DIELECTRIC-CONSTANT APPARATUS FROM WAR SURPLUS
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H. BRADFORD THOMPSON and MAX T. ROGERS Michigan State College, East Lansing, Michigan
T H E measurement of electric dipole moments is of made by very slight alteration of the BC-221 freconsiderable value in studying the structures of mole- quency meter, available on the war-surplus market. cules, and is not an extremely complicated process. No change in the internal circuit is necessary; the A detailed discussion of the theory and the experi- conversion and use of the instrument should not remental procedures involved is given in Le Favre's quire any advanced knowledge of electronics. The monograph,' "Dipole Moments," and an introductory device thus obtained has also been used with a flexible discussion has been written by D a v i d ~ o n . ~The most n~rtnldinphrt~grn as a diffrrrntial n~anornrtrr. 2nd shottld he useful i l l othrr rncnsurtmrnts invol\,ing small capacitance changes.
THE HETERODYNE METHOD8
In the heterodyne method of measuring capacitance changes, widely employed in precise dielectric-constant work on nonconducting liquids, the capacitor to be measured is made part of the tuned circuit of a radiofrequency oscillator, as shown in Figure 1. The frequency, f, of this oscillator depends upon the sizes of the inductance, L, and the total capacitance, C , in this tuned circuit, as indicated by the equation 4ry2 LC = 1
MIXER
OSC.
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Fimre I. Hetaodgna Apparatus for Dielectric-constant Meemm-ments
commonly used procedure requires the measurement of the dielectric constants of a series of solutions of the compound in a nonpolar solvent such as benzene. Such measurements have become a part of the physical chemistry laboratory program in many colleges. The use of this type of experiment might be more widespread if equipment for the necessary dielectric-constant measurements were more readily available. A heterodyne-type capacitance measuring circuit for this purpose, . . . suitable for student or research use,. mav - be
If the total capacitance, C, consists of the "unknond' capacitor or experimental cell (inserted a t X in Figure 1)and a standard variable capacitor, any changes in the cell capacitance may be measured by determining the change in the standard capacitor which is necessary t o return the oscillator frequency to its original value. Accurate reproduction of the original frequency is accomplished by comparing the variable oscillator with a fixed-frequency oscillator, which is generally controlled by a crystal. By means of an electronic "mixer circuit," the heterodyne or "beat" frequency, equal t o the difference between the two oscillator frequencies (or between harmonics of thosefreqoencies), is obtained. When the oscillator frequencies (or harmonics) are nearly equal, the beat frequency will be in the audible range, and may be followed with earphones or a loudspeaker. By ;hanging the variable Eapacitor so as to obtain the lowest possible pitch, the frequency of the variable oscillator mav be made to match that of the crystal oscillator.
LE FBVRE,R. 3. W., "Dipol~>foments," 2nd. ed., Methuen and Co.., Ltd.., London., 1948. DAVIDSON, H. R., J. ~ H E XEUUC., . 27, 598 (1950). ~~~~~
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BC-221
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THE INSTRUMENT
The two radio-frequency oscillators and the mixer in the apparatus described above involve a fair amount of electronic circuitry, and the construction of such an DANIELS,F., 3. H. MATHEWS, 3. W. WILLIAMS, BTAL., "EXperimental Physical Chemistry," 4th ed., MoGraw-Hill Book Co., he., New York, 1949, pp. 238-41
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JANUARY, 1955
instrument for research purposes can take several months. However, the BC-221 frequency ?leter, used by the armed forces during the recent war, contains all 1 the circuit conlponents necessary; the only essential change is addition of a connection for a cable leading t o the experimental cell. This meter is still available, a t prices in the range of $85 t o $125, from a number of war-surplus houses. To make the uecessary alterations, the electronic portion of the BC-221 may he removed fr.om the carrying case by loosening the four large screws on the front panel and then pulling the panel forward. The placement of the connector for the experimental cell is shown in Figure 2. A type 83-II< coaxial connector is satisfactory for this purpose, and requires a S/8-inch hole whirh must be drilled in the front panel. The center or ungrounded terminal of this connector should be soldered to a short length of insulated ire, the other end of whieh should in turn he soldered to the stator (stationary portion) of the variable capacitor as shown in Figure 3. This converts t,he BC-221 to measurement of capacitance. Though no other changes are necessary, the user may find that certain additional alterations add to the convenience of the instrument. The most important of theee is the addition of a line-operated power supply. The BC-221 is normally powered by a 13,i-volt "B" battery and a set of four 1.5-volt cells providing a 6volt "A" supply. Thesc bat,teries are housed in a compartment reached from the back of the case. If the instrumcnt is to he in regular or continuous operation, frequent replacement of the batteries, especially of the 6-volt supply, may be necessary. Substitution of a storage battery for t,he four 1.5-volt dry cells is possibly the simplest solutiou to this problem; however, the construction of a line-operated supply may appear desirahle. The power requirements of the instrument are 10 milliamperes a t 100-150 volts d. c. and 1 ampere a t 6.3 volts a. c. or d. c. The circuit shown in Figure 4 is adequate and should cost about 97 to build. The power supply may he easily constructed to fit into the battery compartment of the instrument. On certain early models of the BC-221 frequency meter a slight change in internal circuitry must be made if an a x . 6.3-volt filament supply is to he used. In these models the d.-c. filament voltage was also used to supply the grid-bias potential for one vacuum tube. Whether a change will be necessary for a particular instrument may be determined by studying the circuit diagram found on the inside of the cover of the battery compartment. If the cathode circuit of the final (righthand) tube in the diagram resembles Figure 5A rather than 5B, it will be necessary t o disconnect the cathode from the Uament lead and reconnect it to ground through a 470-ohm resistor. Figures 5C and 5 0 show the bottom of the socket for a type 76 tube before and after this change. Though certainly not necessary, a second change in internal circuitry may prove convenient if a lineoperated supply is added. The BC-221 is provided
F i g u ~ e3 .
Internal C o n n e c t i o n for Conver-ion of BC-221 for Copacitan==Measurement
vith an interlock feature on the headphone jark so that when the phones are disconnected the power is turned off. This feature is valuable if the instrumeut is battery-powered, as the front cover cannot be closed ~ ~ i t h ounplugging ut the headphones, and the danger of excessive battery draiu OTX-ing to carelessness is reduced. However, if the inst.rument is line-operated this interlock feature may become a nuisance, since the instrument operates most satisfactorily~vhenallowed 60 warm up for an hour or so, and it may not he convenient t o leave the headphones connected during this period. Fortunately, the interlock feature is easily removed. By observing the switching action which takes place on the jack when the headphone plug is inserted and removed, one may find the switch terminals providing the interlock and short them vith a piece of hare wire. CELL CONSTRUCTION
The cell for use xith this instrument should be of such a size that the highest capacitance to be measured will be within the range of the variahle capacitor. The size of this capacitor in the partirular model of BC-221 used may be determined from the circuit diagram inside the hack cover. As an example, if benzene solutions having dielectric constants of 3 or less were to be examined and the size of t:he variable capacitor is 140 micromicrofarads, the air capacitance of the cell might well be 3 0 4 0 micromirrofarads. The co~lstructionof a glass cell has been described
Figvrr 4.
Line-onerated Power Supply
9 GROUND
GROUND A
B
Figure 5. Cinuit Chsngas for Line Operation
by Le FBvre,' and Davidsonz has described a cell equipped with a water jacket. The authors have recently designed a metal cell with Teflon spacers. The cell is best connected t o the instrument by a coaxial conductor with appropriate connector. The outer conductor or shield should be grounded, and should he connected t o the outer cylinder of the cell. In addition, this cable should he as short as possible and should not be moved during a measurement, as the capacitance between inner and outer conductors is included in the apparent capacitance of the cell. OPERATION
While it is beyond the scope of this paper to describe the entire process of dipole moment determination, stepwise instructions for operation of the instrument and determination of the capacitance change upon introduction of the sample solution t o the cell are given below. Before turning on the instrument, the operator should become familiar with the operation of the control with the graduated scale, which controls the variable capacitor within the instrument. (1) Turn on the instrument and allow it t o warm up.
JOURNAL OF CHEMICAL EDUCATION
(2) Set the function-selector switch to "Crystal Check" an$ the range switch t o "Low Range."& (3) Connect headphones a t the phone jack a t the lower left of the control panel. (4) Connect the empty cell to theinstrument. (5) Set the graduated dial a t the upper end of its scale (reading 50.000) and start slowly down scale until a loud, wide beat note is heard. Many different notes will be found as the dial is turned; the one selected for use during the measurement should be loud and broad enough that it may easily be distinguished from its neighbors. (6) Having found a suitable heat note, adjust the dial carefully until the lowest possible pitch is obtained. If the cell is dry and clean. and if the instrument has been allowed towarm up sufficiently, this pitch will not change with time. (7) Record the readings of the scales and vernier. (8) Slowly admit the sample to the cell, noting that the pitch of the audible note changes as the cell is filled. (9) By adjusting the dial, follow the beat note along the scale until the cell is filled and the note stops moving. (10) Again find the lowest possible note and record the scale and vernier readings.6 (11) After the cell is emptied and cleaned, the next sample may be measured by repeating steps 4 through 10. CALIBRATION
The two scales of the variahle capacitor with the vernier reading provide a total of 50,000 divisions. Unfortunately, this scale does not vary linearly with capacitance, so that a calibration curve must be constructed. Perhaps the simplest method of calibration is to connect a calibrated variable capacitor in place of the cell. The number of points necessary to accomplish the calibration will depend upon the accuracy desired in the results; the calibration curve is fairly smooth, thus simplifying the process. If desired, the variable capacitor may be calibrated without recourse to any external standard; this procedure depends upon the presence of a hundred or more audible heat notes throughout the range of the instrument. Each of these notes corresponds to a frequency a t which some harmonic (multiple) of the variable frequency oscillator is equal to some harmonic of the crystal oscillator, so that the variahle oscillator frequency is a rational fraction of the crystal frequency (one megacycle). Starting from the low scale readings
' These two controls remain in these nositions throuehout the measurements; it might even be advisable to remove these two knobs from their shafts to avoid careless changing of the dials and to simplify the appearance of the control panel. Unless the solutions have been maintained at the measurement temperature, sufficient time must be allowed for the sample to come to the temperature of the bath mrrrounding the cell before this final reading is made.
JANUARY, 1955
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and moving "up scale," the strongest and broadest audible signals correspond to ' / a , '/7, '/G, and I/, of one megacycle.' From the equation given above, the capacitance a t each of these points may be obtained. The weaker signals between these values may in turn be identified. For example, the strongest signal between the ones at '"/g'' and "'/I" will be a t a frequency of 2 / of ~ ~one megacycle; this will be about midway between the former two. To each side of "2/,6" will be and "3/12." The strengths of these signals decrease as the numerators of the fractions increase, thus aiding in identification. Signals such as are clearly audible if this many points are desired for calibration. The "spectrum" of audible beats between '''/s" and "'/7" is s h o m in Figure 6. This internal calibration cannot be made in terms of conventional capacitance units unless the size of the coil L in the tuned circuit is known. However, if the cell used is calibrated in terms of the arbitrary units selected for the calibration, this will not matter. Measurement of one known capacitance with this auoaratus will. of course., uermit calibration in terms -~~of micromicrofarads. a trial moment of_-.. of Lthis . apparatus, the dipole . .-I- .I.. As L - ~ C Q ~ Z ~:;:!acelate ::~ -.L:.:cE&te procedure for mezsurement of a dipole moment
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A.
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T h e note at
"'/4"
is beyond the scope of this paper; the method employed has been described by Halverstsdt and Kumler.' The internal consistency of the data was comparable to that obtained in this laboratory using published heterodyne dielectric-constant c i r c ~ i t r y . ~ Density of the solutions and the refractire index of the pure unknown are also necessary t o the calculations; the latter value is often approximated by summing the refractions of the bonds present. I n the present case the molar refraction from the measured refractive index was 33.225, while that obtained fram bond refractions was 33.216. The dipole moment of 1,2-ethanediol diacetate was found to be 2.82 D. The instrument may also serve as a differential manometer by observation of the capacitance between a flexible metal diaphragm and a fixed plate. I t mas thus possible to measure pressures of gases corrosive to mercury and other manometer liquids. An adapted BC-221 is being used in this manner with halogen fluoride vapors.
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may be off scale at the upper end.
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This work mas assisted by a grant from the Atomic Energy Commission. ~--
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' HAI~RSTADT, I. F.,
AND
W. D. KUMLER, J. Am. Cheiz:aoc;
64,2988 (1942). CHIEN,J.-Y., J. CHEX.EDUC., 24, 494 (1947).
