STUDIES ON ~,~,~-TRICHLOROETHANE-BENZENE-O-DICHLOROBENZENE
1275
Dielectric and Thermodynamic Behavior of the System 1,l,l-Trichloroethane-Benzene-o-Dichlorobenzene1v2 by E. M. Turner, D. W. Anderson, L. A. Reich, and W. E, Vaughan Department of Chmistry, University of Wisconsin, Madison, Wisconsin 6,9706 (Received September 6, 1969)
Measurements of the dielectric permittivity and loss at 20’ at various wavelengths in the microwave region are reported for mixtures containing 1,1,l-trichloroethane,benzene, and o-dichlorobenzene. These data are fitted to a microscopic molecular model which assumes that the dielectric behavior is a superposition of Debye processes. The model parameters are interpreted in terms of molecular and liquid structure. The effect of long range dipole-dipole forces on the static and dynamic dielectric behavior is considered in light of existing theories of the internal field. Boiling point diagrams and heats of mixing are reported for this system in order to check for the existence of strong specific short range forces.
Introduction Measurements of the dielectric permittivity and loss at a few wavelengths in the microwave region have been reported for an assortment of normal polar binary liquid mixtures.8 These data are consistent with dielectric relaxation by a superposition of two exponential decay processes. Such behavior would be expected for these systems if the Onsager model applies to the dynamic dielectric properties. Model calculations using the Onsager model have been carried out4J and the data of Kilp, Garg, and Smyth have provided support for the validity of the calculations.e The mixtures were chosen to have widely separated decay times for the individual components. This work reports an investigation of a single binary polar mixture (with nonpolar diluent) at 20” using a large number of wavelengths and concentrations to see if the Onsager model calculations remain valid as the decay times for the individual components approach each other. Boiling point diagrams and heats of mixing were determined to check for the existence of strong intermolecular association, which would invalidate the use of the Onsager model.
Experimental Section Purification of Materials.
1,1,l-Trichloroethane (TCE) was obtained from the Aldrich Chemical Company and was purified by fractional distillation. oDichlorobenzene (DCB) was obtained from Eastman Organic Chemicals and was purified by fractional distillation. Benzene was taken from laboratory stock, and was dried over anhydrous calcium sulfate. Boiling points and refractive indices agreed with values found in the literature. Dielectric Measurements. Static dielectric permittivities were determined by the heterodyne beat technique a t a frequency of 2 RIIHz.7 Measurements of dielectric permittivity and loss at wavelengths of 7.5 and 15 cm were made by the “breadth-
of-the-minimum” techniques, using a coaxial transmission line.’ Centimeter wavelength determinations of the dielectric permittivity and loss were made with apparatus described previously.71~Measurements of dielectric permittivity and loss at a wavelength of 2 mm were made by a free-space oblique inciof the perdence interferometric t e c h n i q ~ e . ~Values ,~ mittivity and loss, solution compositions, and exact wavelengths used are shown in Table I. Thermodynamic Measurements. Boiling point diagrams at atmospheric pressure (740 mm) for the binary mixtures benzene-l,l,l-trichloroethane, o-dichlorobenzene-benzene, and o-diohlorobenzene-l,l,l-trichloroethane were determined using apparatus described in the literature.1° Liquid and vapor (distillate) compositions were found from refractive index measurements using working curves generated from measurements on solutions of known composition. Enthalpies of mixing a t room temperature were determined for the three binary mixtures above using a calorimeter (1) This work waa supported by the National Science Foundation and by the Wieconsin Alumni Research Foundation through the University Research Committee. (2) This work was presented at the Symposium on Dielectric Properties honoring Professor Charles P. Smyth at the 158th National Meeting of the American Chemical Society, New York, N. Y ,, Sept 8, 1969. (3) H. Kilp, S. K , Garg, and C. P. Smyth, J . Chem. Phys., 45, 2799 (1966). (4) R. H. Cole, ibid., 42,637 (1965). (6) D. D. Klug, D. E. Kranbuehl, and W. E. Vaughan, ibid., 50, 3904 (1969). (6) D. E. Kranbuehl, D. D. Klug, and W. E. Vaughan, ibid., 50, 5266 (1969). (7) N. Hill, W. E. Vaughan, A. H. Price, and M. Davies, “Dielectric Properties and Molecular Behaviour,” Van Nostrand Reinhold Company, London, 1969. (8) J. D. Cutnell, D. E. Kranbuehl, E. M. Turner, and W. E. Vaughan, Rev. Sci. Instrum., 40,908 (1969). (9) W. E. Vaughan, W. S. Lovell, and C. P. Smyth, J . Chem. Phys., 36, 636 (1962). (10) F. Daniels, J. W. Williams, P. Bender, R. A. Alberty, and C. D. Cornwell, “Experimental Physical Chemistry,” 6th ed, McGrawHill, New York, N. Y., 1962. Volume 74, Number 6 March 19, 1970
E. M. TURNER, D. W. ANDERSON, 1,. A. REICH,AND W. E. VAUGHAN
1276
Table I : Dielectric Permittivities, Losses, Wavelengths, Mixture Compositions" TCE
1.00
Mole fraction Benzene
-
0
0
0.75
0.25
0
0.50
0.50
0
0.25
0.75
0
0
0
1.ooo
0
0.25
0.75
0
0.50
0.50
0
0.75
0.25
0.25
0
0.75
0.50
0
0.50
0.75
0
0.25
0.33
0.33
0.33
0.25
0.25
0,50
0.50
0.25
0.25
0.25
0.50
0.25
7
5893 (A)0.2174
DCB
2.067 2.525 . . . 0.884 2.100 2.396 . . . 0.578 2.145 2.346 . . . 0.414 2.192 2.339 . . . 0.247 2.408 2.576 . , , 0.435 2.367 2.533 . . . 0.359 2.332 2.425 0.294 2.290 2.274 . . . 0.191 2.329 2.529 ,,. 0.519 2.246 2.519 . . . 0.531 2.166 2.510 . . . 0.765 2.245 2.424 . . . 0.462 2.286 2.488 . , . 0.462 2.204 2.447 . , . 0.534 2,245 2.369 . . . 0.364
1.2602
1.4010
1.7000
5.183 2.378 4.459 1.612 3.648 0.957 2.968 0.453 3.264 1.910 3.262 1.674 3.078 1.285 2.777 0.727 3.692 2.040 4.044 2.212 4.594 2.292 3.606 1.525 3.548 1,708 3.942 1.663 3.277 1,101
5.329 2.355 4.532 1.534 3.760 0.943 3.028 0.425 3.537 2.056 3.334 1.806 3.178 1.345 2.852 0.770 3.755 2.226 4.170 2.335 4.677 2,351 3.725 1.588 3.410 1.755 4.020 1.796 3.398 1.124
5.820 2.412 4.769 1.494 3.958 0.896 3.106 0.387 3.735 2.495 3.698 2.073 3.472 1.522 2.985 0.808 4.203 2.609 4.717 2.641 5.263 2.620 4.188 1.729 4.147 2.036 4.574 1.873 3.756 1.176
Wavelenetha. om 1.9440 2.4385
6.154 2.129 5.137 1.352 4.000 0.797 3.129 0.366 3.953 2.708 3.800 2.204 3.590 1.630 3.097 0.882 4.356 2.718 4.939 2.705 5.488 2.463 4.279 1.747 4.260 2.109 4.658 1.815 3.731 1.206
6.391 2.048 5.159 1,321 4.125 0.803
... .
,
2.6187
2.9058
6.480 1.719 5.219 1.117 4.200 0.679
6.581 1.766 5.296 1.051 4.206 0.626 3.231 0,256 5.066 3.428 4.673 2.574 4.240 1.742 3.451 0.884 5.375 3.163 6.208 2.992 6.727 2.382 4.948 1.698 5.191 2.247 5.468 1.701 4.242 1.203
,
,.,
I
4.532 3.176 4.560 2.418 4.186 1.793 3.343 0.978 5.066 3,083 5.549 3.031 6.046 2.677 4.861 1.867 4.892 2.358 5,304 1.956 4.055 1.392
..
4.413 3.448 4.581 2.704 4.125 1.785 3.327 0.900 5.049 3.069 5.848 3.059 6.417 2.546 4.834 1.745 4.999 2.305 5.390 1.818 4.243 1.220
7.50
15.00
14980
*..
7.228
...
5.670
4.37 0.33
.,.
4,391
...
...
...
...
3.288
* * .
1 . .
. . I
... ...
...
...
... ...
... ...
7.20 1.15 5.88 0.93 4.27 0.66
.
I
...
...
10.573
,
...
...
...
8.205
...
6 364
... ...
4.245
...
I . .
I
...
. . . 9.01 I
.
.
8.29 1.32 7.83 1.14 6,15 0.87
0.98 8.90 1.08 8.16 0.80 6.52 0.71
...
...
...
...
6.46 0.89 5.06 0.73
6.68 0.65 5.26 0.50
...
...
9.619
... 8.888 .
,
I
8.186
... 6.415 ,,.
7.366 ... 6,620 . . I
5.308
...
a The upper numbers are the dielectric permittivities and the lower numbers the losses. Reported permittivities are accurate to & I % except a t 2 mm, 7.5 cm, and 15 cm wavelengths where the accuracy is &3%. Losses are accurate to + l % except a t 2 mm ( f 5 % ) and a t 7.5 cm and 15 cm where the accuracy is 1507, and deteriorates further as the loss exceeds unity. All measurements a t 20".
described in the literature.1° The temperature changes following stepwise addition of one component were measured. The heat capacity of the calorimeter was determined by measuring the temperature change produced by known amounts of electrical work.
Discussion Low Frequency Dielectric Permittivities. Dipole moments were computed from the measurements at 2 MH5 for each of the binary mixtures with benzene using the Onsager equation for mixtures." 8i is the volume fraction, p i is the dipole moment, N i is the (€0 - €mi) Cei (2e0 + 1
€mi)
= c3(2eo ++ 2)' EO(E-~
i
€mi)'
4 ~ N i ~ i '
3kT
(1)
is the number of molecules per unit volume, and high frequency dielectric permittivity for each species. This last quantity may be obtained from fitting the pure polar liquid dispersion measurements to the ~ ~ be used as an estimate. Debye equation, or 1 2 may The calculated dipole moments are shown in Table 11. The Journal of Physical Chemistry
Table 11: Calculated Dipole Moments TCE
1.00 0.75 0.50 0.25 0 0 0' 0
Mole fraction Benzene
0 0.25 0.50 0.75 0 0.25 0.50 0.75
--p,
DCB
0 0 0
0 1.oo 0.75 0.50 0.25
Using ea
1.73 1.66 1.62 1.63 2.05 1.98 2.01 2.01
D-
7
Using
nD2
1.86 1.78 1.74 1.73 2.25 2.17 2.19 2.18
The calculated dipole moments do not vary appreciably with concentration, which supports the use of the Onsager model for describing the static dielectric behavior. The values obtained for the dipole moments depend on the estimates of distortion polarization. Use of T L D for ~ ~ , iinstead of the limiting microwave permittivity at high frequency (E-) corresponds to a partial neglect of atomic polarization and a larger (11) L. Onsager, J.Amer. Chern. Soc., 58,1480 (1936).
STUDIES ON 1,l,~-TRICHLOROETHANE-BENZENE-O-DICHLOROBENZENE Equations 4 and 2 imply that
Table I11 : Calculated Static Permittivities ----Mole TCE
0.25 0.50 0.75 0.33 0.25 0.50 0.25
fraction-Benzene
0 0 0 0.33 0.25 0.25 0.50
--
eo---,
DCB
UsingnD1
Using e m
Exptl
0.75 0.50 0.25 0.33 0.50 0.25 0.25
9.15 8.38 7.46 6.38 7.33 6.42 5.36
9.27 8.42 7.54 6.42 7.38 6.46 5.35
9.62 8.89 8.19 6.41 7.37 6.62 5.31
value for the dipole moment. Dipole moment values reported in the literature vary according to estimates of distortion polarization. Values in debyes for 1,1,1trichloroethane in benzene solution are 1.5, 1.58, and 1.66 and values for o-dichlorobenzene range from 2.0 to 2.35.12 The quantity of interest in this work is the ratio of dipole moments, a quantity which is less sensitive to the method of estimation of distortion polarization than the dipole moment values themselves, provided a consistent procedure is used. The calculated dipole moments may be used in the Onsager equation for mixtures to predict the static dielectric permittivities of the mixtures with two polar components. The results are shown in Table 111. The agreement with experiment is reasonable and use of E- for E,; instead of n D z (and using the corresponding dipole moment values) gives a slightly better fit. Dynamic Dielectric Behavior. Since the polar molecules considered here approximate rigid ellipsoids with the dipole moment along a symmetry axis it is reasonable to assume that the dielectric behavior, in the absence of internal field effects, would be a superposition of Debye processes, that is336213 s i w ( - += )
Ci/(l
+ i w d + (1 - C d / ( 1 + i w d
(2)
where the left-hand side represents the Laplace transform of the negative time derivative of the microscopic correlation function. The relative magnitude of the two dispersion regions depends on the number of moles and the dipole moment of each species according to C d ( 1 - CI)
(3) Two calculations, using the Onsager model which treats the liquid outside of a spherical molecular cavity as a continuum, were used to account for the effect of the internal field and to relate the microscopic model parameters to the dielectric permittivities and losses. The equations are due to Cole4 (eq 4) and a revision discussed by Klug, Kranbuehl, and Vaughans'14(eq 5 ) . =
1277
n1pl2/n2pZ2
e"
- e, - E, 1
~eo
1 - x1 1 iwTz
x1
+ iwTl -!r +
(6)
The dielectric measurements were fitted to eq 5 and 6 using a least squares criterion and treating CI, 71, 72 (or equivalently X I , TI, TZ) and e , as variable parameters. The results are shown in Table IV. C1 equals unity if only one polar species is present in the mixture. With the Cole equation, C1 (71 and n)may be calculated from XI,TI, and Tzusing equations derived by Vaughan and Provder. The agreement between the dielectric measurements and the back calculated curve for a typical system is shown in Figure 1.
10
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
8'
Figure 1. Cole-Cole locus of experimental measurements of the dielectric permittivity and loss at 20". For a mixture containing 3 mol of o-dichlorobenzene per mole of l,l,l-trichloroethane. The solid curve is back calculated from eq 6 using the parameters in Table IV. The dielectric loss of the coaxial point is very low compared to the back calculated value.
The decay times (T1) found for the mixtures with a single polar component are of reasonable magnitude considering the molecular size and shape and they show realistic trends with concentration. The l,l,l-trichloroethane molecule is very symmetrical since the methyl group approximates the chlorine in size. The relatively short decay time found is in accord with the notion that the molecule could undergo rotational diffusion without significant rearrangement of the surrounding liquid. The larger and less symmetrical o-dichlorobenzene molecule diffuses less easily and has a considerably longer decay time. As benzene is added to either mixture, the decay time decreases, paralleling decreases in the solution viscosity and the internal field. The difference in decay times of the two species is such that in the mixtures with two polar components the dispersion region with the shorter decay time may be assigned with confidence to the l,l,l-trichloroethane molecule. The dielectric data for the mixtures with a single polar component were fitted to the empirical (12) A. L. McClellan, "Tables of Experimental Dipole Moments," W. H. Freeman and Company, San Francisco, Calif., 1963. (13) F. Perrin, J . Phys. Radium, 5,497 (1934). (14) H. C. Bolton, J . Chem. Phys., 16,486 (1948). (16) W. E. Vaughan and T. Provder, ibid., 44, 1306 (1966).
Volume 74, Number 6
March 19, 1970
E. A t . TURNER, D. W. ANDERSON, L. A. REICH, AND W. E. VAUGHAN
1278 Table IV : Dielectric Dispersion Parameters" 7 -
TCE
0.25 0.50 0.75 0.33 0.25 0.50 0.25 1-00 0.75 0.50 0.25 0 0 0 0 a
Mole fraction-----
Eq 5
r-------
Benzene
DCB
0 0 0 0.33 0.25 0.25 0.50 0 0.25 0.50 0.75 0 0.28 0.50 0.75
0.75 0.50 0.25 0.33 0.50 0.25 0.25
71
20.0 14.1 11.1 12.8 14.4 10.6 14.1
T2
2.6 2.2 2.3 2.7 2.2 2.5 3.0
CI/(l
0.84 0.84 0.74 0.74 0.85 0.75 0.66
0 0 0 0
1.00 0.75 0.50 0.25
Relaxation and decay times in units of
5.3 5.4 2.6 2.9 5.8 3.0 2.0
w= nzpza
4.4 1.5 0.5 1.5 2.9 0.7 1.5
