A SIMPLE APPARATUS for MEASURING the DIELECTRIC

CONSTANT of NON- CONDUCTING LIQUIDS

BOYD E. HUDSON AND MARCUS E. HOBBS

Duke University,Durham. North Carolina

Two of the more interesting applications of dielectric constant data are the determination of the values of dipole moments and the detection of intermolecular formations in mixtures. The apparatus described .is capable of in- vestigating these jields with reasonable precision. Line drawings of wiring circuits of the receiver and oscillator are giwen. The heterodyne bent, between a broadmst carrier wave and waves, from the oscillator, i s employed to

detect constant capacitance i n the measuring circuit. The apparatus has been used quite successfully by stu- dents i n an elementary physical chemGtry laboratory. The dipole moment of nitrobenzene and the dielectric con- stant of ethyl ether-chloroform mixtures were determined. The results are in good agreement with accepted values. Operations during a measurement are shown to be ex- tremely simple.

T HE increasing importance of a knowledge of dielec- physical discussions of the matters involved. The tric constants of substances is evidenced by the measurement of the dipole moment is dependent on the large number of measurements that have appeared Clansius-Mosotti relation with the interpretation De-

in recent literature. Several methods have been used byes has given it. The equation is in making these measurements, but probably the most precise are the methods based on the heterodyne beat d ( 2 % ~ (a + &) orinci~le.

f = . + 2 d 3

In designing an apparatus for the measurement of In this equation P is the molar polarization, r the dielec- the dielectric constants of liquids one must decide tric constant, M the molecular weight, d the density, what range of constants are to be measured, and what N the number of molecules per mole, or the polariza- the nature of the measured $stances are, other than bility, or the induced moment per molecule per unit simply their dielectric property.' Since the Present field strength, N the dipole moment, k the Boltzman apparatus is designed for non-cdhducting liquids, i t energy constant, and T the absolute temperature. may be used for materials of dielectric constants within The use of the dielectric constant in detecting inter- a range of 2 to 7.' This class of Pure substances and molecular formations in liquids has been employed ex- solutions in which they are the solvents have been the tensively by Earp and Glasstone.l Using evidence from most extensively investigated of all liquids. Dielectric dielectric constant measurements these authors find constant data have a number of applications of which there is probably a hydrogen bonding between trihalo. two of the more interesting are the detection of the gen methanes and such substances as ethers and ke- presence of dipoles and the detection of the formation tones. of intermolecular compounds. For details of the The purpose of the present paper is to describe an measurements of dipole moments reference may be apparatus capable of investigating with moderate pre- made to an excellent elementary treatment given by cision the two phases of study mentioned above, and to S i d g ~ i c k . ~ Dole4 and Mack and Frances give good 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 con- several properties of the materials ' GEMANT. "Liquid dielectrics." John Wiley & Sons, Inc., staut values of approximately one per cent. absolute, New York City, 1933, pp. 1-9. and one-half of one per cent. relative precision. Since

S~GWICK, "Covalent link in chemistry," Cornell University the apparatus is used as an exploratory research too], Press, Ithaca, New York, 1933, Chap. V.

4 DOLE, "Experimental and theoretical chemistry," M C G ~ W - and in the l a h o r a t o ~ of elementary physical chemistry, Hill Book Co., Inc., New York City, 1935, Chaps. XI, XII. -

6 MACK AND FRANCE, "Laboratory manual of physical chem- ' DEBYE, ''Polar molecules," The Chemical Catalog Co ... istry," 2nd ed., D. Van Nostrand Co., Inc., New York City, New Pork City, 1929, pp. 27-35. 1934, pp. 208-16. EARP AND GLASSTONE, J. Ckem. Soc.. 1935, 1709.

366

OSC.

FIGURE 1.-WIRING DIAGRAM OP RECEIVER CIRCUIT T,, Meissner midget ant- coil, 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 trans- former (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; Ca and Cs, 500 MMa. mica; C8 and C,, 0.01 MPD. 400 v. tubular; C, Cm and CU, 0.25 MaD. 400 v. tubular; CIz and CI8, 8 MFD. 550 v. dry electrolytic. Re- sistors 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 oscilla- tor. Otto and Wenzkes have used this principle with apparently excellent results. The condition of main- taining a constant capacitance in the measuring circuit is the most commonly used method in such measure- ments. 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.

RECEIVER

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 -

OTTO AND WENZKB, Ind. Eng. Chem., A n d . Ed., 6,187 (1934).

amplifying action, it serves as a mixer for the oscilla- tions 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 pres- ence 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.

OSCILLATOR

The oscillator employed an RCA 6J7 in an "electron coupled" circuit. The screen grid is by-passed to ground and effectively shields the frequency determin- ing portions of the tube. The alternating radio fre- quencymrrent which reaches the plate affords a means

of coupling which leaves the frequency determining If C, is chosen as 220 MMF. and the parallel condenser portion of the tube virtually independent of voltage, the same, one may use the following specifications for load, and disturbances in the plate circuit. The wiring the inductance if the tuning frequency is to be 1500 diagram of the oscillator and specifications for its parts kilocycles. The coil should be close-wound on a fiber are given in Figure 2. form 2.54 cm. diameter using 42 turns of No. 25 D.S.C.

An essential feature of the oscillator is the National copper wire. The tap is made a t twelve turns from one micrometer dial mounted integrally with the tuning end. The entire oscillator assembly, excepting the condenser C,. The condenser is a straight line capacity measuring condenser, was mounted inside an aluminum

C A B L E TO I

R E C E I V E R I

FIGURE 2.-WIRING DIacnm 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. '/l watt; 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 Co represents nearly its maxi- mum 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

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 pre- viously 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 capac- ity is determined by setting C, in its minimum position and finding the reading on C, that gives the variable 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 COB measures the capacity change in CL.'O A measured volume of the liquid is now intro- duced, 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 measuring condenser proper. The dielectric constant is then given by (if air = 1): c

6 = ACO (liquid)

ACo (air)

This result will not be highly accurate, but even neglecting a calibration of C, it is found to yield good results.

RESULTS

This method of measurement has been applied to mixtures of ethyl ether and chloroform and to the de- termination 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.

shows the dielectric constant results of three students on the chloroform-ether mixtures.

TABLE 1

Studrnls A B

4.34 4.33 5.76 5.78 5.93 5.86 5.61 5.52 4.80 4.80

The results have been corrected to 20°C. using the temperature coefficient found by Coop" for this mix- ture. 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.

TABLE 2

Molar

The method of calculating p is the' same as usually employed for solution measurements a t one tempera- ture. No account has been taken of the atomic polari- zation term. The agreement between these values and those obtained by some investigators using research apparatus is shown in Table 3.

TABLE 3

A ~ l h o l p X 10" 8.8.0.

Jenkins13 3.94 Chang- 3.82 Tiganik" 3.97 Williams'* 3.90 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):

'

18 CHANG, J. Chinesc Chem. Soc., 1 , 107 (1933). " TIGANIK, 2. Physik. Chem., B13, 425 (1931). " War.r*~s. 3. Am. Chem. Soc.. 50. 362 (1928). ---- - ~- . . ' 6 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.

The errors in the present case are surely two to three times the precision estimated by the other investigators in their work. The materials used were of u.S.P. grade, and in the case of benzene had been dried by Drierite and distilled. The density values used in the student calculations were obtained by interpolation from those given by Tiganik.14 The temperature coefficient of density change with temperature was taken as -0.0011 gm./~c./~C. This approximation is quite good enough for student determinations, and affords a real economy in time necessary to perform the experiment. There is the additional value of acquainting the student with the use of the data from the literature, and the use of

permissible approximations in applying the data to particular calculations.

SUMMARY

The apparatus described has been shown capable of moderately precise dielectric constant determinations. Its construction is simple and relatively inexpensive. The use of the equipment by students in elementary physical chemistry has proved entirely satisfactory. With proper calibration i t is capable of being used as an exploratory research apparatus. The operations during a measurement are exceptionally simple and consume little time.