INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent epos the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, prim bleedthrougb, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted Also, if unauthorized copyright material had to be removed a note will indicate the deletion. Oversize materials (e.g^ maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the bade of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. 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.) 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Lai, R. Parshad, Journal of Physics D 6, 1363 (1973). and R. Santinl, Rev. Gen. Electr. 76, 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 MMNHW

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