EDWARD FOREST AND CHARLES P. SMYTH
1302
Microwave Absorption and Molecular Structure in Liquids.
LXIV.
The Dielectric Behavior of Mixtures of Polar Nonassociative Liquids’,’
by Edward Forest and Charles P. Smyth Frick Chemical Laboratory, Princeton University, Princeton, New Jersey
(Received hTovember SO, 1965)
Dielectric constants and losses have been measured a t wave lengths of 575 m., 10.0, 3.22, and 1.25 cm. at 25’ for four binary mixtures of chlorobenzene, bromobenzene, l-chloronaphthalene, and 1-bromonaphthalene, and for solutions of 1-bronionaphthalene and 1chloronaphthalene in benzene. The densities and viscosities have also been determined. The dielectric data of the binary mixtures have been interpreted in terms of two partly superimposed Debye regions whose relative contributions are in the same ratio as the molar concentrations of the components. The results for these binary systems are consistent with the assumption that the relaxation processes are those of molecules rather than larger liquid regions as proposed by some earlier workers for systems which they investigated.
Introduction From his study of the dielectric constant and loss of binary polar mixtures as a function of temperature at constant frequency, Schallamach3 suggested that dielectric relaxation involved relatively large regions in the liquid. Accordingly, if the polar components of a binary mixture are both associative or both nonassociative, so that mixing occurs on the molecular level, the dispersion region should appear to correspond to a single relaxation process. On the other hand, binary mixtures in which one is associative and the other nonassociative yield two dispersion regions. Denney4 measured the dielectric constants and losses of such mixtures as a function of frequency at constant temperature and found his results to be in accord with those of Schallamach. The dispersion regions investigated by Schallaniach and Denney in binary mixtures of nonassociative polar liquids ocburred a t temperatures of the order of - 100”. Bos,~ investigating binary polar mixtures, observed all of the familiar types of complex plane plots encountered in dielectric investigations. Binary mixtures of nitrobenzene and chlorobenzene, which should be representative of the nonassociative type, were found to give semicircular plots indicative of a single relaxation time. In view of the fact that chlorobenzene and nitrobenzene are molecules of similar size and shape, they might be expected, if dissolved in identical Xhe Journal of Physical Chemistry
environments, to yield no more than a slight widening of the dispersion region, which might not be experimentally detectable because of the preponderance of the nitrobenzene contribution arising from the fact that its moment is 2.5 times larger than that of chlorobenzene.6 In view of the relatively small aniount of information available on polar mixtures of the nonassociative type at room temperature, an investigation has been undertaken. Another reason for studying this problem is the fact that many substances have recently been studied in which dielectric relaxation takes place by two simultaneously occurring processes. The results have been analyzed into plausible values for the relaxation times of the two processes, but the successful analysis of (1) This research was supported by the U. S. Army Research Office (Durham). Reproduction, translation, publication, use, or disposal in whole or in part by or for the United States Government is permitted.
(2) This paper represents part of the work submitted by E. Forest to the Graduate School of Princeton University in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (3) A. Schallamach, Trans. Faraday Soc., 42A, 180 (1946). (4) D. J. Denney. J . Chem. Phys., 30, 1019 (1959). (5) F. Bas, Doctoral Dissertation, University of Leiden, Leiden, Holland, 1958. (6) A. A. Maryott and F. Buckley, “Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State,” National Bureau of Standards Circular 537, U. S. Government Printing Office, Washington 25, D. C., 1953.
DIELECTRIC BEHAVIOR OF MIXTURES OF POLAR NONASSOCIATIVE LIQUIDS
simple binary systems will give some evidence as to the soundness of the analyses of the single substances in which two relaxation processes occur. In this initial investigation, the molecules of the compounds chosen are rigid and have electric moments which are of the same order of magnitude.
1303
0.4 r
Experimental 1-Chloronaphthalene, purchased from Matheson Coleman and Bell, was vacuum distilled. The fraction collected within the temperature range 129.0-129.5" E' gave a refractive index nZoD of 1.6330; literature value, Figure 1. Complex plane plot for solution containing 0.20 1.6332. Broniobenzene, purchased from Eastman mole fraction of 1-chloronaphthalene in benzene a t 25'. Kodak Co., was distilled under atmospheric pressure and the fraction coming over between 156.0 and 156.5" ~ 0 ~ was collected. The index of refraction, 7 ~ 1.5606, compared with a literature value of n20D 1.5598. Chlorobenzene, from Eastman Kodak Co., was purified by fractional distillation under atmospheric pressure. The distillate coming over between 133.4 and 133.7" had an index of refraction nZ0D 1.5246 compared ~ 0 ~ 1-Bronionaphwith the literature value 7 ~ 1.5248. thalene, from Eastman Kodak Co., was vacuum distilled a t 4 mm. The fraction collected a t 118" gave &n c' index of refraction nZoD 1.6582 compared with a literaFigure 2. Complex plane plot for solution containing 0.20 ture value of T L ~ O D 1.6588. mole fraction of 1-bromonaphthalene in chlorobenzene at 25". The dielectric constants and losses of the mixtures were measured at wave lengths of 575 m. (giving eo), 10.0, 3.22, and 1.25 cm. at a temperature of 25" by r z , the relaxation times of the two components, e m , the methods which have been previously d e ~ c r i b e d . ~ - ~optical dielectric constant, and C1, the relative amount The density balance and the viscosities were deterof the contribution of component 1, were varied to obmined with an Ostwald type viscometer. tain the best fit of eq. 1and 2 to the experimental data. l1
Results The maximum possible errors in the dielectric constant, e', and the dielectric loss, E", at loss tangents of about 0.2 are estimated as *2 and 5%, respectively. At the lower losses, the experimental error in the actual loss value is within +0.05. The dielectric constants and losses ere first plotted in the complex plane.l0 Figure 1, illustrating the Debye behavior of a mixture of 1-chloronaphtha!ene and benzene in a molar ratio of 1:4, is also typical cf the behavior observed for l-bromonaphthalene ai!d benzene mixed in the same ratio. Figure 2 for the system I-bromonaphthalene and chlorobenzene in the molar ratio 1:4is typical of the complex plane plots observed for the dipolar mixtures. The dielectric. constant and loss measurements were repeated in (ach case and the deviations observed from a symmetrical distribution could not be attributed to experinzental error. The data were, therefore, analyzed to obtain two relaxation times, r1 and r 2 ,corresponding to the two polar components. Initial estimates of r1 and
In these equations, C1 = 1 - Cz, w is the angular frequency, and eo is the static or low frequency dielectric constant. e, was estimated by assuming additive contributions from the respective components, while C1 and Cz were estimated from the relative molar concentrations. Once estimates of C1,Cz, and e, are obtained, initial estimates of r1 and rZ become apparent: The experimental and calculated values of e' and E" are (7) H. L. Laquer and C . P. Smyth, J . A m . Chem. SOC.,70, 4097
(1948). ( 8 ) W. M.Heston, A. D. Franklin, E. J. Hennelly, and C. P. Smyth, ibid., 72, 3443 (1950). (9) F. H.Branin and C. P. Smyth, J . Chem. Phys., 20, 1121 (1952). (10) K.S.Cole and R. H. Cole, ibid., 9,341 (1941). (11) K. Bergmann and C. P. Smyth, J . Phys. Chem., 64,665 (1960).
Volume 69, Number 4
April I965
1304
EDWARD FOREST A N D CHARLES P. SMYTH
given in Table I. The molar volumes, viscosities, and dispersion paranieters are given in Table 11. Since, in the case of each mixture, the number of equations relating the experimentally determined quantities E’ and e’‘ exceeds the number of adjustable parameters by two, the derived parameters form a unique set. Some latitude in the values of the parameters is possible through mutual conipensation but the adjustable interval is relatively small. Figure 3 is a plot of E” vs. log fre1.41.2
Table I : Observed and Calculated Dielectric Constants and Losses at 25’ Wave Mixture ooncn., mole fraction
0.493 broniobenzene in chlorobeiizene 0.500 1-chloronaphthalene in chlorobenzene 0.196 1-chloronaphthalene in Chlorobenzene
~
1.0-
0.198 1-bromonaphthalene in chlorobenzene
E’’ 0.8-
0.60.4-
0,199 1-bromonaphthalene in benzene 0,199 1-chloronaphthalene in benzene
Log f Figure 3. Plot of dielectric loss against log frequency for solution containing 0.20 mole fraction of 1-bromonaphthalene in chlorobenzene. The solid line represents the sum of the resolved dashed curves and the points are the experimentally determined loss values.
quency for the system 1-bromonaphthalene and chlorobenzene in the molar proportion 1:4. The dashed curves are the resolved dispersion regions, the solid line represents their sum, and the points are the experimentally determined loss values. Table I11 consists of the relaxation times, niacroscopic viscosities, and molar volumes of the pure liquids used in this investigation at the temperature of measurement. The relaxation times, viscosities, and molar volumes were determined by other workers in this laboratory.12
Discussion of Results Chlorobenzene, broniobenzene, 1-chloronaphthalene, and 1-bromonaphthalene have nearly the same electric moment. Therefore, the intenial field in the pure liquid state would not be expected to be very different from the internal field in the mixed state. This is evidenced by the fact that the static dielectric constant as well as the molar volume of a given mixture can be expressed by a simple mixing formula of the type EO
+
= XAEOAXBEOB
(3)
where X A and XB are the mole fractions of the components, (io is the static dielectric constant of the mixture, and cOA and €OB are the static dielectric constants of the pure components at the temperature of nieasThe .Journal of Physical Chemistry
length, cm.
Obsd.
Calcd.
Obsd. Calcd.
10.0 3.22 1.25 10.0 3.22 1.25 10.0 3.22 1.25 10.0 3.22 1.25 10.0 3.22 1.25 10.0 3.22 1.25
5.40 4.27 3.15 4.97 3.i4 3.05 5.34 4.26 3.24 5.28 4.25 3.23 2.93 2.66 2.52 2.95 2.69 2.52
5.34 4.33 3.10 4.85 3.74 2.94 5.24 4.33 3.17 5.17 4.23 3.14
0.77 1.47 1.21 1.00 1.17 0.82 0.79 1.36 1.19 0.81 1.30 1.06 0.20 0.28 0.17 0.20 0.29 0.20
,--e’-.
----e”---.
0.75 1.45 1.24 0.94 1.20 0.80 0.74 1.34 1.18 0.76 1.31 1.08
urement. As one might expect, the dielectric constants of the mixtures of 0.20 mole fraction of l-chloronaphthalene and 0.20 mole fraction of 1-bromonaphthalene, respectively, in benzene are considerably larger than predicted by eq. 3. It is apparent that the nonpolar benzene molecules separate the polar halonaphthalene molecules from each other, decreasing the probability of those molecular orientations which exist in the pure liquid and tend to decrease the effective moment and hence the dielectric constant. The amplitudes, C1and Cz, of the resolved regions are seen to be in the same ratio as the molar concentrations of the polar components in the mixtures. Since the polar components all have about the same moment, one would expect this to be the case. I t is thus reasonable to attribute the resolved dispersion regions to the individual components. From this point of view, then, the longer resolved relaxation time has been associated with the component that has the longer relaxation time in the pure liquid state, although the relaxation time of each component is different from that in the pure liquid because of the difference in ’molecular environment. The additivity of the dielectric constant arid the molar volume are consistent with the molecular or microscopic mixing thus indicated. This result is not necessarily in conflict with the conclusions of Schallamach3 and Denney4 for similar mixtures at extremely low temperatures (- looo), where only a single disper(12) E J. Hennelly. U‘ hf Heston, J r , and C T’ SmT t h , J A m Chem SOC, 70, 4102 (1948)
DIELECTRIC BEHAVIOR OF ~ I I X T U R OF E SPOLAR NONASSOCIATIVE LIQUIDS
1305
Table [I : Molar Volumes, Viscosities, Squares of the Refractive Indices, and Dispersion Parameters at 25" Molar M i x t u r e concn., mole fraction
a
0,493 bromobenzene in chlorobenzene 0.500 1-chloronaphthalene in chlorobenzene 0.196 1-chloronaphthalene in chlorobenzene 0.198 1-bromonaphthalene in chlorobenzene 0.199 1-bromonaphthalene in benzene 0,199 1-chloronaphthalene in benzene
5.547 5.341 5.497 5.458 3.026 3.020
volume,
Viscosity,
00.
CP.
nMD
em
0.896 1.442 0,964 1.033 0.925 0.85
2.371 2.509 2.397 2.419 2.380 2.356
2.41 2.61 2.50 2.58 2.47 2.44
103.38 119.57 109.04 109.83 98.93 98.68
Table I11 : LLIolar Volumes, Viscosities, and Relaxation Times of Pure Liquids1*
Substance
Chlorobenzene Brornobenzene 1-Chloronaphthalene 1-Bromonaphthalene
Molar volume,
Viscosity,
CC.
CP.
102.24 105.50 138.88 140.02
0.756 1.08 2.94 4.52
T
10-12,
X 8ec.
10.3 16.4 49.1 86.0
sion region was found. Schallamach attributed the relaxation process to relatively large regions in the liquid With increasing temperature] however, the average lifetime of these regions as well as their size would be expected to decrease until, at room temperatures, their influence upon the relaxation process might well become negligible. The relaxation time of 1-chloronaphthalene is seen to fall from 49.1 X 10-l2 sec. in the pure liquid state (Table 111) to 35 X sec. in the equimolar mixture with chlorobenzene, and to 32 X 10-l2 sec. in the 1:4 mixture with chlorobenzene (Table 11). It is thus seen that the relaxation time of 1-chloronaphthalene is relatively insensitive to further dilution with chlorobenzene over a considerable range of concentration. The viscosities of the mixtures when conipared to the viscosity of pure 1chloronaphthalene show an analogous behavior] although not as pronounced. The relaxation time of 1bromonaphthalene falls froin 86 X 10-l2 sec. in the pure liquid state to 35 x 10-l2 sec. in the 1 : 4 mixture with chlorobenzene, almost equal to that of l-chloronaphthalene in a similar ratio with chlorobenzene, the viscosities of the two mixtures differing by only 0.07 cp., while the viscosity of pure 1-bromonaphthalene is 1.58 cp. greater than that of 1-chloronaphthalene. It is likely that the introduction of the molecules of chlorobenzene results in considerably greater rotational and translational freedom of motion for the relatively flat halonaph-
n X 101*, ra X lo", sec. sec.
18 35 32 35
9.5 13 11 12
ro X 101*,
Cl
sec.
0.50 0.50 0.20 0.20 23.1 18.2
thalene molecules, the greatest effect taking place a t concentrations of chlorobenzene of less than 0.50 mole fraction. Only a small gradual increase in the relaxation time of chlorobenzene is observed with increasing concentration of the halonaphthalenes. The relaxation time of chlorobenzene is greater in the presence of l-bromonaphthalene than in the presence of l-chloronaphthalene. This is probably due to the greater internal friction coefficient arising from the higher polarizability of the bromine. The relaxation time of l-chloronaphthalene falls to 18.2 X 10-l2 sec. and that of l-bromonaphthalene to 23.1 X 10-l2 sec. if benzene is substituted for chlorobenzene in the 1 :4 mixture. This further decrease in the relaxation time which is accompanied by a similar decrease in the viscosity may be attributed to the decrease in the internal field and the internal friction coefficient. The equimolar mixture of chlorobenzene and broniobenzene appears to be slightly anomalous. The relaxation time of broniobenzene increases to 18.5 X 10-l2 sec. while that of chlorobenzene decreases to 9.5 X 10-l2 sec. These values are, however, so close to the pure component relaxation times that the slight anomalies may be the result of experimental error. I t is evident that the dielectric behavior of these binary mixtures of rather similar polar molecules can be represented in terms of the behaviors of the individual molecules. The two relaxation times change with concentration in a manner a t least qualitatively predictable from the change in niolecular environment, there being no evidence that larger liquid regions are involved in the relaxation processes. The satisfactory manner in which the dielectric behavior of these simple binary systems can be represented in terms of two relaxation times gives increased confidence in the methods of analysis which have been applied to single substances in which two relaxation processes can occur siniultaneously .
Volume 69, Number 4
April 1966
