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Dielectric studies of binary mixtures of butanols in nonpolar solvents - solute-solvent interactions
Journd of Molecular Liquids, 34 ( 1987) 257-268
257
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
DIELECTRIC
STUDIES
SOLUTE-SOLVENT
OF BINARY MIXTURES
OF BUTANOLS
IN NONPOLAR
SOLVENTS
-
INTERACTIONS
B. B. SWAIN and G. S. ROY
Post-Graduate (Received
Department
of Physics,
Ravenshaw
College,
Cuttack
753003,
INDIA
17 May 1986)
ABSTRACT
Dielectric Butanol
constant
of binary mixtures
in three nonpolar
solvents
namely
n-heptane
have been measured
parameter
G* based on the significant
these mixtures. interactions calculated
benzene,
at radio frequency.
This parameter
structure
G* reflecting
is found to be influenced
in solvent
corroboration
carbon
tetrachloride, interaction
the non-specific
polarization
dipole
The results
findings
and
model has been calculated
in
solute - solvent
by the nature of the solvent.
environment.
in the earlier
and t-
Eyring's
value of G* has been used for interpreting
the solute domains further
of n-Butanol,i-Butanol
The
interaction
of
of this study finds
of these authors
on excess molar
in these mixtures.
INTRODUCTION
Study of dielectric interesting Frohlich condensed
method
Cl1 linear correlation phase
concentration
benzene,
in mixtures carbon
nature
of three butanols
reflected
of variation
systems provides
curve CZI
in nonpolar
Furthermore,
of g was identical
solvents
free energy namely,
in the value of g
present
it was observed
in seemingly
change
in them both
that though the
non-interacting
nonpolar
in the value of g, excess molar
0 1987ElsevierSciencePub1ishersB.V.
the
has been
earlier i121
and excess
The variation
in the
describing
solvents
We have evaluated
of multimerisation
an
The Kirkwood-
of local ordering
in three nonpolar
and n-heptane.
the nature
yet there was appreciable
0167-7322/87/$03.50
theoretical
by many authors.
at low and high concentrations.
mediums,
bonded
factor, excess molar polarization
tetrachloride
in the solutions
Oster's
of g of polar liquids
corroborated
the linear correlation
in hydrogen
into liquid structure.
factor g is a measure
in such systems.
dependence
experimentally
of mixing
properties
of investigation
258 polarization nonpolar
and excess
solvents.
This obviously
the presence
mdtimeriSation
solute molecules Mecke-Kempter assumed
free energy at the same concentration
especially
cl41
[3,131
environment
in assessing
to the shortrange In Kirkwood's
Eyring
Cl1
model
factor
by Eyring et al. C3,131 the solute-solute
in an environment
G and G* respectively.
of crystalline
and Devonshire
they concluded freedom
environment
effect is directly
of dipolar
interaction
of solvent molecules
namely benzene,
i-Butanol
they explained
liquid,
fluidised
vacancies
correlation
related
of dipoles a
to the liquid stucture
measurements
with
the evaluation
solute and solute molecules
due to angular
correlation
and t-Butanol
carbon tetrachloride
approximation
of number of systems.
Here we have undertaken between
structure,
showed that this theory could even
from static dielectric
measurements.
(holes) in
Thus this model reveals
altered.
Garg and Smyth cl51
species.
relaxation
hole
a gas like
Oscillator
properties
in an associated
is significantly
in a given domain of n-Butanol, solvents
that confers
for the rest of the molecules,
solvent
fact that solvent
GX , a measure
lattice sites
as a significant
an Einstein
and dielectric
the data obtained
dielectric
of two factors
over disorder
that a liquid has an
to a large extent and at such shortrange
of solute molecules
reconcile
Making
of freedom
a nonpolar
can be increased
significant
of vacant
the hole concept
vacancies.
transport
thermodynamical,
of associated
the presence
Extending
for solid like degrees
By introducing
recognises
In
of solute molecules
by values
is an improvement
that a liquid has an excess volume
on fluidised
The model
structure.
Eyring et al postulated the liquid structure.
of a dipole of
values of 8.
and interaction
C41
is free
free from such assumptions.
are reflected
This model which
theory of Lennard-Jones element
interaction
of solvent molecules
the fluid
that central dipole
of the moment
is, however,
in an
a significant
to understand
it is assumed
by
interaction
et al. proposed
correlation
in a local field and space averaging
their model,
can not be
of g at low concentration
the solute-solute
liquid has been taken to be u cos 0 over all possible proposed
and
As such
equilibrium
and as such calculation
of solvent molecules.
structure.
solvent
are in excess.
it has been shown that the model proposed
is useful
modification
to orient
when solvent molecules
solvents
to the effect of between
difficult.
On the other hand, Eyring
in addition interaction
type of concentration-independent
for different
rather becomes
indicates,
of non-specific
for different
in an
of the molecules
in three nonpolar
and n-heptane.
of
259 THEORY
Significant sites
structure
(holes) present
assumed
in a liquid.
to be fluidised
freedom.
C31
theory
vacancies,
In one mole of liquid,
that there are vacant
These disordered
lattice
holes of liquid are
which
are supposed to possess gas like there will be v-vs moles of such vacancies
where V and Vs are the molar volumes Thus each of these fluidised
proposes
in liquid a!d solid phase respectively. confers gas like properties on v-vs
vacancies
v
moles respectively. Thus the partition
function
like and gas like degrees
for a mole of liquid is separated
into solid
of freedom and the mean value of property
x is given
by v-v “S =
where
x,($
+
xg
x, and x
‘+
are values
of this property
in solid and gaseous
states
g respectively. According consists average
grouped
dipole moment
polarization of maximum result
to the significant
of dipoles
polarization
align themselves
to be u2GF/kT where
gas like holes the Kirkwood's orientation
of molecules
The foregoing theory
[31
As a
oriented
to the
molecules
of solid like structure
For
G = cos28 and F is the local field.
Cl31
since free
for gaseous part.
coupled with the concept equation
in
is
of significant
for the dielectric
structure
constants
liquids. c,+2
(E2-Em)2(2E2+E,)
=&z!!(_
where
or antiparallel
factor p2F/3 kT is still retained
assumptions
the direction
in the field.
in the local field is possible
lead to the following
of hydrogen-bonded
3
either parallel
mean dipole moment
of maximum
field is applied,
of domains will tend to orient
The resulting
found by Eyring
to the direction
When an electric
liquid
These dipoles have
sizes.
This leads to the growth of favourably
field direction. the domains.
theory an associated
of various
pcos0 with respect
for the domain.
the dipoles
structure
in domains
"2
3
Vsu2G )2 [V2kT
constant
v -v 2 S) -lJ2 +(--3kT "2
~2
is the dielectric
cm
is taken as square of the refractive
of the polar
N
is the Avogradro
number,
k
is the Boltzmann
constant,
,
liquid
index of the polar liquid
(1)
260 T
is temperature
p
is the dipole moment
"2 V S
G
of polar
is the molar volume
of liquid in solid phase
to angular The addition
Pt
of dipole
increase
between
of molecules solvent
its dielectric
is expected
behaviour.
afresh.
G to account
Thus eqn.
for the changes
(1) can be modified
molecules
due
to alter the liquid
As such the dielectric in an environment
of solvent
The number of such domains
Thus P;
of solute concentration.
identical
in a given domain.
of the domain of solute species
is to be considered
G* replaces
liquid,
interaction
correlation
of a nonpolar
and hence
polarization molecules
of liquid in gas phase
is the molar volume
is a measure
structure
Kelvin,
is now expressed
increase with * as v2G /kT where
in the environment.
to accommodate
such interactions
and is
given by (c--E m )(2E+E m ) =
V 2 X2 C 2 V 3V
41rN -. 3kT
3(E_o+2)2
(X2G + XlG* ,++ 3
where X 1 and X2 are the mole fractions E
is the dielectric
V
is the molar volume
constant
v-v L)I v
of the solvent
(2)
and solute respectively.
of the mixture,
of the mixture,
and other symbols
as defined
earlier. The data for G in pure liquids and G* for varying alcohols
in nonpolar
solvents
have been calculated
compositions
using eqn.
of
(1) and eqn.
(2)
respectively.
EXPERIMENTAL
The experimental
device used for the measurement
etc. are the same as used by one of the authors of measurement
RESULTS
of dielectric
ClO,lll earlier.
constant
The accuracy
is also the same.
AND DISCUSSION
The relevant in Figures
Evaluation the density employing
data has been presented
in Table 1 and some of them displayed
1 and 2. of Vs:
of the polar
With regard
to calculation
liquid at its melting
the density-temperature
relation.
of Vs we have calculated
point by extrapolation
261
0 i-8ut~nol ra t- Ilutanol ~, n - i u t a n o l
1.0
0.8
,,',\
0.6 'l
\ o.4 o 0.2
13
-6 E O.
<~
-02
-1 El
-0~
-2
-3
-4
~,
-s-
0
0,1
0.2
0.3
0.4 O.S
G6
0.7
0.8
0.9 1.0
Mole ~action of" butanols Fig.l Variation of A P and 6°with mote f r a c t i o n o f (hree butanols in Carbon tetrachioride.
262
0.6
jy,
,y,
0
‘
,
f;
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 0.9 1.0 Mole fraction of n- Butanol
Fig.2 Variation of AP and G* with mole fraction of n- Butanol in three non polar solvents.
dt = [ds + 10-3,(t-ts) with the help of relevant Table"
C5I.
Of course
+
lo-6B(t-t,)2
+
10-q~(t-ts)31
data taken from the "International
fi,y and A are omitted
f lO++A Critical
as they are negligibly
small.
Using this value of density at its melting point, we have calculated real cal , a correction has been applied taking molar volume Vs . To find Vs into account
of fractional
volume
change on freezing
C61.
2.345
2.617
2.850
3.200
3.568
6.036
4.660
5.430
5.790
8.500
0.050
0.142
0.200
0.250
0.300
0.360
0.420
0.460
0.600
E
0.840
x2
0.862
0.864
0.864
0.866
0.867
0.868
0.869
0.871
0.873
0.875
d -3 gm.cm
Solvent-Benzene
0.87
-0.15
-0.04
0.09
0.14
0.21
0.27
0.35
0.45
0.75
1.456
3.263 3.653 4.550 4.978 5.740 7.800
0.310 0.390 0.430 0.500 0.600
0.245
1.474
2.900
0.198
1.120
-0.30
-0.27
-0.10
1.301 1.230
-0.03
0.03
0.11
0.18
0.27
0.60
0.84
GX
1.350
1.403
1.537
2.590
0.135
1.590
1.636
2.433
2.300
d -3 gm.cm
0.078
0.045
E
Solvent - Carbon tetrachloride
CG = 1.6391
0.742
2.164 2.384
0.105 0.186
0.600
0.530
0.470
0.400
0.340
0.272
0.763 0.770 0.778 0.791
4.150 4.880 5.980
0.759
3.103 3.500
0.749
2.717
0.743
0.730
-3
0.739
gm.CIU
d
1.996
E
2.106
0.080
0.012
x2
Solven - n-heptane
Table l(a): Variation of G* with concentration of n-Butanol in different solvents at 28'C
__
-0.50
-0.38
-0.31
-0.23
-0.15
-0.09
0.00
0.08
0.10
0.60
G*
2.490
2.640
2.980
3.283
3.610
4.060
4.684
7.630
0.078
0.128
0.190
0.250
0.300
0.360
0.430
0.600
--
2.340
E
0.050
x2
-3
0.850
0.858
0.861
0.864
0.866
0.868
0.869
0.870
0.875
gUl.Cm
d
-0.10
0.01
0.10
0.17
0.23
0.34
0.42
0.66
0.79
G*
0.600
0.500
0.420
0.375
0.319
0.255
0.202
0.136
0.074
x2
-
8.500
6.110
4.460
4.192
3.624
3.142
2.844
2.490
2.400
c
1.190
1.260
1.304
1.351
1.391
1.496
1.482
1.531
1.586
d -3 gm.cm
-0.14
-0.12
0.00
0.11
0.14
0.20
0.24
0.29
0.64
G*
Solvent - Carbon tetrachloride
[G = 1.2701
0.535
0.469
0.405
0.335
0.260
0.194
0.110
0.078
0.022
x2
-
--.
4.770
4.138
3.412
2.986
2.575
2.348
2.135
2.100
1.993
E
0.772
0.768
0.759
0.758
0.754
0.744
0.734
0.733
0.733
---
d -3 gm.cm
Solvent - n-heptane
with concentrationof i-Butanol in different solvents at 28'C
Solvent - Benzene
Table l(b) : Variation of G*
-0.09
-0.08
-0.06
-0.01
0.00
0.03
0.09
0.20
0.32
Gf
-3
3.380
3.780
4.166
5.200
6.270
0.270
0.338
0.400
0.600
0.710
0.818
0.821
0.825
0.830
0.835
0.839
3.200
0.240
0.840
0.840
2.600
2.967
0.211
0.842
g,Ul.Clll
d
0.146
2.461
E
0.01
0.30
0.34
0.38
0.39
0.40
0.84
0.62
G*
-0.12
--
Solvent - Benzene
------
-3
1.340
3.820
4.992 6.100 6.680
0.600 0.720
1.050
1.140
1.210
1.290
1.366
4.240
1.440
3.420
1.484
1.533
1.578
1.632
gUl.ClIl
d
2.966
2.660
2.480
2.340
2.290
E
0.500
0.435
0.380
0.340
0.250
0.199
0.138
0.080
0.040
x2
0.600
0.02 -0.02
0.543
0.480
0.407
0.342
0.268
0.195
0.110
0.080
0.012
x2
0.08
0.17
0.18
0.20
0.22
0.25
0.32
0.48
0.88
G*
Solvent - carbon tetrachloride
CG = 0.7441
4.400
3.910
3.440
2.950
2.660
2.418
2.276
2.120
2.080
1.992
E
: Variation of G* with concentration of t-Butanol in different solvents at 28'C
0.079
x2
Table l(c)
-3
0.01
0.00
0.769
-0.03
-0.02
0.763 0.766
0.00
0.756
0.02
0.746 0.750
0.06
0.10
0.14
0.55
G*
0.745
0.736
0.735
0.731
gll.Clll
d
Solvent - n-heptane
266
i.e.,
“s
real = ";a1 correction
From the calculated
value of G, it is observed
(1.639) and least for t-Butanol interaction dipolar
(n-Butanol
as reflected
- 1.66, i-Butanol
multimers
environment
increase
that solute - solute
> t-Butanol.
- 1.66) is nearly
there is a progressive
As such G* significantly
the nature of interaction
the
shift of changes.
of solute molecules
that the value of G* is ' appearing
It starts from positive
in concentration
value and change
of solute molecules.
The
in an
as concentration
to negative
concentration
the solvent molecules
this change of environment
value of G*.
Dwivedi
at the same result,
Comparing
for change of sign in the
and also Sabesan
for some monoalcohols
factor in the mixture,
apparently
et al.
and carboxylic
this trend with the nature of variation
linear correlation to negative
the cloud of solute molecules.
is responsible Cal
the solute
On the other hand at higher
remain within
and Srivastava
value with
If we look into the environment
remain in a cage of solvent molecules.
Probably
equal,
to steric factors.
solute and solvent, we find that at low concentration
molecules
Since the
(gas phase) value
- 1.64 and t-Butanol
of solute species.
It is observed
arrived
by dipole moment
for n-Butanol
of solvent molecules.
dependent.
between
This indicates
with solvent molecules,
value of G* indicates
that it is maximum
> i-Butanol
order in G value may be attributed
On dilution various
(0.744).
is in the order of n-Butanol
character,
observed
factor
c7,91
acids.
of Kirkwood-Frghlich
change in the sign of G* from positive
keeps pace with the conversion
from 8 multimers
to
a
multimers. For a given solute at a particular
concentration
the larger value of G* implies comparatively correlation.
It is observed
tetrachloride
> n heptane.
excess effect.
that G* decreases From our earlier
that benzene
correlation
of solute molecules
n-heptane.
This is probably
study [121
group and r electrons interaction
in the aromatic
leads to an interacting
favourable
alignment
for carbon
tetrachloride.
interaction
in comparison
of dipoles
tetrachloride
of solute in an environment
the interaction
observed
between
ring of benzene molecule.
environment
such a solvent
angular
tetrachloride
interaction
and
hydroxyl
This
around solute species
of solute species.
Carbon
better
to carbon
carbon
it was seen that
factor exhibited
helps establishing
due to favourable
solvents,
of angular
in the order benzene,
free energy as well as linear correlation This reveals
in different
better reinforcement
and gives
But the case is different
being highly nonpolar
of this solvent
is expected.
to However
in this case to a small extent could be due to
267 polarizable a small
electron
interaction Sabesan
cloud associated
interaction.
of solute molecules
et al. C7l
We further
observe
to change
increased response
in environment
steric hinderances is slow.
compared
concentration
in dipolar
to negative coincides
reinforcement
of angular conclusion
change of dipolar However coincide
moves
solvent
to t-Butanol,
thus preventing
i-Butanol
B-multimers
in polarization findings,
of G* (= 0) from AP(=O)
the OH- bearing
the response
causes a delay
and t-Butanol
It is marginal
an easy approach
As a result
cage.
region
unity. are
concentration due to
therefore.
agrees the
of zero value of G* and AP do not exactlv
containing
is more in case of t-Butanol.
is slow which
when AP starts to become
in as much as the change in the sign of G* reflects
the occurrence
from n-Butanol
crowded,
It is seen
alignment.
in the mixtures
departure
Our present
correlation.
AP in these
But at higher
of polarization.
cr-multimers are in excess which causes an increase
with earlier
the
with g attaining
that in low concentration
causes a reduction
more
slow rate of
interactions.
from positive
on the basis
and t-butanol
excess polarization
this position
in excess which
responds
C121.
that the sign of G* changes
This is explained
in all
alignment
in comparatively
both long and shortrange
Further
concentration
On the other hand due to
with i-butanol
positive
(Fig. 2).
is least.
to other two butanols
study Cl21 we evaluated
taking into account
Hence
conclusion.
in these systems.
associated
This is also reflected
In our earlier
environment
thus leading to
are absent.
that the rate of change of G* with molar
is maximum
change of g with molar
systems
at a similar
This goes to show that the change
solvents.
molecule,
both the factors
in n-heptane
also arrived
of solute in n-Butanol
quickly
with chlorine
In case of n-heptane
carbon
of t-Butanol zero.
As one
atoms becomes more
of solvent molecules
in G* attaining
is rather more
(Fig. 1) the
in i-Butanol.
to form the
in the solvent Consequently
environment
the departure
in t-Butanol.
REFERENCES
1
: Theory of dielectrics,
H. Fr8hlich
2
G. Oster
3
H. Eyring.
London-Oxford,
1958.
: J. Am. Chem. Society, 68 (1946) 2036. M.S. Jhon. Significant
liquid structures,
(John Wiley, New York)
1969.
4
J.E. Lennard
- Jones and A.F. Devonshire,
Ser A (GB), 169 (1939) 317.
Proc.R.Soc.,
London,
International Technology. and London. 6
Y. Marcus.
Critical
Tables
of Numerical
Vol. III & IV, McGraw
Data, Physics,
Hill Book Company.
Chemistry
and
JNC, New York
1928. Introduction
to liquid state chemistry
R. Sabesan,
R. Varadrajan
(Chem.Sc.),
89 (1980) 503.
a
D.C. Dwivedi
9
R. Sabesan.
and M. Sargumoorthy
and S.L. Srivastava
(John Wiley,
London),
1977.
: Proc. Ind. Aca. Sci.
: Indian J. Pure and Aopl.Phys.,
18 (1980) 40. R. Varadrajan
and M. Sargumoorthy
: Indian J. Pure and Apnl.Phys.
19 (1981) 646 LO
B.B. Swain
: Acta Chim. Hung., 117 (1984) 383.
11
B.B. Swain
: JPN. Jour. Appl. Phys., 23 (1984) 930.
12. B.B. Swain and G.S. Roy
: JPN. Jour. Appl. Phvs.. 25 (1986) 209.
13
M.S. Jhon and H. Eyring
: J. Am. Chem. Sot., 90 (1968).
14
R. Mecke and H. Kempter
: Nature. 27 (1939) 853
15
S.K. Garg and C.P. Smyth
: J. Chem. Physics, 43 (1965) 2959.
257
Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
DIELECTRIC
STUDIES
SOLUTE-SOLVENT
OF BINARY MIXTURES
OF BUTANOLS
IN NONPOLAR
SOLVENTS
-
INTERACTIONS
B. B. SWAIN and G. S. ROY
Post-Graduate (Received
Department
of Physics,
Ravenshaw
College,
Cuttack
753003,
INDIA
17 May 1986)
ABSTRACT
Dielectric Butanol
constant
of binary mixtures
in three nonpolar
solvents
namely
n-heptane
have been measured
parameter
G* based on the significant
these mixtures. interactions calculated
benzene,
at radio frequency.
This parameter
structure
G* reflecting
is found to be influenced
in solvent
corroboration
carbon
tetrachloride, interaction
the non-specific
polarization
dipole
The results
findings
and
model has been calculated
in
solute - solvent
by the nature of the solvent.
environment.
in the earlier
and t-
Eyring's
value of G* has been used for interpreting
the solute domains further
of n-Butanol,i-Butanol
The
interaction
of
of this study finds
of these authors
on excess molar
in these mixtures.
INTRODUCTION
Study of dielectric interesting Frohlich condensed
method
Cl1 linear correlation phase
concentration
benzene,
in mixtures carbon
nature
of three butanols
reflected
of variation
systems provides
curve CZI
in nonpolar
Furthermore,
of g was identical
solvents
free energy namely,
in the value of g
present
it was observed
in seemingly
change
in them both
that though the
non-interacting
nonpolar
in the value of g, excess molar
0 1987ElsevierSciencePub1ishersB.V.
the
has been
earlier i121
and excess
The variation
in the
describing
solvents
We have evaluated
of multimerisation
an
The Kirkwood-
of local ordering
in three nonpolar
and n-heptane.
the nature
yet there was appreciable
0167-7322/87/$03.50
theoretical
by many authors.
at low and high concentrations.
mediums,
bonded
factor, excess molar polarization
tetrachloride
in the solutions
Oster's
of g of polar liquids
corroborated
the linear correlation
in hydrogen
into liquid structure.
factor g is a measure
in such systems.
dependence
experimentally
of mixing
properties
of investigation
258 polarization nonpolar
and excess
solvents.
This obviously
the presence
mdtimeriSation
solute molecules Mecke-Kempter assumed
free energy at the same concentration
especially
cl41
[3,131
environment
in assessing
to the shortrange In Kirkwood's
Eyring
Cl1
model
factor
by Eyring et al. C3,131 the solute-solute
in an environment
G and G* respectively.
of crystalline
and Devonshire
they concluded freedom
environment
effect is directly
of dipolar
interaction
of solvent molecules
namely benzene,
i-Butanol
they explained
liquid,
fluidised
vacancies
correlation
related
of dipoles a
to the liquid stucture
measurements
with
the evaluation
solute and solute molecules
due to angular
correlation
and t-Butanol
carbon tetrachloride
approximation
of number of systems.
Here we have undertaken between
structure,
showed that this theory could even
from static dielectric
measurements.
(holes) in
Thus this model reveals
altered.
Garg and Smyth cl51
species.
relaxation
hole
a gas like
Oscillator
properties
in an associated
is significantly
in a given domain of n-Butanol, solvents
that confers
for the rest of the molecules,
solvent
fact that solvent
GX , a measure
lattice sites
as a significant
an Einstein
and dielectric
the data obtained
dielectric
of two factors
over disorder
that a liquid has an
to a large extent and at such shortrange
of solute molecules
reconcile
Making
of freedom
a nonpolar
can be increased
significant
of vacant
the hole concept
vacancies.
transport
thermodynamical,
of associated
the presence
Extending
for solid like degrees
By introducing
recognises
In
of solute molecules
by values
is an improvement
that a liquid has an excess volume
on fluidised
The model
structure.
Eyring et al postulated the liquid structure.
of a dipole of
values of 8.
and interaction
C41
is free
free from such assumptions.
are reflected
This model which
theory of Lennard-Jones element
interaction
of solvent molecules
the fluid
that central dipole
of the moment
is, however,
in an
a significant
to understand
it is assumed
by
interaction
et al. proposed
correlation
in a local field and space averaging
their model,
can not be
of g at low concentration
the solute-solute
liquid has been taken to be u cos 0 over all possible proposed
and
As such
equilibrium
and as such calculation
of solvent molecules.
structure.
solvent
are in excess.
it has been shown that the model proposed
is useful
modification
to orient
when solvent molecules
solvents
to the effect of between
difficult.
On the other hand, Eyring
in addition interaction
type of concentration-independent
for different
rather becomes
indicates,
of non-specific
for different
in an
of the molecules
in three nonpolar
and n-heptane.
of
259 THEORY
Significant sites
structure
(holes) present
assumed
in a liquid.
to be fluidised
freedom.
C31
theory
vacancies,
In one mole of liquid,
that there are vacant
These disordered
lattice
holes of liquid are
which
are supposed to possess gas like there will be v-vs moles of such vacancies
where V and Vs are the molar volumes Thus each of these fluidised
proposes
in liquid a!d solid phase respectively. confers gas like properties on v-vs
vacancies
v
moles respectively. Thus the partition
function
like and gas like degrees
for a mole of liquid is separated
into solid
of freedom and the mean value of property
x is given
by v-v “S =
where
x,($
+
xg
x, and x
‘+
are values
of this property
in solid and gaseous
states
g respectively. According consists average
grouped
dipole moment
polarization of maximum result
to the significant
of dipoles
polarization
align themselves
to be u2GF/kT where
gas like holes the Kirkwood's orientation
of molecules
The foregoing theory
[31
As a
oriented
to the
molecules
of solid like structure
For
G = cos28 and F is the local field.
Cl31
since free
for gaseous part.
coupled with the concept equation
in
is
of significant
for the dielectric
structure
constants
liquids. c,+2
(E2-Em)2(2E2+E,)
=&z!!(_
where
or antiparallel
factor p2F/3 kT is still retained
assumptions
the direction
in the field.
in the local field is possible
lead to the following
of hydrogen-bonded
3
either parallel
mean dipole moment
of maximum
field is applied,
of domains will tend to orient
The resulting
found by Eyring
to the direction
When an electric
liquid
These dipoles have
sizes.
This leads to the growth of favourably
field direction. the domains.
theory an associated
of various
pcos0 with respect
for the domain.
the dipoles
structure
in domains
"2
3
Vsu2G )2 [V2kT
constant
v -v 2 S) -lJ2 +(--3kT "2
~2
is the dielectric
cm
is taken as square of the refractive
of the polar
N
is the Avogradro
number,
k
is the Boltzmann
constant,
,
liquid
index of the polar liquid
(1)
260 T
is temperature
p
is the dipole moment
"2 V S
G
of polar
is the molar volume
of liquid in solid phase
to angular The addition
Pt
of dipole
increase
between
of molecules solvent
its dielectric
is expected
behaviour.
afresh.
G to account
Thus eqn.
for the changes
(1) can be modified
molecules
due
to alter the liquid
As such the dielectric in an environment
of solvent
The number of such domains
Thus P;
of solute concentration.
identical
in a given domain.
of the domain of solute species
is to be considered
G* replaces
liquid,
interaction
correlation
of a nonpolar
and hence
polarization molecules
of liquid in gas phase
is the molar volume
is a measure
structure
Kelvin,
is now expressed
increase with * as v2G /kT where
in the environment.
to accommodate
such interactions
and is
given by (c--E m )(2E+E m ) =
V 2 X2 C 2 V 3V
41rN -. 3kT
3(E_o+2)2
(X2G + XlG* ,++ 3
where X 1 and X2 are the mole fractions E
is the dielectric
V
is the molar volume
constant
v-v L)I v
of the solvent
(2)
and solute respectively.
of the mixture,
of the mixture,
and other symbols
as defined
earlier. The data for G in pure liquids and G* for varying alcohols
in nonpolar
solvents
have been calculated
compositions
using eqn.
of
(1) and eqn.
(2)
respectively.
EXPERIMENTAL
The experimental
device used for the measurement
etc. are the same as used by one of the authors of measurement
RESULTS
of dielectric
ClO,lll earlier.
constant
The accuracy
is also the same.
AND DISCUSSION
The relevant in Figures
Evaluation the density employing
data has been presented
in Table 1 and some of them displayed
1 and 2. of Vs:
of the polar
With regard
to calculation
liquid at its melting
the density-temperature
relation.
of Vs we have calculated
point by extrapolation
261
0 i-8ut~nol ra t- Ilutanol ~, n - i u t a n o l
1.0
0.8
,,',\
0.6 'l
\ o.4 o 0.2
13
-6 E O.
<~
-02
-1 El
-0~
-2
-3
-4
~,
-s-
0
0,1
0.2
0.3
0.4 O.S
G6
0.7
0.8
0.9 1.0
Mole ~action of" butanols Fig.l Variation of A P and 6°with mote f r a c t i o n o f (hree butanols in Carbon tetrachioride.
262
0.6
jy,
,y,
0
‘
,
f;
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9 0.9 1.0 Mole fraction of n- Butanol
Fig.2 Variation of AP and G* with mole fraction of n- Butanol in three non polar solvents.
dt = [ds + 10-3,(t-ts) with the help of relevant Table"
C5I.
Of course
+
lo-6B(t-t,)2
+
10-q~(t-ts)31
data taken from the "International
fi,y and A are omitted
f lO++A Critical
as they are negligibly
small.
Using this value of density at its melting point, we have calculated real cal , a correction has been applied taking molar volume Vs . To find Vs into account
of fractional
volume
change on freezing
C61.
2.345
2.617
2.850
3.200
3.568
6.036
4.660
5.430
5.790
8.500
0.050
0.142
0.200
0.250
0.300
0.360
0.420
0.460
0.600
E
0.840
x2
0.862
0.864
0.864
0.866
0.867
0.868
0.869
0.871
0.873
0.875
d -3 gm.cm
Solvent-Benzene
0.87
-0.15
-0.04
0.09
0.14
0.21
0.27
0.35
0.45
0.75
1.456
3.263 3.653 4.550 4.978 5.740 7.800
0.310 0.390 0.430 0.500 0.600
0.245
1.474
2.900
0.198
1.120
-0.30
-0.27
-0.10
1.301 1.230
-0.03
0.03
0.11
0.18
0.27
0.60
0.84
GX
1.350
1.403
1.537
2.590
0.135
1.590
1.636
2.433
2.300
d -3 gm.cm
0.078
0.045
E
Solvent - Carbon tetrachloride
CG = 1.6391
0.742
2.164 2.384
0.105 0.186
0.600
0.530
0.470
0.400
0.340
0.272
0.763 0.770 0.778 0.791
4.150 4.880 5.980
0.759
3.103 3.500
0.749
2.717
0.743
0.730
-3
0.739
gm.CIU
d
1.996
E
2.106
0.080
0.012
x2
Solven - n-heptane
Table l(a): Variation of G* with concentration of n-Butanol in different solvents at 28'C
__
-0.50
-0.38
-0.31
-0.23
-0.15
-0.09
0.00
0.08
0.10
0.60
G*
2.490
2.640
2.980
3.283
3.610
4.060
4.684
7.630
0.078
0.128
0.190
0.250
0.300
0.360
0.430
0.600
--
2.340
E
0.050
x2
-3
0.850
0.858
0.861
0.864
0.866
0.868
0.869
0.870
0.875
gUl.Cm
d
-0.10
0.01
0.10
0.17
0.23
0.34
0.42
0.66
0.79
G*
0.600
0.500
0.420
0.375
0.319
0.255
0.202
0.136
0.074
x2
-
8.500
6.110
4.460
4.192
3.624
3.142
2.844
2.490
2.400
c
1.190
1.260
1.304
1.351
1.391
1.496
1.482
1.531
1.586
d -3 gm.cm
-0.14
-0.12
0.00
0.11
0.14
0.20
0.24
0.29
0.64
G*
Solvent - Carbon tetrachloride
[G = 1.2701
0.535
0.469
0.405
0.335
0.260
0.194
0.110
0.078
0.022
x2
-
--.
4.770
4.138
3.412
2.986
2.575
2.348
2.135
2.100
1.993
E
0.772
0.768
0.759
0.758
0.754
0.744
0.734
0.733
0.733
---
d -3 gm.cm
Solvent - n-heptane
with concentrationof i-Butanol in different solvents at 28'C
Solvent - Benzene
Table l(b) : Variation of G*
-0.09
-0.08
-0.06
-0.01
0.00
0.03
0.09
0.20
0.32
Gf
-3
3.380
3.780
4.166
5.200
6.270
0.270
0.338
0.400
0.600
0.710
0.818
0.821
0.825
0.830
0.835
0.839
3.200
0.240
0.840
0.840
2.600
2.967
0.211
0.842
g,Ul.Clll
d
0.146
2.461
E
0.01
0.30
0.34
0.38
0.39
0.40
0.84
0.62
G*
-0.12
--
Solvent - Benzene
------
-3
1.340
3.820
4.992 6.100 6.680
0.600 0.720
1.050
1.140
1.210
1.290
1.366
4.240
1.440
3.420
1.484
1.533
1.578
1.632
gUl.ClIl
d
2.966
2.660
2.480
2.340
2.290
E
0.500
0.435
0.380
0.340
0.250
0.199
0.138
0.080
0.040
x2
0.600
0.02 -0.02
0.543
0.480
0.407
0.342
0.268
0.195
0.110
0.080
0.012
x2
0.08
0.17
0.18
0.20
0.22
0.25
0.32
0.48
0.88
G*
Solvent - carbon tetrachloride
CG = 0.7441
4.400
3.910
3.440
2.950
2.660
2.418
2.276
2.120
2.080
1.992
E
: Variation of G* with concentration of t-Butanol in different solvents at 28'C
0.079
x2
Table l(c)
-3
0.01
0.00
0.769
-0.03
-0.02
0.763 0.766
0.00
0.756
0.02
0.746 0.750
0.06
0.10
0.14
0.55
G*
0.745
0.736
0.735
0.731
gll.Clll
d
Solvent - n-heptane
266
i.e.,
“s
real = ";a1 correction
From the calculated
value of G, it is observed
(1.639) and least for t-Butanol interaction dipolar
(n-Butanol
as reflected
- 1.66, i-Butanol
multimers
environment
increase
that solute - solute
> t-Butanol.
- 1.66) is nearly
there is a progressive
As such G* significantly
the nature of interaction
the
shift of changes.
of solute molecules
that the value of G* is ' appearing
It starts from positive
in concentration
value and change
of solute molecules.
The
in an
as concentration
to negative
concentration
the solvent molecules
this change of environment
value of G*.
Dwivedi
at the same result,
Comparing
for change of sign in the
and also Sabesan
for some monoalcohols
factor in the mixture,
apparently
et al.
and carboxylic
this trend with the nature of variation
linear correlation to negative
the cloud of solute molecules.
is responsible Cal
the solute
On the other hand at higher
remain within
and Srivastava
value with
If we look into the environment
remain in a cage of solvent molecules.
Probably
equal,
to steric factors.
solute and solvent, we find that at low concentration
molecules
Since the
(gas phase) value
- 1.64 and t-Butanol
of solute species.
It is observed
arrived
by dipole moment
for n-Butanol
of solvent molecules.
dependent.
between
This indicates
with solvent molecules,
value of G* indicates
that it is maximum
> i-Butanol
order in G value may be attributed
On dilution various
(0.744).
is in the order of n-Butanol
character,
observed
factor
c7,91
acids.
of Kirkwood-Frghlich
change in the sign of G* from positive
keeps pace with the conversion
from 8 multimers
to
a
multimers. For a given solute at a particular
concentration
the larger value of G* implies comparatively correlation.
It is observed
tetrachloride
> n heptane.
excess effect.
that G* decreases From our earlier
that benzene
correlation
of solute molecules
n-heptane.
This is probably
study [121
group and r electrons interaction
in the aromatic
leads to an interacting
favourable
alignment
for carbon
tetrachloride.
interaction
in comparison
of dipoles
tetrachloride
of solute in an environment
the interaction
observed
between
ring of benzene molecule.
environment
such a solvent
angular
tetrachloride
interaction
and
hydroxyl
This
around solute species
of solute species.
Carbon
better
to carbon
carbon
it was seen that
factor exhibited
helps establishing
due to favourable
solvents,
of angular
in the order benzene,
free energy as well as linear correlation This reveals
in different
better reinforcement
and gives
But the case is different
being highly nonpolar
of this solvent
is expected.
to However
in this case to a small extent could be due to
267 polarizable a small
electron
interaction Sabesan
cloud associated
interaction.
of solute molecules
et al. C7l
We further
observe
to change
increased response
in environment
steric hinderances is slow.
compared
concentration
in dipolar
to negative coincides
reinforcement
of angular conclusion
change of dipolar However coincide
moves
solvent
to t-Butanol,
thus preventing
i-Butanol
B-multimers
in polarization findings,
of G* (= 0) from AP(=O)
the OH- bearing
the response
causes a delay
and t-Butanol
It is marginal
an easy approach
As a result
cage.
region
unity. are
concentration due to
therefore.
agrees the
of zero value of G* and AP do not exactlv
containing
is more in case of t-Butanol.
is slow which
when AP starts to become
in as much as the change in the sign of G* reflects
the occurrence
from n-Butanol
crowded,
It is seen
alignment.
in the mixtures
departure
Our present
correlation.
AP in these
But at higher
of polarization.
cr-multimers are in excess which causes an increase
with earlier
the
with g attaining
that in low concentration
causes a reduction
more
slow rate of
interactions.
from positive
on the basis
and t-butanol
excess polarization
this position
in excess which
responds
C121.
that the sign of G* changes
This is explained
in all
alignment
in comparatively
both long and shortrange
Further
concentration
On the other hand due to
with i-butanol
positive
(Fig. 2).
is least.
to other two butanols
study Cl21 we evaluated
taking into account
Hence
conclusion.
in these systems.
associated
This is also reflected
In our earlier
environment
thus leading to
are absent.
that the rate of change of G* with molar
is maximum
change of g with molar
systems
at a similar
This goes to show that the change
solvents.
molecule,
both the factors
in n-heptane
also arrived
of solute in n-Butanol
quickly
with chlorine
In case of n-heptane
carbon
of t-Butanol zero.
As one
atoms becomes more
of solvent molecules
in G* attaining
is rather more
(Fig. 1) the
in i-Butanol.
to form the
in the solvent Consequently
environment
the departure
in t-Butanol.
REFERENCES
1
: Theory of dielectrics,
H. Fr8hlich
2
G. Oster
3
H. Eyring.
London-Oxford,
1958.
: J. Am. Chem. Society, 68 (1946) 2036. M.S. Jhon. Significant
liquid structures,
(John Wiley, New York)
1969.
4
J.E. Lennard
- Jones and A.F. Devonshire,
Ser A (GB), 169 (1939) 317.
Proc.R.Soc.,
London,
International Technology. and London. 6
Y. Marcus.
Critical
Tables
of Numerical
Vol. III & IV, McGraw
Data, Physics,
Hill Book Company.
Chemistry
and
JNC, New York
1928. Introduction
to liquid state chemistry
R. Sabesan,
R. Varadrajan
(Chem.Sc.),
89 (1980) 503.
a
D.C. Dwivedi
9
R. Sabesan.
and M. Sargumoorthy
and S.L. Srivastava
(John Wiley,
London),
1977.
: Proc. Ind. Aca. Sci.
: Indian J. Pure and Aopl.Phys.,
18 (1980) 40. R. Varadrajan
and M. Sargumoorthy
: Indian J. Pure and Apnl.Phys.
19 (1981) 646 LO
B.B. Swain
: Acta Chim. Hung., 117 (1984) 383.
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B.B. Swain
: JPN. Jour. Appl. Phys., 23 (1984) 930.
12. B.B. Swain and G.S. Roy
: JPN. Jour. Appl. Phvs.. 25 (1986) 209.
13
M.S. Jhon and H. Eyring
: J. Am. Chem. Sot., 90 (1968).
14
R. Mecke and H. Kempter
: Nature. 27 (1939) 853
15
S.K. Garg and C.P. Smyth
: J. Chem. Physics, 43 (1965) 2959.