March 5, 1958
DIELECTRIC CONSTANT OF ANTHRONEIN BENZENE
tained by using the O'Dwyer and Sack expression the correspondence obtained by using the Powles expression and then correcting for viscous effects seems more reasonable. With the notable exception of 2-methylnaphthalene, the agreement among the T p / q values is comparable to that in column 3 of Table IV. The apparent anomaly in the high T p / q value for 2methylnaphthalene is significant in that it is the
[CONTRIBUTION F R O M THE
1061
only compound listed in which the direction of the dipolar axis is not nearly parallel to the carboncarbon bond held in common by the two rings. For this reason, therefore, the first six compounds in the table could equally well be grouped together on the basis of "electrical shape," in which case the x preuse of T p / q for purposes of comparison i s to I ferred over the use of T M / ~ . PRINCETON, NEWJERSEY
FRICKCHEMICAL LABORATORY, PRINCETON
UNIVERSITY]
Microwave Absorption and Molecular Structure in Liquids. XXII. The Dielectric Relaxation Times of Three Prolate Ellipsoidal Molecules in Benzene BY DONALD A. PITTAND CHARLESP. SMYTII RECEIVED SEPTEMBER 17, 1957 The dielectric coilstants of benzene solutions of anthrone, fluorenone and phenanthrenequinone have been mealjured a t 1.25, 3.22, 10.0, 25.0 arid 50.0 cm. wave length at temperatures of 20, 40 and 60". The relaxation time and its distribution parameter for each solute have been determined from arc plots of the slopes a t each wave length of the curves for the dependence of dielectric constant and loss upon the concentration of the solute. Anthrone and fluorenone have values of relaxation time which would be anticipated from their molecular sizes and shapes, but the value for phenanthrenequinone is anomalously high. This may be due to a greater volume swept out b y this molecule in orienting about its long axis.
The dielectric relaxation of dipolar molecules in solution provides a means of investigating the viscous drag forces which hinder the rotation of the polar solute molecules. The quantitative effects of solvent viscosity, of the volume and shape of the solute molecule and of position of the dipole moment within the solute molecule are not yet wholly clear. To further the study of the latter factors, the dielectric relaxation properties of three roughly ellipsoidal polar molecules have been examined.
ments of dielectric constant and loss a t 1.25 and 3.22 cm. wave lengths were carried out with wave guide appa.ratus.*~g The standing-wave method of evaluating dielectric loss was applicable for all solutions. 4 coaxial resonant cavity apparatusLo was employed with radiation of 10.0, 25.0 and 50.0 cm. wave length. The concentrations of solutions used in this apparatus were considerably lower than for the wave guide equipment to keep the loaded cavity loss tangent below 0.02. Refractive indices were measured with a Pulfricl~refractometer for the sodium-D line, and densities were determined with a graduated pycnometer, as described by Robertson .I1
Materials.-Anthrone from Brothers Chemical Co. was successively crystallized from benzene and ethanol and thoroughly dried in an Abderhalden pistol. The purified material retained a pale yellow tint; m.p. 155'; lit.3 154155". 9-Fluorenone obtained from Brothers Chemical Co., was recrystallized from absolute ethanol, forming flat needles having a bright yello\%;color. After drying, these melted sharply at 84"; lit.4 84 . 9,10-Phenanthrenequirione obtained from Eastman Kodak Organic Chemicals was twice recrystallized from dioxane and dried in vacuo. The orange needles melted at 208"; lit.*207'. Benzene of analytical reagent grade, Merck and Co., was used without purificatiori. The dielectric loss at 20" and 1.25 cm. wave length was less than lOy0 higher than that obtained with benzene dried over sodium hydride and fractionally distilled immediately before use. The static dielectric constants were 2.2854, 2.2454 and 2.2055 a t 20, 40 and 60", and the refractive indices were 1.5009, 1.4889 and 1.4776. Methods of Measurement.-The static dielectric constant was measured a t a frequency of 520 kilocycles/sec., using heterodyne-beat equipment .6-7 Microwave measure-
Experimental Results The dielectric constant, E', and loss, E " , o.E dilute solutions of polar molecules in non-polar solvents have been shown12 t o be linear functions of concentration for non-associated solutes, that is
(1) This research has been supported by t h e Office of Kava1 Research Reproduction, translation, publication, use a n d disposal in whole or in p a r t b y or f o r t h e United States Government is permitted. (2) This article represents a portion of t h e work submitted b y Mr. Donald A. Pitt t o t h e Graduate School of Princeton University in partial fulfillment of the requirements for t h e degree of Doctor of Philosophy (3) K . H. Xleyer, A n n . C h c m . , Jaslus Licbigs, 379, 37 (1911). (4) "International Critical Tables," McGraw-Hill Book Co., New York, N. Y., 1926. ( 5 ) C. P. Smyth and S. 0. Morgan, THISJOURNAL, 60, 1547 (1928). (6) G L. Lewis and C . P. Smyth: J. Chcm. Phyr., 7, 1085 (1939). (7) L. hl. K u s h n c r a n d C . P. Smyth,Ta1s]ouRNaL,71, 1401 (1949).
e' = el
+
a'cz = a'/cz
where c1 is the mole fraction of the polar solute, and the subscripts 1 and 2 refer t o solvent and solute, respectively. Similarly eo = ffD2
= 2,
e1
+ nocz
(nD)I2
= 01
+
+ ancp
D'CZ
where €0, nD2 and v are the static dielectric constants, the square of the refractive index and the specific volume of the solution, respectively. These experimental data, obtained from measurements of two to five solutions a t each frequency, are given in Table I. Heterodyne-beat nieasurernents of el were used in the calculation of a' a t all frequencies. Measurements of the dielect.ric loss of the pure solvent were used to correct the E" data of solutions for combined wall and solvent: losses. (8) H . I,. Laquer a n d C . P. Smyth, ibid., 70, 4097 (1948). (9) W. M. Heston, A. I3. Franklin, E. J. Hennelly and C. P. Smytb, ibid., 73, 3443 (1950). (IO) D. A. F'itt and C. P. Sniyth, unpublished. (11) G. R. Robertson, I n d . Eng. Chsm., A m / . Ed., 11, 464 (1939). (12) A. D. Franklln, W. M. Heston, E. J. Hennelly and C. P. S m y t h , THISJOURNAL, 73, 3447 (1960).
1062
DONALD
A.
PITT AND
CHARLES P.SMYTH
Vol. 80
The solvent loss was of the order of half the wall conductivity loss at 1.25 cm. wave length.
mately planar configurations, with the dipole moment of each molecule on one of the minor axes of symmetry, perpendicular t o the long axis of the TABLE I molecule. SLOPESFOR THE DEPENDEXCE OF THE DIELECTRIC CoxThe relaxation time of fluorenone in benzene STANT AXD LOSS OF SOLUTIONS o s MOLEFRACTION OF solution has been reported recently by Chau, SOLCTE LeFPvre and Tardif15 from measurements at a Wave length, 200 40' 60" single wave length of approximately 10 cm. Their a,, u , a" Solute cm. a" value of 17.0 X10-l2 sec. a t 26" is only 2% above ;\r?tlirone 1.25 3 . 7 4 . 5 4 . 4 5 . 1 5.3 5 . 4 the value of 16.7 X obtained by interpolation 3.22 7.4 7 . 0 8.7 6 . 9 9 . 5 6 . 2 on the activation energy plot of our data based on 1 0 . 0 14.9 6 . 2 14.7 5 . 0 14.5 3 . 7 measurements a t five wave lengths from 1.25 to 25.0 18.0 3 . 3 1 6 . 8 2 . 5 15.5 1 . 7 50.0 cm. 9-Xitroanthracene in benzene was found 50.0 1 8 . 9 2 . 2 17.3 1 . 4 15.G 0 . 9 by Chau, et al., to have a relaxation time of 28 x Fluorenone 1 . 2 5 3 . 6 4 . 4 4.2 4 . 7 1.8 4 . 9 lo-'* at 12'. This compound, very similar in mo3.22 7 . 5 6 . 3 8 . 5 5 . 9 9 . 2 5 . 2 lecular size, shape and polarity to anthrone, has a 10.0 13.6 5 . 0 13.1 3 , 8 1 2 . 8 2 . 5 similar relaxation time to anthrone, for which a 25.0 1 5 . 8 2 . 4 14.6 1.8 13.6 1 . 4 value 29.4 X may be found from extrapola50.0 16.3 1 . 6 14.9 1 . 1 13.6 0 . 8 tion to 12'. The 1,s-dichloroanthraquinone molePlienan1.2.5 7 . 4 8 . 5 8 . 4 9 . 4 9 . 5 10.0 cule, measured by Fischer16 by a calorimetric threne3.22 1 2 . 8 13.4 15.8 13.4 18.7 12.2 method a t a single frequency, has a relaxation time quinone 10.0 2 7 . 6 13.5 2 9 . 5 11.2 28.2 8 . 3 at 23" of 52.0 X lo-'? sec. Due to the bulk of the 25.0 36.6 8 . 9 3 4 . 3 6 . 2 3 2 . 1 4 . 6 protruding chlorine atoms, such a value might be 5 0 . 0 3 8 . 3 5 . 0 3 5 . 7 3 . 5 3 2 . 3 2 . 3 expected from the results of the present study. It is evident that the values of the relaxation times 01 The relaxation times, T , were obtained by the anthrone, fluorenone and phenanthrenequinone, arc plot method of Cole and C ~ l e . ' ~ *The ' ~ distri- obtained from data a t five high frequencies and the bution parameter, a , was obtained from the arc static dielectric constants, are consistent with the plot, the radius between and the arc center being results of previous measurements a t a single high depressed a r / 2 below the abscissa axis. The high- frequency. frequency intercept of the arc with the abscissa axis The values of the dipole moments in Table I1 are is designated as a , and is listed with values of r and in good agreement with earlier measurements in CY in Table 11. benzene solution for anthrone, 3.66,17and for fluorTABLE I1 enone, 3.351g and 3.29,19 but are somewhat lower S1,oPES F O R THE DEPESDESCEO F STATIC DIELECTRIC C O X than the earlier value, 5.57,*O for phenanthrene-. ST.%ST, SQVARE OF REFRACTIVE I N D E X A S D SPECIFIC TiOLquinone. As this earlier value was the result of ~ T YOS E ~ I O LFRACTION, E WITH IXFIXITE-FREQUESCY IXTER- careful dipole moment measurements, the present CEPTS, DISTRIBUTION PARAMETERS, R E L A X A T I O S TIMES incidentally calculated value is not to be regarded (10-1* SEC.)A N D DIPOLEMOMESTS E.s.LT.-cM.) as superseding it. Teommp., Froni a plot of In I'r as a function of reciprocal Solutc C. a, UD a, 8' a r p temperature, the activation energies and entropies :\ntI>r:>r~e 20 1 9 5 5 0 . 8 0 1 . 3 -0.794 0.14 2 4 . 8 3 6 3 40 17.66 0 . 9 6 1 . 4 - ,843 . I 1 18.4 3 . 6 3 for the relaxation process were determined. The ti0 15.87 1 09 1 . 5 - , 9 2 1 . 0 9 1 3 . 6 X (io values are given in Table 111. 20 40 60
Fluorenone
20
Phenanttirrnerlujnonr
-10
60
16 78 0.87 15.16 0.98 1 3 . 7 4 1.10 40.50 1 27 30.67 1 . 5 2 34.07 1 . 7 2
1.0 1.1
1.2 2.8 3.0 3.1
-
IO 0 11.9
.G9l ,735 ,776 -1.0'37
.I3 .I2 .O!i
11.5
1:
31 3
-1.083
.12 .I?
22.2
-1.l7i
3. 3 3.34 ,
1
l l i
The dipole moment was calculated from thc refractil-e indices and static dielectric constant values by using the equation of Halverstadt and Kuniler1; to el-aluate the molar refraction and molar polarization. The resulting moment values, p , are listed in Table 11. Discussion of Results The three polar molecules anthrone, fluorenone and phenanthrenequinone have planar or approxi0
0
0
0
il
fiqq .
(2A4 __ \\/'
