A SIMPLE APPARATUS for MEASURING the DIELECTRIC CONSTANT of NONCONDUCTING LIQUIDS BOYD E. HUDSON
AND
MARCUS E. HOBBS
Duke University,Durham. North Carolina
Two of the more interesting applications of dielectric detect constant capacitance i n the measuring circuit. constant data are the determination of the values of dipole The apparatus has been used quite successfully by stumoments and the detection of intermolecular formations dents i n a n elementary physical chemGtry laboratory. in mixtures. The apparatus described .is capable of in- The dipole moment of nitrobenzene and the dielectric convestigating these jields with reasonable precision. Line stant of ethyl ether-chloroform mixtures were determined. drawings of wiring circuits of the receiver and oscillator The results are in good agreement with accepted values. are giwen. The heterodyne bent, between a broadmst Operations during a measurement are shown to be excarrier wave and waves,from the oscillator, i s employed to tremely simple.
T
HE increasing importance of a knowledge of dielectric constants of substances is evidenced by the large number of measurements that have appeared in recent literature. Several methods have been used in making these measurements, but probably the most precise are the methods based on the heterodyne beat orinci~le. In designing an apparatus for the measurement of the dielectric constants of liquids one must decide what range of constants are to be measured, and what the nature of the measured $stances are, other than simply their dielectric property.' Since the Present apparatus is designed for non-cdhducting liquids, i t may be used for materials of dielectric constants within a range of 2 to 7.' This class of Pure substances and solutions in which they are the solvents have been the most extensively investigated of all liquids. Dielectric constant data have a number of applications of which two of the more interesting are the detection of the presence of dipoles and the detection of the formation of intermolecular compounds. For details of the measurements of dipole moments reference may be made to an excellent elementary treatment given by S i d g ~ i c k . ~Dole4 and Mack and Frances give good
physical discussions of the matters involved. The measurement of the dipole moment is dependent on the Clansius-Mosotti relation with the interpretation Debyes has given it. The equation is
Hill Book Co., Inc., New York City, 1935, Chaps. XI, XII. 6 MACK AND FRANCE, "Laboratory manual of physical chemistry," 2nd ed., D. Van Nostrand Co., Inc., New York City, 1934, pp. 208-16.
DEBYE, ''Polar molecules," The Chemical Catalog Co... New Pork City, 1929, pp. 27-35. EARPAND GLASSTONE, J. Ckem. Soc.. 1935, 1709.
d( d
f = . + 2
23% (a ~ + &)
In this equation P is the molar polarization, r the dielectric constant, M the molecular weight, d the density, N the number of molecules per mole, or the polarizability, or the induced moment per molecule per unit field strength, N the dipole moment, k the Boltzman energy constant, and T the absolute temperature. The use of the dielectric constant in detecting intermolecular formations in liquids has been employed extensively by Earp and Glasstone.l Using evidence from dielectric constant measurements these authors find there is probably a hydrogen bonding between trihalo. gen methanes and such substances as ethers and ketones. The purpose of the present paper is to describe an apparatus capable of investigating with moderate precision the two phases of study mentioned above, and to show some results that have been obtained. The ap'If the substances are conductors certain modifications of paratus is not presented as an instrument for precise method must be made so that the results are not mixtures of measurements, but will certainly afford dielectric conseveral properties of the materials ' GEMANT."Liquid dielectrics." John Wiley & Sons, Inc., staut values of approximately one per cent. absolute, and one-half of one per cent. relative precision. Since New York City, 1933, pp. 1-9. S ~ G W I C"Covalent K, link in chemistry," Cornell University the apparatus is used as an exploratory research too], Press, Ithaca, New York, 1933, Chap. V. and in the l a h o r a t o ~ of elementary physical chemistry, 4 DOLE,"Experimental and theoretical chemistry," M C G ~ W -
366
'
OSC.
FIGURE 1.-WIRING DIAGRAM OP RECEIVER CIRCUIT T,,Meissner midget antcoil, 150-550 meters, with 365 MMP. tuning condenser (Whalesale Radio Service Company No. K10046). TB.Meissner midget R.F. coil to match TI(W. R. S Co. No. K10047). Ts. Power transformer (W. R. S. Co. No. K5635). LI, Filter choke 10 henries at 50 ma. Condensers as follows: C, and C p 2 gang 365 m a . tuning with trimmers; Cs and C,, 0.1 MaD. 200 v. tubular; Caand Cs,500 MMa. mica; C8 and C,, 0.01 MPD. 400 v. tubular; C,Cm and CU,0.25 MaD. 400 v. tubular; CIzand CI8,8 MFD. 550 v. dry electrolytic. Resistors as follows: Rr,500 ohm. '/. watt; Rs,400 ohm, watt; Ra and Re,100.000 ohm, 1 watt; R4,1 megohm, watt; RE.3000 ohm, '12 watt; R,,25.000 ohm, 1 watt; &. 1000 ohm, 10 watt wire wound. .+
it is of suflicient precision. The condiiion of constant capacitance in the measuring circuit is detected by the beat note between a local broadcast station carrier wave, and oscillations generated by a variable oscillator. Otto and Wenzkes have used this principle with apparently excellent results. The condition of maintaining a constant capacitance in the measuring circuit is the most commonly used method in such measurements. The small receiver and variable oscillator are made from inexpensive parts which may be obtained from any of the wholesale radio houses. The total cost of all parts excluding assemblying time and a small amount of desirable but not necessary machine work is not greater than thiiy-five dollars.
amplifying action, it serves as a mixer for the oscillations from the variable oscillator and the carrier wave. The beat note between the two oscillations is fed to the RCA 6C5 which amplifies the note to the audible range. The rectifier filter system is not elaborate as the presence of some alternating current hum in the receiver output is not objectionable. Figure 1 shows all wiring details of the receiver. The specifications on all parts are complete. The receiver was built on an old chassis; consequently many of the necessary holes were already bored. Such items are usually available at local radio repair shops. A great saving in time may be effected by having some person familiar with such work assemble the parts.
RECEIVER
OSCILLATOR
The receiver consists of one stage of tuned radio frequency using an RCA 6K7, a converter stage using an RCA 6L7, and an audio stage using an RCA 6C5. The 6L7 is a multigrid tube and, in addition to its OTTOAND WENZKB, Ind. Eng. Chem., A n d . Ed., 6,187 (1934).
The oscillator employed an RCA 6J7 in an "electron coupled" circuit. The screen grid is by-passed to ground and effectively shields the frequency determining portions of the tube. The alternating radio frequencymrrent which reaches the plate affords a means
of coupling which leaves the frequency determining portion of the tube virtually independent of voltage, load, and disturbances in the plate circuit. The wiring diagram of the oscillator and specifications for its parts are given in Figure 2. An essential feature of the oscillator is the National micrometer dial mounted integrally with the tuning condenser C,. The condenser is a straight line capacity
C A B L E TO RECEIVER
If C, is chosen as 220 MMF. and the parallel condenser the same, one may use the following specifications for the inductance if the tuning frequency is to be 1500 kilocycles. The coil should be close-wound on a fiber form 2.54 cm. diameter using 42 turns of No. 25 D.S.C. copper wire. The tap is made a t twelve turns from one end. The entire oscillator assembly, excepting the measuring condenser, was mounted inside an aluminum
I I
FIGURE 2.-WIRING D I a c n m OF OSCILLATOR CIRCUIT LI, see text. Condensers as follows: CL, 50 m. National transmitting type No. TMSA-50; Co, Cardwell X T 220 P.S.transmitting type equipped with National "Micrometer" dial; C., Cardwell X T 220 P.S.transmitting type; CI and C2, 100 MMP.mica; C8,0.1 MPD. 400 v. tubular; C, and Cs,0.1 MPD. 200 v. tubular. Resistors as follows: RL,1 megohm. '/lwatt; R2,8000 ohm, 1 watt; Rz,20,000 ohm, 1 watt; R,;35,000 ohm, 1 watt; R6, 350,000 ohm, 1 watt.
type, and in conjunction with the dial mechanism gives good linearity from 50 to 450 divisions of the dial, the scale of which extends from 0 to 500 divisions. The inductance L, was so adjusted that, with the measuring condenser C, set a t minimum capacitance, a beat note between the oscillator and the 1500 kilocycle carrier wave was obtained a t a dial setting of C, of about 450 divisions. This setting of Corepresents nearly its maximum capacitance. The necessity of critical adjustment of inductance L is obviated by employing a variable conpensating condenser in parallel with C., The compensating condenser is shown as C, in Figure 2.
box ten inches by eight inches by seven inches with a one-sixteenth inch wall thickness. MEASURING CONDENSER
The liquid condenser, C,, was mounted on a circular brass plate one fourth of an inch thick. The ground lead from the oscillator, a five-eighth inch copper pipe, was soldered to this plate. The high potential lead was made by running a one-eight inch brass rod through holes in the center of polystyrene resin discs and placing this assembly inside of the five-eighth inch copper tube. The bottom and sides of C, were made by cutting a
three and one-half inch section of three and one-half inch inside diameter brass pipe and soldering a plate on one end of the section. The other end of the pipe was drilled and threaded in three places so as to receive screws which passed through the top plate.g The shaft of the rotor extended up through the top plate, and to the shaft was attached a horizontal three-eighth inch square aluminum rod two and one-fourth inches long. Stops were arranged by means of studs screwed into the top plate. The axm could be stopped a t intervals of GO0, 120°, or 180° rotation. This method enables one to make measurements with the maximum sensitivity allowed by the variable capacity in C,. If the dielectric liquid has a large constant the rotation of C, must be such that the change in capacity can be measured by changing Co. MEASUREMENT
shows the dielectric constant results of three students on the chloroform-ether mixtures. TABLE 1 Studrnls
A
4.34 5.76 5.93 5.61 4.80
B 4.33
5.78
5.86
5.52 4.80
The results have been corrected to 20°C. using the temperature coefficient found by Coop" for this mixture. The actual temperatures of the measurements were 27.8"C. for A , 23.0°C. for B, and 24.5"C. for C. The values obtained agree well with those found by Coop." The materials used were of U.S.P. grade, and no purification other than drying with calcium chloride and a simple distillation was undertaken. A discussion of the possible significance of the curved nature of the graph of e against mole fraction is given by Earp and Glasstone.' The results obtained for the nitrobenzene solutions are given in Table 2.
The mechanics of a measurement are as follows. The rotation of CL is fixed by proper placement of the studs. The allowable rotation is determined as previously indicated. The capacity change in moving C,, from its minimum to the final position is determined with air in CL. The magnitude of the change in capacity is determined by setting C, in its minimum position TABLE 2 and finding the reading on C, that gives the variable Molar oscillator the same frequency as the carrier wave from the broadcast station. This condition is recognized by the absence of a heterodyne beat in the earphones if, with a slight change of Co in either direction, a beat is heard. The arm of C, is now moved to its maximum and then, to return to the camer wave frequency, Co must be changed to some new value. The difference between C, and COBmeasures the capacity change in CL.'O A measured volume of the liquid is now introduced, and the new value of the capacity change in C,, can be determined with the liquid present. The liquid volume should be sufficient to cover all parts of the The method of calculating p is the' same as usually measuring condenser proper. The dielectric constant is employed for solution measurements a t one temperac then given by (if air = 1): ture. No account has been taken of the atomic polarization term. The agreement between these values and ACO (liquid) 6 = those obtained by some investigators using research ACo (air) apparatus is shown in Table 3. This result will not be highly accurate, but even TABLE 3 neglecting a calibration of C , it is found to yield good A~lhol p X 10" 8.8.0. results. Jenkins13 3.94 This method of measurement has been applied to mixtures of ethyl ether and chloroform and to the determination of the dipole moment of nitrobenzene in benzene. The results were obtained by students in an elementary physical chemistry laboratory. Table 1 0
For corrosive materials a beaker may be mounted inside a
metal container, and the container grounded to the top plate. In such cases it would be very desirable to replace Cr. by a condenser made of monel metal, or stainles steel. This is approximately true as the capacity change involved here is so small that errors from inductance in the leads are l e s than 0.2 uer cent.
"
3.82
Chang-
RESULTS
3.97 3.90
Tiganik" Williams'* Present (aver.)ls
3.82
The difference between 3.82 and the other values is surprising only in so far as the difference is not larger.
COOP.Tram. Far. Soc.. 33. 583 (1937). JENKMS,Nature, 133, i06 (1934): '
CHANG, J. Chinesc Chem. Soc., 1 , 107 (1933). " TIGANIK, 2.Physik. Chem., B13, 425 (1931). 18
" War.r*~s.3. Am. Chem. Soc.. 50. 362 (1928). . . ----
-
~-
It is to be noticed that stud& >'has a poor measurement, having no measurement for the 0.0100 M.F. point. The average of E and F is 3.88. '6
The errors in the present case are surely two to three permissible approximations in applying the data to times the precision estimated by the other investigators particular calculations. in their work. The materials used were of u.S.P. grade, SUMMARY and in the case of benzene had been dried by Drierite The apparatus described has been shown capable of and distilled. The density values used in the student calculations were obtained by interpolation from those moderately precise dielectric constant determinations. given by Tiganik.14 The temperature coefficient of Its construction is simple and relatively inexpensive. The use of the equipment by students in elementary density change with temperature was taken as -0.0011 gm./~c./~C.This approximation is quite good enough physical chemistry has proved entirely satisfactory. for student determinations, and affords a real economy With proper calibration it is capable of being used as an in time necessary to perform the experiment. There is exploratory research apparatus. The operations during the additional value of acquainting the student with a measurement are exceptionally simple and consume the use of the data from the literature, and the use of little time.
