M. G. Brown and D. J. T. Hill University of Queensland st. Lucia, Queensland, Australla
A Beat-Frequency Oscillator for Capacitance Measurements
The measurement of dipole moments of polar molecules in solution is an instructive experiment for an undergraduate physical chemistry course. A simple and convenient method involves the measurement of capacitance using a beat-frequency oscillator and a standard variable capacitor. The beat-frequency oscillator described employs solid state and integrated circuit components and has a stability offering capacitance resolution to *0.005 pF, making it suitable for use in both research and undergraduate laboratories. Apparatus employing thermionic tubes has been described by Jen-Yuan Chien (1) and others. One of the difficulties associated with the accurate performance of tube-type heat-frequency oscillators, is to isolate sufficiently the two oscillating circuits in order to avoid "pulling" or locking-in as their difference in frequency approaches zero. Isolation usually requires that the oscillators be separately shielded and that care be taken to prevent mutual coupling of the oscillatom. By using inexpensive solid state devices in a straightforward layout and with no additional shielding, a simple beatfrequency oscillator, free of lock-in, has been produced. Constructional information is given together with details of an undergraduate laboratory experiment. Apparatus
A schematic diagram of the apparatus is shown in Figure 1. The choice of oscillator frequency for a beatfrequency oscillator to be used in measuring dipole moments in solution, has been reviewed by Thompson
4 Figure 1.
Schernotic of brot-frequency oscillator for tho measurement
of copacitonre.
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(2) and will not he discussed here. The operating frequency of the oscillators is 500 kHz. The resonant frequency of the variable frequency oscillator is at all times adjusted to exactly that of the fixed frequency (crystal) oscillator by means of the standard variable capacitor. Correct adjustment is recognized with the aid of headphones and a center-zero microammeter, when the differencefrequency is zero. The differencefrequency is produced by applying the outputs of the oscillators to a mixing circuit. The maximum and minimum values of the standard variable capacitor place a limit to the maximum value of capacitance that may he measured by direct substitution. The accuracy of measurement is determined by the stability of the oscillators, the degree of precision to which the frequency of the variable frequency oscillator may be set and re-set, and the accuracy and resolution of the standard variable capacitor. Description
The mixer used in the apparatus is a dual gate MOSFET (3). Owing to the mutual isolation of the two inputs of this device, coupling between the output circuits of the oscillators can be made low. Optimum input to each gate of the mixer from the oscillators is approximately 1 V peak. The drain circuit of the mixer is resistive and consequently the output of the mixer, which is fed to an integrated circuit operational amplifier, will include the frequencies of both oscillators and the sum of their frequencies as well as their difference. Since only the difference frequency is required, C l l , C12, and R13 (refer to Fig. 2) are included to form a low pass filter. With the value of the mixer imputs as above and a difference frequency of 1 kHz, the input to the amplifier a t that frequency is 0.25 V peak and the voltage at 500 kHz is less than 0.005 V peak. During operation of the apparatus, adjustment to the zero difference frequency condition is indicated initially and approximately by headphones and finally and exactly by a center-zero microammeter. External control of amplifier gain is not considered necessary but it is preset by the feedback resistor R16. For the value of R16 shown in Figure 2, approximately 5 V
Table 1.
Difference Frequency Indication Characteristics of Headphones and Meter Cornbination
Difference frequency (He) ~,
Output voltage (Pin 6)
1000 500
8 8
200
R
Circuit diagrom of 5 0 0 kHz beat-frequency orcillotor
3 3 kohmr resi9tor. 1 0 kohm 1 8 kohm 4 . 7 kohm 1 kohm 2 . 2 kohm 1 0 0 ohmr 5 . 6 kohm 4 7 k0hm 2 2 kohm 4 4 0 kohm 1 . 5 kohm 1 2 0 ohm 3 3 0 ohm
0.1 PF' Preret variable 1 0 0 pF to 6 5 0 pF 0.01 pF 0.0047 pF 0.033 pF 0.0033 pF 220 F .
f250 pA
3N141 tranlirtar pA709C operation01 amplitler BYX22 diode (4 off1 BZY95C12 Zener (1 2 V.) 5 0 0 kHz cryrtd Coil Ll 12 13
Winding details
Wire
D.C. center-zero meter 4k ohmr magnetic headphones Fuse line voltage to 25V power transformer SPST switch
Wound on
3 6 turn. ( t ~ t d l center-tapped 6 turns 4 8 turns Itotal) tapped at 1 8 turns from 12.5 V end 6 turn; 3 4 6 6 5 S.C.E.
peak drive is supplied t o the headphones and this results in an amply loud acoustic output,. The capacitor C16 bypasses all frequencies except those below the low frequency limit of the headphones and thus undue stress or overload of the meter is avoided. Table 1 shows the very satisfactory overall sensitivity of indication by the headphones and meter combination. At a difference frequency of 0.5 Hz there is no tendency for locking-in of the oscillators to occur, hut the wave shape a t this frequency is distorted. The 500 kHz fixed frequency oscillator is crystal controlled, the circuit of which is similar t o that described by Nowicki (4). Stability tests, which were conducted over periods each of 4 hr duration, showed
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that the frequency, as monitored on a Hewlett-Packard frequency counter type 5244L remained within +1 Hz. The variable frequency oscillator circuit is due to Sulzer (5). The operating frequency is 500 kHz when the standard variable capacitor which is connected via about 75 cm of co-axial cable of capacitance approximately 45 pF, indicates approximately 900 pF. When monitored similarly to the fixed frequency oscillator above, and for similar test periods during which the ambient temperature varied as much as +Z°C, the frequency remained within *40 Hz. More importantly however, since capacitance measurements can he made reasonably quickly, the short term stability was shown to be better than 1Hz/min. The standard variable capacitor used with our apparatus is a General Radio type 1422CB, the dial scale of which may he read. to 0.04 pF. A setting of zt1.0 pF different from the value required for zero frequency output results in an output signal of approximately 250 Hz. Thus it will he seen that the setting accuracy of the apparatus would allow the use of a standard variable capacitor which is accurately readable to a tolerance several times smaller than 0.04 pF. Construction Details
The circuit is shown in Figure 2 and component values are listed beneath it. The complete circuit, less power supply, is wired on a 4 in. X 43/4 in. sheet of Lektrokit matrix board. Figure 3 shows the layout adopted. The two oscillators are placed at opposite IC Rl8
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Meter indication
x
inn
Figure 2.
Acoustic out~ut
~4
\
L1
C15 R4 R5 R 6 C7 C5
I l \ l / /
C 8 R 7 R10 0 3 C11 R12 C10
L2 Figure 3.
Components layout of 5 0 0 kHz beat-frequency oscillator.
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corners of the board and feed their signals to the mixer \vhicli is located towards the center. Note that the variablc frequency oscillator output should conrtect to gateNo. 2 (i.e., pin &To. 2) of t,he3N141mixer. The coils are woutid on ferrite pot core assemblies, and they should be carefully waxed prior t o assembly to ensure mechanical stability as well as moisture exclusion. Capacitor CG is an adjustable preset and when set t o a part,icular value the crystal oscillator output will be greatest. Slight adjustment t o increase capacitance will cause the oscillation to cease whereas adjustment t o decrcasc capacitance d l effect a gradual reduction in output before the point of cessation of oscillation is reached. Correct adjustment setting is slightly down the slope of gradual reduction from peak output. I t should be possible t o set this adjustment to provide 1 V peak a t gate KO. 1 (i.e., pin KO. 3) of the mixer.
Table 2.
Typical Results for Chlorobenzene in Benzene at 25'C
Propert,y
Experimental value
Literature value (10)
bensene benzene Po2, chlombensene Pm chlorobensene chlo~.obenaene
2.270 zt 0.001 0.87351 f 0.00007 g e m P 81.6 zt 2.0 cm3 mole-' 31.2 om3 mole-' 1.57 zt 0.06 1)
2.272 0.87370 g c m P 82.8 cma molecL 31 c m ' male-' 1.59 U
r p
Student Experiment
For undergraduate laboratory experiments the solution cell used ~ v a sof a design similar to that described by Shoemaker and Garland (6). The experimental techniques employed and the method used to calculate the dipole moment are essentially those described by Daniels e t al. (7). We have found that a student working alone is able to perform all the experimental work required t o calculate the dioole moment of one nolar substmce in solution in one 3-hr laboratory period. Students are assigned different projects, so that the class as a whole studies solutions of chlorobenzene, o-dichlorobenzene and mdichlorobenzene in a variety of solvetits (for example benzene, n-hexane, and cyclohexane). I n a subsequent seminar period the data obtained by the class are discussed, and various calculations are made using the combined data. The dipole moments of the gaseous solute molecules are estimated using the empirical equation suggested by Smyth (8) r, = w
+ cw (a - 1)
where p, is the dipole moment obtained from measurements in solution in a solvent of dielectric constant ct, and po is the dipole moment of the gaseous solute molecule. The dipole moments of o- and m-dichlorobenzene can be predicted from the dipole moment of chlorobenzene, and used to demonstrate that the benzene molecule is planar. The relatively low dipole moment of chlorobenzene as compared with, say, t-butyl chloride is discussed in terms of resonance, and the relative contributions of t,he various struct,uresestimated alona t.he lines described by Smyth (9). A typical set of results obtained with the inst,rument, described above for solutions of chlorobenzene in benzene a t 25'C are shown in Table 2 and Figure 4. The individual dielectric constants were reproducible to better t,hm 0.0470. The density measurements were ~~
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Figure 4. The concentrotion dependence of the dielectric constant a n d t h e density for mlutions of chlorobenxene in benzene.
made pycnometrically and arc accurate to about one part in lo4. This experiment has proved to be one of the most successful in our second year laboratory coursc. I t is highly rated by str~dentsfor its interest and application t o their study of intermolecular forces. Literature Cited
I41 Nowscrr. J. R., Mvllnrd Tech. Cammun., 4 . 250 (19591. (51 Sutzen. P. G., "Selected Semiomduotor Circuits Handbook," John Wiley N Sons, Ino.. New York. 1960,p. 5-14. (61 S n o ~ m x s n 1). , P.. AND O A R L A NC. ~ . W., "Experiments in Physical
Chemistry," McGre.r\--HiilI3ook Co.. New York, 1961,p. 281. (71 DANIELR. F., WILLIAMS.J. W.. IIENDER.P.. AND COBNWALL. C . D. "Experimental Pilysicai C1,emistry." (6th Ed.). hleOra>$,-Uill. Book Co.,New York. 1962, p. 212. (81 S u r m . C. P.. "Dieleotrio nehavior and Structure." hlecrsiv-llill I h o k Co.. New York. 1966. 0 . 226. (9) SYITII,C. P.. p. 254. (10) LF.F i v n ~R. , J. W., AN" RUSSELL, P., 3. Chem. Soc., 491 (1986)
