482
J. E. BOGGS,C. M. CRAINAND J. E. WHITEFORD
Vol. 61
0.02% of the sum of the terms in parenthesis in eq. The situation is very much the same for potas15a, or 0.01 to C$OK. The values of A, show con- sium chloride, for the term 1000As contributes siderable variation between runs, and in view of the 7.6'% to 104C$O~.The values of 104+0~ derivedI3from sensitivity of this parameter to the vagaries of compression measurements are about 10% more curve-fitting, we estimate that A, may be in doubt negative than those in Table 11, being -51.6,fao by 1.5 units. This could contribute an error of sodium chloride and -45.2 for potassium chloride. 0.9 to 1 0 4 @ for ~ sodium chloride, and it seems Acknowledgment&The authors wish to express reasonable to set 1.0 as the total probable error in their gratitude to Mr. Charles M. Pond of Niles, 1 0 4 d 0directly ~ associated with the ultrasonic meas- Bement and Pond Division of Pratt Whitney, urements and the analytical evaluation of A,. West Hartford, for calibration of the micrometer The value of C$OV used for sodium chloride is scarcely screw, to Mr. Walther Andersen of Andersen in doubt by more than 0.3 cc./mole, which corre- Laboratories, West Hartford, for design of elecsponds to an error of 0.27 in 104C$O~.Thus in the tronic equipment, and to the Office of Ordnance evaluation of 1 0 4 6 0 for ~ sodium chloride the sum Research for financial assistance. of the estimated experimental errors is 1.28 compared to 3.44 contributed by the term 1000Aa. (13) Reference 5, p. 270.
DIELECTRIC CONSTANT MEASUREMENTS ON GASES A T MICROWAVE
FREQUENCIES
,'
~
, , ,
BY JAMES E. BOGGS,CULLENM. CRAINAND JAMES E. WHITEFORD Electrical Engineering Research Laboratory and Departments of Chemistry and h'lectrical Engineering, The University of Texas, Austin, Texas Received November 10, 1066
Dielectric constant measurements have been made on 15 gases a t 30, 60 and 90°, using a frequency of 9400 megacycles. For HCl, SOZ, HzS, CO, CHaCOCHa and CC1F2CC1F2, values for the molar olarization and for the.dipole moment comparable to those reported a t lower frequency were obtained. For CHzClF, ~ F F C C I F and c k c ~ H ~ C z Hno 4 , values a t ower frequency are available in the literature for comparison. For CHaC1, CHClFn, CHClaF, CHaBr, and popsibly CClFa and CClsF, the dielectric constant a t 9400 megacycles is distinctly lower than that ,gt lower frequency. Possible explanations for the lowering are discussed.
'
Most of the measurements of dielectric constants of gases reported in the literature have been made at relatively low frequency; generally less than 1megacycle. The measurements are difficult and great pains must be taken to ensure high precision. In recent years, equipment for making similar meaaurements in the microwave region has become available and is capable of greater precision with much greater ease of operation. A relatively small number of gases has been investigated a t microwave frequencies. consequently it was considered of interest t o make a survey to determine whether dielectric constant values measured a t these frequencies were identical with those measured at low frequencies (the so-called static values). From theoretical considerations, one would expect that the static dielectric constant value would be obtained at all frequencies below the lowest resonance frequency of the dipole being measured. In the region of such a frequency, resonance dispersion would be observed and, at still higher frequencies, the dielectric constant would have a value lower than the static value. Normally, one would predict that the lowest such resonance frequency would be the one corresponding to the transition from the zero to the first rotational energy level. Only for rather heavy molecules would this resonance frequency be lower than the frequencies usu(1) This work has been supported by Air Force Contract AF 33(616)2842. It was presented in part a t the 129th National Meeting of the American Chemical Society, Dallas, Texas, April 9-13, 1956.
ally used for microwave measurements. Nevertheless, the possibility that some unknown type of transition might occur at lower frequency and alter the value of the dielectric constant cannot be ruled out without actual measurement. In the current study, dielectric constants have been measured for P!-i gases and the results compared, when possible, with lower frequency measurements reported in the literature. Experimental Measurements on all of the gases were made using a Crain refractometer.2 The gas sample was contained in a cavity resonator which controlled the frequency of a Pound-type stabilized oscillator. The cavity was immersed in a constant-temperature bath and was connected to a vacuum system through which the sample could be admitted. The temperature of the constant-temperature bath was mainThe gas pressure was read on an tained within f0.05'. ordinary mercury manometer. A second cavity, evacuated and sealed, was immersed in the same bath and used to stabilize a second oscillator. The frequency difference between the two stabilized oscillators was read with the sample cavity evacuated, and the change noted when the sample was introduced. Then, Af/f = e< - 1, where Af is the change in beat frequency, f is the resonant frequency of the evacuated measuring cavity, and e is the dielectric constant of the gas. All of the free gases used were purchased from The Matheson Company and were purified by fractional distillation on a vacuum line. The acetone was of reagent grade and was further purified by fractional distillation. The authors wish to express their appreciation to Mrs. Helene P. Mosher for her assistance in purifying the samples. In a typical measurement, the sample cavity was evacuated and the frequency of the beat note between the two OS( 2 ) C. M. Crain, Rev. Sei. Instr., 21, 456 (1950).
April, 1957
483
DIELECTRIC CONSTANTS OF GASESAT MICROWAVE FREQUENCIES TABLE I
Gas
Microwave P (CC.)
"Static" P (CC.)
Microwave
"Static"
P D (CC.)
P D (CC.)
Microwave P (Debyes)
"Static" (Debyes)
P
7.2 7.0" 1.10 1.08" 30.5" 31.5 10.2 lo.@ 1.63 1.63b 63.7 64. 2b 8.8 10.0" 0.98 0.92' 27.0" 28.1 5.04 4.9d 4.65 4. 65d 0.14 0.12" 17.7 / 2.88 2.88" 183.' CHaCOCHa 184.4 z h 0.46 29.5 33.8 34.4' CClFzClClFz a R. P. Bell and I. E. Coop, Trans. Faraday Soc., 34,1909 (1938). b R. J. W. Le Fevre, J. W. Mulley and B. M. Smythe, J. Chenz. Soc., 276 (1950). c C. T. Zahn and J. B. Miles, Phys. Rev., 32, 497 (1928). d A. van Itterbeek and K. de Cllppelier, Physica, 14, 349 (1948). e C. T. Zahn, Physik. Z . , 33, 686 (1932). f The distortion polarization of acetone has pot J. Am. Chem. Soc., 60, 1633 (1938). The distortion been reported. The molar refraction is 16.2 cc. 0 R. M. FUOSS, polarization of this compound has not been reported. The molar refraction is 21.5 cc. i Fuoss measured this compound a t only one temperature, so the dipole moment could not be determined accurately. HC1
so2 H2S co
cillators was measured. Gas was then admitted to the sample cavity a t a measured pressure and allowed to come to temperature equilibrium. The beat frequency between the two oscillators was determined again. The shift in beat frequency varied from 0.5 to 15 megacycles, depending on the gas and its pressure. Such measurements were made at a series of pressures and extrapolated graphically to 760 mm. pressure. The molar polarization was then calculated by the relation
p = -E - 1
Results The results obtained with acetone vapor are presented as typical. Figure 1 shows the measured dielectric constant plotted against gas pressure a t 30, 60 and 90". In Fig. 2 the resulting values for the molar polarization are plotted against reciprocal temperature. The results from a similar treatment of each of the gases are shown in the tables. Table I shows the results for 6 of the compounds measured. The total molar polarization a t 30" ( P ) ,the distortion polarization (PD)and the dipole moment ( p ) , as measured by us a t 9400 megacycles, are given for each compound together with similar values calculated from literature data at low frequency. The value for the total polarization ,should be accurate to better than 1% and the dipole moment to ztO.01 Debye. The distortion polarization is less accurate, since it involves a rather considerable extrapolation. It can be seen that the values at the two frequencies agree within experimental error in every case except for the dipole moment of HzS. We believe that the value of 0.92 reported by Zahn and Miles in 1928 for the dipole moment of H2S is too lorn, since Hillger and Strandberg,3in 1950, reported a dipole moment of 1.02 for HDS as measured from the Stark effect on the microwave absorption spectrum, and one would not anticipate this large an isotope effect. I n addition to the compounds listed in Table I, Grain.' and Birnbaum and Chattergees have meas(3) R. E. Hillger and M. W. P. Strandberg, Teclinical Report 180, Laboratory of Electronics, Massachusetts Institute of Technology, 1950.
M. Grain, Phus. Rev., 14, 691 (1948). ( 5 ) G. Birnbaum and S. I
