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COMPLEX MICROWAVE DIELECTRIC PROPERTIES OF LIQUIDS, SOLUTIONS AND EMULSIONS

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8418397
P erl, Je ffe ry Phillip
COMPLEX MICROWAVE DIELECTRIC PROPERTIES OF LIQUIDS, SOLUTIONS
AND EMULSIONS
Illinois Institute o f Technology
University
Microfilms
International
Ph.D.
1984
300 N. Zeeb Road, Ann Arbor, Ml 48106
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COMPLEX MICROWAVE DIELECTRIC PROPERTIES OF
LIQUIDS, SOLUTIONS AND EMULSIONS
BY
JEFFERY P. PERL
Submitted in partial fulfillment of the
requirements of the degree of
Doctor of Philosophy in Chemical Engineering
in the School of Advanced Studies of
Illinois Institute of Technology
Approved_
Adviser
.ORIGINAL ARCHIVAL COPY
Chicago, Illinois
May 1984
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ACKNOWLEDGMENT
Chemical Engineers rarely become involved in research of the type
described in this work.
I have therefore found it necessary to seek
guidance from a wide variety of talented people.
First and foremost, I would like to acknowledge my advisor,
Professor D. T. Wasan for allowing me a rather wide latitude in pursuing
my research goals while at the same time keeping the more specific ob­
jectives in focus.
I would like to thank Dr. Howard E. Bussey of the U.S. National
Bureau of Standards, Boulder, Colorado, for his friendship, patience
and above all the many hours spent discussing and demonstrating electro­
magnetic properties measurement techniques. This work would not have
been possible without his guidance. Thanks also to his colleagues at
the Bureau, Messrs. Jesch, McGlaughlin, Jones and Reese for assistance
during my visits there.
Thanks to Professor Robert H. Cole for a two month visit at his
Brown University Dielectric Relaxation Laboratory and to his Research
Associate, Dr. Paul Winsor IV for training on the Time Domain Reflectometry Apparatus, and for their contribution to Chapter III.
Messrs. Art Vogt and Dave Bradley of Electronics and Instrument
Services at IITRI, and Dr. Gerry Saletta and Mr. Joe Sydejko at IIT
provided for the loan of valuable electronic test gear.
Drs. Daryl Doughty and Phil Lorenz of the National Institute for
Petroleum and Energy Research and Mr. Jim Klouda of Elite Electronics
also provided equipment as needed.
A special thanks to A1 Brooks of the Hewlett Packard Company and
his colleagues, Jim Fitzpatrick and Mike Bechtold for the loan and gift
of various pieces of equipment.
Thanks are also due to my friend T.S. Ramakrishnan for assistance
in editing parts of this work,to Professor William M. Langdon for inital
encouragement and continued assistance, to my family and friends who put
up with me, and to Linda Sundin for the many late nights spent pre­
paring this manuscript.
This work was supported in part by DOE Grant DE-AC19-80BC10069 to
Illinois Institute of Technology and by an Amoco Foundation Doctoral
Fellowship awarded to Jeffery P. Perl.
J.P.P.
iii
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TABLE OF CONTENTS
Page
ACKNOWLEDGEMENT....................................................
iii
LIST OF T A B L E S ....................................................
vi
LIST OF FIGURES....................................................
vii
A B S T R A C T ...........................................................
ix
CHAPTER
I.
INTRODUCTION..........................................
1
Complex Dielectric Properties of Liquid Water . . . .
Summary of Work . . .
...............................
II.
COMPLEX DIELECTRIC PROPERTIES OF MACROEMULSIONS USING A
CALIBRATED MICROWAVE RESONANCE CAVITY DIELECTROMETER. .
6
.
6
Introduction......................................
Experimental........................................
R e s u l t s ............................................
Discussion..........................................
S u m m a r y ............................................
III.
1
4
DIELECTRIC RELAXATION OF 1-PROPANOL/WATER MIXTURES.
8
21
32
40
. .
41
Introduction........................................
Experimental........................................
R e s u l t s ............................................
Discussion..........................................
41
43
48
55
MICROWAVE INTERFEROMETRIC DETERMINATION OF DIELECTRIC
PROPERTIES............................................
60
Introduction........................................
Experimental........................................
R e s u l t s ............................................
Discussion..........................................
60
60
63
63
V.
APPLICATIONS..........................................
69
VI.
SUMMARY AND FUTURE W O R K .............................
71
IV.
APPENDIX
A.
STANDARDS USED IN THE PERTURBATION STUDY OF CHAPTER II
AND SAMPLE CALCULATIONS .................................
76
iv
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APPENDIX
B.
Page
DIELECTRIC EQUATIONS FOR THE INTERFEROMETER DESCRIBED
IN CHAPTER I V ..............................................
82
BIBLIOGRAPHY.........................................................
87
v
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LIST OF TABLES
Page
Table
1.
Dielectric Properties of 0/W and W/0 Macroemulsions.
...
31
2.
Dielectric Properties of Related Microwave Studies . . . .
37
3.
Parameters for Two-Time Constant Debye Type Equation
.. .
52
4.
Dielectric Properties of Standard Liquids Determined by
Microwave Interferometry at 23.45 G H z ....................
68
5.
Standard Liquid Reference Calibration Data For the
Microwave Resonance Dielectrometer ......................
81
vi
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LIST OF FIGURES
Figure
1.
Complex Dielectric Properties of Liquid Water.............
Page
3
2.
Microwave Resonance Cavity Apparatus for the Determination
of Liquid Complex Dielectric Properties at 8.193, 9.505
and 11.003 G H z ...........................................
11
3.
Determination of Cavity Length and "Q" Factor Shifts Due
to Insertion of a Sample Liquid Dielectric .............
13
4.
Deviation Between Perturbation Measurements and Exact
Values of Dielectric Constant at 9.505 GHz for Selected
Standard Liquids..........................................
16
5.
Error in Using Perturbation Approximation Relative to
Exact Standard Values as a Function of Perturbation
Measurement................................................
18
6.
Variation of e' with Water Content for the Two Basic
Emulsion Types at 8.193 G H z..............................
22
7.
Variation of e" with Water Content for the Two Basic
Emulsion Types at 8.193 G H z ..............................
23
8.
Simultaneous Determination of Water Content and Emulsion
Type from Loss Tangent, e'Ve1 at 8.193 G H z .............
24
9.
Variation of e' with Water Content for the Two Basic
Emulsion Types at 9.505 G H z..............................
25
10.
Variation of e" with Water Content for the Two Basic
Emulsion Types at 9.505 G H z..............................
26
11.
Simultaneous Determination of Water Content and Emulsion
Type from Loss Tangent, £"/ e' at 9.505 G H z .............
27
12.
Variation of g 1 with Water Content for the Two Basic
Emulsion Types at 11.003 G H z ............................
28
13.
Variation of e" with Water Content for the Two Basic
Emulsion Types at 11.003 G H z ............................
29
14.
Simultaneous Determination of Water Content and Emulsion
Type from Loss Tangent, e"/ e' at 11.003 G H z .............
30
15.
Effect of Dielectric Constant on Electric Field within a
Dielectric Sphere.........................................
34
16.
Dielectric Properties of a Spherically Dispersed W/0
Type M a c r o e m u l s i o n .......................................
36
vii
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Figure
17.
Page
Use of a Normalized Dielectric Modulus, P, to Charac­
terize Suspension Types and Water Contents in Re­
lated Microwave Studies..................................... 39
18.
Time Domain Reflectometry Apparatus of Professor R.H.
Cole, Brown University ...................................
19.
Modified TDR Sample C e l l ...................................... 47
20.
Comparison of Single Time Constant (dashed lines) and
Two-Time Constant (solid line) Debye Representation
of the Dielectric Properties of a .35 Mole Fraction
Water in 1 -Propanol Solution. (Data shown as symbols).
21.
Determination of Starting Values for the Parameters Used
in the Two-Time Constant Equation at 0.35 Mole Frac­
tion W a t e r .................................................. 50
.
44
49
22.
Variation of Fitted Parameters
and
with Mole
Fraction Water ...........................................
53
23.
Variation of Fitted Parameters T . and T _ With Mole
Fraction Water ...........................................
54
24.
Microwave Transmission Interferometer for the Determina­
tion of Complex Dielectric Constant at 23.45 GHz . . . .
61
25.
Sectional View of Variable Pathlength Teflon Sample Cell
Used in the Determination of e* of Liquids by Micro­
wave Interferometry......................................... 62
26.
Determination of a From Variable Pathlength Attenuation
D a t a ........... S ............................................ 64
27.
Determination of AL/At From Variable Pathlength Phase
Shift D a t a .................................................. 65
viii
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ABSTRACT
A microwave cavity resonance dielectrometer has been employed in
a study of the complex dielectric properties of macroemulsions con­
sisting of oil, water and stabilizing surfactant.
A novel method for
the simultaneous determination of emulsion type and water content from
complex dielectric measurements is described.
Also presented is a
reference calibration technique developed for the microwave dielectro­
meter, permitting a convenient experimental routine and quite exact
dielectric measurements if referenced to exact standards.
A voltage
ratio technique, which allows measurement of both low and high loss
samples in the same cavity is also described.
In another study time domain measurements of solutions of 1-pro­
panol and water at seven compositions and 25°C were Fourier trans­
formed to obtain complex permittivities in the range 50 MHz to 8 GHz,
which can be represented by a sum of two Debye relaxation functions.
The principal, slower, one has a relaxation time changing smoothly
from 320 picoseconds (ps) for 1-propanol to 8 ps for water (by extra­
polation from 0.75 mole fraction of water).
The second is quite small
for 1-propanol, but increases with added water, and remarkably has a
relaxation time of ca
20 ps which is independent of concentration to
within the accuracy of the data and fitting.
The significance of the
behavior is discussed in terms of diffusion like models for molecular
reorientations and local conformational changes in hydrogen bonding,
with the conclusion that the later provides a more likely explana­
tion, particularly of the faster relaxation.
ix
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Also presented is a description of a transmission microwave in­
terferometer constructed for the determination of complex dielectric
properties at 23.45 GHz.
A new variable pathlength teflon sample
cell is described. Free space wavelength diffraction correction fac­
tors were also determined.
x
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1
CHAPTER I
INTRODUCTION
The main objective of this thesis has been to apply complex dielec­
tric property measurements to the determination of compositions in liq­
uids, solutions and emulsions of interest to the practicing Chemical
Engineer.
The dielectric constant or relative permittivity, as it is of­
ten called, is a fundamental property of matter and is in general unique
to each substance.
It is measured by electronic apparati and can easily
become part of an automated process control scheme.
As the determina­
tion of water content figures so prominently in this work we will now
examine its unique dielectric properties.
COMPLEX DIELECTRIC PROPERTIES OF LIQUID WATER
In general, the complex dielectric constant is defined as:
e* = e'-ie"
where
e* = complex dielectric constant
e' = real part of e*
e" = imaginary part o ; -£*
Physically e' is a measure of the ability of a material to store elec­
tric field energy, i.e. become polarized, and is proportional to the
capacitance of the material to the capacitance of an equal volume of
free space,
e" is simply a measure of the energy dissipation of an
electromagnetic wave as it passes through the medium.
Naturally, e"
of free space is zero.
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2
Water has a large dipole moment which gives rise to an unusually
large dielectric constant (e* = 78 at 25°C and zero frequency, i.e.,
dc). Debye (1)* noted that as the frequency of measurement increased,
e 1 fell off while e" grew. This is illustrated in Figure 1, a clas­
sical Debye type plot of e' and e" versus log^Q of frequency.
Debye
proposed a simple model based on the frequency dependent vibration
and rotation of the water dipole as it acts to keep the water mole­
cule aligned in an applied AC field.
Thus he proposed
£* = £„,+ (es-e00)/(l+iwT)
which upon separation into real and imaginary components becomes:
£ f = £«, +
(es-£°°)/(1 + (ut)2)
e" = ( e ^ e ^ w x / C l
+
(cot )2 )
where
£g = low frequency (dc) static permittivity
= high frequency limiting permittivity
co
= angular frequency = 2ttF
t
= characteristic relaxation time, seconds
The frequency at which e" is a maximum (Figure 1) is referred to as the
relaxation frequency, F r> at which
cot = 1
Fr = uj/2 tt
^Numbers in parenthesis - Refer to numbered references in the
Bibliography.
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Figure
1.
Complex
Dielectric
>-
Properties
of Liquid
Water
3
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4
These simple Debye equations fail to accurately quantify the dielectric
properties of water over the entire spectrum of frequencies.
They do,
however, provide an excellent qualitative picture of the phenomenon of
the molecular relaxation process seen in liquids, solutions and emul­
sions comprised of one or more polar compounds.
It is basically this
phenomenon that has been taken advantage of in the dielectric measure­
ment applications described in this thesis.
SUMMARY OF WORK
Dielectric Properties of Emulsions.
Mixtures of oil, water and stabilizing surfactant are known as emul­
sions.
Emulsions can exist as dispersion of oil-in-water (0/W), water-
in-oil (W/0) or mixtures of the two.
They play key roles in the produc­
tion of pharmaceuticals, cosmetics and some types of fuel combustion
processes.
In Chapter II of this thesis we describe the study of the
microwave dielectric properties of such systems which led to a dielectric
technique for the simultaneous determination of macroemulsion (emulsions
whose dispersed phase is visible under ordinary light microscopy) type
and water content.
These techniques can be used in place of tedious and
time consuming wet chemical and microscopic methods and provide an elec­
tronic output amenable to computer data acquisition and process control.
Dielectric Properties of Alcohol/Water Solutions
This work, described in Chapter III, was originally undertaken to
develop calibration standards for the dielectric measurement apparatus
employed in the emulsion study (Chapter II) described above.
Of greater
importance and interest to Chemical Engineers, however, is the unique
dielectric relaxation behavior of these mixtures.
The relaxation
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5
frequency for 1-Propanol is located around 0.5 GHz (1 GHz = 10^ Hertz)
while that for water is around 20 GHz at 25.0°C.
The results of this
dielectric study of the relaxation behavior of mixtures indicated a
high degree of interaction between alcohol and water molecules in the
liquid and may shed light on the mechanism(s) responsible for the
phenomenon of azeotropism as seen in the highly nonideal boiling be­
havior of such mixtures.
The relaxation behavior of these systems was also shown to closely
mimic that found in microemulsions and may provide a model of the di­
electric behavior of this industrially important class of emulsions.
Microwave Transmission Experiment
In order to take advantage of the large difference in the dielectric
properties of water and oil a device was constructed to make such measure­
ments at 23.45 GHz.
A transmission type cell was constructed and is
described in detail in Chapter IV.
path length cell
a
In addition to this new variable
free space wavelength correction is also discussed.
Suggestions for future work and several novel applications of di­
electric analysis to Chemical Engineering problems are presented in
Chapters V and VI.
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6
CHAPTER II
COMPLEX DIELECTRIC PROPERTIES OF MACROEMULSIONS USING A
CALIBRATED MICROWAVE RESONANCE CAVITY DIELECTROMETER
INTRODUCTION
The work reported here was undertaken for two related reasons.
The
first, to demonstrate the ability of complex dielectric property measure­
ments at microwave frequencies to determine macroemulsion type and water
content.
The second, to compare these results with other theoretical
and empirical investigations aimed at providing a mechanistic descrip­
tion of the complex dielectric properties of macroemulsions.
The term
macroemulsion refers to a fluid dispersion of either oil-in-water (0/W),
or water-in-oil (W/0) having dispersed phase structures which are visi­
ble under ordinary light microscopy.
Clausse (2)* has noted in his recent extensive review of the dielec­
tric properties of emulsions and related systems that most emulsion
studies have been conductedat relatively low (0.1-100.0 MHz) frequencies.
Microwave measurements have, however, been conducted recently by Foster
and co-workers (3,4) on 0/W microemulsions.
Microemulsions have dis­
persed phase structures which are invisible to ordinary light microscopy
have a large interfacial to dispersed phase volume ratio and are essen­
tially different from macroemulsions.
Representative studies of low frequency macroemulsion studies re­
viewed by Clausse (2) are that of Hanai (5), Sillars (6), and Chapman
(7).
The results of their work may be summarized as follows:
* Numbers in parenthesis - Refer to numbered references in the
Bibliography.
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7
1.
e' of 0/W macroemulsions is essentially independent of frequency
from ca 1-50 megaherz (MHz).
2.
£’ of W/0 macroemulsions exhibits a marked frequency dependence
(dielectric dispersion) over the same range of frequencies.
The mechanism proposed to explain this low frequency dielectric disper­
sion observed in W/0 macroemulsions is that of interfacial polarization,
a frequency dependent accumulation of charge at an interface thought to
be caused by the presence of a nonconducting continuous phase (oil).
In­
terfacial polarization was accounted for by Hanai (5) in his dielectric
shell model of water droplets dispersed in oil. This model, which views
the droplet as an inner core of bulk material surrounded by a surfactant
generated interfacial shell, also qualitatively predicted the presence
of a second dielectric dispersion in both W/0 and 0/W systems at much
higher frequencies having character similar to that of bulk water.
It
should be noted that no low frequency dielectric dispersion was pre­
dicted for 0/W systems.
Clausse (2) provided a numerical solution to Hanais (5) model.
His
calculations of the theoretical dielectric behavior of W/0 systems place
the centers of the low and high frequency dielectric dispersions at ca
52 KHz and ca 30 GHz respectively for a 0.7 volume fraction water (W/0)
system.
The presence of conducting species in the bulk water in W/0
systems has been shown to cause movement of the low frequency disper­
sion towards a higher frequency resulting in an overlap of the two di­
electric dispersions,
(2,8,9).
In a recent experimental investiga­
tion Hanai (9) has shown that the effect of the low frequency (inter­
facial polarization) dispersion is essentally dissipated above ca 50 MHz
in W/0 type macroemulsions prepared in the absence of conducting species.
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Accordingly, the present study examines the complex dielectric pro­
perties of macroemulsions prepared in the absence of conducting species,
at microwave frequencies far removed from the effect of interfacial
polarization.
The experimental technique chosen for this study is that of small
perturbation of a microwave cavity resonator as described by Bethe and
Schwinger (10), Horner et al. (11) and Birnbaum and Franeau (12).
Testing of the apparatus with standards liquids (methanol, acetone, and
water) yielded a systematic deviation between measurements using the
perturbation approximations and generally accepted literature values for
the standard liquids. This led to a reference calibration procedure per­
mitting the accurate determination of e* for lossy liquids over the
range between air ( e ‘=l) and water (e'=65).
The design, calibration and operation of the microwave resonance
apparatus is described in detail.
This is followed by a discussion of
the results of our study of the microwave dielectric properties of macro­
emulsions at 8.193, 9.505 and 11.003 GHz performed with this equipment
and the manner in which the dielectric data may be used to determine
macroemulsion type and water content without resorting to wet Chemical
or microscopic techniques.
A voltage ratio technique which allows the
measurement of e" over a broad range(0.2-35) is also described.
EXPERIMENTAL
Microwave Resonant Cavity Dielectrometer
The apparatus employed in this study is based on the small pertur­
bation approximations developed by Bethe and Schwinger (10) and de­
scribed by Horner et al (11), Birnbaum and Franeau (12), and Soohoo (13).
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9
The original strict requirements for the use of the approximations in
dielectric measurements are:
1.
The fractional change of the resonant frequency, AF/F, or of the
cavity length to maintain resonance at a constant frequency, AL/L,
shall be very small.
Either a small sample or a low permittivity
(complex dielectric constant) is required;
2.
The occurrence of, or the excitation of, degeneracy i.e. more than
one resonance at almost the same frequency shall be avoided so that
the sample does not induce unwanted modes;
3.
The electric field, E, in the sample must be known relative to the
exciting field as is true for the various ellipsoids, e.g. a slim
cylindrical rod sample.
Theoretically, a cylindrical rod sample parallel to the E field
should terminate with the ends in firm contact with the metal sur­
faces of the cavity.
Practically, it is necessary to insert the solid
or capillary tube through holes.
The errors contributed by holes have
been calculated by further application of perturbation theory (Estin
and Bussey (14)) and by higher mode analysis
former method (14) for solid
(Bosisio et al 15,16). The
rods was well checked experimentally,
and may be interpreted as a weakening of the E field by a hole near
the sample end.
An additive correction factor for £', proportional
to e'-l and the ratio of sample radius to cavity height resulted.
modal method
The
(15,16) is useful as it predicts the augmented correction
factor (to be added to e r-l) when the sample is contained in a capil­
lary tube.
The following symbols are defined for the calculations:
c = velocity of light in vacuo, m/sec
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10
C
2
= (kg/kQ ) , dimensionless
db
= decibels below baseline atresonance
F
= frequency, Hz
AF
= frequency shift due to
k
= rnr/L, m 1
sample insertion,
Hz
g
k
o
= 2irF/c, m -1
L
= total cavity length, m
AL
= length decrease required to
reestablish resonance upon inser­
tion of sample
n
= number of i wavelengths in cavity at resonance, n = 5,7,9 at
8.193, 9.505 and 11.003 GHz respectively
Qg
= cavity "Q'1 factor, empty
Qg
= cavity "Q" factor, with sample
R
= magnitude of voltage reflection coefficient at resonance
V
= cavity volume, m
v
= sample volume contained within capillary, m
6 Lg
= Q width factor, empty, m
6Lg
= Q width factor, with sample, m
3
3
In the present study a rectangular waveguide, iris coupled single
port reflection cavity has been drilled to accept glass capillary tubes.
Figure 2, a non contacting variable short with an indicating digital
micrometer drive was employed as the cavity tuning element.
The
cavity is capable of operation at three frequencies, 8.193, 9.505 and
11.003 GHz in the T E . ^ ,
^ 1 0 7 and ^ 1 0 9 modes respectively.
The
sample holes are placed at the E field maximum at the center of the
cavity.
The length of the cavity is adjusted for resonance, i.e. for
minimum reflected power both with and without the sample while
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,CAVITY REFLECTED POWER MONITOR
tn
ISOLATOR
LIQUID
SAMPLE
TUBE
CRYSTAL
DETECTOR
MOVEABLE
PISTON(SHORT)
IRIS-
MICROWAVE
SIGNAL
GENERATOR
7-11 GHz
DIRECTIONAL
COUPLER
RESONANCE CAVITY
Figure 2. Microwave Resonance Cavity Apparatus for the Determination of Liquid Complex Dielectric Pro­
perties at 8.193, 9.505 and 11.003 GHz
12
maintaining a constant frequency and the bandwidth and/or reflection co­
efficient are measured thereby providing the measurement parameters for
a perturbation theory calculation of e' and e".
Refering to Figure 3 the variables AL, 6Lg , and 6Lg are determined
by measuring the dip in reflected power at both empty (dbg ) and sample
(dbg ) resonance conditions.
The half power value in db is calculated
from:
(dbe )i =-10 Log((10"dbe/ 1 0 +l)/2)
2.1a
(dbg )^ =-10 Log((10“dbs/ 1 0 +l)/2)
2.1b
The adjustable short position is varied around the center resonance
location to the value indicated by Equations 2.1a and 2.1b from which-the
shift in center resonance location ( L j + L ^ g ^ - (L-^+L2)g/2 = AL, and
the Q-factor change (6Lg-6Le ) = ( L - j - L ^ - ( L - ^ L ^ are calculated.
The
perturbation equations for the TE^Qn system using length variation to
obtain the resonance and Q-width variation are as follows:
£' = 1 + (V/2v)CAL/L
2 .2
e" = (V/4VH/Q,
sc
2.3
where Q gc is the sample contribution to the total Q.
The inverse of
the total Q with and without the sample may be expressed as:
2.4a
2.4b
where u denotes the skin depth effect and p denotes radiation from the
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0
m
M
§
QC
\
□
UJ
I—
<_>
LU
AL
_l
Ll
LU
cr
St
O
l s2
l s1
Le2 Le1
MOVEABLE SHORT POSITION. CM
Figure 3. Determination of Cavity Length and "Q" Factor Shifts Due to Insertion of a Sample Liquid
Dielectric
14
sample port (Iris ) and Q~* = 0 for the empty cavity case, Q ^ .
Qu
and Qp change very little with a small perturbation sample and it is
therefore sufficient to assume that
2.5
where s and e denote with the sample and empty respectively.
Q g or
Qg may be measured by the resonant bandwidth by means of either fre­
quency or length tuning.
For example, using length the total (or
loaded) empty cavity Q is given by:
2.6
Q ^1 = (<5Le /L)C
where 6L g is the width at the so called half power level (see Figure 3).
By Equation 2.5 assuming a small perturbation
Q sc =
« < V L) " (6Le/L))C
2.7
For practical reasons, e.g., temperature changes, drift of the
oscillator, backlash of the movable short, the measurement of the width
<$L tends to exhibit significant random errors which can be averaged out
by tedious repetitions.
There is a different, simple, precise and
quite accurate method of observing Q-change, i.e., the loss contri­
buted by the sample.
This method, called the voltage ratio method
(Hartshorn and Ward(17)), is well known and straight forward for lower
frequencies using a capacitive holder.
The method was extended to
microwaves (Bussey (18)) by including certain correction factors de­
noted in a review (Bussey (19)) as K
Kg , and Kd<
These factors ap­
proach unity as the perturbation decreases to zero and are assumed to
be one for our small samples.
The method then gives:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
2.8
where
R
e
. 10-dbe/2°, R
s
. 10-dbs/2°
where R is the voltage reflection coefficient at resonance, and s, e
denote with the sample and empty respectively.
The + choice of signs
denote over (+) and under (-) coupling of the resonator.
Our cavity
was undercoupled in all three modes, giving the minus sign in Equation
2.8.
The Q gc obtained by the methods of Equations 2.7 and 2.8 agreed
well in cases that were easily checked, namely the more lossy samples.
The voltage reflection method is, however, far more accurate in deter­
mining Q shifts in low loss samples, while also speeding the process
of data acquisition and was,therefore, used in the present study.
Measurements of e' and e" for the standard liquids, methanol,
acetone and water were conducted at 8.193, 9.505, 11.003 GHz and
24.0 + 0.5 C° using the perturbation Equations 2.2 and 2.3 uncorrected
for sample insertion holes.
Standard reference values of £' and e" to
be used to correct the perturbation approximation for the unknown li­
quids are presented in Appendix A.
A plot of (e'-l)^ against corresponding literature values is pre­
sented in Figure 4.
The values from the perturbation approximation,
(e'-l)p are everywhere greater than the literature values.
As a rough
estimate of the magnitude of error expected in using the perturbation
approximation we have solved Horners (11) exact equations for the case
of a circular cylindrical cavity containing a solid sample rod with no
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16
WATER— %
tmq40 COMPUTER SOLUTION
TO HORNERS EQUATION
/
ACETONE—
METHANOL
.AIR
0
10
20
30
AO
50
60
70
(e’"1,TRUE
Figure 4. Deviation Between Perturbation Measurements and Exact Values
of Dielectric Constant at 9.505 GHz for Selected Standard Liquids
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17
sample holes and compared them to theoretical perturbation results for
the same fractional frequency shift, AF/F.
The TM q AO mo£*e was chosen for the calculation as the field excita­
tion is very similar to our rectangular
cavity.
The ratio of
sample rod to cavity diameter, wavelength and mode (TM q ^q ) were chosen
to agree closely with our experimental conditions to the TE^ q 7 rectan8u_
lar cavity.
Calculations for the TM q ^ q cavity predict a positive devia­
tion between perturbation and exact solution similar to that found in
the perturbation measurements on the standard liquids (Figure 4).
These
results are qualitative as the theoretical sample was lossless, i.e.
e"=0, was contained entirely within the cavity and fields within the
cylindrical and rectangular cavities are not quite the same.
To better illustrate the deviation between the exact and perturba­
tion solutions we have plotted (e*-l)p/ ( £ ,-l)c =A against (e'-l)p for
the Horner (11) calculations (solid line in Figure 5).
Here p and c
stand for perturbation and correct respectively.
A simple straight
line deviation in the relative error, A, occurs.
Using this linear
variation of A with (e'-l)p as a guide we have replotted our
for the standards and air in Figure 5.
data
A best fit (dashed line) was
obtained by linear regression to average out the effects of random er­
rors.
This results in the following relationship which we have used
in the present study to correct the perturbation approximation results.
(e*-l)c = (e,-l)p/(a(e,-l)p + b)
2.10
The values of the constants a and b have been determined by measurement
on the standard liquids.
At 9.505 GHz, a = 1/967, b = 1.0077, for the
Horner (11) calculation, a = 1/1143, b = 0.9998.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.09
.08
WATER
1.07
TE10? DATA POINTS AT 9.505 GHZ
~ 1.06
BEST FIT TO DATA.
i 1.05
^
ACETONE
1.04
BEST FIT TO TM,
CALCULATION
040
^ 1.03
.02
METHANOL
.00
Figure 5. Error in Using Perturbation Approximation Relative to Exact Standard Values as a Function of
Perturbation Measurement.
oo
19
It is of interest to note that the slopes of both the theoretical
(calculated) and experimental studies are nearly equal.
Scatter due to
both random and systematic errors tend to be magnified in this plot of
fractional error but it should be noted that the regression line for
the
experimental data is within ± 1.5% of the points themselves.
We now note some of the systematic errors which arise
in making
dielectric measurements by means of a resonant cavity:
1.
Placement of the sample tube at the E field maximum,
2. - Placement of the sample parallel to the E field,
3.
Effect of sample insertion holes,
4.
Effect of capillary sample tube,
5.
Effect of coupling element (iris),
6.
Effect of non zero loss, i.e. e " * 0 ,
on e 1.
In view of the uncertainties and the demonstrated systematic deviation
between the exact and perturbation calculation of (e'-l), we used the
following simplified reference calibration and measurement procedure:
Reference Calibration Procedure
1.
2.
Determine (e'-l)p from the standards using Equation 2.2,
A straight line correction was found to
be simpler to
use than 2.10
hence
(e'-l)c = a (e'-l)p + b
3.
2.11
Thus calibrated, the instrument is ready for measurement on unknowns.
Measurement Procedure
1.
Measure E* for the unknown samples,
2.
Calculate ( e ’-l)p and e ’^
3.
Determine (e'-l)c from Equation 2.11 (See Appendix A for a and b),
from Equations 2.2 and 2.3,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
20
4.
Then e"c ,* ((e’-l)c/(e'-l)p )e"p .
The last step assumes that the fractional errors in both
and
(e'-l)p are approximately equal as both are driven by the same field
integrals.
Back calculations of E 1 and e" for the standards resulted
in errors of + 2% and + 5% respectively at 9.505 GHz, remarkable over
such a broad range of values, 6 < e'< 67 and 4 < e " < 32.
Emulsion Preparation and Sampling
The purpose of the following procedure is to produce emulsions
with physical characteristics as similar as possible differing only
with respect to type, i.e., W/0 and 0/W, and composition (phase volume
water).
Stable emulsions were prepared using blends of Span 80 (sorbitan
monooleate) and Tween 80 (polysorbate 80).
In the case of W/0 emul­
sions a mixture of surfactant at an HLB number of 6.0 (hydrophile/
lipophile balance) (20) was dissolved in paraffin oil (continuous phase)
at a concentration of ca 10% by weight.
heated separately to ca 65°C.
Both water and oil are then
The heat is removed and both phases are
combined and mixed by propellor for approximately 10-20 minutes, re­
sulting in a dispersed phase (water) concentration of ca 80% by volume.
This mother dispersion of W/0 is then successively diluted with surfact­
ant free continuous phase (oil) by gentle inversion (ca 20 times) in a
graduated cylinder. Prior to the
dielectric measurements, each sample is
analyzed for water content using the Karl Fischer titration method
(21,22) for the determination of water in hydrocarbon mixtures.
Sample
densitities are determined to calculate volume fraction water present
assuming no volume of mixing effects.
The procedure for 0/W emulsion
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
21
preparation is the same with the exception of surfactant blend,
HLB = 10.0, which is placed in the water at ca 10% by weight concen­
tration.
Microscopic observations showed the presence of dispersed phase
agglomerates for both the 0/W and W/0 type emulsions
similar to those
photographed by Chapman (7).
Thus prepared, the samples were drawn into capillary tubes (Drummond
Micro-caps, lul, I.D. = .2 mm, O.D. = .65 mm) and placed into the micro­
wave cavity where the dielectric determinations are made as described
in the previous section.
(Tubes placed in wide side of cavity).
RESULTS
Measurements of the complex dielectric constant of both 0/W and
W/0 type macroemulsions were made over the concentration range of 1878% water by volume using the calibrated microwave resonant cavity
dielectrometer described in the previous section,
e ’ and £ 11 versus
volume fraction water at 8.193, 9.505 and 11.003 GHz are shown in
Figures 6, 7, 9, 10, 12 and 13 respectively and are listed in Table 1.
These figures demonstrate a systematic difference in E 1 and e " for the
two emulsion types over the entire range of composition investigated.
Since the loss tangent, e"/e', appears to enhance this systematic dif­
ference we have plotted this group as a function of volume fraction of
water for both emulsion types in Figure 8, 11 and 14.
We note the fol­
lowing:
1.
e " / e ' is lower for emulsions of water-in-oil (W/0) than for those
of 0/W over the entire range of compositions and frequencies in­
vestigated,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
WATER
CC £
CD^ o
•g -a
"Z. °
ir>o ^
'j-4 <u
%:
LU §
2 S
—) o
=J °
no
>
k
3
,3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LU
I
Basic
cr
Emulsion
Types
at 8.193
GHz
WATER
23
lu
2
ZD
O
.3
the
Figure
7.
Variation
of e" with
>
for
Ll.
Content
<
cr
Water
I—
o
Two
z
o
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
WATER
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
9.
Variation
of e' with
Water
Content
for
the
Two
Basic
Emulsion
Types
at 9.505
GHz
WATER
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
uo
o
LO
o
o
Figure
o
10.
Variation
of e" with
Water
Content
for
the
Two
Basic
U lI
Emulsion Types
at 9.505
GHz
WATER
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
at
e"/e'
Tangent,
Loss
from
Type
Emulsion
and
Content
,3 / . 3
Determination
of Water
(VI
LO
Figure 11.
Simultaneous
9.505 GHz
CO >
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
GHz
Variation
12.
Figure
60
\-
of e' with
Water
Content
for
the
Two
Basic
Emulsion
Types
at 11.003
WATER
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
13.
Variation
of e" with
Water
•2
Content
'vTLU
for
the
Two
Basic
Emulsion
Types
at 11.003
GHz
WATER
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UJ
UJ
,3/„3
Figure 14.
Simultaneous
11.003 GHz
Determination
3
of Water
<
.l o q ;
'Ll.
Content
and
.cpo
Emulsion
cr
Type
from
Loss
WATER
Tangent,
e"/e* at
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
31
”u)
CO r - CO VO
co r^. co r—
rto
I-’ ro oi ‘t
c t O V r- Lfi
c o « tv o o
f— CM
O 00 LO CM
to ^ co co
r— CM CO
vo vo r». i>.
co vo cm cn
in
00 iO CO CM
O CO 00 co
8
_
-
9 .4
1 4 .5
2 7 .9
4 2 .2
6.1
1 0 .8
2 4 .2
3 4 .2
m
o
in
cn
To
^ ■ C O IflO
PO VO f—
* CO
CO CM O OV
o" co" 00* o"
cnCMINr<n vo co co
C-(\J
cn co vo cn
co cm in >—
i— CM CO
cn
CO
To
£
ai
1
i-
c
o
+J
ra
u_
O v f vnvf
N C O lflN
V •
~J
.
,v„,l
cn 00
r—
V.
(U <u
p
s»
W/0
5
0/W
Table 1.
Dielectric Properties of 0/W and W/0 Macroemulsions
CO
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
2.
For volume fractions
of water below 0.5, ef'/e 1 for W/0 emulsions
falls rapidly with decreasing water content at all frequencies
studied,
3.
£"/£' for 0/W emulsions is essentially invariant with volume frac­
tion water and is approximately equal to £ " / £ 1 found for pure water
at each frequency studied.
In principle, Figures at any of the 3 frequencies such as Figure 6 and
7 are sufficient for the simultaneous determination of emulsion type
and water content for dielectric measurements alone.
The examination
of loss tangent in Figure 8, however, allows the immediate, unambiguous
determination of emulsion type for which either Figure 6 or 7 provides
accurate determination of the volume fraction of water.
Plots such
as these may be used for the dielectric determination of macroemulsion
type and water content in industrial and scientific applications which
require rapid determinations without resorting to wet chemical or
microscopic technique.
This technique might also be useful as a means
of determining or monitoring emulsion phase inversion.
With regards
to other applications Klein (23) and Meyer and Schilz (24) have sug­
gested the group (e'-l)/e" for use in a variety of industrial applica­
tions such as the dielectric determination of moisture content in food
and coal.
DISCUSSION
Stratton (25) presented an electrostatics solution for the electric
field strength E inside an isolated sphere of dielectric constant,
surrounded by a continuum of dielectric constant z^ .
Neglecting the
effect of the interface he obtained
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33
E. = 3Eo/((s1 /e2 ) + 2)
where
= electric field inside the sphere
E q = electric field outside the sphere
= dispersed phase (sphere) bulk dielectric constant
= continuum (continuous phase) bulk dielectric constant
At 11.003 GHz for water spheres dispersed in oil this results in
Ei = 3E q /((59/2.5) + 2) = 0.11E q
Thus in the case of water spheres dispersed in oil the E field within
the drop is approximately 10% of the value outside of the drop.
Simply stated, a water droplet is partially shielded from an applied
E-field thereby reducing the measured, or apparent dielectric constant
for such dispersions (see Figure 15).
Conversly, the E field inside
an oil droplet surrounded by water is actually enhanced over the ex­
ternal field.
This provides a qualitative explanation of the reduc­
tion in both e ' and e" for the case of W/0 emulsions as seen in
Figures 6 and 7 and explains the shift in loss tangent, e 'Ve ' between
0/W and W/0 type macroemulsions as seen in Figure 8.
DeLoor (26) re­
viewed various heterogeneous mixture models which attempt to relate the
dielectric constant of such mixtures to their pure component properties.
He noted the effect of dispersed phase shape and predicted that the
microwave frequency dependence of e ' and £" for W/0 type dispersions
would be similar to that of pure water though shifted towards higher
frequencies.
In order to examine this phenomenon we have made a pre­
liminary investigation of the broadband microwave dielectric properties
of a W/0 macroemulsion system consisting of a spherically dispersed
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
15.
Effect
of Dielectric
Constant
on Electric
Field
within
a Dielectric
Sphere
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
water phase and a continuous phase of carbon tetrachloride and paraffin
oil in the ratio of 1/4, CCl^/Oil (similar to that used by Hanai, (9))
Span 80 surfactant at a concentration of 5% by volume in the oil phase
was used to stabilize this 0.4 volume fraction water emulsion.
The
emulsion was prepared by injecting deionized water with a syringe and
22 gauge needle into a propellor stirred mixture of oil and surfactant.
This concentrated dispersion was then diluted with oil!to 0.3, 0.2. and
0.1 volume fraction water by gentle inversion.
Photomicrography showed
the droplets to be in the 10-40 micron diameter range, as opposed to
the agglomerated system previously described.
The dielectric measurements were performed over the range of .057.68 GHz using the Time Domain Reflectometry apparatus of Cole (27,28).
The results for the 0.4 volume fraction water experiment are presented
in Figure 16, a typical Debye type plot of
of frequency.
e* and e” against L o g ^
A list of the results for all four samples at 8.0 GHz
is presented in Table 2.
The negligible dependence of e" on frequency
accompanied by a rapid rise in e" above 5 GHz does indeed indicate a
relaxation frequency, F , similar to or greater than that found in the
pure water where F r = ca 20 GHz at 25°C (80).
It is of interest to compare and contrast the results of our macro­
emulsion study with the microwave dielectric observations made on micro­
emulsions.
Foster and co-workers (3,4) found a pronounced decrease
in
relaxation frequency for 0/W type microemulsions which varied from ca 2
GHz to 15 GHz for samples containing 0.2 to 0.8 volume fraction water
respectively. (This is discussed in greater detail on Page 42 of this
study).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure
16.
Dielectric
CO
Properties
of a Spherically
a§
Dispersed
W/0
Type
Macroemulsion
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 2.
System
Dielectric Properties of Related Microwave Studies
Investigator
Frequency
Volume Fraction Water
e'
e"
Macroemulsion
0/W
Mudgett et al (38)
25°C
3.0 GHz
.25
.50
.75
15.8
32.8
47.6
2.0
4.5
6.3
Sand/Water
Slurry
Kraszewski(39)
25°C
9.4 GHz
.47
.61
.77
.85
40.0
46.5
55.3
57.4
16.1
20.5
25.3
26.8
Water Drops
in Plexiglass
DeLoor(35)
20°C
9.68 GHz
.20
.25
Macroemulsion
W/0
Theoretical
Calculation
Using Hanai
Model
Clausse(l)
20°C
Macroemulsion
W/0 Spherically
Dispersed
Microemulsion
10.0 GHz
0.70
Perl(11)
25°C
8.0 GHz
.1
.2
.3
.4
Foster et al (3)
25°C
9.5 GHz
.2
.4
.6
.8
5.13
5.92
25.0
3.1
4.4
6.2
8.75
5.0
11.0
23.0
41.0
.405
.558
6.5
.16
.36
.95
1.22
3.0
8.0
16.0
25.5
38
Related Microwave Studies
As discussed by Clausse (2) there is a lack of experimental
studies of emulsion systems at microwave frequencies.
Nevertheless,
there have been model systems studied by others which are similar to
the dispersions of W/0 and 0/W examined in the present study.
In
order to compare the results of these other microwave dielectric
studies with our present work we have defined the function
P = ( ( £ " / £ ') s/ ( e " / e , ) w)
where the subscripts s and w refer to the sample and pure water respec­
tively at the frequency of the particular study.
The function P be­
comes a normalized dielectric modulus which serves to characterize de­
viation from pure water behavior.
Figure 17 is a plot of the nor­
malized dielectric modulus, P, versus volume fraction water for the
published studies.
For completeness we have summarized the actual
findings of each investigator in Table 2.
It should be noted that the
data presented in these studies were in graphical form and we accept
responsibility for its conversion to discrete values of £* and £".
From this discussion of the work of others and our present study, we
reach the following conclusions illustrated by Figures 6-14 and 17.
1.
Dispersions of a low dielectric constant material in a high dielec­
tric constant continuum, e.g., 0/W type macroemulsions.exhibit a
microwave dielectric behavior similar to that of pure water as
characterized by the normalized dielectric modulus, P,
2.
Spherical or nearly spherical dispersions of a high dielectric con­
stant in a low dielectric constant medium, e.g., W/0 type macro­
emulsions, show a marked dispersed phase concentration controlled
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.6 r
0/W MICROEMULSION
CL 1.4
in
3
1.2
0/W MACROEMULSIONS TYPE SYSTEMS
2 10
&
£ -8
o
INVESTIGATORS
.6
Q
W/0 MACROEMULSION TYPE SYSTEMS
— I
<
I
.2
2
VOLUME FRACTION6WAf^R
B
O
MUDGETT et al (29)
□
KRASZEWSKI et al (30)
A
DeLOOR (26)
+
CLAUSSE (2)
•
PERL
x
FOSTER et al (3)
9
'°
Figure 17. Use of a Normalized Dielectric Modulus, P, to Characterize Suspension Types and Water Contents
in Related Microwave Studies
40
deviation from pure water behavior,
3.
In spite of the varied microwave frequencies used in the above
mentioned studies the differences observed in e' and e" for 0/W
and W/0 type dispersed phase systems are large enough to provide
an adequate evidence for the means of determining emulsion type
and water content proposed here.
SUMMARY
1.
Knowledge of the broadband dielectric properties of macroemulsions
is essential in the attempt to elucidate the mechanisms governing
such dielectric behavior.
2.
Once the wideband frequency behavior is characterized, singe fre­
quency measurements of the complex dielectric constant of such
systems, particularly in the range of ca 10 GHz, provide a powerful
electronic tool for the determination of macroemulsion type and
watei content.
3.
These dielectric techniques are applicable to a variety of lab
analytical or industrial process
and
quality control situations
where such determinations must be made rapidly, nondestructively
and often noninvasively.
4.
Also presented here is a reference calibration technique for the
microwave cavity resonance dielectrometer employed in this study.
This method accounts for a systematic deviation between literature
values of e' and e" for common standards such as methanol, acetone,
water, etc. and measurements using the small perturbation approxi­
mation.
A voltage ratio method for the determination of e" from
resonant cavity voltage reflection coefficients was found to im­
prove the accuracy of this measurement.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
CHAPTER III
DIELECTRIC RELAXATION OF 1-PROPANOL/WATER SOLUTIONS
INTRODUCTION
The study described in this chapter was conducted by the author
in the laboratory of Professor R. H. Cole at Brown University,
Providence Rhode Island.
The original intent of the work was to pro­
vide additional calibration standards for the microwave resonance ap­
paratus described in Chapter II of this thesis.
This, however, was
only partially successful as the apparatus which will be described in
the following pages has upper limitations on the value of £ 1 that it
can measure.
The results of this study of the complex dielectric pro­
perties of 1-propanol/water mixtures did, however, provide insight in­
to the intermolecular association process occurring in such solutions.
This study also demonstrates the ability of complex dielectric analysis
to determine liquid compositions even in the face of such large
molecular associations.
An attempt by Brost and Davis (31) to use such
mixtures as calibration standards in microwave saturation monitored
core flooding experiments has met with only partial success.
This
might also be due to the effect of association in the alcohol/water
mixtures and will be discussed further in the section on future work.
Measurements of mixtures of two associating polar liquids have
provided considerable support for Schallamach's thesis (32) that if
both or neither of two polar liquids are associated, most of the
relaxation of mixtures of the two can be described by a single relaxa­
tion at intermediate frequencies. (For two non-associated liquids, the
evidence is much less convincing, as discussed in the book of Bottcher
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
and Bordewijk (33).
This suggests a considerable degree of joint cor­
relation in cooperative motion of neighboring molecules, as single
molecules reorienting in an average environment, by rotational dif­
fusion for example, would be expected to produce two more or less dis­
tinct relaxation functions.
Most of the existing evidence to the con­
trary has, however, been obtained at low temperatures and audio or
radio frequencies, hence the interest in behavior at ordinary liquid
temperatures and megahertz to gigahertz frequencies..
Mixtures of 1-propanol and water were chosen for study because of
the large ratio of primary relaxation times (320 ps for 1-propanol and
8 ps for water at 25°C), miscibility at all compositions, and possible
relevance to some recent results for relaxation in a microemulsion
system (1 ps = 10
-12
second).
In work at Brown to be published elsewhere, Dr. G. Delbos
(Bordeaux) made time domain dielectric measurements of water/toluene
microemulsions with sodium dodecylsulfate and 1-butanol as cosurfact­
ants in 5 to 1 mole ratio.
Over a wide range of toluene/water ratios,
he found a simple relaxation centered near 2 GHz which could plausibly
be attributed to interfacial layers between the two with high permit­
tivity of mobile "bound water" and hydroxyl groups of 1-butanol in
the layer.
Foster and coworkers (3) have studied water/hexadecane
microemulsions, with (nonionic) polyoxyethylene 20 sorbitan monostear­
ate (Tween 60) and 1-pentanol as cosurfactants, and found interfacial
relaxation frequencies in the range of 2 to 5 GHz.
It is thus of interest to determine whether alcohol-water solu­
tions in bulk exhibit behavior comparable to that found in microemul­
sions containing these components.
Unfortunately, water is only
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43
slightly miscible with higher alcohols, but the results for 1-propanol as the nearest counterpart in bulk should be of interest for
comparison.
A further possible usefulness of the results can be to
provide data for calibration or test purposes at high frequencies, as
the static permittivities lie in the wide range from 18 to 78 and the
relatively simple relaxation behavior has been defined to several
gigahertz.
EXPERIMENTAL
Measurements to obtain results for the frequency range 50 MHz to
8 GHz were made using time domain reflectometry (TDR) methods developed
at Brown over the past few years (34), (35), (36), (37).
The system
used differs considerably in several respects from the last published
version (35), and is described here in some detail.
Referring to
Figure 18, the step-like tunnel diode voltage pulse is sent to two
coaxial line channels by a power splitter.
The two wave forms, VQ (t)
for channel B and vor(t) for A are reflected from matched sample and
reference cells.
These are equivalent, for both empty, to open cir­
cuits at an increased distance d, which is the effective electrical
length of the cells as sections of coaxial line, and produce reflected
signals V(t) and Vf (t) delayed in time by 2 d/c but otherwise unchanged.
The complex permittivity e* at frequency w of liquid in the sample cell
is obtained from the basic relation
£*(1“) = r d
o
3.1
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44
SAMPLE
REFERENCE
SAMPLING
SCOPE
SAMPLER
50 ohm
•Coaxial Line
IBANDPASS
FILTER
MIXER
•Power Splitter
-Coupler
SIGNAL
ANALYZER
Triggers
•Tunnel Diodes
-
COMPUTER
Figure 18. Time Domain Reflectometry Apparatus of Professor R.H. Cole,
Brown University
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
. - * , P
3.!
where V q and r are Laplace transforms of the open circuit reflection
of VQ (t) and the sample reflection R(t), C = 0.3 mm/ps is the speed
of propagation, and the function f(z) is a high frequency correction
factor discussed below.
As used in this work, the reflected voltage pulse from reference
channel A as sampled and "time stretched" by the coxial line triggers
the signal averager (Tracor Northern Type 570A), which records com­
binations of the synchronous time stretched reflections in the two
channels on the next repetitive sweep after an adjustable signal
averager predelay set to provide a suitable baseline.
This arrange­
ment, made possibly by use of a precision power splitter (Gen.Rad
Type 874PDL) and flexible coaxial lines (Junflon), gives improved
triggering and time referencing.
It also makes possible a greater
reduction of errors from drifts of circuit responses in time by use
of the mixer amplifier to obtain combinations + (A+B) of the two
channel output signals and B, which can be chosen for recording of
critical ones in rapid succession.
The procedure used to acquire the numerical data for use of equa­
tion 3.1 to obtain e* is as follows.
The empty cell difference V(t) -
Vr (t) is recorded first, then after the sample cell is filled the sum
and difference Vr (t) + R(t) are recorded in rapid succession and added
in the signal analyzer to V(t) - R(t), already stored, to give V(t) +
R(t) stored in two memories.
The only significant effect of drift is
then in the value of the very small difference V(t) - Vr (t).
The
stored values are then transferred to an HP-85 computer for Fourier
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
transformation and other processing to calculate £*(w) from equation
3.1, as described in (34), (35).
The high frequency correction function f(z) depends on the geo2
metry of the cell used, but can be expanded as a power series in z ,
and hence in £*, for frequencies below cutoff for higher order modes
of propagation.
In 7 mm diameter cylindrical waveguide, this cutoff
is fm (GHz) = 3 3 / ( 3 8 ) ,
limiting the usable range to 3 GHz for
water with previous cell designs.
The cell used in this work shown in
Figure 19 is a modification, by adding a metal insert, to increase
such cutoff frequencies.
With this design, a correction function
f(z) = 1 + 0.3z^ - 0.3z^ with d = 1.175 mm was obtained by calibration
with deionized water, with a high frequency limit |z| =
for water (with £g = 78.5 at 25°C).
at 25°C).
1.1 or 5 GHz
This limit was verified by tests
This limit was verified by tests at 25°C acetone (£g=21.2),
chloroform (£g = 4.90), and Isopar-G(£g = 2.00).
The last, a mixture
of nonpolar hydrocarbons, is a very useful dielectric calibration
liquid kindly supplied by Dr. E. 0. Forester (Exxon Research and
Engineering Co.).
Above about 3 GHz increasing oscillatory deviations
of known and measured values of £* become apparent which are attribut­
able to a variety of impedance mismatches of the sampler and coaxial
line sections.
These amount to less than ± 5 percent for |e*| <
but can be as great as ± 10 percent for |e *|
>20.
5
An overall cali­
bration procedure to correct such systematic errors has been developed
(39) but was not needed for this work.
Baker "Analyzed" (99.9 percent) 1-propanol and deionized water
were used to prepare the solutions maintained at 25.0 ± 0.1°C by a
bath and monitor system previously described(37).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
Spring
Stainless
S teel
Insert
Thermistor
Probe
W ater
Bath
•Coaxial Line
Figure 19.
Modified TDR Sample Cell
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48
RESULTS
Solutions of water in 1-propanol were measured at seven compo­
sitions in the range from 0 to 0.75 mole fraction water at 25.0 ±
0.1°C.
Numerical Fourier transformation of the TDR response records,
obtained by the procedures described above, then gave values of com­
plex relative permittivity £* = e'-ie" at frequencies from 50 MHz to
8 GHz.
Representative results for 0.35 mole fraction water are shown
in Figure 20.
Almost by inspection of the £* data, the relaxation is seen to
be only approximately of simple Debye form, as shown by the dashed
curves in Figure 20, which are plots of e* and e" as calculated from
3.2
with T chosen to give the absorption maximum of e" at the correct fre­
quency, and
estimated by extrapolation of the e 1 data to infinite
frequency.
The nature of the deviations from a single Debye relaxation is
more evident from the plot in Figure 21 of £' versus coe".
For Debye
behavior, the analysis (40) would give a straight line of slope = -x
from the consequence of equation (3.2) that £' = £g - cote ", while for
two Debye relaxations expressed by
°° T 1 + iw^
1 + iu)X2
the predicted curve is asymptotic to straight lines of different
slopes for iot^ « 1 and W X 2 » 1 (if
Corresponding relations for
£* in terms of £"/w are less revealing for the present situation, but
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with permission of the copyright owner. Further reproduction prohibited without permission.
C
70
8.0
8.5
9.5
10.0
LoQiq Frequency
Figure 20. Comparison of Single Time Constant (dashed lines) and Two-Time Constant (solid line) Debye
Representation of the Dielectric Properties of a .35 Mole Fraction Water in 1-Propanol Solution.
(Data shown as symbols)
Figure
0.35
21.
Mole
Determination of Starting
Fraction Water
[ /Vi68 mhz
Values
for
the
Parameters
Used
in
the
Two-Time
Constant
Equation
at
50
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51
are useful for estimates of e^. This plot is also shown in Figure 21.
It is seen that the experimental curves are at least qualitatively of
this form.
Accordingly, the data were fitted to the function (Equa­
tion 3.3) by numerical iterations to obtain optimum values of e^, e^,
T ^ f and T 2 (eg being known accurately from the low frequency limit of
£').
The parameters were determined by a brute force least squares
analysis to minimize the objective function r2 = 2T[(e T—ec.a.lC )^ +
(e"-e"calc)2 ] using a direct search sweep of the four parameters,
starting with initial estimates based on analytical properties of
Equation (3.3).
Step size changes of one percent with ± 15 percent
sweep range resulted in satisfactory convergence in 20-30 minutes for
the Fortran coded program on the PDP11/10 computer using 24 data
points at 12 approximately logarithmically spaced frequencies.
The best fit parameters obtained are listed in Table 3, together
with the final values of the minimized r2 and of E = (r2/24)1^2 , the
latter to give some idea of the mean error in the fit to the data.
The
frequencies (MHz) for the data used in this analysis are presented at
the bottom of Table 3.
The solid lines in the plots of Figure 20 for
0.35 mole fraction water were calculated from these parameters, with
the circles and crosses from the experimental data.
The fit is seen
to be quite satisfactory, the most noticeable difference being that
the calculated values of e" are a little too large near the loss maxi­
mum.
The values of the permittivities £g ,E^ and
are plotted against
mole fraction X of water in Figure 22, and the values of
Figure 23.
The decrease of
and
in
toward the nearly constant values of T 2
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE
Xw
.75
.65
.50
.35
.25
.15
0.05
0
3;
Parameter for two-t1me constant Debye type equation
es
41.72
34.96
28.64
24.96
22.98
22.04
21.37
20.85
T-jpsec
47.9
68.9
101.7
132.4
169.2
214.7
274.4
318.0
el
17.7
13.9
10.24
6.27
5.17
4.65
4.20
3.98
x2psec
21.5
18.05
23.6
19.1
20.8
20.6
26.5
22.8
eoo
6.4
3.06
3.46
3.72
2.90
3.12
3.27
2.95
r2
3.806
1.8939
1.532
.4654
.1694
.1227
.0882
.0664
E =
+
+
+
+
+
+
+
+
.40
.28
.25
.14
.08
.07
.06
.05
High Freq.
Frequency (MHz)
Low Freq.
0-.65 mF H20:
68.13.100.0.146.8.244.1.316.2.464.2, 3174.0,3662.0,4639.0,5615.0,6592.0,7568.0
.75 mF H20:
68.13.100.0.146.8.244.1.316.2.464.2,
1465.0,1709.0,2197.0,2686.0,3174.0,3662.0
53
0
.2
.8
1.0
X H 20
Figure 22.
Water
Variation of Fitted Parameters e
and e
with Mole Fraction
1
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54
300
0
30
0
0
-2
-4
.6
x
Figure 23.
Water
h
-8
1.0
2o
Variation cf Fitted Parameters t, and t9 With Mole Fraction
1
1
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55
with increasing X makes determination of the parameters increasingly
uncertain, both because of the greater overlap of the two relaxations
and because the effects are at increasingly high frequencies, making
experimental uncertainties in determining the permittivities larger
with a lower usable maximum frequency limit possible.
Measurements
at mole fractions X greater than 0.75 could not be satisfactorily
analyzed for these reasons.
The significance of the changes of the
parameters with X is considered in the discussion.
DISCUSSION
As anticipated from previous evidence mentioned in the introduc­
tion, a slower "principal" relaxation at increasingly high frequencies
is found for increasing water content, rather than a decreasing ampli­
tude with less change in frequency if it were attributed to relaxation
of alcohol molecules in a mixed solvent medium by rotational diffusion
processes.
A further argument against such an interpretation in these
mixtures of polar associating liquids is found in the magnitudes of
the relaxation times x^ for the pure components as compared to those
for non-associating but otherwise similar polar molecules.
The value
x^ = 320 ps for 1-propanol is some forty times longer than the values
T = 7 ps for 1-bromopropane estimated from microwave data of Smyth
et al. (41) at 3, 9.3, and 23.5 GHz.
For water, there is more dif­
ficulty in finding a reasonable comparison liquid, there apparently
being no dielectric relaxation data for either
or HCL for example.
However, Levesque et al (42) found a relaxation time x^ for HCL of about 0.5 ps for dipole (P^) correlations for molecular dynamic (MD)
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56
simulations and the time x^ = 8.3 ps for water is thus larger by a fac­
tor of fifteen.
Both of the comparisons just made indicate a major effect of
joint correlations of molecular dipoles with near neighbors in the neat
liquids, and by inference in solutions of the two.
The concept of well
defined, long lived species associated by hydrogen bonding seems to us
too special as a description of the dynamics responsible, as MD simula­
tions of water, e.g. by Rahman and Stillinger (43), also suggests.
It
is also worth noting that the dynamic differences, as expressed by x.,,
are much greater than the static ones as expressed by the Kirkwood gfactor for example.
The values of g, as inferred from relative static
permittivities, are of order 3.7 to 2.5 for 1-propanol and water (44),
(45), indicating static effects of joint correlations of molecules
with their neighbors which, although large, are much less than the
changes in the time scale for dynamics of these correlations inferred
from the preceding discussion.
As such, the evidence does not support
for these associated liquids the result of Kivelson and Keyes (46)
that a factor g should give the relation of times x with and without
correlations.
The comparison is, however, a bit unfair as the model
of molecular reorienting units in a Brownian dynamical environment
used by the authors would seem ill suited to the present problem.
Similar behavior of the primary x^ relaxation has been reported
by Bertolini et al. (47) for ethanol and 2-propanol solutions with
added water, to mole fraction 0.5 for the first two and 0.15 for the
last, at frequencies from 0.47 to 1.87 or 3.75 GHz.
They represented
their data for a single x^ relaxation decreasing with X.
However, plots
of e' versus toe" for their reported values give indications of higher
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
frequency deviations, particularly at temperatures of 0°C and -26°C,
similar to ours which are more evident because of the wider frequency
range.
An original objective of this work, to test the conjecture that
a microemulsion interface composed of water and 1-butanol might rea­
sonably be expected to exhibit a relaxation at ca 1 GHz, has been rea­
lized in the sense that our most nearly comparable bulk system, of
equimolar water in 1-propanol has a primary relaxation at a comparable
but higher frequency of 1.6 GHz.
The existence of faster secondary
relaxation in the bulk solutions may also have a counterpart for the
interfacial layer, but present evidence is too meager to decide the
question.
The second principal result of this work, which was not anticipaged, was the finding of a need for at least a second relaxation of
increasing amplitude and nearly constant relaxation time T 2 = 22 ± 3
ps, about three times that of pure water (8.3 ps at 25°C) but equal to
that for a secondary relaxation of the neat alcohol.
This has been
found for several alcohols at various temperatures and frequencies.
Early results of Girard and Abadie (48) for 1-octanol at room tempera­
ture indicate T2 = 40 ps, for example, with similar values for other
alcohols .from work of Brot (49).
For 1-propanol, measurements by
Davidson and Cole (44) at low temperatures (-130 to - 150°C) showed
such a relaxation in detail, but at much lower frequencies, and also
a third still smaller and faster relaxation.
Garg and Smyth (50)
found a similar behavior at temperature 20, 40, and 60°C with derived
values of T 2 estimated to give T2=20ps at 25°C, in agreement with our
results (Their value t^=390 ps is, however, considerably larger than
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t ^=320
ps from our and other more recent work).
There is little doubt of the existence of smaller, fast relaxa­
tion processes in alcohols in addition to the primary one, but their
molecular origins have been a subject of considerable conjecture and
debate for many years.
Two quite different kinds of mechanism proposed
with numerous variations are changes in hydrogen bonding, either to.a
new neighbor or within hydrogen bonded "chains"
on the one hand (51),
(52),(53), or to reorientations of unbounded, singly, and multiply
bonded molecular complexes on the other (54) (55).
An extensive dis­
cussion of the pros and cons for the several alcohols which have been
studied is beyond the scope of this paper, but can be found in the
Bottcher-Bordewijk treatise (56).
In the present context, we suggest that the relaxation with T^
unchanged from the value for the neat 1-propanol but increasing specta­
cularly in amplitude an addition of up to 0.75 mole fraction of water
is not to be explained in terms of reorientations of whole.molecules of
either kind, much less any well defined, long lived aggregate.
Rather,
one needs to consider possibilities for reorientation of hydrogen
bonding hydroxyl groups of either species constrained by local "struc­
ture" but not by necessity for appreciable displacements of attached
alkyl groups.
Even cursory study of space filling models of hydrogen
bonded chains suggests plausible conformational changes and shifts in
hydrogen bonding which could meet such requirements, with no obvious
preferred candidates.
Adequate computer simulations can be extremely
useful for such purposes, as shown by the work of Helfand (57) for
the simpler conformational dynamics of single polymer chains, but
would seem to be enormously more complex for any straightforward study
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59
of mixtures of transiently hydrogen bonded chains.
Finally, we suggest two related propositions.
The first is that,
although we have been able to represent the present results reasonably
well by a sum of two distinct Debye relaxation functions, there is no
justification for supposing that either describes a simple dynamical
process rather than sums or combinations of processes with nearly the
same characteristic times on a logarithmic scale.
Indeed, our data
for solutions with mole fraction X from 0.5 to 0.75 give
and T 2
different by less than the factor five sometimes cited as the minimum
for resolving two Debye functions of the same amplitude, as each has
width of e" at half height of 1.1 decades.
Second, it should be possible to improve the definition of the
processes, the faster ones especially, by measurements to higher fre­
quencies and at lower temperatures.
It seems feasible to raise the
upper frequency limit to 10 GHz even for water with £g = 80 by simple
changes in cell design and in calibration of residuals in the TDR in­
strumentation (39), while measurements at 0°C and below should reduce
the frequency ranges of dispersion by a factor of two or more.
These
further mesurements have not yet been possible because of time limita­
tion, but are planned for future work.
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60
CHAPTER IV
MICROWAVE INTERFEROMETRIC DETERMINATION OF
COMPLEX DIELECTRIC PROPERTIES
INTRODUCTION
This chapter, describes the design, construction, operation and
testing of an apparatus which extends our measurement capabilities to
23.45 GHz.
The device shown in block diagram form in Figure (24) is
based on apparatti described by Straiton
and Saxton et al. (60).
and Tolbert (58),Schwarz
(59),
The device is essentially a microwave transmis­
sion type bridge circuit which measures the phase and amplitude change
experienced by an electromagnetic wave as it traverses a sample speci­
men
.
The phase and amplitude shifts are converted into 8 and a,
which are the imaginary and real parts of the complex propagation con­
stant, y = a + j3, from which e*, the complex dielectric constant is
determined:
Y =
a + j B = jw(y * e * ) 2
where
U* = yQ = 1 = permeability of sample material
e* = e'-ie"
A complete set of relations between a, 6, and e* is presented in
Appendix B.
EXPERIMENTAL
The liquid sample is contained in a teflon cell consisting of an
adjustable piston in cylinder arrangement shown in Figure (25).
The
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•SOURCE - KLYSTRON
O
REFERENCE
LEVEL SET ATTENUATOR
SPLITTER'
y
-ISOLATOR
TRANSMITPHASE ANGLE - SLOTTED LINE S.L.
SAMPLEMETERRECEIVE-ATTENUATION PA
ATTENUATION
Figure 24. Microwave Transmission Interferometer for the Determination of Complex Dielectric Constants at
23.45 GHz
o
M
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MICROWAVE SIGNAL
AIR
TEFLONPISTON
*'0" RING RIM SEAL
JQUID FEED
TEFLON-CYLINDER
LIQUID SAMPLE SPACE-
3/2
CELL SECTION
AIR*
/
Figure 25. Sectional View of Variable Pathlength Teflon Sample Cell Used in the Determination of £* of
Liquids by Microwave Interferometry
63
cell thickness is adjustable to allow for phase and amplitude measure­
ments as a function of sample thickness.
The procedure involves bal­
ancing precision attenuator, PA, and slotted line, SL, for a minimum
signal without the sample present.
Then small increments of sample
are introduced into the cell by turning the four cell positioning
screws.
Typically a distance of .05 inch = .1270 cm was used which cor­
responds to one complete turn of each of the 20 thread per inch screws.
Micrometer measurements before and after were used to verify the ac­
curacy of this technique.
procedure is repeated.
sured.
Upon introduction of the sample the balancing
Typically, 9 such increments of sample are mea­
Plots of amplitude and phase versus pathlength are then con­
structed.
The slopes of these graphs, determined with the aid of lin­
ear regression, yield a a n d A L i n decibels/cm and phase angle/cm res
At
spectively.
It should also be noted that lensed horns were employed.
Horn separation was 6 inches and the beam was focused down to a 1 inch
spot size 3 inches away from each horn.
way between the horns. A
The sample was positioned mid­
sample calculation may be found in Appendix B.
RESULTS AND DISCUSSION
Figures (26) and (27) show the results of the determination of ag
and AL respectively for 1-propanol, ethanol, acetone and water from inAt
cremental sample length phase and amplitude measurements. It should be
noted that this variable pathlength method is applied to account for
the effects of reflections at the principle dielectric interfaces, i.e.
air/teflon, teflon/sample, sample/teflon and teflon/air.
The reflec­
tions come about as a direct result of the change in dielectric constant
which occurs at each interface.
Since the reflections are to a first
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o
O
04
S138I03Q
o
o
O
26.
o
Figure
O
Determination
of a
From
WATER
Variable
Pathlength
Attenuation
Data
ACETONE
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0001 X
wd
'U IH S
3SVHd
Figure
27.
2400 r
Determination
of AL From
Variable
Pathlength
Phase
Shift
Data
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
approximation functions of the individual interfaces, measurement at
multiple pathlengths can be used to subtract out their effect.
Another
reason for incremental measurements has to do with phase angle ambi­
guity.
The slotted line section SL in Figure(24) is the recombining
element for the interferometer.
Waves from the source
(reference)
enter at the top while the received signals (signals which have passed
through the sample) enter at the bottom.
The interference patterns
which result are detected by a movable probe (59), (61).
of measurement is 0-180°.
The range
This means that phase shifts such as 45°,
45 + 180 = 225° or 45 + 360 = 405° would appear the same to SL.
The
incremental method precludes the possibility of such ambiguity by
keeping
the incremental phase shifts well below 180°.
Resonance Effects.
Another source of error which arises in these measurements is due
to resonance effects.
This is due to the interaction between sample
specimen and both receive and transmit horns.
To counteract this ef­
fect a variation of the 1/4 wavelength technique described by Little,
et al. (62) and Epstein (63) has been applied.
This technique in­
volves phase and attenuation measurements with the sample at a fixed
position.
The procedure is repeated with the sample displaced i wave­
length towards the transmit horn.
The average of these two readings
for both phase and amplitude are taken as the data pair at each fixed
sample pathlength.
Near Field Free Space Wavelength Correction Factor.
The last aspect to be dealt with arises from the effect of wave
diffraction.
This occurs in closely coupled Transmit/Receive setups
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67
such as the one employed here.
The phenomenon was originally described
by Kerns and Dayhoff (64) and Baird (65) and is of importance in the
microwave interferometric determination of the free space velocity of
electromagnetic energy (light).
The phenomenon acts to lengthen the
effective free space wavelength which occurs in the focused region be­
tween the closely spaced receive and transmit horns.
X = KX
e
o
where
XQ = c/F
c
= Free Space Velocity of Light
F
= Frequency
K
=
Xq
= Nondiffracted Free Space Wavelength of Light
Xg
= Effective Wavelength used in Calculation of £* (See Appendix B)
Diffraction Correction
Constant
Using an approximation technique Bussey (66) has estimated a value of
K = 1.025.
A value of 1.020 was chosen for this study as it produced
values of e* (see
other
workers.
a movable
Table 4) in best agreement with observations
A more exact
of
determination ofXgmight bemade with
probe connected to a micrometer drive.
The probe could be
moved between the two horns (Figure 24) in the vicinty of the sample.
This is a free space analog of a slotted line where the distance be­
tween two successive voltage minima gives i Xg(61).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
68
Table 4. Dielectric Properties of Standard Liquids Determined by Micro­
wave Interferometry at 23.45 GHz
Sample
Temp
1-Propanol
24.0°C
9.74
.530
3.42
.87
3.35
.80
Ethanol
24.5°C
17.09
.665
4.18
1.70
4.25
1.69
7.37
17.5
7.4
36.90 32.5
35.1
Acetone
24.7°C
Water
22.0°C
a^db/cm
35.75
119.8
AL/At
e’
2.03
17.85
3.33
33.28
e"
e’lit e"lit
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
69
CHAPTER V
APPLICATIONS
The following is a brief listing of applications of electromag­
netic properties measurement techniques which might be of interest to
chemical engineers.
Perl (67),(68) has applied the technique of Microwave Absorption
Spectroscopy (69), (70), (31) to the determination of oil and water
saturations in porous sandstone rocks.
This apparatus allows observa­
tion of the two phase flow process in the rocks during enhanced oil re­
covery experiments.
Doughty (71) applied a microwave resonance technique at 9.5 GHz
to the determination of water content in oil-water emulsions.
His
technique does not, however, take into account the difference in di­
electric properties of the two basic emulsion types which has been
described in Chapter II of the present study.
Of interest, however,
is his use of a resonant cavity with sample tube holes drilled in the
narrow side of the cavity.
In this manner the sample cuts across an
electric field whose intensity varies with distance.
This allows a
larger sample tube to be employed,3 mm x 2 mm, outer and inner dia­
meter (compared to the perturbation set-up described in the present
study).
This might be more useful in a flow monitoring scheme.
Prausnitz et al (72) have presented a numerical model for the
prediction of vapor-liquid equilibrium compositions from fundamental
properties measurements.
The most important of these basic proper­
ties is the vapor phase second virial coefficient which itself is re­
lated to the dipole moment.
These dipole moments are usually
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70
determined by measurement of the dielectric constant of the gas (73).
It is of interest to note that, at present, Prausnitz’s model relies
on calculated dipole moments.
He has found large discrepancies in
the case of polar associating molecules such as water, methanol,
acetic acid, etc.
Currently he uses an association parameter (n) to
bring his model calculations in line with experimental observations.
Dielectric studies may serve to quantify such vapor phase associations.
Indeed, the determination of chemical structure has been the primary
goal of most studies of dielectric phenomena; Debye (1), Smyth (73).
More recently, Cole et al.(74),(75) has described a method for the
determination of second virial coefficients from dielectric measure­
ments.
The difference between dielectric properties of water, oil, and
rock have been used in a novel determination of absorbed water-inoil reservoirs (Rau, (76)).
This data, which improves the deter­
mination of reservoir oil saturation, provides information critical
to the drilling of successful (not dry) oil wells.
Ellerbruch (77) presented a microwave method for the measure­
ments of densities and flow rates for cryogenic materials such as
Hydrogen and Nitrogen as liquids or slushes, using resonant cavity
and microwave doppler techniques respectively.
Changes in dielectric constant might occur in chemical reactions
affording a means by which reaction product compositions or rates
could be determined nondestructively and noninvasively.
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71
CHAPTER VI
SUMMARY AND FUTURE WORK
This chapter has been set-up with respect to the separate investi­
gations presented in Chapters II, III, and IV.
Chapter II Dielectric Properties of Emulsions
It would be of interest to investigate the effects of particle
size in such dispersed phase systems.
Here, the low frequency (Mega
Hertz) range may provide more information as the interfacial polariza­
tion effect is quite strong there and may exhibit a greater sensitivity
to drop size.
The effect of surfactant type and concentration should also be
examined.
It is possible that e* of the interfacial layer for 0/W
macroemulsions is sufficiently different from its W/0 counterpart to
explain the difference in dielectric properties of these two basic
macroemulsion types (2), (5).
With regards to this it may be possible
to generate dilute (<10%) surfactant free W/0 type dispersion using a
neutral bouyancy oil phase such as the CCl^/oil mixture (9) described
in this chapter.
Sonication would be the recommended dispersion tech­
nique for creating submicron or micron size droplets.
Chapter III 1-Propanol/Water Solution
The dielectric study described in this chapter was performed over
the range of 50-7800 MHz (0.05-7.8 GHz). The TDR apparatus employed in
this study utilizes an open circuit coaxial transmission line as a
test cell and hence was limited to measurements of e'<20 at Ca 5 GHz.
This limited the study to solutions containing less than .75 mole
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72
fraction watar (Ca .55 weight fraction).
The model developed to de­
scribe the mixture dielectric properties, a two time constant Debye
type representation, required fitting 4 parameters to the data over the
range of frequencies investigated.
It would be useful then to examine
these mixtures in the resonance apparatus at 9.5 GHz and the transmis­
sion apparatus described in Chapter IV at 23.45 GHz.
These apparatti
do not have such upper bounds on their measurement capabilities and
the data might be useful in extending the fit to higher frequencies
while also testing the resonability of such a two time constant hy­
potheses.
With regards to another application Brost and Davis (31) have
used isopropanol/water mixtures to simulate the microwave absorption
properties of water-oil mixtures commonly found in porous media oil re­
covery experiments.
They have attempted to use such solutions to cali­
brate the porous media itself.
Their plots of microwave attenuation
vs. wt% alcohol exhibited a slight nonlinearity at 9.5 GHz and a gross
nonlinearity at CA 24 GHz.
They had assumed that the alcohol/water
mixture absorption would be linear with alcohol content.
This is in
direct conflict, however, with our results presented in this chapter
which suggests a very high degree of interaction between the alcohol
and water molecules in such mixtures which was not seen to vary linearly
with weight fraction.
It would, therefore, be of further interest to
characterize the dielectric properties of such mixtures at typical
core flooding frequencies (9.5 and 23.5 GHz).
Such information would
be useful in our lab where a microwave attenuation core flooding appa­
ratus has become a standard tool for the investigation of multiphase
flow and recovery processes in porous media enhanced oil recovery
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73
experiments. Perl (67).
Chapter IV Microwave Transmission Interferometry at 23.45 GHz
This apparatus differs from those described in the previous chap­
ters in that it is capable of measuring large samples and can in prin­
ciple be applied to measurements in a porous medium.
As it stands now,
however, the technique requires data as a function of pathlength
(sample thickness).
This data is then used in a simple iterative solu­
tion to the complex dielectric constant of a sample assuming a plane
electromagnetic wave in an infinite medium with no reflections or in­
teractions between the sample and container boundaries (see Appendix B).
A mathematical technique developed by Richmond (78) and Bussey
and Richmond (79) does, however, allow in principle for the direct
calculation of £ ' and £".
The method, a digitally implimented recur­
sive technique, simply carries through the exact solution to the field
equations across each dielectric interface i.e. air/sample, thru sample,
sample/air etc.
A drawback to this procedure, however, is its inability
to account for resonance effects which arise from interactions between
the transmit horn and sample front face, and the receive horn and
sample back face. In the present study these effects are averaged out
by the r wavelength method (62),(63) described in this chapter, and this
might be a useful approach if the exact equation method is attempted.
The data acquisition procedure for this experiment is rather tedi­
ous and time consuming.
It requires manual balancing of a precision
attenuator and phase measuring device (micrometer fitted slotted line
section of waveguide).
Also, the determination of phase shift can be
ambiguous as the slotted line range is from 0-180°.
Hence, a true
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74
reading of 45° could also be 45° + 180° = 225° or 45° + 360° = 405°
etc.
In the present study, this was accounted for by the introduction of
small increments of sample liquid into the variable path length cell.
The problem of data acquisition and phase angle ambiguity might be
solved simultaneously be replacing the precision attenuator and slotted
line with a computerized Automatic Network Analyser (ANA).
This device
also known as a signal analyser, is phase locked and capable of re­
solving phase and attenuation changes of Ca .1° and .1 db respectively.
It also has the advantage of stepped frequency operation.
This fea­
ture can allow the direct determination of unambiguous phase shifts by
noting the phase shift differences at two or more frequencies. This
fractional phase shift can then be used to back calculate the total,
true phase shift.
Also, as this device is computer controlled it is
amenable to on line data processing.
This would be useful if the re­
cursive digital technique described above is adopted. Also worthy of
mention is a Universal Microwave Phase-Measuring System developed by
Ernst (80) for use in plasma diagnostic applications.
This system uses
a single sideband with suppressed carrier (SSBSC) (80) method for de­
tecting microwave phase changes and can measure phase shifts of up to
20 it radians (3600°) unambiguously.
Summary
This thesis is concerned with the application of microwave diag­
nostic techniques of interest to chemical engineers.
The techniques
described herein use electromagnetic methods to determine concentrations
and emulsion types, particularly in solutions or dispersions where water
is one of the components.
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75
These electronic determinations can be made rapidly, nondestructively and 'in some cases, noninvasively.
The electronic measurements
also lend themselves to interfacing in a computer process control
scheme.
It should also be noted that the dielectric techniques de­
scribed herein have been devised to take the place of wet chemical and
optical microscopy techniques and also provide an electronic means of
monitoring multiphase flow within a porous media.
Highlighted in this work is:
1)
A dielectric method for the simultaneous determination of
macroemulsion type and water content using a microwave
resonance dielectrometer;
2)
A study which characterized the broadband dielectric pro­
perties of 1 -propanol/water solutions using the technique
of Time Domain Reflectrometry (TDR) and;
3)
Complete description of the design, construction and opera­
tion of a K-Band (23.46 GHz) Microwave Transmission Inter­
ferometer for the determination of complex dielectric pro­
perties of liquids or solids such as porous media.
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76
APPENDIX A
STANDARDS USED IN THE PERTURBATION STUDY OF
CHAPTER II AND SAMPLE CALCULATIONS
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77
Standards Used in the Perturbation Study of Chapter II
The values of e' and e" for the liquid standards used in the micro­
wave resonant cavity standard reference calibration procedure were
chosen as follows:
Methanol: Debye dispersion parameters suggested by Poley (82) as
reported by Buckley Sflid Maryott (83) were used to calculate e' and e"
from
e * = e' - ie" =
using
eg = 32.8,
Acetone:
+ (es-eoo)/(l-(iujT)1-a
A.l
= 5.62 and T = 48.8 x 10- ^2 sec and a = 0.0
e 1 and e" were determined by interpolation of the data
of Smyth et al (84) as reported in Reference 83.
Water:
e' and e" were calculated from Equation A.l using Cole-
Cole (85) dispersion parameters based on a regression analysis of
existing data by Mason et al (8 6 ) and Grant et al (87) as suggested
by Hasted (45), ( 88 ).
The parameters used were:
e
t
= 78.96, e = 4.22,
S
oo
= 8.46 x 10-1 2 sec and a = 0.013.
Sample Calculation for the Resonance Dielectrometer
Ex. acetone at 9.505 GHz
Refer to Figures 2 and 3 on Pages 11 and 13 respectively.
First we rewrite equations 2.2 and 2.3 noting the following re­
lationships.
V = total volume = length x width x height
i.e. V = LWH
v = interior volume of glass capillary tube in cavity
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78
kg = rnr/L = 7ir/(15.285 cm)
kQ = 2irF/c = 2tt 9.505 x 10 9 Hz/3 x 10 10 cm/sec
Substituting these relationships into equation 2.2 for e' and
equation 2.3 and 2.7 for e" we obtain
e* = Ci) -11*11
/u\ U
(TTr H)
(k /k )2 = (i)(W/irr2 )(k /k )2 AL + 1
g O
o n
A.l
Inserting numerical values for the constants above we obtain
(W=.9 inch):
e" = (i)(3800.75)AL + 1
A.4
The cavity is first adjusted to obtain resonance with an empty
sample tube bynoting
the maximum dip below the baseline.
points are thencalculated using equations 2 .1 a
The
and2 .1 b (page
2power
1 2 ).
For acetone at 9.505 GHz the empty resonance dip, dbg = 6.35 db and
the sample dip, dbg = 3.75 db from which:
(dbe )| = 2.11, (dbg )^ = 1.48
A.5
the moveable short position is varied between the % power values from
which the following results were obtained
(L2_Li)s = -0114 cm
A*6
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79
(L,2~L^)e = .0080 cm
A.7
(L2+Ll V 2 = 1*72450
A .8
A.9
(L2+Ll V 2 = 1*73520 cm
Now using
A .6 and A.7
in A.3, and
A .8 and A.9 in
A.4 we obtain
e’ = 21.33
e" = 3.23
Voltage Ratio Calculation of e"
From equation 2.8
R
s
= .649, R
e
= .481
e" = (i)(3800.75)(.008)(.649-.481)/(1-.649) = 3.64
The value of the empty tube Q-factor in A.7, was determined by
repetitive measurement.
This value was, therefore, known to a greater
accuracy (± .0001 cm) and the voltage ratio technique was employed
throughout this work for the determination of e" hence ( e ' - l ^ = 20.33
and
= 3.64 are the measured values obtained using the perturbation
approximation.
These values must now be corrected using the procedure
outlined on page 19, by equation 2.11 and the constants in Table 5.
(e'-l)c = .9259(20.33) + .3920 = 19.22
(e")c = (3.64)(19.22)/(20.33) = 3.44
the final corrected values are
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80
£ 1 = 20.22
e" = 3.44
Smyth (73) found s' = 20.1 and e" = 3.41
Simultaneous Determination of Emulsion Type and Water Content From
Dielectric Measurements on Unknown Emulsion Using the Calibration
Curves in Chapter II
1.
Given an unknown
emulsion with e*=13.0 and e"=6.5 at 11.003
determine type and water content.
tangent e 'V e ’ = 0 . 5 .
GHz,
We first calculate the loss
We see from Figure (14) that this cor­
responds to a 0/W type emulsion. Once the emulsion type has
been determined we find from Figure 12 or from Figure 13 that
this corresponds
2.
to a fractional water content of 0.3.
Given the measured values of e ? and e" = 10,3 at 11.003 GHz,
respectively, we first calculate the loss tangent e 'V e ' = 0 . 3 .
We see from Figure 14 that this corresponds to a W/0 type emul­
sion.
Again, once the emulsion type has been identified one
may use either Figure 12 or 13 to determine the fractional
water content of 0.3.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 5.
Standard Liquid Reference Calibration Data for the Microwave Resonance Dielectrometer
Frequency (GHz)
8.193
(e ’- D p («•
Sample
Methanol
8.85
8.34
Acetone
21.35
19.23
Water
72.76
65.45
9.505
1 )T £"p
e"x
(E1-■Dp
11.003
(*•- -1 )T E"p e"t
(£'--l)p (C- _1)T
E"p e"T
9.70
9.34
7.58
7.48
9.0
8.34
6.56
6.81
3.32
2.99
19.90
19.10
3.6
3.41
19.40
18.93
3.74
3.83
27.14
66.71
62.18
32.6
29.75
61.49
58.39
34.37
32.11
30.0
7.6
Correction Eqn 2.11
Constants
Slope, a
.8975
.9259
.9452
Intercept, b
.1538
.3920
.3690
Correlation
Coefficient
Avg. Error,
Back Calculations
for 3 Standards
.99991
£'=±1.1%
£'=±1 .1%
£'=±1.6%
e"=± 2 .0 %
e"=±2.5%
e "=3.4%
Calibration Line
(e'-l)T =
P = Perturbation Measurement Value,
(e'-l)
+ b
T = True, Standard Reference Value
7.41
82
APPENDIX B
DIELECTRIC EQUATIONS FOR THE INTERFEROMETER
DESCRIBED IN CHAPTER IV
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MICROWAVE TRANSMISSION EQUATIONS
TRANSMISSION EQUATIONS
Phase constant due to the sample
3s =
eo \ P
is
given bySchwarz (59)
((1 + ((1 + (£"/£')2 )i )/2)i
A.l
which for the sake of Brevity will be rewritten as
A.2
where A is everything to the right of the radical in Equation A.l
but the interferometer measures
3
s
- 3
=
o
m
A.3
hence
S
m
+3
o
=3
v/e' A
o *
A.A
where
3 m = 2 3 g(AL/At)
A.5
Adding Equations A.4 and A.5 and rearranging the result we obtain
6? =
but
(1/A + 2 6 g(AL/At)/ 6 0 A )2
A .6
3 =
» A = 1.597 cm as determined by slotted line measureg
Ag
g
ments of the distance, d, between successive minima, i.e. Ag = 2 d
So'f1
o
but here we must substitute
A
for
A
(Baird (65)) to account for
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84
diffraction effects arising from the close placement of the receive
and transmit horns.
We note also the following relationships
A
where
K
e
e
= AK
o e
= diffraction factor at 23.45 GHz
Xq = C/F = 3 x 1010/(23.45 x 109 ) = 1.279 cm
With these substitutions Equation A .6 then becomes (using Kg = 1.02
as described in Chapter IV)
e' = (1/A + (1.634)(AL/At)/A)2
A.7
where AL/At is the slope of the phase versus distance plot (see
Figure 27) in cm of slotted line micrometer travel per unit sample
pathlength, cm/cm
For e" Schwarz (59) gives
e" = 2a 8s/eo2 =
2je'
(ag) A AQ/(8.686)(2Tr)
which at 23.45 GHz and substituting Ag for Aq becomes
A ( .0478)
where ^
A .8
is the slope of attenuation versus distance plot (see Fig­
ure 26) in decibels per unit sample pathlength, db/cm.
It is of interest to notice the non zero Y intercept for the
attenuation plots, particularly those for water and acetone.
This
phenomenon is due to reflection at the two liquid/teflon interfaces.
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85
Determination of ot^ and 8 ^
As discussed above, 8 g is determined from equation A.3 and A.5.
The phase angle, AL, and attenuation determined at each path length as
follows:
1.
Adjust level set to desired maximum attenuation,
2.
Balance bridge for minimum by adjusting slotted line SL and
precision attenuator PA without the cell.
might be 40 db and .350 cm.
Typical readings,
In this example 40 db is now
the maximum sample attenuation that can be measured.
3.
Insert empty cell between horns.
tion.
Readjust phase and attenua­
Typical readings would be 39.4 db and .4827 cm. This
means the cell has a loss of .6 db and a phase angle of .1327
cm.
Just as a matter of interest the teflon thickness is .495
cm and this yields
k k = .1327/.495 which when inserted into
At
equation A.7 (A^l.O) yields £* =2.07,the dielectric constant of
the pure teflon.
4.
Move cell 1/4 wavelength towards transmit Horn by insertion
of shims.
In this work (.96)(l/4) A0 wavelength was employed
Redo the determination of AL and db as in Step 3.
5.
Average AL of Step 3 and 4 to obtain AL to be plotted in
Figure 27.
Do the same with the values of attenuation for
Figure (26).
6 . Determine AL
and a
At
from the slope of the phase data versus
s
pathlength and attenuation vs pathlength.
In this study, the
best straight line through the data was determined by linear
regression.Typical correlation coefficients exceeded .99 on AL/At
and .98 on a .
s
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86
7)
Setting k^, the free space wavelength correction factor equal
to 1 , 0 2 as discussed in the chapter,calculate
using equations A.7 and A. 8 .
e' and e"
Note that the two equations
are coupled and require an Iterative Solution.
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87
BIBLIOGRAPHY
(1)
Debye, P., Polar Molecules, The Chemical Catalogue, New York, 1929.
(2)
Clausse, M., "Dielectric Properties of Emulsions and Related
Systems", in Encyclopedia of Emulsion Technology. Vol. 1,
Chap. 3, Sec. C, P. Becher, ed., 1980.
(3)
Foster, K.R., Epstein, B.R., Jenin, P.C. and MacKay, R.A., "Di-slectric Studies on Nonionic Microemulsions", J. Colloid Inter­
face Sci.. Vol. 8 8 , P. 233, 1982.
(4)
Epstein, B.R., Foster, K.R. and MacKay, R.A., "Microwave Dielectric
Properties of Ionic and Nonionic Microeraulsions" J. Colloid
Interface S ci.. Vol. 95, P. 218-227, 1983.
(5)
Hanai, T., "Electrical Properties of Emulsions", in Emulsion
Science, P. Sherman ed., Academic Press, London and
New York, P. 353-478, 1968.
(6 )
Sillars, R.W., "The Properties of a Dielectric Containing SemiConducting Particles of Various Shapes", sJ. Institution of
Electrical Engineers, Vol. 80, P . 378-394, 1937.
(7)
Chapman, I.D., "The Effect of the Emulsifying Agent on the Dielec­
tric Properties of Water-in-Oil Emulsions", J. Phys. Chem.
Vol. 75, P. 537-541, 1971.
(8 )
LePetit, J.P., Delbos, G., Bottreau, A.M., Marzat, C. and Cabanas,
R., "Dielectric Relaxations of Emulsions of Saline Aqueous
Solutions", J^. Microwave Power. Vol. 12, P. 335-340, 1977.
(9)
Hanai, T., Imakita, T. and Koizumi, N., "Analysis of Dielectric
Relaxation of W/0 Emulsions in the Light of Theories of
Interfacial Polarization", Colloid Polymer Sci., Vol. 260,
P. 1029-3034, 1982.
(10)
Bethe, H.A. and Schwinger, J., "Perturbation Theory for Cavities"
NDRC. Report Dl-117. March, 1943.
(11)
Horner, F., Taylor, T.A., Dunsmuir, R., Lamb, J. and Jackson, W.,
"Resonance Methods of Dielectric Measurement at Centimetre
Wavelengths", J. Institution Elect. Eng. (London), Vol. 93,
III, P. 53 - 6 8 , 1946.
(12)
Birnbaum, G. and Franeau, J., "Measurement of the Dielectric Con­
stant and Loss of Solids and Liquids by a Cavity Perturbation
Method", J. Appl. P hys.. Vol. 20, P. 817-818, 1949.
(13)
Soohoo, R., Theory and Application of Ferrites, Prentice-Hall,
Englewood Cliffs, N.J.jP. 260-266, 1960.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(14)
Estin, A.J. and Bussey, H.E., "Errors in Dielectric Measurements
Due to a Sample Insertion Hole in a Cavity", IRE Trans.
Microwave Theory Tech.. Vol. MTT- 8 , P. 650-653, 1960.
(15)
Li, S.' and Bosisio, R.G., "Composite Hole Conditions on Complex
Permittivity Measurements Using Microwave Cavity Perturba­
tion Techniques", IEEE Trans. Microwave Theory Tech.,
Vol. MTT-30, P. 100-103, 1982.
(16)
Li, S., Akyel, C. and Bosisio, R.G., "Precise Calculations and
Measurements on the Complex Dielectric Constant of Lossy
Materials Using TM q ^q Cavity Perturbation Techniques",
IEEE Trans. Microwave Theory Tech., Vol. MTT-29, P. 10411048, 1981.
(17)
Hartshorn, L. and Ward, W.H., "The Measurement of Permittivity
and Power Factor of Dielectrics at Frequencies from 10^ to
108 CPS," J. IEE (London). Vol. 79, P. 567-609, 1936.
(18)
Bussey, H.E., "Cavity Resonator Dielectric Measurements on Rod
Samples", in Annual Rept. of 1959 Conf. on Electrical In­
sulation. National Academy of Sciences, Washington, D.C.,
NRC Publ. 756, PP. 15-20, 1959.
(19)
Bussey, H.E., "Measurement of RF Properties of Materials A Sur­
vey", Proc. IEEE. Vol. 55, P. 1046-1053, 1967.
(20)
Sherman, P., Emulsion Science, Academic Press, London and New
York, 1968.
(21)
ASTM Procedure, "Water-in-Liquid Petroleum Products by Karl
Fischer Reagent", ANSI/ASTM D-1744-64, American Society
for Testing and Materials.
(22)
ASTM Procedure,"Water using Karl Fischer Reagent", ANSI/ASTM
E-203-75, American Society for Testing and Materials.
(23)
Klein, A., "Microwave Determination of Moisture in Coal: Com­
parison of Attenuation and Phase Measurement", J. Microwave
Power. Vol. 16, P. 289-304, 1981.
(24)
Meyer, W. and Schilz, W .M., "Feasibility Study of DensityIndependence Moisture Measurement with Microwaves", IEEE
Trans. Microwave Theory Tech., Vol. MTT-29, P.732-739,1981.
(25)
Stratton, J.A., Electromagnetic Theory, McGrawHill, P.201-207,1941.
(26)
DeLoor, G.P., "Dielectric Properties of Heterogeneous Mixtures
with a Polar Constituent", Appl. Sci. Res. Sect. 15., Vol.11,
P. 310 -320,1964.
(27)
Cole, R.H., Mashimo, S. and Winsor, IV, P., "Evaluation of Die­
lectric Behavior by Time Domain Spectroscopy, 3, Precision
Difference Methods", J^. Phys. Chem., Vol. 84, P. 786-793, 1980
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(28)
Perl, J.P., Wasan, D.T., Winsor, IV, P., and Cole, R.H., "Die­
lectric Relaxation of 1-Propanol/Water Solutions" Accepted
for publ., J. Molecular Liquids, 1984.
(29)
Mudgett, R.E., Wang, D.I.C. and Goldblith, S.A., "Prediction of
Dielectric Properties in Oil-Water and Alcohol-Water Mix­
tures at 3000 mHz, 25°C Based on Pure Component Properties',*
J. Food S c i ., Vol. 39, P. 632-635, 1974.
(30)
Kraszewski, A., Kulinski, S. and Matuszewski, M . , "Dielectric
Properties and a Model of Biphase Water Suspension at 9.4
GHz", J. A ppl. Phys., Vol. 47, P. 1275-1277, 1976.
(31)
Brost, D.F. and Davis, L.A., "Determination of Oil Saturation
Distributions in Field Cores by Microwave Spectroscopy",
Paper SPE 10110 presented at the 56th Annual Fall Technical
Conf. and Exhib. of SPE of AIME, San Antonio, Texas,
Oct. 5-7, 1981.
(32)
Schallamach, A., "Dielectric Relaxation of Mixtures of Dipolar
Liquids", Trans. Faraday Soc., Vol. 42A, P. 180-188, 1946.
(33)
Bottcher, C.J.F. and Bordewijk, P., Theory of Electric Polariza­
tion. Vol. II, Elsevier, Amsterdam, Second Edition, Chapter
IX, P. 114, 1978.
(34)
Cole, R.H., "Evaluation of Dielectric Behavior by Time Domain
Spectroscopy, II. Complex Permittivity", J. Phys. Chem.r
Vol. 79, P. 1469-1474, 1975.
(35)
Cole, R.H., Mashimo, S. and Winsor IV, P., "Evaluation of Dielec­
tric Behavior by Time Domain Spectroscopy. 3. Precision Dif­
ference Methods", J. Phys. Chem.. Vol. 84, P. 786-793, 1980.
(36)
Cole, R.H. and Winsor IV, P., in Fourier, Hadamard and Hilbert
Transforms in Chemistry, A.G. Marshall, ed., P. 183, Plenum,
New York, P. 183-206, 1981.
(37)
Winsor IV, P. and Cole, R.H., "Dielectric Properties of Electro­
lyte Solutions. 1. Sodium Iodide in Seven Solvents at
Various Temperatures", J^. Phys. Chem.. Vol. 8 6 , P. 24862490, 1982.
(38)
Marcuwitz, N., Waveguide Handbook, McGraw Hill, New York, P. 174,
1951.
(39)
Cole, R.H., "Bridge Sampling Methods for Admittance Measurements
From 500 KHz to 5 GHz, "IEEE Trans. Instrum. Meas., Vol.
IM-32, P. 42-47„ 1983.
(40)
Cole, R.H., "On the Analysis of Dielectric Relaxation Measure­
ments", J. C hem. Phys., Vol. 23, P. 493, 1955.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
90
(41)
Heston, W.M., Hennelly, E.J. and Smyth, C.P., "Dielectric Con­
stants, Viscosities, Densities, Refractive Indexes, and
Dipole Moment Calculations for Some Organic Halides",
J. Am. Chem. Soc., Vol. 72, P. 2071, 1950.
(42)
Levesque, D., Weiss, J.-J. and Oxtoby, D.W., "A Molecular Dynam­
ics Simulation of Rotational and Vibrational Relaxation in
Liquid HC1", J. Chem. Phys.. Vol. 79, P. 917, 1983.
(43)
Rahman, A. and Stillinger, F.H., "Molecular Dynamics Study of
Liquid Water", J. Chem. Phys.. Vol. 55, P. 3336, 1971.
(44)
Davidson, D.W. and Cole, R.H., "Dielectric Relaxation in Glycerol,
Propylene Glycole, and n-Propanol", J^. Chem. Phys., Vol. 19,
P. 1484-1490, 1951.
(45)
Hasted, J.B., "Aqueous Dielectrics". Chapman and Hall, Ch. 3,
P. 89, 1973.
(46)
Knelson, D., and Keyes, T., "Unified Theory of Orientational
Relaxation", J. Chem. Phys., Vol. 57, P. 4599, 1972.
(47)
Bertolini, D., Cassettari, M . , and Salvetti, G., "The Dielectric
Relaxation Time of Supercooled Water", J. Chem. Phys.,
Vol. 76, P. 3285, 1982.
(48)
Girard, P. and Abadie, P., "Experimental Curves of Losses and of
Anomolous Dispersion as a Basis of a Spectral Method", Trans.
Faraday S oc.. Vol. 42A, P. 40-47, 1946.
(49)
Brot, P.C., "Microwave Dispersion and Hydrogen Bonding in Some
Alcohols", Ann. Phys.. Vol. 13-2, P. 714, 1957.
(50)
Garg, S.K., and Smyth, C.P., "Microwave Absorption and Molecular
Structure in Liquids. LXII. The Three Dielectric Dispersion
Regions of the Normal Primary Alcohols", J. Phys. Chem..
Vol. 69, P. 1294-1301, 1966.
(51)
Brot, C., Magat, M . , and Reinisch, L., "Dielectric Dispersion
in the Decimetric and Centimetric Range", Kolloid-Z.
Vol. 134, P. 101, 1953.
(52)
Hassion, F.X., and Cole, R.H., "Dielectric Properties of Liquid
Ethanol and 2-Propanol", J.. Chem. Phys., Vol. 23, P. 17561761, 1955.
(53)
Dannhauser, W., and Fluekinger, A.F., "Liquid Structure and
Dielectric Relaxation of Some Isomeric Methylheptanols",
Phys. Che m . Liquids, Vol. 2(1), P. 37, 1970.
(54)
Bordewij, P., Thesis. Leiden, 1968.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
(55)
(56)
Bordewijk, P., Gransch, F . t and Bottchery C.J.F., "Dielectric
Behavior of Mixtures of 1-Heptanol and 4-Heptanol and the
Fluid Structure of the Monoalcohols ",J. Phys. Chem., Vol.
73, P. 3255, 1969.
Reference (33) P. 253.
(57)
Helfand, E., J. Polymer
(58)
Straiton, A.W., and Tolbert, C.W., "Measurement of theDielec­
tric Properties of Soils and Water at 3.2 cm. Wave Length",
J. Franklin Inst.. Vol. 246, P. 13-20, 1948.
Sci., in Press.
(59)
Schwarz, E.G.,. "Free Space Interferometer for Dielectric Mea­
surements on Sheets", Standardization Engineering,
Practises Study, General Electric Electronics Laboratory
Report, No. 3a, Task 701, 1963.
(60)
Saxton, J.A., Bond, R.A., Coats, G.T., and Dickinson, R.M.,
"Dispersion at Millimeter Wavelengths in Methyl and Ethyl
Alcohols", J. Chem. Phys.. Vol. 37, P. 2132-2138, 1962.
(61)
Ellerbruch, D.A., "UHF and Microwave Phase Shift Measurements",
Proc. IEEE, Vol. 55, P. 960-969, 1967.
(62)
Little, W.E., Ellerbruch, D.A., and Engen, G.F., "An Analysis
of the "Quarter-Wave" Technique of Reducing Errors in UHF
and Microwave Impedance Measurement", IEEE Trans. Micro­
wave Theory Tech., Vol. MTT-15, P. 504-507, 1967.
(63)
Epstein, D . , "Phase
Parallel-Plate
for Insulation
of Technology,
(64)
Kerns, D.M., and Dayhoff, E.S., "Theory of Diffraction in Micro­
wave Interferometry", JL Res. NBS, Vol. 64B P. 1, JanuaryMarch, P. 1-13, 1960.
(65)
Baird, R.C., "RF Measurements of the Speed of Light", Froc. IEEE,
Vol. 55, P. 1032-1039, 1967.
Shift of Microwaves in Passage Through
Arrays", Technical Report XLII, Laboratory
Research. Massachusetts Institute of
August, 1950.
(6 6 ) Bussey, H.E., Personal Communication, U.S. Nat. Bur. Standards
Boulder, CO.
(67)
Perl, J.P., Microwave Spectroscopic Analysis of Surfactant/
Polymer Flooding, MS Thesis, Illinois Institute of Technology,
Chicago, 1979.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
92
(6 8 )
Perl, J.P., Milos, F.S., and Wasan, D.T., "Microwave Spectro­
scopic analysis of Surfactant/Polymer Flooding: Interrela­
tionships Between Chemical Slug Properties, Coalescence
Phenomena, and Tertiary Oil Recovery", Paper SPE 8327,
presented at the 54th Annual Fall Technical Conf. and Exhib.
of the S oc. Pet. E n g , of AIME., Las Vegas, Sept. 23-26, 1979.
(69)
Parsons, R .W., "Microwave Attenuation - A New Tool for Monitoring
Saturations in Laboratory Flooding Experiments", Soc. Pet.
En g . J., P. 302, Aug. 1975.
(70)
Gladfelter, R.E., and Gupta, S.P., "Effect of Fractional Flow
Hystersis on Recovery of Tertiary Oil", Paper SPE 7577
presented at the 53rd Annual Fall Technical Conf. and
Exhib. of the Soc. Pet. Eng, of AIME, Houston, Oct. 1-3,
1978.
(71)
Doughty, D.A., "Determination of Water-in-Oil Emulsions by a
Microwave Resonance Procedure", Anal. Chem., Vol. 49, P. 690694, 1977.
(72)
Prausnitz, J . , Anderson, T . , Grens, E., Eckert, C., Hsieh, R . ,
and O'Connell, J . , Computer Calculations for Multicomponent
Vapor-Liquid and Liquid-Liquid Equilibria, Prentice-Hall,
1980.
(73)
Smyth, C.P., Dielectric Behavior and Structure, McGraw-Hill, 1955.
(74)
Bose, T.K. and Cole, R .H., "Dielectric and Pressure Virial Co­
efficients of Imperfect Gases. IV. C 2 H 4 and C 2 H 4 - Ar Mix­
tures", J. Chem. Phys.. Vol. 54, P. 3829-3833, 1971.
(75)
Copeland, T.G., and Cole, R.H., "Dielectric and Pressure Virial
Coefficients of Imperfect Gases. VII. CF 3 H - Ar and CFH 3 Ar Mixtures", J. C hem. Phys.. Vol. 64, P. 1747-’1751, 1976.
(76)
Rau, R.N., "Microwave Method and Apparatus for Determination of
Adsorbed Fluid in Subsurface Formation", U.S. Patent 4,151,
457, April 24, 1979.
(77)
Ellerbruch, D.A., "Microwave Methods for Cryogenic Liquid and
Slush Instrumentation” , IEEE Trans. Instrum. Meas., Vol.
IM-19, P. 412-416, 1970.
(78)
Richmond, J.H., "Efficient Recursive Solutions for Plane and
Cylindrical Multilayers", Electroscience Laboratory, Ohio
State University, Columbus, 0SU Report 1968-1, Aug. 10,
1965.
(79)
Bussey, H.E., and Richmond, J.H., "Scattering by a Lossy Di­
electric Circular Cylindrical Multilayer, Numerical Values",
IEEE Trans. Ant. Prop., Communication, P. 723-725, 1975.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
93
(80)
Ernst, W.P., "Universal Microwave Phase Measuring System", IEEE
Trans. Instrum. Meas.. Vol. IM-19, P. 354-357, 1970.
(81)
Reference (80), P. 354.
(82)
Poley, J.B., Reference (83) P. 7.
(83)
Buckley, F., and Maryott, A.A., Tables of Dielectric Dispersion
Data for Pure Liquids and Dilute Solutions. U.S. National
Bureau of Standards Circular 589, 1958.
(84)
Smyth, C.P., Reference (83), P. 27.
(85)
Cole, K.S., and Cole R.H., "Dispersion and Absorption in
Dielectrics. I. Alternating Current Characteristics",
J. Chem. Phys.. Vol. 9, P. 341-351, 1941.
(86)
Mason Reference (45), P. 47, and Reference (89), PP. 277, 288.
(87)
Grant Reference (45) P. 47, and Reference(89), PP. 277, 288.
(88)
Hasted, J.B., "Liquid Water: Dielectric Properties", in WaterA Comprehensive Treatment, F. Franks, ed., P. 277, 1972.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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