close

Вход

Забыли?

вход по аккаунту

?

Dielectric relaxation and dispersion studies of polar molecules and their mixtures at microwave frequencies

код для вставкиСкачать
DIELECTRIC RELAXATION AND
DISPERSION STUDIES OF POLAR
MOLECULES AND THEIR MIXTURES AT
MICROWAVE FREQUENCIES
ni
A THESIS
lilt
SUBMITTED TO
THE GUJARAT UNIVERSITY, AHMEDABAD
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
(SCIENCE)
BY
VIPINCHANDRA A. RANA
UNDER THE SUPERVISION OF
DR. A.D.VYAS
PROFESSOR
Qu . Uni. Library
iiiiir
T2378
DEPARTMENT OF PHYSICS
GUJARAT UNIVERSITY
AHMEDABAD-380 009
INDIA
NOVEMBER-2001
ProQuest Number: 3736044
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
ProQuest 3736044
Published by ProQuest LLC (2015). Copyright of the Dissertation is held by the Author.
All rights reserved.
This work is protected against unauthorized copying under Title 17, United States Code
Microform Edition © ProQuest LLC.
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
Proceedings
of the National Conference on
T h e R e c e n t A d v a n c e s in
Microwaves, Antennas & Propagation
M IC R G W A V E 2 0 0 1
November 2-4, 2001
S. Sancheti
D. Bhatnagar
K. B. Sharma
A. K. Bhatnagar
S.S. Jain Subodh PG College
Jaipur
CERTIFICATE
This is to certify that the thesis entitled “ Dielectric Relaxation and Dispersion Studies
of Polar molecules and Their Mixtures at Microwave Frequencies” submitted for the
degree of Doctor of Philosophy to the Gujarat University, Ahmedabad, India is a record
of original investigations carried out by Mr. Vipinchandra A. Rana in the Department of
Physics of this University. This work has not been submitted for any other Degree.
Prof. V. B. Gohel
Head,
Department o f Physics.
ACKNOWLEDGEMENT
I express my deep sense of gratitude to my Research Guide, Dr. A.D.Vyas, Professor,
Department o f Physics, University School o f Sciences, Gujarat University, Ahmedabad
for his inspiring guidance and constant encouragement during the entire period o f
investigation and preparation o f this Thesis.
I am greatly indebted to Dr. V. B. Gohel, Professor and Head, Department o f Physics,
Gujarat University, Ahmedabad for providing laboratory facilities for research work and
constant encouragement.
I am very much thankful to Dr. U.C. Pande, Professor, Department o f Chemistry, Gujarat
University, Ahmedabad for helpful discussions.
I am obliged to Dr. S.C. Mehrotra, Professor and Head, Department o f Electronics and
Computer Sciences, Dr. Babasaheb Ambedkar Marathawada University, Aurangabad for
encouraging to conduct TDR measurement in his laboratory. I am very much thankful to
Mr. N.M.More, Department o f Physics, Dr.B.A.M.University, Aurangabad for his help in
carrying out TDR measurements.
I am very much thankful to Dr. V.M.Vashisth, Physics Department, R.A. Bhavan’s
College o f Science, Ahmedabad for making me acquainted with the laboratory equipment
during my initial stage o f research work.
I am thankful to Mr. M. S. Bhatt, Electronics Engineer, Department o f Physics, Gujarat
University, Ahmedabad for providing useful guidance in developing radio frequency
circuit used for measurement o f static permittivity.
I should appreciate University Grant Commission, New Delhi for providing financial
assistance (Minor Research Project) during course o f my work. I am also thankful to Mr.
P.L.Patel and Mr. Rameshbhai Dudhat (Mechanical Engineer) for giving useful guidance
and help in fabricating standard variable capacitor.
I am indebted to my colleague and friend Dr. P.R,Vyas for his help and inspiration to
carry out this work. I am also very much thankful to Mr. D.H.Gadani, Mr. S.M.Trivedi,
Dr. T.C. Pandya, Mr. A,P.Patel, Mr. K.M.Chauhan, Mrs. A.H.Gharekhan,
Mr.C.V.Pandya and Dr. A.A. Shaikh for their help and encouragement during this work.
I would like to thank my Principal, Dr. J.D.Acharya, C.U.Shah Science College,
Ahmedabad and Mr.P.V.Shah, Head, Department o f Physics, C.U.Shah Science College,
Ahmedabad and other colleagues for valuable help and encouragement to carry out the
work.
I express my appreciation for the constant encouragement given by the faculty members
o f Physics Department, University School o f Sciences, Gujarat University, Ahmedabad. I
am also very much thankful to. non-teaching staff o f the Department o f Physics, Gujarat
University, Ahmedabad for extending their kind co-operation in administrative matters.
I have pleasure to acknowledge my parents and other family members for constant
encouragement and moral support. Special thanks are also due to my wife Paral Rana and
our children Parth and Krupa for sparing me from social obligations during the course o f
this work.
(Vipinchandra A. Rana)
CONTENTS
Chapter I
Chapter II
Description
Page No.
Introduction
1 to 5
References
4
Theoretical Background
6 to 29
2.1 Introduction
6
2.2 Theories of Static Permittivity
7
2.3 Macroscopic Theory of Dielectric Dispersion
13
2.4 Distribution of Relaxation Times
21
2.5 Molecular Theories of Dielectric Dispersion
26
References
Chapter HI
29
Experimental Methods and Evaluation of Different
Parameters
30 to 65
3.1 Methods to Measure Permittivity
30
3.1 (a) Complex Permittivity at Microwave Frequencies
30
(i)
Frequency Domain Technique
(ii)
Time Domain Reflectometry (TDR) Technique 43
31
3.1 (b) Measurement of Static Permittivity
48
3.1 (c) Measurement of Refractive Index
52
3.2 Description of Temperature Control Device
53
3.3 Evaluation of Different Parameters
55
3.3 (a) Methods for Evaluation o f Relaxation Time and
Distribution Parameters
(i)
Concentration Variation along with
Frequency Variation Method
(ii)
55
55
Concentration Variation Method at Single
Frequency
59
3.3 (b) Evaluation of Thermodynamical Parameters
64
References
65
Dielectric relaxation Studies of Non-associative
Polar Molecules and their Binary Mixtures at
Different Temperatures in Benzene Solution
66 1
4.1 Introduction
66
4.2 Experimental
68
4.3 Results and Discussion
69
References
92
Dielectric Dispersion and Relaxation Mechanism of
Some Polar Molecules and their Binary Mixtures
in Benzene Solutions at Microwave Frequencies
94 t
5.1 Introduction
94
5.2 Experimental
95
5.3 Results and Discussion
103
References
110
Dielectric Relaxation in 1-Propanol, Bromoanilines
and Mixtures of 1-Propanol with Bromoanilines in
Dilute Solutions of Benzene
111
6.1 Introduction
111
6.2 Experimental
113
6.3 Results and Discussion
114
References
151
Chapter VII Dielectric Relaxation Study of Mixtures o f I-Propanol
with Aniline, 2-Chloroaniline, 3-ChloroaniIine and
4-FIuoroaniline at Different Temperatures Using
Time Domain Reflectometry
153 to 180
7.1 Introduction
153
7.2 Experimental
154
7.3 Results
154
7.4 Discussion
169'
References
180
Chapter VIII Dielectric Relaxation of Some Rigid Polar
Molecules and Their Binary Mixtures
in Benzene Solution
181 to 191
8.1 Introduction
181
8.2 Experimental
182
8.3 Results and Discussion
182
References
Chapter IX
Summary
191
192 to 195
CHAPTER I
INTRODUCTION
Most everyday objects belong to one o f the two large classes l: conductors and
dielectrics. Conductors are substances, which contain an unlimited supply o f charges that
are free to move about through the material. In dielectrics, by contrast all charges are
attached to specific atoms or molecules they can move within the molecule, but they can
not stray away from it. Various types o f dielectric materials are available and their
properties are o f interest to scientists and technologists working in many fields. Scientists
are interested in dielectric properties o f materials because it can provide an important
approach for understanding their molecular structure.
The most important property o f dielectrics is their ability to be polarized under the action
o f an external electric field2. The permittivity o f the material is defined as the ratio o f the
field strength in vacuum to that in the material for the same distribution o f charges. When
an isotropic polar organic liquid is placed in high frequency electromagnetic field it show
fall o f permittivity with frequency in microwave region o f electromagnetic spectrum 3.
Therefore, the study of dielectric properties o f organic liquids at these frequencies has
gained considerable importance. The measured values o f complex permittivity at various
frequencies are used to evaluate various dielectric parameters viz., relaxation time,
distribution parameter, dipole moment, thermodynamical parameters, excess permittivity,
excess molar polarization and Kirkwood correlation functions. These dielectric
parameters give valuable information about molecular structure, intramolecular motions
and solute-solute and solute-solvent interactions.
The limitation o f dielectric relaxation studies is that the interpretation o f data is not
unique in many cases. Several models or mechanisms may be consistent with
experimental data consequently these studies are not self-contained and as such should be
supported by other physical or chemical techniques to confirm the mechanism proposed.
1
The early dielectric studies were centered at single component systems either in pure state
or its mixture with non-polar solvents. Schallamach 4 initiated dielectric studies in
mixtures of polar liquids, he found that mixtures o f both associated molecules or nonassociated molecules produces single absorption maxima in the dispersion region while
mixtures o f associated + non-associated molecules shows distribution o f relaxation time.
Since then considerable work has been done on study o f dielectric properties o f mixtures
o f rigid + rigid polar molecules 5'9, associated + non-associated 10' 19, associated +
associated molecules 20'30. The dielectric behaviour o f mixtures is influenced by the
relaxation times and dipole moments o f individual components. The solute-solute and
solute-solvent interactions are another factor, which affects the dielectric properties o f
mixtures.
In the present thesis dielectric behaviour o f polar molecules and their binary mixtures in
pure state and in dilute solutions o f benzene has been presented. The polar molecules
selected are non-associative, associative and rigid in nature. Their mixtures are studied at
different temperatures and the mixtures prepared had varied concentration o f its
constituents. One o f the component o f most o f the mixtures whose dielectric properties
are presented here is either aniline or halogen substituted anilines. Prakash and Rai 31
studied mixtures of aniline with nitrobenzene in liquid state and in non-polar solvent
benzene at different temperatures, they found single relaxation time for these mixtures. It
was thought to study mixtures o f halogen substituted anilines with rigid polar molecule to
observe the effect o f halogen substitution on relaxation time o f mixture. The complex
permittivity o f mixtures o f 2-chloroaniline with nitrobenzene and mixtures o f aniline with
benzonitriles is measured at 9.1 GHz at different temperatures, the evaluated values o f
relaxation times indicated solute-solute type o f interaction in these mixtures. The results
o f this study are presented in Chapter IV.
The dielectric relaxation studies in 4-
fluoroaniline and its mixtures with rigid polar molecules pyridine, chlorobenzene and
benzophenone is conducted at different microwave frequencies in non-polar solvent
benzene. The analysis o f dielectric data o f these systems shown that complex plane plots
(a” versus a’) o f these mixtures are Cole-Cole arcs indicating more than one relaxation
processes in these systems, results o f this study is included in Chapter V.
2
The dielectric studies o f mixtures o f amines with alcohols have gained considerable
importance because both amine and alcohols are used in many industrial processes.
Further, primary amine and alcohol have both a proton donor and a proton acceptor
group. It is expected that there will be significant degree o f H-bonding leading to self­
association in pure state in addition to mutual association in their binaries. Study of
dielectric properties o f aniline, 2-bromo, 3-bromo and 4-bromoanilines and their mixtures
with 1-propanol was carried out at 9.1 GHz in dilute solution o f benzene for different
concentrations and temperatures. The evaluated values o f relaxation times and
distribution parameters of mixtures o f these substances show solute-solute and solutesolvent type o f interactions, these studies are presented in Chapter VI. To gain more
information regarding molecular interaction in amines with alcohols dielectric
permittivity and loss o f aniline, 2-chloroaniline, 3-chloroaniline, 4-fluoroaniline, 1propanol and mixtures o f these anilines with 1-propanol was measured for different
concentration using TDR (Time Domain Reflectometry). The evaluated values o f excess
permittivity and Kirkwood correlation factor for these mixtures indicated strong
molecular interaction in these systems, the results are reported in Chapter VII. Chapter
VIII investigates dielectric properties o f mixtures o f rigid polar molecules in dilute
solution of benzene at different temperatures. A brief review o f theories o f dielectric
behaviour is given in Chapter II. Chapter III deals with various experimental techniques
to measure complex permittivity o f polar liquids at microwave frequency and static
permittivity at radio frequency, this chapter also includes description o f apparatus used in
the present investigation and methods to evaluate various dielectric parameters.
3
References
1. Griffiths, D. J,, Introduction to Electromagnetics, (Prentice-Hall Inc., Englewoods
Cliffs, N.J., U.S.A.), Third Edition, (1999).
2. Tareev, B., Physics o f Dielectric Materials, (MIR Publishers, Moscow), (1979).
3. Hill, NJE., Vaughan, W.E., Prince, A.H. and Davies, M., Dielectric Properties and
Molecular Behaviour, ( Van Nostrand-Reinhold Co., London), (1969).
4. Schallamach, A., Trans. Faraday Soc., A (GB), 42 (1946) 180.
5. Hanna, F.F., Ab del-Nour, K.N. and Ghonneium, A.M., Can. J. Phys., 64 (1986)
1534.
6. Madan, M.P., Can. J. Phys., 65 (1987) 1573.
7. Vyas, A.D. and Vashisth, V.M., Indian J. Pure and Appl. Phys., 26 (1988) 484.
8. Subramanian,V., Bellubbi, B.S. and Sobhanadri, J., Pramana J. Phys., 41 (1993) 9.
9. Abd-El-Messieh, S.L., Indian J. Phys., 70B(2) (1996) 119.
10. Tripathi, S., Roy, G.S. and Swain, B.B., Indian J. Pure and Appl. Phys., 31 (1993)
828.
11. Garabadu, K. and Swain, B.B., Indian J. Phys., 68B(3) (1994) 271.
12. Sharma, A., Sharma, D.R. and Chauhan, M.S. Indian J. Pure and Appl. Phys., 31
(1993) 841.
13. Fattepur, R H ., Hosamani, M.T., Deshpande, D.K. and Mehrotra, S.C., J. Chem.
Phys., 101(1994)9956.
14. Chelliah, N. and Sabeasan, R., Indian J. Pure and Appl. Phys., 32 (1994) 425.
15. Syal, V. K., Becker, U., Elsebrock, R. and Stockhausen, M., Z. Naturforsch, 529
(1997) 675.
16. Varadrajan, V. and Rajagopal, A., Indian J. Pure and Appl. Phys., 36 (1998) 13.
17. Madhurima, V., Murthy, V.R.K. and Sobhanadri, J., Indian J. Pure and Appl.
Phys.,36 (1998) 85.
18. Chaudhari, A., Khirade, P., Singh, R., Helambe, S.N., Narain, N.K. and Mehrotra,
S.C., J. Mol. Liq., 82 (1999) 245.
19. Helambe, S.N., Chaudhari, A. and Mehrotra, S.C., J. Mol. Liq., 84 (2000) 235.
20. Stockhausen, M., Utzel, H. and Seitz, Z., Z. fu r Physi Chem. Neue Folge, 133 (1982)
69.
4
21. Utzel, H. and Stockhausen, M., Z Naturforsch, 409 (1985) 183.
22. Kumbharakhane, A.C., Puranik, S.M. and Mehrotra, S.C., J. Chem. Soc. Faraday
Trans.,87 (1991) 1569.
23. Vyas, A.D. and Vashisth, V.M., Indian J. Pure andAppl. Phys., 28 (1990) 550.
24. Mashimo, S. and Umehara, T., J Chem. Phys., 95 (1991) 6257.
25. Stockhausen, M. and Busch, H., Phys. Chem. Liq., 32 (1996) 183.
26. Sato, T., Niwa, H., Chiba, A. and Nozaki, R, J. Chem. Phys., 108 (1998) 4138.
27. Saad, A.L.G., Shafik, A.H. and Hanna, F.F., Indian J. Phys., 72B(5) (1998) 495.
28. Wilke, G., Betting, H. and Stockhausen, M , Phys. Chem. Liq., 36 (1998) 199.
29. Becker, U. and Stockhausen, M., J. Mol. Liq., 81 (1999) 89.
30. Chaudhari, A., Raju, G.S., Das, A., Chaudhari, H., Narain, f4.BL and Mehrotra, S.C.,
Indian J. Pure andAppl. Phys., 39 (2001) 180.
31. Prakash, J. and Rai, B., Indian J. Pure andAppl. Phys., 24 (1986) 187.
5
CHAPTER-II
THEORETICAL BACKGROUND
2.1 Introduction :
Dielectric studies are useful to understand structure o f matter. The present accepted
interpretation of dielectric constant and dielectric loss o f unionized material is based upon
the theory" o f Debye and its other modifications. In this chapter theories concerning
dielectric behaviour o f liquids are presented.
In general molecules o f a substance can be divided into two categories polar and non­
polar molecules. Dipole moment ‘p ’ may be defined as the product o f electric charge and
distance between two charges. Molecules having a centre o f symmetry and zero dipole
moment are known as non-polar molecules while those not having a centre o f symmetry
and a permanent dipole moment are known as polar molecules.
When a dielectric material is subjected to an electric field it get polarized. The total
magnitude o f polarization is due to contribution o f three basic types o f polarizations,
electronic polarization (Pe), atomic polarization (Pa) and orientation polarization (P0).
When a non-polar material is placed in an electric field the electronic motion of
molecules is distorted and the centre o f mass o f electrons is displaced relative to the
nucleus in each atom thereby causing electronic polarization. Also, there is a
displacement o f atomic nuclei relative to one another causing atomic polarization. These
two polarizations together constitute distortion polarization (Pd). If the material is polar,
the permanent dipole moment o f molecules, which are distributed randomly in all
directions, change direction constantly because o f the thermal motion o f the molecule and
tend to orient themselves parallel to the electric field. This type o f polarization is called
orientation polarization. The total polarization (Pt) is thus
P,=Pe + Pa+ Po
= Pd + P0
‘
6
...2.1
Similarly, the total polarizability o f the molecules is given by
a t = cte + eta + a 0
...2.2
where a e, a a and a 0 are electronic, atomic and dipolar contributions to the polarizability.
The polar materials thus have greater permittivity than non-polar ones because o f an
additional amount o f polarization due to orientation. The orientation polarization fells o f
rapidly with rising temperature, therefore, permittivity o f polar materials fells more
rapidly with rising temperature than that o f non-polar materials.
Each o f the three types of polarizability is function o f the frequency o f the applied field.
When the frequency of the applied field is sufficiently low, all types o f polarization can
reach the value they would have a steady field equal to the instantaneous value of
alternating field, but as the frequency is raised the polarization no longer has a time to
reach its steady value. The orientation polarization is the first to be affected. This type of
polarization takes a time of the order 1O'12 to 10‘10 sec to reach equilibrium value in liquid
and solids with moderately small molecules and at the normal temperature; consequently,
when the applied field has a frequency 1010 to 1012 Hz, orientation polarization fails to
reach its equilibrium value and contribute less and less to the polarization as the
frequency rises. It is this fall of the polarizability from a t = a e + a a + a 0 to a t = a e + a a
with its related fell of permittivity and occurrence o f absorption that constitute dielectric
dispersion.
2.2 Theories of Static Permittivity :
The dipole moment o f the molecule o f a substance influences its permittivity and
measurement o f permittivity can be used to calculate the dipole moment. At low
frequency electromagnetic field of moderate intensity all type o f polarizations attain
equilibrium with the applied field in an isotropic polar material and the permittivity o f the
substance is called the static permittivity eo- For investigating the molecular structure and
for the study o f high frequency dielectric behaviour, the static permittivity is very useful.
7
Various theories have been propounded to express relation between permittivity and
dipole moment.
Debye 1 gave a relation connecting the dielectric constant, polarizability and dipole
moment as
e 0 -1
€ 0 +2
47tN
3V
f
4itN
p2
3V [ d 3kT
2.3
where a t is the total polarizability, a d is the induced polarizability (sum o f electronic and
atomic polarizability) and N/V is the number o f dipoles per unit volume.
At very high frequencies only distortion polarization remains, therefore
e . -1
€ . +2
4?tN
3V d
•2.4
— --------= ----------- a d
where s® is the high frequency permittivity.
Hence,
e 0 -1
e 0 +2
e , -1 _ 47tNp2
+2
9kTV
For gases the dielectric constant is so close to 1 that (eo + 2) may be put equal to 3 as a
good approximation. Hence
-1
(
4rcN
a d+
3V
3kT
•
2.6
The Debye equation (2.5) can be used for calculating the molecular dipole moment from
measurement o f static permittivity in the gaseous phase and in the dilute solutions o f
polar compounds in non-polar solvents. O f course, for pure polar liquids, the Debye
equation can not be expected to hold well because o f dipolar interaction between the
molecules. The Debye theory predicts that at moderate temperatures polarization becomes
so great and causes large internal field, that the molecules will spontaneously align
8
themselves parallel to one another, even in the absence o f an electric field, and the
material behaves as ferroelectric. Hence Debye equation can not be applied for pure polar
liquids.
Onsager 2 modified the Debye equation by considering the molecule as a polarizable
point dipole at the centre o f a spherical cavity o f molecular dimension in a continuous
medium o f static permittivity e<>. The radius ‘a’ o f this cavity is defined by the
assumption that
4rcN,a3/3 = 1
that is, the sum o f the volumes o f the spherical cavities is equal to the total volume o f the
material. This assumption that the cavity in which the molecule lies can be treated as a
sphere in a homogeneous medium limits the validity o f the theory to materials in which
there are no strong local forces. The internal field in the cavity consists o f two parts:
(1) the cavity field which would be produced in the empty cavity by the external applied
field; and
(2) the reaction field set up in the cavity by the polarization which the dipole induces in
its surroundings.
The Onsager’s equation for static permittivity is
(g0 - g « X 2 e o +gJ ,_4ftN)i2
e 0 ( e . +2)2
9kTV
Equation (2.7) makes it possible to compute the permanent dipole moment o f the
molecule from the measurement o f permittivity o f the pure liquid, if the density and e®
are known. Although this equation gives better results than Debye equation, it does not
take into account intermolecular interactions, i.e. the dipoles are distributed according to
Langevin’s law. Hence there is considerable discrepancy in case o f those liquids in which
there is strong intermolecular interaction. For gases and dilute solutions o f polar
9
compounds in non-polar solvents, the results o f Debye’s theory are only slightly affected
when the reaction field is taken in to account. The Onsager’s equation makes it possible
to determine the permanent dipole moment from measurements o f concentrated solutions
and pure polar liquids.
The Onsager’s equation generally does not hold good for associated liquids, e.g.,
carboxylic acids, alcohols etc. Kirkwood3 has generalized the Onsager theory in the case
of associating liquids to the orientation correlation o f neighboring molecules as a result o f
short range specific interactions, using stastistical method and he obtained
-
2.8
where p is the molecular dipole moment in the liquid and p* is the sum o f the molecular
dipole moment and the moment induced as the result o f hindered rotation in the spherical
region surrounding the molecule, p* will be equal to p, the moment o f the fixed dipole, if
there is no local ordering. In general p* = gp, where g, the correlation parameter, is a
measure o f local ordering. Hence in equation (2.8) p p* may be replaced by g p2. Thus
the equation reduces to
(e o -!X2 e o +1) _ 4 tiN
-------- r------------ —-— ":r
9 e0
f
3V ^ d
g p 2^
3kTy
- 2 .9
+ r ..zt
The precise calculation o f correlation parameter g provided by statistical mechanics, but
is difficult because o f insufficient knowledge o f liquid structure. It can be calculated from
the permittivity o f the material and the dipole moment o f the molecules but it will be an
empirical parameter.
Frohlich 4 using statistical method throughout obtained a more general expression
(s0 -lX 2 e 0 +l) _ 47TN, mm *
• • •
3 e0
3
kT
10
2.10
where Nj is the number o f units per unit volume, m is the dipole moment o f one o f its
units and m* the average dipole moment o f the spherical region embedded in its own
medium. Introducing the effect o f the elastic displacement o f charge leads to
(e0 -
€„X 2 €0 + ) _ 47CN, mm *
3 e0
3
2n
kT
Since m m* = p p* = g p2 and for spherical molecules replacing p by its value
m =—
—2-12
e« +2
which is the moment in vacuum (po) o f a spherical molecule consisting o f a material of
dielectric constant e® having a dipole moment p at its centre.
Hence using Avegadro number N, the equation reduces to
(go ~ €»X2 go +
e 0 (€ . +2f
) _ 47iNgp„
•2.13
9kTV
Except for the introduction o f the correlation parameter g, this equation is identical with
Onsager’s equation (2.7).
The correlation factor can be expressed as
g = 1 +Z<cos0ij>
...2.14
where ( cos 0y) depends only on the orientation o f the two molecules i. e. the i-th and j-th
molecules.
From equation (2.14) it can be seen that g will be different from 1 when, ( cos 8jj> * 0,
i. e., when there is correlation between the orientations o f neighboring molecules. When
the molecules tend to direct themselves with parallel dipole moments, ( cos 0,j) will be
li
positive and g will be larger than 1. When the molecules prefer an ordering with anti
parallel dipoles, g will be smaller thanl.
Kirkwood-Frohlich equation represents a theoretical advance beyond Onsager’s equation
as it takes in to account the hindrance o f molecular orientation by neighboring molecules.
Kirkwood pointed out that the departure o f ‘g’ from unity is a measure o f degree o f
hindered relative molecular motion arising from short range intermoleeular forces such as
intermolecular hydrogen-bonding. Normal liquids have values o f g nearly equal to 1,
while ‘associated’ liquids have value o f ‘g’ which departs significantly from unity.
It has been observed that the description o f dielectric behaviour o f associated compound
like alcohols, water, nitriles and even polymers in terms o f Kirkwood correlation factor
has generally proved useful. However, in a number o f cases the application o f the theory
is hampered by lack o f knowledge o f molecular configuration or the mode o f association.
Moreover, the equation also contains the approximation involved in treating the polar
molecules as spherical. Scholte5, Abbott and Bolton 6, Buckley7 and Buckingham8, have
extended the Onsager treatment by replacement o f spherical cavity by an ellipsoidal
cavity, obtained somewhat better agreement with the gas moment values for a few
substances. Several attempts 9"n have been made to modify the Onsager equation by
making several assumptions to obtain dipole moment values, which may be in agreement
with the experimental gas values.
Cole 12obtained an expression for static permittivity similar to FrQhlich’s expression, but
his theory differs from the theories o f Kirkwood and Frohlich in the treatment o f
distortion polarization. The method has a special interest because Cole has generalized it
to the case o f an alternating field. His treatment o f distortion polarization is based on the
method developed by Van Vleck 13 to calculate the permittivity o f non-polar liquids. The
state o f the liquid can be described by a set o f displacement vectors and the corresponding
moments. The displacement can be calculated statistically from the external field and the
dipole-dipole forces, assuming the charges to be harmonically bound to their equilibrium
positions. The expression given by Cole is:
12
e 0 -1
e 0 +2
e m -1
+2
4 kN
3 6 0 (eM+2)
g|x 1
3V (e0 +2X2 g0 + e J 3kT
..-215
which on simplification reduces to :
(gp - e .X 2 s t + 6 . )
e 0 (s„ +2)’
4rcN g n 1
5V 3kT ,
2 [6
is in agreement with the Frohlich equation (2.13).
2.3 Macroscopic T heory of Dielectric Dispersion :
In the previous section, permittivity has been calculated for the case where the applied
field is either steady or frequency o f applied field is low. In this section we shall study the
effect o f high frequency electric field to the dielectrics.
At low frequency all the types of polarization can reach the value they would have had in
the steady field equal to the instantaneous value o f the alternating field, but as the
frequency is raised the polarization no longer has time to reach its steady value. The
orientation polarization is the first to be affected. This type o f polarization takes a time o f
the order 10'12 to 10'10 sec to reach its equilibrium value in liquids and solids with
moderately small molecules and at normal temperatures (much longer in polymers);
consequently, when the applied field has a frequency o f 1010 to 1012cycles per second, the
orientation polarization fails to reach its equilibrium value and contributes less and less to
the polarization as the frequency rises. It is this fall o f polarizability from a, = cte + a a +
cto to a = Oe + a a with its related fall o f permittivity and occurrence o f absorption that
constitutes dielectric dispersion. The frequency range in which the dielectric dispersion
occurs, cte and a a remain unchanged, since the distortion polarization o f a molecule takes
much less time to reach equilibrium with an applied field than the orientation polarization
does. This lag in response o f orientation polarization to the applied electromagnetic field
is commonly referred to as relaxation, which may be defined as the lag in the response of
the system to the change in the force i.e., the applied field. The dielectric relaxation
13
occurs when a dielectric material is polarized by the external field and then it relaxes on
removal o f the field. The orientation polarization decays exponentially with time; the
characteristic time o f this exponential decay is called relaxation time which is defined as
the time in which this polarization reduces to 1/e times its original value. In the presence
o f relaxation effects the dielectric constant may conveniently be written as complex
quantity,
e * = e ’_ je ”
...2,17
where e ’ is dielectric constant and e ” is dielectric loss. The loss tangent is defined by,
tan8 =-
•2.18
Debye equation as derived by Frohlich for complex permittivity is,
€ * ==G _ +
6q -6.
l + jcot,
•2.19
separating into real and imaginary parts one obtains,
£Z
e '= e
—
—
- —
fZ
- — —
-
■
l + co2r J
s"=
£ ‘
e-, « ,
•
2.20
2.21
1 + CD
where t m is the macroscopic relaxation time. The variation o f e ’ and e ” with frequency
is shown in Figure-2.1, the frequency being displayed on the logarithmic scale. The
dielectric dispersion covers a wide range o f frequency. It reaches its maximum
14
Figure-2.1 Variation o f e ’ and e ” with frequency
Figure-2.2 Debye semicircle
15
at a frequency (Bm=l/Tm and falls off to half its maximum when
= 0.27 or 3.73
The dielectric loss is thus considerable over frequencies varying in value by a factor more
than 10.
Another way which is generally used to represent experimental results is to construct
ARGAND diagram or complex plane locus in which the imaginary part e ” o f complex
permittivity is plotted against the real part e \ each point corresponding to one frequency,
from equation (2.20) and (2.21) one gets
e 0
“ . y + e" 2 =
6
>
•2.24
)
Thus by plotting e ” against e ’ a semicircle is obtained, as shown in Figure-2.2, with
radius ( e 0 - e«>)/2, its centre being on the abscissa at a distance ( e 0 + e»)/2 from the
origin. The intersection points with the abscissa are characterized by e ’ = e» and e ’ = eo
respectively. An interesting point is that for a given value o f eo and €» the e ”, e ’ curve
is completely defined provided the equations (2.20) and (2.21) are valid, whereas the
frequency range in which the dispersion occurs has no influence on e ”, e ’ curve. Thus
e ”,e ’ curve is independent o f the value o f the relaxation time.
The Debye equation (2.20) and (2.21) have been successful in representing accurately the
dielectric behaviour o f a number o f spherical molecules. Most o f the commonly observed
deviation occurs in the case o f polymers, which do not fit in the Debye equations.
K.S.Cole and R.H.Cole 14 suggested that in this case the permittivity might follow the
empirical relation,
•••2.25
e*= e„
16
where a is a constant having values between 0 and 1 and is called distribution parameter.
It is a measure o f the width o f the distribution. Rationalizing this expression and using
j(,_a) = exp
j7i(l~a)
One obtains,
2.26
-
and
(m0)^ cosfa^j
-
€0 -
2.27
1+ (ox 0)2(1' a) + 2{m 0)(1~°° s i n K
The locus on the complex plane o f which these are the parametric equations can be
obtained by eliminating (ot0. The equation o f the locus is
t
(s o + 1
+ ="2+~:(e o -e „ )ta n ('
rax
\2
This is the equation o f a circle with its centre at
and radius
e js e c
rax^
17
1/
! t v =o “ e J
\2 if
sec2 —
•
2.28
w hen e ” is plotted as ordinates against e ’ as abscissa for different frequencies, an arc o f
a circle is obtained as show n in the Figure-2.3, w hose centre lies below the real axis. This
type o f curve shows a continuous sym m etrical distribution o f relaxation tim es. The
diam eter o f the circle, draw n from the point w here € ’ = €«,, m akes an angle
a%/2 w ith the
abscissa. In the limit a = 0, the Cole-Cole curve reduces to the Debye semicircle.
A num ber o f cases have been reported in w hich the arc is som e w hat skewed (Figure-2.4).
Davidson and Cole 1547 suggested a new em pirical relation to account for such behaviour.
The Cole-D avidson equation is
e * = e m+
- 2 .2 9
(l + jca rj
where P is an empirical param eter having values betw een 0 and 1 is called the distribution
param eter. The shape o f the arc for different values o f p is shown in Figure-2.5.
Rationalizing and putting tan<j> =
e 1—
cotq,
one gets,
= cosp <j>cosP$
- 2 .3 0
: co sp 4>sin P<j>
•••2.31
e0 "
The value o f p determines the angle at w hich the arc cuts the e ’ axis at high frequency
end. The tangent at the high frequency end m akes a n angle Prc/2 w ith the abscissa. This
equation has been successful in representing the behaviour o f substances at low
tem peratures. A s the tem perature is raised, p - » l and thee arc tends to a Debye semicircle.
In certain cases there are tw o distinct relaxation processes w hich occur sim ultaneously. I f
t i and t 2 are the two relaxation tim es, e ’ and e ” are given by eq u a tio n s1S,
€
'~
-
^1
1 + ( cot j ) 2
•••2.32
|
1 + (cot2 ) 2
18
e
Figure-2.3 Cole-Cole arc
Figure-2.4 C o le-D a v id so n arc
19
6o— € 0 0
Figure-2.5 Normalized Cole-Davidson arcs for different values o f P
Figure-2.6 Multiple relaxation processes
20
- 2 .3 3
where Ci and C2 are the relative weights o f each relaxation term and Ci + C2 = 1.
Similarly in some cases, even if there are multiple relaxation processes but they are
distinctly separated, a curve is obtained which can be analyzed into separate Pellat-Debye
curves Figure-2.6.
2.4 Distribution of Relaxation T imes :
The Cole-Cole and Cole-Davidson types c f behaviour can be understood as arising from
the existence o f a continuous spread o f relaxation times, each o f which alone would give
rise to a Debye type o f behaviour. Let G(x) be the distribution function o f relaxation time,
G(x)dx be the function o f the molecules associated at a given instant with relaxation times
between x and x+dx. For such a distribution o f relaxation time equation (2.19) must be
extended to,
- 2 .3 4
1 + jox
From its definition it follows that G(x) satisfies the normalization condition,
00
•••2.35
0
starting from (2.34) following equations are obtained,
- 2 .3 6
and
•••2.37
21
The special form for the distribution function G (t) w as first introduced by W agner 19 who
assum ed that an infinite num ber o f independent causes disturb an original relaxation tim e
to- This assum ption leads to G aussian probability function,
- 2 .3 8
where b is a constant and
x,
U nfortunately Gaussian distribution does n o t lend its e lf to sim ple evaluation.
Fuoss and K irk w o o d 20 suggested an expression for dielectric loss, applicable in particular
to polym eric polar m olecules in a non-polar solvent. They found that the results o f loss
m easurem ents on polym ers might be represented very successfully by the em pirical
relation,
where P is a distribution param eter (p = 1 corresponds to Debye equation) and ©m is the
angular frequency corresponding to m axim um value
o f e ” . The value o f e ”max is
chosen by trial and error to give the best straight line o n a plot o f cosh*1( e ”inax/ € ”) against
log(co) w hose gradient is 2.30 P and w hose intercept on the log © axis gives ©m. The
Fouss-K irkw ood function corresponds to a logarithm ic distribution function,
- 2 .4 0
where
22
The relaxation time x is given by
CO*
The Cole-Cole equation for complex permittivity gives a distribution function,
1
F(s) =
sin arc
•2.41
2% eosh(l - a )s - cos a n
where
S = ln—
This fimction is in practice not very different from Gaussian distribution. The equation
(2.38) and (2.41) can be made to coincide fairly close to each other by a suitable choice o f
the parameter b and a. The Cole-Cole distribution falls o ff more slowly towards extreme
values o f S than the Gaussian distribution. The Cole-Cole distribution is a useful
representation for many experimental results and appears to be reasonable in view o f its
similarity to Gaussian distribution.
Poley21 gave the relation between the Fuoss-Kirkwood ‘p’ and the Cole-Cole ‘a ’ factors
as,
pV2:
cos
1 -a
(l-a )? t
•2.42
The distribution fimction for skewed arc behaviour is given by
f
\
VTo J
sin Pti
7t
for t < x„
•2.43
for x > xn
•2.44
V*0-T,
v To y
Higasi22 has proposed a distribution function,
23
•••2.45
f W = — ;t , < t < t 2
Ax
where xi and x2 are ihe two limiting values of relaxation times. Further,
f
1
= ---- = x, exp --- - x, exp
l2)
e 0n - e „°o
f"Al
l2 ;
•••2.46
•••2.47
= 2 -ta n -(ta n h % )
A
Higasi has pointed out that the more general version
f(x) = — -— , 0 < n < o o
A(x)n
•••2.48
gives right -skewed arc for n<l and left-skewed arc for n>l.
Frohlich 4 considered the case of a molecule, which changes its direction by large jumps
over a potential barrier, rather than in small steps of Debye's diffusive model. He
supposes that the heights of potential barriers are uniformly distributed between H = H0
and H = H0 + V0 so that the fraction of dipoles for which the barrier height lies in the
range dV about Ho + V is dV/V0. The relaxation time for a molecule for which the barrier
height is (Ho + V) is,
x’= A exp
l-Ho+Vl
kT
•••2.49
= to exPf V 1
UtJ
where
f
-
A exp Ho.
v kT
\
24
— ----- ^
J3:3n V
and the relaxation time ranges from To’ to x i \ where Ti’=To’exp(Vo/kT). If distribution o f
relaxation times is described by the function f (t ’), where frT’)d(lnT’) is the fraction o f
molecules which have relaxation times between t and t ’ + d t’, then,
, if t0 < x'< t'j
-
2.50
, otherwise:
-
2.51
f(T')d(lnT’) = ~
:0
or
, , „ d V dV
)— = —
w kT Vn
•••2.52
i (t
kt
,if
Vo
=0
x0 <%<%[
•••2.53
, otherwise
-
2.54
The logarithmic function o f t is, therefore, a rectangular function. The interesting feature
o f Frohlich’s law is that it predicts the temperature-variation o f the width o f the
distribution. I f Vo varies only slowly with temperature, the distribution will become
narrower as the temperature increases, tending to a 8-function as T tends to infinity. This
corresponds qualitatively to the behaviour found in practice. If the internal field
correction is negligible, as will be the case if the polar substance is in dilute solution in
non-polar solvent, the molecular and macroscopic relaxation times are equal, and the
complex permittivity is given by
€*-€«, _ "r f(x')d(ln t')
e0 “ e-
vi
kT \
...2 55
l + 3m '
dx’
-
2.56
v o ^ ' ( l + joox')
On separating the real and imaginary parts and integrating, one obtains,
=
e 0 - e «0
2 \
kT f t_1+GTT,
__
1In
2V0 \J + C0 T0
-
25
2.57
and
kT
e0 -
g*
[tan-1(cot,)-tan ’(ox^)]
•2.58
V0
2.5 M olecular Theories of Dielectric Dispersion :
Debye has given an elegant discussion o f dielectric relaxation o f polar molecules in
liquids. His central results is that the orientational part o f the polarizability depends on the
applied frequency o as, for alternating field
an
a(o) =
- 2 .5 9
1-jox
where x is the relaxation time and ao is the static orientational polarizability. In liquids the
relaxation time is related to the viscosity tj by the approximate relation
47tr|a3
•2.60
kT
where a is the radius o f the molecule, supposed to be spherical. According to Debye the
expression for complex permittivity is,
g * - l M _ 4teN
47tNp2
1
-ad +
g*+2 d
9kT 1+ jox
•2.61
At very high frequencies equation (2.61) reduces to,
-1M
4tiN
g_ +2 d
•a,
- 2 .6 2
Similarly at low frequencies equation (2.61) reduces to,
e 0 -1 M
4rtN
e n +2 d
-
, 4jtNp2
a d +
•••2.63
9kT
26
Substituting these values in equation (2.61) one obtain,
€»-l
g
e,-l
*+ 2
gw
eo- 1
+2
€„+2
On solving the above equation for
1
+2 1 + jOQX
g
*
•••2.64
one gets,
• ——
—e 0-— i- jcot
e 0 +2
+2
•••2.65
€ * = ------------------------
1 . 1
-----------i- jcot--------e 0 +2
€„ +2
Separating into real and imaginary parts, the following expressions are obtained,
6 - €«, .
1
€0 - e .
1+ X 2
e”
X
e 0 - G oo
1+X2
•
2.66
•••2.67
where
+2
COT
Equations (2.66) and (2.67) differ from equations (2.20) and (2.21) only in containing the
quantity x( go+2)/(g ®+2) instead o f xm. The difference arises because the relaxation time
which Frohlich uses, is for macroscopic relaxation processes, while the relaxation time
used by Debye is that o f the microscopic or molecular processes.
Hence,
xm
Gn +2
------- X
—
• • •
e„ +2
2.68
Debye theory gives the same form for the frequency dependence o f the permittivity as the
macroscopic theory, but shows that the macroscopic relaxation time is in all cases larger
than the microscopic relaxation time.
Debye’s theory fails to explain the dielectric behaviour o f majority of liquids. The failure
is due to over simplified model used in the theory and inadequancy o f the Lorentz field as
27
a measure o f internal field in a dipolar-dielectric. By considering Onsager’s model Collie
et a l 23 obtained the result,
(e *- e M)(2 e * +1) _ (2 e 0 +l)(e„ +2)2 4ftNp2
e*
(2e0 + e .)
1
' 27kTV ’ 1-+ jcox
In this theory it is assumed that the dielectric is able to respond completely to thermal
motion o f the dipdles.
Erying24 considered dielectric relaxation as a rate phenomenon like one for viscosity and
diffusion, the concept o f transition o f a dipole over a certain potential barrier was used. A
dipole in liquid may have two equilibrium position which are separated by a barrier o f
definite height. Before the dipole is able to jump to the next equilibrium position it must
acquire an excess o f energy over the average thermal energy from thermal fluctuations.
Erying's theory leads to the following expressions for dielectric relaxation and viscous
flow
f AF* 'l
lwJexpl kT J
f hNl exp
IvJ
- 2 .7 0
( AF* 1
lkTJ
- 2 .7 1
where AF6* and AFn* are the free energies o f activation for dielectric relaxation and
viscous flow respectively and V is the molar volume. A Anther development o f Erying’s
theory has been given by Kauzmann25. He showed that a distribution o f relaxation times
according to Cole-Cole could easily be understood by it. Due to thermal fluctuations the
conditions in the neighborhood o f all the molecules at a given moment are not at all
identical. Thus the free energy o f activation required for a molecule to overcome a
potential barrier varies, Le., there is a distribution o f free energies o f activation. Such a
distribution is a symmetrical one about the mean value and thus accounts for symmetrical
e ’, logo; and e ”, log© curves, since the relaxation rate depends exponentially on the free
energy.
28
R eferences:
1. Debye, P., Polar Molecules, Chemical Catalog Co., New York (1929).
2. Onsager, L., J. Am. Chem. Soc., 58 (1936)1486.
3. Kirkwood, J.G., J.Chem Phys., 7 (1939) 911; Kirkwood, J. G. and Oster, G., J. Chem.
Phys., 11 (1943) 175.
4. Frohlich, H., Theory o f Dielectrics, (Oxford University Press), London (1958).
5. Scholte, T. G ., Physical 15 (1949) 437.
t
6. Abbott, J. A. and Bolton., H.C., Trans. Faraday Soc.,48 (1952) 422.
7. Buckley, F. and Maryott, A A., J. Res. Nat. Bur. Std, 53 (1954) 229.
8. Buckingham, A.D., Australian J. Chem., 6 (1953) 93.
9. Powles, J.G., Trans. Faraday Soc., 51(1955) 377.
10. O’Dwyer, J., Proc. Phy. Soc.,(London), A64 (1951) 1125.
11. Jaffe’, G.,J. Chem. Phys., 8 (1940) 879.
12. Cole, R. H., J. Chem. Phy., 27 (1957) 33.
13. Van Vleck, J. H., J. Chem. Phys., 5 (1937) 556.
14. Cole, K. S., and Cole, R. H., J. Chem. Phys., 9 (1941) 341.
15. Davidson, D.W. and Cole, R. H., J. Chem. Phys., 18 (1951) 1417.
16. Davidson, D. W. and Cole, R. H., J. Chem. Phys., 19 (1951) 1484.
17. Davidson, D. W., Can. J. Chem., 39 (1961) 571.
18. Bergmann, K., Roberti, D. M. and Smyth, C. P., J.Phys. Chem., 64 (1960) 665.
19. Wagner, K.W., Ann Physik, 40 (1913) 817.
20. Fuoss, R. M. and Kirkwood, J.G., J. Am. Chem. Soc., 63 (1941) 385.
21. Bottcher, C. J. F., “Theory o f Electronic Polarization”, Elsevier Publishing Co.,
London (1952).
22. Higasi, K., “Dielectric Relaxation and Molecular structure”.Research Institute o f
Applied Electricity, Sapporo, Japan (1961).
23. Collie, C. H., Hasted, J. B. and Ritson, D. M., Proc. Phys. Soc., 60 (1948) 145.
24. Glastone, S., Laidler, K.J. and Eyring, H., “The Theory o f Rate Processes” McGrow
Hill, New York (1941).
25. Kauzmann, W., Revs. Modern Phys., 14 (1942) 12.
29
CHAPTER-III
EXPERIMENTAL METHODS AND EVALUATION OF DIFFERENT
PARAMETERS
A macroscopic description o f the electrical properties o f a dielectric is provided by its
complex permittivity. The significant external factors on which complex permittivity
depends are frequency, temperature, pressure and the intensity o f applied electric field
Usually complex permittivity o f the materials is measured in frequency domain. In recent
past, time domain reflectrometry 2 (TDR) is used for measurement o f complex
permittivity, because in TDR a single measurement covers a wide frequency range in
short time. Now a days this feature o f TDR is achieved by vector network analyzer 3
(VNA). The following sections in this Chapter describe technique, experimental set up
and methods to measure permittivity at various frequencies used in present investigation.
The evaluation o f different parameters is also included in this Chapter.
3.1 M ethods to M easure Permittivity:
The experimental part of this investigation involves the measurements o f the following
characteristics o f polar molecules and their binary mixtures:
(a) Complex permittivity at microwave frequencies.
(b) Measurement o f static permittivity.
(c) Measurement o f refractive index.
3.1 (a) Complex Permittivity at Microwave Frequencies
Complex permittivity o f polar liquids and their mixtures in dilute solutions was measured
in frequency domain. Time domain technique was used to measure complex permittivity
o f pure liquids and their mixtures at various temperatures.
30
(i) Frequency Domain Technique:
There are several methods to measure complex permittivity o f solutions o f polar liquids
in non-polar solvents in frequency domain, in the present work transmission line method
was used and thus only this method is described here. The basic requirement o f this
method is to determine the phase factor P and attenuation constant a o f the
electromagnetic wave propagating in the dielectric medium. In these methods the power
from the microwave oscillator is transmitted through a co-axial line or through a wave
guide before it is incident on the liquid sample confined in a cell o f the same dimension
as o f the transmission line or wave guide. When the electromagnetic wave is reflected
from the short -circuited termination at the other end o f the dielectric cell, there are two
sets o f travelling waves - incident and reflected, moving in opposite directions in the air
filled space above the dielectric. These two sets o f travelling waves produce stationary
waves.
The study o f the characteristic o f the standing wave in the air filled space above the
dielectric is utilized for measurement o f the dielectric constant and loss. The dielectric
cell may have fixed lengths or there may be arrangement for varying the length o f the
liquid column with the help of a movable plunger forming the short-circuited termination.
The following alternative procedures are followed.
The first method utilizes the measurement o f the terminal impedance o f a shorted wave
guide filled with a dielectric material. The standing wave ratio is measured in the air filled
space o f the wave guide above the dielectric medium when the input signal is reflected at
a short-circuited termination placed immediately behind the dielectric. The dielectric is
inserted in the closed end o f co-axial line or wave guide opposite to the oscillator end,
filling the volume to a height d. Above the dielectric, the standing wave pattern is studied
by moving a probe in the slotted section and used for measurement o f p and a by
following either the graphical method o f Robert and Von Hippel 4 or the analytical
method o f Cripwell and Sutherland 5.
31
The second method utilizes variable length o f the liquid column with the help o f a
movable shorting plunger in the dielectric cell. The value o f the phase constant |3 is
evaluated by measuring the wavelength in the liquid sample and a by measuring either
the amplitude o f reflected wave or the standing wave ratio for different sample lengths.
c
For a liquid sample in a wave guide if the wavelength and attenuation constant in the
dielectric sample are known, then the permittivity e ’ and the loss e ” is calculated from
the following relations (i)*6.
•■•3.1
•••3.2
Where Xq is the free space wavelength, Xc is the cutoff wavelength, Xj is the wavelength
in the dielectric sample in the cell and a is the attenuation constant in it.
Thus the problem o f finding the permittivity and dielectric loss reduces to the
measurement o f
(i)
Wavelength in the sample and
(ii)
The amplitude o f reflected wave or voltage standing wave ratio from which a can
be calculated.
Both the procedures are briefly described below:
Bv Measuring Reflection Coefficient:
The liquid is put in the cell and the plunger is kept at the uppermost position so that the
maximum amount o f liquid is between the plunger and mica window. The reflected
power through a unidirectional coupler is fed to a galvanometer via a crystal detector and
32
the deflection is noted. Now the plunger is moved slowly into the liquid column and
deflections are noted at suitable intervals till the plunger touches the mica window. The,
plot o f the reflected power against the liquid length exhibits a series of maxima and
minima. Wavelength in the liquid, %a, the attenuation per wavelength oX a, can be
calculated from the plot as suggested by Laquer and Smyth 7.
By Estimating V.S.W.R.:
■
'
j
The output from the probe in the slotted section is fed to a galvanometer or to a V.S.W.R.
meter via a crystal detector. The microwave oscillator output is also modulated by an
audio signal if the V.S.W.R. is determined by a V.S.W.R. meter. When the shorting
plunger is moved in the liquid cell as described earlier, the V.S.W.R. meter shows
maxima and minima. The average distance between consecutive minima gives X a/2 .
The attenuation constant for liquids with tan5 > 0 . 1 can be determined by Poley’s
method8. For liquid lengths equal to m kJ2, nX<j/2 and infinite respectively, the standing
wave ratio in the wave guide is determined by moving the probe in the slotted section.
Tne V.S.W.R. can be determined directly when a V.S.W.R. meter is available. In the
alternative, the width at twice minimum power points is determined and used to calculate
the inverse V.S.W.R. pn from the simplified Robert and Von Hippel relation,
Pa
sin0
•3.3
•\/l + sin20
where
„
tcAx
here Ax is the distance between the points o f twice minimum power.
33
If pm, p„ and pco be the inverse voltage standing wave ratio for liquid lengths equal to
mX&!2, nXd/2 and infinite respectively, then their ratios pjp n and p j p® can be given by
the following relations suggested by P o ley 8.
tanh
.
L '
fa Y
V 2 jJ
•3.4
tanh nTttanf — I
L
ujj
t (AVI
•••3.5
tanh mrctan —
UJJ
where
fA
7t tan •
v2
2
For fixed values o f m and n arbitrary values are assigned to 7rtan(A/2) and two curves are
drawn using (3.4) and (3.5). Next the values o f m and n are changed and for each set o f
values o f m and n arbitrary values to 7rtan(A/2) are given and curves are drawn for each
set as described earlier. Once curve for pn/p„ and p j p» are drawn corresponding to
different values o f 7ttan(A/2), these curves can be used to read directly the value o f
7rtan(A/2) from the experimentally measured values o f pn> pm and p®. Thus X& and aX-a
being known, e* and e ” can be calculated from equations (3.1) and (3.2) respectively.
For liquids with low dielectric loss such as dilute solution o f a polar substance in non­
polar solvent, A,d is determined by the method described earlier. But the method for
determination o f attenuation constant is different. Heston et a l 9 pointed out that V.S.W.R.
o f low loss material is large and sensitive to small change in reflection coefficient near
unity which may be utilized to measure the attenuation constant o f low loss dielectric.
In the present investigations Heston’s method has been adopted for short-circuited
termination was used. The input impedance o f the dielectric medium at the interface is
34
p + jta n
\
Z(0)
1 + jtan
J
•••3.6c
2?tx q
where
xo is the distance o f the first minima from the interface,
Xg is the wavelength in the air
filled waveguide and Za is the characteristic impedance o f air medium.
If the length o f the dielectric column is taken as integral multiple o f X^2 and terminated
by a short circuit plunger as shown in the Figure- 3.1 (a) or odd integral multiple o f XJ4
in case o f open circuited termination as shown in the Figure-3.1 (b), then the value o f xo
is zero and hence
Z(0) = p ,
Since Za = 1
•••3.7
we know that
ZCO)*. = Z d tanhvd
- 3 .8
therefore,
p = Zd tanh vd
- 3 .9
where Zd, v and d are the characteristic impedance, propagation factor and length o f the
dielectric medium respectively.
35
36
Figure-3.1 (b) Open circuited termination
d = ^
2
where Xg = guide wavelength.
Thus the equation (3.9) reduces to
p _ z ( nak
mX
It
•3.10
2X„
Equation (3.10) represent a straight line betw een p and n w ith a slope,
X \a
2A,„
Thus,
2Xg ( dp
a
•3.11
X A Vdn
Substituting this value o f attenuation constant a in the equations (3.1) and (3.2) and for
low loss liquid (o Xa/I h)2 is very sm all com pare to one so it can be neglected. Therefore,
w e can w rite the final equation for e ’ and e ” as follows:
A
\2
A
"N
+
}
•3.12
\^dj
and
A
V
%\^ 6 J
V r spN
•3.13
KJv9nJ
Thus the values o f dielectric perm ittivity e ’ and dielectric loss e ” for low loss dielectrics
can be evaluated by m easuring the quantities ^•gs Xi and dp/dn.
37
The advantage o f this method over other methods is that it eliminates the wave guide and
plunger losses, which sometimes are comparable to the losses in dielectric. We have,
therefore, adopted this method for the short-circuited termination.
Microwave benches operating at frequencies J-band (7.22 GHz), X-band (9.1 GHz) and
K-band (19.62 GHz) have been used for carrying out measurements o f permittivity and
dielectric loss. They are shown in Figures-3.2, 3.3 and 3.4 respectively. V.S.W.R,. in each
.
c
case has been measured by a slotted line. The cell containing the experimental liquid is
kept vertical and connected to the main line by an E-plane bend. In the microwave bench,
the liquid filled section of the cell is separated from the rest o f the microwave line by a
thin sheet o f mica. A short-circuiting reflecting plunger is used to vary the length o f the
liquid column. The length o f the liquid column can be adjusted to an accuracy o f 0.001
cm. The temperature o f the cell is maintained constant within ± 0.5 °C by circulating
water in the jacket surrounding the cell. The crystal used for detection o f microwaves at Jband and X-band was 1N23, and 1N26 was used for K-band. The energy waves from the
Klystron source enter the wave guide and pass through the liquid and are reflected back
by a short-circuiting plunger. Thus a standing wave pattern is set up.
With the liquid in the cell and the plunger at the cell window, the probe is set to a
minimum power position. Then the plunger is turned upwards, increasing the depth o f the
liquid until another power minimum is obtained. The length o f the liquid column is
adjusted by moving the plunger for a series o f minima. The distance between two
successive minima is equal to ’
KJ2. For low loss liquids e ’ can be calculated by the
equation
(
- 3 .1 4
e'
v
The dielectric loss is measured by bringing the plunger down to the window and
minimizing the power with the probe. Then the plunger is brought up to various minimum
positions, i.e. liquid lengths equal to n>^/2, where n is an integer and the inverse standing
wave ratio p is measured from the width at double minimum points (Figure-3.5). The
38
vO
L>J
2K 25
KLYSTRON
_
SU PP LY
h_ __________ .
PO W ER
C
1
Figure-3.2 J-Band set-up
ATTENUATOR
FR EQ UEN CY!
M ETER
IF E R R IT E
ISO LATO R
CONSTANT -
. r ur t
TEMPERATURE WATER
S T A N D IN G
WAVE
DETECTOR
GALVANOMETER
PLUNGER DRIVE
M ICROMETER
40
Figure-3.
A T TE N U A T O R
>
MICROMETER PLUNGER
DRIVE
Figurc-3.4 K-Band set-up
STANDING WAVE
DETECTOR
DRIVE
MICROMETER PLUNGER
power
Out put
Probe
position
Subtraction
factor
Figure-3.5 Standing wave pattern near a minimum
Figure-3.6 Correction curve for p
42
value of p„, thus found is corrected because o f the approximation involved in deriving the
equation
xA x
t
A curve showing subtraction factor for different values o f (rcAx )/k g is given in Figure-3.6.
To obtain the absolute value o f pn, correction has to bfe applied for wall losses'and losses
in bends and imperfections in the short. In the present case since the slope o f the curve pn
versus n is used for calculating e ”, the correction is not necessary. The dielectric loss € ”
is given by
f\
V
W ap'
- 3 .1 5
The estimated accuracy o f the above measurements for e ’ and e ” is 1 percent and 5
percent respectively.
(ii) lim e Domain Reflectometry (TDR) Technique:
Complex permittivity o f polar liquids and their mixtures (pure state) were measured using
Time Domain Reflectometry (TDR). In this technique the information is obtained in a
very short time, which, otherwise in the frequency domain requires hours and
considerable instrumentation. The technique uses a pulse, which simultaneously contains
ail the frequencies o f interest. This pulse method has been applied sometimes in the past
for low frequency investigations on dielectrics. Modem tunnel diode pulse generators and
wide band sampling oscilloscopes allow the extension o f this method into the microwave
region, where savings in time and equipment are most pronounced.
Block diagram o f the time domain reflectometer system is shown in the Figure-3.7. It
consists o f a pulse generator which produces a fast rise time step, a sampler that
transforms a high frequency signal into a lower frequency output, and an oscilloscope or
any other display or recording device. In the present investigation the HP 54750 A
43
Figure-3.7 Block diagram o f TDR system
3*5 mm
1*52mm
,:Lt
—
A C TU A L P IN
L E N G TH
Figure-3.8 Fringing field and SMA cell dimensions
44
mainframe set up was used to obtain complex permittivity spectra of the samples in the
frequency range 10 MHz to 20 GHz. In the set up, a fast rising step voltage pulse o f 250
mv with 20 ps rise time and a repetitive frequency o f 1 KHz generated by a tunnel diode
was propagated through a SMA co-axial line system. The sample to be studied was
placed at the end o f co-axial cell with 3.5 mm outer diameter and 1.52 mm inner
conductor and 1.35 mm effective pin length (Figure-3.8), with a line characteristic
impedance o f 50 ohm. The reflected pulse along with the incident pulse was sampled with
t-
-
, «
sampling head. The chang°e in the pulse after reflection from the sample placed in the cell
was monitored. The reflected pulses from the channel without the sample liquid Ri(t) and
with sample liquid Rx(t) were digitized into 1024 points and transferred to the floppy
through the floppy drive attached to the sampling oscilloscope. These recorded pulses
were added [q(t) = Rftt) + Rx(t)] and subtracted [ p(t) = Rftt) - Rx(t)] in the time domain
in the oscilloscope memory after appropriate time shifting and were used for further
numerical analysis using a computer. These waveforms are shown in the Figure-3.10.
The time domain data received by the computer from TDR unit is converted to frequency
domain data using Fourier transforms.
Fourier transforms o f p(t) is obtained by a summation method 10 using equation,
p(co) = T^exp(-iconT)p(nT)
-3 .1 6
n-G
Fourier transform of q(t) is obtained by Samulon’s method 11
q(®) =
Z f c nT) “ ftl(n “ 1)T}] exp(-ioT )
where ® = angular frequency
T = time difference between two adjacent points
N = number o f points i.e. 1024
45
- 3 .1 7
25
*
/?
P
WTHOUT SAMPLE (R K tQ
JQ
o-
k.
o
WITH SAMPLE jR X C t0
d; CT
C7> 3
O
O
>
-
0
~i------------------r~
2-5
50
Time ln s )
Figure-3.9 Reflected pulse with and without sample in a time window o f 5ns
46
Complex reflection coefficient is given by
p * (0 )
c pQa)
•••3.18
jo>d q(<n)
where p(co) and q(o)) are Fourier transforms o f p(t) and q(t). co is angular frequency, d is
the effective, pin length (1.35mm), c is the speed .of light. -
.
, ec
c
Relative complex permittivity is given by
€ *(co) - 1 =
(l-f (o2d z / c 2)p*
•••3.19
(l - co2d 2 / c 2p *)
The data obtained from equation (3.18) are referred to here as ‘raw spectra’ or ‘raw data’.
The above expression was obtained by making two approximations, first, by assuming no
reflection from the transmission line and secondly by assuming that (©d/c)Ve* is very
small compared to unity so that the effect o f multiple reflection can be neglected. Under
most experimental conditions, reflection due to the transmission line can not be neglected.
However, the second effect depends on the type o f the liquid under consideration owing
to these effects, a correction in p* as obtained from equation (3.18) is needed. Cole 12 has
suggested a bilinear correction needed as follows:
e *(©)-! =
(l + A)p*
■3.20
1-Bp*
where A and B are determined experimentally by using two liquids with known dielectric
spectra. The permittivity spectra obtained from equation (3.20) are referred to here as
‘corrected spectra’ or ‘corrected data’.
47
3.1 (b) Measurement of Static Permittivity:
Static permittivity o f solutions was measured at 455KHz by resonance method using the
circuit shown in the figure 3.11. The circuit was developed at the Department o f Physics,
Gujarat University, Ahmedabad. It has a RF oscillator in which FET is used as an active
device and a tank circuit. A secondary circuit loosely coupled to the oscillator circuit c
*
©
.
cpnsists of, a parallel LC circuit tuned to 455RHz with a quartz crystal o f the same
frequency connected across ft. An a.c. millivoltmeter is connected in parallel to the
secondary circuit, which works as a detector. A variable standard capacitor and liquiddielectric cell are connected in parallel externally to the primary tuned circuit.
The standard variable capacitor and the liquid dielectric cell, used in the circuit (Figure3.11) were designed at the Department o f Physics, Gujarat University, Ahmedabad and
were fabricated by a private manufacturer. They are shown in Figure-3.12.
Variable Standard Capacitor:
It consists o f an outer cylinder, which works as a static electrode, and an inner movable
cylinder, which forms another electrode, is attached to a shaft. Shaft forms the axis o f the
two concentric cylinders. A micrometer screw arrangement is made at the other end o f the
shaft. Least count o f micrometer screw is 0.001 cm. By rotating the micrometer screw the
inner cylinder can be moved in or out from the fixed outer cylinder and its position can be
read from micrometer reading. Both the cylinders were electrically isolated. Metallic
contacts were given to the two cylinders for the external connections. Entire assembly o f
the condenser was inhoused in a wooden box and was electrically shielded by warping a
thin aluminum foil around the box.
Liquid Dielectric Cell:
The liquid dielectric cell used in this investigation was a co-axial cylindrical condenser
whose length is 3.0 cm. Diameter o f inner cylinder is 1 cm and inner diameter o f the outer
48
•
Fij»urc-3.11 455 Kl I/, oscillator circuit for static permittivity measurement
x y i&
49
Figure-3.12 (a) Variable standard capacitor
METAL LEADS
TEFLON RODS
COAXIAL METAL CYLINDERS
Figure-3.12 (b) Dielectric cell
50
cell is 1.4 cm. The distance between two co-axial cylinders was kept constant by fixing
teflon rods between the cylinders. Metallic contacts were given to the two cylinders for
external connection. The cylinders were silver plated. The cell was placed in a double
walled pyrex glass container and water was circulated to maintain constant temperature.
About 8.5 ml o f liquid is required to completely fill the cell.
Calibration o f the Standard Variable Capacitor: t ..
_ _
t
^
o
.
,
1
•
•
•
*>
t
'
_ *
„
0
1
c >
•
c
The standard variable capacitor was calibrated by standard multi frequency LCR meter
type 4274 A (Hewelt-Paekard) at Department o f Physics, Sardar Patel University,
Vallabh Vidya Nagar, Gujarat (INDIA). By rotating the micrometer screw the inner
cylinder can be moved in or out from the outer cylinder and accordingly the capacitance
o f the capacitor varies linearly from 165 pF, when inner cylinder is completely out to, 245
pF when inner cylinder is completely in. Capacitance o f the capacitor for a linear vertical
displacement o f the inner cylinder at the interval o f 5mm was measured by this meter.
Then a graph o f scale reading against capacitance was plotted which was found to be
linear. The slope o f which gave the capacitance per mm.
Calibration o f the Liquid Dielectric Cell:
The cell was calibrated using liquids o f known static permittivity. Without the dielectric
•cell in the circuit the capacitance o f the standard capacitor is varied and capacitor scale
reading X is taken at the occurrence o f the resonance. Next the empty dielectric cell is
brought into the circuit and standard capacitor is again adjusted for the resonance. Let the
corresponding scale reading be Y.
(X-Y)C = C e + C’
...3.21
where, C is the Capacitance o f standard capacitor corresponding to unit length o f the
capacitor scale,
Ce is the capacitance o f empty cell,
51
C’ is the stray capacitance for the leads including the capacitance due to insulation etc. in
the dielectric cell.
The dielectric cell is filled with the standardizing liquid. The capacitance o f the standard
capacitor is further changed to obtain the resonance. Let the corresponding scale reading
beZ.
-
Therefore,
-e t
<C
*
* e-
,, .
;
'
.
C ••
^
.
•
(X-Z)C = e 0CE + C’
,
o
...3.22
where, eo is the static permittivity o f the standard liquid.
Subtracting equation (3.21) from (3.22)
( e 0-l)C E = (Y-Z)C
.-. e 0= ~ ( Y - Z ) + l
- 3 .2 3
For the four standard liquids C(Y-Z) was determined and a graph o f €o versus C(Y-Z)
was plotted which resulted into a straight line. Inverse o f the slope o f this line gave the
capacitance CE o f the empty dielectric .cell. Once CE is known static permittivity o f the
unknown liquids can be determined using equation (3.23) and the method described
above.
3.1(c) Measurement of Refractive Index:
Refractive index o f solution for sodium D-line has been measured by a direct reading
Abbe’s refractometer having an accuracy o f 0.1 percent.
52
3.2 Description of T emperature Control D evice:
The temperature o f dielectric cells used for measurements o f complex permittivity at
microwave frequencies and static permittivity at 455 KHz was maintained constant by an
automatic temperature controller device, developed in this laboratory (Figure-3.13). It
consists o f TRIAC and thermometer switch. TRIAC is a controlled rectifier, which can be
switched on, in both positive and. negative naif cycle o f a x . power. Thermometer switch
!*
c
.v
1
consists o f thermometer with mercury column and a "set-screw. One contact o f the wire is
taken from mercury column and other from set-screw, which are connected between point
A and point B. The desired temperature o f the water bath can be adjusted by setting the
screw in the mercury column. If the set temperature with the screw' is more than the actual
temperature (temperature o f water bath), then there is no contact o f mercury in column
with the set-screw. It provides high impedance and the device will work as “open switch”.
A s the temperature increases, the height o f mercury in column w ill increase. When set
temperature is equal to actual temperature (temperature o f water bath), mercury will
touch the set-screw and device will work as “close switch”.
The 230 a.c. voltage is applied between MT 2 and MTi o f TRIAC through heater coil and
neon lamp is connected across the heater. Thermometer switch is connected between gate
and MTi terminal o f TRIAC. Here resistance Rq is used to trigger the TRIAC. Triggering
is synchronized with a.c. voltage waveform and selecting the proper value o f Re, the a.c.
power through the coil can be controlled. The R-C circuit is a protector circuit for TRIAC
known as snubber circuit.
When the thermometer switch is open, the TRIAC will be fired through the coil. It
remains ON, till the voltage between MT 2 and MTi becomes zero, i.e. up to end o f cycle.
Due to current passing through heater, the heater starts its heating process and the
temperature o f water bath go on increasing. When temperature o f water bath will be equal
to set temperature, the thermometer switch will close and the potential o f the gate and
MTi will be equal. The TRIAC will offer very high impedance. N ow , the current will not
pass through the heater coil and the heating action will be stopped by heater.
53
0-1 uf
600V
Figure-3.13 Temperature controller device
54
In short, when the temperature switch (TS) is open, TRIAC is in ON mode, heater is ON
and neon lamp lights. When temperature switch is closed TRIAC is in off mode, heater is
off and neon turns off.
3.3 E valuation of Different Parameters:
3.3 (a) Methods for Evaluation of Relaxation Time and Distribution Parameters:
The measured values o f dielectric constant ( e 5) and dielectric loss ( e ”) are used to
evaluate dielectric relaxation time (x) and distribution parameter (a). There are several
methods available in literature for this, they can be broadly classified in following
categories.
(i)
Frequency variation method using single concentration.
(ii)
Concentration variation method along with frequency variation.
(iii)
Concentration variation method at single frequency.
Since, the present study was carried out in dilute solutions the last two methods were used
for evaluation o f relaxation time and distribution parameter and will be described here.
(i)
Concentration variation along with frequency variation method:
To avoid dipole-dipole interaction the dielectric relaxation studies are frequently carried
out in dilute solutions o f polar substance in non-polar solvent. In this method solutions o f
polar solute in a non-polar solvent is prepared and their permittivity e ’ and dielectric loss
e ” are measured. The permittivity e ’ and dielectric loss e ” so obtained are plotted
against concentration. The plots are linear and can be represented by the following
equations:
e '= e , + a 'w 2
•••3.24
e"= a"w 2
•••3.25
e 0= e 10 +a0w 2
•••3.26
e M= e l00 +aMw 2
•••3.27
Subscript 1 refers to the pure solvent, W2 is the concentration o f the solute in weight
fraction and a’s are the slopes o f the straight lines.
55
The slopes a ’ and a” so obtained are plotted to obtain a complex plane plot. Plots o f
different shapes are obtained from which x and a or P can be calculated.
For rigid molecules obeying Debye equation, the locus o f complex plane plot o f a’
against a” is a semicircle with its center on real axis, and cuts the real axis at ao and a<».
Thus ao and a* are determined but the value o f x is not accurately determined. It may be
estimated with fair accuracy from the interpolated frequency o f the mid-point o f the
semicircle. An alternative graphical or analytical method for such cases is given by Cole
13 which is extremely useful and convenient. Debye equation can be written as
a.
a_ +•
•••
3.28
1 + j© t
Separating real and imaginary parts one gets,
• • • 3.29
a'= a 0 -x(G )a")
,
1 f a” )
• • • 3.30
a = a M+ ------
t{(oj
The advantage o f these equations is that they are linear relations in measured quantities
like a’, a” and a”/co hence, ao, a« and x can be obtained.
In general liquid do not conform to Debye behavior. The complex plane plot falls inside
the Debye semicircle having the centre below the real axis. The Cole-Cole equation for
dilute solutions becomes,
a* = a„ +
ao ~ a .
• • 3.31
,1-a
0 + j ® i o)
56
where a is constant having value between 0 and 1 and is called distribution parameter.
The diameter drawn through the center from a® makes an angle cot/2 with the a ’-axis.
The tangent o f this angle can be found out from the plot, whence
a can be calculated. The
most probable relaxation time To can be found out from the relation,
l =(pXJ - a
...3 .3 2
where v and u are the distance o f experimental point, corresponding to an angular
frequency co, from ao and a® respectively (Figure-3.14)
An alternative method for determining To and a is as follows,
•••3.33
log — = (l - a)log oo + (l - a)log t 0
W
A plot o f log (v/u) against log © gives a straight line whose slope is (1-a) and intercept is
(1-a) log To, from which a and tq can be evaluated.
Data for considerable variety o f dielectrics are consistent with the logarithmically
symmetrical dispersion and absorption dependence on frequency. However, in some cases
asymmetric frequency dependence may occur. The complex plane plot in such cases is
skewed arc (Figure-3.15). Cole-Davidson equation for such a distribution may be written
as,
ao ~ a«
(l + j©T0)p
putting a* = a’-ja ” and separating real and imaginary parts, following relations are
obtained.
a«,Xc0S<t>)P C0SP<1»
a'= a «>+ (a o —
.
a"= (a 0 -a^X co s^ y siaP 't1
•••3.35
•••3.36
57
Figure-3.14 Distances of experimental point ‘P’
Figure-3.15 Coie-Davidson arc
58
and
tan<(> = cox0
Hence,
cot g = tan i t a n - '
P
f
a"
a -a
^
*••3.37
°° / _
A n approxim ate value o f (3 can be obtained from the skewed arc in w hich high frequency
side approaches asym ptotically a line m aking an angle px/2 w ith the real axis o f a ’, to can
be calculated from equation (3.37) by substituting the m easured values o f a’VCa’-a*,) at a
given frequency. The value o f p is then adjusted w ithin the experim ental range for getting
constant value o f to from different frequency data. Know ing to and P, t av can be
calculated as,
t av=T0P
•••3.38
A better m ethod would be to draw normalized curve betw een (a’-aoo)/(ao-aoo) and
a”/(ao-a») for different known values o f p by varying <j> by fixed am ounts. The values o f
these quantities obtained experim entally are also plotted on the sam e graph. The value o f
P can be found out from the curve, w hich fits the experim ental values, the best. Knowing
P, t 0 can be calculated from equation (3.37) by substituting the calculated values o f
a’7(a’-a«,) at a given frequency. The value o f to found for different frequency data w ill
come out to be practically constant.
(ii)
Concentration Variation Method at a Single Frequency:
The difficulty w ith frequency variation m ethod is that for accurate determ ination o f
relaxation tim e and distribution param eter nearly a com plete band o f m icrowave
frequencies is required w hich is rarely available in laboratories. To overcom e this
difficulty a concentration variation m ethod 14,15 at a single frequency are suggested by
G opal K rishna 16 and H ig a s i17.
59
Gopal Krishna’s Method:
In this method the relaxation time and dipole moment are determined. The advantage o f
this method over other consists in eliminating the determination o f density o f the solution
and further when the value o f relaxation time alone is required even the concentration of
the solute in the non-polar solvent need not be determined. The method is based on Debye
equation. For dilute solutions complex premittivity e* (as a function o f frequency) can be
written as:
e*-l
<=„-1 , 47mji2
1
-------- = ----------1------------------e* + 2
+2
9kT 1+ jcox
oon
•••3.39
where n is the number of polar molecules per c.c. Putting e* = e ’- j e ” and splitting the
above equation into real and imaginary parts one obtains,
e'+ e '2+ g"2-2
e . -1 4rmp2
1
-- ----- --------— = --------- 1----------------- ——
(e'+2)2+ e"2
+2
9kT 1 + ©2t 2
3 g"
_ 4nnp2
tox
•••3.40
^
(e'+2)2+ g"2 ~ 9kT l + co2x2
substituting
x _€,2+e'-f g"2-2
(e'+2)2+ e"2
and
3 e"
Y _ (g'+2)2+ e"2
in equation (3.40) and putting
60
p ... ( g * - l )
(em +2)
One gets,
X = P+— Y
- 3 .4 2
(OX
P may be regarded as fairly constant at low concentrations, its variation with
concentration will be negligible in comparison to the error in values o f X and Y due to
experimental error in e ’and e ” at a microwave frequency. Hence if X is plotted against Y
the reciprocal o f the slope o f straight line so obtained will be equal to <bt from which x,
the relaxation time of the solute molecule in solution can be calculated. For estimating p
one can write equation (3.40) as,
X = P + kwd12
' - 3 .4 3
in which
k _ 47iNp2
1
~ 9kTM 1+ © V
in terms o f N, the Avagdros number (N = nM/d^w), where M is the molecular weight of
the polar substance, w is the weight fraction o f the solute and di2 is the density o f the
solution. At low concentration dn varies linearly with w and may be written as
d,2 = d 0(l + aw )
•••3.44
where do is the density o f the solvent. From the graph between X and w the slope
(dX/dw)w ...>0 gives kdo. Whence p can be calculated using equation (3.43).
This method is suitable for medium and high loss liquids because the variation in P are
negligible as compared to those in X and Y and hence it can be considered as constant. In
61
low loss liquids the variation o f P are comparable to those in X and Y hence results
obtained are not accurate.
Higasi Method:
Higasi 17 has proposed that value o f the relaxation time xo and distribution parameter a
can be found out from the measured values o f a’ and a” at a single frequency in the
dispersion region. The Cole-Cole equation expressed in terms o f slopes is,
a * - a M_
a0-a «
1
■••3.45
(l +jfflT0)1_a
putting a* = a’ - ja” and separating into real and imaginary parts one gets
xo
r A 2+ B 2^2 (l-o )
•••3.46
,
2
,A
1 - a = —tan —
n
B
•••3.47
where A = a" (a0 - a„)
•••3.48
B = (a0 - a' Xa'-a*,) - a"2
•••3.49
C = (a'-a„)2 +a"2
•••3.50
For a system with single relaxation time (a = 0), the Cole-Cole equation reduces to
Debye equation which may be written as,
a * -a „
a0
••3.51
(l + jcox)
putting a* = a’ - ja” and separating into real and imaginary parts one gets
62
a '- a ,
_
1
•••3.52
a0- a ra l + co2x2
a" __ cox
a0 - a w l+co2x2
- 3 .5 3
,
1(
a = a« + - —
- 3 .5 4
xVcoj .
and
a'= a0 -x(a"©)
•••3.55
Hence,
a0 -a'
a'-a^
- 3 .5 6
AI'n/a 2
•••3.57
or
CO
where
_ ap aa
•••3.58
2a"
From equation (3.54)
x = ----------
- 3 .5 9
co a'-a,,,
and from equation (3.55)
1 aft - a'
x = ---- -----co a"
- 3 .6 0
63
I f the D ebye equation for single relaxation tim e is valid for the system under
consideration and further the m easurem ents are sufficiently accurate, x can be evaluated
using any o f the above equations.
3.3 (b) Evaluation of Thermodynamical Parameters:
The therm odynam ical quantities viz., free energy o f activation AF€, enthalpy AHe and
entropy o f activation ASecan be obtained by determ ining the relaxation tim e at different
tem peratures using Erying’s rate equation18. The expression for free energy o f activation
is given by
•••3.61
K now ing To and the value o f other constants AFe can be calculated . Substituting the
therm odynam ic relation AF6 = AHe - AS 6 in the above expression and differentiating w ith
respect to 1/T one gets,
•••3.62
ln(Txo) is plotted against the reciprocal o f absolute tem perature. The slope o f the straight
line, w hen m ultiplied by R gives AH6, the m ost probable enthalpy o f activation.
Finally, the m ost probable entropy o f activation is determ ined from the relation,
AFe = A IIe —TASe
•••3,63
64
Referrences:
1. Tareev, B, Physics o f Dielectric Materials, (MIR Publishers), Moscow (1979).
2. Cole, R.H.S. and Windsor, P., J Phys. Chem., 84 (1980) 786.
3. Bramanti, E. and Bramanti, M., J. Micro. Power and Electro. Energy, 30 (1995) 213.
4. Robert, S., Von-Hippel, A., J. Appl. Phys.,17 (1946) 610.
5. Cripwell, F J. and Sutherland. G.B.B.M., Trans. Faraday Soc., 42 A (1946) 149.
6. Smyth, C.P., “Dielectric Behaviour and Structure”, McGraw Hill Book Co.Inc.,New
York (1955).
7. Laquer, H.L.and Smyth, C.P., J. Am.Chem.Soc.,70 (1948) 4097.
8. Poley, J. P.,Appl. Sci. Res., B4 (1955) 337.
9. Heston (Jr.), W. M., Franklin, A. D., Hennelley, E. J. and Smyth, C. P., J. Am. Chem.
Soc., 72 (1950) 3447.
10. Shannon, C. E., Proc. IRE, 37 (1949) 10.
11. Samulan, H. A., Proc IRE, 39 (1951) 175.
12. Cole, R. H., Berbarian, J. G., Mashimo, S., Chryssikos, G., Bums, A. and Tombari,
E., J. Appl. Phys., 66 (1989) 793.
13. Cole, R. H., J. Chem. Phys.,.23 (1955) 493.
14. Potapenko, G. and Wheeler, D., Revs. Mod. Phys., 20 (1958) 143.
15. Radhakrishna Murthy, Ch. D. V. G. L. and Rao Narasimha, J. Sci. Indian Res.,
15B (1956) 346.
16. Gopal Krishna, K. V., Trans. Faraday Soc., 53 (1957) 767.
17. Higasi, K., Bull. Chem. Soc. Japan, 39 (1966) 2157.
18. Glastone, S., Laidler, K. I. and Eyring. H,, “The Theory o f Rate Processes”, McGraw
Hill, New York (1941).
65
CHAPTER-IV
DIELECTRIC RELAXATION STUDIES OF NON-ASSOCIATIVE
POLAR MOLECULES AND THEIR BINARY MIXTURES AT
DIFFERENT TEMPERATURES IN BENZENE SOLUTION
4.1 Introduction :
The dielectric relaxation studies are useful to investigate molecular and intramolecular
motions, solute-solute and solute-solvent interactions 1-3. Since the pioneering work o f
Schallamach
4
attempts have been made by many workers to understand the dielectric
behavior o f several binary liquid mixtures. Schallamach have shown that binary liquid
mixtures in which both the components are either associated or non-associated is
homogeneous and have a single relaxation time, where as the binary liquid mixtures in
which one component is associated and the other is non-associated have a distribution of
relaxation time. Later investigations by B o s5,Denney and associates 6-8 and McDuffie and
co-workers
9' 10
seem to confirm the Schallamach conclusion. On the other hand the
results obtained by Forest and Smyth u , Garg and Kababa 12, Kilp et a l 13 for the mixtures
of two non-associated liquids shown deviations from Schallamach’s findings. They
noticed two dispersion regions and explained that the relaxation processes in the
particular two component systems were those o f molecules rather than larger o f liquid
regions. Thus in last two decades, study o f dielectric behavior o f mixtures o f polar
molecules under varying conditions o f composition and temperature have been carried
out by several workers. These studies helped to understand the nature o f interactions that
exist in the systems and to develop suitable models for liquid relaxation. Madan
14-17
studied some rigid polar molecules and their mixtures in dilute solutions and found that in
the mixture the degree of polarization order decays exponentially just as it does for single
component system.
Srivastava and Sinha
18
studied mixtures o f chloroform and bromoform with
chlorobenzene at three different microwave frequencies and found that their results were
66
in good accordance with the simple Debye model o f dielectric relaxation. Hanna et a l 19
carried out dielectric absorption measurements on dipolar mixtures o f nitrobenzene and
chlorobenzene molecules in non-polar solvents over a range o f microwave frequencies at
different temperatures and observed that in the mixtures the units relax in some form o f
cooperative manner. Prakash and Rai 20 carried out dielectric relaxation study on the
mixtures o f different compositions o f nitrobenzene and aniline in benzene solution at two
microwave frequencies and at different temperatures and found the existence of inter­
association or complex formation at 25 % concentration o f aniline in the mixture. Gandhi
and Sharma 21‘22 studied the dielectric relaxation behavior o f binary mixtures of
associative + associative and associative + non-associative systems o f non-rigid polar
molecules and observed that the dielectric behavior o f the former system is simpler than
the later system. Furthermore, they found that the individual characteristics o f the
constituents are retained in their mixtures for both the types o f the systems.
The earlier measurements o f dielectric properties o f mixtures o f polar molecules in dilute
solutions o f benzene at different temperatures 23 in this laboratory revealed the presence
o f single relaxation process for mixtures o f rigid polar molecules, however, there was
complex formation in the case o f mixtures o f associative molecules. Recently, Singh and
Sharma 24 studied temperature dependence o f dielectric relaxation o f PMA (para methyl
acetophenon), DMSO (dimethyl sulphoxide) and their mixtures in the dilute solutions o f
benzene, they observed that relaxation time o f the mixture increases nonlinearly with the
increase in concentration o f DMSO in the mixture, the result was explained in terms o f
solute- solute and solute- solvent interactions. Abd-El-Messieh 25 studied dielectric
relaxation o f mixtures o f 4-nitrobenzyl chloride and
1,2,3-trichlorobenzene in
carbontetrachloride, decalin and a mixture o f both solvents (1:1) over wide range o f
microwave frequencies and at different temperatures. They found that the relaxation time
o f mixture lies between those found for individuals measured in the same solvent
mixtures, which indicate that there is no detected interaction between two components in
the solvent mixture.
With a view to gain more information.in this area, dielectric relaxation in few nonassociative polar molecules and their binary mixtures in dilute solutions o f benzene have
67
been studied at a single microwave frequency at four different temperatures and the
results are reported in this Chapter. Microwave absorption at 9.1 GHz, static permittivity
and refractive index were measured at four different temperatures. The dielectric data
have been analyzed to yield the most probable relaxation time (xo), distribution parameter
(a) and thermodynamical parameters.
In the present investigation following two systems have been selected.
•
System I :
Aniline (AN)
AN + BN (25% o f BN)
-
AN + BN (50% o f BN)
AN + BN (75% o f BN)
Benzonitrile (BN)
•
System H :
2-Chloroaniline (2-CA)
2-CA + NB (25% o f NB)
2-CA + NB (50% of NB)
2-CA + NB (75% o f NB)
Nitrobenzene (NB)
4.2 Experimental :
Benzonitrile, purum grade (Fluka A.G., Switzerland), 2-Chloroaniline, purest grade
(Merck, Germany) and Nitrobenzene, AR grade (Sd- Fine Chem Co. Ltd., India) were
used without further purification. Aniline, AR grade (Merck, India) and Benzene, AR
grade (Qualigens, India) were used after fractional distillation.
Binary mixtures o f different compositions (3:1, 1:1 and 1:3) o f AN + BN and 2-CA + NB
were prepared by adding them by mole. These mixtures were taken as solute. Five dilute
solutions o f each o f these mixtures as well as individual molecules were prepared using
benzene as non-polar solvent.
68
Permittivity ( e ’) and dielectric loss ( e ”) have been measured for each polar molecules
and their mixtures in benzene solutions at microwave frequency 9.1 GHz, static
permittivity ( go) at frequency 455 KHz and permittivity at optical frequency ( e ro) were
also measured. For the System I all the measurements were made at 20,30,40, and 47 °C.
Whereas for the System II all the measurements were made at 20,30, 40 and 50 °C and
the temperature was controlled within ±0.5 °C by a thermostat. The experimental method
adopted for the measurement o f gq» e ’, e ” and e® have been described in Chapter-Ill.
The measured values o f eo, e ’, e ” and e® are given in Table-4.1. The values o f most
probable relaxation time (t<j) and distribution parameter (a) o f the polar molecules and
their mixtures were calculated using Higasi’s method 26 (described in Chapter-Ill). The
free energy o f activation (AF€), the enthalpy o f activation (AHe) and entropy o f activation
(ASe) were evaluated using the equations (3.61), (3.62) and (3.63).
4.3 R esults and D iscussion :
The slopes ao, a’, a” and a® determined by plotting measured values o f e 0, e \ e ” and e®
against concentration o f single component and mixtures at different temperatures are
listed in Table-4.2. The values o f the most probable relaxation time (tq) and distribution
parameter (a) are listed in Table -4.3.
•
System I: Aniline, Benzonitrile and their Mixtures :
From the Table-4.3 (1) it can be seen that the value o f distribution parameter for
benzonitrile in benzene solution is zero at all temperatures, indicating Debye type
relaxation process in the benzonitrile in benzene solution. This is in agreement with the
observation made by other workers. Hassel and Walker 27 reported 0.06 value o f
distribution parameter for benzonitrile at 15 °C in p-xylene and cyclohexane. Whereas
dielectric data obtained by Madan 28 for benzonitrile at differrent temperatures fitted a
simple Debye semicircle, indicating a zero value o f distribution parameter. Srivastava et
al 29 reported 0.02 value o f distribution parameter for benzonitrile in pure state at 30 °C.
69
Table 4.1 (1)- Values of Go,
g
’, g ”
and Goo of solutions of aniline in benzene at different
temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt.
fr.
g
9.1 GHz
Cone,
’
in wt. fr.
g
”
Optical
CO
TEMPERATURE = 20 UC
0.0083
2.352
0.0133
2.344 0.007
0.0083
2.2494
0.0184
2.374
0.0250
2.371 0.013
0.0184
2.2530
0.0307
2.410
0.0347
2.400 0.020
0.0307
2.2560
0.0365
2.427
0.0423
2.419 0.026
0.0365
2.2575
0.0493
2.466
0.0530
2.438 0.027
0.0493
2.2614
TEMPERATURE = 30 °C
0.0083
2.337
0.0116
2.302 0.007
0.0083
2.2290
0.0184
2.382
0.0286
2.357 0.020
0.0184
2.2320
0.0307
2.394
0.0376
2.388 0.025
0.0307
2.2350
0.0365
2.409
0.0512
2.414 0.032
0.0365
2.2380
0.0493
2.440
0.0634
2.470 0.049
0.0493
2.2410
TEMPERATURE = 40 °C
0.0083
2.317
0.0184
0.0108
2.282 0.012
0.0083
2.2112
0.0179
2.301 0.017
0.0184
2.2141
0.0307
2.369
0.0282
2.324 0.021
0.0307
2.2186
0.0365
2.382
0.0398
2.344 0.029
0.0365
2.2216
0.0493
2.412
0.0497
2.384 0.033
0.0493
2.2231
TEMPERATURE = 47 °C
0.0083
2.273
0.0108
2.242 0.006
0.0083
2.2199
0.0184
2.311
0.0179
2.268 0.009
0.0184
2.2008
0.0307
2.318
0.0282
2.295 0.014
0.0307
2.2052
0.0365
2.341
0.0398
2.337 0.019
0.0365
2.2058
0.0493
2.388
0.0497
2.359 0.209
0.0493
2.2082
70
Table 4.1 (2)- Values of e 0, e ’,e ” and e® of solutions of benzonitrile in benzene at
different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE = 20 °C
0.0036
2.315
0.0036
2.355 0.059
0.0036
2.2320
0.0085
2.396
0.0085
2.414 0.090
0.0085
2.2335
0.0119
2.465
0.0119
2.460 0.112
0.0119
2.2350
0.0159
2.531
0.0159
2.506 0.141
0.0159
2.2365
0.0207
2.602
0.0207
2.556 0.171
0.0207
2.2380
TEMPERATURE = 30 °C
0.0092
2.448
0.0025
2.329 0.032
0.0092
2.2326
0.0134
2.568
0.0044
2.359 0.039
0.0134
2.2335
0.0181
2.622
0.0080
2.412 0.054
0.0181
2.2350
0.0239
2.730
0.0134
2.473 0.097
0.0239
2.2356
0.0280
2.815
0.0162
2.502 0.114
0.0280
2.2365
TEMPERATURE = 40 °C
0.0036
2.272
0.0036
2.322 0.039
0.0036
2.2156
0.0085
2.315
0.0085
2.371 0.058
0.0085
2.2165
0.0119
2.395
0.0119
2.435 0.093
0.0119
2.2171
0.0159
2.457
0.0159
2.482 0.102
0.0159
2.2174
0.0207
2.541
0.0207
2.508 0.130
0.0207
2.2177
TEMPERATURE = 47 °C
0.0036
2.256
0.0036
2.303 0.034
0.0036
2.2052
0.0085
2.336
0.0085
2.356 0.069
0.0085
2.2058
0.0119
2.403
0.0119
2.398 0.084
0.0119
2.2067
0.0159
2.446
0.0159
2.447 0.107
0.0159
2.2073
0.0207
2.551
0.0207
2.491 0.128
0.0207
2.2076
71
Table 4.1 (3)- Values of e 0, e ’,e ” and e ^ o f solutions of 3:1 composition of mixture of
AN + BN in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
e«,
TEMPERATURE = 20 UC
0.0048
2.307
0.0064
2.336 0.020
0.0048
2.2470
0.0114
2.354
0.0130
2.369 0.042
0.0114
2.2485
0.0171
2.388
0.0179
2.359 0.068
0.0171
2.2500
0.0226
2.445
0.0221
2.414 0.083
0.0226
2.2515
0.0285
2.473
0.0312
2.476 0.106
0.0285
2.2530
TEMPERATURE = 30 °C
0.0080
2.281
0.0080
2.326 0.033
0.0080
2.2261
0.0171
2.319
0.0171
2.382 0.050
0.0171
2.2285
0.0205
2.337
0.0205
2.400 0.058
0.0205
2.2291
0.0272
2.376
0.0272
2.426 0.069
0.0272
2.2305
0.0342
2.449
0.0342
2.479 0.089
0.0342
2.2326
TEMPERATURE = 40 °C
0.0064
2.199
0.0064
2.293 0.013
0.0064
2.2136
0.0130
2.276
0.0130
2.322 0.036
0.0130
2.2141
0.0179
2.301
0.0179
2.359 0.041
0.0179
2.2147
0.0221
2.324
0.0221
2.386 0.056
0.0221
2.2156
0.0312
2.374
0.0312
2.422 0.079
0.0312
2.2171
TEMPERATURE = 47 °C
0.0064
2.262
0.0064
2.274 0.016
0.0064
2.2046
0.0130
2.291
0.0130
2.304 0.028
0.0130
2.2052
0.0179
2.346
0.0179
2.345 0.040
0.0179
2.2058
0.0221
2.368
0.0221
2.363 0.051
0.0221
2.2067
0.0312
2.423
0.0312
2.410 0.066
0.0312
2.2076
72
Table 4.1 (4)- Values of e 0, e ’,e ” and e „ o f solutions of 1:1 composition of mixture of
AN + BN in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
€’
6”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE = 20 UC
0.0036
2.300
0.0029
2.327 0.020
0.0036
2.2291
0.0081
2.331
0.0069
2.364 0.031
0.0081
2.2297
0.0121
2.363
0.0112
2.393 0.062
0.0121
2.2305
0.0163
2.436
0.0163
2.448 0.071
0.0163
2.2311
0.0219
2.457
0.0219
2.474 0.087
0.0219
2.2317
TEMPERATURE = 30 °C
0.0033
2.274
0.0033
2.307 0.025
0.0033
2.2291
0.0096
2.328
0.0096
2.372 0.038
0.0096
2.2297
0.0125
2.348
0.0125
2.398 0.054
0.0125
2.2305
0.0167
2.374
0.0167
2.422 0.062
0.0167
2.2311
0.0219
2.431
0.0219
2.462 0.090
0.0219
2.2317
TEMPERATURE = 40 °C
0.0029
2.201
0.0029
2.287 0.018
0.0029
2.2156
0.0069
2.221
0.0069
2.327 0.037
0.0069
2.2165
0.0112
2.270
0.0112
2.356 0.055
0.0112
2.2171
0.0163
2.323
0.0163
2.380 0.067
0.0163
2.2180
0.0219
2.368
0.0219
2.436 0.084
0.0219
2.2189
TEMPERATURE = 47 °C
0.0029
2.225
0.0029
2.277 0.009
0.0029
2.1992
0.0069
2.255
0.0069
2.298 0.029
0.0069
2.1999
0.0112
2.308
0.0112
2.337 0.045
0.0112
2.2008
0.0163
2.376
0.0163
2.363 0.053
0.0163
2.2014
0.0219
2.405
0.0219
2.419 0.062
0.0219
2.2023
73
Table 4.1 (5)- Values of Go,
g ’, g ”
and g * of solutions of 1:3 composition of mixture of
AN + BN in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
€o
in wt. fr.
9.1 GHz
g’
g”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE - 20 °C
0.0041
2.328
0.0046
2.354 0.041
0.0041
2.1992
0.0084
2.378
0.0079
2.377 0.068
0.0084
2.2000
0.0127
2.477
0.0095
2.403 0.076
0.0127
2.2008
0.0174
2.511
0.0127
2.442 0.108
0.0174
2.2014
0.0209
2.559
0.0168
2.476" 0.124
0.0209
2.2022
TEMPERATURE = 30 °C
0.0041
2.255
0.0041
2.311 0.020
0.0041
2.2291
0.0063
2.280
0.0063
2.326 0.031
0.0063
2.2294
0.0082
2.327
0.0082
2.348 0.051
0.0082
2.2296
0.0124
2.382
0.0124
2.414 0.079
0.0124
2.2302
0.0171
2.431
0.0171
2.443 0.102
0.0171
2.2294
TEMPERATURE = 40 °C
0.0041
2.280
0.0046
2.318 0.037
0.0041
2.2186
0.0084
2.327
0.0079
2.352 0.057
0.0084
2.2195
0.0127
2.470
0.0095
2.359 0.074
0.0127
2.2201
0.0174
2.471
0.0127
2.398 0.088
0.0174
2.2216
0.0209
2.487
0.0168
2.451 0.107
0.0209
2.2222
TEMPERATURE = 47 °C
0.0041
2.278
0.0046
2.301 0.042
0.0041
2.2052
0.0084
2.299
0.0079
2.334 0.051
0.0084
2.2058
0.0127
2.384
0.0095
2.347 0.064
0.0127
2.2067
0.0174
2.435
0.0127
2.384 0.084
0.0174
2.2076
0.0209
2.493
0.0168
2.422 0.102
0.0209
2.2088
74
Table 4.1 (6)- Values of e 0, e \ e ” and 1Eco o f solutions of 2-CA in benzene at different
temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
e«
TF.MPF.RATURE = 20 UC
0.0125
2.317
0.0125
2.320 0.011
0.0125
2.3516
0.0210
2.343
0.0210
2.352 0.022
0.0210
2.3532
0.0300
2.372
0.0300
2.371 0.028
0.0300
2.3547
0.0425
2.412
0.0425
2.406 0.036
0.0425
2.3578
0.0547
2.459
0.0547
2.430 0.049
0.0547
2.3639
TF.MPF.RATURE = 30 °C
0.0121
2.433
0.0121
2.315 0.011
0.0121
2.3424
0.0313
2.490
0.0245
2.356 0.022
0.0245
2.3455
0.0405
2.516
0.0338
2.380 0.028
0.0338
2.3486
0.0522
2.591
0.0450
2.414 0.039
0.0450
2.3516
0.0683
2.623
0.0581
2.454 0.054
0.0581
2.3547
TEMPERATURE = 40 °C
0.0099
2.246
0.0099
2.279 0.012
0.0099
2.3372
0.0197
2.267
0.0197
2.318 0.010
0.0197
2.3394
0.0347
2.303
0.0347
2.347 0.024
0.0347
2.3433
0.0477
2.332
0.0477
2.392 0.031
0.0477
2.3464
0.0605
2.371
0.0605
2.414 0.043
0.0605
2.3476
TEMPERATURE = 50 °C
0.0098
2.252
0.0124
2.259 0.008
0.0098
2.3378
0.0191
2.261
0.0212
2.287 0.009
0.0191
2.3412
0.0306
2.289
0.0355
2.318 0.020
0.0306
2.3446
0.0406
2.318
0.0432
2.335 0.026
0.0406
2.3464
0.0519
2.346
0.0546
2.371 0.036
0.0519
2.3486
75
Table 4.1 (7>- Values of eo,
g
’, g ”
and e«, o f solutions o f NB in benzene at different
temperatures.
Cone.
in wt. fr.
455 KHz
Cone.
e0
in wt. fr.
9.1 GHz
e ’
g
”
Cone.
Optical
in wt. fr.
e=o
TEMPERATURE = 20 °C
0.0022
2.284
0.0051
2.382 0.053
0.0093
2.4025
0.0051
2.394
0.0093
2.428 0.071
0.0200
2.4041
0.0102
2.434
0.0143
2.454 0.102
0.0282
2.4062
0.0143
2.534
0.0200
2.534 0.154
0.0378
2.4087
0.0205
2.608
0.0282
2.600 0.197
0.0464
2.4118
TEMPERATURE = 30 °C
0.0064
2.338
0.0049
2.333 0.030
0.0049
2.3354
0.0120
2.396
0.0092
2.382 0.064
0.0092
2.3381
0.0166
2.481
0.0163
2.450 0.085
0.0163
2.3381
0.0227
2.547
0.0185
2.506 0.102
0.0185
2.3394
0.0292
2.609
0.0241
2.536 0.115
0.0241
2.3403
TEMPERATURE = 40 °C
0.0064
2.323
0.0049
2.307 0.019
0.0049
2.3363
0.0120
2.385
0.0099
2.378 0.054
0.0099
2.3378
0.0166
2.475
0.0163
2.438 0.085
0.0163
2.3385
0.0227
2.527
0.0201
2.489 0.111
0.0201
2.3394
0.0292
2.597
0.0241
2.491 0.112
0.0241
2.3403
TEMPERATURE = 50 °C
0.0059
2.523
0.0059
2.302 0.030
0.0059
2.3250
0.0128
2.580
0.0105
2.344 0.047
0.0105
2.3256
0.0178
2.694
0.0153
2.386 0.066
0.0153
2.3272
0.0240
2.749
0.0213
2.454 0.098
0.0213
2.3281
0.0295
2.866
0.0259
2.470 0.111
0.0259
2.3287
76
Table 4.1 (8)- Values of €o, e ’,e ” and e « o f solutions of 3:1 composition of mixture of
2-CA + NB in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
^0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
e®
TEMPERATURE - 20 °C
0.0104
2.354
0.0104
2.340 0.022
0.0104
2.3486
0.0199
2.404
0.0199
2.392 0.048
0.0199
2.3530
0.0315
2.469
0.0315
2.430 0.069
0.0315
2.3501
0.0441
2.569
0.0441
2.472 0.088
0.0441
2.3578
0.0556
2.671
0.0556
2.521 0.121
0.0556
2.3620
TEMPERATURE = 30 °C
0.0105
2.366
0.0105
2.320 0.034
0.0105
2.1742
0.0234
2.423
0.0234
2.378 0.056
0.0234
2.1762
0.0318
2.470
0.0318
2.412 0.071
0.0318
2.1786
0.0427
2.529
0.0427
2.464 0.087
0.0427
2.1809
0.0515
2.593
0.0515
2.506 0.105
0.0515
2.1830
TEMPERATURE = 40 °C
0.0108
2.286
0.0108
2.289 0.012
0.0108
2.3363
0.0254
2.354
0.0254
2.367 0.038
0.0254
2.3394
0.0378
2.408
0.0378
2.426 0.068
0.0378
2.3424
0.0492
2.473
0.0492
2.474 0.082
0.0492
2.3446
0.0634
2.527
0.0634
2.530 0.098
0.0634
2.3470
TEMPERATURE = 50 °C
0.0100
2.415
0.0100
2.271 0.019
0.0100
2.3226
0.0183
2.450
0.0200
2.311 0.030
0.0200
2.3256
0.0294
2.479
0.0296
2.363 0.046
0.0296
2.3302
0.0401
2.544
0.0397
2.396 0.061
0.0397
2.3332
0.0475
2.575
0.0491
2.448 0.072
0.0491
2.3363
77
Table 4.1 (9)- Values o f e 0, <=’, e ” and €a>of solutions o f 1:1 composition o f mixture of
2-CA +NB in benzene at different temperatures.
Cone,
in wt. fr.
455 KHz
Cone,
Go
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
Geo
TEMPERATURE = 20 UC
0.0092
2.368
0.0092
2.371 0.041
0.0092
2.3440
0.0219
2.453
0.0219
2.430 0.081
0.0219
2.3464
0.0322
2.576
0.0322
2.479 0.112
0.0322
2.3486
0.0433
2.652
0.0433
2.543 0.140
0.0433
2.3501
0,0519
2.770
0.0519
2.596 0.169
0.0519
2.3525
TEMPERATURE = 30 °C
0.0095
2.379
0.0095
2.375 0.047
0.0095
2.1786
0.0212
2.457
0.0212
2.438 0.088
0.0212
2.1809
0.0342
2.534
0.0342
2.477 0.107
0.0342
2.1844
0.0458
2.565
0.0458
2.558 0.139
0.0458
2.1860
0.0546
2.750
0.0546
2.640 0.190
0.0546
2.1874
TEMPERATURE = 40 °C
0.0098
2.321
0.0098
2.348 0.034
0.0098
2.3378
0.0189
2.352
0.0189
2.384 0.044
0.0189
2.3394
0.0277
2.406
0.0277
2.446 0.076
0.0277
2.3409
0.0362
2.495
0.0362
2.519 0.109
0.0362
2.3424
0.0465
2.548
0.0465
2.558 0.126
0.0465
2.3440
TEMPERATURE = 50 °C
0.0103
2.283
0.0095
2.296 0.029
0.0095
2.3250
0.0194
2.369
0.0180
2.356 0.049
0.0180
2.3259
0.0280
2.440
0.0286
2.430 0.078
0.0286
2.3287
0.0373
2.505
0.0404
2.491 0.107
0.0404
2.3311
0.0470
2.574
0.0494
2.556 0.134
0.0494
2.3342
78
Table 4.1 (10)- Values of e 0>e ’,e ” and G«,of solutions of 1:3 composition of mixture of
2-CA + NB in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fr.
9.1 GHz
g’
e”
Cone,
Optical
in wt. fr.
G oo
TEMPERATURE = 20 UC
0.0056
2.352
0.0056
2.337 0.029
0.0056
2.3455
0.0102
2.386
0.0102
2.402 0.049
0.0102
2.3461
0.0159
2.470
0.0159
2.418 0.076
0.0159
2.3464
0.0228
2.542
0.0228
2.470 0.114
0.0228
2.3473
0.0329
2.661
0.0329-
2.538 0.148
0.0329
2.3482
TEMPERATURE = 30 °C
0.0059
2.474
0.0059
2.329 0.031
0.0059
2.3393
0.0114
2.512
0.0106
2.344 0.044
0.0114
2.3403
0.0155
2.558
0.0155
2.406 0.071
0.0155
2.3412
0.0215
2.623
0.0171
2.426 0.074
0.0215
2.3433
0.0258
2.640
0.0215
2.439 0.084
0.0258
2.3446
TEMPERATURE = 40 °C
0.0059
2.392
0.0059
2.313 0.029
0.0059
2.3378
0.0114
2.429
0.0114
2.348 0.050
0.0114
2.3394
0.0154
2.475
0.0154
2.394 0.066
0.0154
2.3409
0.0215
2.501
0.0215
2.426 0.081
0.0215
2.3424
0.0258
2.548
0.0258
2.483 0.106
0.0258
2.3440
TEMPERATURE = 50 °C
0.0046
2.277
0.0045
2.291 0.021
0.0045
2.3226
0.0115
2.358
0.0110
2.329 0.038
0.0110
2.3240
0.0199
2.434
0.0160
2.373 0.063
0.0160
2.3250
0.0240
2.521
0.0200
2.410 0.081
0.0200
2.3262
0.0321
2.572
0.0250
2.462 0.096
0.0250
2.3287
79
Table 4.2 (1)- Values of ao, a’, a” and a*, of solutions of aniline, benzonitrile and their
mixtures in benzene solution at different temperatures.
Molecules
a’
ao
a”
3oo
TEMPERATURE = 20 °C
Aniline (AN)
2.65
2.38
0.57
0.30
AN + BN (25 % of BN)
7.21
5.95
2.65
0.25
AN + BN (50% of BN)
10.83
8.40
4.40
0.27
AN + BN (75 % of BN)
15.18
10.50
6.90
0.30
Benzonitrile (BN)
17.02
11.20
7.90
„ 0.36
TEMPERATURE = 30 °C
Aniline (AN)
2.55
2.30
0.53
0.30
AN + BN (25% of BN)
6.25
5.39
2.06
0.24
AN + BN (50% of BN)
9.80
7.70
3.95
0.14
AN + BN (75% of BN)
13.84
10.00
6.10
0.14
Benzonitrile (BN)
15.6
11.00
7.00
0.21
TEMPERATURE = 40 °C
Aniline (AN)
2.45
2.22
0.50
0.30
AN + BN (25 % of BN)
5.70
5.00
1.80
0.16
AN + BN (50% of BN)
8.85
7.25
3.35
0.20
AN + BN (75% of BN)
13.40
10.00
5.79
0.22
Benzonitrile (BN)
14.75
10.80
6.40
0.23
TEMPERATURE = 47 °C
Aniline (AN)
2.33
2.16
0.47
0.23
AN + BN (25 % of BN)
5.17
4.57
1.60
0.13
AN + BN (50% of BN)
7.80
6.50
2.85
0.17
AN + BN (75 % of BN)
12.32
9.80
4.90
0.18
Benzonitrile (BN)
14.00
10.50
5.95
0.23
80
Table 4.2 (2)- Values of aQ, a’, a” and a«of solutions of 2-chloroaniline, nitrobenzene and
their mixtures in benzene solution at different temperatures.
Molecules
a’
ao
a”
3oo
TEMPERATURE = 20 °C
2-Chloroaniline (2-CA)
3.55
2.82
0.92
0.22
2-CA + NB (25 % of NB)
7.00
5.00
2.41
0.25
2-CA + NB (50% of NB)
10.00
6.70
3.80
0.21
2-CA + NB (75 % of NB)
11.70
7.90
4.95
0.22
Nitrobenzene (NB)
15.90
11.20
6.54
0.28
TEMPERATURE = 30 °C
2-Chloroaniline (2-CA)
3.27
2.77
0.90
0.25
2-CA + NB (25% of NB)
6.62
5.16
2.33
0.24
2-CA + NB (50% of NB)
9.00
6.89
3.50
0.26
2-CA + NB (25% of NB)
9.90
7.36
4.10
0.25
Nitrobenzene (NB)
14.28
11.11
5.41
0.27
TEMPERATURE = 40 °C
2-Chloroaniline (2-CA)
2.63
2.30
0.65
0.24
2-CA + NB (25% of NB)
4.96
4.28
1.56
0.22
2-CA + NB (50% of NB)
7.00
5.60
2.70
0.18
2-CA + NB (75 % of NB)
9.28
7.18
3.70
0.27
Nitrobenzene (NB)
12.85
10.38
4.83
0.22
TEMPERATURE = 50 °C
2-Chloroaniline (2-CA)
2.38
2.11
0.56
0.23
2-CA + NB (25% of NB)
4.35
3.92
1.20
0.26
2-CA + NB (50% of NB)
7.20
5.94
2.60
0.24
2-CA + NB (75% of NB)
8.75
7.00
3.40
0.24
Nitrobenzene (NB)
11.90
10.00
4.30
0.21
81
Table 4.3 (l)-Values of relaxation time (x0) and distribution parameter (a) for aniline,
benzonitrile and their mixtures in benzene solution at different temperatures.
Molecules
Relaxation Time
Distribution
inps
Parameter
TEMPERATURE = 20 °C
AN
4.4
0.11
AN +BN (25 % of BN)
8.1
0.00
AN +BN (50 % of BN)
9.5
0.00
AN +BN (75 % of BN)
11.8
0.00
BN
12.8
0.00
TEMPERATURE = 30 °C
AN
4.2
0.11
AN +BN (25 % of BN)
7.0
0.00
AN +BN (50 % of BN)
9.2
0.00
AN +BN (75 % of BN)
10.9
0.00
BN
11.4
0.00
TEMPERATURE = 40 °C
AN
4.1
0.11
AN +BN (25 % of BN)
6.5
0.00
AN +BN (50 % of BN)
8.3
0.00
AN +BN (75 % of BN)
10.2
0.00
BN
10.6
0.00
TEMPERATURE = 47 °C
AN
4.0
0.07
AN +BN (25 % of BN)
6.3
0.00
AN +BN (50 % of BN)
7.9
0.00
AN +BN (75 % of BN)
8.9
0.00
10.2
0.00
BN
82
Table 4,3 (2)-Values of relaxation time (to) and distribution parameter (a) for 2-CA, NB
and their mixtures in benzene solution at different temperatures.
Molecules
Relaxation Time
Distribution
Laps
Parameter
TEMPERATURE - 20 °C
2-CA
6.4
0.18
2-CA + NB (25 % of NB)
9.4
0.14
2-CA + NB (50 % of NB) -
11.1
0.12
2-CA + N B {7 5 % o f NB)
11.7
0.05
NB
10.8
0.05
TEMPERATURE = 30 °C
2-CA
6.0
0.11
2-CA -+ NB (25 % o f KB)
8.4
0.08
2-CA + NB (50 % of NB)
9.3
0.04
2-CA + NB (75 % of NB)
10.2
0.02
8.8
0.04
NB
TEMPERATURE - 40 °C
2-CA
5.2
0.10
2-CA + NB (25 % of NB)
6.6
0.03
2-CA + NB (50 % o f NB)
8.7
0.01
2-CA + NB (75 % of NB)
9.4
0.01
NB
8.3
0.01
TEMPERATURE = 50 °C
2-CA
4.9
0.10
2-CA + NB (25 % o f NB)
5.7
0.02
2-CA + NB (50% o f NB)
8.0
0.01
2-CA + NB (75% of NB)
8.8
0.00
NB
7.7
0.00
83
Table 4.4 (1)- Thermodynamical parameters of AN, BN and their mixtures in benzene
solution.
Molecule
Temp.
af 6
ah 6
ASe
K
kCal/mol
kCal/mol
Cal/mo 1-degree
293
1.91
0.10
-6.20
303
1.97
-6.18
313
2.04
-6.22
320
2.08
-6.20
AN + BN
293
2.27
(25% of BN)
303
2.28
-3.59
313
2.33
-3.63
320
2.38
-3.69
AN + BN
293
2.36
(50% of BN)
303
2.44
-5.39
313
2.48
-5.33
320
2.52
-5.33
AN + BN
293
2.49
(75 % of BN)
303
2.55
-5.85
313
2.61
-5.86
320
2.60
-5.69
Benzonitrile
293
2.54
(BN)
303
2.57
-5.76
313
2.64
-5.78
320
2.68
-5.79
Aniline (AN)
1.20
0.81
0.77
0.83
84
-3.68
-5.29
-5.85
-5.83
Table 4.4 (2)- Thermodynamical parameters o f 2-CA, NB and their mixtures in benzene
solution.
Molecule
Temp.
AFe
AHe
A Se
K
kCal/mol
kCal/mol
Cal/mol-degree
2-Chloroaniline
293
2.13
1.13
-3.42
(2-CA)
303
2.19
-3.50
313
2.19
-3.39
323
2.24
-3.44
2-CA + NB
293
2.36
(25 % o f NB)
303
2.39
-0.34
313
2.34
-0.17
323
2.34
-0.16
2-CA + NB
293
2.45
(50 % of NB)
303
2.45
-2.62
313
2.51
-2.74
323
2.55
-2.78
2-CA + NB
293
2.48
(75 % o f NB)
303
2.51
-4.59
314
2.57
-4.63
323
2.62
•
-4.64
Nitrobenzene
293
2.44
1.61
-2.83
(NB)
303
2.42
-2.67
313
2.48
-2.78
323
2.53
-2.85
2.29
1.66
1.12
85
-0.25
-2.88
-4.64
The relaxation time o f benzonitrile at 30 °C is 11.4 ps which is comparable with 12.8 ps
observed at the same temperature and in the same solvent by Madan l7.
Aniline, being a simple amine has been investigated by many workers. Schneider 30
reported 5.4 ps value o f relaxation time for aniline in benzene solution at 20 °C. Tucker
and W alker31 found 5.1 ps and 0.07 values o f relaxation time and distribution parameter
respectively for this molecule in cyclohexane at 25 °C. Grubb and Smyth 32 found 4.3 ps
and 0.13 values o f relaxation time and distribution parameter respectively for aniline in
benzene solution at 20 °C. Prakash and Rai 20 studied relaxation behaviour o f aniline at
different temperatures and reported 4.5 ps value o f relaxation time in benzene at 35 cC.
The distribution parameter obtained by them was 0.10. Our value o f relaxation time for
aniline 4.2 ps at 30 °C and 0.11 value o f distribution parameter at the same temperature
and in the same solvent is consistent with these results. The finite value o f distribution
parameter for aniline and shorter relaxation time o f it as compered to chlorobenzene (7.6
p s 23 at 30 °C), a rigid molecule o f similar size o f aniline suggest that in aniline appart
from over all rotation there is intramolecular rotation i. e. rotation o f -N H 2 group.
The dielectric data o f polar mixtures were analyzed in a similar manner as for single
component systems. The value o f most probable relaxation time and distribution
parameter for mixtures o f aniline + benzonitrile at different temperatures is also given in
Table-4.3 (1). It is evident from the Table that the value o f distribution parameter for all
the three mixtures investigated is zero at all temperatures, indicating single relaxation
process in the mixtures. This result finds justification from the measurements o f
Schallamach 4 where a single relaxation time is observed in binary liquid mixture
consisting o f non-associating components. Prakash and Rai 20 studied the dielectric
relaxation o f the mixture o f aniline + nitrobenzene in benzene solution at different
temperatures and found similar results.
The values o f relaxation time o f the mixtures increases with the increase o f concentration
o f benzonitrile in the mixture (Table-4.3 (1)), this is may be due to the fact that relaxation
time o f benzonitrile is higher than the relaxation time o f aniline, further, the increase is
non-linear, a plot o f relaxation time o f mixtures against the concentration o f benzonitrile
in the mixtures at different temperatures is shown in the Figure-4.1. The non-linear
86
variations o f relaxation time o f mixtures with benzonitrile concentration in mixture
indicate the complex formation or inter-association in this mixture. Since benzonitrile and
aniline both act as non-associated molecules in dilute benzene solution, the possibility o f
hydrogen bonding is rare, this behavior probably due to formation o f charge transfer
complexes in these mixtures.
•
System II: 2-Choloroaniline, Nitrobenzene and Their Mixtures:
From the Table-4.3 (2) it can be seen that the value o f distribution parameter for
nitrobenzene is near zero or zero at different temperatures. A very small value o f
distribution parameter of nitrobenzene suggests a simple Debye type relaxation
mechanism in this molecule. Hassell and Walker 27 found zero value o f distribution
parameter for nitrobenzene in p-xylene at 60 °C and shown that the dielectric absorption
in this molecule is characterized by single relaxation time 9.0 ps. Prakash R a i20 studied
nitrobenzene over a range of temperature in benzene solution and observed zero value of
distribution parameter at all temperatures. The literature values o f relaxation time
obtained by different workers for dilute solution o f nitrobenzene are 11.5 ps at 19 °C
(Whiffen and Thompson 33),10.3 ps at 25 °C (Cumper et al 34),12.3 ps at 28 °C
(Krishna 35), 11.5 ps at 20 °C (Madan36) and 12.0 at 35 °C (Prakash and R a i20). Value o f
relaxation time obtained by us in the present investigation is 10.8 ps at 20 °C, which
seems to be in reasonable agreement with these determinations.
The observed relaxation time for 2-chloroaniline, 6.0 ps at 30 °C agrees well with
reported values 6.6 ps by Srivastava and Vij 37 at the same temperature and in the same
solvent. The non-zero value o f distribution parameter for this molecule indicates more
than one relaxation processes in this system. Liquid 2- and 3- chloroanilines have been
studied by Bhattacharya 38 at a wave length o f 3.18 cm. From the existence o f a loss
maxima at 30 °C in both cases he inferred that the amino group is free to rotate and the
presence o f a chlorine group does not hinder its rotations in any way. Value o f
distribution parameter for aniline (Table-4.3 (1)) and 2-chloroaniline (Table-4.3 (2)) are
o f the same order. This result also suggests that the substitution o f chloro- group on ortho
position does not hinder the rotation of-bfflt group.
87
Relaxation Time in ps
% Concentration of BN in AN + BN mixture
Figure 4.1- Relaxation time (to) in benzene solution as a function o f percentage
R elaxation Tim e in pi
concentration o f BN in AN + BN mixture at different temperatures.
0
25
50
75
100
% Concentration o f NB in 2-C A + NB mixture
Figure 4.2- Relaxation time (to) in benzene solution as a function o f percentage
concentration o f NB in 2-CA + NB mixture at different temperatures.
88
The dielectric data o f polar mixtures were analyzed in a similar manner as for single
component systems. The value o f most probable relaxation time and distribution
parameter for mixtures o f 2-CA + NB at different temperatures is also given in the Table4.3 (2). A plot o f variation in relaxation time with concentration o f NB in the mixture at
different temperatures is shown in Figure-4.2. The plots are non-linear. This indicates a
solute-solute or solute-solvent type o f complex formation in the mixtures. Furthermore,
value o f relaxation time o f the mixtures at 50 % and 75% concentration o f NB in the
mixture is larger than that o f the individual components. This suggests a stronger
interaction between the constituent molecules o f the mixture at this concentration. It
seems that in the mixture of 2-CA and NB, NB acts as a 7t-acceptor and 2-CA as electron
donor which makes the possibility o f complex formation feasible by donating electrons
from 2-CA to NB.
Thermodynamical Parameters:
The In (toT) aginst (1/T) plots for the.mixtures as well as the individual component
exhibit linear relationships in both the systems showing that the decay o f relaxation time
with temperature is exponential. Typical plots for aniline, benzonitrile, 1:1 composition o f
mixture o f AN + BN. 2-chloroaniline, nitrobenzene and 1:1 composition o f mixture of
2-CA + NB are shown in Figure-4.3 to 4.8. These relationships therefore can be
represented by the rate process equations39 for dielectric relaxation process. The various
thermodynamical parameters viz., the molar free energy o f activation (AF€), the molar
enthalpy o f activation (AHe) and the molar entropy o f activation (ASe) for the dielectric
relaxation
processes
can
be
obtained
using
rate
process
equations.
These
thermodynamical parameters for both the systems are presented in Table-4.4 (1) and
4.4 (2) respectively. From the Tables-4.4 (1) and 4.4 (2) it can be seen that the values o f
activation energies are small, but larger than corresponding enthalpies o f activation and
consequently the entropy o f activation are negative. According to Branin and Smyth 40,
negative entropy o f activation indicates that there are fewer configurations possible in the
activated state and for these configurations the activated state is more ordered than the
normal state.
89
Figure 4.3 - Plot o f In (t0T)
vs
1/T for relaxation process o f aniline.
Figure 4.4 - Plot o f In (t0T) vs 1/T for relaxation process o f benzonitrile.
Figure 4.5 - Plot o f In (x0T) vs 1/T for relaxation process of 1:1
composition of mixture o f AN + BN.
90
Figure 4.6 - Plot o f In (x0T) vs 1/T for relaxation process o f 2-CA.
Figure 4.7 - Plot of In (x0T) vs 1/T for relaxation process o f nitrobenzene.
Figure 4.8 - Plot of In (t0T) vs 1/T for relaxation process o f 1:1
composition of mixture o f 2-CA + NB
91
R eferences :
1. Fisher, E. and Frank, F. C., Phy. Z , 40 (1939) 345.
2. Higasi, K. and Smyth, C. P., J. Am. Chem. Soc. (USA), 82 (1960) 4759.
3. Vaughan, W. E. and Smyth, C. P.,J. Phys. Chem. (USA), 65 (1961) 98.
4. Schallamach, A., Trans. Faraday Soc. A (GB), 42 (1946) 180.
5. Hill, N. E., Vaughan, W. E., Price, A. H. and Davis, M,, Dielectric Properties and
Molecular Behaviour, (Von Nostrand-Reinhold, London), (1969).
6. Denney, D. J. and Ring, R. W., J. Chem. Phys., 23 (1955) 1767.
7. Denney, D. J., J. Chem. Phys., 30 (1959) 1019.
8. Denney, D. J. and Ring, R. W., J. Chem. Phys., 44 (1966) 4621.
9. Me Dufffie (Jr.), G.E., Lamacchia, J.T. and Conord, A. E., J. Chem. Phys., 39 (1963)
1878.
10. Kono, R., Litoviz, T. A. and McDuffie (Jr.), G. E., J. Chem. Phys., 45 (1966) 1790.
11. Forest, E. and Smyth, C. P.,J. Phys. Chem., 69 (1965) 1302.
12. Garg, S. K. and Kabada, P. K., J. Phys. Chem., 69 (1965) 674.
13. Kilp, H., Garg, S. K. and Smyth, C. P., J. Chem. Phys., 45 (1966) 2799.
14. Madan, M. P., J. Mol. Liq., 25 (1983) 25.
15. Madan, M. P., J. Mol. Liq., 29 (1984) 161.
16. Madan, M. P., J. Mol. Liq., 33 (1987) 203.
17. Madan, M. P., Can. J. Phys., 65 (1987) 1573.
18. Srivastava, S. C. and Sinha, M. S., Indian J. Phys., 56 B (1982) 226.19. Hanna, F.F., Ab del-Nour, K. N. and Ghonneim, A. M., Can. J. Phys., 64 (1986) 1534.
20. Prakash, J. and Rai, B., Indian J. Pure andAppl. Phys., 24 (1986) 187.
21. Gandhi, J. M. and Sharma, G. L., J. Mol. Liqs., 38 (1988) 23.
22. Sharma, G. L. and Gandhi, J. M., J. Mol. Liqs., 44 (1989) 17.
23. Vashisth, V. M., PhD. Thesis, (Gujarat University, Ahmedabad, India), (1990).
24. Singh, P. J. and Sharma, K. S., Indian J. Pure andAppl. Phys., 34 (1996) 1.
25. Abd-El-Messieh, S. L., Indian J. Phys., 70B(2) (1996) 119.
26. Higasi, K., Bull. Chem. Soc.(Jpn.), 39 (1966) 2157.
27. Hassel, W. F. and Walker, S., Trans. Faraday Soc (Jpn.), 62 (1966) 2695.
28. Madan, M. P., Z. Phys. Chem. Neue Folge, 86 (1973) 274.
92
.
29. Srivastava, G. P., Mathur, P. C. and Tripathi, K. N., Indian J. Pure and Appl Phys., 9
(1971) 364.
30. Schneider, J., J. Chem. Phys. (USA), 32 (1960) 665.
31. Tucker, S. W. and Walker, S., Can. J. Chem., 47 (1969) 681.
32. Grubb, E. L. and Smyth, C. P., J. Am. Chem. Soc. (USA), 83 (1961) 4879.
33. Whiffen, D. H. and Thompson, H. W., Trans. Faraday Soc.A, 42 (1946) 114.
34. Cumper, C. W. N., Meluikoff, A., Rossiter, R. F., Trans. Faraday Soc.,65 (1969)
2892.
35. Krishna, K. V. G.,Trans. Faraday Soc., 53 (1957) 767.
36. Madan, M. P., Can. J. Phys., 51 (1973) 1815.
37. Srivastava, K. K. and Vij, J. K., Bull. Chem. Soc. (Jpn.), 43 (1970) 2307.
38. Bhattacharya, T. J., Indian J. Phys., 36 (1962) 533.
39. Glasstone, S., Laidler, K. and Erying, H., Theory o f Rate Processes ( Me Graw Hill
Book Co Inc, New York) (1941).
40. Branin, F. H. ( Jr.) and Smyth, C. P., J Chem. Phys., 20 (1952) 1121.
93
CHAPTER-V
DIELECTRIC DISPERSION AND RELAXATION MECHANISM OF
SOME POLAR MOLECULES AND THEIR BINARY MIXTURES IN
BENZENE SOLUTIONS AT MICROWAVE FREQUENCIES
5.1 Introduction :
Dielectric relaxation of mixtures o f anilines with non-associated molecules studied at
single microwave frequency in dilute solutions o f benzene at different temperatures
presented in the previous Chapter indicated that while the solute-solute and solute-solvent
interaction was observed in both the mixtures aniline (AN) + benzonitrile (BN) and 2chloroaniline (2-CA) + nitrobenzene (NB) the relaxation behaviour o f both the systems
is different, the mixture of AN + NB shown zero value of distribution parameter, the
distribution o f relaxation times is observed in the system 2-CA + NB, where, the
distribution parameter is finite. Similar results were obtained when dielectric
measurements were conducted at different microwave frequencies 1,z. Prakash and R a i3
studied mixtures of aniline + nitrobenzene at microwave frequencies and suggested that
the relaxation time of the mixture is influenced by the presence o f component which have
larger value of relaxation time, they obtained zero value of distribution parameter for
these mixtures at different concentration and at different temperatures. Madhurima et a lA
studied dielectric behaviour o f mixtures o f ketones and nitriles at three different
microwave frequencies (5.70,9.70,32.97 GHz) in pure state as well as in dilute solutions
o f benzene. The relaxation behavior o f these mixtures in pure state and in dilute solutions
was different. The mixtures o f pure liquids had shown Debye type o f behaviour. The
complex plane plots of a” vs a’ in non-polar solvent for these mixtures were Cole-Cole
arcs, the finite value of distribution parameter a indicated more than one relaxation
processes. Saad et a l 5 measured complex permittivity o f mixtures o f diol/diol/alcohol in
three non-polar solvents at a wide range o f microwave frequencies and interpreted their
dielectric spectra in three Debye terms.
94
Recently Chitra et a l6 studied dielectric properties o f hydrogen bonded binary system o f
non-associated polar liquid methyl benzoate (ester) and polar liquid aniline in both pure
and equimolar binary mixtures o f methyl benzoate and aniline in dilute solutions o f
benzene at different microwave frequencies. They found that relaxation behavior o f the
mixtures can be presented by Cole-Cole arcs. The relaxation time o f the mixture was
between the values o f the relaxation times o f the components o f the mixture. With a view
to gain more information in this area dielectric measurements on pyridine,
chlorobenzene,
benzophenone,
4-fluoroaniline
and
mixtures
of
pyridine
+
4-fluoroaniline, chlorobenzene + 4-fluoroaniline and benzophenone + 4-fluoroaniline are
carried out at three different microwave frequencies in benzene solution at room
temperature and results are presented in this Chapter.
5.2 E xperimental :
Pyridine, AR grade (Sd Finechem Co.Ltd., India), chlorobenzene, AR grade (Sisco
Research Lab, India), benzophenone, puriss for synthesis grade (Spectrochem Pvt. Ltd.,
India) and 4-fluoroaniline, synthesis grade (Merck, Germany) were used without further
purification. Benzene AR grade (Qualigens , India) was used after fractional distillation.
Binary mixtures o f pyridine + 4-fluoroaniline, chlorobenzene + 4-fluoroaniline and
benzophenone + 4-fluoroaniline were prepared by taking polar components in equal
mole. These mixtures were taken as solute and added to non-polar solvent. Five dilute
solutions o f pyridine, chlorobenzene, benzophenone, 4-fluoroaniline and the mixtures
were prepared by using benzene as non-polar solvent.
The dielectric permittivity ( e 5) and dielectric loss ( e ”) at three different microwave
frequencies 7.22, 9.1, 19.62 GHz were determined for each polar molecules and their
mixtures in benzene solutions. The static permittivity So at frequency 455 KHz and
permittivity at optical frequency e » were also measured. All the measurements were
carried out at 30°C and the temperature was controlled thermostatically to within +0.5°C.
The experimental method adopted for the measurement o f so, e® and, e ’ and e ” at
95
in wt. fr
eo
2.285
2.364
2.437
2.505
2.570
in wt. fr
0.0091
0.0182
0.0302
0.0370
0.0475
0.0475
0.0370
0.0302
0.0182
0.0091
Cone,
2.602 0.045 0.0477
2.551 0.038 0.0373
2.497 0.030 0.0256
2.403 0.021 0.0153
96
2.622 0.079 0.0658
2.549 0.059 0.0506
2.462 0.038 0.0386
2.396 0.024 0.0255
2.322 0.083 0.0137
in wt. fr.
in wt.fr.
2.667
2.587
2.511
2.418
2.335
19.62GHz
Cone
9.1 GHz
Cone,
2.344 0.009 0.0044
7.22 GHz
Cone,
455 KHz
Table 5.1 (1)- Values of €o, e ’, e ” and e® o f solutions o f pyridine in benzene at different frequencies at 30 °C.
0.159 0.0475
0.120 0.0370
0.090 0.0302
0.073 0.0182
0.046 0.0091
in wt. fr.
Cone,
Optical
2.2440
2.2434
2.2425
2.2416
2.2410
in wt. fr
e0
2.240
2.259
2.286
2.307
2.336
in wt. fr
0.0090
0.0183
0.0281
0.0386
0.0493
0.0493
0.0386
0.0281
0.0183
0.0090
Cone,
2.392 0.033 0.0500
2.351 0.027 0.0365
2.331 0.023 0.0281
2.308 0.013 0.0185
97
2.389 0.042 0.0500
2.358 0.032 0.0364
2.350 0.022 0.0275
2.296 0.029 0.0177
2.348
2.329
2.306
2.282
2.263
19.62 GHz
in wt. fr.
Cone
2.293 0.010 0.0092
9.1 GHz
inwt.fr.
Cone.
2.297 0.008 0.0133
7.22 GHz
Cone,
455 KHz
Optical
in wt. fr.
Cone,
0.065 0.0493
0.059 0.0386
0.048 0.0281
0.046 0.0183
0.033 0.0090
Table 5.1 (2)- Values o f eo, e ’, e ” and €<» off solutions o f chlorobenzene in benzene at different frequencies at 30 °C.
2.2291
2.2276
2.2255
2.2245
2.2234
8
UJ
V©
cco
ci
©
c00
co
CM
CM
co
©
CO
CM
©
c©
CO
ci
00
©
co
©
o ©
oo ©
VO
O ©
CD
O
©
CM
©
©
o
©
it
©
©
CO
4—4
©
CO
ci
CN
00
CO
<N
ed
O
*3
ft
o
Table 5.1 (3)- Values o f eo, e ’,e ” and e„ off solutions of benzophenone in benzene at different frequencies at 30 °C.
d
C
o
O
4$
■4-J
>
.s
X
00
cs
O
£
UJ
s
o
o
o
*UJ
ON
t"
CM
ci
Cn
On
cn
CN
in
CM
CO
CM
N
o
CM
O
©
4—4
m
o
00
00
©
oo
*n
cn
CN
o
cm
VO
©
*-<
.—4
<n
T—4 CN co
o o o
o o ©
co
CM
CM MT>
o o ©
© o ©
OO
CN CO
4
—4 *n
©
co m CO
ci cn CM
f— t
o
o
u
±4
C
.s
m
i n
£
UJ
«s
ID
N
X
o
r—
co ©
in
crt ©
o o
© o
it
C*M4
4—4 4
© ©
CM ©
©
it 't
ci
cm '
s
<
o<
d
a
o
O
O
©
©
CM
©
©
00
<N
co
CM*
4—4
co
oCM
©
©
©
©
m
Cco
CM
cm '
.0
It
©
©
©
©
©
00
4—4
o
©
in .-“4
CM CO
© ©
o ©
CM
cCO
©
o
o
u>
CM
■n
rjci
©
CM
in
CM
CO
©
MO
CM
in
c~
©
CM
©
"MC;
ci
r—4 r t
—=1 CO
CN
© o
© ©
rt>n
co
©
©
C
<O
n
it
o
©
©
©
©
©
<fcj
*-*
¥
.2
£
UJ
rv
UJ
N
X
1— *
— 44
4— 4
't
>n
CO
©
©
VO
©
©
©
CO
©
CO
in
it
©
©
00
fc>
©
©
©
©
©
©
oo
©
o ©
co ©
m ©
it it
CM ci
o
cm
CM
K
d
a
o
u
©
in
■"t
d
a
o
O
tfc*
-H
5
4a.
•g
.0
1— 4
4— 4
2.386
2.409
2.485
2.570
2.616
0.0075
0.0182
0.0268
0.0356
0.0444
0.0444
0.0356
0.0268
0.0182
2.562 0.080 0.0444
2.484 0.062 0.0356
2.456 0.048 0.0268
2.396 0.029 0.0182
2.350 0.014 0.0075
in wt.fr.
in wt. fr
GO
in wt. fr
0.0075
Cone,
99
2.556 0.122 0.0605
2.513 0.092 0.0490
2.438 0.073 0.0333
2.398 0.052 0.0257
2.533
2.482
2.439
2.378
2.316
19.62 GHz
in wt. fr.
Cone
2.354 0.030 0.0126
9.1 GHz
Cone,
7.22 GHz
Cone,
455 KHz
Optical
in wt. fr.
Cone,
0.143 0.0444
0.121 0.0356
0.074 0.0268
0.059 0.0182
0.027 0.0075
Table 5.1 (4)- Values o f eo, e ’, e ” and e«>of solutions o f 4-fluoroaniline in benzene at different frequencies at 30 °C.
2.2386
2.2374
2.2356
2.2350
2.2335
in wt. fr
0.0103
2.305
2.362
2.425
2.523
2.574
in wt. fr
0.0103
0.0199
0.0298
0.0393
0.0467
0.0467
0.0393
0.0298
0.0199
Cone,
2.624 0.093 0.0352
2.578 0.074 0.0296
2.478 0.049 0.0222
2.442 0.033 0.0160
Optical
in wt. fr.
0.063 0.0298
0.077 0.0393
2.351
2.381
2.411
2.388 0.055 0.0222
2.443 0.069 0.0296
2.488 0.085 0.0352
0.096 0.0467
0.052 0.0199
2.329
0.039 0.0103
e”
2.347 0.028 0.0160
inw t.fr.
Cone.
2.306
e”
Cone
19.62 GHz
2.330 0.020 0.0118
e’
9.1 GHz
inwt.fr.
Cone.
2.378 0.016 0.0118
7.22 GHz
Cone,
455 KHz
2.2500
2.2485
2.2470
2.2455
2.2440
Table 5.1 (5)- Values o f eo, e ’,e ” and e« o f solutions o f mixture o f pyridine + 4-fluoroaniline in benzene at different frequencies at 30 °C.
001
Table 5.1(6)-Values of Go, g ’, g ” and e ^ o f solutions o f mixture o f chlorobenzene + 4-fluoroaniline in benzene at different frequencies at 30 °C.
o oo m
nr NO
m
On ON ON
rn rn rn
<N (N (N (N
o
o
8
W
o
m
ON
rON
m
(N
cd
o
Q*
o
d
o %
c
O
V .s
W
r.
UJ
o
c
o
U
<b
*
c
£
01
C
w
<b
cj
C
o
U
<<
.2
UJ
UJ
cj
c
o
U
cb
•4—»
>
.2
OO
N
•
'
i
- O
o
y— 1 »— <
o o
o
d
N
t" O
nr
(N o
O
© o
ON
OC NO
(N m nr
© q q
©
©
©
00
OO o
—1
q «
©
©
o
o
o
nf
»— <
© <N NO ON nT
<N rn rn rn
c4 CN (N (N <N
o
o
NO
so
y— *
cn
ON
00
(N
©
o
00
"3o
o
ON m
oo oo
rn nt
<N
(N
<N
(N
ON
ON
IT')
n
"3- O0
o *0
—«
o O
o
d
m
©
<N m
O o
d
o
IT )
NO
m
q
o
lO
nT
q
©
r^
o
o
©
©
m
m
nr
o
(N
00 00 NO IT)
O
*— i •— 1 (N m nr
o o o q o
d
o © o o
</•> NO ON NO (N
» < (N m
NO
o o o o
©
©
©
©
o ©
ON
00 moo ON
<N
«— <
<N
T
ro rn rn nf to
<N <N (N <N CN
VO
Os
©
©
d
00 ON
oo
CM
o O
o o
w—t
<N O
O n ON
m nf
q o
o ©
oc rnn (
oo
N NO
(N rn rn nj- nr
<N <N <N (N <N
SO
o
W
d
so
cj
c
O
u
d
>
_c
as
©
©
©
oo O n
oc
o (N
o
o ©
(N o
ON ON
m nr
q q
o o
Table 5.1(7)~VaIues o f eo, e ’, e ” and e«, o f solutions o f mixture o f benzophenone + 4-fluoroaniline in benzene at different frequencies at 30 °C.
co Os ©
SO t"
Os ©
co C O it
CO
cm' cm' cm' cm'
in
CM
©
if
cm'
%r*
.a
<n
OS
o
o
©
_
CM
co
Os
8
tv
”3
o-t
•f
H,
O
cti
d
fi
o
U
OS
©
CM
o
©
t-1
VO
CM
©
©
l>if
co
©
©
CM
«n
it
o
©
CM
o
©
o'
<»
©
©
ir—<
©
ui
if
<n
©
©
00
o
©
“uj
rOs
CM
CM
Os
CM
co
CM
rH
m
co
CM
«n
Os
o
©
©
CM
©
©
fi
so
CM
©
©
<n
so
©
o
CO
N
ffi
o
CM
SO
Os
*—f
ifcj
o
fi
o
o
Os
©
©
co
CM
T-^
r—»
it
CM
t
©
©
OO
o
It
©
©
00
CO
•a
tm
o
T\
o
"uj
o
<n
o
©
in
r—f
co
cm'
©
oo
co
CM
©
If
CM
It
CM
o
oo
it
CM
m
OS
o
o
©
©
©
CM
O
©
C'- t>
so if
CM CO
©
©
©
©
OO
©
It
©
©
Os
CM
O
Os
if
©
©
VO
©
60
©
t—«
©
UJ
CO
©
00
o
©
_
CO
©
CM
%—t
©
tS
O
©
d
d
C
£
u
.3
o
o* • ©
©
©
©
in
so
co
CM
00
©
it
s©
it
it
CO
©
It
CO
it
wo
cm'
cm'
cm'
CM
as
It.
T—<
©
©
It
©
©
©'
©
in
©
©'
CM
CM
.a
Mf
Os
O
©
o
Os
if
CO
CO
CO
©
©
it
if
VO
it
\o
o
UJ
CM
CM*
CM
CM
<N
S'
os
OS
it
©
©
©
m
*3-
©
©
<n
o
©
UJ
..
UJ
X
o
<N
CM
t>
43
d
fi
5s
O
U
o
IT)
ID
it
co
•n
it
©
<N
43
d
£3
•g
£
O
O
.a
o
o
it
CM
©
©
co
<N
O
O
different microwave frequencies have been described in Chapter-Ill. The measured values
o f Go,
g ’, g ”
and
g «> are
given in the Table-5.1. The values o f most probable relaxation
time (to) and distribution parameter (a) o f the polar molecules and their mixtures were
calculated from measured data using Cole-Cole method o f analysis (described in
Chapter-Ill).
5.3 Results and D iscussion :
The slopes ao, a’, a”, a» determined by plotting the measured values o f Go, g ’, g ” and
g «o
against weight fraction of solute in solution for single component and their binary
mixtures at different frequencies are listed in Table 5.2. a” has been plotted against a’ on
complex plane to evaluate most probable relaxation time (to). Fairly smooth curves could
be drawn passing through the experimental points. For pyridine, chlorobenzene and
benzophenone a Debye type plot with center on the x-axis is observed (Figure-5.1),
whereas for 4-fluoroaniline and for mixtures a Cole-Cole type o f plot with center below
x-axis is observed (Figure-5.2). The most probable relaxation time (x0) and distribution
parameter (a) for pyridine, chlorobenzene and benzophenone are presented in Table 5.3.
The values o f relaxation time increase with the size o f molecule and are in close
agreement with literature values. The zero values o f distribution parameter (a) for these
molecules suggest a simple Debye type relaxation mechanism for these systems, this is
usual behavior o f rigid polar molecules. In comparison to pyridine, chlorobenzene and
benzophenone less data is available in literature on dielectric measurement o f 4fluoroaniline. Dhar et al 14 studied 4-fluoroaniline at different temperatures and 3 cm
wavelength in benzene solution, the value o f relaxation time for this compound reported
by them is 5.1 ps at 30 °C. The values o f relaxation time 5.3 ps (Table-5.3) for 4fluoroaniline in the same solvent and at the same temperature in the present work is in
close agreement with their value of relaxation time. The value o f distribution parameter
(a) for 4-fluoroaniline (Table 5.3) is finite (0.20). Srivastava and Vij 15 studied 2-chloro,
3-chloro, and 4-chloroanilines in benzene solution, they found finite distribution
parameter for these molecules and further, the distribution parameter shown an increasing
trend from 2- to 3- to 4- isomers. The value o f distribution parameter for 4-chloroaniline
103
Table 5.2- Values o f slopes ao, a’,a” and a* of single component as well as their
binary mixtures in benzene solution at different frequencies at 30° C.
Frequency
455
7.22 GHz
9.1 GHz
19.61 GHz
Optical
KHz
Substance
ao
a’
a”
a’
a”
a’
a”
&CO
Pyridine
6.87
6.67
1.10
6.50
1.50
5.85
2.40
0.07
Chlorobenzene
2.43
2.23
0.63
2.10
0.74
1.50
1.10
0.15
Benzophenone
5.87
4.50
2.36
3.58
2.70
1.70
2.37
0.35
4-fluoroaniline
6.59
5.83
1.68
5.50
2.05
4.54
2.48
0.15
7.55
6.75
2.09
6.25
2.38
4.50
3.08
0.19
4.92
4.58
1.14
4.25
1.50
3.28
2.10
0.19
6.25
5.40
2.00
5.10
2.30
3.63
2.70
0.29
Pyridine +
4-fluoroaniline
Chlorobenzene +
4-fluoroaniline
Benzophenone +
4-fluoroaniline
104
Table 5.3-Values of distribution parameter (a), relaxation time (to) and free
energy of activation (AFe) of the single component as well as their binary
mixtures in benzene solution at 30°C.
Substance
Distribution
Relaxation
Free energy
parameter
time (
of activation time in ps
(a)
inps
to)
(AFe)
Relaxation
(Lit. values)
kCal/Mol
Pyridine
0.00
3.7
1.90
3.8 (ref. 7)
3.5 (ref.8)
3.1 (ref.9)
3.2 (ref. 10)
Chlorobenzene
0.00
7.5
2.32
7.8 (ref. 11)
7.7(ref. 10)
8.3 (ref. 12)
Benzophenone
0.00
14.1
2.70
16.0 (ref. 13)
17.4 at 20°C
(ref. 12)
4-fluoroaniline
0.20
5.3
2.11
5.1 (ref. 14)
0.07
6.6
2.25
—
0.03
6.0
2.19
—
0.10
7.8
2.34
Pyridine +
4-fluoroaniline
Chlorobenzene +
4-fluoroaniline
Benzophenone +
4-fluoroaniline
105
—
Figure-5.1 Plots of a" versus a ’ for pyridine (0), chlorobenzene (A) and
benzophenone (0 ) in benzene solution.
Figure-5.2 Plots o f a versus a for 4-fluoroaniline (o), mixtures o f pyridine + 4fluoroaniline (_), chlorobenzene — 4-fluoroaniline (A) and foenzophenone + 4fluoroaniline (x) in benzene solution
106
determined by them at 30°C was 0.25, thus the value o f distribution parameter (a) for
4-fluoroaniline (0.20) in present work appears reasonable. This finite value o f distribution
parameter (a ) for 4-fluoroaniline suggest that there is more than one relaxation processes
in this system. As suggested by several workers, for aniline and substituted anilines this
may be due to rotation o f -N H 2 group around its bond with the benzene ring. This has
also been reflected in the value o f relaxation time o f 4-fluoroaniline. The relaxation time
o f fluorobenzene found by us 16 in our previous studies in benzene solution at 30 °C is 5.7
ps, whereas that of 4-fluoroaniline in the same solvent and at the same temperature is 5.3
ps. Although the molecular size o f 4-fluoroaniline is greater than that o f fluorobenzene
still its relaxation time is less which also suggest that there is an intramolecular rotation
in 4-fluoroaniline. Therefore, the dielectric data was analyzed in terms o f two relaxation
times Ti and T2 , where xi and t 2 are relaxation times corresponding to overall and group
rotations respectively. In terms o f a^ a’, a” and a», the Budo’s 17 equation can be written
for two relaxation processes as
...5,
a0 a"
1+co Tj 1+co Tj
_ CjOt, + G jCQXj
a0 - a K l+co2xf
^
\ + & 2x 2
where C, + C2 =1, Ci and C2 are relative weights contributed by each processes to the
dielectric absorption as whole, ti, x2, Cj and C2 for 4-fluoroaniline was determined using
the method suggested by Bhattacharya et a l 18. The evaluated values o f these parameters
are given in Table-5.4. The value o f relaxation time ( t2) is 2.5 ps for 4-fluoroaniline
which may be attributed to rotation o f -NH2 group and is fairly in agreement with the
literature values 19,20.
The values o f relaxation times of the mixtures o f 4-fluoroaniline with pyridine,
chlorobenzene and benzophenone are also presented in Table-5.3. It is evident from the
Table-5.3 that for mixtures o f 4-fluoroaniline with chlorobenzene and benzophenone the
relaxation times o f mixtures are nearly average o f the individual value o f relaxation time
107
Table 5.4-Values o f resolved relaxation times and their relative weight factors for
4-fluoroaniline and its mixtures with pyridine, chlorobenzene and benzophenone
in benzene solution at 30°C.
Substance
t i inps
r 2inps
Ci
c2
4-fluoroaniline
20.2
2.5
0.32
0.68
16.9
2.3
0.44
0.56
19.4
2.8
0.29
0.71
15.0
2.6
0.54
0.46
Pyridine +
4-fluoroaniline
Chlorobenzene+
4-fluoroaniline
Benzophenone +
4-fluoroaniline
108
o f constituent molecules. This is manifestation o f super-imposed effect o f the pair o f two
components, the wavelength of the maximum absorption o f pairs lying near to each other,
thus giving rise to a broader single relaxation peak, this is in agreement with our earlier
studies for mixtures o f rigid polar molecules21.
In the case o f mixtures o f pyridine + 4-fluoroaniline the relaxation time o f the mixture is
6.6 ps (Table-5.3) while that o f its components are 3.7 ps (pyridine) and 5.3 ps (4fluoroaniline). Thus, the value o f relaxation time o f mixture is higher than that o f its
components. This indicate that interactive association is taking place between pyridine and
4-fluoroaniline molecules through N-H—N type o f hydrogen bond. Similar results were
obtained for the mixture o f pyridine + pyrole and pyridine + indole in dilute solutions by
Gupta etal1.
The value o f distribution parameter (a) for all the three mixtures investigated is finite,
but, less than the distribution parameter o f 4-fluoroaniline, this suggests that there is more
than one relaxation processes in the mixture and further, 4-fluoroaniline retains its
identity in the mixture. It appears that presence o f rigid polar molecules in the mixture
with 4-fluoroaniline produces internal field such that the motion o f -N H 2 is slightly
restricted. The dielectric data of these mixtures is also analyzed in terms o f two relaxation
processes. The relaxation times and their contribution were determined by the method
described for 4-fluoroaniline. The evaluated values o f ii, X2 , Ci and C2 for the mixtures is
also presented in Table-5.4. It is evident from the Table-5.4 that the values o f relaxation
time for group rotation (X2 ) in all the mixtures is o f the same order found for 4fluoroaniline, which suggest that the components in the mixtures retain their identity.
Free energy o f activation (AFe) evaluated using Eyring’s equation 22 for single
component as well as that for binary mixtures is listed in Table-5.3. It can be seen that in
the mixtures o f chlorobenzene + 4-fluoroaniline and benzophenone + 4-fluoroaniline the
free energy of activation lies between those o f its components, whereas in the case of
mixture o f pyridine + 4-fluoroaniline the activation energy is higher than those for its
components, this also suggest that there is complex formation in this mixture.
109
References :
1. Srivastava, S. C. and Sinha, M. S., Indian J. Phys., 56B (1982) 226.
2. Abd-El-Messieh, S. L., Indian J. Phys., 70B(2) (1996) 119.
3. Prakash, J. and Rai, B., Indian J. Pure and Appl. Phys., 24 (1986) 187.
4. Madhurima, V., Murthy, V. R. K. and Sobhanadari, J., Indian J. Pure and Appl. Phys.,
36 (1998) 144.
5. Saad, A. L. G., Shafxk, A. H. and Hanna, F. F., Indian J. Phys, 72 B (1998) 495.
6. Chitra, M., Subramanyam, B. and Murthy, V. R. K., 39 (2001) 461.
7. Gupta, T ., Chauhan, M., Saxena, S. K. and Shukla, J. P., Adv. Mol. Rela. Inter. Proc.,
23 (1982)203.
8. Gowrikrishna, J. and Sobhanadri, J., Indian J. Pure and Appl. Phys., 22 (1984) 599.
9. Madan, M. P., Shelfoon, M. and Cameron, I., Can. J. Phys., 55 (1977) 878.
10. Hanna, F. F. and Abd-El-Nour, Z. Phys. Chem. Leipzig, 246 (1971) 168.
11. Mitra, S. C ., Misra, S. B. and Mehrotra, N. K., Indian J. Pure and Appl. Phys., 16
(1978) 604.
12. Whiffen, D. H., Trans. Faraday Soc., 46 (1950) 130.
13. Madan, M. P., Can J. Phys., 29 (1984) 161.
14. Dhar, R. L ., Sahm, N. and Saxena, M. C., Indian J. Pure and Appl. Phys.,
11 (1973) 337.
15. Srivastava, K. K. and Vij, J. K., Bull. Chem. Soc. Jpn., 43 (1970) 2307.
16. Vyas, A. D. and Vashisth, V. M ., Indian J. Pure and Appl Phys., 26 (1988)
484.
17. Budo, A., PhysikZ, 39 (1938) 706.
18. Bhattacharya, J., Hasan,A., Roy, S.B. and Kastha, G. S., J. Phy. Soc. Jpn., 28 (1970)
204.
19. Khameshara, S. M. and Sisodia, M. L., Adv. Mol. Rel. In t Proc., 21 (1981) 105.
20. Tucker, S. M. and Walker, S., Can. J. Chem., 47 (1969) 681.
21. Vyas, A. D., Vashisth, V, M., Rana, V. A. and Thaker, N. G., J. Mol. Liq.,62 (1994)
221.
22. Glasstone, S., Laidler, K. and Eyring, H., The Theory o f Rate Processes (Me Grow
Hill Book Co. Inc. New York) 584 (1941).
110
* <ML.Mt^ihn ,1,
.ft .Jw
ii^Jt*T
k,
w .R.
DIELECRIC RELAXATION IN 1-PROPANOL, BROMOANILINES
AND MIXTURES OF 1-PROPANOL WITH BROMOANALINES IN
DILUTE SOLUTIONS OF BENZENE
6.1 Introduction :
Alcohols, in particular have been subject o f frequency dependent dielectric measurements
since initial stage of relaxation spectroscopy 1,2. Their long relaxation time did allow for
informative studies already when technical development facilitated measurements only
over a limited range o f microwave frequencies. With the development o f techniques for
dielectric measurement at higher microwave frequencies, studies on dielectric properties
on alcohols in liquid state3,4 and dilute solutions o f non-polar solvent5 have been carried
out by several workers. Remarkable enough spectral shape is often close to Debye
function, with some additional contribution on the high frequency side. Crossely 5
investigated dielectric relaxation of 1-butanol and 1-decanol in some non-polar solvents
the Cole-Cole plots of these systems were unsymmetrical, they analyzed the dielectric
data in terms o f two relaxation times and found that both relaxation times (molecular and
intramolecular motions) were sensitive to the nature o f solvent and solute and their
concentrations. The dielectric relaxation measurements on aliphatic alcohols was carried
out in dilute solutions of benzene in this laboratory at a single microwave frequency6, the
plot o f tanS versus concentration showed a marked deviation in the concentration range
0.02-0.05 weight factor, the IR spectra o f these molecules 7 showed similar results.
Recently Eid et a l 4 investigated some monohydric alcohols at wide range o f microwave
frequencies and interpreted their data in terms o f three Debye type relaxation.
Dielectric properties o f mixture o f alcohols with associative polar molecules including
water have been studied by several workers 8' 14. In these systems apart from self­
association there is a possibility o f hetero association through hydrogen bonding. Less
work has been reported on mixtures o f alcohols with non-associative polar molecules in
ill
liquid 15 as well as in non-polar solvents. Dielectric measurements on mixtures of
methanol with ketones and nitriles were conducted in pure and in non-polar solvent at
different microwave frequencies by Madhurima et al 16, it was observed that their
dielectric behavior can be presented by Cole-Cole plots. Microwave absorption study at
3-cm wavelength of mixtures o f methyl alcohol with methyl acetate, methyl formate,
ethyl formate and acetone in benzene solution by Vardrajan and Rajgopal 17 indicated
solute-solute type o f interactions in these mixtures. Another class o f mixtures o f nonassociative molecules with alcohols which have gained considerable attention are
mixtures o f alcohols with amines, it is due to the fact both are extensively used in
industrial processes. The primary amine and alcohol both have proton doner and proton
acceptor groups. It is expected that there will be significant degree o f hydrogen bonding,
leading to self-association in pure state in addition to mutual association in their binaries.
Oswal and Desai 18 determined excess molar volume VE, viscosity deviation At], excess
viscosity t |E,excess Gibbs energy o f activation AG*E of viscous flow from density and
viscosity measurements for eight binary mixtures of butyl amine with ethanol, propanol,
butanol, pentanoL, hexanol, heptanol, octanol and decanols, they found strong cross­
association through O-H—N bonding between -OH and -N H 2 groups. Liszi et al 19 in
their study o f dielectric constants o f binary mixtures o f alcohols and amine indicated
possibility o f complex formation. Swain20 determined mutual correlation function gab for
mixtures o f aniline with n-propanol, n-butanol and i-butanol using dielectric constant
values measured at radio frequency, it was observed that gab < 1 and minima is near
equimolar range indicating the formation of weak OH—NH complexs. The NMR study
o f dimethyl amine in the hydrogen bonded solvent acetonitrile by Springer Jr. and Devon
21 showed that dimethyl amine forms a stronger hydrogen bond with acetonitrile than with
itself. Investigation of alcohol-amine complexion using dielectric probe by Tripathi et al
22 suggested the complex formation is due to charge redistribution and most likely
complex formation is due to linkage between N ' (proton acceptor) o f amine with H
of
alcohol (proton donor). Dielectric relaxation and structural study o f aniline-methanol
mixture using picosecond time domain spectroscopy Fattepur et al 23 found strong
interaction between solute and solvent molecules at low concentration o f methanol. It is
expected that substitution o f bromo group at ortho-, meta- and para- positions should give
some interesting results on dielectric properties o f mixtures o f alcohols with these
112
bromoanilines. Further, systematic studies on dielectric relaxation o f ortho, meta and para
chloroanilines have been reported by Srivastava and Vij 24, the dielectric data for
bromoaniline in dilute solutions is scattered. Complex permittivity o f 1-propanol,
2-bromoaniline, 3-bromoaniline, 4-bromoaniline and mixtures o f 1-propanol with these
anilines have been measured at 9.1 GHz in dilute solutions o f benzene at different
temperatures. In the following sections measured values o f dielectric permittivity along
with evaluated values o f relaxation time and distribution parameter at different
temperatures o f these molecules and their mixtures are presented. The dielectric data for
aniline (Chapter-IV) has also been included for comparison.
6.2 Experimental :
The samples o f aniline, AR grade (Merck, India) and Benzene, AR grade (Quaiigens,
India) were used after fractional distillation. 2-bromoaniline, purum grade (Fluka A. G.,
Switzerland), 3-bromoaniline, purum grade (Fluka A.G., Switzerland), 4-bromoaniline,
synthesis grade (Fluka A. G., Switzerland) and 1-propanol, AR grade (Sd- Fine Chem
Co. Ltd., India) were used without further purification.
Binary mixtures o f different compositions (3:1, 1:1 and 1:3) o f aniline + 1-propanol, 2bromoaniline + 1-propanol, 3-bromoaniline + 1-propanol and 4-bromoaniline + 1propanol were prepared by adding them by mole. These mixtures were taken as solute.
Five dilute solutions o f each o f these mixtures as well as individual molecules were
prepared using benzene as non-polar solvent.
Permittivity ( e 5) and dielectric loss ( e ”) have been measured for each polar molecules
and their mixtures in benzene solutions at microwave frequency 9.1 GHz, static
permittivity ( e 0) at frequency 455 KHz and permittivity at optical frequency were also
measured. All the measurements were made at 20, 30, 40, and 47 °C and the temperature
was controlled within ± 0.5 °C by a thermostat. The experimental method adopted for the
measurement o f €o, e \ e ” and e® have been described in Chapter-Ill. The measured
values o f e<>> e ’, e ” and e® are given in Table-6,1. The values'of most probable
113
relaxation time (to) and distribution parameter (a) o f the polar molecules and their
mixtures were calculated using Higasi’s method (described in Chapter-Ill).
6.3 Results and discussion :
The dielectric constant ( e ’) and dielectric loss ( e ”) o f aniline, 2-bromoaniline,
3-bromoaniline, 4-bromoaniline and 1-propanol have been plotted against concentration
(weight fraction), the plots are linear. From these graphs slop ao, a’, a”, and a« were found
out and are given in Table-6.2 (1). The relaxation times To and distribution parameter (a)
o f these molecules at different temperatures are presented in Table-6.3 (1).
The relaxation time o f 2-bromoaniline at 30 °C is 6.9 ps and that o f 3-bromoaniline is
13.1 ps incidentally relaxation time of 4-bromoaniline at this temperature is also 13.0 ps.
At 40 °C the relaxation times o f 2-, 3-, and 4-bromoanilines are 5.8,11.4 and 12.5 ps
respectively this indicates that substitution o f bromo group in ortho- to para- position with
respect to amino group in aniline increases relaxation time o f these molecules. Srivastava
and V ij24 studied dielectric relaxation in o-, m- and p-chloroanilines in different solvents
at 25 °C and observed a systematic increase in relaxation time with the shift o f chlorine
group from o- to m- and finally p- position with respect to amino group. They attributed
this rise in relaxation time to effective change in length o f the dipoles. The observed value
o f relaxation time o f 4-bromoaniline at 20 °C, 14.6 ps is in agreement with the reported
value o f relaxation time o f this molecule 15.4 ps by Tucker and Walker 25 at 25°C in
cyclohexane solution. The decrease in relaxation time (to) o f all anilines with temperature
is a usual behavior of polar molecule in non-polar solvent. The finite value o f distribution
parameter a (Table-6.3 (1)) for 2-, 3- and 4-bromoaniline (0.09, 0.13 and 0.21
respectively, at 30 °C) indicate that as in the case o f aniline in bromoanilines also there is
more than one relaxation processes i,e., due to overall rotation and group rotation o f
-Ntfe. There is an increase in distribution parameter when bromo group shifts from ortho-
114
Table 6.1 (1)- Values of e0) e \ s ” and eroof solutions of aniline in benzene at different
temperatures.
Cone,
455 KHz
Cone,
in wt. ff.
So
in wt. ff.
9.1 GHz
s’
s”
Cone,
Optical
in wt. ff.
GcO
TEMPERATURE = 20 °C
0.0083
2.352
0.0133
2.344 0.007
0.0083
2.2494
0.0184
2.374
0.0250
2.371 0.013
0.0184
2.2530
0.0307
2.410
0.0347
2.400 0.020
0.0307
2.2560
0.0365
2.427
0.0423
2.419 0.026
0.0365
2.2575
0.0493
2.466
0.0530
2.438 0.027
0.0493
2.2614
TEMPERATURE = 30 °C
0.0083
2.337
0.0116
2.302 0.007
0.0083
2.2290
0.0184
2.382
0.0286
2.357 0.020
0.0184
2.2320
0.0307
2.394
0.0376
2.388 0.025
0.0307
2.2350
0.0365
2.409
0.0512
2.414 0.032
0.0365
2.2380
0.0493
2.440
0.0634
2.470 0.049
0.0493
2.2410
TEMPERATURE = 40 °C
0.0083
2.317
0.0108
2.282 0.012
0.0083
2.2112
0.0184
2.333
0.0179
2.301 0.017
0.0184
2.2141
0.0307
2.369
0.0282
2.324 0.021
0.0307
2.2186
0.0365
2.382
0.0398
2.344 0.029
0.0365
2.2216
0.0493
2.412
0.0497
2.384 0.033
0.0493
2.2231
TEMPERATURE = 47 °C
0.0083
2.273
0.0108
2.242 0.006
0.0083
2.1993
0.0184
2.311
0.0179
2.268 0.009
0.0184
2.2008
0.0307
2.318
0.0282
2.295 0.014
0.0307
2.2052
0.0365
2.341
0.0398
2.337 0.019
0.0365
2.2058
0.0493
2.388
0.0497
2.359 0.022
0.0493
2.2082
115
Table 6.1 (2)- Values of eo, e ’,e ” and e ^ o f solutions of 2-bromoaniline in benzene at
different temperatures.
Cone,
in wt. ff.
455 KHz
Cone,
GO
in wt. fr.
9.1 GHz
€’
€”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE = 20 °C
0.0060
2.347
0.0092
2.322 0.008
0.0060
2.2650
0.0218
2.356
0.0193
2.335 0.016
0.0218
2.2695
0.0306
2.389
0.0262
2.362 0.024
0.0306
2.2725
0.0384
2.399
0.0382
2.376 0.028
0.0384
2.2747
0.0443
2.426
0.0450
2.387 0.033
0.0443
2.2771
TEMPERATURE = 30 °C
0.0060
2.304
0.0092
2.300 0.006
0.0060
2.2410
0.0218
2.338
0.0193
2.312 0.011
0.0218
2.2440
0.0306
2.369
0.0262
2.334 0.017
0.0306
2.2470
0.0384
2.381
0.0382
2.356 0.023
0.0384
2.2500
0.0443
2.391
0.0450
2.361 0.026
0.0443
2.2524
TEMPERATURE = 40 °C
0.0060
2.290
0.0092
2.277 0.006
0.0060
2.2261
0.0218
2.308
0.0193
2.287 0.010
0.0218
2.2290
0.0306
2.330
0.0262
2.310 0.013
0.0306
2.2314
0.0384
2.356
0.0382
2.318 0.018
0.0384
2.2326
0.0443
2.372
0.0450
2.344 0.021
0.0443
2.2350
TEMPERATURE = 47 °C
0.0060
2.262
0.0092
2.256 0.004
0.0060
2.2112
0.0218
2.278
0.0193
2.279 0.009
0.0218
2.2135
0.0306
2.309
0.0262
2.296 0.014
0.0306
2.2156
0.0384
2.312
0.0382
2.315 0.018
0.0384
2.2177
0.0443
2.330
0.0450
2.326 0.020
0.0443
2.2201
116
Table 6.1 (3)- Values of eo, e ’,e ” and e® of solutions of 3-bromoaniline in benzene at
different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
€0
in wt. fr.
9.1GHz
e’
e”
Cone,
Optical
in wt. fr.
€=oo
TEMPERATURE = 20 °C
0.0119
2.389
0.0083
2.326 0.020
0.0119
2.2530
0.0293
2.469
0.0170
2.352 0.033
0.0293
2.2554
0.0441
2.550
0.0246
2.369 0.048
0.0441
2.2584
0.0518
2.594
0.0311
2.392 0.065
0.0518
2.2605
0.0613
2.627
0.0405
2.414 0.080
0.0613
2.2626
TEMPERATURE = 30 °C
0.0119
2.377
0.0083
2.305 0.014
0.0119
2.2380
0.0293
2.443
0.0170
2.324 0.028
0.0293
2.2395
0.0441
2.515
0.0246
2.352 0.043
0.0441
2.2416
0.0518
2.546
0.0311
2.373 0.058
0.0518
2.2431
0.0613
2.595
0.0405
2.398 0.074
0.0613
2.2443
TEMPERATURE = 40 °C
0.0119
2.349
0.0083
2.289 0.010
0.0119
2.2177
0.0293
2.403
0.0170
2.318 0.025
0.0293
2.2201
0.0441
2.488
0.0246
2.350 0.043
0.0441
2.2225
0.0518
2.529
0.0311
2.356 0.050
0.0518
2.2237
0.0613
2.563
0.0405
2.386 0.066
0.0613
2.2246
TEMPERATURE = 47 °C
0.0119
2.291
0.0083
2.275 0.007
0.0119
2.2067
0.0293
2.400
0.0170
2.305 0.018
0.0293
2.2088
0.0441
2.480
0.0246
2.324 0.026
0.0441
2.2112
0.0518
2.494
0.0311
2.344 0.042
0.0518
2.2127
0.0613
2.535
0.0405
2.375 0.059
0.0613
2.2135
117
Table 6.1 (4)- Values of e 0, e ’,e ” and e® of solutions of 4-bromoaniline in benzene at
different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fr.
9.1GHz
e’
€”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE = 20 UC
0.0100
2.320
0.0099
2.318 0.023
0.0100
2.2590
0.0207
2.357
0.0192
2.361 0.049
0.0207
2.2605
0.0300
2.486
0.0303
2.386 0.070
0.0300
2.2620
0.0391
2.556
0.0400
2.432 0.100
0.0391
2.2650
0.0500
2.575
0.0500
2.481 0.133
0.0500
2.2710
TEMPERATURE = 30 °C
0.0100
2.352
0.0099
2.305 0.024
0.0100
2.2470
0.0207
2.402
0.0192
2.354 0.047
0.0207
2.2485
0.0300
2.440
0.0303
2.394 0.067
0.0300
2.2515
0.0391
2.529
0.0400
2.416 0.090
0.0391
2.2545
0.0500
2.588
0.0500
2.472 0.129
0.0500
2.2560
TEMPERATURE = 40 °C
0.0100
2.279
0.0099
2.295 0.016
0.0100
2.2290
0.0207
2.303
0.0192
2.340 0.039
0.0207
2.2320
0.0300
2.399
0.0303
2.392 0.073
0.0300
2.2350
0.0391
2.498
0.0400
2.414 0.087
0.0391
2.2365
0.0500
2.540
0.0500
2.442 0.096
0.0500
2.2386
TEMPERATURE = 47 °C
0.0100
2,221
0.0099
2.296 0.012
0.0100
2.2156
0.0207
2.360
0.0192
2.339 0.037
0.0207
2.2165
0.0300
2.439
0.0303
2.373 0.064
0.0300
2.2186
0.0391
2.486
0.0400
2.414 0.089
0.0391
2.2201
0.0500
2.508
0.0500
2.448 0.098
0.0500
2.2216
118
Table 6.1 (5)- Values of eo, e ’,e ” and e® of solutions of 1-propanol in benzene at
different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
€»
TEMPERATURE = 20 UC
0.0059
2.309
0.0053
2.342 0.004
0.0064
2.2530
0.0096
2.344
0.0119
2.359 0.010
0.0109
2.2515
0.0154
2.371
0.0213
2.406 0.019
0.0142
2.2500
0.0189
2.403
0.0276
2.430 0.039
0.0192
2.2485
0.0263
2.432
0.0370
2.442 0.055
0.0238
2.2470
TEMPERATURE = 30 °C
0.0059
2.281
0.0076
2.315 0.010
0.0064
2.2380
0.0096
2.313
0.0145
2.359 0.017
0.0109
2.2395
0.0154
2.319
0.0218
2.390 0.028
0.0142
2.2356
0.0189
2.360
0.0280
2.410 0.037
0.0192
2.2335
0.0263
2.389
0.0345
2.440 0.048
0.0238
2.2296
TEMPERATURE = 40 °C
0.0059
2.232
0.0076
2.298 0.010
0.0064
2.2231
0.0096
2.281
0.0145
2.313 0.015
0.0109
2.2201
0.0154
2.291
0.0218
2.339 0.019
0.0142
2.2171
0.0189
2.303
0.0280
2.388 0.029
0.0192
2.2147
0.0263
2.360
0.0345
2.432 0.039
0.0238
2.2135
TEMPERATURE = 47 °C
0.0054
2.273
0.0076
2.254 0.008
0.0064
2.2097
0.0123
2.293
0.0145
2.280 0.013
0.0109
2.2076
0.0154
2.295
0.0218
2.344 0.016
0.0142
2.2029
0.0177
2.311
0.0280
2.369 0.023
0.0192
2.2008
0.0212
2.324
0.0345
2.392 0.030
0.0238
2.1987
119
Table 6.1 (6)- Values of eo, e ’,e ” and e » o f solutions of 3:1 composition of mixture of
aniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fr.
9.1GHz
e’
e”
Cone,
Optical
in wt. fr.
€co
TEMPERATURE = 20 UC
0.0072
2.328
0.0090
2.337 0.005
0.0072
2.2500
0.0182
2.386
0.0185
2.353 0.008
0.0182
2.2524
0.0276
2.406
0.0265
2.392 0.017
0.0276
2.2545
0.0383
2.450
0.0350
2.404 0.026
0.0383
2.2566
0.0453
2.497
0.0422
2.444 0.033
0.0453
2.2590
TEMPERATURE = 30 °C
0.0072
2.299
0.0097
2.326 0.011
0.0072
2.2290
0.0182
2.333
0.0185
2.348 0.019
0.0182
2.2320
0.0276
2.372
0.0289
2.371 0.023
0.0276
2.2344
0.0383
2.426
0.0404
2.400 0.033
0.0383
2.2356
0.0453
2.437
0.0514
2.428 0.043
0.0453
2.2380
TEMPERATURE = 40 °C
0.0072
2.315
0.0096
.2.300 0.006
0.0072
2.2165
0.0182
2.346
0.0216
2.327 0.013
0.0182
2.2171
0.0276
2.379
0.0299
2.380 0.018
0.0276
2.2183
0.0383
2.404
0.0373
2.377 0.023
0.0383
2.2195
0.0453
2.439
0.0498
2.418 0.035
0.0453
2.2201
TEMPERATURE = 47 °C
0.0072
2.275
0.0096
2.286 0.006
0.0072
2.1948
0.0182
2.310
0.0216
2.313 0.011
0.0182
2.1963
0.0276
2.341
0.0299
2.359 0.015
0.0276
2.1978
0.0383
2.371
0.0373
2.361 0.020
0.0383
2.1987
0.0453
2.398
0.0498
2.404 0.029
0.0453
2.1993
120
Table 6.1 (7)- Values of eo, e ’,e ” and e® of solutions of 1:1 composition of mixture of
aniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. ff.
eo
in wt. ff.
9.1 GHz
e’
e”
Cone,
Optical
in wt. ff.
e®
TEMPERATURE = 20 UC
0.0058
2.320
0.0062
2.337 0.005
0.0058
2.2473
0.0121
2.356
0.0149
2.371 0.017
0.0121
2.2460
0.0230
2.396
0.0238
2.396 0.021
0.0230
2.2485
0.0286
2.439
0.0295
2.414 0.026
0.0286
2.2494
0.0348
2.472
0.0367
2.430 0.032
0.0348
2.2506
TEMPERATURE = 30 °C
0.0058
2.310
0.0088
2.315 0.005
0.0058
2.2285
0.0121
2.340
0.0161
2.331 0.012
0.0121
2.2291
0.0230
2.383
0.0237
2.365 0.017
0.0230
2.2297
0.0286
2.401
0.0330
2.404 0.026
0.0286
2.2305
0.0348
2.425
0.0398
2.426 0.036
0.0348
2.2314
TEMPERATURE = 40 °C
0.0058
2.300
0.0051
2.289 0.007
0.0058
2.2067
0.0121
2.319
0.0106
2.295 0.009
0.0121
2.2076
0.0230
2.354
0.0179
2.327 0.014
0.0230
2.2082
0.0286
2.378
0.0250
2.352 0.018
0.0286
2.2088
0.0348
2.399
0.0314
2.377 0.022
0.0348
2.2097
TEMPERATURE = 47 °C
0.0058
2.269
0.0051
2.261 0.005
0.0058
2.1907
0.0121
2.299
0.0106
2.282 0.006
0.0121
2.1910
0.0230
2.321
0.0179
2.304 0.012
0.0230
2.1919
0.0286
2.349
0.0240
2.331 0.013
0.0286
2.1928
0.0348
2.382
0.0314
2.348 0.017
0.0348
2.1934
121
Table 6.1 (8)- Values of eo, e ’,e ” and e«, of solutions of 1:3 composition of mixture of
aniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. ff.
€o
in wt. fr.
9.1 GHz
6’
e”
Cone,
Optical
in wt. fr .
Coj
TEMPERATURE = 20 UC
0.0053
2.352
0.0067
2.340 0.005
0.0053
2.2455
0.0117
2.403
0.0124
2.356 0.013
0.0117
2.2446
0.0146
2.430
0.0192
2.389 0.017
0.0146
2.2434
0.0223
2.453
0.0243
2.408 0.018
0.0223
2.2416
0.0275
2.511
0.0296
2.426' 0.022
0.0275
2.2410
TEMPERATURE = 30 °C
0.0053
2.349
0.0064
2.304 0.005
0.0053
2.2320
0.0117
2.359
0.0114
2.315 0.006
0.0117
2.2305
0.0146
2.388
0.0139
2.326 0.008
0.0146
2.2291
0.0223
2.431
0.0179
2.342 0.014
0.0223
2.2267
0.0275
2.474
0.0249
2.378 0.023
0.0275
2.2255
TEMPERATURE = 40 °C
0.0053
2.279
0.0048
2.282 0.003
0.0053
2.2112
0.0117
2.313
0.0086
2.300 0.005
0.0117
2.2100
0.0146
2.360
0.0097
2.313 0.006
0.0146
2.2088
0.0223
2.388
0.0145
2.326 0.010
0.0223
2.2076
0.0275
2.430
0.0207
2.344 0.016
0.0275
2.2052
TEMPERATURE = 47 °C
0.0053
2.276
0.0048
2.268 0.005
0.0053
2.1957
0.0117
2.286
0.0086
2.273 0.004
0.0117
2.1934
0.0146
2.335
0.0097
2.284 0.006
0.0146
2.1904
0.0223
2.372
0.0145
2.313 0.012
0.0223
2.1889
0.0275
2.405
0.0207
2.337 0.014
0.0275
2.1860
122
Table 6.1 (9)- Values of e 0, e ’,e ” and
of solutions of 3:1 composition of mixture of
2-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fir.
€0
in wt. £r.
9.1 GHz
e’
e”
Cone,
Optical
in wt. if.
TEMPERATURE = 20 UC
0.0080
2.352
0.0070
2.316 0.007 '
0.0080
2.2605
0.0165
2.344
0.0156
2.335 0.013
0.0165
2.2635
0.0300
2.371
0.0235
2.356 0.018
0.0227
2.2656
0.0387
2.420
0.0323
2.367 0.025
0.0300
2.2680
0.0487
2.441
0.0411
2.382 0.029
0.0387
2.2740
TEMPERATURE = 30 °C
0.0080
2.333
0.0070
2.305 0.004
0.0080
2.2455
0.0165
2.347
0.0156
2.318 0.008
0.0165
2.2470
0.0227
2.343
0.0235
2.340 0.012
0.0227
2.2485
0.0300
2.367
0.0323
2.359 0.016
0.0300
2.2500
0.0387
2.415
0.0411
2.378 0.025
0.0387
2.2515
TEMPERATURE = 40 °C
0.0080
2.309
0.0070
2.275 0.003
0.0080
2.2267
0.0165
2.303
0.0156
2.295 0.007
0.0165
2.2285
0.0227
2.329
0.0235
2.311 0.010
0.0227
2.2296
0.0300
2.335
0.0323
2.329 0.016
0.0300
2.2305
0.0387
2.350
0.0411 '
2.342 0.023
0.0387
2.2320
TEMPERATURE = 47 °C
0.0080
2.243
0.0070
2.263 0.002
0.0080
2.2112
0.0165
2.268
0.0156
2.282 0.005
0.0165
2.2118
0.0227
2.288
0.0235
2.287 0.007
0.0227
2.2135
0.0300
2.311
0.0323
2.311 0.011
0.0300
2.2141
0.0387
2.315
0.0411
2.329 0.016
0.0387
2.2156
123
Table 6.1 (10)- Values o f eo, e ’, e ” and €ooOf solutions o f 1:1 composition o f mixture of
2-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. ff.
Go
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. ff.
e=c
TEMPERATURE = 20 °C
0.0075
2.319
0.0040
2.318 0.008
0.0075
2.2476
0.0203
2.364
0.0132
2.337 0.014
0.0203
2.2506
0.0269
2.390
0.0187
2.352 0.016
0.0269
2.2515
0.0367
2.403
0.0249
2.359 0.020
0.0367
2.2536
0.0467
2.428
0.0315
2.378 0.023
0.0467
2.2545
TEMPERATURE = 30 °C
0.0075
2.318
0.0040
2.300 0.006
0.0075
2.2290
0.0203
2.352
0.0132
2.309 0.008
0.0203
2.2305
0.0269
2.378
0.0187
2.333 0.013
0.0269
2.2314
0.0367
2.406
0.0249
2.352 0.018
0.0367
2.2326
0.0467
2.451
0.0315
2.363 0.022
0.0467
2.2335
TEMPERATURE = 40 °C
0.0075
2.303
0.0040
2.284 0.004
0.0075
2.2112
0.0203
2.331
0.0132
2.300 0.008
0.0203
2.2118
0.0269
2.341
0.0187
2.321 0.010
0.0269
2.2127
0.0367
2.386
0.0249
2.327 0.013
0.0367
2.2135
0.0467
2.392
0.0315
2.340 0.018
0.0467
2.2147
TEMPERATURE = 47 °C
0.0075
2.305
0.0040
2.233 0.005
0.0075
2.1993
0.0203
2.320
0.0132
2.287 0.008
0.0203
2.1969
0.0269
2.322
0.0187
2.291 0.009
0.0269
2.1978
0.0367
2.353
0.0249
2.300 0.011
0.0367
2.1993
0.0467
2.386
0.0315
2.328 0.017
0.0467
2.1999
124
Table 6.1 (11)- Values of eo, e \ e ” and e®of solutions of 1:3 composition of mixture of
2-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
Soo
TEMPERATURE = 20 UC
0.0053
2.333
0.0069
2.324 0.009
0.0089
2.2455
0.0130
2.350
0.0114
2.344 0.011
0.0149
2.2452
0.0230
2.378
0.0184
2.359 0.015
0.0228
2.2449
0.0275
2.410
0.0223
2.367 0.020
0.0268
2.2445
0.0324
2.419
0.0305
2.382 0.025
0.0352
2.2440
TEMPERATURE = 30 °C
0.0053
2.298
0.0069
2.304 0.005
0.0089
2.2320
0.0130
2.323
0.0114
2.318 0.007
0.0149
2.2305
0.0230
2.367
0.0184
2.338 0.012
0.0228
2.2291
0.0275
2.372
0.0223
2.356 0.016
0.0268
2.2285
0.0324
2.393
0.0305
2.373 0.021
0.0352
2.2276
TEMPERATURE = 40 °C
0.0053
2.275
0.0069
2.279 0.004
0.0089
2.2127
0.0130
2.279
0.0114
2.288 0.006
0.0149
2.2112
0.0230
2.337
0.0184
2.305 0.010
0.0228
2.2082
0.0275
2.341
0.0223
2.316 0.012
0.0268
2.2067
0.0324
2.350
0.0305
2.350 0.020
0.0352
2.2052
TEMPERATURE = 47 °C
0.0053
2.274
0.0069
2.266 0.002
0.0089
2.1919
0.0130
2.317
0.0114
2.286 0.005
0.0149
2.1910
0.0230
2.339
0.0184
2.298 0.006
0.0228
2.1904
0.0275
2.348
0.0223
2.304 0.008
0.0268
2.1889
0.0324
2.366
0.0305
2.324 0.012
0.0352
2.1874
125
Table 6.1 (12)- Values o f eo, e ’,e ” and e OTo f solutions o f 3:1 composition of mixture of
3-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
inw t. fr.
e0
inwt. fr.
9.1GHz
€’
e”
Cone,
Optical
inw t. fr.
GoO
TEMPERATURE = 20 °C
0.0088
2.340
0.0083
2.322 0.013
0.0088
2.2476
0.0141
2.416
0.0132
2.348 0.028
0.0141
2.2494
0.0208
2.451
0.0206
2.373 0.041
0.0208
2.2515
0.0281
2.476
0.0293
2.390 0.057
0.0320
2.2536
0.0319
2.515
0.0377
2.398 0.069
0.0404
2.2560
TEMPERATURE = 30 °C
0.0088
2.338
0.0083
2.307 0.013
0.0088
2.2305
0.0141
2.378
0.0132
2.333 0.027
0.0141
2.2320
0.0208
2.420
0.0206
2.350 0.040
0.0208
2.2335
0.0281
2.456
0.0293
2.363 0.054
0.0320
2.2350
0.0319
2.460
0.0377
2.404 0.066
0.0404
2.2365
TEMPERATURE = 40 °C
0.0088
2.331
0.0083
2.282 0.013
0.0088
2.2112
0.0141
2.352
0.0132
2.307 0.026
0.0141
2.2127
0.0208
2.388
0.0206
2.337 0.042
0.0208
2.2147
0.0281
2.417
0.0293
2.354 0.050
0.0320
2.2156
0.0319
2.441
0.0377
2.373 0.062
0.0404
2.2171
TEMPERATURE = 47 °C
0.0088
2.294
0.0083
2.277 0.012
0.0088
2.2052
0.0141
2.334
0.0132
2.293 0.018
0.0141
2.2058
0.0208
2.358
0.0206
2.313 0.031
0.0208
2.2067
0.0281
2.374
0.0293
2.335 0.043
0.0320
2.2073
0.0319
2.426
0.0377
2.363 0.059
0.0404
2.2082
126
Table 6.1 (13)- Values o f eo, e ’, e ” and eooof solutions of 1:1 composition o f mixture o f
3-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fr.
9.1 GHz
€’
6”
Cone,
Optical
in wt. fr.
€oo
TEMPERATURE = 20 °C
0.0044
2.359
0.0046
2.326 0.010
0.0044
2.2440
0.0094
2.381
0.0119
2.352 0.022
0.0094
2.2446
0.0171
2.436
0.0182
2.356 0.031
0.0171
2.2455
0.0207
2.452
0.0244
2.394 0.043
0.0207
2.2464
0.0311
2.480
0.0313
2.408 0.057
0.0311
2.2476
TEMPERATURE = 30 °C
0.0044
2.330
0.0046
2.304 0.009
0.0044
2.2290
0.0094
2.355
0.0119
2.326 0.017
0.0094
2.2296
0.0171
2.408
0.0182
2.348 0.029
0.0171
2.2305
0.0207
2.422
0.0244
2.365 0.042
0.0207
2.2314
0.0311
2.453
0.0313
2.390 0.051
0.0311
2.2320
TEMPERATURE = 40 °C
0.0044
2.312
0.0046
2.287 0.008
0.0044
2.2112
0.0094
2.328
0.0119
2.311 0.015
0.0094
2.2118
0.0171
2.383
0.0182
2.326 0.025
0.0171
2.2127
0.0207
2.392
0.0244
2.352 0.035
0.0207
2.2130
0.0311
2.419
0.0313
2.359 0.045
0.0311
2.2135
TEMPERATURE = 47 °C
0.0044
2.274
0.0046
2.279 0.005
0.0044
2.1981
0.0094
2.309
0.0119
2.296 0.013
0.0094
2.1987
0.0171
2.358
0.0182
2.311 0.021
0.0171
2.1993
0.0207
2.364
0.0244
2.339 0.031
0.0207
2.2000
0.0311
2.409
0.0313
2.352 0.036
0.0311
2.2002
127
Table 6.1 (14)- Values of Go,
g ’, g ”
and G«of solutions of 1:3 composition of mixture of
3-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
€0
in wt. f r .
9.1GHz
e ’
g
”
Cone,
Optical
in wt. f r .
G oo
TEMPERATURE = 20 UC
0.0060
2.339
0.0071
2.327 0.012
0.0060
2.2455
0.0108
2.372
0.0119
2.356 0.017
0.0108
2.2452
0.0173
2.411
0.0190
2.382 0.033
0.0173
2.2446
0.0207
2.436
0.0231
2.392 0.038
0.0207
2.2443
0.0259
2.472
0.0303
2.414 0.048
0.0259
- 2.2440
TEMPERATURE = 30 °C
0.0060
2.310
0.0071
2.307 0.008
0.0060
2.2290
0.0108
2.342
0.0119
2.333 0.014
0.0108
2.2284
0.0173
2.384
0.0190
2.346 0.026
0.0173
2.2276
0.0207
2.405
0.0231
2.367 0.036
0.0207
2.2270
0.0259
2.429
0.0303
2.392 0.044
0.0259
2.2261
TEMPERATURE = 40 °C
0.0060
2.299
0.0071
2.291 0.006
0.0060
2.2112
0.0108
2.319
0.0119
2.309 0.014
0.0108
2.2097
0.0173
2.349
0.0190
2.329 0.022
0.0173
2.2088
0.0207
2.390
0.0231
2.346 0.027
0.0207
2.2082
0.0259
2.411
0.0303
2.367 0.035
0.0259
2.2076
TEMPERATURE = 47 °C
0.0060
2.280
0.0071
2.286 0.004
0.0060
2.1987
0.0108
2.297
0.0119
2.300 0.010
0.0108
2.1975
0.0173
2.354
0.0190
2.318 0.019
0.0173
2.1963
0.0207
2.363
0.0231
2.335 0.025
0.0207
2.1957
0.0259
2.405
0.0303
2.363 0.034
0.0259
2.1948
128
Table 6.1 (15)- Values of eo> e ’, e ” and e « o f solutions o f 3:1 composition o f mixture o f
4-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fir.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
Geo
TEMPERATURE = 20 °C
0.0070
'2.333
0.0070
2.335 0.017
0.0070
2.2560
0.0140
2.379
0.0140
2.348 0.034
0.0140
2.2575
0.0210
2.431
0.0210
2.371 0.053
0.0210
2.2590
0.0280
2.452
0.0280
2.390 0.062
0.0280
2.2635
0.0350
2.496
0.0350
2.424 0.098
0.0350
2.2674
TEMPERATURE = 30 °C
0.0070
2.314
0.0070
2.309 0.020
0.0070
2.2440
0.0140
2.354
0.0140
2.340 0.034
0.0140
2.2446
0.0210
2.417
0.0210
2.365 0.055
0.0210
2.2455
0.0280
2.452
0.0280
2.386 0.068
0.0280
2.2476
0.0350
2.489
0.0350
2.410 0.088
0.0350
2.2485
TEMPERATURE = 40 °C
0.0070
2.309
0.0070
2.300 0.015
0.0070
2.2290
0.0140
2.359
0.0140
2.316 0.026
0.0140
2.2305
0.0210
2.381
0.0210
2.348 0.044
0.0210
2.2314
0.0280
2.412
0.0280
2.369 0.060
0.0280
2.2326
0.0350
2.436
0.0350
2.388 0.071
0.0350
2.2335
TEMPERATURE = 47 °C
0.0070
2.271
0.0070
2.291 0.001
0.0070
2.2118
0.0140
2.327
0.0140
2.310 0.021
0.0140
2.2127
0.0210
2.364
0.0210
2.340 0.036
0.0210
2.2135
0.0280
2.398
0.0280
2.363 0.055
0.0280
2.2147
0.0350
2.447
0.0350
2.398 0.072
0.0350
2.2156
.
129
Table 6.1 (16)- Values o f eo, e ’,e ” and eooof solutions o f 1:1 composition o f mixture o f
4-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
e0
in wt. fr.
9.1GHz
e’
e”
Cone,
Optical
in wt. fr.
TEMPERATURE - 20 UC
0.0050
2.324
0.0050
2.315 0.018
0.0050
2.2596
0.0100
2.347
0.0100
2.333 0.025
0.0100
2.2620
0.0150
2.398
0.0150
2.359 0.034
0.0150
2.2635
0.0200
2.427
0.0200
2.378 0.038
0.0200
2.2644
0.0250
2.448
0.0250
2.392 0.051
0.0250
2.2650
TEMPERATURE = 30 °C
0.0050
2.335
0.0050
2.304 0.011
0.0050
2.2425
0.0100
2.341
0.0100
2.315 0.019
0.0100
2.2434
0.0150
2.386
0.0150
2.326 0.024
0.0150
2.2440
0.0200
2.411
0.0200
2.344 0.031
0.0200
2.2470
0.0250
2.447
0.0250
2.380 0.043
0.0250
2.2500
TEMPERATURE = 40 °C
0.0050
2.262
0.0050
2.296 0.012
0.0050
2.2261
0.0100
2.300
0.0100
2.305 0.020
0.0100
2.2267
0.0150
2.305
0.0150
2.322 0.023
0.0150
2.2276
0.0200
2.340
0.0200
2.357 0.041
0.0200
2.2284
0.0250
2.376
0.0250
2.359 0.051
0.0250
2.2290
TEMPERATURE = 47 °C
0.0050
2.209
0.0050
2.284 0.009
0.0050
2.2112
0.0100
2.282
0.0100
2.291 0.012
0.0100
2.2118
0.0150
2.291
0.0150
2.317 0.018
0.0150
2.2127
0.0200
2.317
0.0200
2.344 0.026
0.0200
2.2129
0.0250
2.332
0.0250
2.348 0.042
0.0250
2.2135
130
Table 6.1 (17)- Values o f eo, e ’, e ” and €ooof solutions o f 1:3 composition of mixture o f
4-bromoaniline + 1-propanol in benzene at different temperatures.
Cone,
in wt. fr.
455 KHz
Cone,
€o
in wt. fr.
9.1 GHz
€’
€”
Cone,
Optical
in wt. fr.
e®
TEMPERATURE = 20 UC
0.0082
2.321
0.0050
2.322 0.009
0.0080
2.2590
0.0139
2.397
0.0100
2.340 0.018
0.0139
2.2584
0.0180
2.411
0.0150
2.363 0.028
0.0180
2.2575
0.0230
2.442
0.0200
2.377 0.033
0.0230
2.2566
0.0300
2.489
0.0250
2.400 0.044
0.0300
2.2554
TEMPERATURE = 30 °C
0.0082
2.328
0.0050
2.311 0.005
0.0080
2.2407
0.0139
2.366
0.0100
2.326 0.010
0.0139
2.2404
0.0180
2.406
0.0150
2.342 0.023
0.0180
2.2395
0.0230
2.431
0.0200
2.355 0.032
0.0230
2.2389
0.0300
2.465
0.0250
2.380 0.039
0.0300
2.2386
TEMPERATURE = 40 °C
0.0080
2.309
0.0050
2.286 0.007
0.0080
2.2255
0.0139
2.344
0.0100
2.300 0.012
0.0139
2.2246
0.0180
2.381
0.0150
2.337 0.022
0.0180
2.2237
0.0230
2.430
0.0200
2.339 0.033
0.0230
2.2234
0.0300
2.468
0.0250
2.371 0.036
0.0300
2.2231
TEMPERATURE = 47 °C
0.0080
2.285
0.0050
2.266 0.006
0.0080
2.2082
0.0139
2.333
0.0100
2.304 0.011
0.0139
2.2076
0.0180
2.372
0.0150
2.309 0.019
0.0180
2.2073
0.0230
2.383
0.0200
2.329 0.028
0.0230
2.2067
0.0300
2.416
0.0250
2.348 0.032
0.0300
2.2052
131
Table 6.2 (1) - Values of a<j, a’, a” and a*> of solutions of aniline, bromoanilines and
1-propanol in benzene solution at different temperatures.
Temperature °C
ao
a’
a”
Aniline
20
2.65
2.38
0.57
0.30
30
2.55
2.30
0.53
0.30
40
2.45
2.22
0.50
0.30
47
2.33
2.16
0.47
0.23
2-Bromoaniline
20
2.55
2.01
0.81
0.31
30
2.13
1.79
0.59
0.30
40
1.92
1.65
0.49
0.23
47
1.88
1.66
0.46
0.20
3-Bromoaniline
20
5.13
2.95
2.05
0.19
30
4.68
2.87
1.80
0.13
40
4.29
2.86
1.63
0.13
47
3.95
2.81
1.40
0.13
4-Bromoaniline
20
7.80
4.40
2.55
0.24
30
7.17
4.30
2.44
0.22
40
6.72
4.10
2.20
0.25
47
5.95
3.80
1.96
0.15
1-ProDanol
20
5.64
4.78
1.26
-0.37
30
5.05
4.29
1.12
-0.47
40
4.60
4.05
0.98
-0.51
47
4.00
3.57
0.82
-0.52
132
Table 6.2 (2) - Values o f ao, a’, a” and a» o f solutions o f mixtures o f aniline + 1-propanol
in benzene solution at different temperatures.
Temperature °C
ao
a’
a”
3:1 Mixture o f aniline +l-propanoI
20
3.95
2.73
0.82
0.25
30
3.64
2.60
0.72
0.22
40
3.33
2.50
0.64
0.22
47
3.12
2.40
0.60
0.21
1:1 Mixture o f aniline +1 -Drooanol
20
5.00
3.60
0.94
0.13
30
4.60
3.48
0.92
0.11
40
4.20
3.24
0.79
0.09
47
3.60
3.00
0.70
0.09
1:3 Mixture o f aniline +1-propanol
20
5.80
3.90
0.99
-0.22
30
5.51
3.72
0.92
-0.30
40
5.19
3.50
0.86
-0.32
47
4.95
3.37
0.82
-0.42
Table 6.2 (3) - Values o f ao, a’, a” and a» o f solutions o f mixtures o f 2-bromoaniline +
1-propanol in benzene solution at different temperatures.
Temperature °C
ao
a’
a”
3oo
3:1 Mixture o f 2-bromoaniline +1-•nronanol
20
2.84
2.29
0.78
0.34
30
2.54
2.18
0.63
0.20
40
2.34
2.08
0.50
0.15
47
2.11
1.91
0.45
0.15
Contd...
133
1:1 Mixture of 2-bromoaniline +1--propanol
20
3.20
2.67
0.79
0.16
30
2.70
2.35
0.65
0.12
40
2.57
2.29
0.58
0.10
47
2.38
2.15
0.51
0.09
1:3 Mixture o f 2-bromoaniline +1-■DroDanol
20
3.62
3.20
0.88
-0.17
30
3.28
2.86
0.78
-0.18
40
2.86
2.46
0.70
-0.35
47
2.31
2.17
0.55
-0.35
Table 6.2 (4) - Values o f ao, a’, a” and a*, o f solutions o f mixtures o f 3-bromoaniline +
1-propanol in benzene solution at different temperatures.
Temperature °C
ao
a’
a”
8co
3:1 Mixture o f 3-bromoaniline+1 -propanol
20
6.20
3.30
1.94
0.23
30
5.60
3.10
1.84
0.21
40
5.10
2.88
1.74
0.19
47
4.70
2.70
1.57
0.09
1:1 Mixture o f 3-bromoaniline +1 -DroDanol
20
5.86
3.41
1.78
0.14
30
5.33
3.24
1.65
0.11
40
4.93
3.10
1.43
0.10
47
4.46
2.83
1.24
0.08
Contd...
134
1:3 Mixture of 3-bromoaniline +1-1pronanol
20
6.20
3.60
1.60
-0.08
30
5.55
3.46
1.37
-0.15
40
4.80
3.20
1.17
-0.18
47
4.60
3.18
1.10
-0.19
Table 6.2 (5) - Values of ao, a’, a” and a® of solutions of mixtures of 4-bromoaniline +
1-propanol in benzene solution at different temperatures.
Temperature °C
ao
a’
a”
a®
3:1 Mixture of 4-bromoaniline+1-propanol
20
6.80
3.80
2.60
0.24
30
6.45
3.66
2.51
0.16
40
5.50
3.21
2.20
0.15
47
5.05
3.00
2.00
0.14
1:1 Mixture of 4-bromoaniline +l-proDanol
20
7.30
4.10
2.10
0.26
30
6.40
3.64
1.85
0.20
40
5.91
3.39
1.70
0.17
47
5.45
3.16
1.50
0.12
1:3 Mixture of 4-bromoaniline +1--Dronanol
20
8.14
4.26
1.79
-0.41
30
6.80
3.67
1.56
-0.41
40
6.20
3.60
1.47
-0.34
47
5.70
3.40
1.30
-0.29
135
Table 6.3 (1) - The relaxation time (to) and distribution parameter (a) o f aniline,
2-bromoaniline, 3-bromoaniline, 4-bromoaniline and 1-propanol in benzene solution at
different temperatures.
Temperature
Relaxation
Distribution
°C
Time in ps
parameter
Aniline
20
4.4
0.11
30
4.2
0.11
40
4.1
0.11
47
4.0
0.07
2-bromoaniline
20
8.5
0.09
30
6.9
0.09
40
5.8
0.11
47
5.2
0.09
3-bromoaniline
20
14.9
0.11
30
13.1
0.13
40
11.4
0.12
47
9.7
0.13
4-bromoaniline
20
14.6
0.24
30
13.0
0.21
40
12.5
0.22
47
11.1
0.21
1-Dronanol
20
3.5
0.23
30
3.3
0.23
40
3.0
0.19
47
2.8
0.18
136
Table 6.3 (2) - The relaxation time (to) and distribution parameter (a) of mixtures of
aniline + 1-propanol in benzene solution at different temperatures.
%
Concentration
of aniline in
Relaxation
Distribution
Time in ps
parameter
1-propanol
TEMPERATURE = 20 °C
0
3.5
0.23
25
3.9
0.55
50
4.4
0.45
75
6.5
0.42
100
4.4
0.11
TEMPERATURE = 30 °C
0
3.3
0.23
25
3.5
0.55
50
4.1
0.40
75
5.4
0.43
100
4.2
0.11
TEMPERATURE = 40 °C
0
3.0
0.19
25
3.3
0.56
50
3.5
0.41
75
4.4
0.41
100
4.1
0.12
TEMPERATURE = 47 °C
0
2.8
0.18
25
3.0
0.56
50
3.3
0.30
75
4.1
0.39
100
4.0
0.07
137
Table 6.3 (3) - The relaxation time (to) and distribution parameter (a) of mixtures of
2-bromoaniline + 1-propanol in benzene solution at different temperatures.
%
Concentration
of 2-bromoaniline
Relaxation
Distribution
Time in ps
parameter
in 1-propanol
TEMPERATURE = 20 °C
0
3.5
0.23
25
4.1
0.12
50
5.0
0.18
75
6.9
0.15
100
8.5
0.09
TEMPERATURE = 30 °C
0
3.3
0.23
25
3.9
0.15
50
4.7
0.13
75
5.2
0.13
100
6.9
0.09
TEMPERATURE = 40 °C
0
3.0
0.19
25
3.7
0.18
50
4.1
0.13
75
4.5
0.10
100
5.8
0.11
TEMPERATURE = 47 °C
0
2.8
0.18
25
3.7
0.02
50
3.8
0.12
75
4.1
0.04
100
5.2
0.09
138
Table 6.3 (4) - The relaxation time (t0) and distribution parameter (a) of mixtures of
3-bromoaniline + 1-propanol in benzene solution at different temperatures.
% Concentration
Relaxation
Distribution
of 3-bromoaniline
Time in ps
parameter
in 1-propanol
TEMPERATURE = 20 °C
0
3.5
0.23
25
11.2
0.39
50
13.0
0.28
75
16.6
0.27
100
14.9
0.11
TEMPERATURE = 30 °C
0
3.3
0.23
25
8.3
0.39
50
11.8
0.26
75
15.3
0.23
100
13.1
0.13
TEMPERATURE = 40 °C
0
3.0
0.19
25
6.7
0.38
50
10.5
0.29
75
14.9
0.21
100
11.4
0.12
TEMPERATURE = 47 °C
0
2.8
0.18
25
5.8
0.38
50
9.9
0.31
75
13.8
0.23
100
9.7
0.13
139
Table 6.3 (5) - The relaxation time (to) and distribution parameter (a) of mixtures of
4-bromoaniline + 1-propanol in benzene solution at different temperatures.
%
Concentration
of 4-bromoaniline
Relaxation
Distribution
Time in ps
parameter
in 1-propanol
TEMPERATURE = 20 UC
0
3.5
0.23
25
12.5
0.49
50
14.4
0.31
75
15.5
0.14
100
14.6
0.24
TEMPERATURE = 30 °C
0
3.3
0.24
25
11.5
0.47
50
13.8
0.31
75
15.0
0.13
100
13.0
0.21
TEMPERATURE = 40 °C
0
3.0
0.19
25
9.4
0.44
50
13.4
0.31
75
14.4
0.12
100
12.5
0.22
TEMPERATURE = 47 °C
0
2.8
0.18
25
8.5
0.46
50
12.7
0.34
75
13.9
0.12
100
11.1
0.21
140
to meta- to para- position, this has been observed at all the temperature. This indicates
that hindrance for intramolecular rotation o f-N H 2 is greater in 2-bromoaniline and less in
3-bromoaniline and still less in 4-bromoaniline.
W t fr caf 1-propand in benzene
Figure 6.1-Plot o f tan 6 against concentration for solutions o f 1-Propanol in benzene at
30 °C
Complex permittivity o f aliphatic alcohols was measured in this laboratory 6 in dilute
solutions o f benzene and it was found that tanS-concentration curve show deviation from
linearity in the concentration range 0.02 to 0.05 weight factor for alcohols investigated
i. e., methyl alcohol, ethyl alcohol, n-propyl alcohol and tert butyl alcohol, for n-propyl
alcohol it was about 0.04 weight factor, this indicate that at this and above this
concentration the n-propyl alcohol associates to form species other than monomers. In the
present investigation the concentration o f 1-propanol in benzene was less than 0.04
weight factor and as shown in Figure-6.1 tanS-coneentration curve o f 1-propanol in
benzene solution at 30°C is linear. This indicates that below this concentration there is no
self-association o f alcohol. The observed relaxation time for 1-propanol at 30°C is 3.3 ps
which is in agreement with earlier studies 6 and those reported by Purohit and Sharm a26.
The finite value o f distribution parameter (a ) for 1-propanol at all temperature suggest
multiple relaxation processes in this system. The small values o f relaxation times at all
141
temperatures suggest that at this frequency and dilution predominant mode o f relaxation
in this system is due to rotation o f -O H group around -C -0 bond. Due to lack o f facilities
o f permittivity measurements at higher microwave frequencies the measurements are
carried out at single microwave frequency and therefore the analysis o f the data was not
carried out in terms o f two relaxation processes.
Dielectric
data
for
mixtures
of aniline,
2-bromoaniline,
3-bromoaniline
and
4-bromoaniline with 1-propanol in dilute solutions o f benzene at different temperatures
and concentrations was analyzed as single component system. The permittivity ( e ’) and
dielectric loss ( e ”) o f these mixtures were plotted against concentration, the plots are
linear, from these graphs ao,a\ a” and a® were found out and are given in Table-6.2 (2) to
6.2 (5). The relaxation times and distribution parameters o f the mixtures o f aniline,
bromoanilines with 1-propanol at different temperatures evaluated by Higasi’s single
frequency method are shown in Table-6.3 (2) to 6.3 (5). It is evident from Table-6.3 that
the relaxation times o f mixtures of aniline and bromoaniline with 1-propanol increases
with the increase in concentration of anilines in the mixtures at all temperatures, this is
due to the fact that the relaxation times o f anilines are higher than that o f 1-propanol (at
the present frequency of measurement and dilution). The plots of relaxation time of
mixtures against the concentration of anilines at different temperatures are shown in
Figures 6.2 to 6.9, these figures show that the increase in relaxation time of mixture with
concentration o f anilines is non-linear, at some concentration the relaxation time o f
mixture is higher than its components. This indicates solute-solute types o f interactions
between the anilines and 1-propanol. Further, the maximum deviation in relaxation time
occurs at 75% concentration of anilines in the mixture suggesting a strong molecular
interaction between the molecules in the aniline rich region. Similar results were obtained
by Fattepur et a l 23 in the case of aniline-methanol mixtures. Hydrogen bond formation
between anilines and 1-propanol is possible through NH2-OH and OH-NH 2 type o f
linkage. The higher value of relaxation time ( to) o f 1:3 composition o f 1-propanol +
aniline mixtures than the individual components suggest that the possibility o f NH 2-OH
type o f linkage between aniline and 1-propanol in aniline rich region.
142
To confirm the present results IR spectra o f dilute solutions o f 1-propanol, aniline and 1:3
mixture o f 1-propanol + aniline in carbontetrachloride were obtained (Figures-6.10-6.12).
From the IR spectra it can be seen that the peak at wave number 3636.6 cm'1 in
1-propanol which corresponds to free -O H remains at the same position in the mixture.
But the two characteristic peaks of aniline at wave numbers 3476.6 cm'1 and 3398.4 cm'1
has been shifted to 3471.1 cm'1 and 3394.4 cm '1 respectively in the mixture. These shifts
o f N-H stretching vibration towards lower frequency side suggest that in this mixture at
this concentration aniline is donor while alcohol is a proton acceptor. This is in agreement
with inferences derived by dielectric studies.
The distribution parameters (a) for mixtures o f anilines + 1-propanol at different
temperatures and at all three concentrations is high compared to the a values of
components (Table-6.3 (2)-6.3 (5)), further, it increases with the concentration o f alcohol
in the mixture and reaches maximum when the alcohol concentration is highest i.e., 75%
alcohol and 25% of anilines. The temperature variation o f distribution parameters (a) of
mixture at any concentration show a negligible variation o f this parameter with
temperature. It appears that in these mixtures there is solute-solute and solute-solvent
interactions, providing a variety o f local environments resulting in the domination of
internal group rotation, which is usually independent o f temperature. Rajyam et al 27
studied mixtures o f propyl acetate and propanol and found large value o f distribution
parameter, they attributed this rise due to formation o f complexes via hydrogen bonding,
as mentioned earlier in the present study there is possibility o f hydrogen bonding between
anilines and alcohol resulting in high values o f distribution parameter.
143
0
-I------------------------------------- 1--------------------------------------1
------------------------------------- 1--------------------------------------
0
25
50
75
100
% Cone, of aniline in mixture
Figure 6.2- Variation in relaxation time o f mixtures as a function o f concentration o f
05
N)
Relaxation time m ps.
00
Aniline in 1-propanol at different temperatures.
0
J----------------------------------------- ,----------------------------------------- ,------------------------------------------!------------------------------------------
0
25
50
75
100
% Cono of 2-bromoaniline in mixture
Figure-6.3 Variation o f relaxation time o f mixtures as a function o f concentration o f
2-BA in 1-propanol at different temperatures.
144
O
O)
hO
03
^
O
R elaxation tim e in ps.
0
25
50
75
100
% C o n e o f S -b ro m o a n ilin e in m ixtu re
Figure 6.4-Variation o f relaxation time o f mixtures as a function o f concentration of
Oi
- '4
o
o
io
CM
cn
o
3-BA in 1-propanol at different temperatures.
% C o n e, o f 4 -b ro m o a n ilin e in m ix tu re
Figure 6.5-Variation of relaxation time o f mixtures as a function o f concentration o f
4-BA in 1-propanol at different temperatures.
145
2 0 deg C
CD
P ro p a n o l
K)
R e l a x a t i o n t i m e in p s
- A n ilin e + 1 -
-2 -B A + 1-
CD
P ro p a n o l
■ 3 -B A + 1 -
•tv
P ro p a n o l
- 4 -B A + 1P ro p a n o l
25
%
50
75
C o n c e n tr a to n o f a n ilin e
Figure 6.6- Variation o f relaxation time o f mixtures as a function o f concentration o f
different anilines in 1-propanol at 20 °C.
o
-------------1
-------------1
-------------1
-i--------- ---------------- >
o)
ro
co
4*
o
R e la x a t io n t i m e m p s
o
k>
30 deg C
A n ilin e + 1 p ro p a n o l
2-
B A +1-
p ro p a n o l
3-
B A +1-
p ro p a n o l
4-
BA + 1 -
p ro p a n o l
25
50
75
100
% C o n c e n t r a t io n o f a n ilin e
Figure 6.7- Variation of relaxation time o f mixtures as a function o f concentration o f
different anilines in 1-propanol at 30 °C.
146
40 deg C
hJ
00
-2 -B A + 1propanol
-3 -B A + 1Propanol
-&■
-4 -B A + 1Propanol
o
Relaxation tim e in ps.
-A niline + 1Propanol
25
50
75
100
p
O
o
-Po
P
X
p
O
CD
as a function o f concentration of
ro
— • — Aniline + 1Propanol
—
oo
Relaxation time in ps.
cn
(O
5'
in
Cu
o
5*
a>
c
differen
o
o
I
>
00
Figure
o'
% C oncen tra tio n o f aniline
— + —
2- BA + 1Propanol
3-BA + 1Propanol
— n— 4-BA + 1propanol
25
50
75
1C
% Concentration of aniline
Figure 6.9- Variation of relaxation time o f mixtures as a function o f concentration of
differen t anilines in 1-propanol at 47 °C.
147
<
4
>
■ii
X
2000
W avenumbers ( c m - l )
- -
^
D V U » j||i
^
TT n
"> “» T T T T r*TT T3 T 7
o u o a j
148
J 000
y ouu i
n •n
a a i o i
r ~
OOCT
j^c-y \
Figure-6.10 IR spectra o f dilute solution o f aniline in carbon tetrachloride
3000
ALTRA ANALYTICAL LABOR^TORIES.(AHD).
o
r
<3
f-i
<rd
H
rt
li
m
*->
•r-t
0
01
<U ,‘20
O
d
cot
to
cot
CD
CO
/
3000
I''1'!IvvArA
2000
W avenum bers (cm --1)
flr
k
ALTRA A NATI2YTICAL LABO^ATORIES.(AHD)
Figure-6.11 IR spectra of dilute solution ofl-propanol in carbon tetrachloride
\
*
/ 1 A,
p ’Ai ll
w
CO
►
P*
b
I
ll
-
ooor
to
to
to 7:1
f \
' A
\
00
w
05
roo9
05
Co W
700
$.
CO
» J
149
Figurc-6.12 IR spectra o f dilute solution o f 1: 3 mixture o f 1-propanol + aniline in
carbon tetrachloride
Wavenumbers? (cm~l)
2000
ooor
3000
roG9
P
P
oo
P
r*
<-•*•
&?
P
o
CD
150
References :
1. Mizushima, S.I., Bull. Chem. Soc., (Japan), 1 (1926)163.
2. Mizushima, S.I., Phys. Z , 28 (1927) 418.
3. Lux, A. and Stockhausen, M., Phys.Chem. Liq., 26 (1993) 67.
4. Eid, M.A.M., Hakim, I.K., Abd-El-Nour, Saad, A.L.G. and Stockhausen, M., J Mol.
Liqs., 81 (1999) 225.
5. Crossley J., J Phy. Chem.,15 (1971) 12.
6. Vyas, A. D. and Vashisth, V. M., J. Mol. Liqs.,38 (1988) 11.
7. Vyas, A. D. and Vashisth, V. M., Indian J. Pure and Appl. Phys., 28 (1990) 550.
8. Stockhausen, M., Utzel, H. and Seitz, Z, Z fu r Physi. Chem. Neue Folge, 133 (1982)
69.
9. Utzel, H. and Stockhausen, M., Z. Naturforch, 409 (1985) 588.
10. Stockhausen, M. and Busch, H., Phys. Chem. Liqs., 32 (1996) 183.
11. Becker, U. and Stockhausen, M., J. Mol. Liqs., 81 (1999) 89.
12. Wilke, G., Betting, H. and Stockhausen, M., Phys. Chem. Liq.,36 (1998) 199.
13. Mashimo S. and Umehara, T., J. Chem. Phys., 95 (1991) 6257.
14. Sato, T„ Niwa, H., Chiba, A. and Nozaki, R., J .Chem. Phys., 108 (1998) 4138.
15. Stockhausen, M. and Dachwitz, E., Z. Naturforch, 39a (1984) 646.
16. Madhurima, V., Murthy, V. R. K. and Sobhanadri, J., Indian J. Pure and Appl. Phys.,
36 (1998) 85.
17. Varadrajan, V. and Rajgopal A., Indian J. Pure and Appl. Phys., 36 (1998) 13.
18. Oswal, S. L. and Desai, H. S., Fluid Phase Equi, 161 (1999) 191.
19. Liszi, S., Salmon, T., Ratkovies, F., Acta Chim. Acad. Sci. Hung., 81 (1974) 467.
20. Swain, B. B., Ph. D. Thesis, Uttakal University (India), (1986).
21. Springer (Jr.), C.S. and Meek, D.W., J. Phy. Chem., 70 (1966) 481.
22. Tripathi, S., Roy, G. S. and Swain, B. B., Indian J. Pure and Appl. Phys., 31 (1993)
828.
23. Fattepur, R. H., Hosamani, M. T. and Beshpande, D. K. and Mehrotra, S. C., J. Chem.
Phys., 101 (1994) 9956.
24. Srivastava, K. K. and Vij, J. K., Bull. Chem. Soc. (Japan), 43 (1970) 2307.
25. Tucker, S. W. and Walker, W., Can. J. Chem., 47 (1969) 681.
151
26. Purohit, H. D. and Sharma, H., Indian J. Pure andAppl. Phys., 9 (1971) 450.
27. Rajyam, B. S., Ramsastry, C. V. and Murthy, C. R. K., Indian J. Pure andAppl.
Phys., 18 (1980) 374.
152
CHAPTER-VII
DIELECTRIC RELAXATION STUDY OF MIXTURES OF
1-PROPANOL WITH ANILINE, 2-CHLOROANILINE,
3-CHLOROANILINE AND 4-FLUOROANILINE AT DIFFERENT
TEMPERATURES USING TIME DOMAIN REFLECTOMETRY
7.1 Introduction :
The mixtures o f associated liquids which are capable o f forming hydrogen bonds (e.g.
alcohol, water etc.) with either associated or non-associated liquids is o f special interest
3. The presence o f hydrogen bond brings about considerable change in the relaxation time
and dipole moment o f the binary system with respect to the corresponding values in the
pure components 4. Syal et a l 5 studied dielectric relaxation in the mixtures o f methanol
with morpholines at a number o f microwave frequencies and found that addition o f
morpholines to MeOH leads to alteration o f MeOH relaxation contribution which
indicated a hetero interactions o f structure breaking character. Dielectric properties o f nnitriles in methanol have been studied by Helambe et a l6 using time domain spectroscopy
(TDR) in the temperature range 0-45 °C. They observed a systematic change in dielectric
constant and relaxation time o f solution with the increase in the concentration o f nitrile in
the solution, further the geff values decreased below unity in nitrile rich region indicating
the antiparallel alignment o f the dipoles in the region. Swain 7 from the study o f mutual
correlation factor gab and excess properties like excess molar polarization and excess free
energy o f mixtures o f some alcohols and aniline observed dipolar interaction in the
mixtures. From the measurement o f viscosity and excess molar volumes o f liquid
mixtures o f alcohols with amine Oswal et a l * suggested strong cross association due to
hydrogen bonding between -O H and —NH2 groups. Fattepur et al 9 studied dielectric
properties o f mixtures o f aniline with methanol over entire range o f concentration at the
frequency 10 MHz to 10 GHz using TDR at four different temperatures and found strong
interactive association between aniline and methanol in aniline rich region. The dielectric
153
measurements conducted on mixtures o f 1- propanol with aniline and bromoanilines at
different temperatures and concentration in dilute solutions at single microwave
frequency presented in previous chapter shown existence o f solute-solute and solutesolvent type o f interactions in the mixtures, the IR spectra o f these mixtures hi dilute
carbon tetrachloride (previous chapter) also indicated similar results. To gain more
information in this area dielectric relaxation study on the mixtures o f 1-propanol with
aniline, 2-chloroaniline, 3-chloroaniline and 4-fluoroaniline (in pure state) have been
carried out at different temperatures and results are presented in this Chapter.
7.2 Experimental :
1-propanol, AR grade obtained from Sd-Finechem Co. Ltd. (India) was used after drying
over CaO and fractional distillation. Aniline, GR grade supplied by Merck (India) was
used after fractional distillation. 2-chloroaniline and 4-fluoroaniline both o f synthesis
grade procured from Merck (Germany) and 3-chloroaniline of pract. grade purchased
from Fluka A.G. (Switzerland) were used without further purification The mixtures o f
various volume fractions o f anilines (0-100 %) in 1-propanol were prepared just before
the measurements.
A HP 54750A mainframe set up was used to obtain complex permittivity spectra o f the
samples in the frequency range 10 MHz to 20 GHz. The experimental set up and data
processing have been described in Chapter-Ill. All the measurements were carried out at
20, 30, 40 and 50° C. The temperature o f the sample cell was controlled thermostatically
to within ±1 °C by circulating water through a heat-insulating container, which surrounds
the sample cell.
7.3 Results :
The experimental values o f e * are fitted with the Debye equation
€? *(<i>) = Geo + —
—
- 7 .1
1+ jOT
154
with eo and x as fitting parameters. The value o f e® was kept to be constant, as the fitting
parameters are not sensitive to Goo. A nonlinear least-squares fit method 10 was used to
determine the values of dielectric parameters.
The determined values of static dielectric constant ( g 0) and relaxation time (x) for
solutions of different concentrations of aniline, 2-chloroaniline, 3-chloroaniline and 4fluoroaniline each in 1-propanol at different temperatures are presented in Table 7.1.
The excess permittivity ( g 5e) and excess inverse relaxation time (l/x)E were calculated
using relations
e E= ( e 0 - O ra- [ ( e 0 - e J AX A+ ( e 0 - e „ ) BX B]
- 7 .2
and
(V
E
( l)
x A+ -
A
m
XB
B
where X is mole fraction and suffix m, A and B represent mixture, 1-propanol and
respective aniline in the mixtures.
The experimental values o f both the excess parameters were fitted to Redlich-Kisterr 11
equation
YE
-7.4
k
where YE is either e sE or (1/x) E. The coefficients BK were calculated and used as
guidelines to draw the smooth curves in Figures 7.5-7.12.
The thermodynamic parameters like molar energy o f activation (AH ) and molar entropy
o f activation (AS*) were determined from Erying’s equation 12 utilizing least squares fit
method:
155
x = — exp[(AH * -TAS *) / RT]
kT
- 7 .5
Calculated values o f these thermodynamic parameters for all the four systems studied are
presented in Table 7.2.
The Kirkwood correlation factor g provides information regarding the orientation o f the
electric dipoles in polar liquid !3.
4nNp2p
9kTM B
(e0 —e , j 2 e 0 - e , )
...? 6
e 0 (e . + l f
Modified forms o f this equation have been used to study the orientation o f electric dipoles
in binary mixtures14,15. Two such equations used are as follows:
4tiN / 2P a P a
9kT m a
^ P bP b ^
,.eff
,X 2e Om ^
-0m
MB
>
•••7.7
W l
( e =cm + :
’ Om
where geffis the Kirkwood correlation factor for binary mixture. geff varies between gAand
gB .
and
4tcN P a P a S a v
9kT v M .
! P bP b S b y
MB
8f
y
(e.„
-Om - e .«m,X2
c 0m T ’
••■7.8
[e 0m (€oom +2)2
gAand ge are assumed to be affected by an amount gf in the mixture, gf = 1 for an ideal
mixture, and deviation from unity indicates interaction between the two components o f the
mixture.
Calculated values o f geff and gf using equation (7.7) and (7.8) respectively for all the four
systems at different temperatures are listed in Tables 7.3.
156
Table 7.1 (1)- Static dielectric constant (eo) and relaxation time (x) for aniline +
1-propanol mixture at different temperatures.
Vol. % of
Aniline
eo
x(ps)
eo
*(ps)
TEMPERATURE =20° C
TEMPERATURE =30° C
0
20.45
261.89
19.27
220.0
10
18.08
186.74
17.16
144.81
20
15.82
- 131.7
15.07
105.1
30
14.2
95.9
13.49
74.78
40
12.51
70.85
11.94
56.01
50
11.03
52.5
10.56
43.53
60
9.78
40.54
9.5
31.46
70
8.86
30.43
8.48
25.76
80
7.94
24.2
7.77
20.14
90
7.09
20.6
6.82
17.6
100
6.48
16.59
6.09
14.71
TEMPERATURE = 40° C
TEMPERATURE = 50° C
0
18.8
177.59
17.6
134.53
10
16.41
117.6
15.51
92.43
20
14.51
83.01
13.83
66.95
30
12.93
60.83
12.78
59.29
40
11.48
46.21
10.93
39.61
50
10.18
35.0
9.85
30.06
60
9.21
25.23
9.0
22.97
70
8.33
21.47
8.09
18.85
80
7.52
17.56
7.32
15.58
90
6.75
15.09
6.69
13.13
100
6.09
12.15
6.02
12.15
157
Table 7.1(2)- Static dielectric constant (eo) and relaxation time (x) for
2-chloroaniline + 1-propanol mixture at different temperatures.
Vol. %of
2-chloroaniline
eo
x (ps)
eo
x (ps)
TEMPERATURE =20° C
TEMPERATURE=30° C
0
20.45
261.89
19.27
220.0
10
18.79
209.04
17.92
166.83
20
17.25
160.52
16.55
J29.56
30
15.22
109.04
14.56
91.6
40
13.52
83.46
13.14
70.51
50
11.98
63.52
11.69
56.41
60
10.83
49.37
10.48
42.17
70
9.81
40.2
9.51
35.97
80
8.88
34.47
8.52
26.95
90
8.09
27.71
7.87
24.22
100
7.25
26.22
6.97
22.17
TEMPERATURE=40° C
TEMPERATURE=50° C
0
18.8
177.59
17.6
134.53
10
17.3
141.68
16.35
106.89
20
16.03
112.04
15.06
87.26
30
14.04
78.0
13.5
67.51
40
12.49
58.65
12.13
50.08
50
11.29
47.28
11.06
42.2
60
10.3
36.84
10.01
33.49
70
9.31
30.86
9.11
27.58
80
8.42
25.12
8.34
24.56
90
7.69
22.38
7.41
20.63
100
6.89-
21.48
6.79
18.29
158
Table 7.1(3)-Static dielectric constant (eo) and relaxation time (t) for
3-chloroaniline + 1-propanol mixture at different temperatures.
Vol. % of
3-chloroaniline
€0
x(ps)
e0
t(ps)
TEMPERATURE=20° C
TEMPERATURE=30° C
0
20.45
261.89
19.27
220.0
10
18.83
180.52
18.47
159.8
20
17.86
137.95
17.21
111.84
30
16.89
100.44
16.0
85.57
40
15.81
85.31
15.15
69.21
50
14.87
69.53
14.44
57.6
60
14.27
59.55
13.82
49.12
70
13.66
53.8
13.13
44.9
80
12.99
49.61
12.66
42.17
90
12.55
49.09
12.66
42.17
100
12.07
49.98
11.8
42.58
TEMPERATURE=40° C
TEMPERATURE=50° C
0
18.8
177.59
17.6
134.53
10
17.69
131.47
16.83
105.45
20
16.6
95.92
15.86
76.79
30
15.6
70.94
14.74
57.31
40
14.78
60.85
14.34
50.42
50
14.15
50.34
13.74
43.47
60
13.49
43.38
13.01
37.72
70
12.88
40.47
12.64
35.76
80
12.41
36.93
12.14
33.39
90
11.95
37.33
11.68
32.88
100
11.6
38.12
11.58
34.14
.-r-n,_____ m
..... ...... . ..T,....... . Ul„
, , . I, .
159
____________________
Table 7.1(4)-Static dielectric constant (eo) and relaxation time (x) for
4-fluoroaniIine + 1-propanol mixture at different temperatures.
Vol. % of
■fluoroaniline
sq
x(ps)
eo
x(ps)
TEMPERATURE=20° C
TEMPERATURE=3 0° C
0
20.45
261.89
19.27
220.0
10
19.39
172.3
18.35
154.75
20
18.16
131.66
17.39
109.71
30
17.21
95.77
16.58
79.68
40
16.7
75.5
16.21
64.87
50
16.4
62.57
15.79
51.72
60
16.1
52.45
15.53
44.31
70
16.06
46.19
15.52
40.3
80
15.73
38.58
15.31
36.64
90
15.59
39.61
15.25
33.79
100
15.46
35.92
14.97
32.93
TEMPERATT JRE=40° C
TEMPERATURE=50° C
0
18.8
177.59
17.6
134.53
10
17.66
129.22
16.95
107.85
16.7
90.69
16.34
83.14
30
15.98
68.75
15.55
58.09
40
15.58
53.76
15.07
46.69
50
15.45
45.95
14.7
37.66
60
14.94
39.08
14.65
33.59
70
14.96
33.84
14.61
30.52
80
15.01
31.7
14.38
27.57
90
14.95
30.52
14.21
26.45
100
14.81
29.59
14.27
26.01
20
‘
160
.
Table 7.2 (1)- Molar enthalpy of activation (AH*) and molar entropy of activation
(AS*) for mixtures of aniline + 1-propanol.
Vol. %
AH*
AS*
of aniline
kJ/mole
J/mole/°k
0
14.78
0.218
10
15.67
0.225
20
15.26
0.226
30
10.51
0.213
40
12.71
0.223
50
12.33
0.224
60
12.66
0.227
70
10.19
0.221
80
8.94
0.219
90
7.63
0.217
100
6.35
0.213
161
Table 7.2 (2)- Molar enthalpy of activation (AH*) and molar entropy of activation
(AS*) for mixtures of 2-chloroaniline + 1-propanol.
Vol. % of
AH*
AS*
2-chloroaniline
kJ/mole
J/mole/°k
0
14-78
0.218
10
14.52
0.220
20
12.94
0.216
30
10.03
0.209
40
9.25
0.215
50
8.48
0.209
60
7.69
0.209
70
7.53
0.208
80
6.10
0.206
90
5.05
0.204
100
6.19
0.209
162
Table 7.2 (3)- Molar enthalpy of activation (AH*) and molar entropy of activation
(AS*) for mixtures of 3-chloroaniline + 1-propanol.
Vol. % of
AH*
AS*
3-chloroaniline
kJ/mole
J/mole/°k
0
14.78
0.218
10
11.60
0.211
20
12.46
0.216
30
12.12
0.217
40
10.87
0.215
50
9.60
0.212
60
9.21
0.213
70
7.92
0.209
80
7.88
0.209
90
7.84
0.209
100
7.33
0.207
163
Table 7.2 (4)- Molar enthalpy of activation (AH*) and molar entropy of activation
(AS*) for mixtures of 4-fluoroamline + 1-propanol.
Vol. % of
AH*
AS*
4-fluoroaniline
kJ/mole
J/mole/°k
0
14.78
0.218
10
9.87
0.205
20
9.83
0.208
30
10.40
0.212
40
10.26
0.214
50
10.35
0.216
60
8.95
0.212
70
8.61
0.212
80
6.46
0.206
90
7.78
0.211
100
5.85
0.205
164
Table 7.3 (1)- The Kirkood factors geff and gf for mixtures of aniline + 1-propanol at
different temperatures.
Vol. % of
20° C
30° C
40° C
50°C
g eff
Aniline
geff
gf
0
3.22
1.000 3.12
1.000 3.15
1.000 3.03
1.000
10
2.85
0.926 2.78
0.933 2.74
0.912 2.66
0.920
20
2.48
0.853 2.44
0.863 2.41
0.849 2.36
0.862
30
2.23
0.815 2.18
0.821 2.14
0.803 2.18
0.847
40
1.96
0.769 1.92
0.779 1.90
0.762 1.85
0.769
50
1.72
0.734 1.69
0.746 1.67
0.731 1.66
0.748
60
1.51
0.715 1.51
0.740 1.50
0.728 1.51
0.751
70
1.36
0.730 1.33
0.743 1.35
0.740 1.34
0.753
80
1.21
0.758 1.21
0.795 1.20
0.773 1.19
0.782
90
1.06
0.821 1.04
0.844 1.06
0.840 1.08
0.861
100
0.95
1.000 0.90
1.000 0.93
1.000 0.94
1.000
geff
gf
165
geff
gf
gf.
Table 7.3 (2)- The Kirkwood factors geff and gf for mixtures o f 2-chloroaniline + 1-
Vol. % of
20° C
O
o
propanol at different temperatures.
30° C
C
50°C
2-chloroaniline geff
gf
0
3.22
1.000 3.13
1.000 3.15
1.000 3.03
1.000
10
2.91
0.960 2.86
0.972 2.85
0.960 2.76
0.932
20
2.63
0.927 2.60
0.943 2.59
0.935 2.50
0.901
30
2.27
0.864 2.24
0.875 2.22
0.863 2.19
0.852
40
1.97
0.817 1.98
0.842 1.93
0.816 1.92
0.813
50
1.70
0.780 1.71
0.806 1.70
0.794 1.71
0.798
60
1.50
0.771
1.50
0.789 1.51
0.791
1.51
0.787
70
1.32
0.779 1.32
0.797 1.33
0.794 1.33
0.795
80
1.16
0.807 1.14
0.813 1.16
0.819 1.18
0.831
90
1.02
0.878 1.02
0.898 1.02
0.888 1.00
0.866
100
0.87
1.000 0.86
1.000 0.87
1.000 0.88
1.000
geff
gf
166
geff
gf
geff
gf
Table 7.3 (3)- The Kirkwood factors geff and gf for mixtures o f 3-chloroaniline +
1-propanol at different temperatures.
Vol. % o f
20° C
30° C
40° C
50°C
3-chloroaniline geff
gf
0
3.22
1.000 3.13
1.000 3.15
1.000 3.03
1.000
10
2.64
0.942 2.68
0.981 2.64
0.962 2.58
0.975
20
2.25
0.919 2.23
0.973 2.22
0.925 2.18
0.938
30
1.92
0.898 1.87
0.897 1.88
0.895 1.82
0.893
40
1.62
0.872 1.60
0.879 1.61
0.877 1.60
0.897
50
1.38
0.856 1.38
0.873 1.40
0.875 1.40
0.890
60
1.21
0.865 1.21
0.877 1.21
0.874 1.20
0.876
70
1.06
0.879 1.05
0.880 1.06
0.881 1.07
0.894
80
0.92
0.896 0.92
0.906 0.93
0.905 0.94
0.907
90
0.82
0.941 0.85
0.984 0.82
0.940 0.83
0.930
100
0.72
1.000 0.73
1.000 0.74
1.000 0.76
1.000
g"
gf
167
geff
gf
geff
gf
Table 7.3 (4)-The Kirkwood factors geff and gf for mixtures o f 4-fluoroaniline +
1-propanol at different temperatures.
Vol. % o f
20 UC
-fluoroaniline geff
gf
30 °C
geff
gf
40 °c
geff
gf
47 UC
geff
gf
0
3.22
1.000 3.12
1.000 3.15
1.000 3.03
1.000
10
2.83
0.964 2.76
0.966 2.74
0.951 2.70
0.975
20
2.46
0.918 2.43
0.930 2.40
0.912 2.42
0.952
30
2.17
0.887 2.16
0.902 2.14
0.887 2.14
0.918
40
1.97
0.881
1.97
0.901 1.95
0.882 1.94
0.905
50
1.81
0.888 1.80
0.898 1.81
0.895 1.77
0.899
60
1.67
0.897 1.66
0.906 1.64
0.885 1.66
0.917
70
1.57
0.925 1.56
0.933 1.55
0.912 1.56
0.937
80
1.45
0.937 1.45
0.950 1.47
0.945 1.44
0.947
90
1.35
0.966 1.37
0.981 1.38
0.973 1.35
0.963
100
1.27
1.000 1.27
1.000 1.29
1.000 1.28
1.000
168
7.4 D iscussion :
The variation in static dielectric constant (e<>) and relaxation time (x) with volume fraction
o f anilines in 1-propanol at different temperatures are shown in Figures 7.1-7.4. In an ideal
mixture o f polar liquids, if the molecules are non-interacting, a linear variation in static
dielectric constant and relaxation time with concentration is expected. But, Figure 7.1-7.4
show nonlinear variation in dielectric constant and relaxation time v/ith change in volume
fraction o f anilines in the 1-propanol. This suggests that the intermolecular association is
taking place in ail these systems.
The relaxation times for aniline, 2-chloroaniline and 3-chloroaniline at 20° C are 16.6 ps,
26.2 ps and 50.0 ps [Table 7.1(1)-7.1(3)] respectively. This shows that there is a
systematic increase in relaxation time, when chlorine group shifts from 2- to 3- position
with respect to the amino group. Similar behavior was observed by Srivastava and Vij 16
in their study o f 2-, 3- and 4-chloroanilines in dilute benzene solutions.
The excess properties related to permittivity and relaxation time provide valuable
information regarding interaction between the polar-polar liquid mixtures. The excess
dielectric constant eoE o f the mixtures was calculated using equation (7.2) and was
plotted against the mole fraction o f 1-propanol in the mixtures. The plots are shown in
Figure-7.5 to 7.8. From the plots it can be seen that eoE is negative for all concentrations
o f 1-propanol in the mixture, for all the four systems at all temperatures studied. This
indicates that the molecules of the mixtures may form multimer structures via hydrogen
bonding in such a way that the effective dipole moment gets reduced. It can also be seen
from the plots that eoE is maximum negative at around 0.55 mole fraction o f 1-propanol
in the mixture o f aniline + 1-propanol, 0.60 mole fraction o f 1-propanol in the mixtures
o f 2-chloroaniline + 1-propanol and 3-chloroaniline + 1-propanol and 0.65 mole fraction
o f 1-propanol in mixture of 4-fluoroaniline + 1-propanol at all the temperatures. This
suggests the stronger intermolecular association between the constituent molecules at
these concentrations.
169
o
CM
Static dielectric constan
m
CM
to
t-
r-
o
m
o
V o f, fr. o f aniline
CM
on o
i
o o
m
CM
o
bo
o
co
o
o
io
o
tn o
o o
t-
R e la x a tio n T im e in ps.
o
o
co
0)
c
CO
" c
o
M—
Figure 7.1- Variation o f (a) static dielectric constant e 0 and (b) relaxation time
t with volume fraction of aniline in the mixture at various temperatures.
170
Static dielectric
constant
0 J---------- ,---------- ,-----------,-----------,---- ----0
0.2
0.4
0.6
Vol fr of 2-chloroaniline
0.8
1
CM
d
o
4^
o
k >
00
o
o
CN
Relaxation time in pt
CO
Vol. fr.of 2-chloroaniline
Figure 7.2- Variation of (a) static dielectric constant eo and (b) relaxation time
volume fraction of 2-chloroaniline in the mixture at various temperatures.
t with
171
S ta tic d ie le c tric c o n s ta n t
—
-$ — 20 degC
e — 3 0 deg C
-jftr -4 0 d e g C
X — SO degC
r ".
0.2
0.4
0.6
0.8
R elaxation tim e in ps
Vol. fr. of 3-chloroaniline
0 .2
0 .4
0 .6
0.8
V o l. fr. O f 3 -e h lo ro a n iiin e
Figure 7.3- Variation o f (a) static dielectric constant eo and (b) relaxation
time x with volume fraction o f 3-chloroaniline in the mixture at various
temperatures.
172
Static dielectric
constant
—*— 20 deg C —a— 30 deg C
...* -40 deg C —* — 50 deg C
0.4
0.6
0.8
Vd. fr. of 4-fluoroaniline
—
20degC
—s— 30degC
■ & 40 deg C
—* — SOdegC
8 8 8
Relaxation time in ps.
o
0.2
0.2
0.4
0.6
0.8
Vd. fr. of 4-fluoroaniline
Figure 7.4- Variation o f (a) static dielectric constant eo and (b) relaxation
time x with volume fraction o f 4-fluoroaniline in the mixture at various
temperatures.
173
o
!
-a
t
ro
i
w
Excess dielectric constant
l
Mol. fr. of 1-propanol
Figure 7.5- Excess dielectric constant gqE as a function o f mole fraction o f
1-propanol in the mixture o f aniline + 1-propanol at different temperatures.
Mlfr.CT 1-prcpand
Figure 7.6- Excess dielectric constant goE as a function o f mole fraction o f
1-propanol in the mixture o f 2-chloroaniline + 1-propanol at different
temperatures.
174
Mol. fr. of 1-propanol
Figure 7.7- Excess dielectric constant sqE as a function o f mole fraction of
1-propanol in the mixture o f 3-chloroaniline + 1-propanol at different
temperatures.
- a— 40 deg C —* — 50 deg C
-2 5
Mol. fr. of 1-propanol
Figure 7.8- Excess dielectric constant SoE as a function o f mole fraction o f
1-propanol in the mixture o f 4-fluoroaniline + 1-propanol at different
temperatures.
175
The calculated values o f excess inverse relaxation time ( l/t) E o f the mixtures using
equation (7.3) was plotted against the mole fraction o f 1-propanol in the mixtures. The
plots are shown in the Figures 7.9-7.12. These plots show different trends for different
systems.Following conclusions can be drawn from these plots.
(i)
(1/ t)£ values are negative for all concentrations of 1-propanol in aniline +
1-propanol mixture at all temperatures except at 50° C. This indicates that the
addition o f 1-propanol to aniline has created a hindering field such that the
effective dipoles rotate slowly. At 50° C, for low concentration o f 1-propanol
( l/t) £ is positive, this indicates that at this temperature and concentration, the
molecular interaction produces a field such that the effective dipoles rotate faster,
i. e. the field cooperates in the rotation of dipoles.
(ii)
In case o f mixtures of 2-chloroaniline + 1-propanol ( l/t) E values are positive for
lower concentration of 1-propanol and becomes negative at higher concentration of
1-propanol at all temperatures except at 50 °C. This suggests that at lower
concentration o f 1-propanol the molecular interaction produces a cooperative field
and the effective dipoles have more freedom of rotation. But at higher
concentration o f 1-propanol the molecular interaction produces hindering field
making effective dipole rotations slower. In this mixture at 50 °C no sign inversion
in (1/ t) e value is observed with change in concentration o f 1-propanol. This means
that at this temperature addition o f 1-propanol to 2-chloroaniline has created a
hindering field so that the effective dipole rotates slowly.
(iii)
In case o f mixture of 3-chloroaniline + 1-propanol (l/x)E values are positive for
all concentration of 1-propanol in the mixture at all temperatures, in general. This
suggests the cooperative nature o f the molecular interacting field, providing more
freedom of rotation to the effective dipoles.
(iv)
In case o f mixtures of 4-fluoroaniline + 1-propanol (l/t) E values are positive for
all temperature s except at 50 °C for which those are negative in 1-propanol rich
region. This indicates that the addition of 1-propanol to 4-fluoroaniline has
created a cooperative field such that the effective dipoles rotate faster.
176
From the Table 7.3 it can be seen that geff values for pure aniline are close to unity for all
temperatures studied indicating no dipole correlation. The geff values for pure 2chloroaniline and 3-chloroaniline are less than unity indicating antiparallel alignment o f
dipoles.
In pure liquid state, geff values greater than unity for 4-fluoroaniline and 1-
propanol suggests that these molecules tend to direct themselves with parallel dipole
moments. In all the four systems the geff value decreases from geff value o f 1-propanol to
that o f pure aniline with increase in concentration o f aniline at all temperatures.
The gf values are less than unity for entire range o f concentration o f anilines in 1propanol, in all the four systems at all the four temperatures. The extent o f departure o f g f
from unity represents the degree o f interaction. It is observed that the departure from unity
in these systems is in the order o f aniline > 2-chloroaniline > 3-chloroaniline > 4fluoroaniline. This suggests that the molecular interaction is the strongest in the aniline +
1-propanol system among all the four systems studied.
177
Figure 7.9- The excess inverse relaxation time (l/t) E for aniline + 1-propanol
mixture as a function o f mole fraction o f
1-propanol at different
temperatures.
MoI.fr. of 1-propanol
Figure 7.10- The excess inverse relaxation time ( l/t) E for 2-chloroaniline +
1-propanol mixtures as a function o f mole fraction o f 1-propanol at different
temperatures.
178
( 1 / t)e * 103
M o l- f r . o f 1 - p r o p a n o l
Figure 7.11- The excess inverse relaxation time ( l/t) E for 3-chloroaniline + 1propanol mixtures as a function o f mole fraction o f 1-propanol at different
temperatures
Figure 7.12- The excess inverse relaxation time (l/x)E for 4-fluoroaniline + 1propanol mixtures as a function o f mole fraction o f 1-propanol at- different
temperatures
179
References :
1. Stockhausen, M. and Busch,H., Phys. Chem. Liq., 22 (1996) 183.
2. Mashimo, S. and Umehara, T., J. Chem. Phys., 95 (1991) 6257.
3. Sato, T., Niwa, H., Chiba, A., Nozaki, R., J. Chem. Phys., 108 (1998) 4138.
4. Roy, G.S. and Swain, B.B., Phys.Chem.Liq.,IS (1988) 61.
5. SyaL, V. K., Becker, U., Elsebrock, R. and Stockhausen, M., Z. Naturforsch, 52 (a)
(1997) 675.
6. Helambe, S.N.,Chaudhary, A. and Mehrotra, S.C., J. Mol. Liq. 84 (2000) 235.
7. Swain, B.B., Ph.D. Thesis, (Uttakal University, India), (1986).
8. Oswal, S.L. and Desai, H.S., Fluid Phase Equi., 161 (1999) 191.
9. Fattepur, R.H., Hosamani, M.T., Deshpande, D.K., Mehrotra, S.C., J. Chem.Phys.,
101(11) (1994) 9956.
10. Chaudhari, A., Khirade, P.,Singh,R., Helambe, S.N.,Narain, N.K. and Mehrotra, S.C.,
JM ol. Liq., 82 (1999) 245.
11. Al-Azzawal, S.F., Awwad, A.M., Al-Dulaji, A.M. and Al-Noori, M. K., J. Chem.
Eng. Data, 35 (1990) 463.
12. Glasstone, S., Laidler, K. J. and Erying, H., Theory o f Rate Processes, McGraw Hill,
New York (1941).
13. Kirkwood, J.G., J. Chem. Phys., 7 (1939) 911.
14. Puranik, S.M., Kumbharkhane, A.C.and Mehrotra, S.C., J. Mol. Liq., 50 (1991) 143.
15. Kumbharkhane, A.C., Puranik, S.M. and Mehrotra, S.C., J. Sol. Chem., 22 (1993)
219.
16. Srivastava, K.K. and Vij, J.K., Bull. Chem. Soc. Japan, 43 (1970) 2307.
180
CHAPTER-VIII
DIELECTRIC RELAXATION OF SOME RIGID POLAR
MOLECULES AND THEIR BINARY MIXTURES IN BENZENE
SOLUTION
8.1 Introduction :
Dielectric relaxation in mixtures o f polar liquids has been studied by several workers1'8
because, it gives information about solute-solute and solute-solvent interactions. Less
work has been reported on dielectric relaxation o f mixtures of rigid polar molecules and
few measurements have been carried out on dielectric properties o f mixtures of
nonassociative polar molecules in nonpolar solvents. The dielectric relaxation behavior of
mixtures of rigid polar molecules provides useful information about the relaxation
processes and also helps in developing suitable models for liquid relaxation. Madan 9-13
studied the dielectric relaxation behavior of some rigid polar molecules and their
mixtures and found that the relaxation time o f mixture lies between those found for the
individuals measured in the same solvent mixtures. Recent investigation by Abd-ElMessieh14 on dielectric absorption o f 4-nitrobenzyl chloride, 1,2,3-trichlorobenzene and
cyclohexyl chloride and their binary mixtures in dilute carbon tetrachloride and decalin
carried out over a wide range of frequency and temperature shown similar results. We
studied 15-17 some rigid polar molecules and their mixtures in benzene solution and found
that molecules retain their characteristic dielectric behavior in the mixtures o f nonpolar
solvent, the single relaxation time for mixture indicated the fact that the volume
participating in relaxation is sufficiently large to have a composition indistinguishable
from overall average.
In order to gain more information in this area microwave
absorption in pyridine and its mixture with benzonitrile were studied at different
temperatures in dilute solutions o f benzene and results are reported in this Chapter.
181
8.2 Experimental :
Pyridine, AR grade (Sd Fine-Chem Co.Ltd.) and Benzonitrile, purum grade (Fiuka A.G.
Switzerland) was used without further purification. Benzene, AR grade (Qualigens,
India) was used after fractional distillation. The mixture o f pyridine and benzonitrile was
prepared by talcing polar components in equal mole. This mixture was taken as solute and
added to non-polar solvent. Five dilute solutions o f pyridine, benzonitrile and mixture o f
pyridine + benzonitrile were prepared using benzene as non-polar solvent.
The dielectric permittivity ( e ’) and dielectric loss (€ ”) have been measured for pyridine,
benzonitrile and their binary mixture in benzene solution at microwave frequency 9.1
GHz. The static permittivity eo at frequency 455 kHz and permittivity at optical frequency
e® were also measured. All the measurements were carried out at 20, 30, 40 and 47 °C
and tihe temperature was controlled thermostatically to within ± 0.5°C by a thermostat. The
experimental method adopted for the measurement o f eo, s ’, e ” and e® have been
described in Chapter -III. The measured values o f so, e \ e ” and 6® are given Table-8.1.
The most probable relaxation time (to) and distribution parameter (a) were determined
using Higasi’s single frequency method as described in Chapter-Ill.
8.3 Results and Discussion :
eo. e ’, e ” and e® o f solutions were plotted against weight fraction o f the solute, the
plots are linear, the slopes ao, a’, a” and a« for pyridine and its mixture with benzonitrile
at different temperatures are listed in Table 8.2. The dielectric data for benzonitrile from
our previous studies (Chapter-IV) is also included in this table for comparison. The
values o f most probable relaxation time (to) and distribution parameter (a ) evaluated
using these slopes for systems investigated at different temperatures are presented in
Table 8.3. It is evident from the Table 8.3 that distribution parameter (a) for pyridine and
benzonitrile is zero at different temperatures. Miller and Smyth 18 studied pyridine in
benzene at different temperatures and found zero value o f distribution parameter. A very
small value o f distribution parameter was reported by Halland and Smyth 19 for pyridine.
This is a usual behavior o f rigid polar molecules in non-polar solvents, they exhibit
182
Table 8.1 (1)- Values of Go,
€ ’, g ”
and G<»of solutions of pyridine in benzene at different
temperatures.
Cone,
455 KHz
Cone.
in wt. fr.
eo
inwt.fr.
9.1GHz
g’
g”
Cone,
Optical
in wt. fr.
Goo
TEMPERATURE = 20 °C
0.0044
2.324
0.0044
2.330 0.062
0.0044
2.2596
0.0153
2.391
0.0153
2.422 0.025
0.0153
2.2605
0.0256
2.477
0.0256
2.502 0.041
0.0256
2.2617
0.0372
2.569
0.0372
2.547 0.059
0.0372
2.2626
0.0477
2.646
0.0477
2.619 0.081
0.0477
2.2638
TEMPERATURE - 30 °C
0.0044
2.324
0.0044
2.322 0.008
0.0097
2.2410
0.0153
2.391
0.0153
2.359 0.024
0.0182
2.2416
0.0256
2.477
0.0256
2.462 0.038
0.0302
2.2456
0.0373
2.569
0.0373
2.549 0.059
0.0370
2.2434
0.0477
2.646
0.0477
2.623 0.079
0.0475
2.2440
TEMPERATURE = 40 °C
0.0065
2.336
0.0076
2.322 0.009
0.0065
2.2261
0.0236
2.434
0.0142
2.371 0.018
0.0236
2.2267
0.0296
2.481
0.0220
2.412 0.024
0.0296
2.2276
0.0348
2.516
0.0293
2.449 0.038
0.0348
2.2281
0.0457
2.588
0.0373
2.496 0.045
0.0457
2.2290
TEMPERATURE = 47 °C
0.0065
2.337
0.0076
2.309 0.005
0.0065
2.2177
0.0236
2.429
0.0142
2.346 0.018
0.0236
2.2186
0.0296
2.470
0.0220
2.386 0.023
0.0296
2.2192
0.0348
2.511
0.0293
2.430 0.032
0.0348
2.2198
0.0457
2.575
0.0373
2.470 0.038
0.0457
2.2207
183
Table 8.1 (2)- Values of Go, e ’,e ” and e® of solutions of benzonitrile in benzene at
different temperatures.
Cone,
455 KHz
Cone,
in wt. fr.
eo
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
£co
TEMPERATURE = 20 UC
0.0036
2.315
0.0036
2.355 0.059
0.0036
2.2320
0.0085
2.396
0.0085
2.414 0.090
0.0085
2.2335
0.0119
2.465
0.0119
2.460 0.112
0.0119
2.2350
0.0159
2.531
0.0159
2.506 0.141
0.0159
2.2365
0.0207
2.602
0.0207
2.556 0.171
0.0207
2.2380
TEMPERATURE = 30 °C
0.0092
2.448
0.0025
2.329 0.032
0.0092
2.2326
0.0134
2.568
0.0044
2.359 0.039
0.0134
2.2335
0.0181
2.622
0.0080
2.412 0.054
0.0181
2.2350
0.0239
2.730
0.0134
2.473 0.097
0.0239
2.2356
0.0280
2.815
0.0162
2.502 0.114
0.0280
2.2365
TEMPERATURE = 40 °C
0.0036
2.272
0.0036
2.322 0.039
0.0036
2.2156
0.0085
2.315
0.0085
2.371 0.058
0.0085
2.2165
0.0119
2.395
0.0119
2.435 0.093
0.0119
2.2171
0.0159
2.457
0.0159.
2.482 0.102
0.0159
2.2174
0.0207
2.541
0.0207
2.508 0.130
0.0207
2.2177
TEMPERATURE = 47 °C
0.0036
2.256
0.0036
2.303 0.034
0.0036
2.2052
0.0085
2.336
0.0085
2.356 0.069
0.0085
2.2058
0.0119
2.403
0.0119
2.398 0.084
0.0119
2.2067
0.0159
2.446
0.0159
2.447 0.107
0.0159
2.2073
0.0207
2.551
0.0207
2.491 0.128
0.0207
2.2076
184
Table 8.1 (3)- Values of €o, e ’,e ” and e«> of solutions of mixture of pyridine +
benzonitrile in benzene at different temperatures.
Cone,
455 KHz
Cone,
in wt. ff.
eo
in wt. fr.
9.1 GHz
e’
e”
Cone,
Optical
in wt. fr.
€ oo
TEMPERATURE = 20 UC
0.0067
2.329
0.0067
2.354 0.053
0.0067
2.2650
0.0119
2.401
0.0119
2.428 0.071
0.0119
2.2656
0.0162
2.444
0.0162
2.470 0.089
0.0162
2.2665
0.0212
2.514
0.0212
2.519 0.118
0.0212
2.2674
0.0250
2.578
0.0250
2.539 0.143
0.0250
2.2680
TEMPERATURE = 30 °C
0.0045
2.331
0.0045
2.356 0.040
0.0045
2.2593
0.0081
2.386
0.0081
2.392 0.053
0.0081
2.2596
0.0113
2.422
0.0113
2.414 0.077
0.0113
2.2599
0.0156
2.469
0.0156
2.452 0.093
0.0156
2.2602
0.0216
2.530
0.0216
2.513 0.116
0.0216
2.2605
TEMPERATURE = 40 °C
0.0067
2.347
0.0067
2.333 0.037
0.0067
2.2261
0.0119
2.399
0.0107
2.398 0.057
0.0107
2.2276
0.0162
2.432
0.0164
2.442 0.078
0.0162
2.2291
0.0212
2.511
0.0228
2.517 0.108
0.0228
2.2305
0.0250
2.568
0.0267
2.543 0.117
0.0267
2.2320
TEMPERATURE = 47 °C
0.0067
2.336
0.0067
2.326 0.027
0.0067
2.2320
0.0119
2.421
0.0107
2.352 0.051
0.0107
2.2192
0.0162
2.461
0.0164
2.430 0.074
0.0162
2.2195
0.0212
2.521
0.0228
2.482 0.095
0.0228
2.2201
0.0250
2.574
0.0267
2.517 0.111
0.0267
2.2207
185
Table-8.2 Values o f ao, a’, a” and a» o f single component as well as their mixture
in benzene solution at different temperatures.
Temperature (°C)
a’
a”
a«
PvTidine
20
7.57
7.12
1.74
0.09
30
6.87
6.50
1.50
0.07
40
6.20
5.95
1.18
0.08
47
5.70
5.50
1.00
0.08
Benzonitrile
20
17.02
11.22
7.90
0.36
30
15.60
11.00
7.00
0.21
40
14.75
10.80
6.40
0.23
47
14.00
10.50
5.95
0.23
Pvridine + Benzonitrile
20
12.73
10.20
4.95
0.17
30
12.00
9.90
4.48
0.08
40
11.16
9.54
3.85
0.29
47
10.83
9.33
3.65
0.12
186
Table 8.3- Values o f relaxation time (x0) and distribution parameter (a) o f single
component as well as their mixture in benzene solution at different temperatures.
Temperature
Distribution
Relaxation
(°C)
parameter
time inps
Pvridine
20
0.00
4.3
30
0.00
4.1
40
0.00
3.5
47
0.00
3.2
Benzo nitrile
20
0.00
12.8
30
0.00
11.4
40
0.00
10.6
47
0.00
10.2
Pvridine + Benzonitrile
20
0.00
8.6
30
0.00
8.0
40
0.00
7.3
47
0.00
7.0
187
Table 8.4 - Thermodynamical parameters of single component as well as their
mixture in benzene solution.
Temp
AFe
ah6
a s6
(K)
kCal/mol
kCal/mol
Cal/mol/degree
Pvridine
1.42
-1.63
293
1.90
303
1.95
-1.76
313
1.95
-1.69
320
1.94
-1.64
Benzonitrile
-5.83
293
2.54
0.83
303
2.57
-5.76
313
2.64
-5.78
320
2.68
-5.79
Pyridine + Benzonitrile
-4.29
1.05
293
2.31
303
2.36
-4.31
313
2.40
-4.31
320
2.44
-4.34
188
Debye type relaxation mechanism. The relaxation time obtained for pyridine at different
temperatures is in agreement with the literature values 20-22. As reported in our previous
studies (Chapter-IV) dielectric behavior o f benzonitrile in benzene solution can be
described by Debye type relaxation mechanism, the observed value o f relaxation time for
benzonitrile (Table-8.3) is in agreement with literature value 10.
The dielectric data on binary mixture o f pyridine and benzonitrile were analyzed in a
similar manner as for single component system. The distribution parameter (a) for
mixture at different temperatures have zero value, indicating a single relaxation process.
Further, it is interesting to note that relaxation time (to) o f the mixture at different
temperatures (Table-8.3) are the average value o f the relaxation times o f the components.
The trend is similar to our earlier studies o f mixtures o f rigid polar molecules. This close
agreement offers an evidence to the fact that the each component retain their
characteristic dielectric behavior in the mixture, the single relaxation time o f the mixture
is simply due to overlap o f two Debye type relaxation processes.
A plot o f ln(xoT) versus 1/T o f the pyridine exhibit linear relationship (Figure-8.1),
showing that the decay o f relaxation time with temperature is exponential. Similar results
were obtained in the case o f the mixture (Figure-8.2). These relationships therefore can
be represented by the rate process. Accordingly the free energy o f activation AFe, the
enthalpy o f activation AHe and the entropy o f activation AS6 can be evaluated from
Eyring’s equations (described in Chapter-Ill). These evaluated thermodynamical
parameters for single components as well as for mixture are presented in Table-8.4. It is
evident from the Table-8.4 that the activation energy o f the mixture lies between those
for individuals, which also suggest that the molecules retain their characteristic dielectric
behavior in the mixture.
189
Figure 8.1-Plot of In (x0T) against 1/T for pyridine in benzene solution.
Figure 8.2- Plot o f In (toT) against 1/T for the mixture o f pyridine + benzonitrile
in benzene solution.
190
References :
1. Saad, A.L.G., Shaifik, A. H. and Hanna, F. F„ Indian J Phys., 72B(5)(1998) 495.
2. Chaudhari, A., Raju, G. S., Das, A., Chaudhari, H., Narain, N. K. and
Mehrotra, S.C., Indian J. Pure andAppl. Phys., 39 (2001) 180.
3. Thakur, N. and Sharma, D. R., Indian J. Pure and Appl. Phy., 38(2000)328.
4. Varadrajan, R. and Rajagopal, A., Indian J. Pure and Appl. Phy., 36(1998)13.
5. Madhurima, V., Murthy, V. R. K., Sobhanadri, J., Indian J. Pure and Appl. Phys, 36
(1998) 144.
6. Sit, S. K., Ghosh, N., Saha, U. and Acharyya, S., Indian J. Phys., 71B(4)(1997) 533.
7. Fattepur, R. H., Hosamani, M. T., Deshpande, D. K. and Mehrotra, S. C., J.
Chem.Phys., 101 (1994) 9956.
8. Subramanian, V., Bellubbi, B. S. and Sobhanadri, J., PramanaJ. Phys., 41 (1993) 9.
9. Madan, M. P„ J Mol. Liq., 33 (1987) 203.
10. Madan, M. P.,Can. J. Phys, 65 (1987) 1573.
11. Madan, M P, JM o l Liq, 29 (1984) 161.
12. Madan, M. P., Can. J. Phys., 58 (1980) 20.
13. Madan, M. P., Shelfoon, M. and Cameron, I., Can. J. Phys., 55 (1977) 878.
14. Ebd-El-Messieh, S. L., Indian J. Phys., 70B(2) (1996) 119.
15. Vyas, A. D. and Vashisth, V. M., J. Mol. Liq., 32 (1986) 83.
16. Vyas, A. D. and Vashisth, V. M., Indian J. Pure andAppl. Phys., 26 (1988) 484.
17. Vyas, A. D., Vashisth, V. M., Rana, V. A., and Thaker, N. G., J. Mol. Liq., 62 (1994)
221.
18. Miller, R. C. and Smyth, C. P., J. Am. Chem. Soc., 79 (1957) 308.
19. Holland, R. S. and Smyth, C. P„ J. Am. Chem. Soc., 59 (1955) 1088.
20. Gowarikrishna, J. and Sobhanadri, J., Indian J. Pure andAppl. Phys., 22 (1984) 599.
21. Gupta, T., Chauhan, M., Saxena, S. K. and Shukla, J. P., Adv. in Mol. Relax, and
Inter. Proc., 23 (1982) 203.
22. Suryavanshi, B. M. and Mehrotra, S. C., Indian J. Pure and Appl. Phy., 29 (1991)
482.
191
A TVTS lsTTfc T V
I^JuLAJ: 1 JL K 1 A
SUMMARY
Dielectric relaxation in some polar molecules and their binary mixtures was studied at
microwave frequencies in dilute solutions o f non-polar solvent benzene and in pure liquid
state. While, the complex permittivity o f the polar molecules and their binary mixtures in
dilute solutions was measured in frequency domain, time domain reflectometry (TDR)
technique was used to measure the complex permittivity o f polar liquids in pure state. The
dielectric data was obtained for different temperatures and were used to evaluate
relaxation time, distribution parameter, thermodynamical parameters, excess permittivity,
excess inverse relaxation time and Kirkwood correlation factor. The results have been
used to investigate the dielectric relaxation behaviour o f the polar molecules and their
mixtures and also, to reveal the presence o f the molecular interaction among the
molecular species o f the mixture. The binary mixtures o f polar liquids studied can be
divided into the following three categories.
(I)
Non-associative (flexible) + non-associative (rigid)
(II)
Non-associative + associative
(III)
Rigid + rigid
(II Non-associative (flexible') + non-associative frigid!:
The molecules and their mixtures studied in this category are
(i)
Aniline, benzonitrile and their mixtures.
(ii)
2-chloroaniline, nitrobenzene and their mixtures
(iii)
4-fluoroaniline, pyridine, chlorobenzene, benzophenone and the mixture o f 4fluoroaniline with each o f pyridine, chlorobenzene and benzophenone.
192
Out o f these three systems the first two systems were studied using a single frequency
concentration variation method at different temperatures. The dielectric data was used to
evaluate the relaxation time (to), distribution parameter (a ) and thermodynamical
parameters. The value o f distribution parameter for these molecules suggested the
presence o f group rotation in addition to overall rotation for aniline and 2-chloroaniline, a
single relaxation time has been found for nitrobenzene and benzonitrile. Mixtures o f
aniline + benzonitrile and 2-chloroaniline + nitrobenzene showed different relaxation
behaviour. Simple Debye type relaxation mechanism was found in the former system
whereas more than one relaxation processes was found to exist in the later system. The
observed values o f relaxation time for both the mixtures indicated solute-solute/solvent
type o f interactions. To gain more information dielectric dispersion studies were carried
out for the third system. For this system dielectric measurements were done at room
temperature only. The observed data was analyzed using Cole-Cole method o f analysis to
obtain relaxation time (to) and distribution parameter (a). Pyridine, chlorobenzene and
benzophenone in benzene solution showed Debye type o f relaxation process, but, their
mixtures with 4-fluoroaniline in benzene solution showed more than one relaxation
processes. The analysis was carried out in terms o f two relaxation times for 4fluoroaniline and its mixtures with pyridine, chlorobenzene and benzophenone. It has
been found that the relaxation time for group rotation (T2) is o f the same order for 4fluoroaniline and for mixtures. These results show that the components in the mixture
retained their identity. Molecular interaction through N — H type o f bonding was found in
the mixture o f 4-fluoroaniline with pyridine but no such association was observed in the
mixture o f 4-fluoroaniline with chlorobenzene and benzophenone.
(IDNon-associative + associative:
The molecules and their mixtures studied in this category are,
(i)
2-bromoaniline, 3-bromoaniline, 4-bromoaniline, 1-propanol and the mixtures o f
1-propanol with each o f aniline, 2-bromoaniline, 3-bromoaniline and 4bromoaniline in dilute solutions o f benzene.
193
(ii)
Mixtures of 1-propanol with each o f aniline, 2-chloroaniline, 3-chloroaniline and
4-fluoroaniline in pure liquid state.
Out o f these two systems the first system was studied using single frequency
concentration variation method at different temperatures. The dielectric data was used to
evaluate the relaxation time (io) and distribution parameter (a). The relaxation times o f
aniline, 2-bromoaniline, 3-bromoaniline and 4-bromoaniline showed a systematic
increase in relaxation time when the position o f substituted bromo group is shifted from
2- to 3- to 4- position with respect to -N H 2 group. Similarly the distribution parameter
also increased when bromine group is shifted from 2- to 3- to 4- position with respect to
-N H 2 group. Similar behaviour was observed in the case o f mixtures o f 1-propanol with
bromoanilines at different temperatures in benzene solution. The increase in relaxation
time o f the mixtures showed the similar pattern to that o f individual components. The
non-linear variation o f relaxation time o f the mixture with concentration o f anilines in 1propanol + aniline mixture, indicated solute-solute type o f interaction- The possible
hetero interaction between 1-propanol and aniline through hydrogen bonding is NH2 OH or OH - NH2 type o f linkage. The IR spectra o f 1-propanol + aniline in CCLt favored
the NH2 - OH type o f linkage. The distribution parameter o f the mixtures (aniline, 2-,
3- , and 4-bromoanilines with 1-propanol) at different temperatures is finite, indicating
more than one relaxation processes in these systems.
The measurement o f dielectric properties for the second system (pure liquid) using TDR
technique also provided a good evidence o f solute-solute type o f interactions in the
mixtures o f these molecules. The excess permittivity was found to be negative for all the
mixtures investigated suggesting that the interaction between the molecules be such that
the effective dipole moment of the mixture is reduced. Kirkwood correlation factor geff
for the mixtures as well as the individual components were determined, which provided
useful information regarding the orientation o f the electric dipoles. In aniline no dipole
correlation was observed. 2-chloroaniline and 3-chloroaniline showed anti-parallel
alignment o f dipoles. Whereas 4-fiuoroaniline and 1-propanol showed parallel alignment
o f the dipoles. From the determined value o f gf the strongest molecular interaction was
inferred in the aniline + 1-propanol mixtures among all the four systems studied. It was
194
also inferred that the substitution o f halogen groups in anilines at 2-, 3- and 4- positions
reduces hydrogen bonding between aniline and 1-propanol.
fllD Rigid + rigid:
The relaxation behaviour o f mixtures o f rigid polar molecules has not been studied
extensively. Only one representative mixture o f pyridine + benzonitrile was studied in
dilute solution o f benzene. The results shown that there is an overlap o f two Debye type
of relaxation mechanism. A detailed study at different microwave frequencies (wide
range) o f these molecules would have certainly yielded valuable results and there is a
possibility to resolve dielectric spectra in terms o f two Debye type relaxation processes.
Future Scope:
In this thesis an attempt is made to study the dielectric relaxation behaviour o f some polar
molecules and their binary mixtures and also, to find the presence and the nature of
possible interaction among the molecular species o f the mixtures. The dielectric
relaxation is a complicated process depending on various factors such as dipole moment,
internal field, viscosity, dipolar interaction and probably many other physical parameters.
Furthermore, the interpretation o f dielectric relaxation data is not unique in many cases.
However, if the study is extended to multi frequency measurement covering wider range
o f microwave frequency, it can provide better insight into the relaxation processes taking
place in the polar molecules and their mixtures. Several other physical methods like
measurement o f ultrasonic velocity, density, viscosity and molar volume are found in
literature to study molecular interaction. I f these measurements are also conducted along
with dielectric measurements they will confirm the inferences derived from dielectric
studies.
195
Appendix
List of Publications
1. Dielectric relaxation studies of some polar molecules and their binaiy mixtures in
benzene solutions.
A.D.Vyas and V.A.Rana
Indian Journal o f Pure and Applied Physics, Vol. 36, January 1998, pp. 21-25.
2. Dielectric relaxation in aniline, benzonitrile and their mixtures in benzene
solutions.
A.D.Vyas and V.A.Rana
Indian Journal o f Pure and Applied Physics, Vol. 39, May 2001, pp. 316-320.
3. Dielectric relaxation studies of 1-propyl alcohol and its mixtures with aniline in
benzene solution.
A.D.Vyas and V.A.Rana
Presented at “National Conference on Emerging Trends and Advances in Microwave
Measurements and Techniques (NCMMT-2001) ” Aurangabad , India, March-2001.
(Proceedings to be Published).
4. Dielectric dispersion and relaxation mechanism of some polar molecules and
their binary mixtures in benzene solutions at microwave frequencies.
A.D.Vyas and V.A.Rana
Indian Journal o f Physics, 75A (6), 2001, pp.635-63, (In press).
5. Dielectric relaxation of some rigid polar molecules and their binary mixtures in
benzene solution.
A.D.Vyas and V.A.Rana
Indian Journal o f Pure and Applied Physics, (In press).
6. Dielectric relaxation study of mixtures of 1-propanol with aniline, 2-chloroaniline
and 3-chloroaniline at different temperatures using time domain reflectometry.
V.A.Rana, A.D.Vyas and S.C.Mehrotra
Journal o f Molecular Liquids, (communicated).
7. Dielectric relaxation study of mixtures of 4-fluoroaniiine and 1-propanol.
V.A.Rana, A.D.Vyas and N.M.More
Indian Journal o f pure and Applied Physics, (communicated).
8. Dielectric relaxation in o-bromoaniline and its mixtures with 1-propanol in
benzene solutions.
A.D.Vyas and V.A.Rana
Proceedings o f ‘‘ National Conference on Recent Advances in Microwaves, Antennas
and Propagation, Microwave-2001 ”, Jaipur, India, November,2001.
Indian Journal of Pure & Applied Physics
Vol. 36, January 1998, pp. 21-25
Dielectric relaxation studies of some polar molecules and their
binary mixtures in benzene solutions
A D Vyas* & V A Rana
Department of Physics, University School o f Sciences, Gujarat University, Ahmedabad 380 009
Received 15 May 1997; revised received 4 August 1997; accepted 20 August 1997
Permittivity (e') and dielectric loss (e") of chlorobenzene, nitrobenzene, orthochloroaniline and
mixtures of orthochloroaniline + chlorobenzene, orthochloroaniline + nitrobenzene have been measured
at microwave frequency 9.1 GHz, 10 kHz and optical frequency at 30°C. The relaxation times and
thermodynamical parameters have been determined from the measured data. While the relaxation time
of mixture of orthochloroaniline + chlorobenzene shows absence of any association, the relaxation times
of mixtures of orthochloroaniline + nitrobenzene at different temperatures (20-50°C) indicated presence
of solute-solute and solute-solvent type association. The experimental values of relaxation times of
dipolar mixtures have been compared with the theoretical values obtained by employing different
methods.
1 Introduction
The dielectric relaxation studies are useful to
investigate molecular and intramolecular motions,
solute-solute
interaction
and
solute-solvent
interactions1'2
3*. The early studies were centred at
single component systems either in pure state or its
mixture with non-polar solvents. Recently dielectric
relaxation behaviour of mixtures of polar
molecules4-6 under
varying
conditions
of
composition and temperature has evoked
considerable interest, because it helps in formulating
adequate models of liquid relaxation and also in
obtaining information about the relaxation processes
in mixture. In the present note we report results of
our
studies
on
dielectric
properties
of
orthochloroaniline, chlorobenzene, mixture of
orthochloroaniline + cholorobenzene and mixtures
of orthocloroaniline + nitrobenzene in dilute
solutions of benzene.
measurement of e' was 1% and that o f e" was about
5%. The static permittivity e0 was determined by
using a capacitance measuring assembly type 1620
A, e_ has been taken as the square of refractive
index which has been determined by Abbe
refractometer. Measurements were made at 20, 30,
40 and 50°C and the temperature was
thermostatically controlled to ±0.5°C.
The samples orthochloroaniline purest (Merck,
Germany), nitrobenzene AR grade (Sd Finechem
Co. Ltd., India), chlorobenzene AR grade (SRL
India) were used without any further purification.
Benzene AR grade supplied by Messers BDH was
used after double distillation and drying over
sodium.
The dielectric relaxation time ( t0) and
distribution parameter (a) were calculated using
Higasi's8single frequency measurement method.
2 Experimental Procedure
The dielectric permittivity (e') and dielectric loss
(e") o f solutions at microwave frequency 9.1 GHz
were determined by the measurement of wavelength
in dielectric medium and standing wave ratio, using
a short circuited movable plunger, following the
method suggested by Heston et al.1 and adopted for
short circuited termination. The accuracy of
3 Results and Discussion
The slopes a0, a\ a" and a . determined from the
measured values €0, e', e" and e„ of solution for
single component and mixtures studied are listed in
Table 1. The values of most probable relaxation
time (x0) and distribution parameter (a) for
chlorobenzene, nitrobenzene, orthochloroaniline and
mixtures of orthochloroaniline + chlorobenzene and
orthochloroaniline + nitrobenzene (added in equal
22
INDIAN J PURE APPL PHYS. VOL 36, JANUARY 1998
Table 1 —Values of a' and a" of various substances in benzene solution at different frequency and at different temperatures.
Frequency
9.1 GHz
Substance
10 kHz
<*0
Optical
aM
a’
dm
Temperature = 293°k
Orthochloroaniline
OCA + NB (0.25 of NB)
OCA + NB (0.5 of NB)
OCA + NB (0.75 of NB)
Nitrobenzene
3.55
7.00
10.00
11.70
15.90
2.82
5.00
6.70
7.90
11.20
0.98
2.41
3.80
4.95
6.54
0.22
0.25
0.21
0.22
0.28
0.73
5.41
0.90
0.81
2.33
3.50
4.10
0.15
0.27
0.25
0.25
0.24
0.26
0.25
0.65
1.56
2.70
3.70
4.83
0.24
0.22
0.18
0.27
0.22
0.56
1.20
2.60
3.40
4.30
0.23
0.26
0.24
0.24
0.21
Temperature = 3031c
Chlorobenzene
Nitrobenzene
Orthochloroaniline
OCA + CB (0.5 of CB)
OCA + NB (0.25 of NB)
OCA + NB (0.5 of NB)
OCA + NB (0.75 ofNB)
2.40
14.28
3.27
2.92
6.62
9.00
9.90
2.12
11.11
2.77
2.50
5.16
6.89
7.36
Temperature = 313°k
Orthochloroaniline
OCA + NB (0.25 of NB)
OCA + NB (0.5 of NB)
OCA + NB (0.75 of NB)
Nitrobenzene
2.63
4.96
7.00
9.28
12.85
2.30
4.28
5.60
7.18
10.38
Temperature = 323°k
Orthochloroaniline
OCA+ NB (0.25 ofNB)
OCA + NB (0.5 ofNB)
OCA+ NB (0.75 ofNB)
Nitrobenzene
2.38
4.35
7.20
8.75
11.90
mol) at 30°C in benzene solution are presented in
Table 2. The values o f relaxation time for
chlorobenzene and nitrobenzene in benzene solution
agrees fairly well with literature values9. A very
small value of distribution parameter for
nitrobenzene and zero value o f distribution
parameter for chlorobenzene suggest a simple
Debye type relaxation mechanism in these
molecules. The observed relaxation time for
orthochloroaniline 6.0 ps at 30°C agrees well with
reported values 6.5 ps by Srivastava and Vij10 at the
same temperature and in same solvent. The value of
distribution parameter a(0.11) for this molecule
indicates more than one relaxation processes in this
2.11
3.92
5.94
7.00
10.00
Table 2—The values of relaxation time ( t j and distribution
parameter (a) for individual components and binary mixtures in
benzene at 30°C
Substance
Chlorobenzene (CB)
Nitrobenzene (NB)
Orthochloroaniline (OCA)
OCA + CB
(0.5 Mole fraction of CB)
OCA + NB
(0.5 Mole fraction ofNB)
Relaxation
time in ps
Distribution
parameter
6.4
8.8
6.0
0.00
0.03
0.11
6.1
0.08
9.3
0,04
23
VYAS & RANA: DIELECTRICS OF POLAR & BINARY MIXTURES
the same temperature. The value of relaxation time
system.
The value of relaxation time o f mixture of the mixture indicates that there is no solute-solute
orthochloroaniline + chlorobenzene is 6.1 ps at 30°C or solute-solvent type of interaction in this mixture,
while that of its components are 6.0 ps because the mixture and its components have almost
(orthochloroaniline) and 6.4 ps (chlorobenzene) at same value of relaxation time. But the relaxation
Table 3—The values of relaxation time ( t j and distribution parameters (a) for {OCA + NB) mixtures at different
temperatures in benzene.
Mole fraction of
NB in (OCA + NB
Relaxation
time in ps
Distribution
parameter
Mole fraction o f
NB in (OCA + NB
6.4
9.4
tt.l
11.7
10.8
0.18
0.14
0.12
0.05
0.05
6.0
8.4
9.3
10.2
8.8
5.2
6.6
8.7
9.4
8.3
0.00
0.25
0.50
0.75
1.00
0.10
0.03
0.01
0.01
0.01
Temperature 323°C
Temperature 303°C
0.00
0.25
0.50
0.75
1.00
Distribution
parameter
Temperature 313°C
Temperature 293°C
0.00
0.25
0.50
0.75
1.00
Relaxation
time in pe
0.11
0.08
0.04
0.02
0.04
4.9
5.7
8.0
8.8
7.7
0.00
0.25
0.50
0.75
1.00
0.10
0.02
0.01
0.00
0.00
Table 4—Values of molar free energy, enthalpy and entropy (AFt, AHt, A5e) for dielectric relaxation in the OCA + NB mixtures.
Mole fraction of
NB in (OCA + NB)
mixture
Temp
°K
AFt
kCal/mol
AHt
kCal/mol
ASt
Cal/mol/
degree
0.00
293
303
313
323
2.13
2.19
2.19
2.24
1.13
-3.42
-3.50
-3.39
-3.44
0.25
293
303
313
323
2.36
2.39
2.34
2.34
2.29
-0.25
-0.34
-0.17
-0.16
0.50
293
303
313
323
2.45
2.45
2.51
2.55
1.66
-2.88
-2.62
-2.74
-2.78
0.75
293
303
313
323
2.48
2.51
2.57
2.62
1.12
-4.64
-4.59
-4.63
-4.64
1.00
293
303
313
323
2.44
2.42
2.48
2.53
1.61
-2.83
-2.67
-2.78
-2.85
24
INDIAN J PURE APPL PHYS. VOL 36, JANUARY 1998
Table 5— The experimental values of relaxation time (t0) and theoretically calculated values (t0) for mixtures at 30 C.
Experimental
t 0 in ps
SM
RM
OCA + CB (0.5 Mole fraction
of CB)
6.1
6.2
6.2
6.1
6.1
OCA + NB (0.25 Mole fraction
of NB)
8.4
6.7
6.5
7.4
7.7
OCA + NB (0.5 Mole fraction
of NB)
9.3
7.4
7.1
8.1
8.3
OCA + NB (0.75 Mole fraction
ofNB)
10.2
8.1
7.9
8.5
8.6
time of mixture of orthochloroaniline + nitroben­
zene is 9.3 ps, while that of orthochloroaniline and
nitrobenzene are 6.0 ps and 8.8 ps respectively at
30°C. The value of relaxation time for mixture is
higher than the values of relaxation times of its
components. This indicate a solute-solute or solutesolvent type complex formation in this system. To
get more information this system was studied at
different
temperatures
and
for
different
concentrations. The values of relaxation time ( t0)
and distribution parameter (a) for orthochloro­
aniline, nitrobenzene and their mixtures of different
concentrations and at different temperatures are
given in Table 3. The relaxation time of these
systems is plotted against percentage concentration
of nitrobenzene and the plot is shown in figure 1.
These results also indicate solute-solute or solutesolvent type of interactions in these systems, it seem
that in the mixture of orthochloroaniline and
nitrobenzene, nitrobenzene acts as a rc-acceptor and
orthochloroaniline as electron-donor which makes
the possibility of complex formation feasible by
donating electrons from orthochloroaniline to
nitrobenzene.
The free energy of activation F t , the enthalpy of
activation H e, and entropy of activation Se, were also
evaluated using Eyrings" rate equations, they are
presented in Table 4.
The experimental values of t0 of the mixture of
orthochloroaniline + chlorobenzene and mixtures of
orthochloroaniline + nitrobenzene at 30°C are
compared with the theoretical methods namely
simple mixing rule, reciprocal mixing rule, M.P.
in ps calculated by
Madan
R e la x a tio n tim e {'C o ) in ps
Substance
Yadav & Gandhi
29 3 K
303 K
313 K
323 K
:0
25
50
75
100
125
% of NB in OCA + NB m ixture
Fig. 1— Relaxation time ( t0) in benzene as a percentage of
nitrobenzene in orthochloroaniline + nitrobenzene mixture.
Madan's12 relation and Yadav and Gandhi13 method
in Table 5. It is evident from the table that for
mixture of orthochloroaniline + chlorobenzene the
calculated values by different methods are in
agreement with experimental value. But, for the
mixtures of orthochloroaniline + nitrobenzene the
values calculated by different methods are in general
less than the experimental values. This is due to the
fact that none of the theoretical methods takes into
account the contributions by solute-solute and
solute-solvent interactions and all methods are based
on considerations of molecules of simple structure
and internal fields are not changed.
VYAS & RANA: DIELECTRICS OF POLAR & BINARY MIXTURES
Acknowledgement
5
The authors are thankful to Prof. V B Gohel,
Head, Department o f Physics, Gujarat University,
Ahmedabad for providing laboratory facilities and
constant encouragement. They are also thankful to
Prof. U C Pande, Department o f Chemistry, Gujarat
University for useful discussions.
8
9
References
10
1 Fisher E & Frank F C, Phys Z, 40 (1939) 345.
2 Higasi K & Smyth C P, J Am Chem Soc (USA), 82 (1960)
4759.
3 Vaughan W E & Smyth C P, J Phys Chem (USA), 65
(1961)98.
4 Gandhi J M & Sharma G L, J Mol Liq, 38 (1988) 23.
6
7
11
12
13
25
Vyas A D, Vashisth V M, Rana V A & Thaker N G, J Mol
Liq, 62 (1994) 221-236.
Singh P J & Sharma K S, Indian J Pure & Appl Phys, 34
(1996) 1.
Heston W M (Jr) Franklin A D, Hennely E J & Smyth C
P, J Am Chem Soc, 72 (1950) 3447.
Higasi K, Bull Chem Soc (Japan), 39 (1966) 2157.
Suryavanshi B M & Mehrotra S C, Indian JPure & Appl
Phys, 29(1991)482.
Srivastava K K & Vij J K, Bull Chem Soc (Japan), 43
(1970)2307.
Glasstone S, Laidler K & Eyring H, The theory o f rate
processes (McGraw Hill Book Co. Inc. New York) 1941.
Madan M P, Can JPhys 58 (1980) 20.
Yadav J S & Gandhi J M, Indian J Pure & Appl Phys. 31
(1993)489.
Indian Journal of Pure & Applied Physics
Vol. 39, May 2001, pp. 316-320
Dielectric relaxation in aniline, benzonitrile and their
mixtures in benzene solutions
A D Vyas & V A Rana
Department of Physics . University School of Sciences, Gujarat University, Ahinedabad 380 009
Received 25 September 2000: revised 7 February 2001; accepted 8 March 2001
Complex permittivity at 9.1 GHz, static permittivity and refractive index of aniline, benzonitrile and mixtures of
aniline + benzonitrile have been measured in dilute solutions of benzene at different temperatures (20-47°C). The measured
values of permittivity and dielectric loss have been used to evaluate distribution parameter, relaxation lime and
thermodynamical parameters. The variation of relaxation time for mixtures as a function of concentration of its components
at different temperatures indicates the existence of inter-association or formation of complexes.
1 Introduction
In recent past, study of dielectric behaviour of
mixtures of polar molecules15 under varying
conditions of composition and temperature have
evoked considerable interest. Madhurima et al." have
studied the binary mixtures of methanol with
ketones and nitriles in pure as well as their dilute
solutions in benzene at different microwave
frequencies and found interactive association
between the two species of the molecules. Dielectric
measurements carried out at microwave frequency
in mixtures of orthochloroanilines (OCA) with
nitrobenzene (NB) at different temperatures in
benzene solutions7 show that there is solutesolute/solvent interactions. In order to gain more
information in this area dielectric relaxation in
aniline, benzonitrile and their mixtures in dilute
benzene solutions has been studied. Results are
reported in this paper.
2 Experimental Details
Benzonitrile (purum) supplied by Fluka AG
(Switzerland) was used without further purification.
Benzene (AR grade) supplied by Qualigens (India)
and aniline (GR grade) procured from Merck (India)
were used after fractional distillation. The methods
of sample preparation, measurement of complex
permittivity(e *) at microwave frequency 9.1 GHz
and high frequency dielectric constant(e J were as
described earlier5. The static dielectric permittivity
(e„) at frequency 435 kHz was determined by
resonance method which uses a tuned oscillator
circuit and standard variable capacitor. All the
measurements were carried out at 20, 30, 40 and
47°C and the temperature was controlled
thermostatically to within ± 0.5°C.
The most probable relaxation time t„ and
distribution parameter a were determined using
Higasis’s single frequency* method. The following
equations were used for calculation of T„ and a:
1
9
o
A l + B ‘- 2 ( 1-00
%= —
a)
cz
2
K
- a - — tan
-l ' A '
where A - a"(aQ - a Bo)
B
=
( ciq
-
a )(a'-a00)
->
-
« " *
1
C = (a'-ci00)“ +a"‘’
and to is the angular frequency selected for the
measurement.
The parameters
a , a "and a., are the slopes
obtained from the linear plots of e „ ,e ',e " and e ..
versus weight fractions respectively.
3 Result And Discussion
The slopes ut„ a \ a" and a, determined by
plotting measured values of e u e e
and e co
against concentration of single component and
mixtures tire listed in Tabk 1. The values of trust
probable relaxation time tt„) and distribution
parameter («) using these slopes for aniline and
VYAS & RANA: DIELECTRIC RELAXATION
Table 1 — Values of an, a', a "and (i„ of single component as
well as their mixtures in benzene solution at different
temperatures
Substance
a
«i i
Temperature = 293 K
a
ft
a.
2.38
2.65
Aniline
7.21
5.95
Aniline + BN (0.25 of BN)
8.40
Aniline + BN (0.50 of BN)
10.83
15.18
Aniline + BN (0.75 of BN)
10.50
11.20
17.02
Benzonitrile (BN)
Temperature = 303 K
0.57
2.65
4.40
6.90
7.90
0.30
0.25
0.27
0.30
0.36
2.30
2.55
Aniline
5.39
6.25
Aniline + BN (0.25 of BN)
9.80
7.7(1
Aniline + BN (0.50 of BN)
13.84
10.00
Aniline 4 BN (0.75 of BN)
11.00
Benzonitrile (BN)
15.60
Temperature = 313 K
0.53
2.06
3.95
6.10
7.00
0.30
0.24
0.14
0.14
0.21
2.45
2.22
Aniline
5.70
Aniline 4 BN (0.25 of BN)
5.00
8.85
7.25
Aniline 4 BN (0.50 of BN)
13.40
10.00
Aniline 4 BN (0.75 of BN)
10.80
Benzonitrile (BN)
14.75
Temperature = 320 K
0.50
1.80
3.35
5.79
6.40
0.30
0.16
0.20
0.22
0.23
2.16
4.57
6.50
9.80
10.50
0.47
1.60
2.85
4.90
5.95
0.23
0.13
0.17
0.18
0.23
Aniline
Aniline 4 BN (0.25 of BN)
Aniline 4 BN (0.50 of BN)
Aniline 4 BN (0.75 of BN)
Benzonitrile (BN)
2.33
5.17
7.80
12.32
14.00
benzonitrile at different temperatures are presented
in Table 2. The zero value of distribution parameter
(a ) for benzonitrile in benzene solution at different
temperatures indicates Debye type relaxation
processes for benzonitrile in benzene solution, this
is in agreement with the observations made by
Srivastava et a t\ The relaxation time of benzonitrile
at 30 °C is 11.4 ps which is comparable with 12.8 ps
observed at the same temperature and in same
solvent by Madan'". Jai Prakash and Rai" studied
317
relaxation behaviour of aniline at different
temperatures and reported 4.5 ps value for
relaxation time of aniline in benzene at 35 "C. The
distribution parameter obtained by them was 0 .10.
Our value of relaxation time for aniline 4.2 ps at
30°C and 0.11 value of distribution parameter at the
same temperature is consistent with their results.
The finite value of distribution parameter (a) for
aniline and shorter relaxation time of it as compared
to chlorobenzene, a rigid molecule of similar size of
aniline suggest that in aniline apart from over all
rotation there is intra-molecular rotation i.e. rotation
of -N H 2 group.
The dielectric data of polar mixtures were
analyzed in a similar manner as for single
component systems. The values of most probable
relaxation time (x„) and distribution parameter (a)
for mixtures of aniline + benzonitrile at different
temperatures are given in Table 2. It is evident from
the Table 2 that the value of distribution parameter
(a ) for all the three mixtures investigated is zero at
all temperatures, indicating single relaxation process
in the mixtures. This result finds a justification from
the measurements of Schallamach12 where a single
relaxation time is observed in binary liquid mixture
consisting of non-associating components.
The values of relaxation time (x„) of the
mixtures increase with the increase of concentration
of benzonitrile in the mixture (Table 2), this may be
due to the fact that relaxation time of benzonitrile is
higher than the relaxation time of aniline, further,
the increase is nonlinear. A plot of relaxation time
of mixtures against the concentration of benzonitrile
in mixtures at different temperatures is shown in
Fig 1. The relaxation time of mixtures is also
evaluated taking weighted sum of its components
into account and are presented in Table 3. The
observed values of relaxation times have also been
Table 2 — Values of relaxation time (t„) and distribution parameter (a) of the single component as well as their mixtures in
benzene solution at different temperatures
Temperature (K)
Substance
Aniline
Aniline 4 BN (0.25 of BN)
Aniline 4 BN (0.50 of BN)
Aniline 4 BN (0.75 Of BN)
Benzonitrile (BN)
293
303
313
Xiin ps
(X
To in ps
a
t„
4.4
8.1
9.5
11.8
12.8
0.11
4.2
7.0
9.2
10.9
11.4
0.11
4.1
6.5
8.3
10.2
10.6
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
in ps
320
a
T„in ps
a
0.11
0.00
0.00
0.00
0.00
4.0
6.3
7.9
8.9
10.2
0.07
0.00
0.(X)
0.00
0.00
318
INDIAN J PURE & APPL PHYS. VOL 39, MAY 2001
Table 3 — Calculated and observed values ot relaxation time or the mixtures at different temperatures
Relaxation time in ps
Tem perature (K)
Aniline
Aniline + BN (0.25 of BN)
Aniline + BN (0.50 o f BN)
Aniline + BN (0.75 o f BN)
Benzonitrile (BN)
Calculated
303
313
293
—
—
—
—
6.5
8.6
10.7
6.0
7.8
9.6
5.8
7.4
9.0
5.5
7.1
8.6
—
—
—
—
A -30 'C
a - 4 0 ‘C
X - 4 7 *C
0.0
X
0-25
0-50
293
4.4
8.1
9.5
1 1.8
12.8
303
4.2
7.0
9.2
10.9
11.4
Observed
313
4.1
6.5
8.3
10.2
10.6
320
4.0
6.3
7.9
8.9
10.2
when tan 8 is plotted against concentration of
benzonitrile in aniline + benzonitrile mixture at
different temperatures (Fig. 2). Since benzonitrile
and aniline both act as non-associated molecules in
dilute benzene solution, the possibility of hydrogen
bonding is rare, this behaviour probably is due to
formation of charge transfer complexes in these
mixtures.
0 - 20 C
O'OL
320
X
075
1.0
10-0
CO NCENTRATION OF BN IN M IX TU R E
F ig. 1 — V a ria tio n o f re la x a tio n tim e as a fun ctio n ol
c o n c e n tra tio n o f b e n z o n itrile in m ix tu re
included in the same table for comparison. The table
shows that the observed relaxation time is greater
than the calculated values at all temperatures. This
indicates complex formation or inter-association in
these mixtures. Similar behaviour was observed
0-0
0.0
0.25
0.50
0.75
1.0
CONCENTRATION OF BN IN M IX T U R E
F ig. 2 -— V a ria tio n o f tan 8 in b e n z e n e as a fu n c tio n o f
c o n c e n tra tio n o f b e n z o n itrile in m ix tu re
VYAS & RANA: DIELECTRIC RELAXATION
The log (%nT) against 1/7 plots for the three
compositions of the mixtures ias well as the
Table4— Thermodynamical parameters of single component
as well as their mixtures m benzene solution
Mole fraction Temp
of BN m
K
aniline + BN
mixture
000
293
303
313
320
0.25
293
303
313
320
0.50
293
303
313
320
0.75
293
303
313
320
1 00
293
303
313
320
AF®
k cal/moi
AHS
k cal/mol
ASs
ca!/moldegree
1.91
1.97
2.04
2.08
2.27
2.28
2.33
2.38
2.36
2 44
2.48
2.52
2.49
2.55
2.61
2.60
2 54
2 57
2.64
0.10
-6.2 0
- 6 18
-6.2 2
- 6 20
- 3 68
- 3.59
- 3.63
- 3.69
- 5 29
-5.39
- 5.33
-5.33
-5.85
-5.85
-5.8 6
-5.6 9
- 5 83
- 5 76
-5.78
2 68
1.20
0.81
0.77
0 83
319
entropy of activation indicates that there are fewer
configurations possible in activated state and for
these configurations the activated state is. more
ordered than the normal state.
- 5 79
individual component exhibit linear relationships
showing that the decay of relaxation time with
temperature is exponential. These relationships
therefore can be represented by the rate process
equations13 for the dielectric relaxation processes.
The various thermodynamical parameters i.e. the
molar free energy of activation AFe, the molar
enthalpy o f activation A/7E( and the molar entropy of
activation ASe for the dielectric relaxation processes
can be obtained using rate process equations. These
thermodynamical parameters are presented in Table
4. From the table it can be seen that value of AFe is
least for aniline and highest for benzonitrile while
for their mixtures it lies between these two values at
all temperatures. Variation in AFe value with
concentration of benzonitrile in mixture at different
temperatures is shown in Fig. 3. This graph
confirms our presumption that there is a complex
formation or inter-association in these mixtures. It
can also be seen that, activation energies are larger
than corresponding enthalpies of activation and
consequently the entropies of activation are
negative. According to Branin and Smyth14negative
00
0-25
0-50
0-75
10
CONCENTRATION OF BN IN /M IXTU R E
Fig. 3 — Variation of free energy of activation m benzene as a
function of concentration of benzonitnle m mixtuie
Acknowledgement
The authors are thankful to Prof V B Gohel,
Head, Department of Physics, Gujarat University,
Ahmedabad for providing laboratory facilities and
constant encouragement. They are also thankful to
Prof U C Pande, Department of Chemistry, Gujarat
University, Ahmedabad, for useful discussions.
References
1
Sharma A & Sharma D R, Indian J Pure c&Appl Phys, 31
(1993)744.
2
Sharma, A> Sharma D R & Chauhan M S, Indian J Pure &
Appl Phys, 31 (1993) 841
3
Singh P'J & Sharma K S, Indian J Pure & Appl Phy.\, 34
(1996)388.
4
Fattepur R H, Hosamam M T, Deshpande D K & Mehrotra
S C, J Chan Phys, 101 (1994) 9956.
i
320
INDIAN J PURE & APPL PHYS, VOL 39, MAY 2001
5
Vyas A D.Vashisth V M, Rana V A & Thaker N G ,./ Mol
Liq, 62 (1994) 221.
6
Madhurima V, Murthy V R K & Sobhanadri J, Indian J
Pure & Appl Phys, 36 (1998) 85.
7
Vyas A D & Rana V A, Indian J Pure & Appl Phys, 36
(1998)21.
10 Madan M P, Can J Phys, 65 (1987) 1573.
11 Jai Prakash & Rai Bashisth, Indian J Pure & Appl Phys, 24
(1986) 187.
12 Schallamach A, Trans Farar/ciy Soc-Sec A, 42 (1946) 180
8 - Higasi K, Bull Client Soc, 39 (1996) 2157.
13 Glasstone S, Laidler K & Eyring H, The Theory of wte
processes (McGraw Hill Book Co, New York), 1941, p.
548.
9
14 Branin F H (Jr) & Smyth C P , J Chem Phys, 20 (1952)
Snvastava G P, Mathur P C & Tnpathi K N, Indian J Pitre
& Appl Phys, 9 (1971)364.
1121
Indian J. Phys. 75A (6), 635-638 (2001)
f
.........................................................• ■ • • • • ' ■ - ! * ' /
o - 1C»- l i e C .i........................ ..
IJP A
•. C .............. ....
...
•'
-s.
— an international journal
Dielectric dispersion and relaxation mechanism of some polar molecules and their
binary mixtures in benzene solutions at microwave frequencies
A D Vyas* and V A Rana
Department of Physics, University School oi Sciences,
Gujarat University. AhmedabaJotiU 009, Gujarat
?
c -n u il
Received 10 August 2001. acetified H Septem ber 2001
A bstract
: Dielectric Permittivity ( e ') and dielectric loss ( c" ) of pyridine, chlorobenzene, benzophenone, p-lluoroaniline and mixtures of
pyridine -r p-fluoroaniline, chlorobenzene + p-fluoroanilirie and benzophenone t p-fluoroaniline have been measured at three different microwave
frequencies 7.22, 9.1, 19.61 GHz at 30"C in benzene solution. The static permittivity at 455 KHz and refractive index were also measured. The most
probable relaxation time (r„) and distribution parameter (a ) have been determined from measured data using Cole-Cole method of analysis. The
presence of intermolecular association through hydrogen bonding (N-H— N) was observed in the mixture of pyridine + p-fluoroaniline. The dielectric
data for p-fluoroaniline and mixtures were analysed in terms of two relaxation times r, and
t 2
Keywords
: Dielectric relaxation, distribution parameter, hydrogen bonding
PACS Nos.
: 77.22.Gin
1.
Introduction
Relaxation parameters of polar liquid mixtures are affected by
several factors e.g. the relaxation time of individual components,
their dipole moments and interaction between them. Madan [15] studied some rigid polar molecules and their mixtures in dilute
solutions and found that in mixture polarization order decays
exponentially just as it does for single component system.
Dielectric measurements carried out by Prakash and Rai (6) for
mixtures of aniline + nitrobenzene at microwave frequencies
suggested that the relaxation lime of mixture is influenced by
the presence of component which has larger value of relaxation
time. Intermolecular association in polar liquid mixtures has been
reported by several workers by relaxation as well as dipole
moment studies [7-13], We studied mixtures of o-chloroaniline
wiih nitrobenzene and benzonitrile with aniline in benzene
soluiion ai dillerent temperatures (at a single microwave
frequency) and found that there is solute-solute/solveni type
of interaction ai low concentration of anilines [14,15], With a
view to gam more informadon in this area, we ean ied oui dielectric
measurements on pyridine, chlorobenzene, benzophenone. pfluoroaniline and mixtures of pyridine + p-lluoroaniline.
Correspondin'; Auihor
.
chlorobenzene + p-fluoroaniline and benzophenone + pfluoroaniline at three different microwave frequencies in benzene
solution at room temperature and the results are reported in this
paper,
2. • Experimental details
Pyridine (AR grade) supplied by Sd Fincchem Ltd. (India),
chlorobenzene (AR grade) supplied by Sisco Research Lab
(India), benzophenone (puriss for synthesis) supplied by
Spectrochem Pvt. Ltd. (India) and p-fluoroaniline (for synthesis)
supplied by M erck (Germ any) were used without further
purification. Benzene (AR grade) supplied by Qualigens (India)
was used after fractional distillation. The mixtures of pyridine +
p - flu o r o a n ilin e , c h l o r o b e n z e n e + p - f lu o r o a n ilin e and
benzophenone + p-lluoroaniline were prepared by taking polar
components in equal mole. These mixtures were taken as solute
and added to non-polar solvent. Five dilute solutions of
pyridine, chlorobenzene, benzophenone, p-fluoroaniline and the
mixtures were prepared by using benzene as non-polar solvent.
The dielectric permittivity (£') and dielectric loss (£") at
three different microwave frequencies 7.22, 9.1, 19.61 GHz were
determined by the method suggested by Heston el al [16],
©2001 LACS
636
A D Vyas and V A Rana
adopted (or short circuited termination. The .vatic permittivity
£o at fiequency 455 KHz was determined by resonance method,
which uses a tuned oscillator circuit and standard variable
capacitor, e ^ was taken as a square of refractive index which
was measured by Abbe's refractonieter. All the ineasuiements
were earned out at 30°C and the temperature was controlled
thermostatically to within ± 0.5°C.
3.
and benzophenone are presented in Table 2. The values of
relaxation time increase with the size of molecule and are in
Results and discussion
The slopes ag,a \ a",
determined by plotting the measured
values of £0, e ‘, e " and £„ against weight fraction of solute
in solution for single component and their binary mixtures at
.different frequencies are listed in Table 1. a " has been plotted
against a ' on complex plane to cvaiuate^riost probable
relaxation times ( r 0). Fairly smooth curves could be drawn
Figure 2. Plots of a " versus a' for p-fluoroaniline (O), mixtures of pyridine
-*• p-fluorouiuhnc ( □ ) , chlorobenzene + p-fluoroaniline (A) and
benzophenone + n-fiuoroamlme (x) m benzene solution.
Table 1. Values of slopes
a', a" and «„ of single component as well ,-s their binary mixtures in
benzene solution at different frequencies at 3Q“C
Frequency
455 KHz
Substance
(tu
7 22 GHz
a’
a"
it'
19.61 GHz
a"
a'
a*
Optical
Pyridine
6.87
6 67
1 10
6 50
1.50
5.85
2.40
0.07
Chlorobenzene
2 43
2 23
0 63
2 10
0 74
1 50
1.10
0.15
Benzophenone
5 87
4 50
2.36
3 58
2.70
1.70
2.37
0.35
p-Fluoroaniline
6.59
5 S3
1 68
5 50
2.05
4.54
2.48
0.15
Pyridine +
p-Fluoroaniline
7.55
6 75
2 09
6 25
2.38
4.50
3.08'
0.19
Chlorobenzene +
p-Fluoroanihne
4 92
4 58
1 14
4 25
1 50
3 28
2.10
0.19
Benzophenone +
p-Fluoroamline
6 25
5 40
2 00
5 10
2 30
3 63
2 70
0.29
passing through the experim ental points. For pyridine,
chlorobenzene and benzophenone a Debye type plot with center
on die x-axis is observed (Figure 1), whereas for p-fluoroamline
and for mixtures a Cole-Cole type of plot with center below x-
Figure I. Plots of a" s-min a' lor p\ndine (O). chlorobenzene (A) and
benzophenone ( □ ) in benzene solution
axis is observed (Figure 2). The most probable relaxation lime
(T0) and distribution parameter (a ) for pyridine, chlorobenzene
20ei-NDr=Brp65
9.1 GHz
close agreement with literature values. The zero values c
distribution parameter (a ) for these molecules suggest a simp]
Debye type relaxation mechanism for these systems, which >
usual behavior o f rigid polar molecules. In comparison l
pyridine, chlorobenzene and benzophenone, less data
available in literature on d ielectric m easurem ent o f j
fluoroamline. Dhar e ta l [22] studied p-fluoroaniiine at differe
temperatures and 3 cm wavelength in benzene solution, the vali
of relaxation time for this compound reported by them is 5.1 •
at 30°C. The values of relaxation time 5.3 ps (Table 2) for
fiuoroaniline in the same solvent and at the same temperature
the present work is in close agreement with their value
relaxation time. The value of distribution;parameter (a ) for
fluoroamline (Table 2) is finite (0.20). Srivastava and Vij [1
studied o-chloro, m-chloro, and p-chloroanilines in benze
solution, they found finite distribution parameter for th<
molecules and further, the distribution parameter shown
increasing trend from o- to m- to p- isomers. The value
distribution parameter for p- chloroaniline determined by th
at 30°C was 0.25, thus the value of distribution parameter (
helecirtc dispersion and relaxation mechanism o f some polar molecules etc
lor p-lluomanilinc (0.20) in preseni work appears reasonable.
I his Imue value of distribution parameter (a) I'orp-lluoroaniline
suggest dial iliere is more Ilian one relaxation processes in this
system. As suggested by several workers, for aniline and
'f
Va' UCS of rJistributioo parameter l a ) , relaxation lime (r„) and free energy o f activation
r ) o the single component as weil as their binary mixtures in benzene solution at 30“C.
Distribution
parameter ( u )
Substance
Relaxation
tune (r„)
in ps
a
Free energy
o f aciivation
I A F C) kCal/Mol
Relaxation
time in ps
(Lit. values)
Pyridine
0.00
3.7
1.90
Chlorobenzene
0.00
7.5
2.12
7.8 (ref. 19)
7.7 (ref. 20)
8.3 (ref. 21)
Benzoph enon e
0.0 0
I4 .|
2 .7 0
16.0 (ref. 3)
17.4 at 20 'C
(ref. 21)
p-Fluoroaniiine
0 .20
5.3
2.1 1
5.1 (ref. 22)
Pyridine +
p*Fluoroaniline
0.07
6.6
2.25
-
Chlorobenzene +
p-Fluoroaniline
0.03
6.0
2.19
-
Benzophenone +
p-Fluoroaniline
0.1 0
7.8
2 .3 4
-
substituted anilines this may be due to roiation of -N H , group
around its bond with the benzene ring. This has also been
reflected in the value of relaxation time of p-fluoroanilinc. The
relaxation time of fluorobenzene found by us in our previous
studies in benzene solution at 30°C is 5.7 ps (24], whereas that
of p-fluoroaniline in the same solvent and at the same temperature
is 5.3 ps. Although the molecular size of p-lluoroaniline is greater
than that of fluorobenzene still its relaxation time is less which
also suggest that there is an intramolecular roiation in ptluoroaniline. Therefore, the dielectric data was analysed in terms
of two relaxation times r, and r 2 where r , and r 2 are relaxation
times corresponding to overall and group rotations respectively.
In terms of a0, a \ a" and
the Budo's [25] equation can be
written for two relaxation processes as
a '- a x
these parameters are given in Table 3. The value of relaxation
time ( r , ) is 2.5 ps for p-fluoroanilinc which may be attributed to
rotation of - NH2 group and is fairly in agreement with the
literature values [27,28],
c,
c-,
1+ oTTj'
l+n ;
c*,wr,
l + a rrj1
w
c-)COT s
l+ o rri;
^
where c\
I. c, tind r , are relative weights contributed by
each processes to the dielectric absorption as a whole, r , , r 2 ,
<■ and c, for p-lluuroaniline was determined using ihe method
suggested by Bhattacharya et al [26], The evaluated values of
14X44—Nov^Rrp65
3.8 (ref. 17) '
3.56 (ref. 18)
3.1 (ref. 5)
3.2 (ref. 20)
Table 7>. Values o f resolved relaxation limes and iheir relative weight
factors for p-lluoroaniline and its mixtures with pyridine, chlorobenzene
and benzophenone in benzene solution at 30'C.
Substance
r , in ps
r : in ps
C
-\
p-Fluoroaniltnc
20 .2
2.5
0.3 2
3.68
Pyridine +
p-Fluoroaniline
16.9
2.3
0 .4 4
0 .5 6
Chlorobenzene +
p-FIuoroaniline
19.4
2.8
0 .2 9
0.71
Benzophenone +
p-Fluoroaniline
15.0
2 .6
0 .5 4
0.46
The values of relaxation tim es o f the m ixtures of pfluoroaniline with pyridine, chlorobenzene and benzophenone
are also presented in Table 2. It is evident from the Table 2 that
for m ixtures of p-fluoroaniline with chlorobenzene and
benzophenone the relaxation time of mixtures are nearly average
of the individual value of relaxation time of constituent molecules.
This is manifestation of super imposed effect of the pair of two
components, the wavelength of the maximum absorption of pairs
lying near to cadi other, thus giving rise to a broader single
relaxation peak, this is in agreement with our earlier studies for
mixtures of rigid polar molecules [29],
In the case of mixtures of pyridine + p-fluoroan.line, the
relaxation time of the mixture is 6.6 ps (Table 2) while that of its
638
A D Vyas and V A Rana
components ore 3.7 ps (pyridine) und 5.3 ps (p-nuoro;iniline).
I lius, the vulue of relaxation time of mixture is higher than that
ol its components. 1 his indicates that interactive association is
taking place between pyridine and p-fluoroaniline molecules
through N-H—N type of hydrogen bond. Similar results were
obtained for the mixture of pyridine + pyrolc and pyridine +
indole in dilute solutions by Tridula ct at [ 17).
The value of distribution parameter (or) for all the three
mixtures investigated is linile. but, less than the distribution
parameter p-fluoroaniline, this suggests that there is more than
one relaxation processes in the m ixture and further, piluoroaniline retains its identity in the mixture. It appear* that
the presence of rigid polar molecules in the mixture with pfluoroaniline, produces internal field such that the motion o f NH: is slightly restricted. The dielectric data olThc.sc mixtures is
also analyzed in terms of two relaxation processes. The relaxation
times and their contribution were determined by die method
described for p-fluoroaniline. The evaluated values of r ,, r , ,
£j and c, for the m ix u .es are also presented in Table 3. It is
evident from the Table 3 that the values of relaxation time for
group rotation ( I-,) in all the mixtures is of the same order found
for p-fluoroaniline, which suggest that the components in the
mixtures retain their identity.
Free energy of activation (A Fc ) evaluated using Eyring's
equation [30] for single component as well as that for binary
mixtures is listed in Table 2. It can be seen that in the mixtures of
chlorobenzene + p-fluoroanilinc and benzophenone +pfluoroaniline. the free energy of activation lies between those of
its components, whereas in the case of mixture of pyridine ■+• pfluoroaniline, the activation energy is higher than those for us
components, this also suggests that there is a complex formation
in this mixture.
3)
M I’ Madan J. Mat. Liq. 29 161 (19X4)
H|
M I ’ Madan Cun. J. I’Ins. 58 20 (19X0)
[5J
M l * M adan, M Shelfoon and I Cam eron Can. J. P h y
(1 9 7 7 )
[6 ]
Jai ITakash and Bashisth Kai Indian J. Pure Appl. Phys. 24 187
119S 6)
[7 ]
Azim a L C Saad, Adel H S lialik and Faika F Hanna Indian J. Phys.
7211 (5 ) 495 (1 9 9 8 )
|.S)
It Varadarajan and A Rajagopal Indian J. Pure Appl. Pins. 36 13
(! 99 8)
[9 )
V Siitiiam.mian, B S Bellubbi and J Soblianadn Prumum.-J. Pins.
4 1 9 ( 1 9 9 .3 )
I lu )
A Sharma and D R Sharma Indian J. Pure Appl. Phys. 31 841
(1 9 9 3 )
(It)
Nagosli Tliakur and D R Sharma Indian J. Pure Appl. Phys. 38
.328 (2 0 0 0 )
|
( 1 2)
55 87X
V M adhurim a, V R K M u rlh y and J Sobbanadri Indian J. Pure
Appl. Phys. 36 85 (1 9 9 8 )
(1.3)
V M adhurim a, V R K M u rlh y and J Sobbanadri Indian J. Puie
Appl. Phys. 36 144 (1 9 9 8 )
( 1 4]
A D Vyas and V A Rana Indian J. Pure Appl. Phys. 36 21 (1998)
[ 1 5]
A D Vyas and V A Rana Indian J. Pure Appl. Phys. 39 316 (2001)
f 16]
W M Heston (Jr), A D Franklin, E J Flannely and C P Srtylh Am.
Chem. Sue. 72 3447 (1 9 5 0 )
[ 17]
Tridula Gupta, Mradula Chauhan. S K Saxena and J P Shukla Adv.
Mai. ReUi. Inter. Proe. 23 203 (1 9 8 2 )
[ 18]
J Gowrikrishna and J Sofc-hanadri Indian J. Pure Appl. Pltys. 22
[ 19]
S C I.lilra . S B M is ra and N K M ehrotra Indian J. Pure Appl.
599 (1 9 8 4 )
Phys. 16 604 (1 9 7 8 )
[2 d ]
F F Hanna and A b d -E I-N o u r Z. Phys. Chem. Leipziji 24 6 168
(1971)
[ 21]
D H W hitten Trans. Faraday Sac. 4 6 !3U (1 9 5 0 )
[ 22]
K L D liar. Nccra Salmi and M C Saxena Indian J. Pure Appl.
[ 25]
K K Smastava and J K V ij Bull. Cliem. Sac. Jpn. 43 23C7 (1970)
Phys. I t 3.37 (1 9 7 3 )
[ 24]
A D Vyas am) V M Vashisth Indian J. Pure Appl. Phys. 26 484
( 1988)
Acknowledgments
The authors are thankful to Prof V B Gohel, Head, Department
of Physics, Gujarat University, Ahmcdabad for pres iding
laboratory facilities and constant encouragement. They are also
thankful to Prof U C Pande, Department of Chemistry . Gujarat
University, Ahmedabad for useful discussions.
[ 2 5]
A Budo Phy.uk Z. 39 706 (1 9 3 8 )
[ 26]
J Bhatiacharya, A Hasan, S B Roy and G S Kastha J Phys. Sue.
Jpn. 28 204" (1 9 7 0 )
[ 27]
S M Klumeshara and M L Sisodia Adv. Mol. Pel. hit. Proc. 21 105
(1981)
[ 28]
[ 29]
S M Tucker and S W alker Can. J. Client. 4 7 681 (1 969)
A D Vyas. V M Vashisth, V A Rana and N G Thaker J. Mol. Liq.
62 221 (1 9 9 4 )
References
[ 3 0]
|I]
M V Madan J. Alo t Liq. 33 203 (19X7)
12 1
M H Madan Cun. J. Phys. 65 1573 (19X7)
A. It- :
2D<M~Nov-8:p65
pl t*®01**
S Glassione. K Laidler and H Eyring The Theory v f Rate Pricesses
(N ew York : M c G ra w -H ill) 584 (1 9 4 1 )
v-:- m
Proceedings of National Conference on MICROWAVES, ANTENNAS & PROPAGATION
344
DIELECTRIC RELAXATION IN o-BROMOANILINE AND
ITS MIXTURES WITH n-PROPANOL IN
BENZENE SOLUTIONS
A.D.Vyas1 and V.A.Rana
1Deptt o f Physics, University School o f Sciences, Gujarat University, Ahmedabad-380 009
ABSTRACT
Complex permittivity ( e '. e ”) at 9.1 GHz. Static
permittivity at optical frequency ( e I =nD") of obromoaniline and its mixtures with n-propanol have
been measured at different temperatures (20-47°C) in
dilute solutions o f benzene. The measured values of
permittivity and dielectric loss have been used to
evaluate relaxation times, distribution parameter and
thermodynamical parameters. In the mixtures o f obromoaniline and n-propanol. solute-solute type of
interaction was observed.
INTRODUCTION
Dielectric relaxation studies o f mixtures o f
polar molecules in non-polar solvent has
gained considerable interest because it
provides
information about relaxation
processes in the mixtures and reveal the
nature o f interaction among the molecular
species. Several mixtures hating different
constituents like rigid-rigid, associative +
nonassociative and associative - associative
have been investigated, among these
mixtures the mixtures o f amine and alcohol
is o f special interest because it exhibit cross
association via hydrogen bonding between OH group o f alcohol and -NH; gorup o f
amine. Oswal and D esai[i] determined
excess molar volume VE, viscosity deviation
A5, excess viscosity 5 E, excess Gibb's
energy o f activation AG*E o f viscous flow
from density and viscosity measurements for
different binary mixtures o f amine with
alcohol, they found strong cross-association
through O-H—N bonding between -O H and
-N H 2 groups. Swain[2] determined mutual
correlation function gab for mixtures o f
aniline with n-propanol. n-butanol and ibutanoi using dielectric constant values
measured at radio frequency and suggested
weak OH-NH complexes. Investigation o f
alcohol-amine
complexion
by
using
dielectric probe by Tripathi et a/[3]
suggested that the complex formation is due
to charge redistribution and most likely
complexation is due to linkage between Ns"
Si
(proton acceptor) o f amine with H
of
alcohol (proton donor). Dielectric relaxation
and structural studies o f aniline-methanol
mixture using picosecond time domain
spectroscopy by Fattepur et al[4] shown
strong interaction between solute and
solvent molecules at low concentration o f
methanol. Earlier, we[5] studied the
mixtures o f aniline + n-propanol in dilute
benzene solution and found interactive
association
between
the
constituent
molecules through hydrogen bonding in
aniline rich region. It was expected that
presence o f bromo group at ortho position
with respect to -N H 2 group in 0 bromoaniline should give some interesting
results for its mixture with n-propanol.
Dielectric absorption o f o-bromraniline and
its mixture with n-propanol were measured
in
microwave
region
at
different
temperatures in dilute solutions o f benzene
and the results are presented in this paper.
EXPERIM ENT A DETAILS
The samples o f n-propanol
(AR grade)
supplied by Sd-Finechem (India) and obromoaniiine (purum grade) procured from
Fluka A G (Switzerland) was used without
further purification. Benzene (AR grade)
supplied by Qualigens (India) was used after
fractional distillation. Mixtures o f different
compositions 3:1,1 :i and 1:3 o f n-propanol
and o-bromoaniline were prepared by
Proceedings of National Conference on MICROWAVES, ANTENNAS & PROPAGATION
adding them by mole. These mixtures were
taken as solute and added to non-polar
solvent benzene. Five dilute solutions o f npropanol (w .f.-0.005-0.04), mixture o f 1:3
composition (w.f.-0.007-0.04), mixture o f
1:1 composition (w.f.~0.004-0.032), mixture
o f 3:1 composition (w.f.-0.006-0.03) and obromoaniline (w.f.-0.009-0.0045)
were
prepared using benzene as non-polar
solvent.
The dielectric
permittivity
( e ?) and
dielectric loss ( e ” ) at microwave frequency
9.1 GHz, the static permittivity (eo) at 455
KHz and permittivity at optical frequency
(e K) o f solutions were determined by the
method described earlier[6j.
A ll the
measurements were carried out at 20, 30. 40,
and 47 °C and temperature was controlled
thermostatically to within ± 0.5°C.
Graphs o f 6 o ,e ',e ” and e * against weight
fraction o f the single component as well as
the mixtures as solute in non-polar solvent
were plotted which were found to be linear.
The slopes aQ. a', a” and a,* o f these linear
plots were determined and used to calculate
the relaxation times and distribution
parameter. The most probable relaxation
time ( t0) and distribution parameter (a)
were determined
by Higasi's single
frequency method [7]. Relaxation times t ( l)
and t(2) corresponding to group rotation and
overall rotation respectively were calculated
using the equations proposed by Higasi el al
[ 8]-
RESULTS AND DISCUSSION
The slopes ao, a",a” and a^ o f n-propanol. obromoaniline and their binary mixtures at
different temperatures are presented in Table
1. The values o f relaxation times To, t (1).
t(2) and distribution parameter for single
components as well as the mixture at
different temperatures are presented in Table
TABLE I
Values o f parameters a>, a", a” and a* o f npropanol. o-bromoanilines and their binary
mixtures in benzene solution at different
temperatures.
Temp °C ai
a'
a”
345
a*
n-Propanol
1.26
4.78
5.64
1.12
4.29
5.05
0.98
4.05
4.60
0.82
3.57
4.00
o-Bromoaniline
0.81
2.01
2.55
20
1.79 0.59
2.13
30
0.49
1.92
1.65
40
47
1.88
1.66 0.46
1:3 Mixture o f o-bromoaniline
propanol
0.88
3.62
3.20
20
2.86
0.78
3.28
30
0.70
2.86
2.46
40
0.55
47
2.31
2.17
1: 1 Mixture o f o-bromoaniline
propanol
0.79
20
3.20 2.67
0.65
2.35
30
2.70
0.58
2.57
2.29
40
47
2.38
2.15
0.51
3: 1 Mixture o f o-bromoaniline
propanol
20
2.84 2.29
0.78
2.54
30
2.18
0.63
40
2.34
2.08
0.50
0.45
47
2.1 1 1.91
20
30
40
47
-0.37
-0.47
-0.51
-0.52
0.31
0.30
0.23
0.20
+ n-0.17
-0.18
-0.35
-0.35
+ n0.16
0.12
0.10
0.09
+ n0.34
0.20
0.15
0.15
From the Table II it can be seen that the
relaxation time o f single component as
well as the mixtures decreases with
temperature, which is a usual behavior
o f polar molecules in non-polar solvent.
The non-zero values o f distribution
parameter o f o-bromoaniline and npropanol indicates that more than one
relaxation processes exists in these
systems. The distribution parameter
found by us [5] for aniline at 20°C in
benzene solution was 0.1 1 and that o f obromoaniline found in the present
Proceedings o f National Conference on MICROWAVES, ANTENNAS & PROPAGATION
TABLE II
Values o f relaxation times to, t(1),t(2)
and distribution parameter (a ) o f polar
molecules and their binary mixtures in
benzene
solution
at
different
temperatures.
Temp.
t0
a
t(1)
t (2)
ue
in ps
in ps
3.8
0.12
4.3
o f halo-group on the ortho position does
not hinder the rotation o f -N H 2 group.
Bhattacharya[9]
studied
o-and
mchloroaniline at a wavelength o f 3.18
cm. From the existence o f a loss maxima
at 30°C in both the cases he inferred that
the amino group is free to rotate and the
presence o f chlorine group does not
hinder its rotations in any way.
in ps
n-nrocano 1
20
3.5
4.3
11.9
0.23
4.1
11.9
30
3.3
0.23
40
3.1
0.19
3.8
9.8
3.5
9.2"
47
2.8
0.18
o-bromoaniline
0.09
20
8.5
8.3
11.7
30
7.0
10.0
6.9
0.09
40
5.8
0.11
6.1
9.6
5.2
5.5
8.4
47
0.09
1:3 mixture o f o-bromoaniline + npropanol
4.6
8.4
20
4.1
0.12
30
4.5
9.5
3.9
0.16
4.4
40
3.7
0.18
10.1
47
0.02
3.8
4.4
3.7
1: I mixturte o f o-bromoaniline + npropanol
20
5.0
0.18
5.5
11 8
5.1
30
4.7
0.13
9.3
40
4.1
4.6
0.13
8.6
47
346
8.0
3:1 mixture o f o-bromoaniline + npropanol
20
6.9
0.15
7.0
12.4
30
5.2
0.13
5.6
9.9
40
4.5
0.11
4.9
8.4
47
4.0
0.11
4.5
7.8
investigation in the same solvent and at
the same temperature is 0.09. Thus the
value o f distribution parameter for
aniline and o-bromoaniline are o f the
same order, suggesting that the presence
Figure-1 .Plot o f relaxation time (to)
against concentration o f o-bromoaniline
in the mixture at different temperatures.
0 ----------------------------------------0
25
50
75
103
%Ctrc d ofcrcrrrsrilineinrroiire
Dielectric data for mixtures o f obromoaniline with n-propanol in dilute
solutions
of
benzene
at
different
temperatures
and
concentrations
was
analyzed as a single component system. The
relaxation times and distribution parameter
o f the mixtures at different temperatures
evaluated by Higasi’s single frequency
method are also shown in Table-ll. It is
evident from Table II that the relaxation
times o f the mixtures increases with increase
in concentration o f o-bromoaniline at all
temperatures, this is due to the fact that the
relaxation time o f o-bromoaniline is higher
than that o f n-propanol (at the present
frequency o f measurement and dilution).
The plots o f relaxation time o f mixture
against the concentration o f o-bromoaniline
in the mixtures at different temperatures are
shown in the Figure-1. The figure shows that
Proceedings of National Conference on MICROWAVES, ANTENNAS & PROPAGATION
the increase in relaxation time of mixture
with concentration of o-bromoaniline is non­
linear. This indicates solute-solute type of
interaction between the o-bromoaniline and
n-propanol.
The distribution parameter (a) for mixtures
of o-bromoaniline + n-propanol at_________
TABLE III
Thermodynamical parameters of pol ar
molecules and their binary mixtures in
benzene
ah6
Temp AFe
Cal/
kCal/
K kCal/
MolMol.
Mol.
deg
n-propanol
-2.99
0.90
293
1.78
-3.04
303
1.83
-3.03
313
1.85
-2.97
320
1.85
o-bromoaniline
1.64
293
2.30
2.78
2.27
1.68
303
1.67
313
2.26
1.64
320
2.25
1:3 mixture of o-bromoaniline + n-propanol
-4.08
0.68
293
1.88
-4.11
303
1.93
-4.14
313
1.98
2.04
-4.23
320
1:1 mixture of o-bromoaniline -r n-propanol
1.99
293
1.58
-1.43
-1.51
303
2.03
-1.50
313
2.05
-1.48
320
2.05
3:1 mixture of o-bromoaniline + n-propanol
2.18
2.15
-0.10
293
2.10
0.15
303
0.17
313
2.10
0.16
320
2.10
different temperatures and at all the three
concentrations
have
non-zero
value.
Furthermore, the distribution parameter of
the mixtures shows a negligible variation
with temperature. It appears that in these
347
mixtures there is solute-solute and solutesolvent interactions, providing a variety of
local environments resulting in domination
of internal group rotation, which is usually
independent of temperature. The significant
difference between t(2) and t(l) for
mixtures as well as single components
(Table II) also suggest intramolecular
motion apart from overall rotation of
molecules. Since, the measurements were
conducted at single microwave frequency,
the dielectric data of single component as
well as mixtures were not analyzed in terms
of two relaxation processes.
The temperature dependence of relaxation
time has been used to evaluate the
thermodynamical parameters viz., free
energy of activation (AF6), enthalpy of
activation (AH6) and entropy of activation
(AS6). The evaluated values of these
parameters using rate process equation [10]
for single component and their mixtures are
presented in Table III.
ACKNOWLEDGEMENT
The authors are thankful to Prof V B Gohel,
Head, Department of Physics, Gujarat
University. Ahmedabad for providing
laboratory
facilities
and
constant
encouragement.
REFERENCES
[ 1] S.L. Oswal and H.S.Desai, Fluid
Phase Equilibria, 149 (1998) 359.
[2] B.B.Swain,
Ph.D.Thesis,
Uttakal
University (1986).
[3]
S.Tripathy,G.S.RoyandB.B.Swain,/tt
dian J. Pure & Appl. P/iy.?.,31(1993)
828
[4] R.H.Fattepur,MT.Hosamani,D.K.Deshpa
ndeandS.C.Mehrotra,,/.C6em./>At>'s
101(1994)9956.
[5] A.D.Vyas
and
V.A.Rana,
Presentedat"National Conference On
EmergingTrends & Advances at
Aurangabad,March-2001 "fProc.to be
published).
Proceedings of National Conference on MICROWAVES, ANTENNAS & PROPAGATION
[6]
A.D.Vyas and V A.RanaJndian J.Pure
& Appl. Phys.,39(2001)316.
[7] K.Higasl,Bull. Chem.Soc. (Japan),39
(1966)2157.
[8] K.Higasi,Y.K.ogaandD.Nakamura.Z?t///.C
hem.Soc. (Japan),44(1971 )988.
348
[9] , J.Bhattacharya,/»r/t7m/ Phys,36( 1962)
533
[10] S.GIasstone, K.Laidler and H.Erying,
Theory o f Rate Processes(McGraw
Hill Book Co., Newyork),1941, P. 548.
Документ
Категория
Без категории
Просмотров
0
Размер файла
8 479 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа