Dielectric Constant Meter for Kinetic Studies ROBERT C. AXTM4NK1 T h e Johns Hopkins University, Bultimore, M d . 4 recording heterodyne beat assembly was constructed for determining reaction \elocity constants by following small increments in the dielectric constant of the reaction medium. The project was undertaken to provide a precise means for measuring reactions in which systematic errors from the usual analytical procedures might easily obscure very sniall effects. In one study, a secondorder \elocity constant was determined ten times with an average deviation from the mean of only 0.1270, The method can be further refined for even greater accuracj The electronic circuit which provides for recording a null point bet\+een two oscillators might be useful for other types of kinetic measurements which do not use the dielectric constant as the indicating property.
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I
S PTLDYISG reaction velocities, workers in kinetics have
utilized a wide varietj- of experimental techniques such a3 polarimetry, spectrophotometry, interferometry, dilatometry, and conductivity. These methods give dynamic readings, as opposed to those obtained through analytical niet’hodswhere time lags occur. Even in dynanlic methods, however, it is seldom possible without extensive instrumentation to avoid errors arising from the psychological time interval bemeen the successive moments when the experimenter records a reading and notes the tinie. The word “dynamic,” then, is one of degree; it is the lack of truly dynamic methods that has limited study of fast reactions. Whereas the apparatus described here is limited to studies of nonaqueous and, in general, low dielectric constant systems, electronic devices applicable to aqueous systems but which measure conductance rather than dielectric constant have already been described (1, 5, 6). Jensen and Parrack’s instrument was suggested as a kinetic tool, but the data presented were limited to titration problems. Two fielde for which the piesent instrument shows promise are studies of the kinetics of ketoenol tautomerism and of yarious polymeriiation reactions, for in both cases the dielectric constant of the products may vary widely from that of the reactants. [Some time after this work 1 1 1 was completed, Burrell, Magury, and Melville (3) MlCROMETER published results on the polymerization of styrene obtained n-ith a recording capacitance bridge. These authors, however, treated the change in dielectric constant due to the reaction’s progress as a correction and instead followed the change in dielectric constant n-ith temperature that results from the heat of the reaction.] A third field in which there would be no limitation iniposed by the dielectric constant of the solvent is the study of gas reactions. Here practically any reaction might be measured, provided that there Tvas sufficient difference i n the dipole moments of the reactant and product gases.
micromicrofarad or a change of 0.0007% when the dielectric constant of a solution is 2. When the two oscillators reach a predetermined beat frequency, a second circuit, responsive only to the frequency, actuates a recording clock. Thus by continually setting the micrometer “ahead” of the reaction, the device will automatically record the times corresponding to the various settings. This arrangement in no sense gives absolute values for the dielectric constant, although relative values may be measured to a high accuracy. THE APPARATUS
Oscillators.
The fixed-frequency oscillator, the circuit for which a p ears in Figure 2, was a crystal-controlled Pierce oscillator. Tge crystal was a 1-blc. B T cut with a coefficient of 1 cycle per ’ C. near 25” C. The harmonic output of the crystal was very high, which proved useful in checking drift: the vari6SJ7
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1
1
1
ti/ssv
\-ariable-Frequency Oscillator bSH7
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A fixed-frequency oscillator is heterodyned with a variablefrequency oscillator, the frequency-controlling tank circuit of which is seen in the left of Figure 1. The usual standard capacitor is replaced by an ordinary micrometer spindle which screws into a cylinder. If, in a given system, the dielectric constant decreases as the reaction progresses, the decrease of capacity of the cell is compensated by manually screwing in the micrometer spindle and increasing the capacity of that component of the circuit. Since the micrometer may be read very accurately, very small increments in dielectric constant may be detected. I n the present construction, it is possible to observe differences of about 0.001
I d
Figure 1.
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PRINCIPLE OF THE METHOD
1
BUS
SO
able air capacitor, C-1, allowed small adjustments of frequency to coincide with standard marker signals put out a t 5 mc. by the National Bureau of Standards. These frequency checks were made with a communications receiver which formed an integral part of the entire assembly. Figure 1 shows the circuit for the variable-frequency oscillator, which is of the electron-coupled type. The tuned circuit consists of components which are temperature-compensated. This tuning element was removed from a U. S. Army Signal Corps BC-221 frequency meter, but similar units may be constructed ( 7 ) . The frequency range of the oscillator is 1.8 to 3.2 me., but it was used only at 2 me. in order to heterodyne it with an even harmonic of
1 Present address, Atomic Energy Division, E. I. du Pout de S e m o u r s Bi Co., Inc., -4rgonne National Laboratory, Chicago 80, Ili.
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A N A L Y T I C A L CHEMISTRY the fixed frequency oscillator. After a 2-hour warm-up period, the variable-frequency oscillator was extremely stable, matching the stability of the fixed-frequency oscillator. I n terms of the micrometer capacitor the stability was such that the null point of the tTso oscillators was constant t o 0.002 mm. (a few cycles per second). Both oscillators' heaters were operated from a &volt storage cell in order t o eliminate possible 60-cycle modulation. A 1% regulated alternating current high voltage sup ly was found to \)e steady enough for the plate supply of the fixex-frequency oscillator, but dry cells were used for the plate supply of the variable oscillator. The micrometer ca acitor was mounted on the side of an iron box (which containezboth oscillators) with only the spindle ex-
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Figure 3.
The entire cell had a capacity of approximately 350 nil. Imt might have been smaller (120 nil.) if a different type of capacitor had been used or if the volume above the capacitor had been eliminated. The cell was immersed in an oil-filled 5-gallon Pyres constant temperature bath regulated with a thyratron circuit, and mercury-toluene regulator t o =tO.0lo C. The cell was coiinected t o the variable-frequency oscillator with coaxial cable. Timing Circuit. The varying heat frequency comes from the receiver and goes through amplifiers and a limiter t o a band-pass filter, the output voltage of which is a rapidly decreasing function of the frequency, particularly betn-een 200 and 0 cycles per second. The output of this filter is then presented t o a full-ware rectifier which converts it t o a negative direct, current voltage, the level of which is agaiii inversely proportional t o the frequency. This negative voltage is applied as bias t o a fairly sensitive thyratron. When the frequency is sufficiently low, t,he thyrat#ron fires and causes a surge of plate current sufficient to actuate a relay and hence close anot,lier circuit in a recording clock which prints the time on a taDe t o 0.2 second. hlth&gh the 884 thyratron (see Figure 5 ) tires reproducit)ly M hen the grid voltage is within a volt or so of the necessary value, the frequency ua. rectifier output voltage is 80 steep a t the operating point that the 884 always fires a t the same frequency. Once the 884 has fired, the circuit is reset for the next reading h! momentarily depressing switch S 1. The clock, a Productograph, wa8 manufacUIGROYTER tured hy the Simplev Time Recording Co.
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xlicrometer Capacitor
tending outside. Details of the micrometer construction appear in Figure 3. The handle and outermost cvlinder were grounded to the box: The disk which holds the inner cylinder in place was machined from 0,025-inch Bakelite sheeting. h l l other parts were made of brass. except the micrometer itself. The micromet'er range was 2.5 em. anti could easily be read t o 0.002 mm. Amplifier. The beat frequency was detected in an ordinary coniniunications receiver. This arrangement overcomes the shortcomings of assemblies which directly couple the oscillatore in a mixing stage. The only coupling is through an antenna, inserted in the iron box. h phone jack on the receiver allowed transmission of the audio beat frequency t o (1) a loudspeaker, (2) an oscillograph, or (3) the timing circuit.. This permitted monitoring of t,he oscillat,ors' operat,ion and enabled the experimenter t,o follow the progress of the reaction aurally or visually in addition t.o t,he record made by the timing circuit,. Figure 4 is a block diagram of the ent.ire setup. Dielectric Constant Cell. The reaction chamber consisted of a fixed air capacitor with thirteen plates 3.8 X 4.4 em., spaced 2 mm. apart, insulated with ceramic, and placed inside a i2-mm. piece of Pyrex glass No. 7740 tubing. Kickel wire leads attached t o eit'her side of the capacitor were welded to short, heavy tungsten leads which were sealed into the side of the tubing. A small well under the capacitor allowed a glass-enclosed .4lnico rod t o act as a magnetic stirrer, Stirring was found necessary to effect a rapid mixing of reactants a t the beginning of experiments. A groundglass taper a t the top of the cell served as the opening through which the cell was filled and from which analytical samples were withdrawn.
EXTEnNAL ANTENNA
I
I
-!1 POWER SUPPLY
Figure 4. Block Diagram of Dielectrometer
Figure 5.
Timing Circuit
V O L U M E 2 4 , NO. 5, M A Y 1 9 5 2
785
INTERPRETATION OF DATA
ACCURACY OF METHOD
The capacitance of a cylindrical, concentric two-plate capacitor such as the micrometer described above is directly proportional t o the length of the inner cylinder. In the circuit described, thcx caparitance of the dielectric constant cell is likewise proportional to the dielectric constant of the liquid within it. It follows, tlieii. that changes in dielectric constant of the solution may be read directly on the micrometer. For the micrometer readings to follo~vthe progress of the reaction directly would require that the dielectric constant of a solution be an additive property of the constituents. Heston et ai. have shown that for a dilute solution (less than 0.1 M )of a polar solute in a nonpolar solvent, the dielectric constant of the solution varies linearly with the mole fractiou of the solute ( 4 ) . In a reacting medium where the number of products is equal to the number of reactants, concentration will vary di~ectlywith mole fraction, so that if Heston’s relationship is valid for a niulticomponent r;yetem,
Results obtained using this method for studying the kinetics of the reaction of acetic anhydride with ethyl alcohol in carbon tetrachloride ( 2 ) demonstrate the high precision of which the method is capable. I n a single study the second-order velocity constant was determined ten times with an average deviation from the mean of 0.12%. Even greater precision might have been possible if a less crude reaction cell had been used. The dielectric constant is not the only property which may be studied with essentially this same equipment. For example, i n gas reactions, a mercury manometer with a metal film on the outside of the glass tubing might be substituted as the variable capacitor in place of the dielectric constant cell.
A R = kA[.4]
ACKNOWLEDGMENT
The author wishes t o express his deep appreciation to Donald H. .%ndrews,under whose guidance this instrument was completed. John H. Lehman constructed the reaction vessel.
ill
LITERATURE CITED
Anderson, K., Bettis, E. S.,and Rei-inson. D., .~s.LL. CHEM..22, 743 (1950). ( 2 ) .Ixtmann, R. C., .I. .4m. C‘irixin. Soc., 73, 5367 (1951). (3) Burrell, C. >I., h1agur.y. T. G., and Melville. H. W., Proc. ROU. Soc. ( L o n d o n ) , 205, 309-22 (1952), also pp. 323-35. (4) Heston, IT. M., Jr.. Franklin, .4.D., Hennelly, E. J., and Still-th. C. P., J . Ani. Chem. SOC.,72, 3443 (1950). (5) Jensen, F. W., and Parrack, .I.I,.. IXD. EIFG.C H m r . , A 4 x a ~ ED.. . 18. 595 (1946). ( G I IT.&, P.If., Burkhaltei, T. S . , and Broussard, L., -IN.&L. CHEli., 22, 469 (1950). ( 7 ; Zeluff,V.. and Markus, .J.. “Electronics Manual for Radio Engineers,” p. 227, S e w Yoik, McGraw-Hill Book Co., 1949. R E C E I V Efor D review October 4. 19.51, Accepted Rlarch 5 , 1952. Taken (1)
ir.lwrr A f i is the change in micrometer reading, k is a constant, and 1-4 ] ir the concentration of ally component. Heston’s relationship does appear to apply in at least some multicomponent systems (P). In the case of a second-order reaction with t,he two reactaiitinitially present i n the same concentration, a, the integrated expression for the velocity constant, becomes in terms of thc micrometer readings, R, where the subscripts refer to readings taken at zero, infinite, and 1 time:
k = J
Rr-Ro - Rt)
t a(R,
from the doctoral dissertation of R. C. Axtmann at Johns Hopkins Uni\.ersity, 1950.
Polarographic Studies of Oxygen-Containing Organic Compounds Functional Groups of Autoxidation Products C. 0. WILLITS, CONSTANTINE RICCIUTI, €I. B. KNIGHT, AND DANIEL SWERN Eastern Regional Research Laboratory, Philadelphia 18, Pa.
C
I’IIREXT intercet in autoxidation of fats, oils, paints, s l y rene polymers, rubbers, and gasoline has result,ed in nunierous papers on this subject. Lack of direct means for the qualitative and quantitative determination of the autoxidation products has been a handicap in such studies. Lewis and coworkers (8, 9) obtained well-defined polarograpliic waves for autoxidized methyl oleate, methyl linolenate, and l a d and found that the wave heights were proportional to the concentrations. Bovey and Kolthoff ( I ) also found this to be true of autoxidized styrene polymers. These results suggest the possible usefulness of the polarographic method for the study of autoxidation processes. The use of many different electrolytic solutions in the past has, however, resulted in an accumulation of polarographic data on various organic oxygen-containing groups which c.annot he correlated. Inasmuch as the lithium chloride methanol-benzene electrolytic solution of Lewis and Quackenbush proved satisfactory for the study of water-insoluble compounds, it was believed that this solution would provide the means for obtaining comparable data on water-insoluble as m-ell as water-soluble oxy-
yen-containing organic compounds. A wide variety of pure (,ompounds was selected tvhose oxygen groups have been either detected in autoxidation reaction substances or are suspected of occurring in them. These compounds contained the oxirane, hydroperoxide, peroxide, hydroxy, dihydroxy, keto, diketo, and aldehyde groups attached to various types of organic structures. This study using nonaqueous electrolytic solutions of several classes of oxygen-containing compounds of diverse structural formulas, but having similar groups, has further substantiated the observation of other workers that the polarographic reduction is generally a characteristic of the functional group and its immediate structural environment and not of the compound as a whole. Because the oxygen group is usually the determining factor, it should be possible to identify it in an autoxidized substance from its polarographic waves. The polarographic data also provide a means for measuring the purity of water-insoluble oxygen-containing compounds which are reducible a t the dropping mercury electrode. EXPERIMENTAL
Apparatus and Reagents. A Sargent Model XX polarograph
