CHAPTER I I I

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.

o n c -» T O

<

a

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).