Electrical Conduction in Dielectric Liquids RALPH W. DORNTE The current-voltage relations a t high electrical gradients were obtained for dry, gas-free heptane and benzene a t 23' C. The current measurements were made in both uniform and nonuniform electric fields which were obtained by the use of planeparallel, hemispherical and concentric cylindrical electrodes in glass and quartz cells. A comparison of the experimental results with the requirements of the thermionic emission theory of conduction was made by means of the slopes of the currentvoltage curves. The agreement of the experimentally determined slopes with those calculated by this theory was not satisfactory-a result which may depend upon the roughness of the electrode surfaces. The experimental slope was generally greater than the calculated value, indicating that the electron emission was concentrated on sharp points on the electrode surface. This conclusion was substantiated by experiments showing t h a t the currents were not proportional to the electrode areas in uniform electric fields. The current-volt-
N
General Electric Company, Schenectady, N. Y.
age curves were dependent upon the nature of the electrode surfaces and were influenced b y the polish and adsorbed gases, as well as materials which were removed from the cell by repeated washings with the purified benzene or heptane. The current-voltage characteristics of benzene and heptane were reproducible in a given cell but were difficult to reproduce i n different cells. The slope of current-voltage characteristic for heptane was independent of the temperature in the interval 23' to 97' C. The cold cathode emission of electrons is suggested as a possible mechanism for the electrical conduction in dielectric liquids. In a nonuniform electric field the current was determined by the cathode voltage gradient when it was corrected for the effects of sharp edges as required by either of these conduction mechanisms. The effect of temperature on the current-voltage characteris tics was in agreement with the cold cathode mechanism of conduction.
ONE of the many theories proposed t o explain the
mechanism of electrical conduction in pure dielectric liquids (10) has been particularly successful. Baker and Boltz (2) recently proposed a modification of the thermionic emission theory originally suggested by Edler and Zeier (6). According to this theory the conduction in a pure dielectric liquid results from the thermionic emission of electrons into the liquid at ordinary temperatures. The currentvoltage relation is given by a modified Schottky law with a low work function due to the emission occurring into the dielectric liquid rather than into a vacuum. The currentvoltage curve derived on this basis is given by the equation,
where I F
current, amperes gradient of electric field, volts/cm. D dielectric constant of liquid E = electronic charge =
= =
Baker and Boltz found that the slope of the current-voltage curve for toluene agreed with this equation a t the highest voltages in a uniform field. Plumley (11), however, found that this theory did not account for the current ratios from different metallic cathodes in several pure dielectric liquids. This result may be true only a t the relatively low voltage gradients such as were used in this case. Further work with other liquids seemed desirable in view of this discrepancy and to discover possible limitations of the thermionic emission theory. Such work is also of value because of its immediate bearing on the electrical breakdown mechanism which is so intimately connected with the conduction problem.
Current-Voltage Studies Constant potential d. c. of either polarity was obtained from a full-wave rectifier composed of a 15,000-volt transformer, two kenotrons, and a capacitor (0.25 microfarad, 20,000 volts). A Variac and voltmeter in the primary circuit of the rectifier provided satisfactory voltage control and measurement. The rectifier was operated on a special generator to avoid fluctuations which interfered with the current measurements. A resistor of 1 megohm was always connected between the rectifier and measuring cell to limit the arc current in case of a breakdown. A single-tube (FP-54) d. c. amplifier was used to measure currents ranging from 10-14 to 10-6 ampere (4, 13). Six grid resistors (106 to lo'* ohms) were mounted on the circumference of a polystyrene disk which was rotated t o select the appropriate resistor for any current. This amplifier was operated as a null instrument so that the current measurements depended only on the value of the grid resistor and the opposing potential applied to the grid by a potentiometer. The amplifier was very stable and only temporarily unbalanced by a breakdown in the liquid cell. The cells for studying the current-voltage relations in benzene and heptane are shown in Figures 1 and 2. The inner quartz insulating beads or rods were provided with skirts at the ends to give a lon leakage path between the measuring electrode and the guard. #he figures illustrate the construction of the glass cells; the quartz cells were slightly different in that the leads were sealed in through thin molybdenum ribbon (0.0013 X 0.1 cm. wide). The filament and cylinder for the cylindrical cells (Figure 1) were molybdenum; the internal diameter of the cylinders for these cells was 0.954 cm. A lap weld was necessary in the construction of these molybdenum cylinders. The clearance between the guard and measuring electrode was 0.013 cm. in the plane-parallel cells (Figure 2), and the measuring electrode area was 2.01 sq. cm. During the current measurements the guard was maintained at the same potential as the measuring electrode by a connection to the potentiometer on the amplifier. The auxiliary bulb was attached to the cells for the experiments in which the electrodes were washed with purified heptane or benzene. For this purpose the liquid was slowly distilled without 1529
INDUSTRIAL AND ENGINEERIKG CHEMISTRY
1530
ebullition from the bulb into the cell by maintaining a 10' C. temperature ditrrrenee hetwean them. The distillate w s poured back into the auxiliary bulb, and the operation was repeated until the lovest currents were obtained; this indicated that all soluble 01 suspended material was concentrated in the auxiliary bulb. This procedure was used by Martin (9) for the preparation of optically clear liquids. The cells with
VOL. 32, NO. 11
ment, F'/z. The polaiity of the filament is designated by the signs in this figure. The ratio of the calculated voltage gradients at the filament and at the cylinder was 125 in these experiments; hence the abscissas of Figure 3 (left) show the square root of the cathode voltage gradients only for the filament negative. For the filament positive the square rootLf the cathode voltage gradients is roughly one tenth (4125) of the abscissas shown. Since the voltage gradient at the filament is proportional to the applied voltage, the curves show that for the same applied voltage, the larger current was obtained with the filament negative. The same data are plotted in the right-hand graphs of Figure 3, where the square root of the voltage gradient at the cathode is the abscissa. The limiting slope of the current-voltage characteristic based on the cathode voltage gradient was ahnormally high with the filament positive; in fact, the experimental slopes were about twenty fold greater than the slope calcnlated by Equation 1. The currents measured in the cylindrical cells seem to depend upon the voltage gradient a t the filament even when the filament was anode. This behavior is apparently inconsistent with the thermionic emission theory but can be explained on the basis of voltage gradient prevailing at the sharp edge of the lap weld in the cylinder. An analysis of this field problem by Poritsky (13) showed that the gradient a t such an edge equals .the gradient at the filament when the edge has 5 radius of curvature of approximately 0.1 p. Microscopic examination of the lap weld indicated that such a radius of curvature was reasonable for a sheared edge of molybdenum. It may be concluded that the lack of coincidence of the ciirren&voltage characteristics on
FIGURE1. CYLINDRICAL GLASSCELL hemispherical electrodes were similar to the cell shown in Figure 2; the guard merely shielded the lead to the measuring hemispbere. The electrodes for these cells were highly polished to of the beneeik and heptane have been described (5).
Results with Heptane and Benzene A comparison of the experimental results for heptane and hensene with the thermionic emission theory may be made on the hasis of the slope of the curves obtained by plotting the logarithm of the current as a function of the square root of the voltage gradient. It is evident from Equation 1 that the slope of these cnrves is determined by the dielectric constant of the liquid and the temperature. The calculated slope at 23' C. for heptane (0= 1.926) is 0.0090 and for benzene ( D = 2.274) is 0.0097 at the same temperature. The voltage gradient in the cylindrical cells is given by the equation V (2) r ln(r*/rd where V = applied voltage r,, n = respective radii of filament and cylinder I = intermediate radius at which voltage gradient is desired.
p=-
The current-voltage characteristics for heptane at 23' C. obtained in experiments C-2 and C-14 are shown in Figure 3 (left) where logarithm of the current, I, is plotted aa a fnnction of the one-half power of the voltage gradient at the fila-
FIQURE 2. G u s CBLLWITH PL&N~-PABA%~L ELIiCTROnES
changing filament polarity arises from difficulty in determining gradients at sharp edges of the cylinder. This analysis further indicates that the cathode gradient determines the current in the nonuniform field prevailing in the cylindrical cells. The results of several experiments with heptane a t 23" C. in the cylindrical cells are summarised in Table I; the effects of filament polarity, adsorbed hydrogen, and the washing of
INDUSTRIAL AND ENGINEERING CHEMISTRY
NOVEMBER, 1940
:F
(V/c m)
1531
,
+
F i ( V /cm)T
FIGURE 3. CURRENT-VOLTAGE CHARACTERISTICS OF HEPTANE AT 23" C. IN CYLINDRICAL CELL,SHOWING POLARITY WITH GAS-FREEAKD HYDROGEN-TREATED MOLYBDENUM ELECTRODES EFFECTOF FILAMENT F1lz refers t o the voltage gradient at the filament (left) and at the cathode (right).
the cell upon the limiting slope in the highvoltage region are tabulated. The limiting slopes were calculated on the basis of the cathode voltage gradient as well as the voltage gradient at the filament. Some of the currentvoltage relations found in experiment C-13, which illustrated the effect of washing the cell, are shown in Figure 4. The main feature resulting from the washing procedure was a progressive shift of the curves to the right, indicating the removal of suspended matter or soluble materials originating from the glass and electrodes. The curves indicating the minimum current at a fixed voltage gradient of either polarity were reproducible in a given cell within * 2 0 per cent, which was the precision attainable in the current measurements. When the residual heptane, left in the auxiliary bulb after the washing procedure, was poured into the cell, the curves were shifted back to their original positions. Repetition of the washing again shifted the curves to
the right. KO further change in the p o s i t i o n o r s l o p e of t h e c u r v e s w a s accomplished b y n-ashing the cell more than about eight times. The experimental slopes based on t h e voltage gradient a t the cathode exceeded t h e calculated s l o p e (0.0090) about 30-45 per cent with the filament cathode, even after the washing procedure in the quartz cell which was expected to give the most satisfactory agreement. Baker a n d Boltz (2) showed that points on the cathode s u r f a c e may increase the slope over that calculated by Equation 1. The deviation of the slopes was several hundred per cent when the filament was anode. These d e v i a t i o n s have been shown t o arise from the sharp edges of the c y l i n d e r , which
TABLE I. RESULTSWITH DRIEDAND DEGaSSED HEPTANEI N MOLYBDENUM CYLINDRICAL CELLSAT 23' C. Expt. NO.
C-2
Filament Diameter, Cm. 0.0076
C-13 I
Filament Polarity
Cathode gradient
+-
0.068
0.007
Slope, d logI/d(FI,2) Filament gradient
0,007 0.006
0.0076 Cell not washed
I1
Cell washed 2 times
111
Cell washed 4 times
IV
0,009
0.145 0,009
Cell washed 8 times
0.145 c-14
0.0076
C-15
0.0127
C-17
0.0025
C-28
0.0076
Adsorbed Hs
Quartz cell not washed Quartz cell washed 2 times Quartz cell washed 2 times
1532
INDUSTRIAL AND ENGINEERING CHEMISTRY
The results of current measurements with hemispherical electrodes in quartz cells are summarized in Table 11. The electrodes were carefully polished before assembly and degassing except in experiment C-24, where the high potential electrode was roughened by coarse emery cloth. The current-voltage relations with degassed hemispherical electrodes still were dependent upon polarity in the quartz cells before the washing procedure; after the cell was washed, the current-voltage curve was the same on either polarity. The curves obtained in experiments C-21 and C-24 after the cell was washed are shown in Figure 5. During experiment C-24 the electrodes were illuminated by the total radiation of a quartz mercury arc (Uviarc) at a distance of 10 cm. An in-
IO-'
-a -5
VOL. 32, NO. 11
10-8
H
TABLE 111. RESULTSIN PLANE-PARALLEL NICKEL ELECTRODE CELLS WITH GUARDED MEASURING AREAOF 2.01 SQ. Cnr:
IO-^
Expt.
Cm.
NO.
47 C-4
0.076 0.066
C-6
0,089
lo-'o
C-7
0
C-18 I
FIGURE4. CURRENT-VOLTAGE CHARACTERISTICS OF HEPTANEAT 23" C. IN CYLINDRICAL CELLWITH GASFREEMOLYBDENUM ELECTRODES, SHOWING EFFECTOF FILAMENT POLARITY AND WASHING TEE CELL P I 2 refers t o the voltage gradient at the filament.
makes the calculation of the gradient unreliable; hence all comparisons with theory must be based on results with the filament as cathode. The electron emission from the filaments of these cells before filling and after contact with the heptane vapor indicated that the surfaces were clean and had normal work functions which were unaffected by the heptane. The current-voltage curves with hydrogen adsorbed on the molybdenum electrodes were not reproducible, as shown by the variation in the slopes. The conductivity of benzene a t low voltages also has been found to depend upon the hydrogen content of the electrodes by Edler and Knorr (6).
197
0.076
I1
I11 c-20
0.076
Polarity Heptane
+ +-
++ --
+ +++ ++ + Benzene
CB-3
0
0.076
CB-4
0.084
CB-5
0.076
slope, .1 lop I / d ( F l / ? !
0.013 0.015 0.016) 0.014 0,022
0,022 0.024 0.023
:: :!:} : : E}
0.069
0.032
::t:i }
};:
:::;;1
+-
:::::}
+-+
E;E:E\
-
+-
970c'
0.015 0.015 0.022 0.032 0,034 0.023 0.038
:,:::]
90' C. Quartz cell not washed Cell washed 4 times Cell washed 8 times Quartz cell not washed Cell washed 2 times Cell washed 4 times Cell washed 8 times Cell not washed Cell washed 2 times Cell washed 6 times Cell not washed Cell washed 6 times Solid 0' C.
Cell not washed Cell washed 4 times
Temperature 23' C.. unless otherwise noted.
ON DRIED AKD DEGASSED HEPTANE WITH HEMISPHERICAT. creased current due to the ultraviolet radiation TABLE 11. RESULTS ELECTRODES IN QUARTZ CELLSAT 23" C . was easily distinguished in the low-voltage region but was not detectable in the high-voltage Expt. Electrodes Polarity Slope, d log I/d(F"¶) No. region. This behavior indicates the absence of Cell not 0 036 C-21 0.076 xr 0 ionization by collision in the conduction mechawashed 0 009 +Cell washed nism for heptane. The current increment due 0.043 2 times 0 031 to the radiation was nearly independent of the Cell washed 0.031 +8 times 0.031 voltage and varied approximately as the inverse C-24 0.096 Mo roughened ::;I;} Cellwashed not square of the distance between the electrodes +-and the arc. Cell washed 6 times The deviations of the slopes for hemispherical electrodes from the calculated value were greater than were found with the cylindrical cells. The experimental slopes were always larger than the calculated value which may be caused 0.0081 by emission from points; only in the case of t,he experiments with roughed electrodes (C-24)
E?
+
+
:::::}
NOVEMBER, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
and in the presence of oxygen (C-23) was the calculated slope obtained. Baker and Boltz (9) also found that the calculated slope was more readily obtained in the presence of adsorbed oxygen, The results of conduction experiments with heptane and benzene in cells with plane-parallel nickel electrodes are summarized in Table 111. A typical set of current-voltage curves (experiment C-18) resulting from the washing of the quartz cells is shown in Figure 6, which gives the data for the highpotential electrode positive. The main effect of the washing procedure was to shift the curves to the right with but slight changes in their slopes. An important requirement of the thermionic emission theory for conduction is the temperature coefficient predicted by Equation 1. The slope [d log I / d ( P I * ) ] for heptane should decrease from 0.0090 at 23" C. to 0.0071 a t 90" C. or 0.0069 a t 97" C. I n experiments C-6 and C-7 the slopes of the curves were unchanged in this temperature range. The currents a t the higher temperatures were about 30 per cent greater over the entire voltage range. KO temperature coefficient for the slope of the curves was found in the present work, although a 20 per cent decrease in the slope is required by Equation 1. I n one experiment the circular measuring area in a cell with plane-parallel electrodes was divided into a 60" and a
10-6r-10-8
I
I
300" sector so that the current to each sector could be measured. I n Figure 7 the initial current distribution is shown as well as the final distribution after washing the cell. The currents were not proportioiial to the electrode areas, even after repeated washing of the cell, and approached proportionality only near breakdown. This result definitely indicates the predominant role of points or small active areas on the electrode surface in determining the total current. The distortion of the field a t the edges of the sectors and guard apparently did not affect the observed currents since the current in the cells with plane-parallel electrodes was independent of the polarity. All edges of the sectors and guard were rounded as a result of the polishing operation. The characteristic curves for dry, gas-free benzene with degassed nickel electrodes are shown in Figure 8, which gives the initial and final current measurements after washing the cell as well as the measurements on solid benzene obtained in experiment CB-4. The experimentally determined slopes also exceeded the calculated value (0.0097 a t 23' C.) as in the case of heptane. The relatively slight difference in currents for liquid and solid benzene indicate that ionic conduction is not a n important factor in the mechanism. The slopes of the current-voltage curves found in the present work with benzene and heptane were generally greater than the slope calculated on the basis of the thermionic emis-
I
c z5-
IO-*
1533
Io-8
IO-*
/'
H
1O-l0
l
0
'
'
"
F
1 c.
FIGURE 5 (left).
CURREiiT-LrOLTAGE CHARACTERISTICS OF HEPTANB AT 23' WITH GAS-FREEIIEMISPHERICAL ELECTRODES, SHOWING EFFECTS OF ROCGHENED ELECTRODE ASD ULTRAVIOLET RADIATION FIGGRE 6 (center). CURRENT-VOLTAGE CHARACTERISTICS OF HEPTANE AT 23" C. WITH GAS-FREE PLAUE-PAR ALLEL NICKEL ELECTRODES, SHOWING EFFECT OF REPEATED WASHISGOF THE CELL FIGURE7 (right). CURRENT DISTRIBUTIOX FOR HEPTANE AT 23" I N C E L L WITH GAS-FREEP L 4 N E - P A R I L L E L ELECTRODES HAVING 60" AND 300" SECTORS
c.
I, before washing cell; 11, after repeated washing of cell.
INDUSTRIAL AKD ENGINEERING CHEMISTRY
1534
IO-
VOL. 32, NO. 1 P
with the cylindrical cell in experiment C-13 and with planeparallel electrodes in experiment C-18 are shown in Figure 9, 10-I where the reciprocal of the voltage gradient a t the cathode is the abscissa. The m a g n i t u d e of t h e currents observed in 10-9 heptane and benzene are nearly comparable to the cold cathode currents obtained by ilhearn (1) in I 10-1' vacuum, although the currents in the die l e c t r i c l i q u i d are from ten to one hundred fold greater for the same gradi0." ents. T h i s effect might be expected on the view that a dielectric medium generally lowers the work function (8). The effects of gases adsorbed on the electrodes are the same FIGURE 8 ( l e f t ) . CTRREST-VOLTAGE CHARACTERISTICS O F LIQUID BENZESEAT 23" C. ASD SOLID BENon the basis of either ZENE AT 0" c. the modified Schottky I, before washing cell; 11, after washing. theory or the field DATAFOR HEPTAXE AT 23' C. PLOTTED ACCORDINGTO FIELD FIGURE 9 ( Y i Q h t ) . ('URREKT-\'OLTAGE EMISSION, EQUATION 3 emission t h e o r y , since both theories i n v o l v e t h e work function of the cathode. The essential difference of the two sion theory. This behavior may arise from sharp points on mechanisms of obtaining electrons in the dielectric liquid is the electrode surface, and hence the results do not necessarily in the temperature effect. I n the thermionic emission theory invalidate the theory. A serious objection to this theory, the slope of the current-voltage characteristic is an explicit however, is the disagreement between the experimental and function of the dielectric constant and the temperature; in theoretical temperature coefficient for the slope of the curfield emission theory the slope is independent of temperarent-voltage relation. The temperature coefficient should ture. The present results are in agreement with the field presumably be valid for emission from points or plane suremission theory in this respect. It is difficult to distinguish faces. between the two electron emission mechanisms by means of A discussion of conduction mechanisms in pure dielectric current measurements alone since the main difference in the liquids should consider the possibilities of cold cathode emistwo theories is involved in the exponential terms of the equasion since i t provides a means of obtaining electrons in the tions. liquid which is quite similar t o the modified Schottky theory. A number of factors which influence the current in dielectric Literature Cited liquids, such as surface irregularities and adsorbed gas on the (1) Ahearn, A. J., P h y s . Rev., 44, 277 (1933); 50, 238 (1936). electrodes, are known to affect the cold cathode currents in (2) Baker, E. B., and Boltz, H. A., Ibid., 51, 275 (1937). vacuum ( 1 ) . The field emission currents are concentrated (3) Dornte, R. W., J . Applied Phys., 10, 514 (1939). on sharp points on the cathode surface and are quite erratic (4) Dubridge, L. A., P h y s . Rev., 37, 392 (1931). until the electrodes are conditioned by the passage of cur(5) Edler, H., and Knorr, C. A., 2. physik. Chem., 158, 433 (1932). (6) Edler, H., and Zeier, O., 2. P h y s i k , 84, 356 (1933). rent a t high voltage. The theory of the cold cathode emis(7) Fowler, R. H., and Nordheim, L., Proc. Roy. SOC.(London), sion (7, 14) leads to the equation, A119, 173 (1928). dI n 1 - --2F - 6.8 X l o 7 @3 / 2 d(1lF) P
where
T
(3)
= work function
p = experimentally determined parameter which corrects
the applied field for surface irregularities
The present current measurements are satisfactorily represented by Equation 3 in the high-voltage region in all cases, and for the case of the cylindrical cells this equation is satisfactory even a t rather low gradients. The results obtained
(8) Kalabukhov, N.. 2.P h y s i k , 92, 143 (1934); 93, 702 (1935). (9) Martin, W. H., J . P h y s . Chem., 2 4 , 4 7 8 (1920);, (10) Nikuradse, A., "Das flussige Dielektrum , Berlin, Julius Springer, 1934. (11) Plumley, H. J., P h y s . Rev., 52, 194 (1937). (12) Poritsky, H., private communication. (13) Rochow, E. G., J.Applied Phys., 9, 664 (1938). (14) Stern, T. E., Gossling, B. S., and Fowler, R. H., Proc. R o y . ,Sot. (London), A124, 699 (1929). PREBENTED as part of the Symposium on Electrical Insulation beforr t h e Division of Industrial and Engineering Chemistry at the 99th M w t i n g of t h e American Chemical Society, Cincinnati, Ohio.
