DONALD A. PITTAND CHARLES P. SMYTH
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analysis of the soot for soluble and volatile constituents are consistent with a pyrolysis mechanism of carbon formation involving polymerization of acetylene to large aromatic molecules. The question of oxygen involvement in the mechanism cannot be settled on the basis of this work, but there are indications that it does not take part in
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a rate-controlling step of the mechanism. Acknowledgment.-The author wishes to thank Dr. C. E. Welling of this Laboratory for several helpful discussions and Messrs. J. L. Parsons and J. C. Neerman for performing, respectively, the infrared and ultraviolet and the mass spectrometric analyses reported herein.
MICROWAVE ABSORPTION AND MOLECULAR STRUCTURE IN LIQUIDS. XXVI. THE DIELECTRIC RELAXATION TIMES OF TWO LARGE OBLATE ELLIPSOIDAL MOLECULES IN BENZENE SOLUTION1n2 BY DONALD A. PITTAND CHARLES?. SMYTH Contribution from the Friclc Chemical Laboratory, Princeton University, Princeton, N . J . Received September 11 1968
The dielectric relaxation times of metal-free hepta henylchloro henyl-porphyrazine and of ferric octaphenylpor hyrazinc chloride have been determined in benzene solution, Eased on dieictric constant data at 1.25, 3.22,.10.0, 25.0 an850.0 cm. wave len ths at temperatures of 20,40 and 60”. The dipole moment of the chloroporphyrazine lies in the plane of the great ring, whife that of the ferric complex is perpendicular to the molecular plane. The relaxation time of the former is close to that czlculated by equations taking into account the microscopic viscosity. The ferric complex, with a relaxation time 5 / 2 that of the chloroporphyrazine, is better described by a relation involving the macroscopic solvent viscosity. It is evident that relaxation occurs through two different modes of orientation. The dipole moments, atomic polarizations and the energies and entropies of activation for dielectric relaxation are given. A new dielectric measuring apparatus is described, consisting of a coaxial line resonant cavity. The transmission-line equations provide a simple derivation of the traiismission of power through the cavity as a function of the cavity dimensions and of the dielectric properties of the liquid filling the cavity. The apparatus is usable over a wide frequency range and is especially applicable to measurements of the dielectric constant and loss of dilute solutions.
The theoretical modela for dielectric relaxation of a solute molecule orienting in a continuum can be approached through investigations of solutions in which the molecular size of the solute is much greater than that of the solvent. In the past, solubility considerations have limited such studies to polymeric materials. While aqueous solutions of proteins4 behave electrically as large rigid ellipsoids in a continuous medium, polymers in nonpolar solvents show predominantly segmental orientation. The octaphenylporphyrazine complexes possess adequate solubility in benzene to allow the measurement of their dielectric relaxa tion, and are of well-defined, roughly ellipsoidal shape. Two of these complex planar molecules have been prepared. The dipole moment is located in the plane of I and perpendicular to the plane of 11. The dielectric relaxations in benzene solutions of these ellipsoids of revolution have been investigated and will be discussed in terms of their shapes and the positions of their dipole moments. (1) This research has been supported by the Office of Naval Research. Reproduotion, translation, publication, use and disposal in whole or in part by or for the United States Government is permitted. (2) This article represents a portion of the work submitted by Donald A. Pitt to the Graduate School of Princeton University in partial fulfillment of the requirements for the degree of Doctor of Philosophy* (3) P. J. W.Debye, “Polar Molecules,” Chemical Catalog Co., New York, N. Y., 1929. (4) J. L. Oncley, “The Electric Moments and the Relaxation Times of Proteins .,” in E. J. Cohn and J. T. Eduall, “Proteins, Amino Acids, and Peptide8,”Reinhold Publ. Corg., New York, N. Y., 1943.
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CJh caH6 I, Me = 2H4X1 = C1 11, Me = Fe ++,XI = H, X1 = C1-
Experimental Methods The static dielectric constant eo was measured with heterodyne-beat apparatus’-* a t a wave length of 577 meters, and the density was determined with an Ostwald-Sprengel pycnometer Wave guide measurements of dielectric constant and loss a t 1.25 and 3.22 cm. wave length were carried out on apparatus reviously described,lOJl using the standing wave ratio tecgnique. Resonant Coaxial Cavity Apparatus .-The cavity, as inch illustrated in Fig. 1, consists of a water-jacketed (5) C. P. Smyth and S. 0. Morgan, J . A m . Chem. Soc., 60, 1547 (1928). (6) G. L. Lewis and C. P. Smyth, J . Chem. Phys., 7 , 1085 (1939). (7) L. M. Kushner and C. P. Smyth, J. A m . Chem. SOC.,71, 1401 (1949). (8) A. J. Petro, C. P. Smyth and L. G. 8. Brooker, i b i d . , 78, 3040 (1956). (9) G. R. Robertson, Ind. Ene. Cham., Anal. E d . , 11, 464 (1939). (IO) H. L. Laquer and C. P. Smyth, J. A m . Chem. S o c . , 70, 4097 (1948). (11) W. M. Heston, A. D. Franklin, E. J. Hennelly and C. P. Smyth, ibid., 74, 3443 (1960).
DIELECTRIC RELAXATION TIMES OF LARGE OBLATEELLIPSOIDAL MOLECULES
April, 1959
i.d. tube, lapped after fabrication for uniform bore, a shortcircuit fitting, and 6/82 inch 0.d. inner conductor, all silver plated. The center conductor is drilled and tapped for a polytetrafluoroethylene spacer which provides an opencircuit termination of low loss. While a short-circuit could also have been used, the cavity length necessary for a given number of resonances would thereby be increased. Energy is introduced and sampled for detection, through two small rotatable magnetic cou ling loops very near the shortcircuit. The degree of couping is kept as low as possible, consistent with a detectable output signal. The cell is fitted with a standpipe to allow filling from the bottom, with flow through perforations in the olytetrafluoroethylene plug and the short-circuit fitting. &e micrometer system, Fig. 2, utilizes a 12 inch precision-ground hardened steel screw of 1 mm. pitch, and a similarly ground bronze bushing. A revolution counter, reading in mm., is provided, and the head is divided to allow estimation to lo4 cm. The assembly is mounted on a heavy supporting member with guide rods and a loading device to minimize backlash. Four square-wave modulated high-frequency generators are in use with this cavity. Two are tuned concentric-line oscillators, the Hewlett-Packard Model A (range 500-1300 Mc.p.6.) and the Hazeltine Model 1050-13 (range 900-1300 Mc.p.s.), the latter having greater R.F. power. Their frequency is adjusted to give a minimum audio beat frequency with the 50 Mc.p.s. signal of the Hazcltine Model 1134 frequency calibrator. This unit contains a 10 Mc.p.s. crystal-controlled oscillator and a quintupler circuit, and is calibrated by beating against the 10 Mc.p.6. transmission of radio station WWV, National Bureau of Standards, Washington, D.C. Two klystrons, a type 707B (ca. 3,000 Mc.p.s.) and a type 2K23 (ca. 4,850 Mc.p.s.), are operated at fixed frequencies from stabilized power supplies. The 2K23 feeds into a wave guide section having a tunable capacitative feed to coaxial cable. The cavity is matched to each generator and to the IN21 crystal detector with triple stub tuners, and the transmitted power is measured with a Hazeltine Model 1052-A tuned amplifier. Cavity Transmission Function.-The weak coupling between the coupling loops and the cavity cell, with negligible loop-loop interaction, permits the analysis of the microwave circuit in terms of an e uivalent low-frequency circuit having a constrtnt coefficient o? mutual inductance By this means, it can be shown12 that the output meter of‘the tuned amplifier will show a deflection proportional to the square of the cavity admittance seen at the short-circuit, looking toward the open circuit. The part of the cell past the center conductor appears as a circular wave guide beyond cut-off,.and the use of the spacer gives a low termination 108s essentially independent of the loss of the li uid dielectric. The resonating portion of the cell is, therecore, only that part between the short-circuit and the end of the inner conductor. The cavity admittance, for an inner conductor depth d , and a characteristic admittance Y Oof the coaxial line, is Y E Y,(Y., Yo tanh y d ) / ( Y o Yo,tanh yd) S Y o tanh yd ( 1 ) As a result of the open-circuit design, its admittance Yo, is neglected. I n these expressions, y = cy j @is the propagation constant of the wave in the medium, a is the attenuation constant, and @ = 2n/X is the phase constant. The cavity resonates when the susceptance given by eq. 1 is equal in magnitude and opposite in sign to the susceptance in the direction of the short-circuit. This occurs when dn = (2n - 1) r/2p (2n - l)h/4 (2) where d n is the depth, measured from the short-circuit, a t the nth resonance. This is applicable when dn is considerably greater than 25 mm., the length of the sliding contact fingers. The admittance a t the point of resonance is given by Yn 2 Yoctnh ad, (3) The power transmission throu h the cavity may be expressed as the function Tn,the ratio ofthe power at a depth d to that transmitted at the nth resonance peak, Tn E tanh2 yd tanhe ad, (4) Measurement Technique.-The distance between resonance peaks, from eq. 2, is k/2, a half-wave length in the di-
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(12) D. A. Pitt, Ph.D. Diasertation, Prinoeton University, 1957.
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Fig. l.-Httlf section view of the coaxial resonant cavity cell: 1, inner conductor; 2, short circuit; 3, glass-Kovar liquid seal; 4, rotatable magnetic coupling loop; 5, polytetrafluoroethylene open circuit fitting; 6, reservoir cover; 7 , sample reservoir; 8, type N coasial fitting; 9, stuffing box; 10, water jacket. electric. Measurements must be conducted at depths well beyond the contacting fingers of the short-circuit fitting. Dielectric loss in the medium introduces a slight asymmetry of the resonance peak, and hence aome error in locating d,. This may be neglected within the limitations on attenuation mentioned below. While the peak is sharp only for low-loss media, the phase change through a resonance is seen from eq. 4 to be rapid, and largely independent of loss. The interferometric technique of Branin13 may be applied for materials of tan 8 > 0.05 by the introduction of a phase reference signal between the cavity output stub tuner and the crystal detector. The half-power widths of these resonance peaks are used to evaluate e’’ for low-loss dielectrics. The distance between dn and the points a t which T n = 0.5 is found by expansion of eq. 4. This gives, for ( 6 d ) n
