www.elsevier.com/locate/molliq

Journal of Molecular Liqu

Dielectric relaxation study of substituted nicotinates

and their ternary mixtures

Shilpi Agarwal, Deepak Bhatnagar*

Microwave Laboratory, Department of Physics, University of Rajasthan, Jaipur 302004, India

Received 21 July 2003; accepted 2 November 2004

Available online 26 January 2005

Abstract

The dielectric relaxation behaviour of three nicotinates, namely benzyl-nicotinate (BN), methyl-isonicotinate (MIN), and ethyl-nicotinate

(EN), and their ternary mixture compositions are studied at different temperatures by applying signals at different frequencies viz. microwave

frequency of 10.16 GHz, optical frequency, and static frequency of 300 Hz. Different dielectric parameters like es, el, eV, eU, s(0), s(1), s(2),lD(s), and l0(s) have been determined for individual nicotinates and their ternary mixture compositions by using measured data. The

experimental values of s(0) for the ternary mixture compositions are compared with the corresponding values calculated by different

theoretical relations.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Dielectric relaxation; Nicotinates; Ternary mixtures

1. Introduction

In recent years, different workers [1–6] have reported the

dielectric relaxation studies of polar compounds and their

binary solutions in dilute solutions of nonpolar solvents.

The dielectric parameters of polar solutes from dilute

solution parameters are also obtained [7], but the adopted

process is long and does not provide exact values of

dielectric parameters of polar solutes due to the presence of

solute–solvent interactions. A straightforward and more

accurate method proposed by Yadav and Gandhi [8] is used

here to determine dielectric parameters of polar liquids by

taking them directly (without diluting them) in the measure-

ment cell. Such studies on dielectric samples give much

information about the role of internal fields acting inside the

dielectric sample and provide an idea about intermolecular

and intramolecular relaxation inside the dielectric sample.

Different workers [9–11] have investigated individual polar

compounds but very little work on higher order systems has

been reported [6,12]. With these considerations, the

0167-7322/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.molliq.2004.11.002

* Corresponding author.

E-mail address: dbhatnagar_2000@rediffmail.com (D. Bhatnagar).

relaxation behaviour of three individual nicotinates, namely

benzyl-nicotinate (BN), methyl-isonicotinate (MIN), and

ethyl-nicotinate (EN), and their ternary mixture composi-

tions are studied at different frequencies viz. at microwave

frequency of 10.16 GHz, optical frequency, and static

frequency of 300 Hz without diluting them. The reaction

field of dipoles influences the orientation of the molecule,

which produces an internal field effect within the dielectric

sample. Therefore relaxation occurs by cooperative effect,

which involves a group of molecules rather than single

molecules. The ultimate aim of these studies is to observe a

macroscopic relaxation time, which should be corrected to

give a microscopic value. Although different theories

provide an idea about the macroscopic relaxation time or

most probable relaxation time s(0), Frohlich’s expressions

yield sufficiently accurate results for undiluted compounds.

2. Experimental details and theory

The experimental setup and procedure employed for the

present investigations are described elsewhere [7]. The

dielectric constant eV and dielectric loss eU for the dielectric

ids 121 (2005) 105–109

S. Agarwal, D. Bhatnagar / Journal of Molecular Liquids 121 (2005) 105–109106

material under investigation at microwave frequency are

given by:

eV ¼ k0kc

� �2

þ k0kd

� �2

1� adbd

� �� �2ð1Þ

eW ¼ 2k0kd

� �2 adbd

� �ð2Þ

Here k0, kc, and kd are free space wavelength, cutoff

wavelength, and wavelength in the dielectric sample,

respectively. ad is the attenuation constant of the material

measured in nepers per meter, and bd is the phase shift per

unit length of the sample measured in radians per meter and

are experimentally measured by the following relations:

ad ¼2:302

2hlog

ffiffiffiffiffix1

p

2ffiffiffiffiffix2

p � ffiffiffiffiffix1

p� �

ð3Þ

bd ¼2pkd

ð4Þ

Here x1 and x2 are readings of power meter without and

with a liquid sample of length h in the dielectric cell. Three

liquid nicotinates of standard grade are used as dielectric

samples. These compounds are used as such without further

purification. Five ternary mixture compositions are prepared

by mixing them in different ratios by weight. The

corresponding mole fractions are calculated by using the

usual relations and are shown in Table 1.

Table 1

Experimental dielectric parameters of individual nicotinates and their ternary mix

Number Name of the sample Temperature

(K)

es

1 Benzyl nicotinate 300 8

310 8

320 7

2 Methyl isonicotinate 300 19

310 19

320 19

3 Ethyl nicotinate 300 21

310 21

320 21

4 Ternary mixture I (BN+MIN+EN),

0.0254+0.7356+0.2390

300 19

310 19

320 19

5 Ternary mixture II (BN+MIN+EN),

0.1414+0.6116+0.2470

300 18

310 18

320 18

6 Ternary mixture III (BN+MIN+EN),

0.4551+0.2598+0.2851

300 14

310 14

320 14

7 Ternary mixture IV (BN+MIN+EN),

0.4198+0.1243+0.4559

300 15

310 15

320 15

8 Ternary mixture V (BN+MIN+EN),

0.1608+0.1183+0.7209

300 19

310 19

320 19

The dielectric parameters for individual components and

their ternary mixture compositions are obtained experimen-

tally at three different frequencies. The first set of

observations is taken at a frequency of 10.16 GHz. Using

Eqs. (1) and (2), eV and eW are calculated at different

temperatures and are shown in Table 1. In the next step,

dielectric constant es at static frequency (300 Hz) for all the

samples is obtained at different temperatures using a

Toshniwal RL-09 dipole meter that works on the principle

of hetrodyne beat method. Finally the dielectric constant

el=nD2 at optically high frequency is determined by

squaring the refractive index nD for the samples, obtained

by using Abbe’s refractometer. The precision of measure-

ment for the wavelength with the available X-band micro-

wave test bench is F0.001 cm. Corresponding to this

accuracy value, the errors in the measurement of eV and eWare estimated. For simplification, involved errors due to

nonzero impedance of the short circuit plunger, curvature of

the mica window separating the E-plane band from

dielectric cell, and clamping gaps in the waveguide section

are ignored. The errors of measurement are calculated by

using the conventional method of error analysis [13]. This

relation is valid even if the precision of respective measure-

ments differs. With this method, the accuracy of the

measurement for eV is found to be F1% while for eW, it isF5%. The temperature of the liquid samples was kept

constant within F0.5 K by using a constant temperature

water bath.

Debye’s equation derived by Frohlich has been used to

determine the experimental value of the most probable

ture compositions

el eV eW Relaxation time values (ps)

s(0) s(1) s(2)

.05 2.59 3.28 0.292 41.2 6.6 256

.02 2.56 3.26 0.289 40.9 6.5 259

.97 2.52 3.23 0.284 40.5 6.3 261

.28 2.28 3.65 0.623 52.9 7.1 398

.25 2.27 3.63 0.619 53.2 7.1 395

.21 2.22 3.60 0.615 52.7 7.0 393

.66 2.27 4.06 0.785 49.1 6.9 354

.63 2.24 4.05 0.783 48.8 6.8 352

.59 2.21 4.01 0.778 48.9 6.8 351

.56 2.29 3.78 0.651 52.1 7.1 382

.53 2.27 3.72 0.649 51.7 7.0 382

.49 2.26 3.69 0.648 51.0 6.8 382

.28 2.33 3.72 0.615 51.3 7.0 374

.24 2.30 3.68 0.612 50.9 6.9 373

.21 2.29 3.65 0.610 50.7 6.9 371

.83 2.42 3.62 0.507 48.1 6.7 350

.81 2.39 3.58 0.505 48.1 6.6 348

.78 2.36 3.55 0.502 47.9 6.6 346

.65 2.40 3.69 0.556 47.9 6.9 338

.62 2.38 3.66 0.555 47.9 6.8 337

.58 2.35 3.64 0.553 47.7 6.7 337

.18 2.32 3.89 0.687 48.9 6.9 351

.16 2.29 3.87 0.684 48.7 6.8 350

.13 2.26 3.84 0.682 48.6 6.8 348

Table 2

Comparison between most probable relation times of undiluted samples with that obtained with dilute solution method

T=310 K

Name of compound Relaxation time (s(0)) inthe dilute solution (ps)

Relaxation time (s(0)) whencompound is undiluted (ps)

Dipole moment (in Debye units)

in the dilute solution

Dipole moment (in Debye units)

using Onsager’s relation

Benzyl nicotinate (i) Benzene—4.7 40.9 (i) Cyclohexane—2.78 3.37

(ii) Cyclohexane—11.5 (ii) 1,4 Decalin—3.19

(iii) 1,4 Decalin—14.2

Ethyl nicotinate (i) Benzene—3.6 53.2 (i) Cyclohexane 3.46

(ii) Cyclohexane—9.4 (ii) 1,4 Decalin—2.58

(iii) 1,4 Decalin—2.2

Methyl isonicotinate (i) Benzene—5.7 48.8 (i) Cyclohexane 3.19

(ii) Cyclohexane—14.0 (ii) 1,4 Decalin—2.56

(iii) 1,4 Decalin—10.1

S. Agarwal, D. Bhatnagar / Journal of Molecular Liquids 121 (2005) 105–109 107

relaxation time s(0) while the other two relaxation times s(1)(for molecular rotation) and s(2) (for intermolecular rotation)

are obtained using the method of Higasi [14] and Higasi et

al. [15] by taking es, el, eV, and eU values in place of slope

values as, al, aV, and aU used in the dilute solution method.

These relaxation times are:

s0 ¼1

x

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffies � eVeV� el

� �sð5Þ

s1 ¼1

xeW

eV� el

� �ð6Þ

s2 ¼1

xes � eV

eW

� �ð7Þ

Here x is the angular frequency of the applied e.m. wave.

s(0), s(1), and s(2) are related with each other by the relation

s 0ð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½s 1ð Þs 2ð Þ�

p.

The dipole moment values lD(s) and l0(s) at static

frequency are calculated using Debye’s and Onsagar’s

equations [16], respectively. Experimental values of es,el, eV, eU, s(0), s(1), and s(2) for individual nicotinates and

their ternary mixture compositions are listed in Table 1 The

measured most probable relaxation times s(0) for individualnicotinates obtained without diluting them and after diluting

them are compared in Table 2. The most probable relaxation

times s(0)mix for the ternary mixture compositions calculated

using three theoretical relations, namely simple mixing rule,

reciprocal mixing rule, and a method proposed by Yadav

Table 3

Comparison between experimental and calculated s(0) values at a temperature of

Number Name of the sample s(0) (ps) Experimental s(0) (ps) Valuat 310 K

SM rule

1 Ternary mixture I 51.7 43.62

2 Ternary mixture II 50.9 40.75

3 Ternary mixture III 48.1 33.17

4 Ternary mixture IV 47.9 35.66

5 Ternary mixture V 48.6 44.73

and Gandhi [8] at 310 K, are listed in Table 3 and are

compared with measured results. The percent deviation

between computed and measured values is shown. These

relations are:

s0ð Þmix ¼X3i¼1

xisi ð8Þ

1

s0

� �mix

¼X3i¼1

xi

sið9Þ

s0ð Þmix ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX3i¼1

xis2i

X3i¼1

xi

vuuuuuuut ð10Þ

where

X1 ¼x1

e2V� el2

� e3V� el3

� ;X2 ¼

x2

e1V� el1

� e3V� el3

� ; and

X3 ¼x3

e1V� el1

� e2V� el2

� Here xi=1, 2, 3 are mole fractions of individual

components in the mixture composition and subscript i=1,

310 K for ternary mixture compositions

es calculated using Percentage error in s(0) values

RM rule Y&G method SM rule RM rule Y&G method

61.28 51.78 +15.63 �18.52 �0.16

63.21 51.0 +19.94 �24.18 �0.19

68.79 48.22 +31.04 �43.01 �0.25

63.06 47.75 +25.52 �31.65 +0.31

52.89 48.78 +7.96 �8.82 �0.37

Table 4

Comparison between dipole moments calculated with Debye’s relation and Onsager’s relation

Number Name of the sample MW Density Dipole moment (at 310 K) (in Debye units)

lD l0

1 Benzyl nicotinate 213.24 1.165 1.83 3.37

2 Methyl isonicotinate 137 1.160 1.84 3.19

3 Ethyl nicotinate 151 1.107 2.01 3.46

4 Ternary mixture I (BN+MIN+EN),

0.0254+0.7356+0.2390

142.12 1.148 1.88 3.27

5 Ternary mixture II (BN+MIN+EN),

0.1414+0.6116+0.2470

151.34 1.148 1.92 3.35

6 Ternary mixture III (BN+MIN+EN),

0.4551+0.2598+0.2851

175.69 1.147 1.98 3.53

7 Ternary mixture IV (BN+MIN+EN),

0.4198+0.1243+0.4559

175.37 1.138 2.01 3.56

8 Ternary mixture V (BN+MIN+EN),

0.1608+0.1183+0.7209

159.36 1.123 2.01 3.49

S. Agarwal, D. Bhatnagar / Journal of Molecular Liquids 121 (2005) 105–109108

2, and 3 stands for the first, second, and third individual

component of the mixture. lD(s) and l0(s) values for

different samples at 310 K are shown in Table 4.

3. Discussion and conclusions

An examination of Table 1 shows that among the three

individual nicotinates, ethyl-nicotinate (EN) has the highest

values of dielectric parameters es, eV, and eW while benzyl-

nicotinate (BN) has the lowest values of the same parameters.

Ternary systems show that at each temperature, the dielectric

constants es, el, and eV, and dielectric loss eW decrease with

the increase of the heavier component (BN) in the mixture.

This concludes that ethyl-nicotinate and methyl-isonicotinate

(MIN) have more contributions towards eV and eW values in

comparison to benzyl-nicotinate, which has the lowest values

of dielectric parameters. For a particular concentration of the

mixture, the variation of these parameters with temperature

has the same trend and order as that of the individual

components. This indicates that the internal fields of the

individual components are nearly equal to that for the mixture

composition. The ternary systems of different compositions

(having almost identical dipole moments) do not show any

systematic change in es, el, and eV at different frequencieswith the change in their compositions. This indicates that

there is an association among the constituent molecules

showing the presence of strong molecular interactions in the

mixtures. The reason for this result is that in every mixture

composition, the molecules of benzyl-nicotinate are nonrigid

and associative in nature; therefore the molecular interactions

among the solute components in mixtures cannot be ruled

out. Although the other constituent of mixture compositions,

methyl-isonicotinate, has nonrigid and nonassociative mol-

ecules, there may be sufficient association among the

constituent molecules of the mixture compositions due to

association of molecules of benzyl-nicotinate with other

molecules. The nonrigidity of all molecules creates more

molecular interaction.

The relaxation times for individual components (under

undiluted condition) are found higher than their respective

dilute solutions as shown in Table 2. The possible reason for

this difference is that dipole–dipole interactions present in

polar molecules in individual samples obstruct the molec-

ular orientation, which may be considered absent in the

dilute solution. The value of relaxation times s(1), s(2), ands(0) of substituted nicotinates and their ternary compositions

decreases systematically with increase in temperature. With

the rise in temperature, viscosity of samples decreases and

hence frictional resistance for dipolar orientation decreases.

At higher temperatures, besides change in molar volume and

effective length of dipole, the rate of loss of energy due to a

larger number of collisions dominates and hence molecules

reorient with faster rate while the applied field changes its

direction.

Examination of s(1) and s(2) values in Table 1 for the

individual nicotinates and their ternary mixture composi-

tions indicates that a large difference beyond any exper-

imental error exists between s(1) and s(2) values. This

indicates that the contribution of intramolecular relaxation is

higher in comparison to intermolecular or overall molecular

relaxation. Following this, it appears that methyl-isonicoti-

nate shows higher contribution towards intramolecular

relaxation than ethyl-nicotinate or benzyl nicotinate.

For each sample, the rate of decrease of s(2) with the rise

in temperature is more significant in comparison to s(1) ands(0) values. This suggests that relaxation time corresponding

to overall rotation falls off at a faster rate with temperature

in comparison to the internal group rotation. This confirms

the fact that in polar liquids, the intramolecular relaxation

process is more dominating although significant values of

s(1) also show contributions of the intermolecular relaxation.

s(0) values for the ternary mixture compositions

obtained experimentally at 310 K are compared with

corresponding calculated values obtained by three theo-

retical methods using Eqs. (8), (9) and (10) in Table 3.

The percentage error between calculated values by simple

mixing rule and reciprocal mixing rule is sufficiently large

S. Agarwal, D. Bhatnagar / Journal of Molecular Liquids 121 (2005) 105–109 109

for different compositions, but this is within +1% with the

method proposed by Yadav and Gandhi [8]. This indicates

that both earlier theoretical methods do not provide a good

agreement between theoretical and experimental values.

This behavior was expected because both earlier theoretical

methods have not taken into account the contributions by

intermolecular and intramolecular interactions. Both these

theoretical methods assume that molecules have simple

structure and the internal fields do not change within

dielectric samples, which is not true in reality. Hence

theoretical methods for prediction of accurate s(0) values forany higher order systems must be developed in such a way

that they contain terms representing intermolecular inter-

actions between dissimilar molecules, changes brought in

internal field, and molecular structure and affinities between

dissimilar as well as similar molecules. Although the

method of Yadav and Gandhi [8] also fails to include these

terms in the present studies, we obtained a large agreement.

However in an earlier paper [12], the difference between

measured and computed results with this method, too, was

reported.

The experimental values of dipole moments lD(s) and

l0(s) at static frequency are obtained by using Debye’s and

Onsager’s relations [13], respectively, for individual nic-

otinates and their ternary mixture compositions and are

listed in Table 4. The values of the dipole moments of

mixtures have the same order as those of the pure

components. This again indicates that for the ternary

mixtures, the internal field in the individual components

would not be much different from the internal field of the

mixture. It is evident that lD(s) values calculated by

Debye’s equation are found lower than those l0(s) values

calculated by Onsager’s relation. This result is on expected

lines because in Onsager’s relation, due consideration was

given to the presence of internal fields while the presence of

internal fields was neglected in Debye’s relation. Therefore

the dipole moment values calculated from Onsager’s

relation are in better agreement with those obtained for

dilute solutions as shown in Table 2.

It can be concluded from the present study that the

method of using individual components directly in the

dielectric cell (without diluting them) is more convincing

and straightforward in understanding the intermolecular and

intramolecular relaxations in mixture compositions. How-

ever it cannot be used for highly polar liquids because in

that case, most of the incident microwave power will be

reflected back to form standing waves in the wave guide.

Acknowledgement

The authors are thankful to the DST (Jaipur) and

University of Rajasthan, Jaipur, for providing financial

support to S.A. in carrying out this work.

References

[1] S.I. Abd-El Messieh, J. Mol. Liq. 95 (2002) 167.

[2] R.J. Sengwa, R. Chaudhary, S.C. Mehrotra, Polymers 43 (2002) 1467.

[3] A.K. Bansal, P.J. Singh, K.S. Sharma, Indian J. Pure Appl. Phys. 39

(2001) 329.

[4] G.D. Rewar, D. Bhatnagar, Indian J. Pure Appl. Phys. 39 (2001) 707.

[5] R.J. Sengwa, K. Kaur, Polym. Int. 49 (2000) 1314.

[6] A. Volmari, H. Weingartner, J. Mol. Liq. 98–99 (2002) 295.

[7] R.A. Jangid, J.S. Yadav, D. Bhatnagar, J.M. Gandhi, Indian J. Pure

Appl. Phys. 33 (1995) 135.

[8] J.S. Yadav, J.M. Gandhi, Indian J. Pure Appl. Phys. 31 (1993) 489.

[9] Krishanji, A. Mansingh, J. Chem. Phys. 41 (1964) 827.

[10] S.K. Roy, K. Sengupta, S.B. Roy, Bull. Chem. Soc. 49 (1976) 663.

[11] A. Mathur, M.C. Saxena, Indian J. Pure Appl. Phys. 15 (1977) 130.

[12] G.D. Rewar, D. Bhatnagar, J. Mol. Liq. 102/1–3 (2003) 129.

[13] H.J. Fischbeck, K.H. Fischbeck, Formula, facts and constants,

Springer-Verlag, Berlin, 1987.

[14] K. Higasi, Bull. Chem. Soc. 39 (1966) 2157.

[15] K. Higasi, Y. Koya, M. Nakamura, Bull. Chem. Soc. 44 (1971) 988.

[16] O.V. Singh, Indian J. Pure Appl. Phys. 21 (1983) 339.