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(18)B. M. Oughton and P. M. Harrison, Acta Crystallogr.. 12, 396 (1959). (19)M. 0.Chaney and L. K. Steinrauf, Acta Crystallogr., Sect. B, 30, 711 (1974). (20)L. E. Sutton, 0. Kennard, H. M. Powell, and D. H. Whiffen, Chem. SOC., Spec. Pub/., No. 18 (1965). (21)G. Birnbaum, Acta Crystallogr., 23, 576 (1967). (22)iUPAC-IUB Commission on Biochemical Nomenclature, J. Mol. Bo/. 52, l(1970). (23)A. Bondi. J. Phys. Chem., 68, 441 (1964) (24)A. D. Rae, J. Chem. Phys., 5 0 , 2672 (1969). (25)R. H. Dunhill and J. R. Pilbrow, J. Chem. Phys., 45, 1474 (1966). (26)J. A. McMillan and D. J. Cravens, J. Chem. Phys., 57, 3268 (1972). (27)M. E. Martell and M. Calvin, “Chemistry of the Metal Chelate Cornpounds”, Prentice-Hall, Englewood Cliffs, N.J., 1956,p 35. (28)J. H. M. Thornley, B. W. Mangum, J. H. E. Griffiths, and J. Owen, Proc.
Phys. SOC.London, 79, 1263 (1961). (29)C. Chow, K. Chang, and R . D. Willett, J. Chem. Phys., 59, 2629 (1973). (30)P. A. Narayama and K. V. L. N. Sastry, J. Chem. Phys., 57, 3266 (1972). A, 1516 (1968). (31)D. E. Billing and B. J. Hathaway, J. Chem. SOC. (32)M. J. Bew, D. E. Billing, R. J. Dudley, and B. J. Hathaway, J. Chem. SOC. A, 2640 (1970). (33)R . J. Dudley and B. J. Hathaway, J. Chem. SOC.A, 2799 (1970). (34)A. Dijkstra, Acta Crystallogr., 20, 588 (1966). (35)J. F. Blount, K. A. Fraser, H. C. Freeman, J. T. Szymanski, and C. H. Wang. Acta Crystallogr.,22, 396 (1967). (36)M. Bonamico, G. Dessy. A. Mugnoli, A. Vaciago, and L. Zambonelli, Acta Crystallogr., 19, 886 (1965). (37)G. Narongiu, €. C. Lingafelter, and P. Paoletti, horg. Chem., 8, 2763 (1969).
Dielectric Dispersion in n-Propylbenzene Thomas G. Copeland and Donald J. Denney. Department of Chemistry, Hamilton College, Clinton, New York 13323 (Recelved Ju/y 25, 1975) Publication costs assisted by Hamilton College
Dielectric dispersion in n-propylbenzene has been studied between 150 and 138 K over the frequency range lo2 to lo5 Hz. The results are described accurately by the Cole-Davidson skewed-arc function which has been used previously for a large number of liquids and has generally been interpreted as indicating the importance of cooperative intermolecular effects in the dynamical behavior. The interpretation of earlier work on similar compounds in terms of a few discrete relaxation times is examined.
Introduction Static’s2 and dynamic) dielectric properties of a number of alkyl benzenes have been measured at room temperature and above. The dispersion behavior is somewhat ambiguous because of the limited number of microwave frequencies used and the small values of dielectric increment and loss arising from the small dipole moments (0.1 to 0.5 D). Since viscosity studies by Barlow, Lamb, and Matheson4 indicated that several of these alkyl benzenes would undercool it appeared that the dispersion spectrum could be examined in the audio-radiofrequency region at low temperatures and its character determined more easily. Of the three materials tried in this study (isopropylbenzene, n butylbenzene, and n-propylbenzene) only the latter could be undercooled sufficiently. A second reason for studying the dispersion behavior of these compounds is to enable comparisons to be made between the spectra of nonhydrogen bonded liquids with low and high dipole-dipole interactions. Extensive data are available for a number of aliphatic bromide^^-^ (g 2.0 D). Dilution of the dipole interaction by solution measurements in a readily undercooled solvent (2-methylpentane) led to disappointing results since the resulting dispersion could not be characterized by any simple analytic funct i ~ n(The . ~ present authors believe this result was due to a combination of dispersions of solute and solvent which, though in quite different frequency ranges in the pure state a t the same temperature, probably overlap significantly in the mixture because the molecular environments are similar.) With the alkyl benzenes the dipole interactions should
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The Journal of Physical Chemistry, Vol. 80, No. 2, 1976
be considerably smaller though differences in molecular shape and bond moment distribution may make it difficult to make precise quantitative estimates. Experimental Section n-Propylbenzene was deoxygenated by a stream of nitrogen and then distilled over P2O5 through a Vigreux column in a nitrogen atmosphere. The middle portion of the distillate was stored under nitrogen. This portion showed only one peak on the gas chromatograph and the static dielectric constant and refractive index at 20°C were in good agreement with literature values: €0 = 2.370 (2.3721b), n D = 1.4921 (1.49201°). Dielectric constant (6’) and loss (e’’) measurements in the range lo2 to lo4 Hz were made with a General Radio 1620A capacitance measuring assembly and extended to lo5 Hz with a Cole-Gross bridge.ll The three-terminal coaxial cell had a nominal air capacitance of 8 pF and calibration showed that stray capacitance effects were negligible. Temperature measurement and control were accomplished as described previously.12 Static dielectric constants were measured from 298 to 138.3 K and dispersion parameters determined from 149.4 to 138.3 K. The n-propylbenzene could be cooled to the lowest temperature used and then reheated slowly through the melting point with no evidence of freezing, either visual or electrical. For a given temperature, errors in the dielectric constant (assuming no error in the air capacitance) are estimated to be in the range 0.2-0.3% while loss values may have errors of 441% a t the frequency extremes although 1-2% is more
211
Dielectric Dispersion in n-Propylbenzene likely in a wide range around the loss maximum. The room temperature air-capacitance value was used in all calculations. The listed temperature is estimated to be within 0.2’ of the correct value.
Results Complex plane plots of the data were asymmetric and were analyzed in terms of the Cole-Davidson equation13 =
- ip = 6 1 + ( € 0 - €1)/(1-k iwT0)’
(1)
where €0 and €1 are the low- and high-frequency limits of the dielectric constant, d, w is the angular frequency (= 2 ~ f ) TO , is a characteristic relaxation time, and 0 is a dimensionless parameter in the range 0 to 1. The parameters T O , 0, and €1 were determined with the aid of a GE TSS/645 computer. Trial values were incremented over a range consistent with the observed complex plane plots and the best fit was taken to be the set of parameters which minimized the function
xw((crfobsd
TABLE I: Dielectric Dispersion Parameters for n-hopylbenzene T,K EO E, lo6 r o ,sec fl
293.3 248.9 205.2 149.4 147.4 146.4 145.3 144.5 143.5 142.5 141.5 140.5 139.5 138.3
2.370 2.465 2.581 2.777 2.786 2.790 2.794 2.797 2.803 2.806 2.812 2.815 2.820 2.824
2.466 2.472 2.474 2.475 2.475 2.477 2.478 2.477 2.478 2.480 2.479
2.58 5.58 8.12 13.0 18.5 31.8 50.4 76.5 141 254 473
S
0.75 0.74 0.745 0.72 0.74 0.71 0.71 0.715 0.675 0.655 0.635
0.033 0.010 0.018 0.021 0.045 0.025 0.033 0.024 0.019 0.027 0.037
L
I
- ~f’ca1cd)/.frobsd)2] 1’2
M where M is the number of frequencies. As shown in Table I, the values of S range from 0.01 to 0.045 with about 90% of the contribution from deviations in loss values. Calculated and observed values of d and t r f for one temperature are plotted in Figure 1. The agreement for each frequency is well within the experimental errors cited above. Table I lists a representative set of dispersion parameters taken from two runs. Generally e l values are estimated to have a precision of f0.005 and 0 of f0.02. These estimates may be exceeded somewhat a t the highest two or three temperatures in the dispersion region where the highfrequency portion of the spectrum is least well defined. 70, the cutoff relaxation time of the Cole-Davidson representation, has the temperature dependence generally observed for undercooled liquids in the region where the viscosity exceeds about lo2 P (see Figure 2). The curve is slightly convex toward the abscissa in a log TO - 1/T plot. The asymmetry parameter, 0, increases with increasing temperature but the temperature range is too small to allow any extrapolations. A value of 0 = 1 corresponds to the familiar Debye locus representing a single exponential relaxation process. One interesting contrast between the relaxation behavior of n-propylbenzene and that in the aliphatic bromides lies in the apparent absence in the former of any appreciable deviations from the Cole-Davidson (skewed-arc) analytic function a t high frequencies. One could argue that the lowest temperatures used were not such as to show these deviations in the frequency range used. However, comparison of the €1 values found here with values of nb, n t (refractive index extrapolated to zero frequency considering only electronic polarization), and 6- (which adds to n! a contribution due to atomic polarization) extrapolated to the same temperature region indicates there can be little contribution from high-frequency deviations. [Room temperature values of n, are taken from ForziatilO and the contribution from atomic polarization is based on Altshuller’slb assumption that the value for n-propylbenzene is the same as that for the nonpolar 1,3,5-trimethylbenzene. Values of ng, n?, and em in our temperature range were calculated assuming
-
10
Lp
L1
L) 0.1
-,1w1rP, , , ,
,
1
, ,
E’ ,
,
1
, , , ,
1
1
,
Flgure 1. Complex plane diagram for n-propylbenzene at 139.5 K: 0, observed values; X, values from eq 1 using parameters in Table 1. (Numbers beside points are frequencies in kHz.)
t
6.6
6.8
7.0
7.2
Figure 2. Log TO (relaxation time parameter) vs. reciprocal absolute temperature for n-propylbenzene.
the Clausius-Mossotti relation for each to be temperature independent. T i m m e r r n a n ~ ’gives ~ density values for n propylbenzene from 296 to 177 K and it is a linear function of T over this range. Also, Barlow et al.4 found the density to be linear within 0.1% from 320 to 150 K. Extrapolation to the region of interest here (149 to 138 K) can be made The Journal of Physical Chemistry, Vol. 80. No. 2. 1976
212
with an error estimated to be less than 0.5%.] The results are shown in Figure 3. In contrast to the usual observation, the observed e l is slightly less than the calculated n& (0.30.8%) and about 2.5% less than the calculated em. Some of this discrepancy can be attributed to the temperature dependence of the geometric cell capacitance which decreases by about 0.25% in going from 298 to 95 K. The presence of voids in the glassy sample may also have made some contribution but the effect would have had to be reproducible since the eo values in two separate runs were the same within 0.002. It is probable that the high value of e- is due to an overestimate of the atomic contribution to the molar refraction. In any event any high-frequency contribution to the orientation polarization, ordinarily estimated as (€1 n;)/(eo - e l ) , would appear to be much less than the 3 to 5% observed for isoamyl bromide. Altshullerlb calculated a dipole moment at 293 K of 0.35 using the Onsager equation with em to account for the electronic and atomic contributions. At 149 K we calculate 0.32 using em and 0.36 using q. There do not seem to be any reliable vapor data.
Discussion Hassell and Walker? interpreted their microwave data for several monoalkyl benzenes in the range 15-6OoC in terms of two relaxation regions, each characterized by a single exponential. The interpretation was based on an apparent resolution of e’ vs. we’’ plots into two straight lines. Only six frequencies were available and, therefore, the resolution is not convincing. If one plots, in the same way, a dispersion corresponding to eq 1, one can obtain two reasonable “straight” lines within experimental error if the frequencies used are less than 4 or 5 times that of the loss maximum as in Hassell and Walker’s data. The present work suggests that the resolution is not physically meaningful. The low temperature behavior of n-propylbenzene is similar to that found in many other liquids in which no specific association effects, e.g., H bonding, are present as indicated by the success of the Onsager equation in giving reasonable values for the dipole moment, values which are essentially constant over a wide temperature range. Although the temperature region here is much lower than that used by Hassell and Walker, work on isoamyl brornide5s6s8and n-octyl iodide7 indicates that the basic character of the dispersion remains unchanged over a wide temperature interval with a continuous change in the parameters. Although the dipole moment of n-propylbenzene and isoamyl bromide differ by a factor of about 6, there are no essential differences in the dispersion behavior, indicating that dipolar interactions based on the overall molecular moment play an insignificant role in determining this behavior. The @ values in n-propylbenzene (0.64-0.74) are somewhat higher than those in isoamyl bromide (0.57-0.61) a t temperatures where the dispersion frequencies are comparable but we are not prepared to speculate, at the present time, on the molecular origins of this difference. Glarum: Adam,15 Anderson and Ullman,16 and Zwan-
The Journal of Physical Chemistry, Vol. 80,No. 2, 1976
Thomas G. Copeland and Donald J. Denney
2.8-
++--’b--0-
€ 0
++e+-+-y-*
2.7-
2.61
i
2.5
E,
n: 6I
o-o-o-o-o-o-o-a-o-o-o-
t
na J
i.8
I
I
7.0
IOOO/T (Kl I
I
7.2
I
7.4
Figure 3. Dielectric constants and refractive indices for n-prop Ibenzene vs. reciprocal absolute temperature. The lines (ern. n:) were calculated assuming temperature independence of the Claus-
d,
ius-Mossotti function.
zig17 have all proposed models of the dynamical behavior of dielectric fluids that, with appropriate choice of parameters, give rise to an asymmetric dispersion. The common feature in all of these models is the importance of intermolecular cooperative effects. Distributions of relaxation times due to intramolecular modes cannot be ruled out in all cases, especially a t higher temperatures where the relative importance of cooperative effects may diminish, but there should be clear molecular reasons for invoking these and this does not appear to be the case for the simple monoalkyl benzenes. Acknowledgment. This work was supported in part by the National Science Foundation URP Program.
References and Notes (1)(a) A. P. Altshuller, J. Phys. Chem., 57, 538 (1953);( b ) \bid., 58, 392 (1954). (2)C. W. N. Cumper, A. I. Vogel, and S. Walker, J. Chem. SOC.,3640 (1957). (3)W. F. Hassell and S. Walker, Trans. Faraday SOC..82, 861 (1966). (4)A. J. Barlow, J. Lamb, and A. J. Matheson, froc. R. SOC.London, Ser. A, 292, 322 (1966). (5) D. J. Denney, J. Chem. Phys., 27, 259 (1957). (6)S.H. Glarurn, J. Chem. fhys., 33, 639 (1960). (7) F. I. Mopsik and R. H. Cole, J. Chem. fhys., 44, 1015 (1966). (8)J. G.Berberian and R. H. Cole, J. Am. Chem. SOC.,90, 3100 (1968). (9)D. J. Denney and J. W. Ring, J. Chem. Phys., 44, 4621 (1966). (IO)A. F. Forziati, J. Res. Natl. Bur. Stand., 44, 373 (1950). (11) R. H. Cole and P. M. Gross, Jr., Rev. Sci. Instrum., 20, 252 (1949). (12) D. J. Denney and J. W. Ring, J. Chem. Phys., 39, 1268 (1963). (13)D. W. Davidson and R. H. Cole, J. Chem. Phys., 19, 1484 (1951). (14)J. Timmermans, “Physico-chemlcal Constants qf Pure Organic Compounds”, Elsevier, New York, N.Y., 1950.
(15)G. Adam, J. Chem. fhys., 43, 662 (1965). (16)J. E. Anderson and R. Ullman, J. Chem. Phys.. 47, 2178 (1967). (17)R. Zwanzig, J. Chem. Phys., 38, 2766 (1963).
