the equation representing gassing rate are given in Table I along with various statistical estimates of the parameters . T o estimate the parameters the equation was put into logarithmic form:
+
log dP/dt = log k n log(V
-
V,)
+ u log P
(9)
Estimates of the parameters are found by the method of least squares. All computations were performed with the IBM 650 calculator; 8, and 8, represent standard deviations of n and u, respectively, and d2 represents total residual variance of the log rate. R2 is the square of the multiple correlation coefficient R. Table I represents computations made using data covering different voltage ranges-for 4 to 11 kv., 4.5 to 11 kv., and 5 to 11 kv. Because uncertainties exist in the low voltage runs it was important to determine how widely the results differ when lower voltage runs were progressively deleted and the parameters recalculated. Although estimates of the parameters do change somewhat, there is reasonably good agreement among the various voltage ranges. From all the experimental results and statistical considerations. a value of V,= 3.03=0.5 kv. is the best choice. Values for the other parameters at V,=3 for the 4 to 11 kv data are: n = 1.82, u = -0.160, and k = 0.060.
An indication of how the proposed equation reproduces the actual data can be obtained by comparing calculated pressure-time curves with experimental ones. Integration of the rate equation gives the following relation between pressure and time.
v"/
I1 K V
__
( 1 5 0 - 1 5 4 KV./CM.I
CALCULATED
...... E X P E R I M E N T A L
5
10
T~~,~,,,2Ro,~
z5
3o
Figure 1 1. Comparison of calculated curves with experimental curves using various values of V,
Using the parameters in this equation, pressure-time curves were computed for 4, 6, 8, and 11 kv. These curves are plotted in Figure. 10 where they are compared with experimental curves, for which the range is indicated. The lack of sensitivity of the equation to V, (see discussion of voltage stress and determination of V,) is also reflected in the fact that similar plots using another V, and appropriate parameters will give comparable curves with slightly poorer fit (illustrated in Figure 11 at 11 kv.).
Interpretation Comparison of Results with Other Studies. There is only one other study ( 4 ) ,known to the authors, in which the effect of voltage on gassing rate was studied in any detail. The experimental conditions are not the same as in the present study, so that differences in results may be attributed to this fact. Beaven, Cockburn, and Thompson (4) found a gassing rate that was a linear function of the voltage, in contrast to the exponential function of the voltage found in the present work and shown in Figure 6. Their results also indicated that there was a threshold stress of 12 to 16 kv. per cm. below which no gassing occurred. They could not obtain gassing when their electrodes were completely immersed in oil., Assuming that they tried their maximum stress, this means that gassing did not occur at somewhere between 40 and 50 kv. per cm. This checks fairly well with the value of 40 kv. per cm. reported here. I n gassing studies of Nederbragt (ZZ), concave pressure-time curves similar to the data of the present work were obVOL. 50. NO. 6
*
JUNE 1958
963
35
tained. Nederbragt began with an evacuated system, although, in his case both gas and liquid phases were stressed (alternating current stress, high frequency). Most of the gassing curves reported by Berberich (5) under conditions somewhat similar to Nederbragt’s (low frequency, however) were linear. In another study, Worner (34) reported that gassing rate increased as voltage increased. He used a concentric electrode system, in which both liquid and gas phases were stressed and in which air at 1 atm. covered the oil. The voltage data are meager and might possibly be interpreted to indicate little if any dependence of gassing rate on voltage, which seems unreasonable and is in sharp contrast to the present work. Once bubbles are formed and the oil gases continuously, there is a good deal of similarity between the conditions of this work and other studies. However, lack of quantitative agreement shows that there are factors still unrecognized, and differences in experimental conditions may well be the controlling influence. Exponential relationships between voltage and time have been shown in studies of electrical discharges in insulating liquids (32). Relation to Life Studies of Capacitors. One objective of this study was to find a mechanism responsible for the power relationship between life and stress which has been observed in capacitors. Previous studies by McLean and Egerton (20)showed that for chlorinated aromatic impregnant capacirors a t 100’ C. under direct current stress the following equation fitted the data. L
=
Life
=
AVB
(12)
where A is a constant for a given temperature and capacitor type, Vis the voltage, and B is equal to -4 to -6. Later studies with mineral oil-impregnated capacitors under direct current stress also show this behavior (77). Limited data (30) on alternating current tests of both mineral oil and Aroclorimpregnated capacitors show an inverse 5th power law when internal heating is minimized and a moderate range of stresses is used. The “fifth power” life law deduced from accelerated life-test studies on capacitors does not explicitly use a threshold voltage. This does not mean one does not exist, but it is possible that compared to the stresses employed (500 volts per mil to 1000 volts per mil and higher) a threshold stress may be negligible. Now for comparative purposes in attempting to relate the life law and the gassing rate expression, a value of V,=O is assumed in the proposed equation. From the data at V,=O for the 4- to 11kv. data the exponent of the voltage term is 3.7. Assume also that B = - 4 in the life law. Then
964
L
=
AV-4
Gassing rate =
kV3.7 P-0.16
(13)
(14)
For first approximations the pressure term is neglected, for over the range that this relation is valid the voltage term is more important and the voltage exponents are considered equal in magnitude. After rearranging Equations 13 and 14 and equating them, Equation 15 follows. L =
where k”
=
k”
gassing rate
(15)
Ak’
Equation 15 indicates that the life is inversely proportional to gassing rate. The concept of a starting voltage has been used in the study of capacitors. In a study of oil-impregnated capacitors on alternating current Church and Garton (8) used a discharge detector sensitive to at least 10-’2 coulomb per discharge and found that no discharges occurred below a stress of 200 to 800 kv. per cm. Austen and Hackett (2) found a threshold voltage and an exponential relation between life and a stress. Recent work (78) on the breakdown of liquid dielectrics suggests that a fourth power relation between life and stress in capacitors may involve long-time formation of a conducting bridge of colloidal particles followed by a short-time thermal breakdown. Perhaps the prime importance of the present study in relation to the life of capacitors is that gassing rate is like the life, an exponential function of stress. This makes it possible to relate gassing rate to life, even if it is not strictly a first power relation. (It may be that the relation is closer to one in which the life is inversely related to the square of the gassing rate.) This result, together with the evidence of previous studies showing that stabilizers which improve life also markedly decrease gassing. suggests that the gassing phenomenon may be an important factor in the degradation and failure of capacitors. Elucidation of Initiation Mechanism. ROLE OF GAS PHASE. In the earlier study (3) it was suggested that initiation of the gassing process occurs as a discharge in a gas phase originating from residual dissolved air not removed by the degassing process. As a result of ionization processes occurring in a gas bubble, ions were considered to collide with oil molecules causing them to break up into free radicals. This tentative initiation mechanism lacked confirming experimental evidence. The present results of pressure effects, though not conclusive, strongly suggest that under present experimental conditions, a discrete gas phase is essential to starting the gassing process. The actual detail of how this gas phase enters, whether by ionization processes as sug-
INDUSTRIAL AND ENGINEERING CHEMISTRY
gested above or by other means, is still not known. However, the following model is suggested. It is assumed that at the electrode surface an electron enters a gas phase-i.e., some gas nucleus or bubble. The field accelerates this electron until it reaches the edge of the gas phase. This boundary consists of hydrocarbon molecules of the oil. Providing the distance available is sufficient and the pressure in this gas phase is such that the mean free path is great enough, the electron will pick up enough energy to break a carbon-hydrogen bond. H o w do the observations of the present study fit into this picture? Experimentally it was shown that bubbles formed during gassing decreased in size and eventually disappeared as the external pressure increased. Increase of pressure and decrease in size reduce the probability that an electron will acquire sufficient energy to break a bond. A pressure dependence of V, would also fit into this picture (29). Such a model must be considered quite naive, but quantitatively reasonable numbers can be assigned. The bond dissociation energy of a carbon-hydrogen bond is 87.3 kcal. per mole, which is equivalent to 3.78 ev. To acquire this energy, under a stress of 150 kv. per cm. (the highest used in this study) an electron in a gas would require a mean free path of 2.52 X 10-5 cm. (neglecting the difference in dielectric constant between gas and liquid phases). Such a mean free path is possible under the experimental conditions obtaining in the present study. Using the above value as the minimum radius for a bubble, the pressure inside of a bubble, Pi,of such a size can be calculated using the equation, Pi = 2y/r. For y = 30 dynes per cm.; Pi = 2.36 atm., when the external pressure is assumed to be zero. Kinetic theory data for oxygen (from viscosity measurements) give a value of the mean free path X = 0.0406 cm. for electrons in oxygen at a pressure of 1 mm. of mercury ( I ) . Because the mean free path and pressure are inversely related, the mean free path calculated at the pressure of 2.36 atm. in a bubble is 2.27 X 10-5 cm. Such a mean free path is possible in a bubble ofradius 2.52 X cm. [The concept of the mean free path tends to put a conservative estimate on the efficiency of the process being considered, The present calculation implies that once an electron is involved in a collision (in the kinetic theory sense) it loses all its energy and is ineffective for the process of bond rupture.] Only slightly larger bubbles with slightly lower pressures would prove adequate. For the lowest stresses used in the studies, of about 40 kv. per cm, similar calculations show that a mean free path of 1 X l o 4 cm. (1 micron) is required, and a mean free path of 9 X 10-5 cm. is calculated
L I Q U I D DIELECTRIC G A S S I N G as possible. The bubble sizes are much smaller than the dimensions of the electrode system. I n studies of capacitor breakdown it has been suggested that voids too small to give detectable discharges are always present. Church and Carton (8) believe this argument is not convincing. In their work a single bubble whose volume was 10-9 cc. could be detected. A spherical bubble of this volume has a radius of 6.2 X cm. The bubble sizes proposed here can be an order of magnitude smaller, so they could exist without being detected by a corona set having the sensitivity used (10-l2 coulomb). If calculations similar to the above are made using a lower stress (40 kv. per cm.) and the external pressure is increased by '/a atm., the pressure inside the bubble is increased, and a mean free path of only 5.8 X 10-5 cm. is possible, whereas 1X cm. is required. The estimate of the pressure inside the bubble is based on the assumption that the bubble radii remained constant at the value determined for zero external pressure and that the increment of '/a atm. was then added. This estimate is on the low side and arises from the fact that the bubble has probably decreased in size. A consideration of Equation 19, when expressed in terms of PO and P,, indicates that an increase in PO results in a more than equal increase in P,. With the diminished path the electron no longer can gain sufficient energy and so it cannot break bonds, and the whole process stops. This may explain why gassing stops as pressure is increased. EFFECTOF EXTERNAL PRESSUREON GASSING RATE. Within the framework of the above model, there seem to be mechanisms for explaining the observed influence of external pressure on gassing rate. These mechanisms assume that rate of bond rupture, and hence the rate of gas formation, is a function of the number of bombarding electrons which have sufficient energy to break a bond. If external pressure can influence this number, gassing rate will be affected. For example, if there is a distribution in bubble sizes an increase in pressure would decrease the number of bubbles of a size necessary for electrons to acquire the required energy. If a distribution of path length is considered, the number of electrons whose path lengths are considerably larger than average (which energywise may be very effective for the process of bond rupture), are sharply reduced as pressure is increased (72). The effect of internal pressure and external pressure on gassing rate can be summarized in the following equation:
IO0
1
I
Figure 12.
K V. Effect of external pressure on gassing rate
IO
Rate is independent of pressure a t 0 pressure but decreases with pressure increase
where dp/dt is the gassing rate a t constant voltage, Pi the internal pressure, P, is the pressure due to surface tension, Ph the hydrostatic pressure due to the head of oil, and P the external pressure. The results of the present study are shown in Figure 12 where log rate is plotted against log pressure. When external pressure, P,is nearly zero the rate is roughly independent of P. As P increases, the rate is known to decrease. However, because the bubble radius is not known, it is not evident just how rapidly the gassing rate will change. At sufficiently high pressure. the gassing process should stop completely. Measurable gassing has been found to stop at about 200 to 300 mm. of mercury at the highest stress used. EVIDENCE FOR GASPHASE. The most striking visible evidence for the importance of a discrete gas phase is the dynamic experiment in which the gassing process appears to stop as the pressure in the gas phase above the oil is increased above a certain value. As the pressure increases u p to this point, bubble size decreases and the bubbles eventually disappear. The other evidence of the pressure dependency of gassing rate also speaks for the importance of the gas phase in continuing the gassing process. The decrease of the bubble radius
with increase of external pressure follows from a consideration of the equation of static equilibrium for a bubble in the body of a liquid. This equation indicates that the pressure inside a bubble is larger than the external pressure by an amount due to surface tension (23). For spherical bubbles this has the form Pi = Po
+ 2y/r
(17)
where
Pt = pressure inside the bubble PO = total pressure outside the bubble 7
y
= radiusofbubble = surface tension
The pressure, P,,in the interior of the bubble with radius r and consisting of n molecules can be represented by the gas law (28). Substituting the gas law into Equation 17 gives K/r3 = PO
+ 2y/r
(18)
which on rearranging gives
PO = K/r3 -
2y/r
(19)
where K is a constant (79). When Poincreases, the right side must also increase. This occurs when 7 decreases, which is in agreement with experimental observation. The physical difficulty of increasing to infinite pressure as the bubble grows VOL. 50, NO. 6
JUNE 1958
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smaller is never met because as the pressure increases the equilibrium conditions are upset. The gas diffuses out of the bubble into the surrounding liquid which is undersaturated, and the bubble disappears. A review of the literature on cavitation and bubble formation reveals phenomena that support the contention that gas nuclei must be present before the gassing phenomena can get started ( 7 7. 13, 76. 24, 26, 33). I n cavitation studies the hypothesis has been advanced that some gas nuclei must be present to bring about cavitation-Le., cavitation occurs in a liquid only when gases are present in the form of nuclei. \$’hen the gas is truly dissolved (molecularly dispersed), cavitation will not occur ( 9 ) . Various experimental techniques in cavitation studies are used to eliminate or produce nuclei. The production of nuclei favors cavitation; their elimination hinders cavitation. During gassing tests various experimental alterations of the gassing conditions were made as described below. In each case conditions favoring production of nuclei made it easy to start gassing, and conditions hindering their production or eliminating them made it difficult or impossible to initiate gassing. Upon such a correlation, the hypothesis is advanced that gas nuclei are present and are important for the initiation of the gassing process. In certain tests the voltage stress was removed for a number of hours after the system was gassed and some pressure was built up. It was difficult to start the gassing after the period of standing. During standing, gas nuclei would have had a chance to dissolve (6, 10). I n gassing tests where it was difficult to start gassing, air was bled into the cell and it was agitated to get air into the solution. The cell was replaced in the system and stress applied with an atmosphere of pressure above the surface. It was not possible to initiate gassing. However, as soon as the pumps were turned on and the system was evacuated to a low pressure, gassing started very quickly. The lowering of pressure produces a supersaturated condition, TZ hich can be relieved by bubble formation (6. 27). lYhen a bubble is formed in the region of stress the gassing is initiated. Bubbles were formed during the evacuation. In the previous study (3): extensive degassing increased the induction period. which was defined as the interval of time between reaching operating voltage and the first sign of gassing. Degassing of the liquid decreases the ready availability of gas nuclei as removal of dissolved gas makes the nuclei disappear by solution into gas-free liquid or removes them completely (74). Studies have been made on the effect of gas nuclei and gas content on such properties of liquid dielectrics as dielec-
966
tric breakdown strength. In a review Buttner (7) indicated that all factors which impede formation of nuclei usually increase dielectric strength. Gas content per se may not be as important as its influence on the availability of gas nuclei. This is suggested by theoretical studies on the tensile strength of liquids (79) which show that maximum weakening of water by air dissolved at a pressure of 1 atm. is only 0.5%. I n recent studies Maksiejewski and Tropper (27), showed that with undegassed electrodes the direct current breakdown strength of hexane was pressure-dependent. Watson and Higham (29) studied the effect of pressure on breakdown strength of oils and found that the breakdown can result from a number of mechanisms, depending on conditions. Their alternating current tests under subatmospheric conditions show a pressure-dependence for initiation of gassing. That gas nuclei and dielectric strength are related is indicated by Werner (31) who showed that addition of quinones to mineral oils increased their direct current dielectric breakdown strength by about 10%. The previous gassing study clearly showed the strong effect of quinones in inhibiting the gassing of oils. The ideas advanced here should be checked by further experimental study. High speed photography of the electrode region could give further information regarding the formation site of the bubbles and distribution of bubble sizes. By using higher voltages, further information about starting voltages as a function of pressure could be obtained. For many practical situations, as in the case of capacitors (at power frequencies) where large liquid and solid interfaces exist, the contribution that gas nuclei make to the gassing phenomena is of considerable importance. The study of capacitor systems under high pressures might be worth while. Acknowledgment
Thanks are expressed to J. \ I T . Tukey and M. E. Terry for their advice on the statistics of the problem and especially ro Shirley Reed Lvho programmed and guided all the statistical computations. The authors are grateful to D. A. hfcLean for his interest in this work and his helpful discussion of the manuscript. References
(1) k n o t , F. L., “Collision Processes in Gases,” 4th ed., p. 52, Methuen & Co., London, 1950. (2) Austen, A. E. W., Hackett, W.,J . Znst. Elec. Engrs. (London) 91, Pt. 1; 298 (1944”. (3) Basseches, Harold, McLean, D. A,, IND.ENG.CHEM.47, 1782 (1955). (4) Beaven, G. H., Cockburn, J. A , , Thompson, C. N., J . Znst. Petrol. 35, 735 (1949).
INDUSTRIAL AND ENGINEERING CHEMISTRY
(5) Berberich, L. J., IND. END. CHEM. 30, 280 (1938). (6) Briggs, H. B., Johnson, J. B., Mason, W. P., J . Acoust. SOC. Am. 19, 664 (1947). ( 7 ) Buttner, G.. Felten and Guilleaume Rundichau’28. 34 (1950). Church, H. F.; Garton,’C. G., Proc. Znst. Elec. Engrs. (London) 100, Pt. IIA, 111 (1953). Connolly, W.,Fox, F. E., J . Acoust. SOC. Am. 26, 843 (1954). Dean, R. B., J . Appl. Phys. 15, 446 (1944). Fox. F. E.. Herzfeld. K. F.. J . Acoust. Sic. Am.’ 26, 984 11954).‘ (12) Gray, T. S., “.4pplied Electronics,” 2nd ed., M.I.T. Technology Press, Cambridge, Mass., 1954. (13) Harvey, E. N., McElroy, W. D., Whiteley, A. H., J . Appl. Phys. 18, 162 (1947). (14) Harvey, E. S.,Whiteley, A. H., McElrov. W. D.. Pease. D. C.. Barne3, ‘ D. F., Cel/uiar camp: Physiol. 24, 23 (1944). (15) Honig, R. E., J . Chem. Phys. 16, 105 (1348). (16) Hueter, T. F., Bolt, R. H., “Sonics,” M‘ilev, New York. 1955. (17) Koerber; G. G., Kafer, J. A., Weeks, J. R., Bell Telephone Laboratories, Murray Hill, N. J., private communication, May 13, 1934.. (18) Kok, J., Corbey, hf. M., Appl. Sci. Research B4, 474 (1955); B6, 197 (1956). (19) Kuper, C., Travena, D. H., Proc. Phys. Soc. (London) A65, 46 (1952). (20) McLean, D. A., Eqerton, L., IND. E K G . CHEM. 37, 73 (1945). (21) Maksiejewski, 3. L., Troppcr, H., P m . Ins.. Elec. Engrs. (London) 101 Pt. 11, 183 (1954). (22) Sederbragt, G. W., J . Znst. Elec. Engrs. (London) 79, 282 (1936). ;23) Partington, J. R., ”An Advanced Treatise on Physical Chemistry, Vol. 11. The Properties of Liquids,” p. 171, Longmans, Green, London, 1951. (24) Pease, D. C., Blinks, L. R., J . Phjs. 3 Colloid Chem. 51, 556 (1947). (25) Robertson, A. J. B., “Mass Spectrometry,” p. 81, Methuen & Co., London, 1954. ( 2 6 ) Rosenberg, 14.D., .\caustics Research Lab., Harvard University, Tech. Memo. 25 (Aug. 8, 1952). (27) Schweitzer, P. H., Szebehely, V. G., J . Appl. Phys. 21, 1218 (1950). (28) Volmer, M., “Kinetics of Phasc Formation.” trans. from German ed. p. 99, Steinkopff, Leipzig, 1939 [by Intelligence Dept. AMC (FTS-7068-RE: AT I KO. 81935), Reel C]. (29) Watson, P. K., Higham, J. B., Proc Inst. Elec. Engrs. (London) 100, Pt. IIA. 168 11953). (30) Weeks, J. R., Bell Telephone Laboratories, Murray Hill, N. J. unpublished data, August 1948. (31) Werner, J. K., Spector, C. J., McLean, D. A,, Presented at Conference on Electrical Insulation, Div. Eng. and Ind. Research, Natl. Research Council, Pocono Manor, Pa., Oct. 19, 1953. (32) rvhitehead, S., “Dielectric Phenomena, 11. Electrical Discharges in Liquids,” p. 89, Ernst Benn, London, 1928. (33) Willard, G. W., J . Acoust. Soc. Am.25, 669 (1953). (34) Worner, T., Erdd u. Kohle 3, 427 (1950).
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RECEIVED for review June 22, 1957 ACCEPTEDDecember 11, 1957
