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Dielectric relaxation study of formamide-propylene glycol using timedomain reflectometryV. V. Navarkhelea; M. K. Bhanarkarb

a Department of Physics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, Indiab Department of Electronics, Shivaji University, Kolhapur 416004, Maharashtra, India

Online publication date: 13 June 2011

To cite this Article Navarkhele, V. V. and Bhanarkar, M. K.(2011) 'Dielectric relaxation study of formamide-propyleneglycol using time domain reflectometry', Physics and Chemistry of Liquids, 49: 4, 550 — 559To link to this Article: DOI: 10.1080/00319104.2010.508041URL: http://dx.doi.org/10.1080/00319104.2010.508041

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Physics and Chemistry of LiquidsVol. 49, No. 4, July–August 2011, 550–559

Dielectric relaxation study of formamide–propylene glycol using

time domain reflectometry

V.V. Navarkhelea* and M.K. Bhanarkarb

aDepartment of Physics, Dr. Babasaheb Ambedkar Marathwada University,Aurangabad 431004, India; bDepartment of Electronics, Shivaji University,

Kolhapur 416004, Maharashtra, India

(Received 31 May 2010; final version received 10 July 2010)

Using picoseconds time domain reflectometry, dielectric relaxation studieshave been carried out for formamide (FMD)–propylene glycol (PLG)mixtures over the frequency range from 10MHz to 20GHz at varioustemperatures. The dielectric parameters, i.e. static dielectric constant ("0)and relaxation time (�), have been obtained by Fourier transform and leastsquares fit methods. The excess dielectric properties and Kirkwoodcorrelation factor of the mixtures have also been determined. TheKirkwood angular correlation factor is greater than one (geff4 1) inFMD-rich region and less than one (geff5 1) in PLG-rich region, whichindicates that in the mixture the dipole pairs have been formed in such away that their orientation is parallel in FMD-rich region and antiparallelin the PLG-rich region.

Keywords: dielectric constant; excess dielectric properties; Kirkwoodcorrelation factors; formamide–propylene glycol

1. Introduction

Dielectric relaxation spectroscopy [1], which measures the complex permittivity ofa ample as a function of frequency of the applied electric field, is a powerful tool forthe investigation of the behavior of conducting fluids, and it provides invaluableinsights into their dynamics and structure [2]. The dielectric relaxation studies onbinary mixtures are important for the understanding of hydrogen bonding,intermolecular interactions and dynamics of liquid mixture [3–7]. Amides andglycols have attracted the attention of a number of researchers in different fieldsbecause of high dielectric permittivity and biological applications [8–11]. The amiderepresents an important class of organic solvents due to high polarity, strongsolvating power and large liquid state range [12,13]. In this study, the dielectricrelaxation properties of formamide (FMD)–propylene glycol (PLG) mixtures over awide range of concentrations at different temperatures ranging from 20�C to 40�Cusing a time domain reflectometer (TDR) in the frequency range from 10MHz to20GHz. In this study, FMD has been considered as solution A and PLG as solutionB. The excess dielectric properties, Kirkwood correlation factor and thermodynamicproperties for the binary mixtures have been determined.

*Corresponding author. Email: vvn_bamu@yahoo.co.in

ISSN 0031–9104 print/ISSN 1029–0451 online

� 2011 Taylor & Francis

DOI: 10.1080/00319104.2010.508041

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2. Experimental

2.1. Chemicals and sample preparation

The chemicals used in this study are of spectroscopic grade with 99.9% purity andwere used without further purification. The solutions were prepared by mixing FMDwith PLG at 11 different volume percentages of PLG (0% to 100%) in steps of 10%.

2.2. Apparatus

The apparatus used in this study was Tektronix 7854 sampling oscilloscope with7512 TDR unit. In this apparatus, a fast-rising step voltage pulse of 200mVamplitude and 25 ps rise time with reflection frequency of 1KHz is generated andpropagated through a coaxial transmission line. The sample is placed at the end ofthe coaxial transmission line in a standard military application (SMA) coaxial cell.The SMA cell used for this study had 3.5mm outer diameter and 1.35mm effectivepin length. The step pulse generated by a tunnel diode and the pulse which isreflected from the sample cell were sampled by a sampling oscilloscope in the timewindow of 5 ns. The reflected pulse without sample R1(t) and with sample Rx(t) weredigitised with 1024 points in the oscilloscope memory and then transferred to a PCthrough a general purpose interface bus (GPIB) card.

The temperature controller system with water bath and a thermostat has beenused to maintain a constant temperature within the accuracy limit of ��C.The sample cell is surrounded by a heat insulating container through which watermaintained at a constant temperature using a temperature controller systemiscirculated.

3. Data analysis

The time-dependent data was processed to obtain a complex reflection coefficientspectrum �*(!) over the frequency range from 10MHz to 20GHz. Fouriertransformation was given by Shannon [14] and Samulan [15] as

��ð!Þ ¼c

ð j!d Þ� �ð!Þ=qð!Þ½ �, ð1Þ

where � (!) and q (!) are Fourier transforms of [R1(t)�Rx(t)] and [R1(t)þRx(t)],respectively, c the velocity of light, ! the angular frequency, d the effective pin lengthand j¼ � 1.

The complex permittivity spectra "*(!) were obtained from reflection coefficientspectra �*(!) by applying calibration method given by Cole et al. [16]. The examplesof complex spectra ("*(!)) of FMD–PLG solutions for three temperatures are shownin Figure 1(a) and (b), respectively. The Cole–Cole plots of pure FMD–PLGsolutions for three temperatures are shown in Figure 2(a) and (b), respectively.The experimental values of "* are fitted with Debye equation [17–19].

"�ð!Þ ¼ "1 þ"0 � "11þ ð j!�Þ½ �

, ð2Þ

where "0, "1 and � are fitting parameters. In Equation (2), "0 is the staticpermittivity, � the relaxation time and "1 the permittivity at high frequency.

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A nonlinear least squares fit method [20] was used to determine the values

of dielectric parameters.The information related to binary mixture interaction of FMD–PLG may be

obtained by excess properties [21] like excess permittivity and excess inverse

relaxation time in the mixture. The excess permittivity is defined as

"E ¼ ð"0 � "1Þm � ð"0 � "1ÞA � XA þ ð"0 � "1ÞBXB

� �, ð3Þ

where X is the mole fraction and suffixes m, A and B represent mixture, liquid

A (FMD) and liquid B (PLG), respectively. The excess permittivity may provide

qualitative information about the formation of new structure in the mixture

as follows:

(1) "E¼ 0: Indicates that solutions A and B do not interact.(2) "E5 0: Indicates that solutions A and B interact in such a way that the

effective dipole moment gets reduced.(3) "E4 0: Indicates that solutions A and B interact in such a way that the

effective dipole moment increases.

100

120

80

60

40

20

00 5 10 15 20

Frequency in GHz

0 5 10 15 20

Frequency in GHz

50

45

40

35

30

25

20

15

10

5

0

Com

plex

per

mitt

ivity

Com

plex

per

mitt

ivity

e'

e''

e'

e''

(a)

(b)

Figure 1. Dielectric spectrum of pure FMD (a) and pure PLG (b) for three temperatures.

552 V.V. Navarkhele and M.K. Bhanarkar

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The excess inverse relaxation time is defined as

ð1=�ÞE ¼ ð1=�Þm � ð1=�ÞA � XA þ ð1=�ÞB � XB

� �, ð4Þ

where (1/�)E is the excess inverse relaxation time which represents the averagebroadening of dielectric spectra in the resonance spectroscopy given by Mehrotra

and Boggs [22] and Ahire et al. [23].The information regarding the dynamics of binary mixture interaction is as

follows:

(1) (1/�)E¼ 0: There is no change in the interaction of solutions A and B.(2) (1/�)E5 0: The interaction of solutions A and B produces a field such that

the effective dipoles rotate slowly.(3) (1/�)E4 0: The interaction of solutions A and B produces a field such that

the effective dipoles rotate faster, i.e. the field will cooperate in the rotation

of dipoles.

3.1. The Kirkwood model

The Kirkwood correlation factor g [24] provides information regarding theorientation of the electric dipoles in polar liquids.

60

50

40

30

20

10

00 20

20100

40

4030 50

60 80 100 120Dielectric constant

Dielectric constant

25

20

15

10

5

0

Die

lect

ric lo

ssD

iele

ctric

loss

(a)

(b)

Figure 2. Cole–Cole plot of pure FMD (a) and pure PLG (b) for three temperatures.

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For a pure polar liquid, the Kirkwood correlation factor g may be obtainedby the expression

4�N�2�

9KTMg ¼ð"0 � "1Þ 2"0 þ "1ð Þ

"0ð"1 þ 2Þ2, ð5Þ

where � is the dipole moment, � the density at temperature T, M the molecularweight, K the Boltzman constant, N the Avogadro’s number, "0 the static dielectricpermittivity and "1 the dielectric permittivity at high frequency, often representedby the square of the refractive index.

Modified forms of this equation which have been used to study the orientationsof electric dipoles in the binary mixtures are given by Kumbharkhane et al. [25,26];two such equations used are as follows:

4�N

9kT

�2M�MMM

XM þ�2F�FMF

XF

� �geff ¼

"0m � "1mð Þ 2"0m þ "1mð Þ

"0mð"1m þ 2Þ2� � , ð6Þ

where geff is the Kirkwood correlation factor for a binary mixture, which variesbetween gM and gF.

4�N

9kT

�2M�MgMMM

XM þ�2F�FgFMF

XF

� �g f ¼

"0m � "1mð Þ 2"0m þ "1mð Þ

"0m "1m þ 2ð Þ2

ð7Þ

gM and gF are assumed to be affected by an amount g f in the mixture. For an idealmixture, g f

¼ 1 and deviation from unity may indicate the interaction between thetwo components of the mixture.

4. Results and discussion

Figure 3 illustrates the experimental values of static dielectric permittivity ("0) ofFMD–PLG binary mixture with increasing volume fraction of PLG for differenttemperatures. The dielectric permittivity decreases with increase in temperature aswell as increase in the volume fraction of PLG. The decreases in dielectric

120

100

80

60

40

20

0

Die

lect

ric p

erm

ittiv

ity

0 10 20 30 40 50 60 70 80 90 100

Volume percent of PLG

T=20°C

T=30°C

T=40°C

Figure 3. Experimental values of static dielectric constant for FMD–PLG binary mixtureat different temperatures.

554 V.V. Navarkhele and M.K. Bhanarkar

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permittivity with increase in temperature might be due to rapid fall in orientationpolarisation, because the increased thermal motion reduces the alignment of the

permanent dipoles [27]. The decrease in dielectric permittivity with increase in

volume fraction of PLG may be due to increase in the size and shape of the complex

molecules after h-bonding interaction. This could be attributed to the decrease in thenumber of dipoles in the complex, which may lead to decrease in the volume of

the rotating molecules [28].The experimental values of relaxation time for FMD–PLG binary mixture for

different temperatures are plotted in Figure 4. The relaxation time for FMD–PLG

binary mixture increases with increase in concentration of PLG and decreases withincrease in temperature. The increase in relaxation time of the FMD–PLG binary

mixture with increase in concentration of PLG may be due to the greater size and

shape of the solute (PLG) than that of solvent (FMD). The decrease in relaxation

time with increase in temperature may be possibly due to increase in volume, increase

in effective length of the dipole caused by increase in temperature, and partly dueto decrease in sample viscosity [29].

As seen from Figures 3 and 4, in an ideal mixture of polar liquids, if the molecules

are interacting, a nonlinear variation in dielectric permittivity and relaxation time

with concentration is expected, and the same is inferred from these figures.

This confirms that the intermolecular association is taking place in the system.The results are in agreement with the earlier results of Navarkhele and Bhanarkar

[30].The excess property related to permittivity and relaxation time provides

significant information regarding interaction between the polar–polar liquid

mixtures. The excess dielectric permittivity of the mixtures was calculated usingEquation (3) and its variation with mole fraction of PLG for the three temperatures

is plotted in Figure 5. The values of "E are negative up to 55% of mole fraction

of PLG and positive for the rest of the mole fraction of PLG in the liquid

mixtures. The negative values of "E in FMD-rich region are probably due to thecreation of a less polar structure leading to a lower macroscopic permittivity.

The positive values of "E suggest that the effective number of dipoles in the

400

350

300

250

200

150

100

50

0

Rel

axat

ion

time

0 10 20 30 40 50 60 70 80 90 100

Volume percent of P LG

T=20°C

T=30°C

T=40°C

Figure 4. Experimental values of relaxation time for FMD–PLG binary mixture at differenttemperatures.

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mixture might be greater than the corresponding average number in the pure liquids,probably due to the creation of a new structure leading to a higher macroscopicpermittivity [6].

Figure 6 illustrates the variation in excess inverse relaxation time (1/�)E

with a mole fraction of PLG which was calculated using Equation (4) at 20�C,30�C and 40�C. The values of (1/�)E are negative up to 0.65mol fractions ofPLG and positive for the rest of the mole fractions of PLG in the liquid mixtures.The negative values of (1/�)E indicate that the addition of PLG to FMD hascreated a hindering field such that the effective dipole rotates slowly. The positivevalues of (1/�)E indicate that the PLG–FMD interaction produces a field such thatthe effective dipoles rotate faster, i.e. the field will cooperate in the rotationof dipoles.

The Kirkwood angular correlation factor (geff) and (g f ) values for variouscompositions of the mixture are represented graphically in Figure 7(a) and (b).The geff4 1 in the FMD-rich region indicates that in the mixture the dipole pairshave been formed in such a way that their orientation is parallel up to 0.3molfraction of PLG. The geff5 1, indicates that in the mixture the dipole pairs have been

20

10

0

–10

–20

–30

–40

Exc

ess

inve

rse

rela

xatio

n tim

e

0.1 0.2 0.3 0.5 0.7 0.8 0.9 1Mole fraction of PLG

T=20T=30

T=40

Figure 6. Experimental values of excess inverse relaxation time (1/�)E for FMD–PLG binarymixture at different temperatures.

80

60

40

20

–20

–40

–60

–80

–100

0

Exc

ess

perm

ittiv

ity

T=20

T=30

T=40

0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9Mole fraction of PLG

Figure 5. Experimental values of excess permittivity ("E) for FMD–PLG binary mixtureat different temperatures.

556 V.V. Navarkhele and M.K. Bhanarkar

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formed in such a way that their orientation is antiparallel in the PLG-rich region.The (g f) values are greater than one for all compositions and at all temperatures.This might indicate that the system will be oriented in such a way that the effectivedipole will be greater than corresponding values of pure liquids.

4

3.5

3

2.5

2

1.5

1

0.5

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Kirk

woo

d fa

ctor

(ge

ff)K

irkw

ood

fact

or (

geff)

T=20°CT=30°C

T=40°C

T=20°C

T=30°C

T=40°C

Mole fraction of PLG

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mole fraction of PLG

1.8

1.6

1.4

1.2

1

0.8

0.6

(a)

(b)

Figure 7. Experimental values of effective angular Kirkwood correlation factor (geff) (a) andKirkwood factor (g f ) (b) for FMD–PLG binary mixture at different temperatures.

Table 1. Experimental values of enthalpy and entropy as afunction of PLG.

Volume %of PLG

Enthalpy (DH )(JKmole�1)

Entropy (DS )(Jmole�1K�1)

00 12.95(0.22) 1.97(0.00)10 14.45(0.22) 0.54(0.00)20 07.0214(0.20) 1.11(0.00)30 02.28(0.18) 0.57(0.00)40 01.74(0.18) 0.50(0.00)50 06.42(0.19) 1.50(0.00)60 11.17(0.20) 4.44(0.01)70 04.31(0.18) 0.65(0.00)80 04.21(0.18) 1.17(0.00)90 04.05(0.18) 2.66(0.00)100 03.63(0.17) 1.52(0.00)

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5. Conclusions

. The values of static dielectric constant of the binary mixture are found to bein the range 31–110 and they decrease with the addition of PLG in FMD.

. The relaxation time (�) increases with the addition of PLG in FMD, whichmay be due to the increasing molecular size of PLG.

. The excess permittivity is negative in FMD-rich region and positive inPLG-rich region. This indicates that effective dipole moment of the mixturereduces in FMD-rich region and increases in PLG-rich region.

. The excess inverse relation time (1/�)E values are negative up to 70% molefraction for all the temperatures studied, which confirms that the dipolerotates slowly in the FMD–PLG binary mixtures and rotates fast in thePLG-rich region.

. In the mixture, the dipole pairs are formed and they orient in the paralleldirection in FMD-rich region and in antiparallel direction in PLG-richregion, which is confirmed from the (geff) values.

. The thermodynamic parameters of the system have been studied and arereported in Table 1.

Acknowledgements

The authors thank Prof. S.C. Mehrotra, Head, Department of Computer Science and IT,Dr Babasaheb Ambedkar Marathwada University, Aurangabad, for his valuable guidance.The authors also thank Dr V.P. Pawar, Maharashtra Udaygiri Mahavidyalaya, Udgir, for hishelp during the study. They also thank Dr P.W. Khirade and Head, Department of Physics,Dr Babasaheb Ambedkar Marathwada University, Aurangabad, for providing theexperimental (TDR) facility.

References

[1] R. Buchner, in Novel Approaches to the Structure and Dynamics of Liquids,

edited by J. Samios and V.A. Durov (Kluwer, Dordrecht, 2004), Vol. 133, pp. 265–288.[2] H. Weingartner, A. Knocks, W. Schrader, and U. Kaatze, J. Phys. Chem. A 105, 8646

(2001).[3] S. Mashimo, S. Kuwabara, S. Yogohara, and K.J. Higasi, Chem. Phys. 90, 3292 (1989).

[4] R.H. Cole, J.G. Berbarian, S. Mashimo, G. Chryssikos, A. Burns, and E. Tombari,

J. Appl. Phys. 66, 793 (1989).

[5] S.M. Puranik, A.C. Kumbarkhane, and S.C. Mehrotra, J. Micro. Power EM Energy 26,

196 (1991).[6] M.T. Hosamani, R.H. Fattepur, D.K. Deshpande, and S.C. Mehrotra, J. Chem. Soc.,

Faraday Trans. 91, 623 (1995).[7] S.M. Puranik, A.C. Kumbarkhane, and S.C. Mehrotra, Indian J. Chem., Sect A 32, 613

(1993).[8] W.D. Kumlar and C.W. Porter, J. Am. Chem. Soc. 56, 2549 (1934).[9] W.W. Bates and M.E. Hobbs, J. Am. Chem. Soc. 73, 2151 (1951).

[10] S.J. Bass, W.I. Nathan, R.M. Meighan, and R.H. Cole, J. Phys. Chem. 68, 509 (1964).[11] V.V. Navarkhele and M.K. Bhanarkar, Phys. Chem. Liq. 47, 231 (2009).[12] J. Barthel and H.J. Gores, in Chemistry of Non-aqueous Solutions, Current Progress,

edited by G. Mamantov and A.J. Popov (VCH, New York, 1994).

558 V.V. Navarkhele and M.K. Bhanarkar

Downloaded By: [Navarkhele, V. V.][INFLIBNET India Order] At: 09:42 14 June 2011

[13] M. Weissermel and H.J. Arpe, Industrial Organic Chemistry, 2nd ed. (VCH,

Weinheim, 1993).

[14] C.E. Shannon, Proc. IRE 37, 10 (1949).[15] H.A. Samulan, Proc. IRE 39, 175 (1935).[16] R.H. Cole, J.G. Berbarian, S. Mashimo, G. Chryssikos, A. Burns, and E. Tombari,

J. Appl. Phys. 66, 793 (1989).[17] S. Havrilliak and S. Negami, J. Polym. Sci. 14, 99 (1966).[18] K.S. Cole and R.S. Cole, J. Chem. Phys. 9, 341 (1941).

[19] D.W. Davidson and R.H. Cole, J. Chem. Phys. 18, 1484 (1950).[20] P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw

Hill, New York, 1969).[21] M. Tabellout, P. Lanceleur, J.R. Emery, D. Hayward, and R.A. Pethrick, J. Chem. Soc.,

Faraday Trans. 86, 1493 (1990).[22] S.C. Mehrotra and J.E. Boggs, J. Chem. Phys. 66, 5306 (1977).[23] S. Ahire, A. Choudhary, M. Lokhande, and S. Mehrotra, J. Sol. Chem. 27, 993 (1998).

[24] J.G. Kirkwood, J. Chem. Phys. 7, 911 (1939).[25] A.C. Kumbharkhane, S.M. Puranik, and S.C. Mehrotra, J. Chem. Soc., Faraday Trans.

87, 1569 (1991).[26] A.C. Kumbharkhane, S.M. Puranik, and S.C. Mehrotra, J. Sol. Chem. 22, 219 (1993).[27] N.E. Hill, W.E. Vaughan, A.R. Price, and M. Davies, Dielectric Properties and Molecular

Behavior (Van Nostrand Reinhold, London, 1969).[28] K. Dharmalingam, K. Ramachandranan, P. Shivgurunathan, P.B. Undre, P.W. Khirade,

and S.C. Mehrotra, Bull. Korean Chem. Soc. 27, 300 (2007).[29] K. Dharmalingam, K. Ramachandranan, P. Shivgurunathan, P.B. Undre, P.W. Khirade,

and S.C. Mehrotra, Physica B 387, 203 (2007).[30] V.V. Navarkhele and M.K. Bhanarkar, J. Mol. Phys. 107, 1823 (2009).

Appendix

Notations

"1 dielectric permittivity at high frequency"0 static dielectric permittivity� relaxation time

� and � distribution parameters�*(!) reflection coefficient spectra

! angular frequency"*(!) complex permittivity spectra

� (!) and q(!) Fourier spectraC speed of lightd pin length

R1(t) reflected pulse without sampleRx(t) reflected pulse with sample�(!) Fourier transform of �(t)q(!) Fourier transform of q (t)�(t) subtracted pulse R1(t)�Rx(t)q(t) added pulse R1(t)þRx(t)

PLG propylene glycolFMD formamide

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