2616
S. CHANDRA AND J. PRAKASH
Dielectric Relaxation in a,w-Dibrornoalkanes in Benzene Solution1
by Suresh Chandra* and Jai Prakash Department of Physics, Uni8ersity of Goralchpur, Goralchpur, India
(Received February 1, 1071)
Publication costs borne completely by The Journal of Physical Chemistry
The dielectric constant and loss of 1,3-, 1,4-, 1,5-, and 1,6-dibromoalkanesin dilute benzene solutions have been measured at 35’ at the frequencies 450 kHz, 3.9 GHs, 24.7 GHz, and 36.8 GHz. It has been observed that the dielectric behavior of these a,w-dibromoalkanes can be represented by a skewed arc plot which is interpreted as a result of intramolecular cooperative relaxation phenomena.
1. Introduction
3. Results and Discussion
Molecular behavior as derived through dielectric relaxation measurements in liquids has long been a subject of controversy because of the ambiguity concerning the form of internal field correction.2 I n pure polar liquids the internal field effects are quite pronounced due to a large dipolar field. The situtation is simplified if the dielectric behavior of a polar molecule is studied in a nonpolar solvent. This allows the solute molecules to be examined in a quasiisolated state. The value of the dipole moment in solution is close to the gaseous value and the relaxation time is microscopic. I n general, it is less complicated to analyze the dilute solution dielectric data. I n this paper the values of the dielectric constant and loss of four a,@-dibromoalkanes (namely 1,3-dibromopropane, 1,Cdibromobutane, l,bdibromopentane, and 1,B-dibromohexane) in benzene solution at different frequencies and 35” are reported. An asymmetric distribution of relaxation time has been obtained in all these cases giving skewed arcs when dielectric loss is plotted against dielectric constant in a complex plane. The results are discussed in terms of characteristic relaxation time and asymmetric distribution parameter which may be either due to intramolecular cooperative relaxation phenomena or multiple relaxation times.
The dielectric behavior is generally represented as a plot between e’’ and e’ in a complex plane. For dilute solutions, some authors6r8have preferred a plot between a” and a’, where a” and a’ are the dielectric loss a d dielectric constant slopes, respectively. The values of a’ and a” can be evaluated from the experimental values of e’ and e” for dilute solutions of different concentrations. Five dilute solutions of varying concentrations in the mole fraction range (0-0.0510) have been used to obtain the values of a’ and a”. These values are given in Table I. The accuracy of measurement of a’ is f1% and of a” *5%. Plots of a” us. a’ for the four a,w-dibromoalkanes in benzene solution are given in Figure 1 which are obviously asymmetric (skewed arcs). The skewed arcs can be analyzed in terms of either (i) Davidson-Cole representation which may result from inter- or intramolecular cooperative phenomena or (ii) superposition of two or more noninteracting Debyetype relaxations. For the present case two probable relaxations are due to end-over-end molecular rotation and end group-CH2Br group rotation. The Davidson-Cole’ type formula is
2. Experimental Section The value of the dielectric constant and loss at 35” of these substances in benzene solution was determined at 450 kHz, 3.87 GHz, 24.65 GHz, and 36.81 GHz. The experimental arrangement was essentially the same as used by us3t4earlier. The standing wave method was used for evaluating the complex dielectric constant. The refractive index was measured at 35” using an Abbe refractometer. Substances of the Purum grade were obtained from M/S Fluka AG (Switzerland) which were further purified by fractional distillation. Benzene supplied by 21,’s RDH (India) was fractionally distilled thrice before use. The Journal of Physical Chemistry, Vol. 76, N o . 17, 1971
__a,_--
a* a0
- a,
(1
+
1 iwTos)@~o’
where a* = a’ - id’, ps0l is the asymmetric distribution parameter associated with the characteristic re(1) This paper forms a part of the Thesis submitted by Jai Prakash for the Ph.D. degree, Gorakhpur University, 1969. (2) (a) C. P. Smyth, “Dielectric Behaviour and Structure,” McGrawHill, New York, N. Y.,1955; (b) N.E.Hill, W. E. Vaughan, A. H. Price, and M. Davies, “Dielectric Properties and Molecular BP haviour,” Van Nostrand-Reinhold, London, 1969. (3) S. Chandra and D. Nath, J . Chem. Phys., 51, 5299 (1969). (4) S. Chandra and J. Prakash, ibdd., 54, 5366 (1971). (5) W.M. Heston, Jr., A . D. Franklin, E. J. Hennelly, and C. P. Smyth, J . A m e r . C h e n . SOC.,72,3443 (1950). (6) W. F. Hassel, M. D. Magee, S. W. Tucker, and S. Walker, Tetrahedron, 20, 2137 (1964). (7) D. W. Davidson and R. H. Cole, J . Chem. Phys., 19, 1484 (1951).
DIELECTRIC RELAXATION IN ~,~-DIBROMOALKANES IN BENZENE SOLUTION 3
2617
r (A) 1.3-
3
ft
I
a
Table I : Complex Slopes of Some a,w-Dibromoalkanes in Benzene Solution at 35" Substance
l13-Dibromopropane
1,5-Dibromopentane
l,&Dibromohexane
Frequency of measurement
a'
450 kHz 3 . 8 7 GHz 24.65 GHa 36.81 GHz Optical 450 kHz 3 . 8 7 GHz 24.65 GHz 36.81 GHz Optical 450 kHz 3 . 8 7 GHz 24.65 GHz 36.81 GHz Optical 450 kHz 3 . 8 7 GHz 24.65 GHz 36.81 GHz Optical
5 . 7 1 (ao) 5.60 3.44 2.89 0 . 0 9 (a,) 5.96 (ao) 5.66 2.71 2.18 0.07 (a,) 7.14 ( U O ) 6.70 2.92 2.50 0 . 1 8 (a,) 7 . 4 1 (ao) 6.68 2.64 2.12 0 . 1 3 (a,)
a"
0.77 2.42 2.48
1.18 2.39 2.22 1.50 2.60 2.35 1.88 2.30 2.07
laxation times (res) in solution, and ao and a, are the static dielectric constant and optical dielectric constant slopes, respectively. a, has been determined from a' us. a"/w plots and given in Table I. a, can also be evaluated from a plot between concentration and square of the refractive index provided that e, = n2D. The values of a, calculated by both these methods agree, which suggests that for these cases e, = n% is a valid approximation. Separating real and imaginary parts of eq 1 and rearranging, we get
Equations 1 and 2 can be used for finding the values of psol and T ~ ~The . locus of eq 1 is a semicircle at the lowfrequency end which asymptotically reduces to a straight line at the high-frequency end. This line makes an angle psOl.rr/2 with the real axis, thus giving the value of psol. Then, 7c9is evaluated using eq 2. The calculated values of psOl and 7os are given in Table 11. The increasing value of psol with decreasing chain length means that the molecules tend to behave more and more as rigid spherical molecules with decreasing chain length. Similar behavior is also obtained by Vaughan, Lovell, and Smyth* for n-alkyl bromides. The decreasing value of psol with increasing chain length suggests that the segmental reorientations become increasingly possible as the number of C-C bonds increases. This is in conformity with the results obtained in the pure liquid state for these substance^.^ The value of T~~ is found to increase with the increasing chain length, which is due to the increase in the molecular size. Similar behavior has also been observed for some a,w-dichloroalkanes in pure liquid and benzene solution by US.^ An idea about the effect of the dipolar field can be sought by comparing the dielectric relaxation parameters of a substance in pure liquid state and dilute solutions in nonpolar solvent. Table I1 also presents such a comparison. The values of p are higher for solution showing that the distribution of relaxation time decreases or becomes more symmetrical. The values of T~~ are lower than the corresponding values in the pure liquid because of the presence of a relatively smaller dipolar field in solution. The smaller value of rCsin solution also suggests that there is little contribution from the rotation of the molecule as whole.lo A new distribution function for analyzing dielectric relaxation parameters in the systems exhibiting intramolecular rotating groups has been suggested by Higasi, et aZ.,ll and Vaughan, et aL8 They have been able with this distribution function to explain successfully the dielectric behavior of n-bromoalkanes. This distribution function, however, has been found to fail for a,wdibromoalkanes. l2 The present dielectric behavior can also be analyzed in terms of superposition of two noninteracting Debyetype di~persions'~ which could not be done by us with (8) W. E. Vaughan, W. S. Lovell, and C. P. Smyth, J. Amer. Chern. Soc., 90, 6318 (1968). (9) 9. Chandra and R. A. Yadav, unpublished work. (10) G. P. Johari, J. Crossley, and C. P. Smyth, J . A m e r . Chem. Soc., 91,5197 (1969).
(11) K.Higasi, K.Bergmann, and C. P. Smyth, J . Phys. Chem., 64, 880 (1960). (12) 9. K.Garg and C. P. Smyth, unpublished work. (13) A. Budo, Phys. Z., 39,706 (1938). The Journal of Physical Chemistry, Vol. 76, N o . 17,1971
S. CHANDRA AND J. PRAKASH
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Table I1 : Comparison of the Dielectric Relaxation Parameters in Pure Liquid and Benzene Solution of Some a,w-Dibromoalkanes at 35" ro X
rz X
sec
X 10'2, sea
20.7 7.3 33.0 12.3 37.5 15.0 47.4 20.7
12.9 6.4 22.2 9.1 23.0 11.2 26.4 14.4
2.5c 2.8 2.50 3.1 2.5' 2.8 2.5c 3.2
10'2, Substance
1,3-Dibromopropane
Statea
Lb 0.57 B
1,4Dibromobutane
Lb B
l,5-Dibromopen tane
Lb B
1,6-Dibromohexane
p
Lb B
0.73 0.55 0.67 0.54 0.63 0.53 0.59
TI
10'2, sec
a L and B stand for "pure liquid" and "benzene solut,ion," respectively. b S. Chandra and J. Prakash, J. Chem. Phys., 54, 5366 (1971). Average value.
certainty due to lack of measurements a t the higher frequency side. However, an approximate value of 71 (end-over-end relaxation time) and 7 2 (-CH2Br group rotation relaxation time) can be obtained from a plot between a' vs. a"w as suggested by Cole.14 The plot between a' vs. a"w in the present case is found to consist of two slopes from which 71 and 7 2 have been calculated. These values are also given in Table 11. Within the uncertainties16 inherent in the experiment and method of analysis the value of 72can be considered to be independent of chain length. The values of 7 2 in solution and pure liquid agree and hence it can be
The Journal of Physical Chemistry, Vol. 76, No. 17,1071
identified with -CH2Br group rotation relaxation which is expected to be independent of the surrounding. This value is also comparable to the -CH2Cl group rotation sec) relaxation16value (3.0 X 10-l2 sec and 3.6 X which is a similar group. The value of 71 is increasing with the chain length as rceand hence can be identified with the end-over-end rotation relaxation time. The values of 71 in solution are lower than 71 in pure liquid as expectede2" However, it may be remarked that 71 and 7 2 obtained by such an analysis are only approximate and no knowledge about the relative weight factors of the two relaxation processes can be had. Thus, it is seen that both the representations in terms of a Davidson-Cole plot or two relaxation mechanism explain the results equally satisfactorily. The accuracy of the measurement is such that it cannot establish the preference of one model over the other. However, the evidence that r2in solution and pure liquid are approximately the same gives weight to the two relaxation model though intramolecular cooperative phenomena cannot be completely ruled out.
Acknowledgments. We thank Professor D. Sharma for his keen interest, Professor Krishnaji for helpful discussions, and Dr. S. C. Srivastava for his help in the measurements. (14) R. H. Cole, J. Chem. Phys., 23, 493 (1955). (15) M. D. Magee and 8. Walker, Trans. Faraday Soc., 62, 3093 (1966) (16) 5. Dasgupta and C. P. Smyth, J. Amer. Chem. Soc., 90, 6318 (1968). I
