585 EXCHANGE The Measurement of Dielectric Constants DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JOHN FITCH KING February, 1921 EASTON, PA.: ESCHBNBACH PRINTING Co. 1922 The Measurement of Dielectric Constants DISSERTATION SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS HOPKINS UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY JOHN FITCH KING February, 1921 EASTON, PA.: ESCHENBACH PRINTING Co. 1922 ACKNOWLEDGMENT. The writer wishes to express his gratitude to Dr. Walter A. Patrick under whose guidance this work was done and to thank Drs. Frazer, Reid, Lovelace and Thornton for laboratory and class room instruction. An expression of appreciation is due the late Professor Granville R. Jone- for his interest and help. The writer also takes this opportunity to thank Dr. E. O. Hulbert and Mr. Gregory Breit of the Department of Physics who were frequently consulted during the difficult construction of the dielectric apparatus. THE MEASUREMENT OF DIELECTRIC CONSTANTS. This preliminary paper contains a description of a bridge method for measuring dielectric constants of liquids in which use is made of audion bulbs both as a source of exciting current and as a means of determining the balance point of the bridge. Our interest in the dielectric constant is due to the suspected close relationship that exists between this constant and the solvent power of liquids. That there is a relation between the swelling powers of liquids and their dielectric constants is apparent from a casual review of the experimental data. However, there are many exceptions to the rule and our effort is directed toward the possibility of finding a more general relationship. Accordingly, we planned first to measure the dielectric constants of a series of liquids and mixtures of the same and also the swelling power, or as it is incorrectly called the "solvent" power, that these exerted upon a certain sample of cellulose nitrate. Our choice of a suitable method for the measurement of dielectric con- stant was greatly influenced by the result of a year's work in this field by one of the authors. This work (unpublished) was done in University College, London, together with Professor F. G. Donnan and resulted in the conviction that there is no satisfactory method for the measurement of dielectric constant of liquids possessing a specific conductivity greater than that of conductivity water. In this work the Drude 1 method as well as Schmidt's 2 modification was carefully investigated, using a well constructed apparatus in which special attention was paid to the exciting energy and the end-point detectors. A 30cm. spark induction coil was employed, operated with a mercury break interrupter. This induction coil was connected to a Tesla converter, the energy from which was used to excite the primary circuit of the testing apparatus. Neon tubes were prepared and the most sensitive ones were used in determining the end- point. The results of the experiments with this apparatus showed that neither from the standpoint of precision nor from the standpoint of the ability to measure the dielectric constants of conducting liquids, does this apparatus have the advantages which have been claimed for it over other methods. When liquids that possessed a conductivity only slightly greater than that of conductivity water were used, the minima became 1 Drude, Z physik. Chem., 23, 267 (1897). 2 Schmidt, ibid., 27, 343 (1898). very obscure, and furthermore during the measurement a large increase in the temperature of the liquid was observed, indicating that energy absorption was taking place. This energy absorption increased with the increase in frequency of the electric wave. This is important from the chemist's viewpoint since it is commonly understood that an increase in the frequency of the electric wave enables one to measure the dielectric constant of a conducting liquid. Many experiments were made with the well-known bridge method as developed by Nernst. 3 Special attention was given here to the source of alternating current. Electrically driven tuning forks of various fre- quencies within the telephonic range were used, as well as a variety of other well-known interrupters. The sharpest minima, however, were obtained with a small Wehnelt break. All manner of changes in the apparatus did not develop an arrangement which was especially satis- factory. The principal objection was the lack of precision. The sources of current producing the more symmetrical electric waves gave minima which extended over a large portion of the setting scale. From a theoretical consideration of the distribution of an alternating current in a Wheatstone bridge, we decided to use as our source of alter- nating current an apparatus which would furnish a symmetrical wave. This is an important factor in the measurement of dielectric constant for the assurance of a sharp and true minim^t. Professor Flemming 4 has given it consideration in his statement, "It may be pointed out incidentally that no accurate balance or well defined zero can be obtained unless the electromotive force applied to the bridge has a very true sine wave form. Hence no arrangement such as a buzzer, hummer or current interrupter of any kind can be substituted for the sine curve alternator or for an al- ternator and a wave filter." We used a frequency of about 1000 cycles per second since this is within the telephonic range and gives a pitch easy to detect and since there is nothing to be gained by using a higher frequency. The work of one of us cited above showed that there is greater energy absorption at higher frequencies. Flemming has treated this matter theoretically and has shown that greater dissipation of current due to the dielectric occurs at higher frequencies. With a slightly conducting liquid in our cell we have to measure the capacity similar to that of a leaky condenser. Flemming has shown that the energy loss in a poor dielectric due to an alternating current can be divided into two parts, the first due to conductivity which is probably electrolytic in nature and the second to a conductivity which is nearly proportional to the frequency. The first is the regular direct current conductance while the second has been called an alternating current conductance. 1 Nernst, Z. physik. Chem., 14,622 (1894). 4 Fleming, Proc. Phys. Soc. London, [2] 23, 117 (1911). In the method worked out by Nernst, the ratio arms of the bridge consisted of two resistances and the other arms consisted of an unknown capacity which was balanced by a measuring condenser. In order to make the impedance in the ratio arms of the same magnitude as the im- pedance in the balancing arms, it was necessary to use very large resist- ances with the possibility of introducing self-induction into those arms of the bridge. We used air condensers in all four arms. Air condensers are to be desired because of their more constant capacity and the smaller f chance for leakage. Since, with a conducting solution in our dielectric cell condenser, we f had to balance a leaky condenser, we used a non-inductive resistance : shunted around the measuring condenser in the balancing arm of the bridge. Although Flemming 4 has shown that it is not possible to duplicate a leaky condenser by means of a condenser and a resistance in parallel, we were able to prove that up to a certain limiting value of shunted con- ductivity it was possible to obtain true values of the capacity of the con- denser. Much attention has been given by conductivity workers and workers on the bridge method for the measurement of dielectrics to the phone used to detect the minima. The minimum current possible in the bridge is determined by the current necessary to excite the phones. This minimum current is still large enough to cause trouble in the matter of heating effects, polarization, etc. A small current is to be desired, but using a small current and one of symmetrical wave form much difficulty is ex- perienced in reaching a minimum. To overcome this difficulty we used the thermo-ionic amplifier of recent development. With this improved apparatus, consisting of a source of alternating current of symmetrical wave form, a symmetrical bridge, each arm of which offered an impedence of the same magnitude, and with an extremely small current flowing through the bridge, the use of which was made possible by the amplifier in connection with the telephones, we hoped for an improvement in the accur- acy of our measurements. The Vreeland oscillator is without doubt the best source of alternating current of sine wave form, but the cost of the Vreeland oscillator led us to turn to the electron tube as our source of current. By an arrangement in which an electron tube, a condenser and an induction coil are connected in a circuit, it is possible to obtain an alternating current of symmetrical wave form. With this arrangement by properly varying the plate voltage, the temperature of the filament, the capacity and the induction, it is possi- ble to obtain different currents varying from a few tenths of a milliampere or less to 25 amperes and with a frequency varying from ^ cycle per second to 50 million cycles per second. 6 6 Hall and Adams, /. Am. Chem. Soc., 41, 1515 (1919). PHONES BRIDGE ANPLIFHEIR DIELECTRIC CONSTANT APPARATUS We used the "Marconi Vacuum Tube" type V.T.I. In the drawing, T is the vac- uum tube, C the condenser, and I the induction coils. The audion plate was charged with 120 volts by dry cells while the filament was heated with a current of . 7 ampere and 4 volts supplied from lead storage cells. The two induction coils consisted of about 300 turns of No. 32 wire each wound around a laminated iron core. The lead to the bridge was coupled to this with about 50 turns on the secondary coil. At C are two variable Murdock condensers connected in parallel. By adjustment of these condensers we obtained a frequency of about 1000 cycles per second. During the first part of our work we used the laboratory current to charge the plates in the electron tubes both in the amplifier and in the oscillator. Great difficulty was experienced from external noises caused from other electrical apparatus running in the building which tended to obscure the minimum and greatly tried the patience of the operator; but when dry cells were used to supplant the laboratory current the results were most gratifying. In the construction of the bridge, two variable Murdock air condensers were used in the ratio arms. 6 The condensers had a capacity of about . 0005 microfarad and the scales were divided into 180 divisions. In any series of measurements these condensers were set and the moving pointer sealed by means of sealing wax. These condensers 6 These condensers as well as most of the wireless apparatus were purchased from the Wireless Specialty Co. of Boston. 9 are represented by d and C in the drawing. In the measuring arm of the bridge were the following parts. 1. A variable vernier condenser, C 3 in the drawing, "DeForest" type, with a ca- pacity of 0.0015 microfarad. The ccale was divided into 100 divisions. The vernier had a capacity of about 180 degrees per scale division. The pointer on this scale was ex- tended about 75 cm. to an enlarged scale of some 2200 divisions of 1 mm. each, thus en- abling us to set the condenser with a much greater precision. In making a measurement, the setting was made on the large scale and then the accuracy of the scale was tested by means of the vernier condenser. The vernier was moved by means of a lever operated from the center of the room. This was done to prevent the introduction of capacity into the bridge from the operator's body. If after making a setting on the large scale, the vernier, by a small movement to the right and to the left, passed through a minimum, we assumed the setting to be correct. 2. Connected in parallel with this measuring condenser was a second Murdock condenser, C 3 ', from which about half of the plates had been removed. The recording pointer of this condenser was also extended to an enlarged scale. It was possible to use the large condenser for changes in dielectric from 2 to about 26 and over and the small condenser for changes from 2 to 7, gaining a 5-fold increase in sensitivity. The vernier setting-lever was used for testing the setting of the minimum when either con- denser was used. When C 3 was used, C 3 ' was locked in a fixed position, the scale of C 3 calibrated and the measurements made. When it was desired to use C 3 ' as the measuring condenser, C 3 was locked and the small condenser scale was calibrated. 3. RI is a non-inductive resistance made by filling a conical glass tube with "Man- gani" solution (121 g. of mannitol plus 41 g. of boric acid). The resistance of this tube could be varied by varying the distance between the electrodes or by moving a plunger down into the ground glass conical part of the tube, thereby decreasing the cross section. The stem of the plunger fitted into a hard rubber cap which was threaded. The small thread on the screw of the cap made possible a very sharp setting of the re- sistance. This was extremely important when any great conductivity was possessed by the liquid being measured. In some cases it was found that turning the cap one or two mm., involving the very slight accompanying displacement of the plunger in the tube, entirely obscured the minimum. Previous workers have called attention to the importance of the resistance used to compensate the conductivity. It has been suggested that as the conductivity increased and the electrodes in the liquid resistance were moved closer together, a capacity was introduced in the resistance tube which in- volved an error in the capacity of the measuring condenser. That this is not the true explanation can easily be shown by a consideration of the voltage consumption in the measuring arm of the bridge. A simple calculation is sufficient to illustrate this point. Consider the bridge, with capacities C\ and C 2 balanced against capacities C 3 and C 4 the latter being shunted with resistances R\ and R 2 respectively. Then Zi/Z 2 = Z 3 /Z 4 where Z is the impedance; if C\ = Cz, and both C\ and 2 are air condensers, Zi =Zz, and therefore Z 3 = Z 4 . Let us suppose that C t is composed of 2 concentric cylinders 0.2 cm. apart and having an electrode surface of 50 sq. cm. Furthermore, let the dielectric be alcohol having a dielectric constant of 25 and a specific conductivity of 1 X 10 ~ 7 mho. The capacity of such a condenser is Ka/4wd 900,000 = 0.00055 mf. The re- sistance of such a cell is therefore (50/0.2) X 10 ~ 7 = 2.5 X 10 ~ 6 mho = 0.4 X 10 5 ohm. The impedance of the above capacity and resistance in parallel may be most easily calculated by obtaining the vectorial sum of the admittances due to capacity and re- sistance. The admittance due to capacity at a frequency of 1000 is 2ir. 1000C = 2 X 3. 1416 X 1000 X 5 X 10-^ = 3. 1 X 10 ~ 6 . Therefore the admittance of the combina- 10 tion is V(2.5 X lO" 6 ) 2 + (3.1 X lO" 6 ) 2 = 2.52 X lO" 6 . The impedance is 1/2.52 X 10" 6 = 0.396 X K^ohm. This calculation shows that the impedance of the whole bridge arm is largely determined by that of the resistance alone and that the quantity which we wish to measure, the capacity, only slightly affects the total impedance. In other words, an accurate measurement of capacity cannot be made at a frequency of 1000 cycles per second if the impedance due to resistance is less than that due to capacity. This is an important consideration for the determination of the limit of conductivity. It has been commonly overlooked in dielectric-constant measurements of conducting solutions. 4. In the fourth arm of the bridge was a condenser, C 4 , shunted by a Mangani solution resistance. This condenser acted as a tare condenser and the resistance was used to balance the conductivity of the liquid when the dielectric cell condenser was placed on the Cs arm of the bridge in the differential method of measurement which was used. Our purpose in finally adopting the differential method was to eliminate any errors due to an unsymmetrical arrangement of the bridge such as different self-in- ductances of the wires, mutual capacities of the condensers, etc. Also by the differential method twice the ordinary displacement on the measuring scale is obtained for a given change in dielectric. The dielectric cell was composed of two co-axial platinum cylinders, 2.2 cm. X 6 . 3 cm. and 1 . 9 cm. X 6 . 3 cm., respectively, which were set in the ground glass stopper of a glass cup. This cup was mounted on a hard rubber base. The platinum cylinders were firmly fastened at each end to prevent any possible displacement during a set of measurements. These cylinders as well as the cup were easily cleaned between measure- ments by washing several times with alcohol and ether and then drying in a stream of air. It was so arranged that the whole dielectric cell could be placed in a holder in a thermostat if at any time the accuracy of the work should demand close temperature control. The dielectric cell was arranged by means of a rocking commutator so that it could be placed in parallel first with C 4 and a reading taken and then in parallel with C 8 and the difference in reading taken. During the calibration of the scale and during any series of measurements, Ci, C2, and C 4 were sealed, Cs being the only condenser whose capacity was changed. The amplifier was a two-step type triode E to which a third step was added by means of an amplifying transformer and an electron tube, thus giving a 1000 fold amplification. The plates were charged at 40 volts from dry cells and the filaments were heated by a current of . 7 ampere and 6 volts from lead storage cells. This amplifier was used in connection with a set of Baldwin wireless telephones. These telephones have non- adjustable mica diaphragms and were especially suited for wireless work for the recep- tion of very weak signals. Their resistance was 2000 ohms. In any determination, the amplifier was adjusted by changing the temperature of the filaments to give the greatest sensitivity and then was not changed during an entire calibration and set of measure- ments. This was in keeping with the care always exercised during a set of readings to vary nothing but the liquid in the dielectric cell and the capacity of the measuring con- denser. It was only by employing the greatest precaution along these lines that con- sistent and comparable results could be obtained. For instance, before the rocking commutator was used in the differential method of measurement, a wire was moved from C 4 to Ci in order to change the dielectric cell from parallel with C 4 to parallel with C|. It was discovered that the movements of this fine short wire caused the shifting of the minimum many divisions on the recording scale. Again, before the final setting was made by the use of the vernier condenser lever operated at a distance from the bridge, it was found that effects produced by the operator's body either entirely ob- scured the minimum or shifted it a few hundred divisions. 11 The first set of measurements on the bridge was made for the purpose of determining the sensitivity of the apparatus. Before using the differ- ential method it was found that we were able to get very sharp minima when the ratio of the condensers in the ratio arms was other than one to one. This made it possible to magnify the deflection of the dielectric cell on the measuring condenser. With benzene in C, the dielectric cell, C 3 the measuring condenser gave in 4 experiments, 430, 430, 430, and 390; with ether it gave 840, 905, 1070, and 1205, respectively. In the last measurement a change in dielectric of from 2.22 to 4.35 caused a change on the setting scale of the measuring condenser of 815 divisions, which means (setting to one division on the scale and one di- vision is one millimeter) that one division on the scale is equivalent to a change in dielectric of 0.0026. These measurements could be made on Cs'. When made on C$' which possessed a 5-fold sensitivity, one scale division was equivalent to a change in dielectric of 0.0005. No attempt was made to carry this study further as it was not desired to reach this sensitivity. For our measurements we needed a sensitivity which would keep the read- ings of a change in dielectric of from 2 to 26 on the scale. A set of measurements was made by the differential method and the same satisfactory balancing of the bridge was obtained. Investigation was next made of the effect of an added non-inductive resistance to an air condenser whose capacity was being measured by the differential method. This resistance was balanced out by a resistance in parallel to the condenser in the balancing arm. a. b. a-b. diff. Condenser alone 497 293 204 Condenser plus resistance in parallel 505 260 245 41 As the resistance decreased, the difference between the true capacity and the observed capacity increased. Next a 22,000-ohm resistance was shunted around the condenser whose capacity was being measured. As the capacity was increased, the amount that the minimum was shifted due to the shunted resistance decreased. It was also found that there was less shifting of the minimum due to the shunted resistance if the ratio condensers as 1:1. The reason for this can be seen from the following calculation. If the impedance of the ratio arms is the same, i. e., if C\ = C 2 , then C$ = C in the presence of conductivity due to ,R only on condition that Cz is shunted with an equal resistance. On the other hand, if C\ does not equal C 2 , the ratio of C 3 to C 4 will not equal the ratio of C\ to C 2 even under the condition that R& is equal to R^. A single calculation is sufficient to bring out this point. Let C/C 2 = a/b; thenZ 3 /Z 4 = b/a; orA 3 /A 4 = a/b (1) where Z is the impedance, and A is the admittance. Further let R 3 = R* x. A = the vectorial sum of C 3 + 12 = VcJ + (!/*); and ^ = Vc 4 2 +(i/* 2 ) FromEq. loVc Squaring, a' C 4 2 + = & 2 C 3 2 + ? = j , a 2 a 2 (a 2 fr 2 ) &~ 2+ 6 2 a 2 C 4 2 x* C, a . /a 2 -6 2 i (3) From this general equation one can see that the ratio of Ct to C" 4 is equal to the ratio of C\ to C 2 only when the product C 4 x is large. Inas- much as C is the capacity of the condenser being measured we can increase the product only by working with dielectrics of small conductivities, that is of large values of x. In other words, it is possible to obtain a greater sensitivity by making the ratio of the ratio condensers greater than 1; however, this cannot be done for liquids having appreciable conductivity. The effect of the introduction of the maximum conductivity of the Mangani resistance tubes shunted around an air condenser was studied. As shown by the following observation, no appreciable shifting of the mini- mum resulted. c. 6. a-b. Ai^ condenser alone 1488 321 1167 Air condenser plus maximum conductivity of re- sistancetube 1498 330 1168 The same results were obtained when the dielectric cell was used. Dielectric cell alone, c. 6. a- 6. Empty 1636 1588 48 Filled with ether 1701 1523 178 Dielectric cell plus maximum conductivity of resistance tube, Empty 1633 1585 48 Filled with ether 1700 1522 178 In all measurements of dielectric constants only those liquids were meas- ured whose conductivity could be balanced out with the tested Mangani solution resistances. The condensers in the ratio arms were now set at 90, i. e., at a ratio of 1:1, condensers Ci, Qj, and C 4 were sealed, Ca was locked into position and the scale on Ca was calibrated by filling the dielectric cell with the above liquids. The calibration curve is given on the chart with the curves for the dielectric measurements. 13 CALIBRATION DATA, Liquid. D. C. a. b. a-b. Carbon tetrachloride 2.25 1268 1160 108 Ether 4.35 1320 1115 205 CfiH 6 + CeHeNOa 15.9 1380 860 720 Alcohol 25.8 1795 640 1155 The following tables give the results of the dielectric measurements of the different mixtures with interpolation values from the curves. The points on the calibration curve were re-checked between measurements so as to assure no change in the values of the bridge. The liquids were not allowed to stand exposed to the air during a measurement, because in some cases the conductivity increase due to the absorption of water vapor from the air was such as to introduce an error in the observed value of the capacity of the dielectric cell. The conductivity of alcohol was observed to increase considerably upon exposure to the air for a few seconds. At the end of a half hour or less the conductivity had increased beyond that which could be balanced out with the maximum conductivity of the Man- gani resistances. DIELECTRIC CONSTANTS OF MIXTURES OF BENZENE IN ETHYL ALCOHOL. Dielectric constant. 20.6 23.2 25.8 DIELECTRIC CONSTANTS OF MIXTURES OF ETHER IN ALCOHOL. Alcohol % Dielectric by weight. constant. 80 20.6 90 23.2 100 25.8 DIELECTRIC CONSTANTS OF MIXTURES OF CARBON TETRACHLORIDE IN ALCOHOL. Alcohol % by weight. Dielectric constant. Alcohol % by weight. Dielectric constant. Alcohol % by weight. 2.28 40 10.8 80 10 4.3 50 13.1 90 20 6.5 60 15.5 100 30 8.6 70 18.0 Alcohol % by weight. Dielectric constant. Alcohol % by weight. Dielectric constant. 4.35 40 10.9 10 5.7 50 13.1 20 7.2 60 15.5 30 8.9 70 18.0 Alcohol % by weight. Dielectric constant. Alcohol % by weight. Dielectric constant. Alcohol % by weight. Dielectric constant. 2.25 40 14.5 80 22.6 10 5.4 50 17.0 90 24.2 20 8.6 6' 19.1 100 25.8 30 11.7 70 20.9 Summary. 1. A bridge method for the measurement of dielectric constants is described. 2. Preliminary measurements of the dielectric constants of mixtures of ethyl alcohol and benzene, ethyl alcohol and ether, and ethyl alcohol and carbon tetrachloride are given. BIOGRAPHY. John Fitch King was born in Ohio, October 13, 1894. His early educa- tion was received in the public schools of Youngstown, Ohio. His pre- paratory work for college was done in Rayen School in Youngstown. He attended Oberlin College and the University of Wisconsin and received the degree of Bachelor of Arts from Oberlin College in 1917. In the fall of 1917 he was enrolled as a student in the graduate department of chem- istry of Johns Hopkins University. February, 1918, he enlisted in the U. S. Army and was stationed at the University laboratory in research on war gases. The following school year was spent at Harvard University where he received the degree of Master of Arts. In the year 1919-1920 he returned to the Johns Hopkins University. He was appointed In- structor of Chemistry in the University September, 1920. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL PINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO SO CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. I935 3nffl^Q / OCT 31 1935 vwjan OJ/Q ) C ^ 3U ** JAM 1QCQ JM!X ^ o IJOJ r . Sj *Hfe ->., : V Mi JAN 2 TQ46 ... '.-n^f 26FebDEAD LD 21-100m-7,'33 Binder Gaylord Bros. Makers Syracuse, N. Y. PAT. JAN 21, 1903 YC 1106 UNIVERSITY OF CALIFORNIA LIBRARY '. *