A note on the temperature dependence of dielectric strength in supercooledliquidsS. S. N. Murthy Citation: The Journal of Chemical Physics 100, 6102 (1994); doi: 10.1063/1.467072 View online: http://dx.doi.org/10.1063/1.467072 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/100/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Temperature dependence of intermediate-range orders in the viscosity-temperature relationship ofsupercooled liquids and glasses J. Chem. Phys. 132, 104504 (2010); 10.1063/1.3353926 Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystaland in a model supercooled liquid J. Chem. Phys. 126, 204906 (2007); 10.1063/1.2741553 Temperature, density, and pressure dependence of relaxation times in supercooled liquids J. Chem. Phys. 116, 5033 (2002); 10.1063/1.1452724 Dependence of supercooling of a liquid on its overheating J. Chem. Phys. 107, 7964 (1997); 10.1063/1.475057 Further Note on the Temperature Dependence of the Viscosity of Liquids J. Appl. Phys. 24, 1067 (1953); 10.1063/1.1721445

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A note on the temperature dependence of dielectric strength in supercooled liquids

s. s. N. Murthy School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110 067, India

(Received 25 October 1993; accepted 6 December 1993)

The dielectric strength (de) of a dipolar liquid is often found to obey a simple relation of the forml

-3

(1)

where, EO, E"co are the limiting dielectric constants for the low and high frequencies; A, B I are empirical constants; fJ., is the dipole moment of the rotating unit, d is the density of the liquid, and W is the molecular weight. Though Eq. (1) is introduced as an empirical equation, it has some physical meaning in the sense that by putting A = 0 and B I = 18.3 (with fJ., expressed in Debye units) in Eq. (1), leads to the expression for d.E of a gas which has a theoretical background. l Not enough work has been done to see the validity of Eq. (1) in the supercooled state, but three recent reports4- 6 indicate a deviation from Eq. (1) in the super­cooled region.

In order to investigate the cause of the above deviation from Eq. (1), we have measured the dielectric strength of a number of liquids over the entire liquid range from boiling temperature down to the glass transition temperature. Re­garding the. purity of the samples and the details of measure­ments the reader may consult our earlier papers4

,7,8 published in this journal. The inaccuracy in the measured EO values is less than 1%. In Fig. 1, we have summarized the results in the form of dE(Wf fJ.,zd) plotted against 103fT. (We have also included the data of other workers3,S,9-11). The values of fJ., (taken in benzene) and the values of d are collected from Refs. 12 and 13. We have not included the temperature (T) dependence of d as it is found to be a much weaker function of temperature.14 However, the T dependence of E"co (taken as 1.05n1) has been incorporated. A deviation from a straight­line in Fig. 1 and hence from Eq. (1) is .noticed in some of the liquids. These deviations are not due to crystallization and, in fact, many of the liquids shown in Fig. 1 are noncrys­tallizable. All the data points where crystallization is sus­pected during the course of measurement are avoided in the plots shown in Fig. 1. The measure.d value of B I in Eq. (1) is found to be in the range of 30-60 for the true liquid side [for which Eq. (1) is almost valid in all the liquids] as compared to 18.3 for noninteracting dipoles (gas). In addition, A is found to be nonzero in liquids.

It is well known that in the supercooled region polariza­tion occurs chiefly by the reorientation of the whole mol­ecule due to cooperative motion, and the intramolecular ro­tation is usually very much hindered. If one looks at Fig: 1, from this point of view, one may notice that deviations from Eq. (1) are found only in the case of liquids which have a

significant intermolecular contribution to the polarization in the true liquid state. For example, in I-bromobutane, there is a significant contribution from the end group -CHzBr rota­tion in the true liquid state,S but in the supercooled state this contribution diminishes due to the hindrance of -CHzBr ro­tation because of the large liquid viscosity; and by necessity the polarization occurs chiefly by cooperative movement of the molecules as a whole.8 However, in I-bromo-2-methyl propane, the -CH2Br rotation is hindered even in the true liquid state, due to the presence of -CH3 group on the !Uiddle carbon atom and the corresponding curve shows no deviation from Eq. (1) even in the supercooled liquid state. In l-iodobutane, the end group -CHzI is more hindered than the -CHzBr group in I-bromobutane,8 and the deviation from Eq. (1) in the former is lesser than in the latter. In TIP,

50 2.8

2.6 €ot

400 2.4

2.2/'

2.0 300

~

3=~ w <I 200

100 , . .-,

0 1 2

3 4

--1

-," ~

v

3 4

5 6 7 8

.-13 .. ..-•• 12 ~

~

-'~ .-

6

7 5 6 7 11 12

103 KIT

FIG. 1. Variation of AE' W/ f.L2d with 103fT in a number of liquids (Refs. 4, 7, and 8). The curves are terminated at the boiIing- and glass-transition temperatures. The curves labeled are (1) 1-bromo-2-methylpropane (Refs. 9 and 11), (2) I-bromabutane, (3) 1-iodobutane, (4) 1-bromo-3-methylbutane (Ref. 9), (5) tritolylphosphate (TTP), (6) n-propylnitrite, (7) diethylphthalate (DEP) di-n-butylphthalate (DBP), (9) di-n-octylphthalate (DOP), (10) phe­nyl salicylate (salol), (11) benzylacetate (BA), (12) isopropylbenzene (Refs. 7 and 15), and (13) n-propylbenzene '(Ref. 10). For the last two the variation shown is that of EO' .

6102 J. Chern. Phys. 100 (8), 15 April 1994 0021-9606/94/100(8)/6102/2/$6.00 © 1994 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

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Letters to the Editor 6103

the main dipole is at th~ center of the molecule and the side groups contribute less significantly to polarization and inter- . estingly enough Eq. (1) is almost valid throughout the liquid range. Similarly, in the cases of IPB, BA, and DBP, etc., ,the deviation from Eq. (1) can be explained as due to significant contribution from the intramolecular rotation4,7,8 which is ab­sent to a very large extent in the supercooled state.

Thus, our study reveals that deviation from Eq. (1) is expected only in liquids which have a significant intramo­lecular contribution to polarization in their true liquid state, as the nature of mechanism changes to a mechanism which is predominantly intermolecular in nature in the supercooled state and this cross over results in a change in the effective dipole moment. From this study it is also clear that the de­viation from Eq. (1) cannot be taken as evidence for a struc­tural change. It is interesting to note that a simple formula as given by Eq. (1) describes the T dependence of t1€ of the

liquid over the entire range of its existence and is worthy of further theoretical consideration.

lH. Frohlich, Theory of Dielectrics (Clarendon, Oxford, 1958). 2F. X. Hassion and It H. Cole, J. Chern. J:?hys. 23, 1756 (1955). 3R. F. Grant and D. W. Davidson, J. Chern. Phys. 33,1713 (1960). 4S. K. Nayak and S. S. N. Murthy, J. Chern. Phys. 99, 1607 (1993). sp. K. Dixon, Phys.Rev. B 42, 8179 (1990). 6L. J. Jorat, G. A. Noyel, and 1. R. Huck, IEEE Trans. Electr. lnsu!. 26, 763

(1991). 7 Gangasharan and S. S. N. Murthy, J. Chern. Phys. 99, 9865 (1993). 8S. S. N. Murthy, 1. Sobhanadri, and Gangasharan, J. chern. Phys. 100, 4601 (1994).

9D. J. Denney, J. Ci).ern. Phys. 27,257 (1957). lOT. G. Copeland and D. J. Denney, J, Phys. Chern. 80, 210 (1976). 11 A. Das, A. Ghatak, and A. Hasan, Bull. Chern. Soc. Jpn. 46, 1345 (1973). 12R. C. Weast and M. J. Astle, CRC Handbook of Physics alid Chemistry,

63rd ed. (CRC, Florida, 1982). . 13 A. L. McCellan, Tables of Experimental Dipole Moments (W. H. Freeman,

San Francisco, 1963). 14 A. R. Ubbelohde, Melting and Crystal Structure (Clarendon, Oxford,

1965), p. 297. 15K. Higasi, K. Bergmann, and C. P. Smyth, J. Phys. Chern. 64,880(1960).

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