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Microwave characterization and thermal processing of cementitious materials

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A Bail & Hoiweii information C o m p an y
300 North Z aa o R oafl Ann Arpor Ml 48106-1346 USA
313 761-4700 800 521-0600
NORTHWESTERN UNIVERSITY
Microwave Qariettri ration
and
O m t m I Processing
of
C— antitlous Materials
A DISSERTATION
SUBMITTED TO THE GRADUATED SCHOOL
IN PARTIAL rULnLLHENT OF THE RBQUIREMEMTS
for the degree
DOCTOR OF PHILOSOPHY
Field of Electrical Engineering
by
John Tse-Yuan Chang
EVANSTON, ILLINOIS
June 1995
l
UMI Number: 9537410
Copyright 1994 by
Chang, John Tse-Yuan
All rights reserved.
ONI Microfora 9537410
Copyright 1995, by UMI Coapany. All rights reserved.
This aicrofora edition is protected against unauthorized
copying under Title 17* United States Code.
UMI
300 North Zeeb Road
Ann Arbor, MI 48103
©
Copyright by John T. Chang
All Rights Rsssrvsd
1994
ii
ABSTRACT
MICROWAVE CHARACTERIZATION AND THERMAL PROCESSING
OF CQfENTITIOUS MATERIALS
John Tse-Yuan Chang
Low power microwave characterization techniques have provided a
means to measure non-invasively different porosities in hydrating
cementitlous materials.
Total capillary porosity is determined by
measuring the constitutive parameters of the hydrating specimen.
The
constitutive parameters are then related to the capillary porosity
through effective medium theories.
Archie's empirical law have shown to
provide a convenient relationship between conductivity and capillary
porosity.
Gel porosity is determined by combining a microwave
measurement of capillary porosity and a weight loss measurement of total
porosity.
Closed capillary porosity is measured by first eliminating the
accessible capillary pore water via vacuum resulting in the presence of
only closed capillary fluids.
Subsequent microwave measurements of this
specimen lead to the determination of closed capillary porosity.
High power microwaves have been used to thermally process
cementitlous material under two different research programs.
The result
of these processes enhances the compressive strength of both fresh and
ill
aged mortar speclaens.
Thermal processing of frssh ctasnt aortar Increases the aarly
strength of the aaterlai without deleterious effects as the speciaen
ages.
This type of process accelerates hydration and decreases
porosity.
The aanufacture of polyaer impregnated concrete through microwave
induced polymerization have shown to increase the compressive strength
by aore than 400%.
Microwaves were used to assist the polymerization of
aonoaers intruded into cured aortar speciaans.
The effect of total
Impregnation as well as partial impregnation have shown to be beneficial
in lap roving material properties.
A new dynamic multimode applicator have been designed and
constructed which provides uniform heating of the speciaen and efficient
coupling of energy between the aicrowave source and the speciaen.
iv
ACKNOWLEDGEMENT
I like to express sy deepest gratitude and appreciation to ay
advisor and aentor Dr. Morris E. Brodwin for his unyielding perseverance
and guidance throughout ay endeavors.
The countless hours of
discussions which he has unselfishly presented to ae have provided the
uncoasttn opportunity to explore and enjoy the essence of scientific
research.
I like to thank Dr. Surendra Shah for his guidance, suggestions,
and for providing unlialted access to the facilities necessary for the
coapletlon of this work.
His graciousness in including ae in technical
discussions as well as various functions associated with the Advance
Ceaent Based Materials Center have developed ay interests in the fields
of civil engineering and aaterial science.
I like to thank the aeabers of the coaalttee Dr. Carl Kannewurf,
Dr. Allen Taflove, and Dr. Haalin Jennings for their tiae, suggestions,
and interests in this work.
I like to acknowledge the following people for their participation
and contributions to this researchi Dr. Mosango Moukwa, Dr. Barbara
Lewis, Dr. Haalin Jennings, Dr. Bruce Christensen, Dr. Francis Young,
Dr. G. K. Sun, Mr. Stephen Christo, Mr. Roy Hutchison, Mr. Dan Chu, Mr.
Joe Hetz, Hr. Hike Greenley, Mr. Steve Albertson, Mr. John Chlrayil, Hr.
Ken Lehaann, Mr. Jia Hahn, and aany others.
Financial support for this work was supplied froa the National
Science Foundation Center for Advanced Ceaent Based Materials and is
sincerely acknowledged.
v
DEDICATION
I like to dedicate this work to ay faailyt ay father, Peter ChiaChih Chang; ay aother, Jenny Bi-Hua Tung Chang; ay brother, Jaaes Chang;
and ay grandparents.
vi
TABLE OF CONTENTS
A B S T R A C T ........................................................... H i
ACKNOWLEDGEMENT ...................................................
v
D E D I C A T I O N .......................................................
vi
TABLE Or C O N T E N T S ................................................... vii
LIST OF T A B L E S .................................................... xiil
LIST OF F I G U R E S ...................................................
xv
CHAPTER 1
Introduction
.....................................................
1
Literature Survey .................................................
4
CHAPTER 2
CHAPTER 3
Transmission Line Methods for theMeasurement of Constitutive Parameters
of Cementitlous Materials between 500MHzand 10GHz
...............
23
3.1
Introduction...........................................
23
3.2
Optimum frequency form e a s u r e m e n t ......................
23
vli
3.3
24
Theory
CHAPTER 4
Dielectric Properties and Physical Structures
(Effective Medlua Theories) ......................................
32
4.1
Introduction..........................................
32
4.2
An historical o v e r v i e w ................................
34
4.3
Models suitable for the Initial study of ceaentltlous
Materials .............................................
40
4.3.1
A dielectric sphere in adielectric aedluM . . .
40
4.3.2
Rayleigh's Model ..............................
44
4.3.3
BruggeMan's sysMetrical Model
................
45
4.3.4
BruggeMan's asyMMetrical Model .................
47
4.3.5
Looyenga's Model ..............................
47
4.3.6
The constitutive paraMeter dependency on
frequency.......................................
48
4.4
Archie's enplrlcal Mixture law ........................
50
4.5
Conclusion............................................
52
CHAPTER 5
Microwave Measureaent of Porosity In Ceaentltlous Materials■ Total
Capillary Porosity
...............................................
53
5.1
Introduction..........................................
53
5.2
Theory of Microwave aeasureaents
53
5.3
Measureaent of total capillary porosity
viii
....................
.............
54
5.4
Application to caaantltlous materials
5.5
Comparison of microwave poroslmetry with mercury
intrusion poroslmetry(HIP)
5.6
................
67
..........................
70
Discussion and c o n c l u s i o n ............................
70
CHAPTER 6
Microwave Measurement of Porosity In Cementitlous Materialsi Gel and
Closed Capillary Porosity .........................................
76
6.1
Introduction..........................................
76
6.2
Theory and definitions................................
77
6.2.1
Microwave measurements ........................
77
6.2.2
Total capillary porosity ......................
77
6.2.3
Gel p o r o s i t y ..................................
78
6.2.4
Closed capillary porosity
....................
78
Experimental procedure ................................
79
6.3
6.4
6.5
6.3.1
Determination of gel p o r o s i t y ................
79
6.3.2
Determination of closed capillaryporosity . . .
79
Results and discussion................................
81
6.4.1
Gel porosity m e a s u r e m e n t s ....................
81
6.4.2
Closed capillary pore measurements ............
81
Conclusion............................................
88
CHAPTER 7
Microwave Thermal Processing of Cement Mortars
7. l
..................
89
Introduction..........................................
89
lx
7.2
Theraal processing a e t h o d s ............................
89
7.3
Experlaental procedures
99
7.4
..............................
7.3.1
Mixing, casting, and curing procedures ........
100
7.3.2
Theraal processing...............................100
7.3.3
Post processing t e s t s ...........................102
R e s u l t s ................................................. 103
7.4.1
The effect of alcrowave heatingonstrength
7.4.2
The effects of alcrowave heating on
aicrostructure
. .
103
................................
105
7.4.3
Nature of i a p r o v e a e n t .......................... 105
7.4.4
Coaparison to surface heating.. ...............
7.4.5
The effect of delay h e a t i n g .................... 116
112
7.5
Iaportance of unifora h e a t i n g ...........................118
7.6
Conclusion............................................... 121
CHAPTER 8
Microwave Induced Polyaeriration of Monoaer
Iapregnated Hardened Ceaent .......................................
123
8.1
Introduction............................................. 123
8.2
S u r v e y ................................................... 123
8.3
Experlaental procedure.................................. 126
8.3.1
Speciaen preparation ..........................
8.3.2
Iapregnatlon.....................................127
8.3.3
Hlcrowave polyaerlzatlon
8.3.4
Coapressive strength
x
...................
126
130
.......................... 135
8.4
8.5
8.6
R e s u l t s ................................................. 135
8.4.1
Total impregnation ............................
135
8.4.2
Partial impregnation............................. 137
Discussion............................................... 145
8.5.1
Totally Impregnated specimens
8.5.2
Partially Impregnated specimens
................
145
..............
145
Conclusion............................................... 150
CHAPTER 9
A New Applicator for Efficient Univorm Heating Using a Circular
Cylindrical Geometry
.............................................
151
9.1
Introduction............................................. 151
9.2
D e s i g n ................................................... 152
9.3
Experimental r e s u l t s .....................................156
9.3.1
Uniform h e a t i n g ................................. 156
9.3.2
Mode identif i c a t i o n ............................. 160
9.3.3
Applicator matching
9.3.4
Comparison of rectangular and circular
..........................
geometries with respect to load variations
...
167
169
APPENDIX A
Theory and Applications of the Modified InfiniteSample Method
..............................
174
A.1
Theoretical derivations
A. 2
Fortran code used for the coaxial l i n e .................. 179
A. 3
Fortran code used for the w a v e g u i d e .................... 183
xi
174
APPENDIX B
The Electrical Field Distribution of a Dielectric Sphere in a Dielectric
M e d i u m ............................................................. 188
APPENDIX C
Rayleigh aodel
...................................................
196
APPENDIX D
Bruggeaan symmetric aodel ........................................
200
APPENDIX E
Bruggeaan asyaaetric aodel
.......................................
204
...................................................
207
APPENDIX F
Looyenga aodel
R E F E R E N C E S ......................................................... 213
V I T A ............................................................... 221
xii
LIST OF TABLES
TABLE I
Summary of important publications ................................
21
TABLE II
Modal mixtures and measured constitutive parameters...............
57
TABLE III
Dielectric properties of aqueous
ionfilledsolutions..............
68
TABLE IV
Results tabulated in terms of day of curing, w/c, and various
porosities.........................................................
87
TABLE V
Summary of significant thermal processingstudies..................
95
TABLE VI
Parameters considered under the thermal processing program to study
fresh cementitlous materials......................................... 104
TABLE VII
Vacuum-pressure cycles and the depth of the impregnation of the monomer
solution............................................................. 136
TABLE VIII
Average effective compressive strength of partially impregnated
specimens and control specimens...................................... 142
TABLE IX
Listing of theoretical resonant modes and corresponding applicator
lengths.
Degenerate nodes are indicated by a common resonant length.153
xlil
TABLE Z
Listing of Identified aodes end Che difference in cavity length between
the Measured and predicted aodes..................................... 165
xiv
LIST or FIGURES
riGURE 1 Attenuation versus tiae using the free space aethod
FIGURE 2
9
Real and laaglnary parts of the coaplex peralttivity as a
function of tlae since alxlng
withwater.............................. 13
FIGURE 3
Theoretical curve to aodel the hydration process............14
FIGURE 4
Overlay of the heat of hydration curves onto the relative
peralttivity and conductivity
FIGURE 5
curves.Type I OPC, w/c-0.40............ 17
The heat of hydration, relative peralttivity, and conductivity
curves as a function of tlae since alxlng with water for different water
to ceaent ratios...................................................... 19
FIGURE 6
A scheaatic dlagraa of the infinite saaple aethod.......... 26
FIGURE 7
Effective aedlua concept used by Kraszewskl, et. al.........38
FIGURE 8
A dielectric sphere iabedded in a dielectric aedlua of a
different dielectric constant......................................... 41
FIGURE 9
Bruggeaan's syaaetrical aodel............................... 46
xv
FIGURE 10
Measured conductivity versus known porosity of water-solid
mixtures.
Application of Archie's law to data........................ 58
FIGURE 11
Application of effective medium theories to the conductivity
data presented in Figure 10........................................... 62
FIGURE 12
Application of effective medium theories using dielectric
constant.............................................................. 63
FIGURE 13
Parallel capacitor plate model of two component homogeneous
mixtures.............................................................. 65
FIGURE 14
Microwave porosity and theoretical porosityversus the degree
of hydration of w/c-0.5............................................... 71
FIGURE 15
Microwave porosity measured as a function of time of
hydration for water-to-cement ratios and cement types.................73
FIGURE 16
Microwave conductivity versus frequency andtime of hydration
for OPC w/c-0.44...................................................... 75
FIGURE 17
Porosities versus the days of curing for w/c-0.3.......... 82
FIGURE 18
Porosity versus the days of curing for w/c-0.5.............83
xvi
FIGURE 19
Porosity versus the water-to-ceaent ratio for 1 day cured
speclaens............................................................. 84
FIGURE 2®
Porosity versus the water-to-ceaent ratio for the 7 day cured
speclaens............................................................. 85
FIGURE
21 Phase dlagraa of hydration products froa Verbeck........... 98
FIGURE
22 Mercury intrusion results for 1 day speclaens............. 106
FIGURE
23 Mercury intrusion results for the 7 day speclaens......... 107
FIGURE
24 Mercury intrusion results for28 day speclaens............ 108
FIGURE 25
Percentage hydration versus time.......................... 109
FIGURE 26
The results of the coapresslon strength tests on DSP with and
without evaporation.................................................. 113
FIGURE 27
Coaparlson between coapressive strength iaproveaents of
alcrowave processed speclaens and conventionally heated speclaens.... 115
FIGURE 28
Effects of heating tlae delay on coapressive strength
xv11
117
FIGURE 29
Results of the teaperature profile test for ceaent aortar.120
FIGURE 30
Teaperature of the speclaens at different locations versus
the tlae of heating using distributed water loads and alcrowave
transparent turntable................................................122
FIGURE 31
Scheaatlc diagraa of the iapregnation chaaber............ 129
FIGURE 32
Scheaatlc diagraa of the aovlng end wall aultlaode
applicator........................................................... 132
FIGURE 33
Experlaental setup used in studying unifora heating...... 133
FIGURE 34
BPO content versus tlae and teaperature relationship to the
percentage polyaerlzatlon(froa Steinberg, 1967)..................... 134
FIGURE 35
Percentage increase in coapressive strength of 1 day cured
fully iapregnated speclaens in coaparlson to 1 day control
speclaens............................................................ 138
FIGURE 36
Percentage laproveaent of polyaerized specimens over the 28
day control speclaens................................................ 139
FIGURE 37
Scheaatlc diagraa of the cross section of a partially
iapregnated speciaen................................................. 141
xviii
FIGURE 38
Effective percentage Improvement of the partially Iapregnated
7 day cured specimens................................................ 1*3
FIGURE 39
Effective percentage improvement of the partially impregnated
28 day cured specimens............................................... 144
FIGURE 40
Percentage weight gain of the fully iapregnated
specimens............................................................ 146
FIGURE 41
Schematic diagram of the moving end wall multimode
applicator........................................................... 155
FIGURE 42
Enlarged view of the magnetic field coupling mechanism.... 157
FIGURE 43
Experimental setup used in studying uniform heating.......158
FIGURE 44
Orientation of the samples and positions of the thermometers
in the a) microwave oven and b) new applicator. (Not to scale)...... 159
FIGURE 45
a) Temperature profile of cement mortar processed in a
commercial microwave oven, b) temperature profile of cement mortar
processed in the new applicator...................................... 161
FIGURE 46
Schematic diagraa of the experimental setup to identify
resonance and observe mode overlap................................... 163
xlx
FIGURE 47
The reflected signal as a function of the angular position of
the aotor driven rotating disk for an unloaded (solid line) and a loaded
(dotted line) applicator............................................. 164
FIGURE 48
Reflection coefficient as a function of applicator length
aatched at minimum and maximum cavity lengths........................ 168
FIGURE 49
Magnitude of the reflection coefficient as a function of the
length of the applicator under matched conditions for 600ml water
load................................................................. 170
FIGURE 50
Magnitude of the reflection coefficient as a function of
applicator length for different degrees of loading................... 171
FIGURE 51
Comparison of rectangular and circular applicators with
respect to absorbed power as a function of load variation............172
FIGURE 52
A pictorial diagram of the cascaded transmission
line....175
FIGURE 53
A dielectric sphere Imbedded in a dielectric medium of a
different dielectric constant........................................ 190
FIGURE 54
N number of dielectric spheres imbedded in a dielectric
medium with a different dielectric constant bounded by a arbitrary large
sphere............................................................... 197
xx
FIGURE
55 Equivalent dielectric aedlua as the previousfigure........ 198
FIGURE
56 Bruggeaan's syaaetrlcal aodel............................. 201
FIGURE
57 Looyenga's aodel.......................................... 208
FIGURE
58 A aodel defined to be equivalent to thepreviousfigure...209
xxl
CHAPm 1
Introduction
The versatile applications °* nicrowavas have bsan exploited
leading to a battar understanding of pora propartlas in canantltlous
aatarlals.
In addition, aicroweves hava baan shown to provlda a aaans
to procasa canantltlous aatarlals that results in considerable
laproveuanta in physical propartlas, especially coapressive strength.
The content Is delineated Into two parts.
The first part, Chapter
2 through Chapter 6, will focus on using low power nicrowavas as a
characterization tool to study the pora propartlas of hydrating
canantltlous aatarlals.
The second part, Chapter 7 through Chapter 9,
will focus on using high power nicrowavas to laprove the physical
propartlas of fresh and aged canantltlous aatarlals.
A literature survey of prior studies on the dielectric properties
of canantltlous aatarlals In the alcrowave region will be presented in
Chapter 2.
Chapter 3 begins with a discussion on selecting the
appropriate aeasurenant frequency.
The theoretical background and
dlscrlptlons of lnstrunentatlons will conclude this chapter.
Chapter 4
presents an overview of appropriate effective aedlun theories which
night be applicable In nodeling ceaentltlous aatarlals.
Chapter 5
coablnes what was learned froa Chapter 3 and Chapter 4 to establish the
use of alcrowave surface spectroaeter to aeasure total capillary
porosity.
In essence, total capillary porosity Is evaluated non-
destructlvely by neasurlng the alcrowave constitutive paraawters of the
1
2
hydrating specimen.
The constitutive parameters, aapaclally tha
conductivity, ara ralatad to tha capillary poroalty through affactlva
medium thaorlaa.
Archie's aaplrical law provides tha nost convenient
relationship between conductivity and capillary porosity.
Chapter 6 further develope what was established In Chapter 5 to
aeasure gel porosity and closed capillary porosity.
In summary, gel
porosity Is evaluated by calculating the difference between the total
porosity and the capillary porosity.
The total porosity Is determined
from weight loss measurements of an oven dried specimen.
The capillary
porosity Is determined through microwave measurements.
Closed capillary porosity Is measured by first eliminating the
accessible capillary pore water via vacuum.
The subsequently measured
microwave conductivity Is related to the closed capillary porosity
through Archie's law.
Chapter 7 begins the discussion on the use of microwave heating to
process hydrating cementltlous materials.
Microwave heating of fresh
cement mortar have been shown to Increase the early strength of the
material without deleterious effects as the specimen ages.
This type of
process accelerates hydration and decreases porosity.
Chapter 8 presents an alternative means of using microwave heating
to Improve the strength of hardened cementltlous materials.
It Involves
the use of microwave heating to Induce the polymerization of monomer
Impregnated hardened cement mortar.
Polymer impregnated concrete via
microwave Induced polymerization Is shown to Increase the compressive
strength by more than 408%.
The effect of total impregnation as well as
3
partial lapragnatlon hava shown to ba banaficlal In laproving tha
aatarlal propartiaa.
Tha concluding chaptar prasanta tha davalopaant of tha dynaalc
aultlaoda applicator which algnlflcantly facllitatad a aora coaplata
undaratandlng of controlling alcrowava tharaal procaaalng by providing
aora uni fora haatlng of tha apaclaana and affldant coupling of anargy
batwaan tha aourca and tha apaclaana.
CHAPTER 2
Literature Survey
This chapter will review prior studlss on CjS-I^O (trlcalclua
silicate-water) bsssd aaterials using sicrowavs characterization.
Portland caaant will ba eaphaslzed.
DaLoor In 1961 publlshad a papar on
tha affact of aolstura on tha dlalactric propartlas of hardanad Portland
caaant pastas.1 Tha dlalactric propartlas of tha pastas wars aaasurad
In tha fraquancy ranga of 0.1 to 10tff(z and at 3GHz, 3.75GHz, 7.45GHz and
9.375GHz.
Eaphasis will only ba placsd on tha studlas aada at tha
alcrowava fraquanclas.
water to caaant ratios.
ratio of 0.26.
Flva spaclaens war* prepared with different
Two spaclaens ware alxed with water to caaant
One of these spaclaens was cured for one aonth under
water, tha second was cured for seven weeks under water.
Tha other
three spaclaens were alxed with water to caaant ratios of 0.24, 0.31,
and 0.36.
All three spaclaens ware cured under water for one aonth.
After the water curing periods, the speciaens were placed In a
100*C oven for tan days.
over PjOj for one week.
period and weighed.
Tha saaplas were then placed In a desiccator
The saaples are reaoved after this drying
Tha dielectric propartlas were also detarained.
After the Initial aeasureaents, the saaples were left In the laboratory
ataosphere at approxlaately 20*C and 50-70% relative hualdlty.
The
saaples were weighed and the dielectric properties were then aeasured at
various tlaes.
The percentage of aolsture content of each speclaen was
deterained by calculating the weight gained and dividing by Its dry
4
5
weight.
The dielectric aeeeureaente at 3.0 GHz, 3.75 GHz, 7.45 GHz and
9.375GHz were Bade uelng the Roberts and von Hlppel Method.2 This
aethod has often been referred to as the short circuited line method.
Waveguides were used.
The frequency of study dictates the size of an
appropriate waveguide.
The electromagnetic wave Is Incident upon a
saaple filled section of the waveguide which Is terminated by a short
circuit.
The reflected signal cause by the transition between the
saaple and the short circuit causes a standing wave to be foraed.
The
standing wave ratio and the shift In the alnlaua position of the
standing wave relative to the position alnlaua of a standing wave as
caused by a short circuit placed at the front surface of the saaple are
used In the calculation of the constitutive paraaeters of the saaple.
DeLoor referenced his prior work on heterogeneous Mixtures2 to
conclude that at the alcrowave frequency Measurements, free water is the
primary cause of losses In water saturated hardened ceaent.
This
conclusion was mainly due to the observed consistent Increase In the
dielectric losses as the aolsture coaponent increased.
One Interesting
statement that he aade, and alght be of later Interest to our present
study, was that "... the Cole-Cole plot of a heterogeneous Mixture
of
which one of the components shows relaxation (with properties which can
be plotted on a seal-circular Cole-Cole arc) also will be a seal-clrcle,
or at least nearly so, with the relaxation tlae shifted to shorter
tlaes(higher frequencies)."
6
J. B. Hasted and M. A. Shah published two papers in 1964 and 1965
on the studies of microwave absorption by water In various building
materials4,1.
The 1964 paper displayed the results of a study of
dielectric properties at 3GHz, 10GHz, and 24GHz of concrete, mortar,
hardened cement paste and different types of brick for different
moisture contents.
The goal of this study was to provide more
Information about the dielectric properties of these different systems
In hopes that It would be possible to predict the water content of
arbitrary building materials.
The measurements were performed by using the Roberts and von Hlppel
method.4 The sample thicknesses were, on the average, 2 cm for 1-band,
1 cm for S-band, and 0.3 cm for K-band.
Hasted and Shah's studies on hardened cement paste are particularly
Interesting.
The water to cement ratios for the prepared samples were
0.22, 0.28, 0.325, 0.034, and 0.4.
Ordinary Portland cement was used.
The samples were placed in a mold and allowed to hardened for three
months prior to the experiment.
discussed.
The curing conditions were not
The specimen preparation for loading and unloading water was
described as followsi
"The specimens are dried by evacuation, to a pressure of 0.01
torr, for several hours; the process is terminated when no further
change can be detected In the dielectric properties on further
evacuation; acceleration of the drying...Is achieved by heating to
temperatures 60-80°C.
Loading water Into the specimen Is carried
out under vacuum with an estimated quantity of distilled water, and
7
the absorbed water la allowed to homogenize for a period of up to
72 hours; the loaded speclaen la wiped, quickly weighed and
transferred to the waveguide."
The results of the study for the case where water was added to the
hardened ceaent showed an Increasing trend of both the relative
permittivity and conductivity as the water content Increased.
The
effect of water to ceaent ratios on the complex permittivity for the
hardened pastes did not show significant variations.
There were no
further quantitative discussions aade on the study of ceaent pastes.
The 1965 paper described studies on the dielectric properties of
aerated concrete at 3GHz and 10GHz.
Aerated concrete consisted of
ceaent paste alxed with a small proportion of alualnua powder.
The
material was then heated In an autoclave where the alualnua becomes
oxidized,
producing enough hydrogen to aerated the alx resulting In a
very porous material.
The hardened Material was capable of absorbing
74% of water by volume.
The technique used to determine the dielectric properties was
identical to that used In the previous paper.
The saaple thicknesses
used In the microwave measurements were approximately 2 cm for the 3GHz
measurement and 0.8 cm for the 10GHz measurements.
The results of the 1965 paper showed that dielectric measurements
of hardened pastes with added water could be closely modeled by
Bottcher's mixture theory using spherical inclusions.
8
Mlttaann and Schlude in 1975 presented a study of tha alcrowave
absorption of hydrating caaant pasta ovar long parlods between 8.5GHz
and 12.3GHz.7 Tha study was parforaad to aonltor tha variation of tha
dlalactric propartlas of caaant pasta as a function of tlaa since alxlng
with water, tha water to caaant ratio, tha frequency, and tha aoisture
content.
Two aethods of aeasureaent were used.
tha free wave aathod.
horn.
The prellalnary aathod was
It consisted of a transaltting and receiving
Tha saaple was placed between tha horns.
Tha Insertion loss
of the signal was deterained by aeasuring tha difference In the signal
strength between tha transaltted and tha received signal.
Tha saaples
were casted in tha cylindrical disk geoaetry with 30ca in dlaaeter and
3ca In thickness.
aeasureaents.
The saaples were stored In polyethylene bags between
Figure 1 shows the result of attenuation as a function of
the duration of hydration.
The free wave aethod does not yield the
relative peraittivlty or conductivity of the spaclaens.
The second aethod took advantage of a network analyzer.
The
saaples were casted into waveguides of 10aax22.8m i in dlaenslons.
saaples were 2Gaa In thickness.
The
The network analyzer was used to
aeasure the power ratio of the eapty waveguide and the saaple filled
waveguide.
The peraittivlty and conductivity could be Inferred froa the
change in power ration as the frequency Is varied.(They referenced a
alcrowave technique study by Tinga1)
This study, however, only
deterained the attenuation of the signal after transalssion through the
saaple.
9
110 0H« |
I
1
c
SO
JO My*
OimSsw ml hysrattow
Plgurs 1
Attamistlon v « n u s tine using tha frss spaca sstbod.
10
It was shown that at 10GHz, tha attanuatlon of tha apaclaana tracks
tha water to caaant ratio.
Tha graatar tha watar to caaant ratio, tha
graatar tha attanuatlon.
Tha affact of absorption and dasorption of watar on tha dlalactric
propartlas wars aada on 20 dlffarant hardanad caaant pasta spaclaans
with watar to caaant ratio of 0.4.
Tha spaclaans ware dried In a 105°C
oven after 28 days of sealed storage.
The absorption phenoaena was
studied by placing each speclaen In a dlffarant desiccator with
dlffarant relative hualdltles as sat by hydrostatic solutions.
relative hualdlty varied between 0% and 98%.
Tha
Tha aethod of varying the
relative hualdlty within tha desiccator was not clearly described.
Tha
desorption phenoaena was studied by first placing tha rest of the dried
spaclaans In a 98% relative hualdlty chaaber after which tha spaclaens
were separated into different desiccators with lower relative
hualdltles.
All of the speclaens were allowed to equilibrate In the
desiccators for 3 aonths.
The dielectric properties of each of the speclaens were then
aeasured.
The dielectric properties depended upon whether the aoisture
within the saaple was applied by the absorption aethod or the desorption
aethod.
It was not clear froa the report whether the results of using
the absorption aethod led to higher dielectric properties or lower
dielectric properties.
Thera was no axtenslva discussion of tha nature of the differences
in variations in the dielectric properties In teras of the aoisture
loading aethod.
The authors only suggested that alcrowave
11
characterization of ceaent paste aey be used to eonitor the state of
free water.
Reboul in 1978 provided a study of the dielectric properties of
tricaldua silicate (abbreviated as CjS) during the first 30 hours of
the hydraulic reaction.*
A resonant cavity perturbation aethod was
used to determine the dielectric properties of the specimen. **
chosen
The
rectangular resonant cavity resonates at 3GHz in the TEju node.
The cylindrical saaple has a diameter of 4aa.
The saaple is inserted
into the center of the cavity parallel to the short axis.
the saaple was not specified.
The length of
The water to CjS ratio was 0.35.
The
specimen retains its shape via the support of glass and plastic tubes.
The relative peraittivlty and conductivity of the saaples were
determined through the aeasureaent of the adalttance and the resonant
frequency of the cavity with and without the speclaen.
The author,
however, did not present the results in terms of the material
constitutive parameters, ratner only presented the results in terms of
the normalized admittance of the cavity containing the saaple.
She
monitored the normalized adalttance of hydrating C3S for the first 30
hours.
She divided the results into different periods in which she
suggested possible correlations to hydration mechanisms known at that
time as suggested by other authors.
Gorur, Salt, and Wlttaann in 1982 studied the dielectric properties
of ceaent paste during the first 48 hours of hydration.11 The
12
dielectric properties were deterained through the aeasureaents of the
alcrowave S-peraaeters froa an autoaated network analyzer.
Ordinary
Portland ceaent paste with water to ceaent ratios of 0.3, 0.35, and 0.4
was used.
The speclaen geoaetry was aolded to fit a 10aaz22.5aa
rectangular waveguide.
The thickness of the saaple was
Bm.
The
alcrowave frequency used was 9GHz.
Figure 2 shows the real and laaglnary parts of the coaplex
peraittivlty as a function of tlae since nixing with the water to ceaent
ratio as the third paraaeter.
They suggested that the decrease In the
relative peraittivlty corresponds to a decrease In the aaount of free
water.
An Interesting aspect of their study was the aodellng of the
results as described by two exponential curves.
general curve for 6'.
Figure 3 shows a
The syabols were defined as
/ ' - ( / , -f?) «**
Oststc
t
''*tZ
t ^ t
f| was the starting value, f,' and f," are the asyaptotic values for the
two segaents,
\ Is the transition tlae, and tj and t2
the Intercepts
of tangents on the asyaptotes.
These exponential curves were best fitted to the experlaental
results. They aeasured different ceaent alxtures and tabulated values of
13
)0
25
70
0.35
w /c
IS
10
i t C-0
w /c 0 .3 5
5
w /c
0
Plgura 2
laal and laaginary parts of tha caaplax paraittivity as
fraction of tiaa slnca airing with watar.
a
14
------- -
rigurs 3
Theoretical eurva to aodel tho hydration process.
15
w/c ratio, tj, tj and t2.
No quantitative comparison with tha chaalcal rataa of tha hydration
was nade.
Hanry In 1982 measured tha dlalactric propartlas of hydrating
caaant pasta at 5GHz for 15 hours lsaadlataly aftar mixing with
watar12.
Ha usad a cavity parturbation aathod slallar to that used by
Reboul.
Tha spaclaens ware two types of portland caaant, CjS and CjA.
Tha watar to solid ratio was 0.5 for all saaples.
Ha suggested that at
5 GHz, tha dielectric losses observed ware predominantly due to that of
bound watar.
This was a surprise and contradicted previous authors of
as DeLoor11 and tflttaann and Schlude1*.
Ha further triad to
empirically correlate tha measured dielectric losses with tha aaount of
watar raactad.
It was difficult to determine how ha was able to sake this
correlation.
Although tha dielectric loss as a function of tlae since
alxlng with watar shows great variations, tha results of three slallar
experiments showed distinctly different results.
Moukwa at. al. In 1990 provided an extensive study of different
types of caaant pasta as a function of tha first 24 hours of alxlng at
tha alcrowave frequency of 10GHz.1*'1* A discussion of tha correlation
between tha dlalactric properties and chaalcal processes was wade.
was shown that tha variation in tha dielectric propartlas during tha
hydration period coincided with tha heat evolved during hydration.
It
16
The constitutive paraaeters were aeasured by the infinite saaple
aethod.17 The paste was poured into a rectangular waveguide such that
the saaple butted against a thin alca sheet.
The electroaagnetic wave
transaltted into the ceaent paste is partially reflected by the paste.
The Interference produced was then used to derive the relative
peraittivlty and conductivity of the saaple.
The saaple was thick
enough and the attenuation of the electroaagnetic wave inside the paste
was sufficiently great such that no reflection occurred at the far end
of the saaple.
Hence the saaple appears to be electrically infinite in
thickness.
ASTH types I, II, and III Portland ceaents were used in the study.
The effect of water to ceaent rations of 0.3, 0.4, and 0.5 was studied
on type I ceaent.
The variation of the dielectric properties of the
different types of ceaent was studied using a water to ceaent ratio of
0.4.
The Influence of calclua naphthalene sulphurate superplastlclzers
on the type I ceaent paste with water to ceaent ratio of 0.3 was
assessed.
The heat of hydration for each of the alxed pastes were aeasured
using a Langevant caloriaeter.18,17
The variations in the aeasured relative peraittivlty and
conductivity curves for different ceaent pastes during the first 24
hours of alxlng with water were correlated with the heat of hydration
curves.
Figure 4 shows the overlay of the heat of hydration curves onto
the relative peraittivlty and conductivity curves of type I OPC with
water to ceaent ratio of 0.40.
Tin*, hours
(b)
Figure 4
Overlay of the heat of hydration curvee onto the relative
permittivity and conductivity curves. Type I OFC, Wc-d.40.
18
Consider first the conductivity curve of Figure 4.
The decrease in
conductivity after the doraant period was approximated by three line
segaents.
Line 1 corresponded with the period where the heat of
hydration varies with a high rate of development.
Lines 2 and 3
correspond to periods where the heat of hydration decreases in the
slower and slowest rates of development, respectively.
The trend of the
relative peraittivlty generally follows the trend of conductivity.
The effect of water to ceaent ratios on type I ceaent was shown to
accelerate the hydration process byi
1) shortening the dormant period
2) increase the rate of heat development
3) increase the aaximua heat generated which now occurs earlier
4) providing a more rapid deceleration of the evolved heat after
the aaxiaua has been reached.
The effect of water to ceaent ratio on the constitutive parameters
also resulted in very noticeable variations.
Figure 5 shows the heat of
hydration, relative peraittivlty, and conductivity curves as a function
of tlae for different water to ceaent ratios.
ratios used were 0.3, 0.4, and 0.5.
The water to ceaent
The significant points highlighted
were the end of the doraant period(represented by letters 0), the
aaxiaua heat generated(represented by letters M), and the end of the
first deceleration in the heat development(represented by letters C).
It was shown, in general, that the highlighted points in
the heat of
hydration curves corresponded well with the variation in the
ri*ire 5 The heat of hydration, relative peraittivlty. Mid conductivity
oirves aa a function of tine since airing with eater for different eater
to ceaent ratios.
constitutive paraaeters for any sort of caaant whether be its type,
water to ceaent ratio, or the addition of superplasticizers.
It was suggested that the variations in the conductivity during
hydration corresponds to the chaalcal processes that occur when free
water has be changed to bound water.
It was concluded thati 1) the changes in conductivity and relative
peraittivlty could be associated with the different stages during the
hydration process; 2) the constitutive paraaeters are sensitive to the
water to ceaent ratio and the type of ceaent; and 3)
the constitutive
paraaeters correlates well with the heat of hydration curves.
Chew, Olp, Otto, and Young in 1990 developed a new coaxial lineiapedance analyzer systea to aonitor the hydration processes of
ceaentltious materials2*'21.
They aeasured the constitutive paraaeters
of ceaent saaples between 10 M
line probe.
iz and 3GHz using an open ended coaxial
The saaple is butted against the end of the probe.
This
surface contact aethod allows a slaple and convenient Beans to measure
the dielectric properties.
on ceaent paste and mortar.
A preliminary experiment had been performed
However, no extensive study has yet been
performed on the dielectric properties of cementltlous materials.
Table I summarizes the cited works.
It can be seen that work prior
to 1978 had been done only on hardened ceaent pastes.
These studies
concentrated primarily upon the effect of absorbed free water on the
dielectric properties of hardened ceaent pastes.
The studies since
21
TABU I
Suaaary of important publications
Maaa(s)
(yaar)
Daloor
1961
J. B.
Hastad
and M. A.
Shah
1964
hardanad
hydrating
Corralation with
othar
tasts
yas
(OPC)
no
no
yas
(OPC)
no
yas
(OPC)
no
no
yas
(OPC)
no
yas
(c,s)
Typa(s) of caaant
pasta studiadi
no
Fraquancy
ranga of
study
Mathod of
aaasurtaants
.IMtelflMiz
3, 3.75,
7.45,
9.37GHz
Bridga
Von
Hippal
3, 19,
and 24GHz
Von
Hippal
3GHz and
19GHz
Von
Hippal
no
8.5GKZ
and
12.3GHz
Praa wsva
aathod
and
oatworfc
analyzar
ya*
(CjS)
no
3GHz
Rasonant
cavity
yas
(OPC)
yas
(OPC)
DO
9GHz
Bacwork
analyzar
Hanry
1982
no
yas
no
5GHZ
Houkwa,
at. al.
1991
yas
(OPC)
yas
(OPC)
yas
19GHZ
yas
(OPC,
■ortar)
yas
(OPC,
aortar)
no
1M1Z-3GHZ
1965
Wittaan
and
Schluda
1975
Raboul
1978
Gorur,
Salt, and
tflttaan
1982
Olp,
Otto,
Chaw, and
Young
1991
Cavity
pareurba*
tlon
aathod
Infinita
saapla
aathod
Batwork
analyzar
22
1978 have added the Initial 24 hours of hydration.
The aost
interesting information obtained froa these results was that there seeas
to be a general consensus that the variations in the dielectric
properties of hydrating ceaentitlous naterlals are due primarily to the
changes in the state of water.
All of the earlier studies, prior to 1975, used the Roberts and von
Hippel short circuited line aethod to determine the dielectric
properties of the specimen.
The aajor drawback of this aethod for
measuring high conductivity materials is the need to have a thin enough
saaple such that the incident signal will not only penetrate the saaple
but be reflected back froa the short circuit.
Other aethods that have been used were the resonant cavity
perturbation aethod, the network Impedance analyzer aethod, and the
infinite saaple aethod.
The draw backs of the resonant cavity
perturbation aethod are the small saaple sizes and the limitation to
single frequency aeasureaents.
The draw back of the network analyzer
arises froa the large errors in measuring materials with extreme
constitutive paraaeters.
Only the infinite saaple aethod places no
significant limitation upon the saaple thickness, wide band frequency
aeasureaents, and is simple to lapleaent.
The details pertaining to
this aethod will be discussed in the next chapter.
CHAPTER 3
Transmission Lina Methods for tha Haaauramant of Conatltutiva Paramatars
of Camantitloua Matariala between 500Miz and 10GHz
3.1
Introduction
To study tha non-intruaiva interaction between alcrowavaa and
camantitloua matariala, a microwava varslon of tha infrarad surface
spectrometer was designed and constructed.
is well established22.
The theoretical background
This apparatus is a derivative of the method
used by Moukwa at. al.22, and Christo2*.
This method has been refer to
by the previous authors as the "infinite sample method".
The range of
frequencies applicable using this apparatus will be between S M M i z and
10GHz.
Two types of measurements based upon one theory have been used.
One of these uses tha rectangular waveguide and the other uses a coaxial
line.
The waveguide provides measurements at the frequency of 10 GHz.
The coaxial line provides the wide band frequency measurements up to 6.5
GHz.
The lower frequency limit of 500 Miz has been set by the
limitation of the experimental apparatus, specifically the length of the
standing wave apparatus.
3.2
Optimum frequency for measurement
The premise of going into the microwave frequency region to study
the dielectric properties of cementltlous materials was based upon the
following idea.
Hydrating cement is first delineation into a two
23
24
coaponent material, capillary watar and remaining material.
Tha
remaining aatarlal la actually a congloaaratlon of unhydratad and
hydratad caaant, aggregates, chaalcally coablnad watar, and gal watar.
Tha distinction la basad upon tha fact that tha alactroaagnatic flald
axcltas dlpola rotation In tha capillary watar resulting In a first
ordar affact on tha obsarvad reflection.
high conductivity and dlalactric constant.
only a second ordar affact.
This Is aanlfested In taras of
Tha reaaining aatarlal has
Therefore, tha observations are doalnated
by tha quantity of capillary watar.
This Idea subsequently leads to tha
pursuit of a relationship between tha aeasured dlalactric propartlas and
tha quantity of capillary watar present.
It appears than that tha optlaua frequency to observe tha changes
of state of watar froa tha free state to tha bound state Is at tha
frequency where tha relaxation peak of free watar occurs.
A review of
the literature shows that this frequency occurs between 18 and 24GHz.25
However, In practice, a lower frequency of 10GHz was for aajority of the
aeasureaents.
This Is possible because of the broad peak of the
relaxation curve.
Furthermore, this frequency has bean selected partly
for laboratory convenience and partly to accoaaodate large aggregate
dlaanslons which makes aeasureaents at higher frequencies aora
difficult.
3.3
Theory
The constitutive paraaeters of high loss aaterlals can be
determined at alcrowave frequencies by using the Infinite saaple aethod.
25
nil* aethod takes advantage of transmission line theories in relating
the observable quantities of a transmission line with the constitutive
paraswter of an unknown material.
the Infinite saaple aethod.
Figure 6 shows a schematic diagram of
The unknown material Is place in one
section of the transmission line, B.
froa the source, A.
The microwave signal Is Incident
A standing wave is created as a result of the
presence of the unknown saaple.
The magnitude of the standing wave Is
observed by the crystal detector penetrating Into the transmission line.
The variation of the standing wave at different points within the
transmission line Is observed by moving the crystal detector along a
small slot cut In the longitudinal direction of the transmission line.
A theoretical relationship between the constitutive paraaeters and the
standing wave characteristics allows the constitutive paraaeters of the
unknown material to be calculated.
The standing wave characteristics
needed are the standing wave ratio and the shift In the position of the
standing wave minimum relative to the position of the standing wave
minimum when the saaple is replaced by a short circuit.
It has been
assumed that the saaple has enough loss such that the skin depth of the
incident wave upon the saaple Is much shorter in distance than the
physical saaple length.
Hence, the saaple appears to be electrically
Infinite In extend.
The freshly alxed ceaent paste is fluid In consistency and
therefore a teflon plug has been made to fit snugly In the cross section
of the transmission line.
The addition of this plug modifies the
theoretical calculations of the method.
1) Position
MIMUI
2) VSWR
Detector
A
T
€
Sample
Teflon
P*“g
Variable frequency
source
(HPI3S0B)
Reference
plaint A‘
A
SLOTTEDLINE
Figure 6
A schematic diagraa of the infinite saaple aethod.
27
The modified theoretical calculations can be quantitatively
summarized as follows.
A derivation has been provided In Appendix A and
the symbols are described there.
reference plane.
Consider A' of Figure 6 to be the
Fros fundamental transmission line theories2*, the
lapedance of the cascaded line at A' as viewed from the direction of the
generator Is
_ Z^.coahtrd) ♦Z^lnh(rd)
t'
'
*
"*Ti*cosh (r<f) ♦sinhdVf)
r Is the propagation constant within the spacer,
#3)
d is the thickness of
the spacer.
The values of
line used.
and
depend upon the type of transmission
Zt|^ lf and Z^ for a coaxial line are respectively
(5)
b/a is ratio between the outer conductor and the inner conductor of the
coaxial line.
zip Zor * waveguide are respectively
(9)
*i-— ^—
where 'i' is replaced by either 'sample' or 'sp' accordingly.
the shorter dimension of the waveguide.
and
a' la
are the
■agnetlc permeabilities of the air filled line, spacer filled line, and
the saaple filled line, respectively.
The magnetic peraeabilities of
the spacer filled line and the saaple filled line are Identical to the
magnetic permeability of free space,
e,,
and c||<flt are the
electrical permittivities of the air filled line, spacer filled line,
and the saaple filled line.
The electrical permittivities of the spacer
filled line and the air filled line are complex values
29
(!•)
and
(U)
where
and ct|^ lf* are the relative permittivities of the spacer and
the saaple, respectively,
and gg|^ lT are the conductivities of the
spacer and the sample, respectively.
• is the radial frequency of the
applied signal.
The normalized Impedance of Z(A') is related to the standing wave
ratio and the phase shift relative to a reference short placed at the
reference plane A' by
Z (A')
S-jt*n±
Z*
I-jStan*
2
where S is the standing wave ratio and • is the phase shift.
The constitutive parameters of the unknown saaple can be solved for
by combining equations (3), (4), (5), and (10) to (12) for the coaxial
line and equations (3), and (6) to (12) for the waveguide.
The solutions for the coaxial line are
30
,
i Jtr( a ^ » i " h ( r d ) -co.h(rd) ]a
*•
— sinh(rd) -XcosbdVJ)
. - . a , V 5 » i * « * > - - > « * > )■
-^-cinhdVi) -Xco«h(Tci)
(13)
(14)
*«p
T Is the propagation constant of the tzansalsslon line inside the spacer
and
S-j tan ( )
«
1
(15)
1-jstan ( ) i/®o
The solutions for the waveguide are
(16)
r - * '
(17)
where
Z<psinh(rd) -ZqA'coBhiTd)
Z0Jl'Z^ainh(rd) -cosh(rd)
(18)
31
T m -------- *
1 -jStUl*
(19)
CHAPTER 4
Dielectric Properties and Physical Structures
(Effactive Mediua Theories)
4.1
Introduction
The goals of this chapter are to provide a historical overview of
the study of sixtures and to choose and apply feasible theories for the
modeling of hardened ceaentitlous materials.
It is proposed that
effective medium theories will facilitate better understanding of pore
structures. The effective medium theories provide a means to relate the
effective dielectric properties of a mixture with the dielectric
properties and the volume fractions of the constituents of this mixture.
A two component mixture composing of capillary water and remaining
material will be assumed for the hardened cementltlous pastes.
The
remaining materials consists of hydration products, unhydrated cement,
aggregates, and gel water.
There are two facets associated with the effective medium theories.
The first one is the prediction of the dielectric properties of a
mixture when the dielectric properties and the volume fractions of the
constituents are known.
The second facet is the delineation of the
dielectric properties and/or volume fractions of the constituents of the
mixture when the effective dielectric properties of the mixture are
experimentally determined.
The "inverse problem” terminology has often
been associated with this second aspect of effective medium problems.
The present proposal will concentrate on modeling hardened cement pastes
32
33
using the inverse problem ideas.
The development of effective medium theories is based upon
fundamental electromagnetic concepts of fields, electric moments, and
polarizations.
The theories generally begin with the study of the
effect of external fields on a medium composed of at least two different
materials such that one material can be said to be suspended In the
other material, an inclusion.
The extension to more complex mixture
systems is then built upon the overall dielectric effect of
systematically Increasing the density of Inclusions such that a
generalized effective medium equation Is determined.
This method of
systematically increasing the lnhomogenelty of a material la often
preceded by basic assumptions and simplifications about the physical and
dielectric properties of the constituents of the mixtures in order to
maintain an analytically manageable form.
The assumptions about the physical properties of the constituents
of the mixture are generally limited to the shape of one of the
constituents.
The assumptions concerning the dielectric properties
often appears in the form of constraints placed upon the degree of
electrical association between the individual inclusions among each
other as well as between the different constituents of the mixture.
The modeling of hardened cementltlous materials using effective
medium theories will begin with the assumption that the hardened cement
paste is a two component mixture where spherical water inclusions are
dispersed in the background matrix of hardened cement paste.
He will
34
then determine which of the well established effective medium theories
can be best used to model these pastes.
4.2
An historical overview
Studies of the electrical properties of mixtures dates back to the
early nineteenth century27.
Contributions to the study of mixtures for
the first one hundred years were sparsely distributed.
The primary
motive for the early studies was to correlate dielectric constant with
the microscopic properties of matter.
Molecular structures were
generally modeled by conducting spheres lmswrsed In a dielectric medium.
Avogadro In 1806 touched upon this problem.
proposal of the problem In 1837.
Faraday provided a brief
Mossottl In 1850 published a paper
deriving explicitly the polarizablllty of a mixture consisting of
conducting spheres impregnated In a dielectric medium.
reden.ed independently Mossottl's equation2*.
Clausius in 1879
Lorenz In 1880 derived
a corresponding equation In terms of the index of refraction29. In
approximately ten years prior to this work, Lorentz also derived an
equivalent equation through the introduction of the internal field2*.
The equation derived by Lorenz and Lorentz approached that derived by
Clausius and Mossottl at low frequencies.
This collective relationship
have since been referred to as the Clausius and Mossottl relationship.
Maxwell in 1873 approach the problem of mixtures In the spirit akin
to the previously mentioned authors21.
His derivation is based
predominantly upon current flow through a media with high resistivity
inclusions.
35
Rayleigh In 1892 derived the dielectric constant of a cubical array
of Metallic spheres laaersed within a dielectric aedlua32.
His result
duplicated the Clausius and Mossottl Model.
J. C. Maxwell Garnett in 1904 rederlved the Clausius and Mossottl
relation and used it in his derivation of an effective index of
refraction in his study of glasses with Metallic inclusions33.
He
approached the problea through the analysis of Maxwell's equations for
alternating field within the Metallic doped glasses.
The aMount of publication done after Garnett's work increased
draaatlcally.
Authors have extended the studies to various inclusion
shapes and various aaount of inclusion concentrations.
(Highlights of
land nark works will be provided in the next section.)
The Mixture
relations with arbitrary inclusion shapes were derived eapirlcally by
Wiener in 19123*.
Wagner in 1914 proposed a Mixture relation for low
concentration spherical inclusions slallar to that derived by
Rayleigh33.
Lichtenecker in 1924 derived an eapirlcal relationship for
Mixtures with arbitrary inclusion shapes33.
It should be noted that
all of the previously derived Mixture relations are valid only for
dilute inclusions where the Interactions between neighboring inclusions
are neglected.
Bruggeaan in 1935 derived a two Mixture relation for
spherical particles and disk shaped particles that renains valid for
higher concentrations37.
One relation is in a sysMetrical fora.
second relation is in a non-sysMetrical form.
The
The result of his
derivations is the introduction of a new effective aediua concept.
discussion of this concept will be Made shortly.
Sillars in 1937
A
extended the mixture relationship derived by Wagner for Inclusions of
oriented spheroids1*.
Bottcher In 1945 rederlved Bruggeaan's
symmetrical mixture relation for spheroidal inclusions using
polarizabllity concepts1*.
Polder and Van Santen in 1946 extended
Bottcher's relationship to randomly oriented ellipsoids**.
Kaaiyoshi
in 1950 derived a relationship for arbitrary inclusion shapes*1.
Corkua in 1952 derived a relation for conducting spherical inclusions
where the permittivity of the inclusions is much greater than the
permittivity of the dispersed medium using the Clausius and Mossottl
model*2.
Nlesel in 1952 derived a relationship for ordered
ellipsoids*1.
Landauer in 1952 once again rederlved Bruggeaan's
symmetrical relation**.
Frlcke in 1953 derived a relationship for both
random and ordered ellipsoids*1.
Kubo and Nakamura in 1953 derived a
relationship for arbitrary inclusion shapes**.
Altschuller in 1954
derived a relationship for conducting ellipsoids*7.
Reynolds** and
Pierce** in 1955 derived, independently, empirical relationships for
arbitrary inclusion shapes.
DeLoor in 1956 derived a relationship for
randomly oriented ellipsoids**.
Looyenga in 1965 introduced a new
model in the derivation of a mixture relation for spherical
inclusions*1.
His model is also valid at high concentrations of
inclusions.
The work done between 1967 and 1973 were predominantly
generalizations of previous works from two component to multicomponent
mixtures.
A summary of these results is tabulated in Tinge's 1973
37
It It also around this time that network and percolation concepts
for describing various conduction mechanisms becaae firmly established.
An excellent paper on this subject is by Kirkpatrick in 1973s3.
Another fine publication on this subject is the second half of
Landauer's 1977 publication**.
Percolation and network theories are
predominantly a low frequency phenomena.
While extremely interesting,
these theories are beyond the focus of the present research.
Kraszewskl, et. al. in
1976 Introduced
water suspensions within a solid matrix55.
a different means to model
He first assumed that the
medium has a finite thickness t, and an effective propagation constant
r, shown
in Figure
7.
He then considered the suspension to be
consisting of a sum of infinite number of thin water and dry substance
layers where the thicknesses are much less than the wavelength of the
applied field.
In so doing, he was able to neglect multiple reflections
and subsequently add up the differential thicknesses to equate the
mixture to a medium consisting of distinctly separated constituents; one
of water with a thickness tj and propagation constant Tj and the other
of the solid material with a thickness tj and propagation constant I*;.
He was able to obtain an effective medium equation under the assumptions
that tj-tj+tj and
r,—rj-*-r2.
Although there are many other effective medium models that have
been developed recently, their complexities do not warrant any further
discussions at this stage of the study.
Many of the previously reviewed studies were obtained through
m
Figure 7
Effective aedlua concept used by Kraszevskl, et. al.
Ui
CD
39
indirect source* such as survey articles.
One of the most comprehensive
publications on the subject is written by Van Beek in 1967**.
His
paper provides a full summary of the theoretical aodels up to the tlae
of his publication.
Due to the nuaerous aodels presented,
pursue any detailed derivations of the aodels.
he did not
It is necessary to refer
to the original sources for aore comprehensive derivations.
The next
survey was written by Hasted in 1973 where he devoted an entire chapter
on the subject in his book Aqueous Dielectric57.
His treataent on the
subject is easy to coaprehend due to its textbook format.
However, it
is difficult to gain a historical feel of the development of the
subject.
A view into the history of the subject is provided best by
Landauer in 1977**.
He provides an excellent look into the progress of
the subject since its conception.
1986 and 1988 papers**'**.
Another survey is by Banhegyi in his
His work is based upon the nuaerical
analysis and subsequent coaparison of the established mixture models.
It is not only a good compilation of nuaerous theories but it is also a
good source to quickly determine what type of model is best suited for
certain applications.
Finally, mixtures have been recently studied
through the less classical computer methods of percolation and network
theories.
The work presented by Clec, et al in 1990 is a very extensive
view of the present, active studies*1.
The original study of heterogeneous media is closely related to the
study of polar materials.
It is thus valid to aention a very well
written work provided by Bottcher in his Theory of Electric
Polarization*4.
He also has a very nice section elaborating on a few
4C
of the landmark mixture relations.
4.3
Models suitable for the initial study of cementltlous materials
A review of a selected number of existing models will now be
presented.
The choices were made in order to provide both a basic
understanding of the numerous methods developed in the study of mixtures
and to model cementltlous materials on a fundamental level.
The selection of models that will be analyzed more closely aret the
Rayleigh model, the Bottcher model, the Bruggeaan model, and the
Looyenga model.
The format of the presentation will follow certain
sections of Bottcher's Theory of electric polarization.
4.3.1
A dielectric sphere in a dielectric medium
For those unfamiliar with the mixture theories, a qualitative
review of a fundamental electrostatic problem will first be presented.
A more rigorous derivation have been placed in Appendix B.
This is the
problem on the effect of a dielectric sphere of one dielectric constant
placed within a medium of a different dielectric constant under the
effect of an externally applied homogeneous electric field.
The
constituents of the cement mixture will be assumed to be non-metallic.
The derivations can be described qualitatively as follows.
Figure 8 shows a schematic of a static electric field Eg directed in the
positive z axis applied to a dielectric sphere with dielectric constant
41
Flgura 8
A dlalactrlc sphara
dlffarant dialactrie constant.
iabaddad
in a dlalactrlc
aadiua of
a
42
equal to e2, and radius a, placed within a dielectric medium with
dielectric constant, fj.
Laplace's equation aust be solved for the
potential distribution both inside and outside of the boundaries of the
sphere using the boundary conditions.
The resulting potential in the
two regions are
*l
BtZ
(21)
Recall that an external field E| directed in the positive z axis in a
homogeneous medium will give rise to a potential
• — E0Z
Consider
charge,
' and
(22)
'» as th* potentials due to an apparent surface
then the potential shown in (20) and (21) can be said to be
(24)
where the apparent surface charges will result in effective potentials
in vacuum
43
'•*
<jCl
(25)
,25’
* -
(26)
can be also viewed as a potential caused by an ideal dipole at the
center of an evacuated spherical cavity with radius a with a dipole
■oaent
» « - ^ 2 _ 2 L a JfiLz
*2+2*1
(27)
^
Furtheraore, the field that is associated with the potential
is
(28)
*2+2€l
The total field within the dielectric spheres is then
,29)
Details of this derivation appears in Appendix B.
44
4.3.2
Rayleigh's aodel
Rayleigh's aodel is an extension of the previous exaaple where
instead of having one sphere dispersed in the dielectric medium, there
are a multiple nuaber of spheres dispersed in the dielectric aedlua.
The effect of the aany spheres can be equated to that caused by a single
sphere with a dielectric constant of
where
»
a' 3
2
<
“ •
is the voluae fraction of the saall spheres where a' is the radius of
the effective large sphere and N is the nuaber of inclusions within that
large sphere.(See Figure 53, Appendix C)
This extension is based upon the assuaptlon that the induced
dipoles will not Interact with its neighboring induced dipoles.
the dilute Mixture aodel.
This is
A detailed derivation has been included in
Appendix C.
Equation (30) is the first effective aediua relationship.
aethods have been used to derive this relation.
Various
Synonymous names given
to this relation are Clauslus-Mossotti relation, Lorenz-Lorentz
relation, Wagner relation, Maxwell-Garnett relation, and the aean field
approxiaation.
Extensions of this aodel to other inclusion shapes have
45
been u d i by Slllars for ellipsoids and Fricks for oriented ellipsoids.
4.3.3
Bruggeaan's syaaetrlcal aodel
Rayleigh's aodel is satisfactory only for very dilute aixtures.
Nuaerous scheaes have been developed in expanding it to higher
concentrations aixtures.
One scheae is Bruggeaan's syaaetrlcal aodel.
Consider Figure 9 where the alxture is coaposed of a volume
fraction 6j of dielectric spheres with a dielectric constant of
iaaersed in an "effective" dielectric aedlua with dielectric constant of
C(.
Furthermore, there is another alxture coaposed of a volume fraction
l-6j of dielectric spheres with a dielectric constant of e, iaaersed in
the saae "effective" aedlua with a dielectric constant of £(.
It can be shown, by studying the polarization of each of the
dielectric aaterlals, that
ti_1
3C#
1 2C,+«&
(32)
2
A detailed derivation has been placed in Appendix D.
(32) is Bruggeaan's syaaetric relations.
Synonyaous naaes given
for this aodel are Bottcher's alxture relation, Coherent Potential
approxiaatlon, and T>aatrix approxiaation.
Extensions of this aodel to
other inclusion shapes were aade by Polder and van Santen^, and Hsu(*
for oriented ellipsoids.
Figure 9
Bruggeaan'e syaaetrlcal aodel.
47
4.3.4
Bruggeaan's asyaaetrlcal aodel
For the asyaaetrlc aodel, the pezalttlvlty la given by
(“ ) ^■(1-fij)
*•
(33)
In essence, this relation Is deteralned by consistently using
Rayleigh’s relation for Infinitely dilute aixtures while continuously
adding lnflnlteslaally saall aaount of Inclusions.
A detailed
derivation of this aodel has been Included In Appendix C.
Synonyaous naaes of this aodel are differential effective aedlua
approxlaatlon, self consistent aethods, and integral aethod relations.
Extensions of this aodel to other inclusion shapes have been aade by
Niesel for randoaly oriented needles and flakes**, Meredith and Tobias
for oriented spheroids**, Morabin et. al. for spheroids*7, and Velnberg
for spheroids**.
4.3.5
Looyenga's aodel
A third extension of Rayleigh's aodel for application to higher
concentration aixtures is Looyenga's aodel.
Due to the aatheaatical
coaplexlty of the derivation, only the result is presented.
rigorous solution Is presented in Appendix F.
aodel derived by Looyenga is
The
The effective aedlua
48
This aodsl has been Independently derived by Landau and Liftschitz**.
Extensions of this aodel to other Inclusion shapes have been aade by Lai
and Parshad7*.
4.3.6
The constitutive paraaeter dependency on frequency
We will now develop the appropriate equations for alternating
fields.
The extension of previously stated alxture laws to alternating
fields begins with the assuaptlon that the wavelength of the alternating
field aust be auch greater than the radius of the largest dlaenslon of
the Inclusions.
This is known as the quasi-static criteria.
The
extensions are aade by replacing all dielectric constants with coaplex
permittivities
0* 1
and
1371
The justification for these substitutions has been elegantly developed
by Dukhin.71
The result of applying this substitution to the Rayleigh aodel
where the inclusions are weakly conducting spheres results in the well
known Maxwell-Wagner equations
49
(38)
The Maxvell-Wagner equations predict a dielectric loss phenoaenon when
view over a frequency range.
This effect is aost pronounce when the
inclusions of the alxture are weakly conducting aaterials.
The
extension of the Maxwell-Wagner equations to other inclusion shapes have
been done by Sillars72 and by Fricke73.
The extension of Bruggeaan's syaswtrical relation to alternating
fields have been studied by Bottcher.
The result is
<1~1 +6
3C;
were €
<a- l
(39)
2«;^
represents coaplex peraittivity.
The extension of (39), (52) to oriented ellipsoids have been done by
Hsu1*.
The extension of Bruggeaan's asyasmtrical aodel to alternating
fields has been studied by Hanai7* which can be represented as
The extensions of these equations to other inclusion shapes have been
aade by Boned and Peyrelasse7* for randoaly oriented ellipsoids and by
Boyle77 for parallel oriented ellipsoids.
50
The extension of Looyenga's aodel to alternating fields can be
represented as
The extensions of these equations to oriented ellipsoidal Inclusion
shapes have been aade by Banhegyl78, Boyle79, and Davies8*.
These coaplex equations are finally in the fora such that they will
be used to deteraine the total pore voluae of hardened ceaentitious
pastes.
4.4
Archie's eapirical alxture law
An eapirical alxture foraulation that is capable of determining the
open pore voluae of a porous aedlua was introduced by Archie in 194 281.
The formula originated through the study of electric logging for
petroleum products in sedimentary rocks.
relationship between the DC resistivity
porosity of the rocks.
Archie determined a
of fluid filled rocks and the
His original formula is
Rfj~F^Rw
(42)
where Rg is the DC resistivity of the fluid filled rock, R, is the
resistivity of the fluid, and F is define as the "formation factor".
The formation factor has been found to be related to the porosity of the
rock through
51
/r-d-*
where
9 la the porosity of the rock and a la the "cementation”
<43>
factor.
The porosity la the volume of pore apace divided by the total voluae.
The ceaentatlon factor has been shown to be consistently between the
values of 1.5 and
2.9 for a wide range of sedimentary rocks.
(42) can be transformed into a more consistent formalism of the
previous sections by converting the equation from a resistivity form
into a conductivity form.
The conductivities will be represented by
0-4-
(«5)
Substituting (43), (44), and (45) into (42) results in the more useful
version of Archie's law
In discussing Archies's law, one assumes thatt 1) only
interconnecting pore spaces are contributing to conductivity, and 2)
only the pore fluids conduct electrical currents.
Archie's law, as mentioned previously, was developed from the study
of petroleum exploration.
It is therefore not surprising to find many
52
papers analyzing and applying Archie'a law.
presented by Sen and Chew In 1983**.
A very Interesting work was
The article derives Archie's law
froa the Bruggeaan-Hanal alxture relationship for spherical Inclusions.
The derivation also determined the ceaentatlon factor, a, to be
precisely 1.5.
4.5
Conclusion
Five effective aedlua models have been presentedi Rayleigh’s aodel,
Bruggeaan's symmetrical aodel, Bruggeman's asymmetrical aodel,
Looyenga's aodel, and Archie's empirical law.
It Is accepted that
Rayleigh's aodel is generally applicable only for dilute mixtures.
It
is also well known that the Bruggeaan models and the Looyenga aodel fits
experimental data with varying degree of success.13
CHAPTER 5
Microwave Measurement of Porosity In Ceaentitlous Materialsi Total
Capillary Porosity
5.1
Introduction
A microwave technique has been developed in the previous chapters
to study, non-lnvaslvely and non-destructively, the dielectric
properties of hydrating ceaentitlous materials.
In the present chapter,
this technique will be used to experimentally determine the capillary
porosity of these materials.
The theory behind the microwave
measurements is briefly reviewed.
The relationship between microwave
constitutive parameters and capillary porosity will then be established
and applied to ceaentitlous materials.
Finally, a discussion on the
merits of microwave poroslaetry will be presented.
5.2
Theory of microwave measurements
The constitutive parameters of high loss materials can be
determined at microwave frequencies by using the microwave surface
spectrometer.
This is described fully in Chapter 3.
In this method the
unknown material is subjected to an incident signal from the microwave
source and surface reflections are measured.
The reflection
characteristics lead to the experimental determination of the
constitutive parameters, conductivity and dielectric constant.
The
calculations assume that the sample has enough loss such that the
incident signal does not penetrate to the far end of the specimen and
53
54
thus the staple appears to be electrically infinite.
5.3
Measurement of total capillary porosity
By definition, total capillary porosity is the ratio of the volume
of the capillary pores to the total voluae.
In this section the
relationship between total capillary porosity and microwave constitutive
parameters are discussed.
The basic thesis is based upon the
delineation of hydrating cement into two components, capillary water and
remaining material.
The remaining material is a conglomeration of
unhydrated and hydrated cement, aggregates, chemically combined water,
and gel water.
The distinction is based upon the fact that the
electromagnetic field excites dipole rotation in the capillary water
resulting in a first order effect on the observed reflection.
This is
manifested in terms of high conductivity and dielectric constant.
remaining material has only a second order effect.
The
Therefore, the
observations are dominated by the quantity of capillary water.
Two
component mixtures with known porosities have been selected to model
hydrating cementltlous materials.
The primary criteria in the selection
of these model mixtures is that they are water mixed with low microwave
conductivity solids.
In order to cover the broadest range of porosities
possible in a hydrating cementitious material, it was necessary to use
different types of model mixtures such as water and sand, water and
glass beads, and fresh or cured cement pastes of known porosities.
relationship between microwave parameters and porosities was then
determined from microwave measurements of these models.
It is
The
55
necessary to emphasize at this point that although thare presently
exists other Methods to determine capillary porosity, the Microwave
technique is the only non-destructive and non-invasive Method.
Model Mixtures having porosities below 0.3 were type I Portland
ceaent pastes with w/c-0.5 cured for 1, 7, and 28 days.
The porosity is
"known" froM combining the results of the ignition loss test, which
determines the degree of hydration(AS1M number C-308), and the Power13rowyard model on the properties of hydrating cement14.
The Power-
Browyard aodel provides a relationship between capillary porosity,
water-to-ceaent ratio, and the degree of hydration.
The capillary porosity in terms of voluae fraction is
w
-0 .36 (1.477) M
♦ - ----
(47)
0.317 ♦ —
c
The degree of hydration, a, is determined from
• ■4.1667
(48)
*1010
where w ^ is the constant weight of the sample after being heated in a
105*C oven and Wjm is the corresponding weight at 1010*C.
Model Mixtures that have porosities between 0.3 and 0.45 were
either Mixtures of water and sand or water and glass beads.
This was
accomplished by filling the specimen holder with water, then packing in
the solid material.
The porosity was varied by using different particle
56
size*, varying from 75 to 1100 alcrons.
The porosity was determined by
weight loss aeasureaents when the speclaen was dried at 105*C.
Model mixtures that have porosities between 0.4 and 0.7 were fresh
cement pastes.
The porosity of the fresh ceaent was obtained by using
the water-to-ceaent weight ratio and the assuaption that negligible
hydration has taken place.
The water-to-ceaent weight ratio(wt/c,) to
water-to-ceaent voluae ratio (wf/cT) conversion is8*
»» ( cat3).
specific volume of H2Q
cv an3
cm specific volume of cement
gZ0)
gm
(49)
TABLE II summarizes known capillary porosities and measured constitutive
paraaeters of the aodel mixtures.
Figure 10 shows a graph of known
capillary porosity versus conductivity of these aodel mixtures.
data points are represented by the solid circles.
The
The solid line
represents a best fit curve using a second order polynomial.
The
aicrowave aeasureaents were done at 10GHz where the response to ion
content is auch less than dipole relaxation88. This point will be
further elaborated in a later section.
Figure 10 also shows the application of Archie's law87,88 using
different formation factors, a.
Archie's law provides an empirical
relationship between the measured conductivity and the capillary
porosity.
It relates the observed conductivity of a fluid filled porous
aediua, c, with the conductivity of the fluid, o}, and the porosity of
that aediua, 0,
57
TABLE II
Model mixtures end measured constitutive parameters.
Model
Known
Conductivity
Porosity
Dielectric
Constant
(S/m)
0.12
OPC w/c-0.5
(cured 28 days)
OPC w/c-0.5
0.20
(cured 14 days)
0.26
OPC w/c-0.5
(cured 7 days)
OPC w/c-0.5
0.30
(cured 1 day)
0.35
Glass beads
0.35
Sand
OPC w/c-.18
0.4
(2.2% superplasticlzer)
Sand(75-100mlcron)
0.45
0.48
OPC w/c-.3
White cement w/c-0.5 0.62
0.7
OPC w/c-1.0
Tap water
1.0
2.39
10.2
3.17
11.3
3.39
12.2
4.98
15.9
4.48
4.1
5.63
25.4
23.8
19.5
6.5
7.7
9.8
12.6
19.1
25.5
24.3
30.0
35.8
50.8
58
1.00
capillary
0.40
0.20
porosity
_ _ m = 1.50
m = 1.35
0.80
Known
porosity
»»•« K n o w n
m = 1.20
0.00
0.00
5.00
10.00
15.00
20.00
Conductivity ( S / m ) at 10GHz
Figure It
alxtures.
Measured conductivity versus known porosity of water-solid
Application of Archie's law to data.
59
(50)
°o
where
■ is the formation factor determined empirically.
It can be seen that the total capillary porosity versus
conductivity is encompassed by Archie’s law with a formation factor
varying between 1.2 and 1.5.
It is very interesting to note the close
fit of Archie's law to the data when considering that this law was
originally observed for DC conductivity aeasureaents.
A more fundamental relationship between the constitutive
parameters and the capillary porosity would be one that can be derived
from first principles.
Effective aediua theories appear to provide the
promising theoretical link.
Four fundamental effective aediua
relationships have been selected.
These are* 1) Rayleigh’s
relationship, 2) Bruggeaan's symmetrical relationship, 3) Bruggeaan's
asymmetrical relationship, and 4) Looyenga's relationship.
The premise of all of these relationships is based upon the
assumption that the mixture is coaposed of spherical inclusions of one
material dispersed homogeneously in another aediua.
of these theories is presented in Chapter 4.
relationship is
An indepth review
In summary, Rayleigh's
Bruggeaan's syaaetrlcal relationship is
3«*
Bruggeaan's asyMetrlcal relationship is
and Looyenga's relationship is
where
2*^3
61
€,’ Is th« effective complex permittivity
6,
are the respective complex permittivities
E' is the effective dielectric constant
E. , are the respective dielectric constants
*f*
E(* is the effective dielectric loss
E} 2
sre the respective dielectric losses
6j 2 are the respective volume fractions
Dielectric loss is related to conductivity via
O m1
Under the present circumstances, 6j
&
(58)
«^ual to ♦ .
Figure 11 is identical to Figure
10 except for the addition of the
porosity prediction of the four effective medium theories applied to the
dielectric measurements and, for the sake of clarity, the omission of
Archie's law.
It can be seen that Bmggeman's asymmetric theory
provides the closest fit to the data.
It is interesting to note also
that Bruggeman's asymmetric relation has been used to derive
low frequency form of Archie's law*9.
the DC or
Itappears that this
relationship can be used to predict the porosity of any two component
cement like mixtures.
Figure 12 shows the graph of known porosity versus the dielectric
constant of the model mixtures.
Since Archie's law is a conductivity
relationship, it has been omitted.
Note that the porosity versus the
dielectric constant of the model mixtures appears to be linearly related
and can be expressed by a best fit curve of
62
• • • • • Known
1.00 n
_
_
_
p o r o s ity
C a l c u l a t e d from
Calculated from
Calculated from
Calculated from
Rayleigh e q u a t i o n
B ruggem an sym m etric equatioj
B r u g g e m a n a s y m m e t r i c eqi
>n
Lo o y en g o e q u a t i o n
Porosity
0.80 Looyenga
0.60 Bruggeman ^
Known
symmetry
/
0.40 -
s
/
/
^Bruggeman
asym m em
: Rayleigh
0.20
-
0.00 i i i r i i i i i | i i i i i i i i i '|*i i i i i i i i-t“| i i i i i i i i i |
0.00
5.00
10.00
15.00
20.00
Conductivity ( S / m ) at 10GHz
Figure 11 Application of effective aediua theories to the conductivity
date presented in Figure 10.
m
1.00
> M e o s u r e d porosity
m
. _
C ol c u lo te d
Calculated
Calculated
Calculated
f r o m Royleigh e q u a t i o n
from B ruggem an symmetric
from B ruggem an asy m m e tri
from Looyenga equation /
quation
equation
Known
Porosity
0.80
Looyerfga
0.60
0.40
Rayleigh
0.20
0.00
0.00
20.00
60.00
40.00
Dielectric con sta n t at 10GHz
n ^ i r e 12
constant.
Application of
effective aediua theories using
dielectric
64
(59)
4-0.021«c-0.034
where E( is the aeasured effective dielectric constant.
A fascinating aspect of this relationship between capillary
porosity and the
dielectric constant is that an alaost identical
relationship can
be derivedby a parallel plate capacitor analog,
Figure 13.
This figure shows a parallel plate capacitor,
lnhoaogeneously filled with two different perfect dielectric materials
having dielectric constants of
Aj as shown.
and E, and corresponding areas Aj
The position of the
and
inner dielectric rod is arbitrary.
The distance between the parallel plates is d.
The capacitance of the
structure is
(60)
This leads to an effective dielectric constant for the composite filling
of
(61)
where
A-A^Aj
(62)
65
Ai
d
Pigure 13
mixture*.
Parallel capacitor plata aodel of two component hoaogeneous
66
Recall that poroaity la define aa
4, - —
Tl
V
■—
A
(«3)
where Vj correaponda to the volume the encloaed dielectric rod and V is
the total volume of the structure.
Upon solving (61) for Aj/A and
substituting with (63), it leads to an analog relationship between
porosity and dielectric constant of the material
h—
•
(64)
1 «r«i
where E( is the aeasured alcrowave dielectric constant and Ej and E- are
the corresponding dielectric constants of the components of the
composite.
In a mixture of water and sand, the dielectric constants are
Ej-50 and E.-3.7, respectively.
Substituting theses values into the
above equation leads to a linear relationship between porosity and
dielectric constant
^-0.02164.-0.080
(65)
Note that this linear relationship is independent of physical size and
depends only upon material parameters.
Upon comparing the analog result
with the empirical relationship, (59), it can be seen that the slopes
are very close and the deviation in the intercept may be within
67
experlaental errors.
This procedure is slailar to the one used in
iapedance spectroscopy In which a circuit equivalent represents a real
aaterlal.
However, in the present case, the equations relates real
properties of Materials and not those of equivalent circuits.
This section has established the feasibility of using Microwave
constitutive parameters to determine the total capillary porosity.
It
was shown that total capillary porosity is related to Microwave
parameters in three ways.
The porosity-conductlvlty relationship is
described enplrically by Archie's law and fundamentally by Bruggeman's
asynmetrlc model.
The porosity-dielectric constant relationship is
described by a parallel plate capacitor analog.
The remainder of this
study will use the porosity-conductlvlty relationship.
5.4
Application to ceaentitlous Materials
The application of Microwave conductivity aeasureaents to determine
the porosity of ceaentitlous Materials depends on the assumption that
the measured conductivity is not influenced by the ionic content of pore
fluids.
It was previously stated that at 10GHz, the Microwave response
does not depend upon ionic contents, and now, support of this assuaption
will be presented.
When water is Mixed with ceaent, salts are dissolved
resulting in an ion rich aqueous solution that increases ion
concentration over tiae.
TABLE III shows the variation of the
constitutive parameters at two frequencies and various salt
concentrations.*
One of the advantages of using Microwave
68
TABLE III
Dielectric properties of aqueous ion filled solutions.
conductivity
S/a
i£_ugjz
water (25C)
sodlua chloride
0.1 aolal
0.3 aolal
0.5 aolal
0.7 aolal
as_22to
water(25C)
sodlua chloride
0.1 aolal
0.3 aolal
0.5 aolal
dielectric <
16.5
55.0
16.8
17.5
17.8
18.4
54.0
52.0
51.0
50.0
2.0
76.7
3.0
5.0
7.0
75.5
69.3
67.0
Experlaental results of 10GHz microwave aeasureaents of extracted pore
solutions froa type I OPC paste after 25 hours of curing*
0.5 aolal
18.0
55.0
69
frequencies is the dlainutlve effect of ion concentration on the
aeasured constitutive paraaeters as frequency increases.
Note that at
10GHz and at 0.5 aolal concentration, the difference in conductivity
froa water is 8% and the difference in dielectric constant is 7%.
results are within experlaental errors for our aeasureaents.
These
On the
other hand, at 3 GHz, the difference in conductivity is 250% and the
difference in peraittlvlty is 12.6% for siailar ion concentrations.
These observations support the above assuaption.
Because the tabulated values are based upon single ion solutions
while actual pore fluid contains various aixtures of ions, it was
necessary to verify experlaentally the negligible effects of ions in the
pore solutions.
The ion concentrations of pore fluids extracted by
aeans of a die press was aeasured along with the aicrowave paraaeters.
Ion concentrations were aeasured at different instances during the first
25 hours into hydration and shown to have a aaxiaua concentration of
approxiaately 0.5 aolal for a type I ceaent paste with a w/c-0.4 at the
end of 25 hours.
These solutions are coaposed predoainately of sodlua
ions and potassiua ions.
The aicrowave paraaeters of the extracted
fluids were then aeasured and shown to have negligible variations in
coaparison to tap water.
This further supports the assuaption that
aicrowave paraaeters can be used as a direct indicator of the capillary
porosity in a hydrating speciaen.
70
5.5
Coaparlson of aicrowave porosis* try with aercury Intrusion
porosiastry(HIP)
Microwave characterization of hydrating ceaentitlous aaterlals is
especially valuable because it is both non-destructive and non-invasive.
This aethod can be applied in-situ and need not be restricted to the
laboratory.
To further validate the aicrowave results we coapare the
porosity deterained using aicrowaves with that deterained froa HIP.
The
aicrowave porosity was deterained froa a neat type I OPC paste with a
water-to-ceaent ratio of w/c-0.5.
Three speclaens were cast in x-band
waveguides and tested iaaedlately after casting and, at 1, 7, and 28
days.
Figure 14 shows experlaental aicrowave and theoretical porosities
versus the degree of hydration.
The solid line is the theoretical
porosity deteralne froa (47) calculated for w/c-0.5.
Because the MIP
data for w/c-0.5 as a function of degree of hydration was not available,
available data on speclaens with w/c-0.4 and 0.6 are presented91'*.
5.6
Discussion and conclusion
The aicrowave surface spectroaeter presented in this paper provides
a siaple, non-invasive, and in-sltu Beans to aeasure total capillary
porosity of water filled porous aedla.
By aeasurlng the aicrowave
constitutive paraaeters, the capillary porosity can be calculated using
any of the following proceduresi a high frequency analog of the
eapirical Archie's law, a first principle derived Bruggeaan's
relationship, or a dielectric filled parallel plate capacitor aodel.
The use of the spectroaeter to aeasure total capillary porosity in
71
0.70
Theoretical(w/c = 0.50)
••••• Microwave porosilty(w/c = 0.50)
a a a a a MIP porosity(w/c = 0.40)
***** MIP porosity(w/c = 0.60
n
Porosity
(cm 3/
| 0.50
0.30
0.10
0.00
0.20I
0.40
0.60
0.80
1.00
Degree of hydration
Figure 14 Microwave porosity and thaorstlcal porosity versus the degree
of hydration of w/c-3.5.
72
hydrating ceaentitlous aaterial is shown to be correct even though the
pore fluid contains numerous Ionic species.
This is the laaedlate
consequence of proper selection of the aeasurlng frequency where the
aeasured constitutive paraaeters are due to the first order effect of
dipole relaxation of water aolecules.
The optlaua frequency is at 24
GHz where water aolecules have aaxlaua dipole rotation and thus exhibit
aaxiaua aicrowave conductivity.
However, since the dielectric
loss(conductivity) behavior has a fairly broad peak52, 10GHz was
selected as the aeasureaent frequency.
At this frequency, aggregate
size effects are ainiaized and ease of workability during placing of the
speciaens is increased.
Prior work’* presented aicrowave conductivity and dielectric
constant as a function of tiae for different water-to-ceaent ratios and
different types of ceaents.
porosity.
The saae data can now be used to track
The result of such a study is suaaarlzed in Figure 15 where
aicrowave porosity of 5 different aaterials are plotted as a function of
tiae of hydration.
This graph clearly deaonstrates the value of the
aicrowave aeasureaents since it provides data not obtainable by any
other aethod.
Ignition loss and aercury poroslaetry aethods introduce
error bars in the tiae aeasureaents and, aore iaportantly, alter
structure.
Interpretation of the results are Halted since the degree
of hydration are typically not unifora in tiae.
Nevertheless, the
typical trend of increasing water-to-ceaent ratio being scaled by
increasing porosity is evident.
73
1.00 1
XX4XX OPC I w/c = 0.3
ooooo OPC 1 w/c=0.4
0.80 -
••••• C3S w/c=0.3
♦•♦•*C3S mortar w/c=0.3, s/c=2.5
a a a a a Wlilie cement w/c=0.3
03
ou
o 0.60
O °o0 o
04
2oo
0)
>
CO
« - 0 .° °
• ° _o o oo
x xA*
I 0.40
o
<*>
* x^
x
♦ *
* *
0.20
-
•
•
x
A*Ax A<a
*
* *
*
♦ *
0.00
* A< A
x
*
*
*
{ i i i i i i i i i | i i i it t i i » | i i i i i i i i > | > I i i i i i i i | i) r ri i > i t |
10
15
20
25
Time - hours
Figure 15 Microwave porosity asssursd ss s function of tlas of hydration
for water-to-ceaent ratios and caasnt types.
74
Exploratory studio describe the behavior of constitutive
paraaeters as a function of frequency and tiae of hydration.
Figure 16
shows the conductivity versus frequency and tiae of hydration for type I
OPC w/c-0.44.
Note that significant conductivity variations occur not
only in tiae but in frequency as well.
Further endeavors of these
studies aight provide Insight into the relationships between the
constitutive paraaeters, frequency, degree of hydration, and structure.
There exists nuaerous electromagnetic techniques available aside
froa the aicrowave spectroaeter.
At low frequencies, in the KHz to MHz
range, impedance spectrometry have been widely used,5',<'97.
the results are dominated by response to ion content.
However,
A similar
difficulty appears at intermediate frequencies, in the MHz to low GHz
range91.
It is very difficult to separate ionic effects froa pure
dipole relaxation in low frequency range, while at higher GHz
frequencies, the response to dipole relaxation is of first order and
thus represents solely the total capillary porosity.
(S/m)
Conductivity
Figure IS Microwave conductivity versus frequency end tiae of hydration
for OPC w/c-0.44.
CHAPTER 6
Microwave Measurement of Porosity In Ceaentitlous Materials! Col and
Closed Capillary Poroalty
6.1
Introduction
Pora charactarlatlcs In ceaentitlous materials are known to
dominate many of the material properties ranging from mechanical
strength to durability**'1N. Microwave measurements provide a means
to study pore characteristics under in-situ, non-destructive, and noninvasive conditions.
They also lead to a more accurate and precise
means to obtain Insights into the behavior of hydrating cementltlous
material.
The previous chapters established the theoretical basis and
the methods needed to measure total capillary porosity using the
microwave spectrometer.
This chapter will Incorporate that knowledge to
measure gel porosity and closed capillary porosity.
The basis of microwave measurements Is that the electromagnetic
fields interacts differently with capillary water and the remaining
constitutive components of the material.
Furthermore, the non-Invasive
characteristic of the microwave technique is highly desired since It
avoids the removal of the pore content which typically alter structure
and hence the performance of the material.
In the following, the microwave poroslmetry technique will be
summarized.
The theories used to aeasure gel porosity and structurally
dependent capillary pore porosity will be developed next.
Experimental
procedures and discussions of the results will concluded this chapter.
76
77
6.2
Theory and definitions
6.2.1
Microwave M M u r w m u
The constitutive parameters of high loss aatarlala can ba
datanlnad at alcrowave fraquanclaa by using tha alcrowave spactroaatar
previously daacrlbad.
In this aathod tha unknown aatarlal Is subjected
to an Incident signal froa tha alcrowava source and surface reflections
are aeasured.
Tha reflection characteristics lead to tha experimental
determination of the constitutive parameters, conductivity and
dielectric constant.
Tha calculations assuae that tha saaple has enough
loss such that the incident signal does not penetrate to the far end of
the specimen and thus the saaple appears to ba electrically infinite.
6.2.2
Total capillary porosity
It has bean established that the microwave spectroaeter can be used
to measure total capillary porosity.
To suaaarlze, capillary water at
alcrowave frequencies have a first order effect on the alcrowave
constitutive parameters of the material.
This fact leads to the
development of a relationship between total capillary porosity and
alcrowave constitutive parameters.
One such relationship is Archie's
law which relates the observed conductivity of a fluid filled porous
aediua with the conductivity of the fluid and the porosity of the medium
where
78
■ la tha empirically determined formation factor
a la tha conductivity of tha alxtura
o4 la tha conductivity of tha high loaa component, water.
Tha formation factor hava baan shown to ba 1.35 In tha raglon of e>0.35
and 1.20 In tha raglon of •< 0.35.
6.2.3
Gal porosity
In contraat to capillary water, gal water doaa not appear to
axhlblt high microwave conductlvltlaa.
This la due to tha behavior of
gal watar where tha rotational freedom of watar aoleculea are lapeded by
tha aaall size of tha pores.
This fundamental difference provides an
opportunity to easily determine tha gal porosity by ccabining a
alcrowave aaaauraaant of total capillary porosity and a weight loss
aeasureaent of evaporable watar porosity; where evaporable watar
porosity describes both gal and capillary porosity by having tha saaa
boiling point of 100*C.
Gal porosity Is thus tha difference between tha
total capillary and evaporable watar porosity.
6.2.4
Closed capillary porosity
This section presents a method to aeasure closed capillary
porosity.
By definition, closed pores contains capillary fluids which
are Inaccessible from the surface.
In contrast, accessible pores are
regions where pore fluids can access the surface of the specimens at one
or more points.
The development of this technique Is motivated by the
desire to better classify different capillary structures.
Furthermore,
79
this method provides an Insight into the accuracy of traditional
poroslaatry methods1*1,1*2 where closed or isolated pores are
inherently Ignored.
It is emphasized here that alcrowave measurement,
by virtue of the non-invasive technique, are independent of where the
capillary water resides.
However, by combining this structurally
Independent property of alcrowave measurements with proper specimen
preparation, structural properties can be extracted.
6.3
Experimental procedure
6.3.1
Determination of gel porosity
Four type I OPC pastes were cast into x-band waveguides.
Two
specimens have water-to-cement ratio of 0.3, two specimens have waterto-ceaent ratio of 0.5.
Two specimens, one from each water-to-ceaent
ratio were tested after 1 day of curing.
were tested after 7 days.
The remaining two specimens
On the test day the total capillary porosity
is determined from the alcrowave conductivity measurements.
specimen is then weighed.
The
This weight is the sum of the reacted and
unreacted cement, the total capillary water, and the gel water.
The specimen is next heated at 105*C to remove all of the
evaporable water.
The resulting weight loss difference is used to
determine the evaporable water porosity.
By definition, gel porosity is
the difference between total capillary and evaporable water porosity.
6.3.2
Determination of closed capillary porosity
Closed capillary porosity is determined by combining the alcrowave
80
surface spectrometer measurement and tha effectively elimination of the
accessible capillary pores.
Recall that the origin of alcrowave
capillary porosity measurements is directly due to the high microwave
constitutive parameters of water at alcrowave frequencies.
The removal
of the pore fluids In the accessible pores will result in a material
having only closed capillary pores filled with fluids.
Upon microwave
characterization, the capillary porosity thus determined will be the
closed capillary porosity.
The effective elimination of the accessible
capillary pore fluids can be accomplished by placing the specimen under
vacuum.
Microwave x-band waveguides were used to caste Type I OPC pastes
with water-to-cement ratios of 0.3 and 0.5.
The alcrowave conductivity
were measured at 1 day and 7 days into hydration.
specimens were weighed and evacuated for 7.5 hours.
After measurement the
The evacuation time
was selected by considering the need to purge all accessible water and
to minimize the degree of hydrating during evacuation period.
In other
words, a more ideal procedure will be to evacuate the specimens until
constant weight to ensure complete accessible pore fluid removal.
However, it must be noted that a primary constraint in the available
time for evacuation is present due to the continuous hydration process
taking place during evacuation.
After evacuation, the microwave conductivity of the specimens were
measured again.
The subsequent porosity determined from the dielectric
properties-poroslty equations will be the "closed" capillary porosity.
81
6.4
Results and discussion
6.4.1
Gel porosity asasursaents
The results of these tests are supported by the theories based upon
the behavior of total capillary porosity and gel porosity as a function
of the degree of hydration and the water-to-ceaent ratio1*3.
Recall
that as hydration proceeds, total capillary and total water porosity
decreases while gel porosity increases.
Further, at a given degree of
hydration, both total capillary porosity and total water porosity
Increases as water-to-ceaent ratio increases while gel porosity is
Independent of water-to-ceaent ratio.
The trends of decreasing total capillary porosity and Increasing
gel porosity as the degree of hydration increases for water-to-ceaent
ratios of 0.3 and 0.5 are shown in Figure 17 and Figure 18.
The trends
of Increasing total capillary porosity as the water-to-ceaent ratio
increases for the 1 day and 7 day cured speciaens are shown in Figure 19
and Figure 20, respectively.
Note how the evaporable porosity and total
capillary porosity increases as the water-to-ceaent ratio increases but
the gel porosity reaains relatively constant.
The slight increase alght
possibly be attributed to the slightly higher hydration rate for higher
water-to-ceaent ratio speciaens.
6.4.2
Closed capillary pore aeasureaents
The results of these experiments are presented in TABLE IV.
It
shows the day of testing, the degree of hydration, the water-to-ceaent
ratio, the aeasured total capillary porosity, and the aeasured closed
82
0.60 -|
x xx x x Evaporable porosity
QfiOQP Capillary porosity
•14AP Gel porosity
□□□□□ Gel porosity from
Power-Brownyard
model
Porosity
0.40 -
0.20
-
0.00 #
0
2
4
6
Time (days)
FlflMr* 17
Porosities versus the days of curing for w/c-0.3.
8
83
Evaporable porosity
QflOQ^ Capillary porosity
•
Gel porosity
0.60
Porosity
0.40 -
— o
0.20
0.00
-
+
0
2
4
6
Time (days)
Figure 18
Porosity versus the days of curing for v/c-0.5.
8
84
<**»* Evaporable porosity
Q£OQp Capillary porosity
•
Gel porosity
0 .6 0 -i
Porosity
0 .4 0 -
0.20
-
0.00
0.2
0 .3
0 .4
0 .5
0.6
w /C
Figure 19
speciaens.
Porosity vsrsus ths water-to-ceaent rstlo for 1 day cured
85
0.00
*** * * Evaporable porosity
0£O££> Capillary porosity
•
Gel porosity
-]
Porosity
0.40 -
0.20
-
0.00
0.2
0 .3
0 .4
0 .5
0.6
w /c
Figure 2t Porosity vsrsus ths water-to-ceaent ratio for tha 7 day cured
speciaens.
86
capillary porosity.
Expactad bahavlors of total capillary porosity as a
function hydration tlaa and tha water-to-ceaent ratio can ba raadlly
saan.
Note that total capillary porosity decraasas as tha hydration
lncraasas.
Further, total capillary porosity lncraasas as tha water-to-
ceaant ratio Increases.
however, Is not obvious.
Tha behavior of tha closed capillary pores,
Tha closed capillary porosity of tha spaclaan
with water-to-ceaent ratio of 8.3 Increases as the hydration Increases.
This can be attributed to the fact that as hydration proceeds, the
connectivity of the pores will subsequently decrease resulting In aore
closed pores.
However, this was not observed for speciaens with water-
to-ceaent ratio of 0.5 where the opposite was observed.
A possible
resolution of this seealngly contradicting observation night be obtained
by considering the effect of the different water-to-ceaent ratio and the
structural changes during hydration.
Consider what happens to the
accessible capillary porosity as hydration proceeds.
Accessible
capillary porosity Is the difference between the total capillary
porosity and the closed capillary porosity.
Low water-to-ceaent ratio
speciaens showed a significant decrease In the accessible capillary
porosity as a function of hydration.
Whereas, the high water-to-cenent
ratio spaclaens show roughly the saae accessible capillary porosity.
Due to the higher density of low water-to-ceaent ratio speciaens, the
accessible capillary porosity speciaens Is expected to decrease as
hydration proceeds.
On the other hand, because the speciaens were only
processed for 7.5 hours under vacuua and not evacuated to constant
weight, the higher water-to-ceaent ratio aeasureaents are not truly
87
TABLE IV
Results tabulated In t a n a of day of curing, w/c, and various
poroaltlas.
cloud
cipilliry
poroilty
icetnllli
poroilty
1.(2
•
• 42
1.3
• 24
1.17
«.1P
1.3
•.17
a.14
♦ 13
15
I.(I
•
• it
1
1.5
1.37
e.25
•.12
7
15
#.27
1.14
•.13
Dir
t/c
frtik
1.3
1
7
frill
totil
cipilliry
poroilty
Indicative of closed capillary porosities since the time It takes under
evacuation seems to require significantly longer evacuation.
Furthermore, because the connectivity of higher weter-to-cement ratio
speciaens are necessarily higher, there exists high portions of
accessible capillary pores, hence the accessible pores reaalns the saae
Irrespective of the tlae of evacuation.
Further Investigation will be
necessary to verify these hypotheses.
The next phase of this research would be to coapare these results
with KIP measurements.
accessible porosity.
Recall that the porosity aeasured by HIP Is the
Microwave techniques can then be used to check
this measurement. The procedure would be to first characterize the total
88
capillary porosity.
aeasured.
Naxt, tha closad capillary porosity will ba
Tha dlffaranca between thasa two porositlas should ba tha
accasslbla porosity.
6.5
Conclusion
Tha rasults froa thasa first ordar axparlaants show that It Is
posslbla charactarlza dlffarant capillary pora structures by coabining
alcrowave poroslaetry with dlffarant speclaen praparatlons.
Tha
techniques also hints at tha possibility of studying ln-situ tha
evolution of capillary pores during all stages of hydration.
It should ba esphaslzed hare that there exists a large aaount of
literature on tha Investigation of pora structure developeaent and
associated properties.
Taylor provides a nice suassary on available
techniques to study pore behaviors.1*2 Selected bibliographies can also
be found there.
In our exploratory axparlaants, we hypothesized that
the alcrowave exhibits a first order effect only with capillary water
and not gel water or other types of water such as Interfacial water.
Further Investigation is necessary to verify these ideas.
CHAPTER 7
Microwave Thermal Processing of Camant Hortars
7.1
Introduction
Procaaalng methods which Improve tha mechanical and mlcrostructural
properties of hydrating cementltlous materials are of ever present
Interest.
This chapter presents the findings of our program on using
microwave energy to thermally process hydrating cementltlous material
which have previously shown to Improve the compressive strength.
motivations drive this study.
The first Is to explore the extent of
compressive strength Improvements.
effects on microstructure.
Three
The second Is to consider the
The last Is to establish the origin of the
Improvements In terms of the heat source and the specimen heating
profile.
The chapter has been delineated Into three sections.
A review of
recent studies on applying microwave energy to thermally process
cementltlous materials will be summarized.
It will be followed by
detailed descriptions of the experimental procedures from mixing,
casting, and curing to the different tests applied to processed
specimen.
In the final section the results of the experiment will be
discussed.
7.2
Thermal processing methods
A survey In the literature on the thermal processing of
cementltlous materials reveals the following different approaches for
89
99
applying haat and prassurat 1) aicrowave heating, 2) tharaal shock, 3)
hot conerata, and 4) staaa curing at both low and high praasura.
Tha aost significant variables assoclatad with tha application of
haat and pressure arei tha tlae into hydration whan tha haat is applied,
tha duration of tha haating, tha target taaperature, tha rata of haating
and cooling, and tha pressure applied to tha specimen during processing.
Microwave heating
Microwave tharaal processing of ceaentitious materials prior to
1987 did not show any lsproveaent in the long tera properties of the
materials1**.
An examination of the experimental conditions showed
that the poor results were probably due to applying too auch power and
thereby generating internal watar vapor and resulting deleterious
structure.
In 1987 and 1994, Xuequan, et. al.1*5,1** presented a
comparison between alcrowave heating, low pressure steaa curing, and
rooa temperature curing.
After intermittently applying microwave energy
to cement mortars with w/c-®.44 and s/c-2.5, an over 40% Increase in the
3 day strength and a 2-5% Increase in the 28 day strength in comparison
with rooa teaperature cured saaples was reported.
In comparison to low
pressure steaa curing, they aaintalned that alcrowave heating
signiflcantlly decreased the processing time without the typical
strength losses observed at 28 days.
Christo1*7 performed an extensive study using alcrowave heating to
process fresh ceaent sorters.
Effects of alcrowave heating on flexural
and compressive strengths, hydration products, and pore structures were
91
presented.
The results showed an increase in the early age strength of
cement mortar with slight improvment in 28 day strength.
These
improvements were attributed to decreases in water content due to
evaporation, the development of smaller porosity, and the production of
different quantities of hydration products.
After one day of curing, he
obtained a maximum compressive strength Increase of approximately 28%.
Hutchison, et. al.iw extended this study to show that the primary
effect of heat treatment with the corresponding strength improvment Is
due to the acceleration of degree of hydration during the early periods
of curing. He also showed that there were no detrimental long term
effects.
Thermal Shock
The second method of heat treatment on hydrating cementltlous
material Is thermal shock.
In this method, the specimen is subjected to
a high rate of temperature increase during the early hydration period
and maintained at this elevated temperature until testing.
Alexanderson1** performed the thermal shock method to maximum
temperatures between 30*C and 100*C, at various intervals after nixing.
He concluded from the 28 day tests that a delay of between 1 and 4 hours
before shocking will Increase the loss in compression strength, where as
longer delays resulted In less strength loss.
Hot Concrete
The third method of heat treatment to improve the physical
92
properties of ceaentltloue materiel is the preheating of the Individual
Ingredients.
This Is known as hot concrete.
Lapinas11* showed that
when the constituents were preheated to 79*C via steam, there were
significant lnprovements In early strength.
The study consisted of
preheating the constituents prior to mixing and casting, and
subsequently compressive strength tested at 2, 4, and 6 hours and at 28
days into hydration.
The study showed that after 6 hours, the test
specimen obtained 50% of the 28-day strength of the control specimen,
but at 28 days, there was a 30% loss In comparison to the control.
Berger111 studied the effect of preheating on the development of
microstructure In cement pastes.
He showed that Increasing temperature
results In an increase In the number of Ca(OH)2 nuclei, a decrease In
nucleation time, and a decrease in the growth rate of Individual
crystals.
In addition, the size of the CH crystals decreased with
increasing temperature.
Because Ca(OH)2 crystals are considered the
weaker products of hydration, decreasing the growth rate of the
individual crystals suggests that the resulting product will have
smaller crystal size leading to a denser and, hence, a stronger material
even though the number of the Ca(OH)2 nuclei Increases.
However, as the
material ages, the larger number of Ca(OH)2 crystals will ultimately
lead to more crystals and hence a weaker material.
Kjellsen112,113 studied the effect of preheating on the
development of pore structure.
After specimens were mixed at prescribed
temperatures, pore structure was studied by mercury intrusion
poroslmetry and backscattered electron imaging.
This study showed that
93
the higher the curing temperature, the greater the total porosity due to
an Increase In larger pores.
The development of larger pores might also
explain why the long term effects of elevated temperature on strength Is
deleterious.
Low Pressure Heat Treatment
This class of thermal processing uses heat generated by either
steaa or hot water bath.
exceed 100*C.
The temperature of the specimens does not
Although the use of low pressure heat to accelerate the
curing of cementltlous materials can be traced back to the late
nineteenth century, only recent works will be reviewed.
Ravina115 performed a study of compressive strength as a function
of temperature, with specimens subjected to temperatures ranging from
15*C to 45*C.
Cooling or heating was Initiated Immediately after
casting, and was maintained for 24 hours.
After removing the specimen
from the mold, they were cured at 20*C and 65% relative humidity until
testing.
This study showed that optimum strength occurs when the
specimen was treated at 20*C and tested at 90 days.
Also, richer mixes
or lower water-to-cement ratios were shown to be more sensitive to
temperature at an earlier age than leaner mixes or higher water-toceaent ratios.
Malinowski115 Independently repeated work done in 1963 by
Hansen115, showing again that when speciaens are pre-cured at elevated
temperatures prior to steam curing, early strength is further Improved
when the speciaens were subjected to both longer pre-curing period and
94
higher teaperatures, with the caveat that the 28-day strength for ill of
the thermally processed speciaens was at least 35% lower than the
control.
Optimum results were obtained In speciaens pre-cured for 6
hours at ambient conditions and then cured at teaperatures between 60*C
and 80*C until testing.
Malinowski also observed a significant increase
in expansion of speciaens which were not pre-cured.
Rossetti117 showed that low pressure steaa curing of C3S(tricalclua silicate) reduces the induction period of hydration.
He
processed speciaens under isothermal hydration at 24*C, 40*C, 60*C, and
90*C iaaediately after alxlng and maintaining the elevated teaperatures
until testing.
In speciaens processed above 60*C, the product contained
aore liae and had a lower specific surface, thus reducing strength.
In
general, until around 100 hours after aixing, the higher the
temperature, the higher the percent hydration.
cross-over effect was observed«
Around 100 hours, a
at that point, higher teaperatures led
to a lower percentage of hydration.
This effect was attributed to the
development of coarser hydration products produced as a result of the
accelerated heating.
Parcevaux11® studied the effect of temperature and pressure on
pore size distribution in Portland ceaent slurries.
He showed that
increasing teaperature causes ceaent hydration to proceed differently
and at higher rates, resulting in the generation of larger pores.
TABLE V summarizes these recent studies of low pressure heat
treataent.
In brief, these studies show that increasing teaperatures«
1) increases porosity;
TABLE V
S i w i r y of significant tharaal processing studies.
U v ln i
Nallnowakl
Roaaattl
Parcavaux
Cenent type
Portland
conont
Portland
<T*
Portland
eaaant
Optlaua eaap.
ae«c
(only atudlod
i N t M M 154S*C)
«e-se*c
M*C
below M * C
Op ti on t l M
Of tTMCMflt
eurod at
•lavatad
taap.
curad at
alavatad
tan-
cured at
alavatad
tanp.
(laotharaal
hydration)
not
praaantad
Optlaa
precuring
tlJM
not prooantad
< houra
not praaantad
not
praaantad
Shore t a n
effect on
atrength
not praaantad
not praaantad
before 1SS
houra■
hitftor
pareant
hydration and
hlghar
atrangth
not
praaantad
bayond 1SS
hourai
lower pareant
hydration and
louar
atrength
Effect an
porooicy
Sot praaantad
Sot praaantad
..
......
Sot praaantad
Zneraaaaa
with eanp-
96
2) increases the percentage of early hydration which Increases
early strength; and
3) decreases long tern strength by as such as 30%.
Autoclaving
No other aethod of thermal processing of ceaentitious saterial has
been studied sore than autoclaving, which uses high teaperature and high
pressure to accelerate the curing and iaprove the early strength of
concrete.
The doalnatlng difference between this process and other
theraal processes is the significant alteration in the chealstry of the
hydration process.
It has been enclosed in the present discussion only
for cospleteness and will not be used to coapare to the alcrowave
process.
The cornerstone of autoclaving lies in three papers written by
Menzel in 193411*, 193512*, and 1936121.
The studies showed that when
ceaentitious aaterial is subjected to higher teaperature and pressure,
calclua hydroxide reacts with fine silica to fora Insoluble products at
a faster rate than when the speciaen is aolst cured.
Optlaua results
are obtained when pre-autoclave curing is done in a aolst ataosphere for
24 hours laaedlately after aixing and the speciaen is slowly heated in 5
hours to
3 5 0 T and pressurized at 120psl at this elevated teaperature
for 9 hours, follow by 10 hours of cool down to aablent teaperature.
Under these conditions, a 330% increase in coapressive strength was seen
after 3 days, along with a reduction in drying shrinkage.
It was
eaphasized that laproveaent occurs only when a suitable aaount of fine
97
silica Is added to the alx.
Verbeck1^ performed a study which suggested that the general
chesilcal and physical nature of hydration products are unaffected by
teaperature below l«0*C during curing, while teaperatures above 10O*C
affect the rate of curing, which subsequently affects product strength.
This study showed that a higher curing teaperature Increases the l-day
coapresslve strength but decreases the 28-day strength, due prlaarlly to
an Increased rate of hydration.
However, this Increased rate also
results In non-unlfora hydration products because of lncoaplete
diffusion during product foraatlon.
The study also showed that
teaperature and CaO-SiO, aole ratio determines the structural type of
CaO-SiO, formed.
Figure 21 shows the phase diagram of calciua silicate
in relation to these two variables.
Teaperature and pressure were
determined by selecting the desired properties of the product.
general, It is advantageous to
aaterial.
In
In
obtain a high strength/low shrinkage
this case, 350*F at aole
ratio between 1<1 and 2.5 1 1 can
be expected to produce the desired results, since
C-S-H and
tobermorite are strong but exhibits large shrinkage while C,S alpha is
weak but shrinks very little.
The aain
drawback of this process
speciaen must
be maintained at aaxiaua
is the length of tiae the
teaperature, usually for 8 to12
hours and the need to adhere to specific alx ratios.
Redmond1*3 showed
that this tiae can be reduced to 5 to 6 hours if the speciaen is presteaaed for 1.5 to 4.5 hours after aixlng.
98
600
sn o tl i t*
brand ite
500
Temperature ,
u.
Gyrolite
400
300
Toberm o n te
C j S a Hydrate
200
100
Calcium
Silicate
Hydrate
C a 0 - S i 0 9 Mole Ratio
Figure 21
Phase dlsgrae of hydration products froe Verbeck.
99
7.3
Experimental procedures
The effect of microwave heating on the physical properties of
hydrating cementltlous materials were studied through the following
program.
The procedures used for the microwave processing were adapted
from the studies of Christo and Hutchison.
The specimens were processed
In both a commercial microwave oven and a dynamic multimode alcrowave
applicator which was designed and constructed in our laboratory.
A
comparison of the resulting properties using these two different
alcrowave applicators provides insight Into the reproducibility and the
conditions necessary for proper speciaen preparation and processing.
Next, to determine whether microwave processing had a-thermal effects,
surface heating was used to replicate the teaperature-tiae profile of
the alcrowave processed speciaens.
Additional tests on the processed
speciaens were performed to further identify effects of alcrowave
heating on aicrostructure.
These included mercury intrusion
poroslaetry, Ignition loss, weight loss measurements due to evaporation,
and x-ray diffraction.
Finally, selected speciaens underwent thermal
shock procedures to provide some data on the effect of delaying the
onset tiae of heating.
The following description of experimental procedures have been
delineated Into 3 sections.
The first section describes the mixing,
casting, and curing of all of the specimens.
The second section
describes the different microwave processing schemes. The final section
describes the different tests applied to the processed speciaens.
100
7.3.1
Mixing, casting, and curing procedures
Mortar speciaens were nixed with type I OPC according to ASTM C-190
specifications having a water-to-ceaent ratio of 0.44 and a sand-toceaent ratio of 2.5 which corresponds to a water-to-solld ratio of 0.13.
Speciaens with other coaposltlons will be discussed where appropriate.
Speciaens were casted lsaedlately after alxlng Into 4cax4caxl6cn
rectangular styrofoaa molds bonded with latex adhesive, a bottom lining
of 0.2m
transparent plastic, and a latex sealant on the walls to
prevent seepage.
The aolds were transparent to alcrowave fields.
After
processing, described below, speciaens were placed In a 100% relative
hualdlty envlronaent and de-aolded after 1 day.
They underwent further
curing in saturated liae water until tested according to ASTM C-511.
All reference speciaens were iaaedlately placed into 100% relative
hualdlty environaents for 1 day, then de-aolded and placed in saturated
llae-water until testing.
7.3.2
Theraal processing
a)
Microwave heating
Initial alcrowave processing experlaents were perforaed in a
commercial oven.
Subsequent processing utilized a dynamic aultiaode
applicator which provided aore unifora heating of the speciaens.
The coaaercial oven, General Electric Model JE 2851H, features the
usual on-off controller with 10 duty cycle settings and a magnetron
rating of 700 watts.
The lowest setting, at which all processing was
perforaed, had a aeasured duty cycle of 14%.
Prior experiments12*
101
showed that sorter speciaens with water-to-ceaent ratio of 0.44 and a
sand-to-ceaent ratio of 2.5 processed within 0.5 hour of nixing
exhibited optlaua laproveaent when heated for 40 ainutes at which tiae
the teaperature had risen to 60*C.
These paraaeters were therefore
selected in subsequent processing.
The dynaalc aultlnode applicator has been fully described by Chang
and Brodwin125.
It was specifically designed to provide efficient
energy coupling and unifora heating of speciaens at 2.45GHz.
Its
circular cylindrical design Incorporates a aotorlzed endwall for
periodic variation of the cavity length.
to scan 19 resonant aodes.
The endwall can be positioned
Close-proxlaity resonant nodes are a
function of the length of the applicator, providing significant aode
overlap in the presence of a load.
The node overlap results in constant
input lapedance as the length of the cavity changes.
The input
iapedance of the applicator can therefore be aatched over a range of
different loads.
b)
Surface heating
As noted earlier, it was desired to deteralne whether a-thermal
effect was present due to electroaagnetlc oscillations. To test this
idea, we replicated the alcrowave heating profile
aethod.
by a surface heating
Mortar speciaens heated to about 60*C in 40 ainutes duplicated
conditions observed during alcrowave processing.
This was accoaplished
by placing a 1500 watt space heater and two 150 watt heat laaps inside a
closed environaent, with the laaps 4 inches above the speciaen.
102
Specimens heated this way were later tested for compressive strength at
1, 7, and 28 days.
c)
Thermal shock
The third Method of thermal processing used In our study was the
thermal shock method.
The purposes of these experiments were two fold:
first, to determine If a rapid rise In the temperature of cementltlous
specimens affects the compressive strengths as reported In the
literature; and second, to determine whether the final properties of the
material are significantly affected by the delay of heating.
After
casting at room temperature, the specimens were placed Into a 47*C
bath
after 2, 3, 4, 5, and 6 hours, respectively until the test date.
7.3.3
Post processing tests
Compressive strength tests were performed on specimens to failure.
Prior to the tests, specimens were either surface grounded and/or capped
with a molten sulfur solution to obtain parallel end faces.
ratios for the compression strength tests were 2il.
The aspect
After compressive
strength testing, selected specimens were used for mercury Intrusion
poroslmetry to study the pore structure.
The effects of microwave
processing on the degree of hydration were also studied, using the
Ignition loss technique according to ASTM C-114 guidelines.
Finally, x-
ray diffraction was performed to determine the Influence of microwave
processing on the products of hydration.
103
7.4
Results
TABLE VI shows a insiin of the different paraaeters considered In
considered in this study.
The heat sources Included those froa
alcrowave heating, surface heating, and thermal shock treataent.
The
table tabulates significant aspects of the experlaents such as the
coaposltlon of the mixture, the period of delay prior to thermal
processing, various alcrostructural studies, and other specimen
characteristics.
order.
The discussion of the results will be In the following
First, the effect of alcrowave processing method on the strength
of the material will be presented.
Next, evidences leading to the
possible cause of the Improvement will be discussed.
These Include the
Information obtained froa mercury Intrusion poroslaetry, Ignition loss,
x-ray diffraction quantitative analysis, and weight loss measurements
due to water evaporation during thermal processing.
7.4.1
The effect of alcrowave heating on strength
The principle effect of microwave thermal processing is the
improvement in early compressive strength.
day showed an average of 29% increase.
strength of an unprocessed specimen.
The improvement after one
This corresponds to the 3 day
The trend of the data at 1, 7, and
28 days exhibited that microwave effects on strength dominates in the
early stages of hydration.
At 28 days, the treated samples have
comparable strength as the reference.
A coaparatlve study between the
microwave thermal processing scheme and other schemes is quite difficult
due to the tremendous differences In the application and origin of
104
TABLE VI
Parameters considered under the thermal processing program to study
fresh cementltlous materials.
llcrown
8 applicator
Com type ore
•/c
8.44
i/c
2.5
Delaytlaei 15
koara
Coaprcuirt
Struyth
DP
pm
IyaitioaIon pm
I*ray
rt*
dlffnctioD
traporatioa M
ofnter
ao
Oaifon
beatiag
Tutdatci
OPC
I.M
2.5
8.5
OPC
8.45
8.5
Coaratioaal
btatlay
lalfora
applicator
OPC
8.44
2.5
8.5
OPC
8.44
2.5
8.5
TWnalBock
OPC Bita C,s
8.5 8.35
8.5
2.8 8.8
2.8
1,2.3,4,5,4
PM
7**
PM
ao
BO
pm
80
M
JW
PM
PM
T**
BO
PM
PM
PM
1,7,aed28dayi
105
heating.
The dominating advantage of alcrowave processing is the
aechanlsa of internal heat generation which provides uniform heating and
short processing time.
7.4.2
The effects of alcrowave heating on alcrostructure
Measurements by mercury intrusion porosiaetry showed that there
were significant decrease in
theporosity of processed specimens.
Figure 22, Figure 23, and Figure
and 28 day tested specimens.
24 show the HIP results froa the 1, 7,
Itcan be seen that in all cases there has
been a decrease in the totalporosity of the
specimens.
microwave treated
This result is in contrast to other heating methods which
showed greater porosity after treatment.
It appears that strength
improvements are correlated by a decrease in porosity.
7.4.3
Nature of iaproveaent
One of the primary motivations of this study was to seek out the
source(s) of the iaprovement in compressive strength.
The following
three tests were performed in this endeavors 1) ignition loss, 2) x-ray
diffraction, 3) weight loss measurements.
l) Ignition loss
The enhancement of compressive strength by alcrowave thermal
processing has been shown to be partly due to the acceleration of
hydration process12*.
Figure 25.
Percent hydration versus time is plotted in
The results demonstrate that microwave energy acts as an
106
Hg Volume, c c /g m
0.10
0.08
0.06
Intruded
0.04
Microwave processed
Control
0.02
0.00
0.001
Figure 22
0.01
0.1
1
Radius, um
Mercury intrusion results for 1 day speciaens.
10
1«7
Hg Volume, c c /g m
0.10
0.08
0.06
Intruded
0.04
Microwave processed
Control
0.02
0.00
0.001
Figure 23
0.01
0.1
Radius, um
1
Mercury Intrusion results for the 7 day specimens.
10
108
Hg Volume, c c /g m
0.10
n
0.08
0.06 -
Intruded
0.04
Microwave processed
Control
0.02
0 .0 0 H—
0.001
Figure 24
0.01
0.1
1
Radius, um
Mercury Intrusion results for 28 day specimens.
10
109
percent
00.00
Hydration
00.00 -I
40.00 -
20.00
I
-
X
-
• Microwave processed
X Control
0.00
?
1111
1
t—
i— I I I II11
1---1— TTTTTTl
10
100
T
Time - hours
Figure 25
Percentage hydration versus tiae.
1 ! I II I11
1000
110
accelerator only during the first 24 hours.
However, since the percent
hydration at 24 hours for the processed speclaens and the control are
slailar while the strength results exhibited significant difference,
additional aechanisas aust further contribute to the enhanceaent of
strength.
2) x-ray diffraction
Prellalnary analysis using x-ray diffraction of 1 day processed
speclaens showed a greater reduction in the CjS peak for the alcrowave
processed aortars than in the reference.
This supports the data
obtained froa the ignition loss test suggesting that alcrowave heating
accelerates hydration.
3) Weight loss aeasureaents
The laproveaent in coapresslve strength of alcrowave treated
speclaens has been previously attributed to the reduction of water-toceaent ratio due to water evaporation during alcrowave processing'” .
This idea has been further investigated in the following aanner.
specific questions were posed.
Two
The first question is to deteralne the
effect on coapresslve strength when evaporation is inhibited by covering
the speciaen top with a alcrowave transparent vapor barrier aaterial.
The second question is to deteralne the effect on coapresslve strength
at a higher rate of heating when evaporation is both uninhibited and
Inhibited.
Up to this point all tested speclaens allowed water evaporation
Ill
(hiring processing at the top surface.
Weight loss Measurements showed
that a change in the water-to-solid ratio of 0.01 occurred under the
present heating scheme of reaching 60*C after 40 minutes of processing.
This change in water-to-solid ratio corresponds to a change of water-tocement ratio in a mortar speclaens from 0.44 to 0.37.
The procedure in the present experiment is essentially the same as
all previously described microwave treatments.
outlined below.
The differences are
DSP(denslfied small particles) specimens were mixed
with water-to-ceaent ratio of 0.18.
The compositions of the DSP cement
consisted of 5% silica fume mixed with white cement.
The water-to-solid
ratio corresponds roughly to that of previously described mortar
speclaens.
DSP were selected because of the interesting strength
properties which have recently been observed118.
After casting, two molds were placed within the coamercial
microwave oven for processing.
One mold was covered with a thin
polyethylene sheet which prevented evaporation during heating.
The
second mold was not covered and duplicated all previously processed
specimens.
Two heating schedules were used.
The first adjusted the power
level via a miter load which provided heating of the specimens to 60*C
in 40 minutes.
The power associated with this heating schedule is
defined to be at power level 1.
The second schedule also used a water
load to adjust the power level.
In this case the speclaens were heated
to 60*C in 20 minutes.
The power associated with this heating schedule
is defined to be at power level 2.
112
After heat treatment, the speclaens were weighed to determine the
weight losses during evaporation.
Finally, the speclaens were placed In
the controlled environment and cured until testing.
The results of the coapresslve strength versus power levels are
shown In ?.
It can be seen that evaporation Inhibited speclaens showed
a significantly greater coapresslve strength than the uninhibited
speclaens.
This Indicated that the strength Improvements are not due to
the decrease of the water-to-cement ratio.
Furthermore, all of the alcrowave processed speclaens are never
greater than that of the control.
This observation counters the results
observed for the mortar and suggests that what was observed In mortar
specimens cannot be readily translated to other materials.
In addition,
the choice of the heating schedule depends upon the materials to be
processed.
To summarize this section, alcrowave thermal processing of
mortar Improves the 1 day strength.
cement
With this Improvement is the
corresponding decrease in porosity, acceleration of hydration during the
early period, and is not due to the decrease in the water-to-ceaent
ratio arising froa water evaporation during processing.
In fact, it was
observed that evaporation should be prevented in order to obtain greater
Improvements.
7.4.4
Comparison to surface heating
Another motivation of this study was to establish the effect of
113
Microwave processed with plastic covering
Microwave processed without plastic covering
00.00 n
Compressive
strength, MPa
O — Control
60.00 -
40.00 - Power level 0
Power level 1
Power level 2
All initial w/solid = 0.18
5* silica fume
4* superplasticizer
3 day test
20.00
0.00
1.00
2.00
Power level
Figure 26
The results of the compression strength tests on DSP with and
without evaporation.
114
different heat sources and heating profiles.
Comparison between
alcrowave processed speclaens with surface heated specimens has been
done to determine the effect of heat sources on the strength of
material.
Figure 27 shows the result of this study.
It presents a
comparison between the coapresslve strengths of the microwave and
surface heated specimens as a function of the test date.
In general,
there is only a slight improvement In strength when using microwave
heating. It is important to note that the surface heating process is
quite different from the processes reviewed In the introduction.
The
objective of using this form of heating Is to reproduce the same
temperature profile and loss of water due to evaporation observed during
microwave processing.
The results of this experiment show that, in
fact, microwave heating do not play an a-thermal role.
When comparing
the strength of the processed specimens with the controls, it is the
combination of heating parameters such as the target temperature, and
the specimen temperature profile which leads to the improvements.
The advantage of microwave processing becomes apparent when the
specimens size is taken into consideration.
Due to the small specimen
size the surface temperature does not deviate far from the internal
temperature.
However, as the thickness of the specimens increases,
conventional heat processing leads to increasingly non-uniform heating
due to low thermal conductivity.
With internal heat generation of
microwave processing, the desired temperature profile can be obtained in
industrial sized structures.
115
Compressive
strength, MPa
00.00 1
I
I
40.00 -
20.00
-
I
• Microwave processed
* Conventional heating
0.00
7— I t f T I— I— | T-J — 1— I— I— I— I f I I— I— |— I— I— I— I— I— I— I— I— I— |
0.00
10.00
20.00
30.00
Time, days
Figure 27
Comparison between coapresslve strength laprovements
■icrowave processed specimens and conventionally heated specimens.
of
116
7.4.5
The effect of delay heating
Once It has been established that the improvement observed for
alcrowave processed speclaens were not a-theraal, experlaents were
perforaed to deteralne the effect of tiae delay in the application of
heat.
The procedure was adapted for OPC aortar froa a study on C,S
aortar by Berger1*'.
The experiaental procedures are as follows.
speclaens were alxed at rooa teaperature.
the elevated teaperature of 47*C.
All but one set of
The exception was prealxed at
After nixing, the speclaens were cast
In polypropylene cylinders, producing speclaens lea in dlaaeter and 2ca
high.
The polypropylene alnlaized teaperature differentiations within
the speclaen as they were subjected to thermal shock.
The sized of the
speclaens were selected such that thermal conductivity of the material
can be neglected and the speclaen teaperature can be assumed to reach
the target uniformly.
Due to the higher variation of material
properties due to the saall dimensions of the casted specimens, a
ainlaua of six speclaens were used for each test points.
After casting,
selected specimens were placed in a 47*C water bath at one hour
intervals beginning at one hour after mixing and until six hours after
nixing.
The heated speclaens remained in the water bath until the test
date. The reference saaples were cast and cured at 24*C.
Figure 28 shows the results of the gain or loss in coapresslve
strength of 16 and 27 day old specimens relative to the control versus
the tiae delay in heat application.
The results are siuatarized as
24 C
47 C
2tirs
3hrs
-ihrs
CURING REGIME(24C->xhr->47C)
16d
Figure 28
276
Effects of heating tine delay on coapresslve strength.
118
follows.
The samples placed into the 47*C bath after 2 hours have such
higher 27 day strength than the reference.
The saaples placed into the
bath after 3 to 6 hours do not show the saae effect.
The saaples cast
and cured at 47*C do not have as good strength as those cast and cured
at 24*C.
7.5
Iaportance of unifora heating
The experimental data presented in this section are detailed
studies concerning with the uniformity of heating of cement based
specimens using microwave energy.
Prior to the availability of the
dynamic multimode aicrowave applicator in which power applied to heat
the specimens can be controlled by external circuitry, water loads were
necessary to absorb excess delivered power in the coasMrcial oven.
The
following shows that caution is necessary when using water loads for
power reduction since the quantity and location of the loads often
causes tremendous non-uniform heating in the specimens.
This effect
will subsequently cause significant variations in compressive strengths
of the material.
Uniformity of heating was monitored in situ by measuring specimen
temperature at various points in the specimen using either 6 or 9
petroleum liquid based thermometers.
The thermometers were previously
tested to show negligible absorption of microwave energy which would
have cause erroneous temperature readings.
Figure 29 shows the results of the temperature profile experiment
duplicating precisely the location, the mixture ratio, and the amount of
119
water load used In the cowwrclal alcrowave oven.
The lowest power
setting on the alcrowave oven (PI) and 600al of water was used to
achieve the selected power level to be delivered to the speclaens.
water to ceaent ratio was 0.44, the sand to ceaent ratio was 2.5.
theraoaeters were used, T1 to T6.
The
Six
The figure clearly shows the
treaendous variation In teaperature at different locations of the two
speclaens.
Note especially that the teaperature variation is not random
but depends precisely on the location In the oven.
This result shows
that large statistical variations In coapresslve strength are expected
due to this non-unlfora heating.
This experlaent was then follow by a study of whether the
observation of large teaperature variation Is due to the heterogeneous
properties of aortar used.
used.
In this second experlaent, OPC paste was
The power was set as In the above experlaent.
The water-to-
ceaent ratio was chosen to be 0.45.
The results of the teaperature uniformity test on ceaent aortar
shows once again that there Is a large variation in teaperature at
different points of the speclaens as shown in Figure 29.
It was
concluded that the cause of the non-unlfora heating was in fact not due
to the different aaterlal properties but is doainated by the power
absorbing water loads.
The was verified by the following experlaent.
A combination of a alcrowave transparent autoaatic turntable and
the distribution of the water load at different positions within the
oven was selected.
This combination allows the speclaens to pass
through the non-unlfora fields existing in the oven resulting in a tiae
120
100.00
-
T1
T2
• •• ♦ • T3
90.00 -
* * * * * T4
T em perature,
CJ
00.00
o o a a o T5
***** T6
-
70.00 -
60.00 *
t
50.00 -
0
40.00 -
♦
• '
* a
30.00 -
•
O
t
o
o
o
o
°
<
20.00
10.00
-
-
0.00 I
0.00
i i i i i i i i | i i r-r i i i i i | i 1 1 1 1 1 1 1 1 I r n -T - r 1 I IT T |
10.00
20.00
30.00
40.00
Time, m in
600 ml
water
Figure 29
Results of the teaperature profile test for ceaent aortar.
121
average uniform heating of the specimens.
The distribution of the
water load into smaller portions and the placement of these divided
loads at properly spaced locations minimized the field perturbing
effects of the high conductivity water loads which was concluded to be
one of the causes of non-unifora heating.
Figure 30.
The results are shown in
It can be readily seen that there has been a large
improveaent in the variation of the teaperature of the speclaens.
These experiments show that knowledge of the alcrowave heating
characteristics such as field distribution in the applicator are pre­
requisites in order to produce speclaens with uniform properties.
7.6
Conclusion
In the precast ceaent industry, steam heating is often used to
accelerate curing.
In this process, there is a delay of one or more
hours before the steam is applied.
The teaperature is then raised at a
moderate rate, 11 to 33 degrees celsius/hour, to the maximum desired for
the particular product, 66 to 80 degrees celsius.
is a long term one, usually not exceeding 18 hours.
The steaming process
One reason for the
long treatment tiae is the slow Increase of internal teaperature due to
thermal conductivity, which, of course, is dependent upon the size of
the object.
In contrast, alcrowave processing, with interior heat
development, is much quicker and, in less than an hour, achieves the
desired result.
Further, the microwave processed material is always
stronger than the reference, in contrast to reported decreases in
compressive strength over long time periods with steam curing.
122
100.00 n
90.00 -
***** A2
ooooo A3
82
P
80.00 -
B3
70.00 -
• * * • * C2
♦♦♦♦♦ C3
60.00 -
Jh 50.00 40.00 30.00 20.00
-
1 0 . 0 0
-
0.00
0.00
10.00
SOal water
30.00
40.00
50*1 water
turn eabla
SOal water
150al water
Figure 3* Teaperature of th* speclaens at different location* versus the
tiae of heating using distributed water loads and alcrowave transparent
turntable.
CHAPTER 8
Microwave Induced Polymerization of Monomer
Impregnated Hardened Cement
8.1
Introduction
Physical properties of cementitious materials are highly dependent
upon porosity.
Considerable improvement of properties such as tensile
strength, flexural strength, durability, and especially compressive
strength are achieved when the pore spaces are filled with the solid
polymer, poly(methyl methacrylate), PMMA.
The low viscosity liquid monomer, methyl methacrylate, MMA, is
intruded into a cement specimen thereby filling the capillary pores as
well as any voids or cracks.
Through polymerization, this liquid is
transformed into the solid polymer
tWh.
Due to various drawbacks, the
use of prior polymerization schemes such as ionizing radiation,
promoter-catalysis, and conventional thermal-catalysis have had limited
applications.
This chapter shows that microwave energy can be used as a thermalcatalytic technique to provide a simple, efficient, and safe method to
produce polymer impregnated concrete, PIC.
8.2
Survey
The distinctive difference between PIC and other polymer
cementitious materials is the filling of pores of hardened specimen with
a monomer and subsequent polymerization.15®""
123
Two comprehensive
124
reports lay the foundation for our study, Steinberg1^ and Fowler1".
In short, Steinberg observed that the coapresslve strength of PIC Is
Increased by 390%, the tensile strength Is Increased by 300%, the
modulus of elasticity Is Increased by 80%, the modulus of rupture Is
Increased by 250%, the flexural modulus of elasticity Is Increased by
50%, the freezing and thawing properties are Improved by 300%, and the
water absorption Is decreased by 95%.
In view of all of these advantages, It Is surprising that the use
of PIC Is not more wide spread.
This anomaly can be traced In one
aspect to the difficulties encountered in the methods of polymerization
of the impregnated specimens.
Polymerization is the process of linking individual monomer
molecules into a long repeated monomer chain with enhanced physical
properties.
centipoise*.
In the present case for htiA, the monomer viscosity is 0.34
The density is 810kg/m3, the vapor pressure is 85mm at
0°C, the boiling point is 77*C, and the solubility in 25*C water is
7.4%.
Since pure MMA is unstable at room temperature, chemical
inhibitors are use to prevent runaway polymerization.
A chemical
initiator, benzoyl peroxide, BPO, is used to aid polymerization by
decomposing the inhibitor and
generating free radicals.
To make the
polymer more rigid, more resistant to solvents, and increasing the
softening point, a cross-linking agent, trlmethylolpropane
trimethacrylate(T W I M A ), is used.
In general, the physical properties of P M A are: a softening point
1 centipoise*.01 grams/(cm-sec)
125
at 100*C, coapresslve strength of 16000psi, and a nodulus of elasticity
of 60000psi.
In order to produce the polyaer, the monomer, the
Initiator, and the cross linking agent are mixed together to make the
aonomer solution.
Actual polyaerization proceeds with the addition of
either the promoter or the application of an external energy source.
Coamonly used polymerization schemes are ionization radiation,
promoter-catalysis, and conventional thermal-catalysis.
In ionization
radiation, gamsu rays, emitted by cobalt-60, produce free radicals in
the monomer solution.
of the source.
The polymerization rate depends upon the strength
In comparison with conventional heating, ionization
radiation avoids large thermal gradients.
Further, initiators and
promoters are not necessary.
The primary disadvantages of this method is the high cost of the
radiation source, the need for biological shielding, and the low
polymerization rate.
The radiation dosage to polymerize
monomer
intruded concrete is approximately 2x10* rads with a processing time of
5 hours.
Additional consideration is the radiation attenuation inside
the specimen.
In promoter-catalysis, promoters or accelerators are used to
decompose the organic peroxide initiators.
The higher rate of
decomposition produces the necessary free radicals for polymerization to
take place at ambient temperature without the need for external energy
source.
The primary disadvantage with this method is the difficulty in
obtaining predictable polymerization times since the induction period
for polymerization begins immediately upon adding the promoter.
In conventional thermal-catalysis, heat Is used to decompose the
organic peroxide Initiator.
For a given aaount of BPO, polymerization
will take place If the saaple Is kept at an elevated teaperature for the
required tiae.
The prlaary disadvantage with this aethod Is the large
theraal gradient associated with surface heating.
Subsequently, lengthy
processing period Is necessary In order to alnlalzed theraal gradients
and to provide unifora heating.
8.3
Experlaental procedure
A 4 stage process to study the effect of alcrowave induced
polyaerlzation of the lapregnated aonoaer has been developed.
These
stages, separately described below, arei 1) saaple preparation, 2)
impregnation, 3) alcrowave polyaerlzation, and 4) coapresslve strength
testing.
Saaple preparation includes alxlng, casting, curing, and drying in
preparation for aonoaer lapregnation.
Impregnation involves the
preparation of the aonoaer solution and the procedures which lead to
total and partial lapregnation.
Microwave polyaerlzation describes the
microwave applicator as well as the details pertaining to total
polyaerlzation.
The coapresslve strength testing section delineates the
preparation of the speclaens for failure testing.
8.3.1
Speclaen preparation
All speclaens were cast into plastic, PVC, circular cylindrical
molds; 2 inches diameter, 4 inches high.
Mortar specimens, with
a
127
sand-to-ceaent ratio of 2.5 and water-to-ceaent ratios of 0.3, 0.4, 0.5
ware usad.
Six speciaens ware used for each of the three water-to-
ceaent ratios.
Three saaples acted as controls, and the other three
were used as test speciaens.
The constituents were alxed together
according to the ASTH C305-82 standard.
The aolds were then filled with
the aortar and placed In a vacuuaed sealed container and shaken for 30
seconds to eliainate large, air-filled voids.
The speciaens were
reaoved froa the container, placed in a 100% humidity environment, and
allowed to cure in the aolds for 24 hours.
After 24 hours, all
speciaens were deaolded and further cured, except for the 1 day
speciaens, in a saturated calclua solution until the test date.
The 1
day speciaens were placed iaaediately in a 150*C oven to stop the
hydration.
The 7 days and 28 days cured speciaens were similarly
treated on the specified test dates.
Reanant free water was reaoved by
keeping the saaples in the oven until their weight becaae constant.
The
tiae required for drying ranged froa 2 days for the 1 day cured
speciaens to approximately 4 days for the 28 day cured speciaens.
After
drying was coaplete, the saaples were placed in a desiccator until the
next stage of the experimental process.
8.3.2
Impregnation
Figure 31 shows a scheaatic of the apparatus used to impregnate the
aortar speciaen with the aonoaer solution. A vacuum pump, laboratory air
supply, and flask filled with the aonoaer solution were attached through
valves leading to the chamber containing the speciaens.
The aonoaer solution was prepared by using 95% MIA
and 5% by
voluae of the cross linking agent triaethylolpropane trlaethacrylate,
1>4PTMA.
4% of the chealcal initiator benzoate peroxide, BPO, by weight
of the MIA solution was added laaedlately prior to iapregnation.
8.3.2.1
Total iapregnation
Total iapregnation was observed for 1 day cured speciaens with
w/c-0.3, 0.4, 0.5.
The entrapped air was reaoved by
evacuating the
saaple filled chaaber for 0.5 hours with a vacuua produced by a
mechanical roughing puap.
After 0.5 hour, the chaaber was sealed, and the vacuum line valve
was closed.
The aonoaer was then Introduced into the chamber, totally
iaaersing the speciaens.
The samples were then pressurized at 40 PSI
for 1.5 hours.
Total iapregnation was also observed for 28 day cured speciaens
with w/c-0.3.
This was achieved by using an extended iapregnation cycle
in which the vacuua period was 12 hours and the pressurizing period was
12 hours.
8.3.2.2
These were the only totally impregnated specimens.
Partial iapregnation
Partial iapregnation was observed for the remaining saaples with
various vacuua/pressure procedures.
Relevant details regarding these
speciaens are discussed in the subsequent section where the results are
described.
"Donated by Roha and Haas.
Figure 31
Schematic diagram of the iapregnation chaaber.
130
8.3.3
Microwave polymerization
After the iapregnation process, the speciaens were inserted back
into their original aolds to ainiaize surface evaporation of the
aonoaer.
These alcrowave transparent plastic aolds were used to
ainiaize evaporation during the heating period.
To aeasure teaperature during polyaerlzation, a thermometer was
casted into an iapregnated sample and processed.
After complete
polyaerlzation, this sample was subsequently included with iapregnated
unpolymerized speciaens to aonitor the teaperature during microwave
exposure.114
The alcrowave applicator had been especially designed and
constructed to provide efficient energy coupling and uniform heating of
speciaens at 2.45GHz.
The applicator is a circular cylindrical cavity
with a diameter of 32.8 ca and a motorized endwall producing periodic
variation of the cavity length between 17.8 ca and 33.0 ca.
The
positions of the endwall cause 19 distinct and identified modes to be
scanned.
The close proximity of the resonant aodes as a function of the
length of the applicator provides significant aode overlap in the
presence of a load.
The aode overlap results in a constant input
lapedance as the length of the cavity changes. The input impedance of
the applicator can therefore be aatched over a range of different loads.
Figure 32 shows a scheaatic of the cross section of the applicator.
The
waveguide feed is positioned with the narrow side wall contiguous to the
applicator wall and a coupling hole is drilled coaaon to both
structures.
Six beyond cutoff observation tubes, placed on the side of
131
the applicator, and a aeshed screen In the front endwall were provided
to enable the aonltorlng of the speciaens.
The feeding waveguide is
equipped with an adjustable short and loop coupling to control input
lapedance.
The experlaental setup is shown in Figure 33.
The source is a
Raytheon (aodel PGM-100) alcrowave generator operating at 2.45GHz with
electronic control of output power.
approxiaately 400 watts.
The aaxiaua available power is
The speciaens were supported by a 0.25 inch
thick styrofoaa platform such that the geoaetrlc center of the speciaens
are in the center of the applicator when the applicator is in it
shortest length.
Coaplete polyaerlzation of the iapregnated aonoaer solution using
alcrowave theraal-catalysls depends upon the BPO content, the speciaen
teaperature, and the duration of alcrowave exposure.
Specific BPO content and the speciaen teaperature dictates the
degree of polyaerlzation.
A graph of the percentage of polyaerlzation
versus the percentage of BPO as a function of teaperature is shown in
Figure 34 froa Steinberg.
Froa the graph, useful paraaeters for this
study are 4% BPO and 11 ainutes of alcrowave exposure raising the
teaperature to at least 85*C.
After exposure, the speciaens were
aaintalned at the elevated teaperature in an insulated container for 1
hour to ensure coaplete polyaerlzation.
Coaplete polyaerlzation is
indicated by the lack of the pungent odor associated with the aonoaer
solution.
The teaperature-tlae history of the speciaens during the
alcrowave exposure coabined with the aass of the speciaens indicated
VIEWING HOLES
TOP
VIEW
\
s
u.
r*
MOVING
WALL
\
N•
waveguioe
tttpire 32 Schematic dlagraa of the aovlng end wall aultlaode
applicator.
COUPLING
LOOP
ADJUSTABLE
COUPLING
SHORT
eh *
RAYTHEON
MICROWAVE
SOURCE
Pl^ira 33
IMOVING
ENOWALL
Experimental setup used In studying uniform heating.
MOTOR
DRIVEN
WHEEL
134
'30IXOU3J
167 *F
73 *C)
IA 02N 30
1.0
2.0
3.0
TIMC FOR 100% POLYMERIZATION, hr
4 .0
Figure 34 BPO content versus tine and teaperature relationship to the
percentage polyaerlzation (froa Steinberg, 1967)
135
that 230 watts arc needed to process one kllograa of aortar.
8.3.4
Coapresslve strength
All speciaens were ground and sulphur capped to ensure parallel end
surfaces.
The speciaens were then Inserted Into a Soiltest Model CT-710
coapresslve strength testing aachlne.
8.4
Results
The results of the polyaerlzed speciaens have been delineated in
tents of either total or partial iapregnation.
The vacuua/pressure
cycles and the depth of the Iapregnation for different w/c ratios and
curing days are tabulated in TABLE VII.
Note that total Iapregnation
appears only for the 1 day cured speciaens for all w/c ratios and the 28
day cured speciaen with w/c-0.3.
In addition, the depth of iapregnation
Increases with the w/c ratio for the 7 day speciaens but reaalns
constant for the 28 day speciaen.
In the discussion section.
This point will be considered further
Coaplete iapregnation is characterized by a
hoaogeneous shading of the cross section of a tested speciaen.
For
partially iapregnated speciaens the different shadings indicate Halted
aonoaer penetration.
The coapresslve strength results for the totally iapregnated
speciaens will be presented first.
8.4.1
Total iapregnation
A bar graph of the percentage increases in the coapresslve strength
136
TABLE VII
Vacuua-pressure cycles and the depth of the iapregnation of the aonoaer
solution.
w/c
e.3
e.3
e.3
e.3
e.3
e.«
e.«
e.«
e.«
e.4
e.s
e.s
e.s
e.s
e.s
Pressurlzatlon
tlae
(hours)
K n e a d of
Depth ot
netlon
Intrusion
(ca)
e.s
l.S
total
>2.5
e. s
l.S
partial
e.s
e .s
l.S
partial
l.S
12.e
12.e
partial
1.8
12.8
12.e
total
»2.S
e .s
l.S
total
>2.5
e .s
l.S
partial
1.3
e. s
l.S
partial
l.S
i2.e
12.e
e.s
12.e
partial
12.e
partial
1.8
2.1
l.S
total
>2.S
e .s
l.S
partial
l.S
e.s
l.S
partial
l.S
12.e
12.e
partial
12.e
12.e
partial
Cure tlae
evacua­
tion tlae
(days)
(hours)
1
7
28
7
28
1
7
28
7
28
1
7
28
7
28
V o t e ■ D i a a e t e r of eeaple ie 5 . lea.
iw e -
1.7
2.2
137
of the PIC speciaens over the corresponding control speciaens as a
function of the water-to-ceaent ratio is shown in Figure 35.
speciaens were processed after 1 day of curing.
All
Note the draaatlc
increases in the coapresslve strength as the water-to-ceaent ratio
Increases.
The average coapresslve strength of these PIC speciaens used for
each water-to-ceaent ratio ranges froa l2000psi(83MPa) to
15000psl(103HPa).
Approxlaately a five fold increase in the coapresslve
strength for the polyaerized, 1 day cured, w/c-0.5 speciaen over the 1
day control was observed.
A further coaparlson of the 1 day polyaerized speciaens with the 28
day control speciaens is shown in Figure 36.
Note that the 1 day PIC
speciaens are significantly stronger than the 28 day cured speciaens.
Total iapregnation was also observed for speciaens cured for 28
days with w/c-0.3.
A 50% iaproveaent was observed.
The average
coapresslve strength of the polyaerized speciaens is 14000psl(96MPa).
The average coapresslve strength of the control speciaen is
9000psi(62MPa).
8.4.2
Partial iapregnation
The depth of iapregnation of the aonoaer solution into a particular
speciaen principally depends upon paraaeters such as peraeability, pore
connectivity, pressure gradient on the aonoaer solution, and aonoaer
viscosity.
Other researchers have studied the effect of partially
iapregnated polyaerized concrete.135
They noted that, in terms of the
X Incraasa
In com praaalva
a tr a n g th
500%
400% -
300% -
200%
-
100%
-
0%
0.3
0.4
0.5
w /c
Figure 35
Percentage Increase in coppressive strength of 1 day cured
fully iapregnated speciaens in coaparison to 1 day control speciaens.
100X
control c tro n g tb
sox 4 OX -
X incroooo
SOX -
Soy
-
of 28
SOX
7 OX -
eox -
30X -
10X OX
0.3
0.4
0.5
w /c
Figure 36 Percentage laproveaent of polyaerized speciaens over the 28 day
control speciaens.
140
depth of Iapregnation, a 7 day cured concrete speciaen(w/c-0.56,
aggregate/c-5.33) dried for 96 hours In a 105*C oven has a 2 ca depth
after 1.5 hours of soaking and a 3 ca depth after 48 hours of soaking.
The present study on aortar exhibited depths of Iapregnation for
the 7 day speciaens as 0.8ca for w/c-0.3, 1.3ca for w/c-0.4, and 1.5ca
for w/c-0.5.
The depth of Iapregnation for the 28 day speciaens is
approxlaately 1.5ca for all water-to-ceaent ratios.
A comparison of the
degree of iapregnation between concrete and aortar cannot be nade due to
the vastly different nature of the aaterials.
The coapresslve strength data of partially iapregnated polyaerized
speciaens have been organized to study the effects of water-to-ceaent
ratios and duration of curing.
Coaparison between speciaens Is
complicated due to the different depth of Impregnation.
In order to
obtain a suitable coaparison, it was decided to introduce an effective
coapresslve strength.
A schematic diagraa of the cross section of a
partially impregnated specimen is shown in Figure 37.
The effective
compressive strength of the partially iapregnated speciaens is defined
to be the failure force of the speciaen divided by the cross-sectional
area of the iapregnated region of the speciaen.
It is assuaed in this
simple coaparison that the uniapregnated regions do not contribute to
the observed strength.
The numerical results for the effective
coapresslve strength of the partially impregnated speciaens are
tabulated in TABU! VIII.
The percentage laproveaent of the PIC over the
control is shown in Figure 38 for the 7 day cured speciaen and in
Figure 39 for the 28 day speciaens.
141
Evaporation Rogion
Unimpragnmad Rogion
Poiymarizad Rogion
Plguro 37
Schoaotic
iapragnatad apaclaan.
dlogroa
of
tho
croao
ooctlon
of
o
partially
142
TABLE VIII
Average effective coapresslve strength of partially Iapregnated
speciaens and control speciaens.
7 day
w/c
e.3
e.«
e.s
28 day
Polyaanzad
Control
Polyaanzad
Contra1
75MTa
4Ml
93MPa
•3MPa
leeeepai
cseepai
isseepai
sieepai
94HPa
42HPa
iMeepai
cieepat
useepai
toeepax
ieeMPa
2<HPa
74»*a
S9MPa
useepai
sseepai
ie7eepsi
seeepai
suaa
97HPa
300%
260% -
effective
X InerMN
In s tr e n g th
240% 220%
200%
-
160% -
120 %
-
100%
-
60% 60% 40% 20%
-
0%
0.3
0.4
0.6
w /c
Figure 38 Effective percentage laproveaent of the partially iapregnated
7 day cured speciaens.
SOX
In s tr e n g th
20X
effective
30X
X InerMM
40X
10X
OX
0.3
0.4
OS
w /c
Fi^ire 39 Effective percentage laproveaent of the partially Iapregnated
28 day cured speciaens.
145
8.5
Discussion
Ths rssults of this study shows the feasibility of using microwaves
to Induced the polymerization of monomer impregnated hardened cement
mortar.
The present section will discuss further the results of the
coapresslve strength tests and the depth of impregnation.
8.5.1
Totally impregnated speciaens
Totally impregnated speciaens show dramatic laproveaent in
compressive strength.
ratio increases.
The laproveaent Increases as the water-to- cement
The percentage weight gain of the polyaerized
specimens relative to the control is shown by the bar graph of
Figure 40.
The percentage weight gain also Increases as the water to
cement ratio increases.
Recall that the coapresslve strength of the
polymer itself is approximately I6000psl and the compressive strength of
the cement mortar is on the order of 4000psi.
The combination of weight
increase and percentage strength improvement increases as the water-toceaent ratio increases suggests that the improvement depends on the
amount of polymer in the speciaen.
The advantages of the 1 day PIC
improvements over the 28 day controls presented in Figure 36 is evident.
8.5.2
Partially impregnated specimens
There are three points of discussion regarding partially
impregnated specimens• 1) coapresslve strength, 2) depth of
iapregnation, and 3) the vacuum/pressure cycle of impregnation.
10%
8%
-
weight gotn
otter
p o ly m e riz a tio n
9% -
0%
0.3
0.4
0.5
w /c
Percentage weight gain of the fully iapregnated speciaens.
146
Figure 40
147
1) Coapresslve strength
The 7 day partially Iapregnated speciaens show coapresslve strength
laproveaent Increases In a slallar Banner as the 1 day fully Iapregnated
speciaens even though the percentage laproveaents are not as great as
the 1 day speciaens.
This lower laproveaent Is due to Increased control
strength and lessened degree of Iapregnation due to lower porosity and
permeability of 7 day speciaens.
Contrary to the 7 day speciaens, the 28 day partially Iapregnated
speciaens show strength laproveaent decreases as the water-to-ceaent
ratio Increases.
One reason for this behavior can be found by coaparing
the iapregnation depth of the 7 and 28 day speciaens with the percentage
weight gain of the 28 day speciaens.
The 28 day partially iapregnated
speciaens exhibit constant depth of Iapregnation suggesting that there
is a H a l t to the iapregnation depth governed by the age of the
material, Irrespective of the water-to-ceaent ratio.
Under these
clrcuastances the 28 day partially Iapregnated speciaens exhibit a
simple linear laproveaent over the control speciaens in which the
coapresslve strength of the speciaen likewise decreases as the water-toceaent ratio increases, Table VIII.
2) Depth of iapregnation
A primary concern with partially impregnated speciaens is the
desirability to know the depth of iapregnation.
A means to calculate
the depth is by adapting Darcy's law governing permeability1’*
148
2_ kt
AP A
df 9 na Q
where
1-depth of iapregnation in ca
kj-coefflcient of permeability in ca/sec
j,-viscosity of water in poise
^■viscosity of aonoaer in poise
df-density of aonoaer in ga/ca*
g-acceleration due to gravity in ca/sec*
A-cross sectional area of saaple in ca2
AP-change in pressure along the direction of flow of aonoaer in
dynes/ca*
q-flow rate of aonoaer in ca'/sec
For example, the 7 day, w/c-0.5 speciaen undergoing 1.5 hours of
pressure in a 40psi environment has a depth of iapregnation, 1-0.162cib
when k j - T x W ’ca/s, A-203caJ, AP- 40psi, and q-6.2xl0‘3 ca3/s.
A coaparison of this predicted depth of iapregnation with the
observed depth of iapregnation of l-1.5ca shows a significant
discrepancy.
This can be attributed to the use of ceaent paste
permeability in the calculation as opposed to the use of ceaent aortar
permeability since the later is not known.
Although the permeability of
an ideal aortar/concrete speciaen is dominated by the permeability of
ceaent pasted, the interfacial properties between the paste and the
aggregates generally results in significant Increases in the
permeability of the speciaen.
149
The use
Iapregnation
of Dsrcy's law in the present fora to predict the depth of
of an laaersed speciaen in a pressure chaaber should be
used only as an estlaated since AP is a function of tlae due to pressure
increases in the interior of the speciaen as aore aonoaer is
iapregnated.
3) Vacuua/pressure cycle
When considering the effect of different vacuua/pressure cycle, it
was
observed that the 7 dayand 28 day speciaens behave siallarly in
terms of coapresslve strength iaproveaents for both the 2 hour
process(0.5 hour of vacuua/1.5 hours of pressure) as well as the 24 hour
process(12 hours vacuua/12 hours of pressure).
The difference occurs
only in increased iapregnation depth for longer vacuua/pressure cycles
which is manifested in the nuaerlcal Increases of coapresslve strengths
of corresponding specimens.
The benefits froa longer vacuum/pressure
cycles is offset by the decrease of iapregnation rate as the aonoaer
penetrates deeper into the speciaen.
Further study is necessary to
determine an optiaua vacuua/pressure cycle for specific applications.
An anoaaly was observed for the 28 day, w/c-0.3 speciaen using the
24 hours iapregnation cycle.
iapregnation.
These saaples showed full aonoaer
This can be attributed to the significant defects and
voids present in the speciaens due to lower workability associated with
such a low water-to-ceaent ratio.
The presence of these defects
resulted an increase in the accessibility of the aonoaers to the
interior of the speciaens.
150
8.6
Conclusion
The effect of filling th« pore spaces in cured aortar speciaens of
different water-to-ceaent ratios with PtftiA have been shown to laprove
the coapresslve strength treaendously in both fully iapregnated and
partially iapregnated speciaens.
The iaproveaents in the coapresslve strengths of the polyaerized
speciaens using alcrowave polyaerlzation Is coaparable if not better
than using other methods.
Although only the coapresslve strengths have been studied in this
work, it is possible to infer froa prior studies that other physical
properties will correspondingly be laproved.
CHAPTER 9
A Hew Applicator for Efficient Unlvorm Heating Using a Circular
Cylindrical Geometry
9.1
Introduction
Applicators for electromagnetic thermal processing are designed to
achieve two important goalsi uniform temperature distribution and
efficient coupling between source and applicator.
Uniform temperature distribution, for most materials with a small
teaperature rise, is produced by developing a time averaged uniform
field distribution.
Efficient coupling is accomplished by obtaining a
constant input impedance, independent of teaperature rise and sample
size.
Both goals are achieved by choosing an applicator with a large
number of closely spaced modes appearing in an empty resonant cavity.
When the tuning is varied, the modes are scanned and the field at any
point will vary in orientation and amplitude.
Averaged over tlae,
different points will experience the same average field intensity.
When
a sample is inserted, the time averaged field in the sample will become
more uniform.
In addition, the presence of the sample will decrease the
"0” of the empty modes, and cause significant aode overlap.
Mode
overlap tends to even out the input impedance and yield a relatively
constant impedance.
In coaparison with applicators based upon a rectangular geometry, a
circular geometry produces a more uniform field, and an input lapedance
151
152
that la sufficiently constant to anabla efficient power absorption for a
variety of loads.
In this paper, we shall first describe how the applicator was
designed, and then present experimental results establishing unifora
heating. Identification of the observed aodes, and the beneficial
results of aode overlap.
9.2
Design
A comparison of rectangular versus circular applicators shows that
for a given cross sectional dimension, the circular design exhibits a
much larger number of aodes than the rectangular one.
A movement of the
end wall therefore scans a larger number of modes In these applicators.
A circular design was chosen with an Inner diameter of 12.9 inches(32.8
cm) to provide a convenient size for heating samples of ceaentltlous
materials.137
The excitable aodes In a cylindrical cavity depend upon
both diameter and length of the applicator.1M
In the present design,
one of the end trails of the applicator Is movable and provides a
variation of cavity length from 7 Inches(17.8 cm) to 13 Inches!33.0 cm),
resulting in the possible excitation of 38 resonant nodes at 2.45GHz.
TABU! IX Is a listing of the theoretical resonant nodes and the
corresponding applicator lengths.
The excitation of each node depends
on the position of the non-contacting moving end wall.
However, whether
the mode Is observed depends upon the method of coupling from
source waveguide to the applicator.
the
1S3
TABLE IX
Listing of theoretical resonant aodes and corresponding applicator
lengths.
Degenerate aodes are indicated by a coaaon resonant length.
X§pty
applicator
leasts
(l a c n e s )
R e s o n a n t nods
x§pty
applicator
lenptn
(I n c & e s )
Resonant aode
TN312
7.344
TC412
l§.444
TCI 13
7.441
|TM114
1§.4§7
TC312
7.441
TC§14
1§.4§7
TM413
7.S3S
TM412
14.955
TC312
7.414
TN313
ll.§2§
TX213
7. 747
TS314
1 1 . 1§1
TS222
7.914
TSS13
1 1 . 1§1
TC413
4. IPS
TT223
11.474
TM113
4. IPS
TN214
12.129
TK313
4.324
TS11S
12.335
TCS22
4.443
TC414
12.394
TMX22
4.443
TX124
12.414
TM213
9.§97
TUP 15
12.554
TX413
9.294
TIM 2 4
12.722
Til 2 3
9.312
TX215
12.912
T M e23
9.S42
TNI 2 3
12.945
TS114
9.444
TS§23
12.945
TM S14
IS.§47
TS§15
13. sea
T S 214
1§.33§
TM115
is.sea
154
In order to scan these aodes, an adjustable end wall was designed
to aove In a reciprocating manner driven by an external aotor.
Figure 41 shows a schematic of the cross section of the applicator.
The
feed is via a waveguide with the narrow side wall contiguous to the
applicator wall and a coupling hole coaaon to both structures.
Six
beyond cutoff observation tubes, placed on the side of the applicator,
and a aeshed screen in the front endwall were provided to monitor the
specimens.
The fixed endwall or cover plate is then bolted onto the
aain cylindrical section.
The feeding waveguide is equipped with an
adjustable short and loop coupling to control input impedance.
The movable endwall was designed with a cascade of quarter wave
sections with vastly different characteristic impedances which transfer
the final iapedance to a very low value at the front wall surface
resulting in a non-contacting short circuit.13’
The structure is excited by a common aperture between the side wall
of the waveguide and the applicator wall as indicated above.
Waveguide
excitation was chosen over coaxial line excitation in anticipation of
operating the applicator at high power.
The common wall design operates
by loop coupling and thus electric breakdown problems are avoided.
The
waveguide is skewed at 45 degrees to the major axis of the applicator to
increase the number of modes that can be excited.
The center of the
coupling aperture is 3.5 inches(8.9 cm) from the front wall.
A novel means of controlling the coupling of the magnetic field
from the waveguide to the applicator provides not only a smooth coupling
VIEWING HOLES
TOP
VIEW
-{HHHHHlr
N.
U.
r*
MOVING
WALL
MOTOR
\
Figure «i
x.
waveguioe
Schematic diagram of the moving end vail multimode applicator.
156
adjustment but also a simple means to achieve a matched applicator.
Figure 42 shows a diagram of the magnetic field coupling mechanism.
In
the side view is shown a wire loop connected to the end of a threaded
metallic rod such that both the orientation as well as the vertical
position of the loop can be varied.
The combination of the variable
loop mechanism and the variable short in the waveguide section enables
optimal coupling of the generator to the applicator when loaded with
different specimens.
The degree of coupling is determined by observing
the input impedance of the applicator.
Detailed construction diagrams for the applicator are available
upon request to the authors.
9.3
9.3.1
Experimental results
Uniform heating
The experimental setup is shown in Figure 43.
The source is a
Raytheon (model PGH-100) microwave generator operating at 2.45GHz with
electronic control of output power.
approximately 400 watts.
The maximum available power is
The processed specimens consisted of two
styrofoam molds filled with fresh cement mortar.
are 0.25 inches thick.
rectangular prisms.
The walls of the molds
The mortar is formed into 4 cm x 4 cm x 16 ci
Six alcohol thermometers were used to monitor the
temperature of the specimens.
The early experiments used a commercial
microwave oven manufactured by General Electric (model JE2851H), 800
watts, and Figure 44a shows the position of the two molds in the oven.
The GE oven has a dimension of 16 inches x 13.5 inches x
157
TOP VIEW
GENERATOR
SIDE VIEW
VARIABLE
SHORT
WAVEGUIDE
L
a ppl ic a t o r
Figure 42
COUPLING
LOOP
Enlarged view of the magnetic field coupling mechanism.
adjustable
COUPLING
LOOP
RAYTHEON
MICROWAVE
SOURCE
Fl^ire 43
COUPLING
SHORT
AW
I MOVING
ENOWALL
Experimental setup used in studying uniform heating.
MOTOR
ORIVEN
WHEEL
159
Microwave
(o)
oven
BQOoH
(Tap vk«|
New applicator
t
(b)
T4
TS
Ti
(Top
n
T2
73
Plguro 44 Orientation of the Maples and positions of the theraoaeters in
the a) microwave oven and b) new applicator. (Mot to scale)
16®
12 inches (4®.6 ca x 34.3 ca x 30.5 ca) with an overhead ceiling
stirrer.
T1-T6 represent the positions of the theraoaeter.
teaperature uniforalty within the saaple can be aonltored.
Thus
Note that a
beaker filled with 600al of water is also placed in the oven to lower
the energy absorbed by the saaples to prevent steaalng and fracturing
even at the lowest power setting.
Figure 44b shows the placeaent of
slallar saaples and theraoaeters in the new applicator.
The speciaens
were supported by a 0.25 inch thick styrofoaa platfora such that the
geoaetrlc center of the speciaens are in the center of the applicator
when the applicator is in it shortest length.
Figure 45a is a plot of
individual teaperatures as a function of tiae within the conventional
aicrowave oven.
Figure 45b shows slallar results in the new applicator.
The eaphasis is placed upon the range of teaperature scattering; where
the new applicator has shown to result in auch less variation in
teaperature than the coaparable data for the aicrowave oven.
9.3.2
Mode identification
In order to validate the assuaptlon of the excitation of aany
aodes, it is necessary to identify the excited aodes.
The first aethod
of identifying the aodes is to aonltor the reflected signal on a strip
chart recorder as the spectrua of aodes are scanned.
The aodes are then
identified by Batching the predicted resonances with the observed
ainiaua reflected signals.
The second aethod is to use dielectric and
aagnetic probes to perturb the electric and aagnetic fields,
respectively.
It is well known that the insertion of a dielectric into
161
n
• • • • • T3
100.00
•••••T*
90.00
00.00
70.00
60.00
M.00
CL 40.00
30.00
20.00
-
10.00
-
0.00
10.00
0.00
20.00
30.00
Time (min)
100.00
90.00 -
CJ
00.00
««• T3
•
T4
• • • T5
-
70.00 -
0)
u oouw 3
® 00.00 M
0)
a . 40.00 i
30.00 -
E-
20.00 i,
10.00 -
0.00
0.00
10.00
00.00
30.00
Time (min)
n o u n 45
«) Taaparaturo proflla of eaaant aortar procasaad In a
cooaarcial aicroaaw own, b) taaparatura prof11a of caaant aortar
procasaad in tha naw applicator.
162
a region of high alactric field will lower the resonant frequency with
a slallar result for a aagnetic aaterlal Inserted into a region of high
aagnetic field.1* ’1*1 This aethod locates the field variations within
the applicator by the perturbation of the resonant frequency thus
identifying the specific resonant aode.
Although this aethod is precise
in Identifying specific resonances through the aapplng of electric and
aagnetic field variations, it was found to be a auch aore tedious and an
unnecessarily detailed aeans of Identifying resonant aodes.
The
resonant length aethod was used.
The waveguide was connected to an HP8350B signal generator,
directional coupler, and strip chart recorder as shown In Figure 46 and
a typical result Is shown in Figure 47.
The abscissa represents the
angular position of the driving disc with 0-0 corresponding to the
endwall closest to the front of the applicator.
The range, rc/2 to
n, is
continued in the lower diagraa.
A reference setting of coupling was necessary to deteraine the
resonances of the unloaded applicator.
To coapare with later data for
the aatched case, the applicator was first loaded with 600al of water
divided Into four styrofoaa cups, endwall positioned at 0-0, and aatched
by adjusting the coupling loop and short circuit.
The load was reaoved
and the solid line was observed.
Each relative alnlaua of the unloaded resonator (solid line)
corresponds to a specific resonant aode and is identified by calculating
the resonant length.
The results are shown in TABLE X.
nineteen resonances were observed.
Note that
When coaparlng TABLE X with the
163
AMPLIFIER
COUPLING
COUPLING
LOOP
SHOffT
HP8350B
IMOVING
enowall
wheel
Figure 46
Schematic diagram of the
resonance and observe mode overlap.
experimental
setup
to
identify
REFLECTED
SIGNAL
164
POSITION OF CNOWALL (6 . Podion)
Figure 47 The reflected signal as a function of the angular position of
tha aotor drlvan rotating disk for an unloadad (solid line) and a loaded
(dotted line) applicator.
165
TABLE X
Listing of identified aodes and the difference in cavity length between
the measured and predicted aodes.
Raaoaant m 4 i
lapty raao n a a t
cavity laaptb
(l a e a a a )
A Saaluta dlfZaraaca
kttHMS
aapariaaatal and
ebaoratical laaytba
(lacbaai
TE213
7. 777
#.#3#
T E 2 2 2 (a a b l » u o u a )
7.111
e.ese
T C 2 2 2 (a a S l R u a u a )
7.993
#.#75
T S S 13, TM113
S.2#5
#.•99
TS313
S . 437
e. i n
s.see
#.#•3
TMS23
9.431
• .in
Til 14
9.9S3
e.
1M(I
e.S2i
TCS22,
TS112
TMS14
TM114.
tie 14
TS314 or TSS13
(a a b i « u o u a )
us
IS.<14
e.
11.195
#.•93
123
Oaldan t i f l a d
11.490
TS223
11.97#
0.3C7
TM214
13.#32
#.#9#
TS124
13.479
TMeiS
13.97#
e.#«2
e.eae
TNS24
13.799
• .•73
is.iee
e.
13.199
#.3#9
TN123.
thus,
Tie 23
nets
139
theoretical calculations of T A B U IX, important differences should
benoted.
TABUS IX presumes a perfect cavity and Ignores the coupling
aechanlsa which shifts the resonant lengths froa their ideal value and
affects their observation.
Whether an allowable aode (TABLE IX) will be
observed (TABLE X) also depends upon the orientation and Insertion of
the coupling loop and the position of the short circuit.
It is
therefore expected that soae of the allowable aodes aay not be strongly
coupled and thus would not be observed.
Upon coaparison with T A B U IX
note that there are 31 distinct allowable resonances (there are 7
degenerate aodes).
Since nineteen resonances were observed, twelve
allowable resonances were not sufficiently coupled to produce observable
variations in reflection.
If another endwall position had been chosen
and the applicator were aatched, a different reflected signal profile,
corresponding to different excited resonances, would have been observed.
In soae instances the aeasured resonant length falls in between
theoretical values and consequently the particular aode cannot be
Identified.
These are the aablguous aodes of T A B U X.
The degenerate
aodes are indicated by two separate entries in the resonant aode coluan.
Since the thesis is that uniform heating depends priaarlly upon the
number of aodes and not specific field configurations, no atteapt was
Bade to determine these configurations.
The dotted line, Figure 47, represents the reflected signal with
the previously described load and matched applicator.
Note how smoothly
this curve varies with 6, signifying a considerable amount of aode
overlap and resulting constancy of input iapedance.
167
The effect of initially Batching at a different cavity length is
shown in Figure 48.
Here the magnitude of the reflection coefficient as
a function of cavity length for the applicator matched at the two
extreae cavity lengths is presented.
Note that the reflection
coefficients in the two cases are significantly different froa each
other but the length averaged reflection coefficient is about the saae
for both cases.
9.3.3
Applicator Batching
The coupling aperture can be viewed as a very short section of
beyond cutoff waveguide with an insertion loss of 11.1 dB for the given
length14* This calculation presents an upper bound to the insertion
loss since is ignores higher order excitation.
Thus the aperture
diameter was too saall to provide efficient coupling.
An initial
suggestion to improve coupling was to load the aperture with a material
with high dielectric constant and low loss thus electrically increasing
the size of the aperture.
This idea proved ineffective due to the high
reflection of energy froa the dielectric-free space interface.
These
experiaents led to the developaent of the described loop coupling
scheae.
The applicator was aatched in the following way.
1) The load was Inserted and the endwall set at an arbitrary position.
2) The coupling loop, position and orientation, was adjusted for nininum
reflection as observed by the directional coupler.
circuit was adjusted to ainiaize reflection.
Then the short
This procedure was
168
Magnitude of the reflection coefficient
1.00 -I
; o o o o o m a t c h e d a t minimum cavity length
m a t c h e d a t m a x im u m cavity length
0.80
0.60
♦
+
0 .4 0 -
0.20
o
-
o
o
♦
o
0 .0 0 T ‘ T »
7.0 0
I I
f »
| I
9.00
I 1 I
I I I H
I I I 'P
' T T I T T T . 1 T"|
11.00
13.00
Length of the a p p lica to r(in ch es)
Figure 48
Reflection coefficient as a function of applicator
aatched at nlniaua and aaxiaua cavity lengths.
length
169
repeated until a reasonable ainiaua was obtained.
3) The observation was then shifted to the standing wave Machine and the
procedure repeated until a aatch was obtained.
Figure 49 shows the Magnitude of the reflection coefficient as a
function of the length of the cavity when the applicator was Matched at
a cavity length of 7.3 inches(18.5
c m
).
Note that the MlniMUM power
efficiency when the cavity length is 10.2 inches (25.9 ca) is 96% and
the results support the thesis that a large nuaber of overlapping nodes
leads to a nore constant input lapedance.
Figure 50 shows the effect of different loads, 600nl and 1200nl of
water, on the Magnitude of the reflection coefficient as a function of
the length of the cavity.
Both styrofoan and pyrex containers were used
and positioned at different parts in the applicator and it was found
that neither the Material of a low loss container nor the position of
the loads had a significant effect on the results.
It can be seen that
the larger load results in a SMOother variation in the reflection
coefficient.
This result demonstrates that a larger number of
overlapping Modes leads to a reduced variation in input lapedance as the
load is increased and therefore the applicator becoaes less sensitive to
load variations.
9.3.4
Coaparlson of rectangular and circular geoaetrles with respect to
load variations
It is expected that the circular applicator would be less
sensitivity to the size of the load than the rectangular applicator due
170
coefficient
0.20
Magnitude
of the
0.30
reflection
0.40
0.10
0.00
7 .0 0
9 .0 0
Length
11.00
13.00
the applicator(inches)
Figure 49 Magnitude of the reflection coefficient as a function of the
length of the applicator under aatched conditions for 600el water load.
171
Magnitude of the reflection
coefficient
1.00
o o o o o 6 00m l of water load in 4 cu p s
♦
i 2 0 0 m l of water load in 8 c u p s
0.80
0.60
0.40
0.20
0.00
7.00
9.00
11.0 0
13.00
Length of the ap p lica to r(in ch es)
Figure 50
Magnitude of the reflection coefficient as a function
applicator length for different degrees of loading.
of
172
Power
absorbed(w atts)
800.00
600.00
400.00
200.00
0Q£Q£ water in r e c t a n g u la r oven
aaaaa water in new ap plica tor
0.00
/
|
0.0 0
I
I
I
I
I
!
1
I
I
|
500.00
i
I
I
I
I
*
I
i
I
t
J
1000.00
:
:
I
i
'
«
i
1500.
Total volu m e(m l)
Figure 51 Comparison of rectangular and circular applicators with respect
to absorbed power as a function of load variation.
173
to aatchlng and aode overlap.
comparison.
Figure 51 shows the results of this
The ordinate represents the total power absorbed In the
water load as the voluae is varied.
Note that the circular applicator
is aatched with the 600al voluae, and as the load is increased or
decreased, less power is absorbed.
The rectangular applicator, however,
shows a aonotonlc Increase in absorbed power as the voluae is increased.
Thus the circular applicator is less sensitive to load size.
The
relative position of the two curves is due to the different aagnetron
power levels.
9.4
Conclusion
A new applicator has been described that exhibits the following
improvements when coapared with a standard aicrowave oven.
1.
A more uniform teaperature distribution.
2.
Higher efficiency.
3.
Lessened sensitivity to load variation
These results are obtained by scanning the larger number of modes in a
circular geoaetry where aode overlap reduces the variation in input
iapedance.
APPENDIX A
Theory and Applications of the Modified Infinite Saaple Method
A.l
Theoretical derivations
Figure 52 shows a diagraa of a saaple filled coaxial line with a
teflon spacer with a thickness of d.
The iapedance of the air filled
coaxial line is
(68)
The iapedance of the air filled waveguide is
(69)
The iapedance of the spacer filled coaxial line is
(70)
and the corresponding equation for the waveguide is
(71)
174
175
Z,ample
1
2 Reference
i plane A'
Figure 52
A pictorial diagraa of tha cascaded transmission line.
176
The impedance of the staple filled coaxial line la
2%
ln(^) [ItsSOiS]^
a
€,^
(72)
and for the waveguide
X
9l0
(73)
2a'
where
where '1' Is replaced by either 'O', 'sp' or 'saaple' accordingly,
b/a la ratio between the outer and Inner dimensions of the coaxial line,
a' la the smaller dimension of the waveguide.
p|, ji|p, and nIlipit are the
magnetic permeabilities of the air filled line, spacer filled line, and
the sample filled line, respectively.
The magnetic permeabilities of
the spacer filled line and the sample filled line are identical to the
aagnetic permeability of free space, *i,.
ct, e|p, and Clup;t are the
177
electrical permittivities of the air filled line, spacer filled line,
and the sample filled line.
The electrical permittivities of the spacer
filled section and the air filled section are complex values
(76)
and
m
where e|p' and
mm m'
-i °
(77)
are the relative permittivities of the spacer and
the sample, respectively.
a|p and o|#^ le are the conductivities of the
spacer and the sample, respectively.
« Is the radial frequency of the
applied signal.
The normalized Input Impedance of the cascaded spacer and sample
filled line Is related to the standing wave ratio and the phase shift
relative to a reference short circuit by
(78)
where S Is the standing wave ratio and • is the phase shift.
The impedance of the cascaded spacer and sample filled line is related
to the impedances of the individual sections by
,.A _ [g— i.co8h(rd) ♦Z^lnhd'd))
2
[ ^ * J*coah(r<J) ♦sinhd'd) ]
zn>
(79)
The relative permittivity and the conductivity of the unknown saaple can
be solved for by equating the two load lapedances and making the
appropriate substitutions.
l
The result for the coaxial line is
. A*/5Zsinh (I'd) -cosh (I'd) ,.
1J
(set
. X J e Z s i n h (rd) - c o s h (rd) ,,
■ l w l m l — *— ® - --------------------]2
(81)
^=-sinh(rd)-Xcosh (fd)
-=-sinh(rd) -^cosh(rd)
r is the propagation constant of the transsisslon line inside the spacer
and
S-jt*n(4)
Jm ---------- Z---- L_
l-jStan(3)
&
The results for the waveguide are
(82)
179
o * - « Im[
2ai
)2-±-
(84)
»»o
Z_sinh(rcD -ZgA'comhird)
B * — * ------------— ----------Zr,A,Z~J±tBivh.(Td) -cosh(rd)
(85)
where
S-jtan*
^
(86)
1 -jStan&
Two Fortran codes have been written to solve for the constitutive
properties.
A.2 contains the code used for the coaxial line.
contains the code used for the wave guide.
A.2
Fortran code used for the coaxial line
PROGRAM JCFSREF
C
THIS CODE CALCULATES THE
C
THE INFINITE SAMPLE COAXIAL LINE SYSTEM WITH A TEFLON
C
C
SPACER
COMPLEX PERMITTIVITY OF
A.3
180
C
INPUTS WILL BE FREQUENCY, DIELECTRIC CONSTANT AND
C
CONDUCTIVITY
C
OF THE SPACER, THE THICKNESS OF THE SPACER, THE SWR, AND
C
CHANGE IN SW MINIMUM
REAL*4
ESPACE,CSPACE,D ,FREQ,SWRDB,DELTXMIN,PI,MUO,E0
REAL*4
W,LAMBDA,ALPHA,BETA,PHI,SWR,XMINSH,XMINID
REAL*4
ESAM, CONSAM
COMPLEX*8
AJ,ESPC0M,GAM1A,A,TEMP,SH,CH,DUM
INTEGER BOO
WRITE(*,*) ' ENTER THE DIELECTRIC CONSTANT OF THE
1
SPACER '
READ(*,*) ESPACE
WRITE(*,*) ' ENTER THE LOSS TANGENT OF THE SPACER ’
READ(*,*) CSPACE
WRITE(*,*) ' ENTER THE THICKNESS OF THE SPACER(M) '
READ(*,*) D
10
WRITEP,*)
' ENTER THE FREQUENCY (GHz) '
READP,*) FREQ
FREQ-FREQ*1.E9
WRITE(*,*) ' ENTER THE SWR OF THE UNKNOWN LOAD (dB) '
READP,*) SWRDB
WRITE(*,*) ' ENTER THE POSITION MIN OF THE SHORT(CM) '
READCO
XKHISH
XMINSH-XMINSH* 1. E- 2
WRITE(*, *) ' ENTER THE POSITION KIN OF THE UNKNOWN
1
LOAD(CM)'
READ(*,*) XMINLD
XMDHD-XMINLD* 1. E-2
DELTXMIN-XMINID-XMINSH
PI-ACOS(-1.)
MUO-1.2566E-6
EO-8.8544E-12
W-2.*PI*FREQ
LAMBDA-3.E8/FRE0
AJ-(0.,1.)
ESPCOM-(0.,0.)
ESPCOM-E0*ESPACE-AJ*CSPACE*E0*ESPACE
APPROXIMATE VALUES FROM RAMO
***•**••*
ALPHA-CSPACE*W*SQRT(MUO*EO*ESPACE)/2.
BETA- (1. +CSPACE* *2/8. )*W*SQRT (MU0*E0*ESPACE)
GA»MA-(0. ,0. )
GAMtA-ALPHA*AJ *BETA
WRITEC,*)
'PROPAGATION CONSTANT WITHIN SPACER '
WRITE (*, *) GAMfA
PHI-PI*4.*PI*DELTXMIN/LAMBDA
WRITEC,*)
'PHASE SHIFT Or SPACER-LOAD '
WRITEC,*) PHI
SWR-SWRDB/20.
SWR-10.**SWR
A- (SWR-AJ*TAN(PHI/2.))
1
/{(l.-AJ*SWR*TAN(PHI/2.))*SQRT(E0))
WRITEC,*)
' A - ', A
SH-(CEXP (GA»f«A*D)-CEXP (-1. *GAF«iA*D)) /2.
CH- (CEXP {GAH4A*D)+CEXP (-1. *GA»HA*D)) /2.
WRITEC,*)
'GA»t!A*D - ', GAM4A*D
WRITEC,*)
’SD1H(GAM1A*D) - ', SH
TEMP-(A*CSQRT(ESPCOM)*SH-CH)/
1
(SH/CSQRT(ESPCOM)-A*CH)
ESAH-(1./E0)*REAL(TEHP*TEMP)
COHSAM— 1. *W*AIHAG (T M > * T E M P )
WRITE(*,*) 'THE RELATIVE DIELECTRIC CONSTANT OF THE
1
SAMPLE IS '
WRITEC,*) ESAM
WRITE(*,*) 'THE CONDUCTIVITY OF THE SAMPLE IS (S/M)
WRITEC,*) CONSAM
WRITEC,*)
’THE LOSS TANGENT IS ’
WRITEC,*) -l.*REAL(TB(P*TEMP)/AIMAG(TEMP*TIMP)
WRITEC,*)
'RELATIVE COMPLEX PERMITTIVITY '
WRITEC,*) TEMP*TD4P/EO
WRITEC,*)
'DO YOU WANT TO REPEAT ? (1-YES, 2-NO) '
READC,*) BOO
IF (BOO.ESQ. 1) GOTO 10
END
A.3
Fortran code used for the waveguide
PROGRAM EEFSREF
C
THIS CODE CALCULATES THE
COMPLEX PERMITTIVITY OF
C
THE INFINITE SAMPLE WAVEGUIDE SYSTEM WITH A TEFLON
C
SPACER
C
C INPUTS WILL BE FREQUENCY, DIELECTRIC CONSTANT AND
C
CONDUCTIVITY
C
OF THE SPACER, THE THICKNESS OF THE SPACER, THE SWR, AND
CHANGE IN SW MINIMUM
REAL*4
ESPACE,CSPACE,D,FREQ,SWRDB,DELTXHIN,PI,MUO,E0
REAL *4
W ,LAhfJDA,ALPHA,BETA,PHI,SWR,XMINSH, XMINID
REAL*4
ESAM, CONSAM, AAA, THETA, Z0
COMPLEX*8
AJ,ESPCOM,GA»MA,A,
TDff,SH,CH,DUM,B ,ZSP,ESAMCOM
INTEGER BOO
WRITE(*,*) ’ ENTER THE DIELECTRIC CONSTANT OF THE
SPACER '
READ(*,*) ESPACE
WRITE(*,*) ’ ENTER THE LOSS TANGENT OF THE SPACER '
READ(*,*) CSPACE
WRITEC,*)
' ENTER THE THICKNESS OF THE SPACER(M)
'
READ(*,*) D
WRITEC,*)
' ENTER THE WIDTH OF THE WAVEGUIDE(M)
'
READC,*) AAA
WRITEC,*)
' ENTER THE FREQUENCY (GHz) '
READC,*) FREQ
FREQ-FREQ*1.E9
WRITEC,*)
' ENTER THE POSITION MIN OF THE SHORT(CM) '
READC,*) XMINSH
WRITEC,*)
'ENTER THE SWR OF THE UNKNOWN LOAD (dB) '
READC,*) SWRDB
WRITE(*,*) ’ OTTER THE POSITION MIN OF THE UNKNOWN
LOAD(C M )'
READC, *) XMINIJ)
DELTXHIN-(XMINID-XMINSH)*1.E-2
PI-ACOS(-1. )
MU0-1.2566E-6
E0-8.8S44E-12
W-2CPITREQ
LAMBDA-3.E8/FREQ
LAMBDA-LAMBDA/SQRT(1.-(LAMBDA/(2*AAA))**2)
AJ-(0.,1.)
ESPCOM-(0.,0.)
ESPCOM-E0*ESPACE-AJ*CSPACE*E0*ESPACE
APPROXIMATION OF THE PROPAGATION CONSTANT OF SPACER*
GAFtIA-(0. ,0. )
GAM1A-CSQRT( (PI/AAA)**2 - MU0*ESPACE*E0*W**2
1
*(1.-AJ*CSPACE/(2.*MU0*W**2))**2 )
WRITEC,*)
'PROPAGATION CONSTANT WITHIN SPACER '
WRITEC,*) GAFMA
PHI-PI+4.*PI*DELTXMIN/LAMBDA
WRITEC,*)
'PHASE SHIFT OF SPACER-LOAD '
WRITEC,*) PHI
SWR-SWRDB/20.
SWR-10.**SWR
A-(SWR-AJ*TAH(PHI/2.))/(1.-AJ*SWR*TAN(PHI/2.
WRITEC,*)
' A - ’, A
SH-(CEXP (GAH4A*D)-CEXP (-1. *GA»tiA*D))/2.
CH-(CEXP (GA»t<A*D)-KTEXP (-1. *GAMMA*D) )/2.
WRITEC,*)
'GA»tlA*D - ', GA»t4A*D
WRITEC,*)
'SINH(GA>tiA*D) - ', SH
ZO-SQRT(MUO/EO)/SQRT(l.-(3.E8/(2.*AAA*FREQ))
ZSP-CSQRT(MUO/ESPCOM)
1
/CSQRT(1.-1./
1
(2.*AAA*FREQ*CSQRT(MUO*ESPCOM))**2 )
B-(ZSP*SH-Z0*A*CH)/(Z0*A*SH/ZSP-CH)
ESAMCOM-(MU0+(B/(2.*AAA*FREQ))**2/MU0)/B**2
TDfP-(A'CSQRT(ESPCOM)*SH-CH)/
1
(SH/CSQRT(ESPCOM)-A*CH)
ESAM-(1./E0)*REAL(ESAMCOM)
CONSAM--1.*W*AIMAG(ESAMCOM)
187
SKIN - (2.*SQRT(ESAM*EO)*SQRT(1.-(1./(2.*FREQ*AAA*
1
SQRT(MUO*BO*ESAM)))))/ (SQRT(MUO)*CONSAM)
OPEN (UNIT - 7, FILE - 'LPTli')
WRITEC,*)
1
'THE RELATIVE DIELECTRIC CONSTANT OF THE
SAMPLE IS '
WRITEC,*) ESAM
WRITEC,*)
'THE CONDUCTIVITY OF THE SAMPLE IS (S/M) '
WRITEC,*) CONSAM
WRITE(7,123) ESAM,CONSAM,SKIN
•123
FORMAT(3F15.4)
CLOSE(7)
WRITEC,*)
'THE LOSS TANGENT IS '
WRITEC,*) -1 ■*AIMAG (ESAMCOM)/REAL (ESAMCOM)
WRITEC,*)
'RELATIVE COMPLEX PERMITTIVITY '
WRITEC,*) ESAMCOM/EO
WRITEC,*)
'DO YOU WANT TO REPEAT ? (1-YES, 2-NO) '
READC,*) BOO
IF (BOO.EQ.l) GOTO 10
END
APPENDIX B
The Electrical Field Distribution of a Dielectric Sphere in a Dielectric
Hediua
A review of the nomenclature that will be used in the following
derivations will be provided at this tiae.
The potential due to an
ideal dipole is
{orrl
(87)
r3
where m is the vector of the dipole aoaent and r is the vector direction
of observation.
(87) can be written as
+ - Oncoa*)
ra
(88)
The potential due to a non-ideal dipole is
(mcoaO) ^ ms2 (Scoa’B-ScosO) „
ra
2r*
(89,
where the distance of observation, r, is auch greater than the
separation between the opposite poles of the dipole, s.
The solution of aany of these problems will entail the solving of
Laplace's equation.
The general solution of Laplace's equation in
spherical coordinates is
188
189
V*#«0
(»)
• “£ (ABr 8^-5£ - ) P B (coa«)
a«c
-T
(91)
where P3(cos0) are the Legendre polynomials.
Figure 53 shows a schematic a static electric field E| directed in
the positive z axis applied to a dielectric sphere with dielectric
constant equal to
e-* end radius a placed within a dielectric medium with
dielectric constant equal to
Laplace's equation must be solved for
both inside and outside of the boundaries of the sphere.
The general
solution to Laplace's equation in spherical coordinates is
(92)
The solution of Laplace's equation in region 1 is
(93)
) P_(cos6)
The solution of Laplace's equation in region 2 is
(94)
i?e
Figure 53
A dielectric sphere labedded In a dielectric aediua of
different dielectric constant.
a
191
V * 4 ,-0
►a- t
(95)
co.«)
Ft
(96)
1
In order to determine the coefficients Ag, Bs, Ca, end Da, the boundary
conditions aust be satisfied
(♦,) r _«-fi’
orcoa0
(97)
{98)
or
(100)
(l01)
and
#2
is bounded at r-0
(102)
192
Combining (94) and (97) recults in
* 1
Aj - 0
for
n
K - -E,
for
n - 1
and
B,
— jSjPa (c°s0)-£orc°«0
£•#
f103)
f
Combining (96) and (102) results in
Da - 0
for all n
and
Q tm^ C ar nP n (c 080)
(104)
Combining (98), (103), and (104) results in
B„
,n*l
for
«Cn«»
n # 1
B,
- j - w
for
(105)
n - 1
Combining (101), (103), and (104) results in
(106)
193
( Ba1'n *1.--)Pa (cosO) -a^cos®] - c , ^ n C . a a ,P.(coa6
-c, gfl(n4l)
a®
for n
0
m€tnCBMa l
} (1*7)
(1«8)
1
2B
* ■!
c
*aui
(109)
for n - 1
In order to satisfy both (105) and (108), both CQ and BQ aust be zero.
Coabining (106) and (109) results in
B.ma2Bt
1
(110)
°«a*2«i
c . ~3ca3>
(in)
*7+2*1
Finally, coabing Ba-0 and CD-0 for n<>l with (103), (104), (110), and
(111) results in
,U J’
194
1
- **
B.Z
^
(H3)
Recalling that an external field E, directed In the positive z axis In a
homogeneous medium will give rise to a potential
• — ECZ
Consider
(114)
4.4 ' and 4/4 to be defined as the potentials due to an apparent
surface charge,
then the potential shown In (112) and (113) can be said
to be
*,-•1 ♦ •
<U5>
• .- • a
(116)
where the apparent surface charges will result in effective potentials
in vacuum
,,,7)
€2*2tx
(118)
195
(117) can be also viewed as a potential caused by an Ideal dipole at the
center of an evacuated spherical cavity with radius a with a dipole
aoaent
mm
aiB0E
Furthermore, the field that is associated with the potential
«,♦2^
g0
0
(119)
is
(120)
The total field within the dielectric spheres is then
3C
«MD
APPENDIX C
Rayleigh model
Froa (119), each sphere will have a apparent dipole aoaent of
«■[
* 2~<l 1 a }E0r
(122)
Figure 54 shows a scheaatic of N spheres placed within a larger sphere
with a radius a ’.
The total dipole aoaent of N spheres will be
,123’
If the larger sphere is now considered to have a uniform!effective)
medium with a dielectric constant
et as shown in Figure 55, then by the
saae formalism as the previous example the effective dipole moment of
the large sphere will be
I12*'
If
et is selected to cause ^ to be equal to
(123) and (124) results in
196
then combining
197
Figure 54 N nueber of dielectric spheres iebedded in a dialactrlc eediua
with a different dielectric constant bounded by a arbitrary large sphere.
198
Figure 55
Equlvelent dielectric eediua as the previous figure.
199
(125)
a*N
mO
« / 2«,
(126)
or
(127)
*****
(Cj -Cj )
where
a 3JV
(128)
is the volume fraction of the saall spheres.
Equation (127) is the first effective medium relationship.
methods have been used to derive this relation.
Various
Synonymous names given
to this relation are Clauslus-Mossotti relation, Lorenz-Lorentz
relation, Wagner relation, Maxwell-Garnett relation, and the mean field
approximation.
Extensions of this model to other inclusion shapes have
been made by Sillars for ellipsoids and Frlcke for oriented ellipsoids.
APPENDIX D
Bruggeman symmetric model
Equation (127) is a satisfactory relation only for very dilute
mixtures.
Numerous schemes have been developed in expanding it to
higher concentrations mixtures.
One scheme is Bruggeman’s symmetrical
model.
Consider Figure 56 where the mixture is composed of a volume
fraction 6j of dielectric spheres with a dielectric constant of
immersed in an "effective” dielectric medium with dielectric constant of
er
Furthermore, there is another mixture composed of a volume fraction
l-6j of dielectric spheres with a dielectric constant of e, immersed in
the same "effective" medium with a dielectric constant of e(.
The polarlzabillty of the "effective" medium with the "effective"
dielectric constant is
P-
<c»~1)go
(129)
4m
Recalling that the effective field within the dielectric sphere immersed
in a dielectric medium is given by (121), the internal field within the
sphere with a dielectric constant of e, is then
The total polarization caused solely by the spheres with a dielectric
200
figure 56
Bruggeaan's syaaetrical aodel.
202
constant of
Is
...
(131)
*>
—
Combining (130) and (131) results In
(132)
Siailarly the field within the dielectric spheres with dielectric
constants of
is
(133)
The total polarization caused by the voluae fraction 6,* of dielectric
spheres with dielectric constant equal to £• is
(134)
2 2
4ff
Containing (130) and (131) results in
(135)
Recalling that the sua of the voluae fractions is
203
1-V«2
(136)
The total polarization of the aixture aust be conserved
P-P^Pj
(137)
Finally, coabine this with (129), (132), and (135) results in
3«#
1 2«#*Cj
(138)
2 2t9+€7
Equation (138) is the Bruggeaan's syaaetric relations.
Synonyaous
naaes given for this aodel are Bottcher's aixture relation, Coherent
Potential approxiaation, and T-aatrix approxiaation.
Extensions of this
aodel to other inclusion shapes were aade by Polder and van Santen*1*
for oriented ellipsoids and Hsu1M for oriented ellipsoids.
APPENDIX E
Bruggeaan asyaaetrlc aodel
Another aodel that la applicable to higher concentration mixtures
la alao an extension of Rayleigh'a relation repeated here
(139)
This aodel la obtained by doing the following substitution
«,
by
by
«i
a
*>
t #*A«.
(14B)
«#
(141)
k
by
t s
;
(142)
resulting in
...
2«9+2Ac,+«#
204
A»a
*2*290 1 ~b2
(143)
205
r
i
1-1 *2
3C.*2Ac.
Ac, _ (3c,*2Ac,) (C,-C,)
AA,"
(144)
C,+2C,
«i*2c,
1
(145)
l-A,
which is approxicately equal to
A « , . 3t,(Ca-C,)
AA,
for €(» > A C (-
c ,+2 c ,
1
(146)
i-A,
In the infiniteslaal licit this becoaes
3«.<«a-4.> 1
35^
C,*2C.
(147)
1-6,
The solution of this differential equation with the boundary conditions
of
C,(6,-0)-Cj
(148)
C.(«,-l)-C2
(149)
and
206
results in
-
1
(€,-€.) ( ^ ) 7 -(l-fia) («,-«*)
0*
Equation (150) Is Brugqeaan's asymmetrical relation.
(1M)
In essence,
this relation is determined by consistently using Rayleigh's relation
for infinitely dilute mixtures while continuously adding infinitesimally
snail anount of inclusions.
Synonymous names of this model are differential effective medium
approximation, self consistent methods, and Integral method relations.
Extensions of this model to other inclusion shapes have been made by
Niesel for randomly oriented needles and flakes1**, Meredith and Tobias
for oriented spheroids1**, Morabin et. al. for spheroids1*', and
Veinberg for spheroids1**.
APPENDIX r
Looyenga model
A third extension of Rayleigh’s aodel for application to higher
concentration mixtures is Looyenga's aodel.
The schematic dlagraa is
shown in Figure 57.
Consider two concentric spheres under an externally applied uniform
electric field.
The saaller sphere has a radius of a and a dielectric
constant of
The larger sphere has a radius of b and a dielectric
constant of
This is Identical to Rayleigh's problem in which the
solution is repeated here
,J-<1------ ]
(151)
(151) can be rearranged to give
a -
2S l h
(152)
* 2Cj +C# C^C,
where 6,a becomes a function of
C
Consider now that the effective dielectric constant is composed of
a different mixture as shown in Figure 58 where
CjH/Al,
207
(153)
208
Figure 57
Looyenga'• aodel.
209
Flgur* 58
A aodel defined to be equivalent to the previous figure.
210
t4»t.-At.
(154)
and the new voluae fractions
fijel-fla
&a
foz
for
t, medium
(155)
t4 medium
(156)
Further consider a Taylor series expansion of 6. about ia£(
fl2 (t.-At.)
Aj (t.+At.)
(t.) -At.Aj (t.) (At.)
(t.) ♦...
-&a (t.) ♦At.Ajft.) (At.) **"(«.) ♦• • •
The key is to relate 6,' to 6^{e4-aet), M e . )» and
)-
*157 >
(l58)
Consider
*;-(l-A;)«a (t.*At.) ^ a « a (t.-At.)
(159>
..
(t.)
a 6 a (t.-At.) ~A2 (t.+At.)
(160)
or
Combining (157), (158), and (160) results in
211
*•_ i _ l r
* J* 2 T [
14«.
(161)
Rayleigh’s solution of Figure 57 is
fl._
2c.+2At,*<.-Ac.
2 2c#+2Ac#*e# c#-»-Ac#-«.*A«#
(162)
(163)
* 6c,*4Ae,
(164)
* 2
6 €#
Combining (161) and (164) results in
(165)
3«#6a («#) *26£(c#) "0
Solving (166) with the following boundary conditions
results in
6,-0
for
6,-1
for
et
■ 6;
(166)
212
l
1
« 7 -«7
l
i
« 7 -.7
*2
«1
(167)
or
(168)
This Is Looyenga’s relation.
Landau and Liftschitz1*9.
It has been independently derived by
Extensions of this aodel to other inclusion
shapes have been made by Lai and Par shad15*.
REFERENCES
1.
C. P. D« Loor, Appl. Scl. Res. B 9, 297 (1961).
2.
A. R. von Hlppel,
York, 1952).
3.
G. P. de Loor, Phd Thesis (Excslslor, Leiden, 1956).
4.
J. B. Hasted and H. A. Shah, British J. Appl. Phys. 15, 825 (1964).
5.
M. A. Shah, J. B. Hasted, and L. Moore, British J. Appl. Phys. 16,
1747 (1965).
6.
A. R. von Hlppel,
York, 1952).
7.
F. H. Wlttaann, and F. Schlude, Ceaent and Concrete Research 5, 63
(1975).
8.
W. R. Tinga and E. M. Edwards, J. Microwave Power 3, 114 (1968).
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J. P. Reboul, Revue Physique Appliquee 13, 8i383 (1978).
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Dielectric Materials and Applications (Wiley, New
10.
M. Sucher and J. Fox, Handbook of Microvave Measurements,
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K. Gorur, M. K. Salt, and F. H.
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12.
F. Henry, Ph.D. Thesis,
1982).
Vols. I,
Wlttaann, Ceaent and Concrete
(Universit* Pierre et Marie Curie, Paris,
13.
G. P. De Loor, Appl. Scl. Res. B 9, 297 (1961).
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F. H. Wlttaann, and F. Schlude, Ceaent and Concrete Research 5, 63
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15.
M. Moukwa, M. Brodwln, S. Christo, J. Chang, and S. P. Shah, Ceaent
and Concrete Research 21, 863 (1991).
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S. M. Christo, M.S. Thesis (Northwestern University, Evanston, II,
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17.
M. Sucher and J. Fox, Handbook of Micromave Measurements,
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213
Vols. I,
214
18.
C.E.R.I.L.H., Hesure de la chalaur da hydration daa ceaents par la
aethod du calorleaatra da langebant, Lab/6827, 2.7 (1976).
19.
W. Eital, Silicata Sclanca V, 428 (1966).
28.
W. C. Chaw, K. J. Olp, and G. Otto, IEEE Trans. Gaos. Raa.
Sans. 29, 42 (1991).
21.
G.
Otto, W. C. Chaw, and J. F. Young, IEEE Trans. Instr. Maas.
48, 4 i742 (1991).
22.
Suchar and J. Fox, Handbook of Microwave Measurements, Vols. I,
II, III (Brooklyn Polytechnic Press, New York, 1963).
M.
23.
M. Houkwa, M. Brodwin, S. Christo, J. Chang, and S. P. Shah, Ceaent
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1504
Electrodynamics of Continuous Media
VITA
John Tse-YUan Chang
Birthplace i Taiwan
B.8.I.I. Northwestern University 1988
H.S.E.K. Northwestern University 1969
List of Publications
REFEREED JOURNAL PAPERS
1. M. Moukwm, M. Brodwln, S. Christo, J. Chang, and S.P. Shah, "The
Influence of the hydration process upon alcrowave properties of
cementa", Ceaent end Concrete Research, vol. 21, pp. 863-872, 1991.
2. R.6. Hutchison, J.T. Chang, H.H. Jennings, and M.E. Brodwln,
"Thermal acceleration of portland ceaent aortars with alcrowave energy",
Ceaent end Concrete Research, vol. 21, pp. 795-799, 1991.
3. J. Cheng and M. Brodwln, "A new applicator for efficient uniform
heating using a circular cylindrical geometry’, Journal of Microwave
Power end Electromagnetic Energy, vol. 28, no. 1, pp.32-48, 1993.
4. J. Cheng and M. Brodwln, "Microwave characterization of notarial*
using the variable Impedance method", submitted.
5. J. Cheng, M. Brodwln, and J. Hatz, " Microwave polymerization of
monomer impregnated concrete", submitted.
6. J. Chang and M. Brodwln, "Uniform microwave heating of fresh
mortar", submitted.
7. B.J. Christensen, T.O. Mason, H.M. Jennings, J.T. Chang, and M.E.
Brodwln, "Measurement of porosity In hardened cement pastes using
microwave energy", manuscript In preparation.
8. J. Chang and M. Brodwln, "Microwave characterization of the
development of capillary porosity of hydrating cementltlous materials",
manuscript In preparation.
9. J. Chang and M. Brodwln, "A precise resonant cavity method to
characterize low loss/thin section materials", manuscript In
preparation.
221
222
w u t m a
papers
1.
J.T. Chang and M.E. Brodwln, "A noval dynamic high ordar multimode
microwave applicator*, Proceedings of tha 27th Microwave Power
Symposium. Mash. D.C., International Microwave Power Institute, p. 100,
1992.
* 2. M. Moukwa, M. Brodwln, S. Christo, J. Chang, and S.P. Shah,
"Microwave characterization of ceaent hydration", Materials Research
Society Symposium Proceeding, vol. 245, pp. 253-258, 1992.
3.
M. Brodwln and J. Chang, "A new alcrowave oven for efficient
uniform heating based upon a circular cylindrical geoaetry", SMBO
International Microwave Conference Proceedings. Sao Paulo, Brazil, pp.
723-727, 1993.
* 4. J. Metz, J. Chang, M. Brodwln, "Microwave Induced polymerization
of aononer impregnated hardened ceaent", 1994 Soring Meeting of the
Materials Research Society. San Francisco, California, 1994.
5. M. Brodwln and J. Chang, " Microwave characterization of cementsi
total capillary porosity", International Microwave Power Institute.
Chicago, 1994.
6. M. Moukwa, M.E. Brodwln, S.P. Shah, "Microwave heating applied to
the curing of Mortars”, International Conference on Microwave and High
Frequencies, Nice, France, pp. 209- 212, 1991.(acknowledged)
* Refereed conference paper
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