CHAPTER III EXPERIMENTAL TECHNIQUES AND METHOD OF MEASUREMENTS
46
3.1 MICROWAVE MEASUREMENTS FOR DIELECTRIC STUDIES
a) INTRODUCTION
As has been discussed in the preceding chapter, dielectric
properties are concerned with the response of the 'medixan to the
electromagnetic field passing through it. Dielectric parajrieters r
could be estimated by investigating propagation characteristics
of the electromagnetic field. Experimental techniques for such
investigations depend upon the range of frequency of the
investigating electromagnetic field. In the lov;er frequency
range (less than 100 MHz) lumped circuit methods and in the
higher frequency range (above 100 MHz) distributed circuit
methods are used. Various techniques of lumped circuit methods
and distributed circuit methods have given by number of research
workers (Von Hippel, 195^; Flugge, 1956; Hasted, 1961;
Montgomery, 19^7; Ragan, 19^; Staler, 19^; Hill et al., 1969;
Sisodia and Raghuvanshi, 1979; Scaife, 1971).
In the present reported work microwave waveguide techniques
for investigating dielectric properties of polar molecules in
non-polsr solvents have been used. In the fol!lov;ing sections,
brief theory and techniques of microwave measurements are
discussed:
b) THEORY
Propagation characteristics of electromagnetic waves
47
propagating dovm the waveguide filled with the dielectric could
be analysed by solving Maxwells equations with proper boundary
conditions. Electromagnetic wave propagating in the dielectric
medium suffers change in its phase and amplitude. Sinusoidally
changing electric field with the angular frequency to of the
microwave source at a point in the waveguide can be represented
with the real part of E e'' ^ ^, At a distance x from it the
value of the electric field could be given by the follov:ing
relations (Smyth, 195?):
E^ = E pj ' e " " (3.1)
where
or E^ = V ^ ^ " * ' • I' '-e"'''''' (3.3)
These relations show that the phase of the wave changes by f ,x
and its amplitude decreases by the factor e as the wave
traverses a distance x of the waveguide. So ^, is called the
propagation constant, p, the phase constant and «^, is the
attenuation constant.
For-the rectangular waveguide filled with the dielectric,
propagation constant ^^ is related with the complex dielectric
48
constant of the medium (Scaife, 1971) through the relation:
d^TT X X
(3A)
where X^ i s the free-space wavelength and Ac i s the cut-off
v/avelength for the pa r t i cu l a r mode of propagation and depends
upon the dimensions of the waveguide. 6 i s the complex
pe rmi t t i v i ty of the f i l l e d d i e l e c t r i c medium and can be wr i t ten
as :
6 = e - j 6 (3.5)
Separating real and imaginary parts of the equation (3-^), we
get
.2
6 = 271
1 -<<X
'•' ^^^P^A
(3.6)
(3.7)
(f)' For low loss liquids, the term |-5—- ) is very small and- hence
it can "be neglected in comparison to unity. Therefore,
equations (3.6) and (3.7) can be written as:
/ ty^ • (t (3.8)
49
With the help of these relations, permittivity ( 6 ) and
dielectric loss ( £ ) of the dielectric medium filled in the
waveguide can be determined from the measured values of °<J^^ and :
R. . The value of ^ the phase constant can be determined by-
measuring the wavelength (Ad) in the dielectric medium and is
given by the relation, B, = -~- . The attenuation constant ^'^^ Act
(<=<4).could be determined by measuring the amplitude of the
reflected wave from the dielectric medium or from the VSWR
measurements in the section of the waveguide.
Based on the above theory, Roberts and Von Hippel (19^6)
gave a method for measurements of complex dielectric constant.
In this method, the dielectric under test is contained in the
section of the waveguide AB which is short circuited at its end
B. Microwave signal from its source at a fixed frequency passes
through the dielectric after passing through the slotted section.
This is shown in the Fig. 3.I.
Because of the superposition of forward going waves and
reflected waves from the interface A, standing waves are formed
in the space in front of the sample. First the measurements
of VSWR and first position of minima from interface A are made
without the dielectric but with the B end short circuited.
51
Then measurements of VSWR and first position of voltage minimum
from the interface A are made with the dielectric filled in
the section AB with B end short circuited. Shifting of the
first minima from interface A with the dielectric filled depends
upon the wavelength of EM v;ave in the dielectric and on sample
dimensions or in other words depends upon the dielectric
permittivity ( 6 J of the medium. VSWR measurements with the * —
dielectric in the waveguide changes from its corresponding
value without the dielectric. This decrease in VSWR measurements
depends upon the lossy nature of the dielectric, hence could be
related with the dielectric loss < fc ) of the dielectric medium.
An electrcmagnetic v;ave travelling through medium 1 (air)
strikes normally to the medium 2 (dielectric), a part of it
gets transmitted and a part gets reflected. Because of the
superposition of forward going wave and reflected wave, standing
wave pattern is formed in the space in front of the dielectric
medium. The transverse electric field component in the space
in front of the dielectric medium can be written as:
E y
2 e ' - ^'^ 1 . r e ^ ^ -o (3-10)
where Vj i s the propagation constant in medium 1 and i s
r e l a t ed with a t tenuat ion constant ( =<i ) and phase sh i f t constant
( 8 ) through the r e l a t i on
y, = ' i + j ft
52
The ref]ection coefficient r can be written as:
r l e -j2\);
(3.11)
The input impedance at the interface x = 0 can be expressed as:
'1
1 + r
1 - r. (3-1?)
vrhere Z is the impedance of medium 1. If attenuation in medium 1
is negligible, the inverse voltage standing wave ratio can be
written as:
/ E_ mm E max
1 + Ir (3.13)
If x^ is the distance of the first minima from the dielectric o
interface, expression for the impedance Z at the dielectric
boundary can be written as (Scaife, 1971):
/ - j tan (, x^)
1 - 2 f tan ( , x^) (3.1^)
If medium 2 is short circuited at the end B, the input impedance
at X = 0 csn be written as:
( o S.C Z tanh V^ d (3.15)
53
where Zp,^, and d are characteristic impedance, propagation
constant and the length of the medium 2 respectively.
Equating equations (3.1^) and (3'15), >e get
' / - ;5 tan ( x^)
1 - j / tan (^ x^)J
or substituting B = 2 Tr/\
= Zp tanh Y d (3.16)
tanh Y d
2Trd
! - > tan
2Tr X,
>r
, . . / . . ( - ^ )
(3.17)
By measuring x the shift of the first minima from the interface
J the inverse standing wave ratio and Ao^ the waveguide
wavelength in the medium 1, it is possible to evaluate the
R.H.S. of equation (3.1?) and hence the L.H.S. may be evaluated
as a complex quantity. Von Hippie (195^) prepared charts for
the further evaluation of Y^ d from the complex value of left
hand side of equation (3.17).
From the above analysis, it is clear that experimental
techniques involved in the Von Hippie method is simple. But in
calculating the results frOTi the experimental data, the
computational effort involved are considerable.
Depending upon the type of the dielectric mediijm number
of simplifications of the above method have been suggested
O-i
(Williams, 1959; Dakin and Works, 19^7; Corfield et al., 1961;
Rao, 1966; Bannet and Calderwood, 1965"; Fatuzzo and Mason, 196^;
Brydon and Hepplestone, 1965; Surber, 19^8; and Foley, 1955
method).
For low loss liquids, Heston et alo (1950) have suggested
a method which results into good simplification of the Von
Hippie method. According to this method, liquid sample of
length equal to integral multiple of ^d/2 placed in contact
with the short circuit may be taken. Then the value of x the o
distance of the first minima from the interface will be zero
and from equation (3«1^) ve have
^^o^S.C. " / (since Z = 1) (3-18)
/ From equat ions (3-15) and ( 3 . 1 8 ) , we ge t
/ = Z2 tanh ( \ d) (3-19)
K Since \ = ^^A-^ 1\ r<X. > d = n . -^^ (where n = 1 , 2 , 3 , *+. . . )
a n d Z ^ = ^ ^ ^
P u t t i n g these in equa t ion (3*19) , we have
j = -r— • tanh ^7
A 3
tanh
tanh
^^JiXx
y)°<^M^
55
For lov/ loss substances, tanh = tan Y l ^ d Ac(
2 2 -so
/ = ^ A^ °<^ Aoi
^ T cKcL AJL
(3 .20 )
In t h i s equation, contr ibut ion to j comes frorr? two types of
l o s s e s , one i s from d i e l e c t r i c losses of the d i e l e c t r i c medium
and second from the plunger res i s tance and waveguide wall -losses.
Losses due to plunger and v;aveguide v;alls may be -eliminated by
p lo t t ing a graph between J and n and the slope of t h i s graph
gives the value of o<^^
o< 2A
t t dn
Substituting this value of c<j^ in equations (3.8) and (3*9) / //
for lov/ loss dielectrics, we get the values of ^ and 6 as:
and //
Ac
2 /A.1 h. 1^
(3.31)
(3-?2)
56
/ Thus, the values of d ie lect r ic permittivity ( £ ) and the
" d i e l e c t r i c l o s s ( ^ ) for low l o s s d i e l e c t r i c s can be eva lua t ed
by measuring the q u a n t i t i e s Ac , Aj. and d f /dvi . In the p r e s e n t
r e p o r t e d work, t h i s method has been used.
c ) X-BAND EXPERIMENTAL SET-UP
Microwave X-band r e c t a n g u l a r waveguide t e s t bench for
d i e l e c t r i c s t u d i e s of low l o s s l i q u i d s ha.ve been s e t up by the
au thor in the E l e c t r o n i c s / S o l i d S t a t e Research Labora tory of
Physics Department, Himachal Pradesh U n i v e r s i t y , Simla-171005.
The block diagram of the s e t up i s shovrn in the F i g . 3 . 2 . This
exper imenta l s e t up c o n s i s t s of microwave sou rce , Klys t ron
power supply, an i s o l a t o r , screvr t u n e r , frequency me te r ,
v a r i a b l e a t t e n u a t o r , s t and ing wave d e t e c t o r , s l o t t e d s e c t i o n ,
'VSVTR meter , E-plane band, d i e l e c t r i c c e l l , coo l ing Ten and the
t h e r m o s t a t .
A RK 2K25 Raytheon Klystron has been used as a source of
microwave pov/er. The Klys t ron i s mounted on a tunab le k l y s t r o n
mount (Model XM 2 5 1 , SICO, I n d i a ) and was ope ra ted by w e l l
r e g u l a t e d power supply (Model BTP-10, I n d i a ) . The beam v o l t a g e
ou tpu t of t h i s power supply can be v a r i e d con t inuous ly from 25C
t o 35c v o l t s and the r e f l e c t o r v o l t a g e from -10 t o -210 v o l t s .
Klys t ron i s w e l l i s o l a t e d from the r e s t of the microwave bench
by f e r r i t e i s o l a t o r (Model X717, ECIL, I n d i a ) . The f e r r i t e
<a'
K>
X - 1
> z o m X m
2 m z H >
m H C •D
° 3C —
1 °
O 7} i (« " c
H a
w <
-1
° 3C —
1 °
O 7} i (« " c
H a
w <
-1
57
0>
u o
- 3
a
Oo
1-2
l-\
1-0
=i-Water
X-Band Waveguide
Water
E - Plane band
FIG. 3-3 X-BAND DIELECTRIC CELL
59
isolator protects the microwave source from the reflected wave
signals progressing towards the microwave source. In this waj'-
it prevents frequency variation due to load and ensures better
stability of the incident waves.
A direct reading frequency meter (Model X71C, ECIL, India)
having a frequency range of 8.? to 12 GHz, accuracy +. C.^%,
resolution 5 WHz and a 1dB dip at resonance, have been connected
after the ferrite isolator for frequency determination of the
microwave signals.
The standing wave detector has a tunable probe (Model UA230,
ECIL, India) and a co-axial detector mounted on a carriagej
which accomodates 1N23B crystal. The carriage is fitted on a
slotted line section (Model U210,.ECIL, India). The probe
penetration could be varied according to the requirements
(maximum upto 8 mm). The rectified output of the standing wave
detector is fed to VSWR meter (U186, ECIL, India). The liquid
dielectric cell fitted with E-plane band (Model XC71C, SICO,
India) is connected to the slotted line.
Based upon the design suggested by Krishnaji et al. (19^8),
thp dielectric cell v/as specially fabricated for this
experimental set up and is shovm in Fig. 3.3. The cell consist
of an rectangular X-band waveguide section of length ?? en.
On one side, it is fitted with a micrometer driving arrangement
60
capable of moving the short circuiting plunger in the waveguide
section. A thin mica sheet is held pressed between the other
end of the waveguide section and E-plane 90° b?nd. Around the
waveguide section of the cell, a water jacket for circulating
therrnostated water so as to control the temperature of the
liquid in dielectric cell has been provided. The temperature
of liquid xonder investigation is controlled to +_ C.^^C by a
thermostat (MLW-Baureihe U? , German make). In order to prevent
v all losses and losses from the short circuiting plunger, the
cell as well as short circuiting plunger were silver coated.
Microwaves emitted from the Klystron reach the short
circuiting plunger of the dielectric cell after passing through
various microwave components (as shown in Fig. 3«?) snd the liquid
solution contained in the dielectric cell betvreen mica sheet and
short circuiting plun,ger. They suffer complete reflection from
the surface of short circuiting plunger and trace back their
path. In this way in the path between ferrite isolator- and
short circuiting plunger because of the superposition of forv ard
going waves and reflected waves, standing wave pattern is formed.
In the slotted section of the wave guide, standing wave pattern
can be used for VSWR and shifting of the minima position
measurements. The precision of this test bench was tested by
measuring the dipole moments of purified acetone, methanol and
pyridine. The values of our measured dipole moment were found
61
to be within + 2%, in agreement v;ith the values found in the
l i t e r a t u r e (Pirnental and McClellan, I96O; Smyth, 1955).
d) PRCCSDURE FOR MEASUREMENTS
Equations (3.?1) and (3«?2) were used for the de te r r ina t ion
of d i e l e c t r i c constant ( 6 ) and d i e l e c t r i c loss ( 6 ) in the
microwave frequency range a t X-band. These equations require
the measurement of free-space wavelength ( Ao), the cut-off
wavelength ( Ac )> the wavelength in the wa"«'-eguide ( A^), the
wavelength in the d i e l e c t r i c ( A^) and inverse voltage standing
wave r a t i o ( / )•
Ao could be calculated from the frequency of microwaves,
using re l a t ion C = f.^^o , where C i s the ve loc i ty of e l e c t r o -
magnetic rad ia t ions = 3 x 1 0 cm/sec and f i s the frequency
of the microwaves. Ac i s the cut-off wavelength for TE^^ mode,
for rectangular waveguide and i t s value i s taken as 2a, where a
i s the broader dimension of the rectangular waveguide.
For the determination of A« , Xji, and inverse voltage
standing wave r a t i o ( / ) the follovring steps of procedure were
follov/ed:
1. Assembled the equipment as shown in the Fig. 3 .2 .
2. Energized the Klystron and obtained su i tab le power leve l
in SWR meter by adjusting r e f l ec to r voltage', modulation
62
frequency, modulation ajnplitude and tuning the tunable
probe of the slotted section. Power level was adjusted
with the help of variable attenuator so as to have SWR meter
reading in the 30 dB scale.
3. Short circuiting plunger of the dielectric cell v/gs
carefully moved so as to touch the nica sheet of the cell.
h. The detecting probe connected with SWR meter v/as moved
along the slotted section of the vra- -eguide and the standing
waXre pattern was recorded. Twice the distance betvreen two
successive minima was taken as the value for AA, •
5. Dielectric cell v;as filled with the required liquid by
taking out the plunger. The plunder vras moved again into
the cell carefully so as to touch the mica sheet.
6. Movable probe was kept at the position of minima on the
slotted section. Then the plunger was moved upv7?rd, and
the standing v/ave pattern was recorded. 'The distance
betv/een tv/o successive minima yields the value of A(i/2.
7. Inverse voltage standing wave ratio (/,) was measured by
following double minima method as follov::
i) The plunger was moved down to the mica windov;, so that
the liquid length be zero.
ii) Moved the probe carriage along the line to obtain a
minimum reading in the SWR meter.
liekftl Fradeth Uaiversity Librirf SIMLA—0
63
iii) Adjusted 'Gain' controls to obtain a reading of 3.C
on the dB scale.
iv) Moved the carriage along the line to obtain a reading
of full scale (0) on the dB scale on each side of the
minimuin, noted the probe carriage position.
v) Recorded the probe carriage position in the above steps
as x and Xp respectively.
The inverse voltage standing wave ratio (/ ) was calculated
by the relation:
/= i - —i ^3.23)
vi) Steps (ii tc v) were repeated by keeping the plunger
at different positions in steps of ^d/2 and the values
of / were calculated by applying equation (3-?3)«
The measured values of f were plotted against n (the number
of minima in the dielectric) and the slope T—• v;as deternined
for each solution. By substituting these measured and calculated
values in equations (3.?1) and (3.?2), the values of 6 and £
could be evaluated for each solution.
Overall estimated accuracy of measurements for £ is C ?
to 1^ and for ^ is 2 to h%.
64
3.? DENSITY MEASUEEMENTS
The densities were measured using a sealed type py.cnometer
of 20 cm capacity. The pycnometer was calibrated using
conductivity water at different temperatures. Measurements of
densities at different temperatures were made by keeping the
pycnometer in a constant temperature thermostat bath. The
measured values of density are accurate within +, O.Ch%.
3.3 VISCOSITY MEASUREMENTS
An Ubbelohde suspended level viscometer with flow time
756.^ sec for conductivity water at 25°C v as used for viscosity
measurements at different temperatures. The viscometer v;as
suspended in a water thermostat, having a glass window to note
the effux time. The viscometer required no correction for kinetic
energy. The kinematic viscosities (CSt) were converted into
absolute viscosities (cP) using density values measured for each
solvent by a sealed specific gravity type of a pycnometer of
20 cm- capacity. The viscometer was first calibrated with
conductivity water and then the observations were taken v/ith
different liquids whose viscosity was to be measured. Experimental
liquids were poured in the viscometer and allowed to remain
there till a constant temperature was attained. A mild suction
was applied so that the liquid rose and filled the upper bulb,
v;hich had reference marks on its two ends. After releasing the
bo
suction, the time of fall between the two fixed marks is noted.
The runs were repeated until three determinations within + C.2
sec were obtained. The expression used for calculating the
viscosity of unknown liquid is given by
y\ d.t ^ = (3.21.) \ ^o-^o
where " and " ^ are the coefficient of viscosities of the
unknown liquid and that of the conductivity water respectively,
t andvt^ are their effux times and d and d are the densities 0 o
at the experimental temperature. The overall accuracy of the
viscosity measurements was estimated to be +. 0.^%.
3.if DETERMINATION OF DIPOLE MOMENT AND DIELECTRIC' RELAXATION
TIME
Depending upon different mode^Is and theories of dielectric
dispersion and dielectric relaxation discussed in the second
chapter, various methods (Hill et al., 1969; Exner, 1975;
Min kin et al., 1970; Scaife, 1971; Le Fevre, 196V; Smith, 19^7;
Bottcher, 1952; Smyth, 1955) have been suggested for the
determination of dipole moment and relaxation time of polar
molecules. Dielectric dispersion behaviour of dilute solutions
of polar molecules in non-polar solvents approximates to the
dielectric dispersion behaviour of vapour state, of polar
66
molecules. For such dilute solutions, theories of vapour state
of polar molecules could be easily extended. Depending upon
these extensions, number of methods (Wolf, 19?9; Hedestrand,
1929; Lefevre and Vine, 1937; Halverstadt and Kumler, 19^2;
Weissberger, 19^9; Fujita, 1957; Higasi, 1952; Guggenheim, 19^9;
Ghosh and Acharyya, 1978; Cumper et al., 1969; and Hassell et al.,
196^) have been suggested.
Mostly these methods involve the preparation of several
solutions of increasing weight concentrations (W) of polar
solute in non-polar solvents, measurement of their permittivity
and computation of, solute polarization. Extrapolation to
infinite dilution is carried out in order to find out the
solute polarization at infinite dilution. Then by making use
of the Debye formula, the value for the dipole moment of polar
molecule could be determined. Different methods are mostly
because of different extrapolation procedures used. A good
critical review has been presented by Prakash (1976). . In the
present work, Gopala Krishna's method (1957) of concentration
variation at single frequency has been used.
GoT3ala Krishna's Method;
As has been discussed in the second chapter, Debye's
equation for complex permittivity of dielectric medium as a
fimction of frequency of the applied field can be written as:
€ ^ - 1 ^oc- 1 ^TT N, f 1 4 c - 1 +
^TT N^i^
^oo-^ 2
+ . 9 KT £*+ 2 G^-»r 2 . 9 KT 1 + ju^/i;
67
(3.25)
where N^ i s the number of iflolecules per u n i t volume. P u t t i n g
6 = £ - j ^ in aha
imaginary p a r t s , we ge t
^ I II
6 = £ - j ^ in ahove equat ion and s e p a r a t i n g i t s r e a l and
6 + 6 + € - 2 =
4o- 1
9 KT *1
1
C ^ ' . 2 ) 2 . 6 " ^ =
oo 9 KT *1 - K U J V
3€ =
9 KT
OJT;
( € ^ * 2 ) 2 . e"^ =
9 KT 1 + W^TT*'
P u t t i n g ,% >
£ + 6 + ^'' - 2 A - • ^
( 6 + 2 ) 2 * ^//^
3e ^ V _
(€%2)2 .£"^
^ - 1 € + 2
We can write
^ * -hi ^3.26)
F may be regarded constant over the range of concentration of
dilute solutions of polar molecules in non-polar solvents. It
is because of the fact that the experimental errors in the
68
determination of £ and 6 for d i l u t e solut ions a t microvrave
frequencies are higher than the va r i a t ion in F due to change in
concentration of d i l u t e so lu t ions . Slope of the curve Y and X
can give us the value of T* the re laxat ion time of the polar
molecules in non-polar solvents .
For the determination of dipole moment ^ equation (3.26)
can be wr i t t en as :
P + K W d^2 (3-27)
where
Vir N H N d.5 W K = "-j-r , N = — ^ ~
9 KT (1 +t>J^'r'^) M
N is the Avogadro number, M is the molecular weight of polar
substance, W is the weight fraction and d.^ is 'the density of
the solution. At low concentration range, variation of density
of the solution with v eight fraction W may be taken as linear
given by the relation
^12 = %^' ^ '^^^
where d is the density of the solvent. Straight line curve
between X and W gives its slope ^ as Kd . Frc5m this the value
of dipole moment may be calculated using the following relation;
89
9K T M
ir Nd 1 + (S)
dX
dW (3-?8)
Thus this method consist in preparing number of dilute
concentrations of polar solute in non-polar solvent. Microwave
techniques may be used to measure real and imaginary part of
the complex permittivity of these dilute solutions. Corresponding
value for X and Y may be calculated from the measured values of / //
dielectric constant 6 and dielectric loss 6 . The slope of
the straight line plot of Y versias X of equation (3.26) can give
the value for the dielectric relaxation time of polar molecules
in non-polar solvent. Straight line plot of X versus W can give
us the value for •TTT. The value for the dipolp moment of the
polar molecule may be calculated using the relation (3.28). For -
the last so many years, this method has been successfully used
by so many research workers (Krishna et al., 1972; Mehrotra
et al., 1976; Mathur and Saxena, 1977; Mitra et al., 1978;
Somevanshi et al., 1978; Deogaonkar et al., 1979; Ghosh et al.,
1980; Khameshara and Sisodia, 1980) for their research studies
concerning dielectric relaxation and dipole moment determination
of polar molecules in non-polar solvents from microwave
absorption data.
This method makes use of the Debye theory of dielectric
relaxation. So it hag limitations of its validity arising
because of the assumptions used in the Debye theory like spherical
70
nature of polar molecules, assumption of Lorentz field and the
continuous nature of the surrounding medium of the rotating
dipole. This method gives very satisfactor3'' results for very
dilute solutions of polar molecules in non-polar solvents in
v/hich dipole-dipole interactions are absent. Moreover, this
method gives single value for the dielectric relaxation time of
polar molecules in non-polar solvent. Hence this method can be
successfully applied for the study of polar molecules having
single relaxation mechanism. For polar molecules in non-polar
solvent having multiple relaxation mechanism other methods
suggested by Higasi et al. (1971) can be used.
3.5 DETERMINATION OF THERMODINAMIC PARAMETERS
Thermodynamical energy parameters [free energy of
activation ( A F ) , enthalpy of activation ( A H ) , entropj'- of •
activation (AS)) for the dielectric, relaxation process and
the viscous flow process have been determined using the relations
given by Eyring et al. (19 +1) for the rate process:
h f ^^e \ X ^ — exp (3.29)
KT \ RT /
Z\Ffe = ZlHfe - T A S ^ ( 3 . 3 c )
hN ' / AF. \ y\ r. — exp (3 .31)
^ V \ RT y
71
and
AF>| = -^Hi, - T AS,^ (3 .32 )
M v/here V i s the molar volunp and equal to T , where M i s the
molecular weight and d i s the d e n s i t y of the s o l v e n t a t a b s o l u t e
tempera ture T. A F^ , AH^ and AS^ are the f ree energy,
en tha lpy and the en t ropy of a c t i v a t i o n for the r e l a x a t i o n p rocess
and A Fyj , A^Y) and ASv> a re the cor responding energy
parameters for the v i s cous flow.
These thermodynamic parameters can be de termined i f the
r e l a x a t i o n time I ' , d e n s i t y d, v i s c o s i t y "O and tempera ture T
are known.
Taking the logar i thm t o the base ten of equat ion (3 .29)
one g e t s
A He ASfc 2.303 log ( 1' X T) = 2 .303 log 2. + -
^ RT R
A p l o t of log ( T ' X T) a g a i n s t 1/T w i l l give a s t r a i g h t l i n e
wi th slope equal t o AHg. /2.303R from which AH^ can be
c a l c u l a t e d . From equat ion ( 3 . 2 9 ) , one ge t s
AF^ = 2 .303 RT log J (3 .33 )
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Knowing t* and T, AFf. i s e v a l u a t e d . Now A Sg i s eva lua ted
froiri equat ion ( 3 . 3 0 ) .
S i m i l a r l y t a k i n g the logar i thm t o the base ten of the
equat ion (3«3'')> one g e t s
2 .303 log >) = 2 .303 log ^ + ^ -C ^ RT R
P l o t of log>| v e r s u s 1/T should give a s t r a i g h t l i n e wi th s lope
equal t o AEr\ / 2 .303H from which AHYI can be c a l c u l a t e d .
From equat ion (3«31) , one ge t s
AF>. = 2 .303 RT log I — X ^ I (3.3V)
V i s the molar volume and i s found from the d e n s i t y a t d i f f e r e n t
t empera tu res and knowing "^ and T, AF-M can be ca l cu l a t ed . , 1
Knowing A Fyj and A HYI , A Syi can be c a l c u l a t e d from
equa t ion (3*32) .
3,6 PURIFICATION OF CHEMICALS
The chemicals were purified before use and the procedure
for their purification was as follows:
i) Acetamide; (Riedel, Germany) vras purified by repeated
crys tallizations.
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i i ) N-Methylacetamide: (E. Merck, GermanjO vfas pur i f ied by-
repeated ( three times) c r y s t a l ] i z a t i o n s .
i i i ) N,N-Dimethylacetai7iide: (E. Merck) v/as kept over molecular , o ,
sieve M- A for h-Q hours and then d i s t i l l e d through a long v e r t i c a l f rac t iona t ing column and the middle f ract ion was used.
iv ) Formamide; (Riedel Pure) was heated a t 80-90°C for 2-3 hours
to decompose ammonium formate present in the solute to formic
acid and ammonia. Ammonia escaped as a gas leaving behind free
acid over sodamide under reduced pressure in order to n e u t r a l i s e
the free acid and to remove the s l i g h t amount of water which may
be present in the so lu t e . The process of treatment of the solute
with sodamide vras repeated th r ice before a f ina l d i s t i l l a t i o n
without sodamide under the reduced pressure car r ied out . The .
f ract ion (b .p . 77-78°C) was co l lec ted . This d i s t i l l e d product
was further pur i f ied by f rac t iona l cr j '^s tal l isat ions.
v) N-Methylformamide; (Fluka) was pur i f ied by d i s t i l l a t i o n under
reduced pressure , through a long v e r t i c a l f rac t ionat ing column
a f te r drying i t over molecular sieves h A for ^8 hours. The
middle fract ion was re ta ined for use.
v i ) N^N-Dimethylformamide: (E. Merck) v;as kept over molecular
74
, o , sieve M- A for M-8 hours and then distilled under reduced pressure
through a long vertical fractionating column and the middle cut
vas collected for use.
vii) Tetramethylurea; (Fluka) was purified by refluxing over
activated alumina for 2*+ hours and followed by fractional
distillation through a long vertical fractionating column and
the middle fraction was used within a week to avoid decomposition.
viii) Benzene; (BDH Analar) v;as purified hy refluxing over sodium
metal for 6-8 hours and then distilling through a long vertical
fractionating column. The middle fraction was used for the'
present studies (b.p. 80°C).
ix) 1;^-Dioxanet (E. Merck) was purified hy refluxing over
sodium metal for 6-8 hours follov ed by distillation through a
long vertical fractionating column. The middle fraction vras
collected for use (b.p. 101°C).
x) Carbon tetrachloride; (BDH Analar) was distilled through a
long vertical fractionating column and the middle fraction vas
collected (b.p. 76.5°C).