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University Microfilms international Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8418397 P erl, Je ffe ry Phillip COMPLEX MICROWAVE DIELECTRIC PROPERTIES OF LIQUIDS, SOLUTIONS AND EMULSIONS Illinois Institute o f Technology University Microfilms International Ph.D. 1984 300 N. Zeeb Road, Ann Arbor, Ml 48106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. COMPLEX MICROWAVE DIELECTRIC PROPERTIES OF LIQUIDS, SOLUTIONS AND EMULSIONS BY JEFFERY P. PERL Submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy in Chemical Engineering in the School of Advanced Studies of Illinois Institute of Technology Approved_ Adviser .ORIGINAL ARCHIVAL COPY Chicago, Illinois May 1984 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENT Chemical Engineers rarely become involved in research of the type described in this work. I have therefore found it necessary to seek guidance from a wide variety of talented people. First and foremost, I would like to acknowledge my advisor, Professor D. T. Wasan for allowing me a rather wide latitude in pursuing my research goals while at the same time keeping the more specific ob jectives in focus. I would like to thank Dr. Howard E. Bussey of the U.S. National Bureau of Standards, Boulder, Colorado, for his friendship, patience and above all the many hours spent discussing and demonstrating electro magnetic properties measurement techniques. This work would not have been possible without his guidance. Thanks also to his colleagues at the Bureau, Messrs. Jesch, McGlaughlin, Jones and Reese for assistance during my visits there. Thanks to Professor Robert H. Cole for a two month visit at his Brown University Dielectric Relaxation Laboratory and to his Research Associate, Dr. Paul Winsor IV for training on the Time Domain Reflectometry Apparatus, and for their contribution to Chapter III. Messrs. Art Vogt and Dave Bradley of Electronics and Instrument Services at IITRI, and Dr. Gerry Saletta and Mr. Joe Sydejko at IIT provided for the loan of valuable electronic test gear. Drs. Daryl Doughty and Phil Lorenz of the National Institute for Petroleum and Energy Research and Mr. Jim Klouda of Elite Electronics also provided equipment as needed. A special thanks to A1 Brooks of the Hewlett Packard Company and his colleagues, Jim Fitzpatrick and Mike Bechtold for the loan and gift of various pieces of equipment. Thanks are also due to my friend T.S. Ramakrishnan for assistance in editing parts of this work,to Professor William M. Langdon for inital encouragement and continued assistance, to my family and friends who put up with me, and to Linda Sundin for the many late nights spent pre paring this manuscript. This work was supported in part by DOE Grant DE-AC19-80BC10069 to Illinois Institute of Technology and by an Amoco Foundation Doctoral Fellowship awarded to Jeffery P. Perl. J.P.P. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS Page ACKNOWLEDGEMENT.................................................... iii LIST OF T A B L E S .................................................... vi LIST OF FIGURES.................................................... vii A B S T R A C T ........................................................... ix CHAPTER I. INTRODUCTION.......................................... 1 Complex Dielectric Properties of Liquid Water . . . . Summary of Work . . . ............................... II. COMPLEX DIELECTRIC PROPERTIES OF MACROEMULSIONS USING A CALIBRATED MICROWAVE RESONANCE CAVITY DIELECTROMETER. . 6 . 6 Introduction...................................... Experimental........................................ R e s u l t s ............................................ Discussion.......................................... S u m m a r y ............................................ III. 1 4 DIELECTRIC RELAXATION OF 1-PROPANOL/WATER MIXTURES. 8 21 32 40 . . 41 Introduction........................................ Experimental........................................ R e s u l t s ............................................ Discussion.......................................... 41 43 48 55 MICROWAVE INTERFEROMETRIC DETERMINATION OF DIELECTRIC PROPERTIES............................................ 60 Introduction........................................ Experimental........................................ R e s u l t s ............................................ Discussion.......................................... 60 60 63 63 V. APPLICATIONS.......................................... 69 VI. SUMMARY AND FUTURE W O R K ............................. 71 IV. APPENDIX A. STANDARDS USED IN THE PERTURBATION STUDY OF CHAPTER II AND SAMPLE CALCULATIONS ................................. 76 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B. Page DIELECTRIC EQUATIONS FOR THE INTERFEROMETER DESCRIBED IN CHAPTER I V .............................................. 82 BIBLIOGRAPHY......................................................... 87 v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES Page Table 1. Dielectric Properties of 0/W and W/0 Macroemulsions. ... 31 2. Dielectric Properties of Related Microwave Studies . . . . 37 3. Parameters for Two-Time Constant Debye Type Equation .. . 52 4. Dielectric Properties of Standard Liquids Determined by Microwave Interferometry at 23.45 G H z .................... 68 5. Standard Liquid Reference Calibration Data For the Microwave Resonance Dielectrometer ...................... 81 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Figure 1. Complex Dielectric Properties of Liquid Water............. Page 3 2. Microwave Resonance Cavity Apparatus for the Determination of Liquid Complex Dielectric Properties at 8.193, 9.505 and 11.003 G H z ........................................... 11 3. Determination of Cavity Length and "Q" Factor Shifts Due to Insertion of a Sample Liquid Dielectric ............. 13 4. Deviation Between Perturbation Measurements and Exact Values of Dielectric Constant at 9.505 GHz for Selected Standard Liquids.......................................... 16 5. Error in Using Perturbation Approximation Relative to Exact Standard Values as a Function of Perturbation Measurement................................................ 18 6. Variation of e' with Water Content for the Two Basic Emulsion Types at 8.193 G H z.............................. 22 7. Variation of e" with Water Content for the Two Basic Emulsion Types at 8.193 G H z .............................. 23 8. Simultaneous Determination of Water Content and Emulsion Type from Loss Tangent, e'Ve1 at 8.193 G H z ............. 24 9. Variation of e' with Water Content for the Two Basic Emulsion Types at 9.505 G H z.............................. 25 10. Variation of e" with Water Content for the Two Basic Emulsion Types at 9.505 G H z.............................. 26 11. Simultaneous Determination of Water Content and Emulsion Type from Loss Tangent, £"/ e' at 9.505 G H z ............. 27 12. Variation of g 1 with Water Content for the Two Basic Emulsion Types at 11.003 G H z ............................ 28 13. Variation of e" with Water Content for the Two Basic Emulsion Types at 11.003 G H z ............................ 29 14. Simultaneous Determination of Water Content and Emulsion Type from Loss Tangent, e"/ e' at 11.003 G H z ............. 30 15. Effect of Dielectric Constant on Electric Field within a Dielectric Sphere......................................... 34 16. Dielectric Properties of a Spherically Dispersed W/0 Type M a c r o e m u l s i o n ....................................... 36 vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 17. Page Use of a Normalized Dielectric Modulus, P, to Charac terize Suspension Types and Water Contents in Re lated Microwave Studies..................................... 39 18. Time Domain Reflectometry Apparatus of Professor R.H. Cole, Brown University ................................... 19. Modified TDR Sample C e l l ...................................... 47 20. Comparison of Single Time Constant (dashed lines) and Two-Time Constant (solid line) Debye Representation of the Dielectric Properties of a .35 Mole Fraction Water in 1 -Propanol Solution. (Data shown as symbols). 21. Determination of Starting Values for the Parameters Used in the Two-Time Constant Equation at 0.35 Mole Frac tion W a t e r .................................................. 50 . 44 49 22. Variation of Fitted Parameters and with Mole Fraction Water ........................................... 53 23. Variation of Fitted Parameters T . and T _ With Mole Fraction Water ........................................... 54 24. Microwave Transmission Interferometer for the Determina tion of Complex Dielectric Constant at 23.45 GHz . . . . 61 25. Sectional View of Variable Pathlength Teflon Sample Cell Used in the Determination of e* of Liquids by Micro wave Interferometry......................................... 62 26. Determination of a From Variable Pathlength Attenuation D a t a ........... S ............................................ 64 27. Determination of AL/At From Variable Pathlength Phase Shift D a t a .................................................. 65 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT A microwave cavity resonance dielectrometer has been employed in a study of the complex dielectric properties of macroemulsions con sisting of oil, water and stabilizing surfactant. A novel method for the simultaneous determination of emulsion type and water content from complex dielectric measurements is described. Also presented is a reference calibration technique developed for the microwave dielectro meter, permitting a convenient experimental routine and quite exact dielectric measurements if referenced to exact standards. A voltage ratio technique, which allows measurement of both low and high loss samples in the same cavity is also described. In another study time domain measurements of solutions of 1-pro panol and water at seven compositions and 25°C were Fourier trans formed to obtain complex permittivities in the range 50 MHz to 8 GHz, which can be represented by a sum of two Debye relaxation functions. The principal, slower, one has a relaxation time changing smoothly from 320 picoseconds (ps) for 1-propanol to 8 ps for water (by extra polation from 0.75 mole fraction of water). The second is quite small for 1-propanol, but increases with added water, and remarkably has a relaxation time of ca 20 ps which is independent of concentration to within the accuracy of the data and fitting. The significance of the behavior is discussed in terms of diffusion like models for molecular reorientations and local conformational changes in hydrogen bonding, with the conclusion that the later provides a more likely explana tion, particularly of the faster relaxation. ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Also presented is a description of a transmission microwave in terferometer constructed for the determination of complex dielectric properties at 23.45 GHz. A new variable pathlength teflon sample cell is described. Free space wavelength diffraction correction fac tors were also determined. x Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 CHAPTER I INTRODUCTION The main objective of this thesis has been to apply complex dielec tric property measurements to the determination of compositions in liq uids, solutions and emulsions of interest to the practicing Chemical Engineer. The dielectric constant or relative permittivity, as it is of ten called, is a fundamental property of matter and is in general unique to each substance. It is measured by electronic apparati and can easily become part of an automated process control scheme. As the determina tion of water content figures so prominently in this work we will now examine its unique dielectric properties. COMPLEX DIELECTRIC PROPERTIES OF LIQUID WATER In general, the complex dielectric constant is defined as: e* = e'-ie" where e* = complex dielectric constant e' = real part of e* e" = imaginary part o ; -£* Physically e' is a measure of the ability of a material to store elec tric field energy, i.e. become polarized, and is proportional to the capacitance of the material to the capacitance of an equal volume of free space, e" is simply a measure of the energy dissipation of an electromagnetic wave as it passes through the medium. Naturally, e" of free space is zero. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 Water has a large dipole moment which gives rise to an unusually large dielectric constant (e* = 78 at 25°C and zero frequency, i.e., dc). Debye (1)* noted that as the frequency of measurement increased, e 1 fell off while e" grew. This is illustrated in Figure 1, a clas sical Debye type plot of e' and e" versus log^Q of frequency. Debye proposed a simple model based on the frequency dependent vibration and rotation of the water dipole as it acts to keep the water mole cule aligned in an applied AC field. Thus he proposed £* = £„,+ (es-e00)/(l+iwT) which upon separation into real and imaginary components becomes: £ f = £«, + (es-£°°)/(1 + (ut)2) e" = ( e ^ e ^ w x / C l + (cot )2 ) where £g = low frequency (dc) static permittivity = high frequency limiting permittivity co = angular frequency = 2ttF t = characteristic relaxation time, seconds The frequency at which e" is a maximum (Figure 1) is referred to as the relaxation frequency, F r> at which cot = 1 Fr = uj/2 tt ^Numbers in parenthesis - Refer to numbered references in the Bibliography. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1. Complex Dielectric >- Properties of Liquid Water 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 These simple Debye equations fail to accurately quantify the dielectric properties of water over the entire spectrum of frequencies. They do, however, provide an excellent qualitative picture of the phenomenon of the molecular relaxation process seen in liquids, solutions and emul sions comprised of one or more polar compounds. It is basically this phenomenon that has been taken advantage of in the dielectric measure ment applications described in this thesis. SUMMARY OF WORK Dielectric Properties of Emulsions. Mixtures of oil, water and stabilizing surfactant are known as emul sions. Emulsions can exist as dispersion of oil-in-water (0/W), water- in-oil (W/0) or mixtures of the two. They play key roles in the produc tion of pharmaceuticals, cosmetics and some types of fuel combustion processes. In Chapter II of this thesis we describe the study of the microwave dielectric properties of such systems which led to a dielectric technique for the simultaneous determination of macroemulsion (emulsions whose dispersed phase is visible under ordinary light microscopy) type and water content. These techniques can be used in place of tedious and time consuming wet chemical and microscopic methods and provide an elec tronic output amenable to computer data acquisition and process control. Dielectric Properties of Alcohol/Water Solutions This work, described in Chapter III, was originally undertaken to develop calibration standards for the dielectric measurement apparatus employed in the emulsion study (Chapter II) described above. Of greater importance and interest to Chemical Engineers, however, is the unique dielectric relaxation behavior of these mixtures. The relaxation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 frequency for 1-Propanol is located around 0.5 GHz (1 GHz = 10^ Hertz) while that for water is around 20 GHz at 25.0°C. The results of this dielectric study of the relaxation behavior of mixtures indicated a high degree of interaction between alcohol and water molecules in the liquid and may shed light on the mechanism(s) responsible for the phenomenon of azeotropism as seen in the highly nonideal boiling be havior of such mixtures. The relaxation behavior of these systems was also shown to closely mimic that found in microemulsions and may provide a model of the di electric behavior of this industrially important class of emulsions. Microwave Transmission Experiment In order to take advantage of the large difference in the dielectric properties of water and oil a device was constructed to make such measure ments at 23.45 GHz. A transmission type cell was constructed and is described in detail in Chapter IV. path length cell a In addition to this new variable free space wavelength correction is also discussed. Suggestions for future work and several novel applications of di electric analysis to Chemical Engineering problems are presented in Chapters V and VI. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 CHAPTER II COMPLEX DIELECTRIC PROPERTIES OF MACROEMULSIONS USING A CALIBRATED MICROWAVE RESONANCE CAVITY DIELECTROMETER INTRODUCTION The work reported here was undertaken for two related reasons. The first, to demonstrate the ability of complex dielectric property measure ments at microwave frequencies to determine macroemulsion type and water content. The second, to compare these results with other theoretical and empirical investigations aimed at providing a mechanistic descrip tion of the complex dielectric properties of macroemulsions. The term macroemulsion refers to a fluid dispersion of either oil-in-water (0/W), or water-in-oil (W/0) having dispersed phase structures which are visi ble under ordinary light microscopy. Clausse (2)* has noted in his recent extensive review of the dielec tric properties of emulsions and related systems that most emulsion studies have been conductedat relatively low (0.1-100.0 MHz) frequencies. Microwave measurements have, however, been conducted recently by Foster and co-workers (3,4) on 0/W microemulsions. Microemulsions have dis persed phase structures which are invisible to ordinary light microscopy have a large interfacial to dispersed phase volume ratio and are essen tially different from macroemulsions. Representative studies of low frequency macroemulsion studies re viewed by Clausse (2) are that of Hanai (5), Sillars (6), and Chapman (7). The results of their work may be summarized as follows: * Numbers in parenthesis - Refer to numbered references in the Bibliography. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 1. e' of 0/W macroemulsions is essentially independent of frequency from ca 1-50 megaherz (MHz). 2. £’ of W/0 macroemulsions exhibits a marked frequency dependence (dielectric dispersion) over the same range of frequencies. The mechanism proposed to explain this low frequency dielectric disper sion observed in W/0 macroemulsions is that of interfacial polarization, a frequency dependent accumulation of charge at an interface thought to be caused by the presence of a nonconducting continuous phase (oil). In terfacial polarization was accounted for by Hanai (5) in his dielectric shell model of water droplets dispersed in oil. This model, which views the droplet as an inner core of bulk material surrounded by a surfactant generated interfacial shell, also qualitatively predicted the presence of a second dielectric dispersion in both W/0 and 0/W systems at much higher frequencies having character similar to that of bulk water. It should be noted that no low frequency dielectric dispersion was pre dicted for 0/W systems. Clausse (2) provided a numerical solution to Hanais (5) model. His calculations of the theoretical dielectric behavior of W/0 systems place the centers of the low and high frequency dielectric dispersions at ca 52 KHz and ca 30 GHz respectively for a 0.7 volume fraction water (W/0) system. The presence of conducting species in the bulk water in W/0 systems has been shown to cause movement of the low frequency disper sion towards a higher frequency resulting in an overlap of the two di electric dispersions, (2,8,9). In a recent experimental investiga tion Hanai (9) has shown that the effect of the low frequency (inter facial polarization) dispersion is essentally dissipated above ca 50 MHz in W/0 type macroemulsions prepared in the absence of conducting species. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Accordingly, the present study examines the complex dielectric pro perties of macroemulsions prepared in the absence of conducting species, at microwave frequencies far removed from the effect of interfacial polarization. The experimental technique chosen for this study is that of small perturbation of a microwave cavity resonator as described by Bethe and Schwinger (10), Horner et al. (11) and Birnbaum and Franeau (12). Testing of the apparatus with standards liquids (methanol, acetone, and water) yielded a systematic deviation between measurements using the perturbation approximations and generally accepted literature values for the standard liquids. This led to a reference calibration procedure per mitting the accurate determination of e* for lossy liquids over the range between air ( e ‘=l) and water (e'=65). The design, calibration and operation of the microwave resonance apparatus is described in detail. This is followed by a discussion of the results of our study of the microwave dielectric properties of macro emulsions at 8.193, 9.505 and 11.003 GHz performed with this equipment and the manner in which the dielectric data may be used to determine macroemulsion type and water content without resorting to wet Chemical or microscopic techniques. A voltage ratio technique which allows the measurement of e" over a broad range(0.2-35) is also described. EXPERIMENTAL Microwave Resonant Cavity Dielectrometer The apparatus employed in this study is based on the small pertur bation approximations developed by Bethe and Schwinger (10) and de scribed by Horner et al (11), Birnbaum and Franeau (12), and Soohoo (13). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 The original strict requirements for the use of the approximations in dielectric measurements are: 1. The fractional change of the resonant frequency, AF/F, or of the cavity length to maintain resonance at a constant frequency, AL/L, shall be very small. Either a small sample or a low permittivity (complex dielectric constant) is required; 2. The occurrence of, or the excitation of, degeneracy i.e. more than one resonance at almost the same frequency shall be avoided so that the sample does not induce unwanted modes; 3. The electric field, E, in the sample must be known relative to the exciting field as is true for the various ellipsoids, e.g. a slim cylindrical rod sample. Theoretically, a cylindrical rod sample parallel to the E field should terminate with the ends in firm contact with the metal sur faces of the cavity. Practically, it is necessary to insert the solid or capillary tube through holes. The errors contributed by holes have been calculated by further application of perturbation theory (Estin and Bussey (14)) and by higher mode analysis former method (14) for solid (Bosisio et al 15,16). The rods was well checked experimentally, and may be interpreted as a weakening of the E field by a hole near the sample end. An additive correction factor for £', proportional to e'-l and the ratio of sample radius to cavity height resulted. modal method The (15,16) is useful as it predicts the augmented correction factor (to be added to e r-l) when the sample is contained in a capil lary tube. The following symbols are defined for the calculations: c = velocity of light in vacuo, m/sec Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 C 2 = (kg/kQ ) , dimensionless db = decibels below baseline atresonance F = frequency, Hz AF = frequency shift due to k = rnr/L, m 1 sample insertion, Hz g k o = 2irF/c, m -1 L = total cavity length, m AL = length decrease required to reestablish resonance upon inser tion of sample n = number of i wavelengths in cavity at resonance, n = 5,7,9 at 8.193, 9.505 and 11.003 GHz respectively Qg = cavity "Q'1 factor, empty Qg = cavity "Q" factor, with sample R = magnitude of voltage reflection coefficient at resonance V = cavity volume, m v = sample volume contained within capillary, m 6 Lg = Q width factor, empty, m 6Lg = Q width factor, with sample, m 3 3 In the present study a rectangular waveguide, iris coupled single port reflection cavity has been drilled to accept glass capillary tubes. Figure 2, a non contacting variable short with an indicating digital micrometer drive was employed as the cavity tuning element. The cavity is capable of operation at three frequencies, 8.193, 9.505 and 11.003 GHz in the T E . ^ , ^ 1 0 7 and ^ 1 0 9 modes respectively. The sample holes are placed at the E field maximum at the center of the cavity. The length of the cavity is adjusted for resonance, i.e. for minimum reflected power both with and without the sample while Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ,CAVITY REFLECTED POWER MONITOR tn ISOLATOR LIQUID SAMPLE TUBE CRYSTAL DETECTOR MOVEABLE PISTON(SHORT) IRIS- MICROWAVE SIGNAL GENERATOR 7-11 GHz DIRECTIONAL COUPLER RESONANCE CAVITY Figure 2. Microwave Resonance Cavity Apparatus for the Determination of Liquid Complex Dielectric Pro perties at 8.193, 9.505 and 11.003 GHz 12 maintaining a constant frequency and the bandwidth and/or reflection co efficient are measured thereby providing the measurement parameters for a perturbation theory calculation of e' and e". Refering to Figure 3 the variables AL, 6Lg , and 6Lg are determined by measuring the dip in reflected power at both empty (dbg ) and sample (dbg ) resonance conditions. The half power value in db is calculated from: (dbe )i =-10 Log((10"dbe/ 1 0 +l)/2) 2.1a (dbg )^ =-10 Log((10“dbs/ 1 0 +l)/2) 2.1b The adjustable short position is varied around the center resonance location to the value indicated by Equations 2.1a and 2.1b from which-the shift in center resonance location ( L j + L ^ g ^ - (L-^+L2)g/2 = AL, and the Q-factor change (6Lg-6Le ) = ( L - j - L ^ - ( L - ^ L ^ are calculated. The perturbation equations for the TE^Qn system using length variation to obtain the resonance and Q-width variation are as follows: £' = 1 + (V/2v)CAL/L 2 .2 e" = (V/4VH/Q, sc 2.3 where Q gc is the sample contribution to the total Q. The inverse of the total Q with and without the sample may be expressed as: 2.4a 2.4b where u denotes the skin depth effect and p denotes radiation from the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 m M § QC \ □ UJ I— <_> LU AL _l Ll LU cr St O l s2 l s1 Le2 Le1 MOVEABLE SHORT POSITION. CM Figure 3. Determination of Cavity Length and "Q" Factor Shifts Due to Insertion of a Sample Liquid Dielectric 14 sample port (Iris ) and Q~* = 0 for the empty cavity case, Q ^ . Qu and Qp change very little with a small perturbation sample and it is therefore sufficient to assume that 2.5 where s and e denote with the sample and empty respectively. Q g or Qg may be measured by the resonant bandwidth by means of either fre quency or length tuning. For example, using length the total (or loaded) empty cavity Q is given by: 2.6 Q ^1 = (<5Le /L)C where 6L g is the width at the so called half power level (see Figure 3). By Equation 2.5 assuming a small perturbation Q sc = « < V L) " (6Le/L))C 2.7 For practical reasons, e.g., temperature changes, drift of the oscillator, backlash of the movable short, the measurement of the width <$L tends to exhibit significant random errors which can be averaged out by tedious repetitions. There is a different, simple, precise and quite accurate method of observing Q-change, i.e., the loss contri buted by the sample. This method, called the voltage ratio method (Hartshorn and Ward(17)), is well known and straight forward for lower frequencies using a capacitive holder. The method was extended to microwaves (Bussey (18)) by including certain correction factors de noted in a review (Bussey (19)) as K Kg , and Kd< These factors ap proach unity as the perturbation decreases to zero and are assumed to be one for our small samples. The method then gives: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 2.8 where R e . 10-dbe/2°, R s . 10-dbs/2° where R is the voltage reflection coefficient at resonance, and s, e denote with the sample and empty respectively. The + choice of signs denote over (+) and under (-) coupling of the resonator. Our cavity was undercoupled in all three modes, giving the minus sign in Equation 2.8. The Q gc obtained by the methods of Equations 2.7 and 2.8 agreed well in cases that were easily checked, namely the more lossy samples. The voltage reflection method is, however, far more accurate in deter mining Q shifts in low loss samples, while also speeding the process of data acquisition and was,therefore, used in the present study. Measurements of e' and e" for the standard liquids, methanol, acetone and water were conducted at 8.193, 9.505, 11.003 GHz and 24.0 + 0.5 C° using the perturbation Equations 2.2 and 2.3 uncorrected for sample insertion holes. Standard reference values of £' and e" to be used to correct the perturbation approximation for the unknown li quids are presented in Appendix A. A plot of (e'-l)^ against corresponding literature values is pre sented in Figure 4. The values from the perturbation approximation, (e'-l)p are everywhere greater than the literature values. As a rough estimate of the magnitude of error expected in using the perturbation approximation we have solved Horners (11) exact equations for the case of a circular cylindrical cavity containing a solid sample rod with no Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 WATER— % tmq40 COMPUTER SOLUTION TO HORNERS EQUATION / ACETONE— METHANOL .AIR 0 10 20 30 AO 50 60 70 (e’"1,TRUE Figure 4. Deviation Between Perturbation Measurements and Exact Values of Dielectric Constant at 9.505 GHz for Selected Standard Liquids Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 sample holes and compared them to theoretical perturbation results for the same fractional frequency shift, AF/F. The TM q AO mo£*e was chosen for the calculation as the field excita tion is very similar to our rectangular cavity. The ratio of sample rod to cavity diameter, wavelength and mode (TM q ^q ) were chosen to agree closely with our experimental conditions to the TE^ q 7 rectan8u_ lar cavity. Calculations for the TM q ^ q cavity predict a positive devia tion between perturbation and exact solution similar to that found in the perturbation measurements on the standard liquids (Figure 4). These results are qualitative as the theoretical sample was lossless, i.e. e"=0, was contained entirely within the cavity and fields within the cylindrical and rectangular cavities are not quite the same. To better illustrate the deviation between the exact and perturba tion solutions we have plotted (e*-l)p/ ( £ ,-l)c =A against (e'-l)p for the Horner (11) calculations (solid line in Figure 5). Here p and c stand for perturbation and correct respectively. A simple straight line deviation in the relative error, A, occurs. Using this linear variation of A with (e'-l)p as a guide we have replotted our for the standards and air in Figure 5. data A best fit (dashed line) was obtained by linear regression to average out the effects of random er rors. This results in the following relationship which we have used in the present study to correct the perturbation approximation results. (e*-l)c = (e,-l)p/(a(e,-l)p + b) 2.10 The values of the constants a and b have been determined by measurement on the standard liquids. At 9.505 GHz, a = 1/967, b = 1.0077, for the Horner (11) calculation, a = 1/1143, b = 0.9998. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. .09 .08 WATER 1.07 TE10? DATA POINTS AT 9.505 GHZ ~ 1.06 BEST FIT TO DATA. i 1.05 ^ ACETONE 1.04 BEST FIT TO TM, CALCULATION 040 ^ 1.03 .02 METHANOL .00 Figure 5. Error in Using Perturbation Approximation Relative to Exact Standard Values as a Function of Perturbation Measurement. oo 19 It is of interest to note that the slopes of both the theoretical (calculated) and experimental studies are nearly equal. Scatter due to both random and systematic errors tend to be magnified in this plot of fractional error but it should be noted that the regression line for the experimental data is within ± 1.5% of the points themselves. We now note some of the systematic errors which arise in making dielectric measurements by means of a resonant cavity: 1. Placement of the sample tube at the E field maximum, 2. - Placement of the sample parallel to the E field, 3. Effect of sample insertion holes, 4. Effect of capillary sample tube, 5. Effect of coupling element (iris), 6. Effect of non zero loss, i.e. e " * 0 , on e 1. In view of the uncertainties and the demonstrated systematic deviation between the exact and perturbation calculation of (e'-l), we used the following simplified reference calibration and measurement procedure: Reference Calibration Procedure 1. 2. Determine (e'-l)p from the standards using Equation 2.2, A straight line correction was found to be simpler to use than 2.10 hence (e'-l)c = a (e'-l)p + b 3. 2.11 Thus calibrated, the instrument is ready for measurement on unknowns. Measurement Procedure 1. Measure E* for the unknown samples, 2. Calculate ( e ’-l)p and e ’^ 3. Determine (e'-l)c from Equation 2.11 (See Appendix A for a and b), from Equations 2.2 and 2.3, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 4. Then e"c ,* ((e’-l)c/(e'-l)p )e"p . The last step assumes that the fractional errors in both and (e'-l)p are approximately equal as both are driven by the same field integrals. Back calculations of E 1 and e" for the standards resulted in errors of + 2% and + 5% respectively at 9.505 GHz, remarkable over such a broad range of values, 6 < e'< 67 and 4 < e " < 32. Emulsion Preparation and Sampling The purpose of the following procedure is to produce emulsions with physical characteristics as similar as possible differing only with respect to type, i.e., W/0 and 0/W, and composition (phase volume water). Stable emulsions were prepared using blends of Span 80 (sorbitan monooleate) and Tween 80 (polysorbate 80). In the case of W/0 emul sions a mixture of surfactant at an HLB number of 6.0 (hydrophile/ lipophile balance) (20) was dissolved in paraffin oil (continuous phase) at a concentration of ca 10% by weight. heated separately to ca 65°C. Both water and oil are then The heat is removed and both phases are combined and mixed by propellor for approximately 10-20 minutes, re sulting in a dispersed phase (water) concentration of ca 80% by volume. This mother dispersion of W/0 is then successively diluted with surfact ant free continuous phase (oil) by gentle inversion (ca 20 times) in a graduated cylinder. Prior to the dielectric measurements, each sample is analyzed for water content using the Karl Fischer titration method (21,22) for the determination of water in hydrocarbon mixtures. Sample densitities are determined to calculate volume fraction water present assuming no volume of mixing effects. The procedure for 0/W emulsion Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 preparation is the same with the exception of surfactant blend, HLB = 10.0, which is placed in the water at ca 10% by weight concen tration. Microscopic observations showed the presence of dispersed phase agglomerates for both the 0/W and W/0 type emulsions similar to those photographed by Chapman (7). Thus prepared, the samples were drawn into capillary tubes (Drummond Micro-caps, lul, I.D. = .2 mm, O.D. = .65 mm) and placed into the micro wave cavity where the dielectric determinations are made as described in the previous section. (Tubes placed in wide side of cavity). RESULTS Measurements of the complex dielectric constant of both 0/W and W/0 type macroemulsions were made over the concentration range of 1878% water by volume using the calibrated microwave resonant cavity dielectrometer described in the previous section, e ’ and £ 11 versus volume fraction water at 8.193, 9.505 and 11.003 GHz are shown in Figures 6, 7, 9, 10, 12 and 13 respectively and are listed in Table 1. These figures demonstrate a systematic difference in E 1 and e " for the two emulsion types over the entire range of composition investigated. Since the loss tangent, e"/e', appears to enhance this systematic dif ference we have plotted this group as a function of volume fraction of water for both emulsion types in Figure 8, 11 and 14. We note the fol lowing: 1. e " / e ' is lower for emulsions of water-in-oil (W/0) than for those of 0/W over the entire range of compositions and frequencies in vestigated, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. WATER CC £ CD^ o •g -a "Z. ° ir>o ^ 'j-4 <u %: LU § 2 S —) o =J ° no > k 3 ,3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LU I Basic cr Emulsion Types at 8.193 GHz WATER 23 lu 2 ZD O .3 the Figure 7. Variation of e" with > for Ll. Content < cr Water I— o Two z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. WATER 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 9. Variation of e' with Water Content for the Two Basic Emulsion Types at 9.505 GHz WATER 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. uo o LO o o Figure o 10. Variation of e" with Water Content for the Two Basic U lI Emulsion Types at 9.505 GHz WATER 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. at e"/e' Tangent, Loss from Type Emulsion and Content ,3 / . 3 Determination of Water (VI LO Figure 11. Simultaneous 9.505 GHz CO > Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. GHz Variation 12. Figure 60 \- of e' with Water Content for the Two Basic Emulsion Types at 11.003 WATER 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 13. Variation of e" with Water •2 Content 'vTLU for the Two Basic Emulsion Types at 11.003 GHz WATER 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UJ UJ ,3/„3 Figure 14. Simultaneous 11.003 GHz Determination 3 of Water < .l o q ; 'Ll. Content and .cpo Emulsion cr Type from Loss WATER Tangent, e"/e* at 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 ”u) CO r - CO VO co r^. co r— rto I-’ ro oi ‘t c t O V r- Lfi c o « tv o o f— CM O 00 LO CM to ^ co co r— CM CO vo vo r». i>. co vo cm cn in 00 iO CO CM O CO 00 co 8 _ - 9 .4 1 4 .5 2 7 .9 4 2 .2 6.1 1 0 .8 2 4 .2 3 4 .2 m o in cn To ^ ■ C O IflO PO VO f— * CO CO CM O OV o" co" 00* o" cnCMINr<n vo co co C-(\J cn co vo cn co cm in >— i— CM CO cn CO To £ ai 1 i- c o +J ra u_ O v f vnvf N C O lflN V • ~J . ,v„,l cn 00 r— V. (U <u p s» W/0 5 0/W Table 1. Dielectric Properties of 0/W and W/0 Macroemulsions CO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 2. For volume fractions of water below 0.5, ef'/e 1 for W/0 emulsions falls rapidly with decreasing water content at all frequencies studied, 3. £"/£' for 0/W emulsions is essentially invariant with volume frac tion water and is approximately equal to £ " / £ 1 found for pure water at each frequency studied. In principle, Figures at any of the 3 frequencies such as Figure 6 and 7 are sufficient for the simultaneous determination of emulsion type and water content for dielectric measurements alone. The examination of loss tangent in Figure 8, however, allows the immediate, unambiguous determination of emulsion type for which either Figure 6 or 7 provides accurate determination of the volume fraction of water. Plots such as these may be used for the dielectric determination of macroemulsion type and water content in industrial and scientific applications which require rapid determinations without resorting to wet chemical or microscopic technique. This technique might also be useful as a means of determining or monitoring emulsion phase inversion. With regards to other applications Klein (23) and Meyer and Schilz (24) have sug gested the group (e'-l)/e" for use in a variety of industrial applica tions such as the dielectric determination of moisture content in food and coal. DISCUSSION Stratton (25) presented an electrostatics solution for the electric field strength E inside an isolated sphere of dielectric constant, surrounded by a continuum of dielectric constant z^ . Neglecting the effect of the interface he obtained Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 E. = 3Eo/((s1 /e2 ) + 2) where = electric field inside the sphere E q = electric field outside the sphere = dispersed phase (sphere) bulk dielectric constant = continuum (continuous phase) bulk dielectric constant At 11.003 GHz for water spheres dispersed in oil this results in Ei = 3E q /((59/2.5) + 2) = 0.11E q Thus in the case of water spheres dispersed in oil the E field within the drop is approximately 10% of the value outside of the drop. Simply stated, a water droplet is partially shielded from an applied E-field thereby reducing the measured, or apparent dielectric constant for such dispersions (see Figure 15). Conversly, the E field inside an oil droplet surrounded by water is actually enhanced over the ex ternal field. This provides a qualitative explanation of the reduc tion in both e ' and e" for the case of W/0 emulsions as seen in Figures 6 and 7 and explains the shift in loss tangent, e 'Ve ' between 0/W and W/0 type macroemulsions as seen in Figure 8. DeLoor (26) re viewed various heterogeneous mixture models which attempt to relate the dielectric constant of such mixtures to their pure component properties. He noted the effect of dispersed phase shape and predicted that the microwave frequency dependence of e ' and £" for W/0 type dispersions would be similar to that of pure water though shifted towards higher frequencies. In order to examine this phenomenon we have made a pre liminary investigation of the broadband microwave dielectric properties of a W/0 macroemulsion system consisting of a spherically dispersed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 15. Effect of Dielectric Constant on Electric Field within a Dielectric Sphere 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 water phase and a continuous phase of carbon tetrachloride and paraffin oil in the ratio of 1/4, CCl^/Oil (similar to that used by Hanai, (9)) Span 80 surfactant at a concentration of 5% by volume in the oil phase was used to stabilize this 0.4 volume fraction water emulsion. The emulsion was prepared by injecting deionized water with a syringe and 22 gauge needle into a propellor stirred mixture of oil and surfactant. This concentrated dispersion was then diluted with oil!to 0.3, 0.2. and 0.1 volume fraction water by gentle inversion. Photomicrography showed the droplets to be in the 10-40 micron diameter range, as opposed to the agglomerated system previously described. The dielectric measurements were performed over the range of .057.68 GHz using the Time Domain Reflectometry apparatus of Cole (27,28). The results for the 0.4 volume fraction water experiment are presented in Figure 16, a typical Debye type plot of of frequency. e* and e” against L o g ^ A list of the results for all four samples at 8.0 GHz is presented in Table 2. The negligible dependence of e" on frequency accompanied by a rapid rise in e" above 5 GHz does indeed indicate a relaxation frequency, F , similar to or greater than that found in the pure water where F r = ca 20 GHz at 25°C (80). It is of interest to compare and contrast the results of our macro emulsion study with the microwave dielectric observations made on micro emulsions. Foster and co-workers (3,4) found a pronounced decrease in relaxation frequency for 0/W type microemulsions which varied from ca 2 GHz to 15 GHz for samples containing 0.2 to 0.8 volume fraction water respectively. (This is discussed in greater detail on Page 42 of this study). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 16. Dielectric CO Properties of a Spherically a§ Dispersed W/0 Type Macroemulsion 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2. System Dielectric Properties of Related Microwave Studies Investigator Frequency Volume Fraction Water e' e" Macroemulsion 0/W Mudgett et al (38) 25°C 3.0 GHz .25 .50 .75 15.8 32.8 47.6 2.0 4.5 6.3 Sand/Water Slurry Kraszewski(39) 25°C 9.4 GHz .47 .61 .77 .85 40.0 46.5 55.3 57.4 16.1 20.5 25.3 26.8 Water Drops in Plexiglass DeLoor(35) 20°C 9.68 GHz .20 .25 Macroemulsion W/0 Theoretical Calculation Using Hanai Model Clausse(l) 20°C Macroemulsion W/0 Spherically Dispersed Microemulsion 10.0 GHz 0.70 Perl(11) 25°C 8.0 GHz .1 .2 .3 .4 Foster et al (3) 25°C 9.5 GHz .2 .4 .6 .8 5.13 5.92 25.0 3.1 4.4 6.2 8.75 5.0 11.0 23.0 41.0 .405 .558 6.5 .16 .36 .95 1.22 3.0 8.0 16.0 25.5 38 Related Microwave Studies As discussed by Clausse (2) there is a lack of experimental studies of emulsion systems at microwave frequencies. Nevertheless, there have been model systems studied by others which are similar to the dispersions of W/0 and 0/W examined in the present study. In order to compare the results of these other microwave dielectric studies with our present work we have defined the function P = ( ( £ " / £ ') s/ ( e " / e , ) w) where the subscripts s and w refer to the sample and pure water respec tively at the frequency of the particular study. The function P be comes a normalized dielectric modulus which serves to characterize de viation from pure water behavior. Figure 17 is a plot of the nor malized dielectric modulus, P, versus volume fraction water for the published studies. For completeness we have summarized the actual findings of each investigator in Table 2. It should be noted that the data presented in these studies were in graphical form and we accept responsibility for its conversion to discrete values of £* and £". From this discussion of the work of others and our present study, we reach the following conclusions illustrated by Figures 6-14 and 17. 1. Dispersions of a low dielectric constant material in a high dielec tric constant continuum, e.g., 0/W type macroemulsions.exhibit a microwave dielectric behavior similar to that of pure water as characterized by the normalized dielectric modulus, P, 2. Spherical or nearly spherical dispersions of a high dielectric con stant in a low dielectric constant medium, e.g., W/0 type macro emulsions, show a marked dispersed phase concentration controlled Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.6 r 0/W MICROEMULSION CL 1.4 in 3 1.2 0/W MACROEMULSIONS TYPE SYSTEMS 2 10 & £ -8 o INVESTIGATORS .6 Q W/0 MACROEMULSION TYPE SYSTEMS — I < I .2 2 VOLUME FRACTION6WAf^R B O MUDGETT et al (29) □ KRASZEWSKI et al (30) A DeLOOR (26) + CLAUSSE (2) • PERL x FOSTER et al (3) 9 '° Figure 17. Use of a Normalized Dielectric Modulus, P, to Characterize Suspension Types and Water Contents in Related Microwave Studies 40 deviation from pure water behavior, 3. In spite of the varied microwave frequencies used in the above mentioned studies the differences observed in e' and e" for 0/W and W/0 type dispersed phase systems are large enough to provide an adequate evidence for the means of determining emulsion type and water content proposed here. SUMMARY 1. Knowledge of the broadband dielectric properties of macroemulsions is essential in the attempt to elucidate the mechanisms governing such dielectric behavior. 2. Once the wideband frequency behavior is characterized, singe fre quency measurements of the complex dielectric constant of such systems, particularly in the range of ca 10 GHz, provide a powerful electronic tool for the determination of macroemulsion type and watei content. 3. These dielectric techniques are applicable to a variety of lab analytical or industrial process and quality control situations where such determinations must be made rapidly, nondestructively and often noninvasively. 4. Also presented here is a reference calibration technique for the microwave cavity resonance dielectrometer employed in this study. This method accounts for a systematic deviation between literature values of e' and e" for common standards such as methanol, acetone, water, etc. and measurements using the small perturbation approxi mation. A voltage ratio method for the determination of e" from resonant cavity voltage reflection coefficients was found to im prove the accuracy of this measurement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 CHAPTER III DIELECTRIC RELAXATION OF 1-PROPANOL/WATER SOLUTIONS INTRODUCTION The study described in this chapter was conducted by the author in the laboratory of Professor R. H. Cole at Brown University, Providence Rhode Island. The original intent of the work was to pro vide additional calibration standards for the microwave resonance ap paratus described in Chapter II of this thesis. This, however, was only partially successful as the apparatus which will be described in the following pages has upper limitations on the value of £ 1 that it can measure. The results of this study of the complex dielectric pro perties of 1-propanol/water mixtures did, however, provide insight in to the intermolecular association process occurring in such solutions. This study also demonstrates the ability of complex dielectric analysis to determine liquid compositions even in the face of such large molecular associations. An attempt by Brost and Davis (31) to use such mixtures as calibration standards in microwave saturation monitored core flooding experiments has met with only partial success. This might also be due to the effect of association in the alcohol/water mixtures and will be discussed further in the section on future work. Measurements of mixtures of two associating polar liquids have provided considerable support for Schallamach's thesis (32) that if both or neither of two polar liquids are associated, most of the relaxation of mixtures of the two can be described by a single relaxa tion at intermediate frequencies. (For two non-associated liquids, the evidence is much less convincing, as discussed in the book of Bottcher Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 and Bordewijk (33). This suggests a considerable degree of joint cor relation in cooperative motion of neighboring molecules, as single molecules reorienting in an average environment, by rotational dif fusion for example, would be expected to produce two more or less dis tinct relaxation functions. Most of the existing evidence to the con trary has, however, been obtained at low temperatures and audio or radio frequencies, hence the interest in behavior at ordinary liquid temperatures and megahertz to gigahertz frequencies.. Mixtures of 1-propanol and water were chosen for study because of the large ratio of primary relaxation times (320 ps for 1-propanol and 8 ps for water at 25°C), miscibility at all compositions, and possible relevance to some recent results for relaxation in a microemulsion system (1 ps = 10 -12 second). In work at Brown to be published elsewhere, Dr. G. Delbos (Bordeaux) made time domain dielectric measurements of water/toluene microemulsions with sodium dodecylsulfate and 1-butanol as cosurfact ants in 5 to 1 mole ratio. Over a wide range of toluene/water ratios, he found a simple relaxation centered near 2 GHz which could plausibly be attributed to interfacial layers between the two with high permit tivity of mobile "bound water" and hydroxyl groups of 1-butanol in the layer. Foster and coworkers (3) have studied water/hexadecane microemulsions, with (nonionic) polyoxyethylene 20 sorbitan monostear ate (Tween 60) and 1-pentanol as cosurfactants, and found interfacial relaxation frequencies in the range of 2 to 5 GHz. It is thus of interest to determine whether alcohol-water solu tions in bulk exhibit behavior comparable to that found in microemul sions containing these components. Unfortunately, water is only Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 slightly miscible with higher alcohols, but the results for 1-propanol as the nearest counterpart in bulk should be of interest for comparison. A further possible usefulness of the results can be to provide data for calibration or test purposes at high frequencies, as the static permittivities lie in the wide range from 18 to 78 and the relatively simple relaxation behavior has been defined to several gigahertz. EXPERIMENTAL Measurements to obtain results for the frequency range 50 MHz to 8 GHz were made using time domain reflectometry (TDR) methods developed at Brown over the past few years (34), (35), (36), (37). The system used differs considerably in several respects from the last published version (35), and is described here in some detail. Referring to Figure 18, the step-like tunnel diode voltage pulse is sent to two coaxial line channels by a power splitter. The two wave forms, VQ (t) for channel B and vor(t) for A are reflected from matched sample and reference cells. These are equivalent, for both empty, to open cir cuits at an increased distance d, which is the effective electrical length of the cells as sections of coaxial line, and produce reflected signals V(t) and Vf (t) delayed in time by 2 d/c but otherwise unchanged. The complex permittivity e* at frequency w of liquid in the sample cell is obtained from the basic relation £*(1“) = r d o 3.1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 SAMPLE REFERENCE SAMPLING SCOPE SAMPLER 50 ohm •Coaxial Line IBANDPASS FILTER MIXER •Power Splitter -Coupler SIGNAL ANALYZER Triggers •Tunnel Diodes - COMPUTER Figure 18. Time Domain Reflectometry Apparatus of Professor R.H. Cole, Brown University Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 . - * , P 3.! where V q and r are Laplace transforms of the open circuit reflection of VQ (t) and the sample reflection R(t), C = 0.3 mm/ps is the speed of propagation, and the function f(z) is a high frequency correction factor discussed below. As used in this work, the reflected voltage pulse from reference channel A as sampled and "time stretched" by the coxial line triggers the signal averager (Tracor Northern Type 570A), which records com binations of the synchronous time stretched reflections in the two channels on the next repetitive sweep after an adjustable signal averager predelay set to provide a suitable baseline. This arrange ment, made possibly by use of a precision power splitter (Gen.Rad Type 874PDL) and flexible coaxial lines (Junflon), gives improved triggering and time referencing. It also makes possible a greater reduction of errors from drifts of circuit responses in time by use of the mixer amplifier to obtain combinations + (A+B) of the two channel output signals and B, which can be chosen for recording of critical ones in rapid succession. The procedure used to acquire the numerical data for use of equa tion 3.1 to obtain e* is as follows. The empty cell difference V(t) - Vr (t) is recorded first, then after the sample cell is filled the sum and difference Vr (t) + R(t) are recorded in rapid succession and added in the signal analyzer to V(t) - R(t), already stored, to give V(t) + R(t) stored in two memories. The only significant effect of drift is then in the value of the very small difference V(t) - Vr (t). The stored values are then transferred to an HP-85 computer for Fourier Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 transformation and other processing to calculate £*(w) from equation 3.1, as described in (34), (35). The high frequency correction function f(z) depends on the geo2 metry of the cell used, but can be expanded as a power series in z , and hence in £*, for frequencies below cutoff for higher order modes of propagation. In 7 mm diameter cylindrical waveguide, this cutoff is fm (GHz) = 3 3 / ( 3 8 ) , limiting the usable range to 3 GHz for water with previous cell designs. The cell used in this work shown in Figure 19 is a modification, by adding a metal insert, to increase such cutoff frequencies. With this design, a correction function f(z) = 1 + 0.3z^ - 0.3z^ with d = 1.175 mm was obtained by calibration with deionized water, with a high frequency limit |z| = for water (with £g = 78.5 at 25°C). at 25°C). 1.1 or 5 GHz This limit was verified by tests This limit was verified by tests at 25°C acetone (£g=21.2), chloroform (£g = 4.90), and Isopar-G(£g = 2.00). The last, a mixture of nonpolar hydrocarbons, is a very useful dielectric calibration liquid kindly supplied by Dr. E. 0. Forester (Exxon Research and Engineering Co.). Above about 3 GHz increasing oscillatory deviations of known and measured values of £* become apparent which are attribut able to a variety of impedance mismatches of the sampler and coaxial line sections. These amount to less than ± 5 percent for |e*| < but can be as great as ± 10 percent for |e *| >20. 5 An overall cali bration procedure to correct such systematic errors has been developed (39) but was not needed for this work. Baker "Analyzed" (99.9 percent) 1-propanol and deionized water were used to prepare the solutions maintained at 25.0 ± 0.1°C by a bath and monitor system previously described(37). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 Spring Stainless S teel Insert Thermistor Probe W ater Bath •Coaxial Line Figure 19. Modified TDR Sample Cell Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 RESULTS Solutions of water in 1-propanol were measured at seven compo sitions in the range from 0 to 0.75 mole fraction water at 25.0 ± 0.1°C. Numerical Fourier transformation of the TDR response records, obtained by the procedures described above, then gave values of com plex relative permittivity £* = e'-ie" at frequencies from 50 MHz to 8 GHz. Representative results for 0.35 mole fraction water are shown in Figure 20. Almost by inspection of the £* data, the relaxation is seen to be only approximately of simple Debye form, as shown by the dashed curves in Figure 20, which are plots of e* and e" as calculated from 3.2 with T chosen to give the absorption maximum of e" at the correct fre quency, and estimated by extrapolation of the e 1 data to infinite frequency. The nature of the deviations from a single Debye relaxation is more evident from the plot in Figure 21 of £' versus coe". For Debye behavior, the analysis (40) would give a straight line of slope = -x from the consequence of equation (3.2) that £' = £g - cote ", while for two Debye relaxations expressed by °° T 1 + iw^ 1 + iu)X2 the predicted curve is asymptotic to straight lines of different slopes for iot^ « 1 and W X 2 » 1 (if Corresponding relations for £* in terms of £"/w are less revealing for the present situation, but Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with permission of the copyright owner. Further reproduction prohibited without permission. C 70 8.0 8.5 9.5 10.0 LoQiq Frequency Figure 20. Comparison of Single Time Constant (dashed lines) and Two-Time Constant (solid line) Debye Representation of the Dielectric Properties of a .35 Mole Fraction Water in 1-Propanol Solution. (Data shown as symbols) Figure 0.35 21. Mole Determination of Starting Fraction Water [ /Vi68 mhz Values for the Parameters Used in the Two-Time Constant Equation at 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 are useful for estimates of e^. This plot is also shown in Figure 21. It is seen that the experimental curves are at least qualitatively of this form. Accordingly, the data were fitted to the function (Equa tion 3.3) by numerical iterations to obtain optimum values of e^, e^, T ^ f and T 2 (eg being known accurately from the low frequency limit of £'). The parameters were determined by a brute force least squares analysis to minimize the objective function r2 = 2T[(e T—ec.a.lC )^ + (e"-e"calc)2 ] using a direct search sweep of the four parameters, starting with initial estimates based on analytical properties of Equation (3.3). Step size changes of one percent with ± 15 percent sweep range resulted in satisfactory convergence in 20-30 minutes for the Fortran coded program on the PDP11/10 computer using 24 data points at 12 approximately logarithmically spaced frequencies. The best fit parameters obtained are listed in Table 3, together with the final values of the minimized r2 and of E = (r2/24)1^2 , the latter to give some idea of the mean error in the fit to the data. The frequencies (MHz) for the data used in this analysis are presented at the bottom of Table 3. The solid lines in the plots of Figure 20 for 0.35 mole fraction water were calculated from these parameters, with the circles and crosses from the experimental data. The fit is seen to be quite satisfactory, the most noticeable difference being that the calculated values of e" are a little too large near the loss maxi mum. The values of the permittivities £g ,E^ and are plotted against mole fraction X of water in Figure 22, and the values of Figure 23. The decrease of and in toward the nearly constant values of T 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE Xw .75 .65 .50 .35 .25 .15 0.05 0 3; Parameter for two-t1me constant Debye type equation es 41.72 34.96 28.64 24.96 22.98 22.04 21.37 20.85 T-jpsec 47.9 68.9 101.7 132.4 169.2 214.7 274.4 318.0 el 17.7 13.9 10.24 6.27 5.17 4.65 4.20 3.98 x2psec 21.5 18.05 23.6 19.1 20.8 20.6 26.5 22.8 eoo 6.4 3.06 3.46 3.72 2.90 3.12 3.27 2.95 r2 3.806 1.8939 1.532 .4654 .1694 .1227 .0882 .0664 E = + + + + + + + + .40 .28 .25 .14 .08 .07 .06 .05 High Freq. Frequency (MHz) Low Freq. 0-.65 mF H20: 184.108.40.206.220.127.116.11.316.2.464.2, 3174.0,3662.0,4639.0,5615.0,6592.0,7568.0 .75 mF H20: 18.104.22.168.22.214.171.124.316.2.464.2, 1465.0,1709.0,2197.0,2686.0,3174.0,3662.0 53 0 .2 .8 1.0 X H 20 Figure 22. Water Variation of Fitted Parameters e and e with Mole Fraction 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 300 0 30 0 0 -2 -4 .6 x Figure 23. Water h -8 1.0 2o Variation cf Fitted Parameters t, and t9 With Mole Fraction 1 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 with increasing X makes determination of the parameters increasingly uncertain, both because of the greater overlap of the two relaxations and because the effects are at increasingly high frequencies, making experimental uncertainties in determining the permittivities larger with a lower usable maximum frequency limit possible. Measurements at mole fractions X greater than 0.75 could not be satisfactorily analyzed for these reasons. The significance of the changes of the parameters with X is considered in the discussion. DISCUSSION As anticipated from previous evidence mentioned in the introduc tion, a slower "principal" relaxation at increasingly high frequencies is found for increasing water content, rather than a decreasing ampli tude with less change in frequency if it were attributed to relaxation of alcohol molecules in a mixed solvent medium by rotational diffusion processes. A further argument against such an interpretation in these mixtures of polar associating liquids is found in the magnitudes of the relaxation times x^ for the pure components as compared to those for non-associating but otherwise similar polar molecules. The value x^ = 320 ps for 1-propanol is some forty times longer than the values T = 7 ps for 1-bromopropane estimated from microwave data of Smyth et al. (41) at 3, 9.3, and 23.5 GHz. For water, there is more dif ficulty in finding a reasonable comparison liquid, there apparently being no dielectric relaxation data for either or HCL for example. However, Levesque et al (42) found a relaxation time x^ for HCL of about 0.5 ps for dipole (P^) correlations for molecular dynamic (MD) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 simulations and the time x^ = 8.3 ps for water is thus larger by a fac tor of fifteen. Both of the comparisons just made indicate a major effect of joint correlations of molecular dipoles with near neighbors in the neat liquids, and by inference in solutions of the two. The concept of well defined, long lived species associated by hydrogen bonding seems to us too special as a description of the dynamics responsible, as MD simula tions of water, e.g. by Rahman and Stillinger (43), also suggests. It is also worth noting that the dynamic differences, as expressed by x.,, are much greater than the static ones as expressed by the Kirkwood gfactor for example. The values of g, as inferred from relative static permittivities, are of order 3.7 to 2.5 for 1-propanol and water (44), (45), indicating static effects of joint correlations of molecules with their neighbors which, although large, are much less than the changes in the time scale for dynamics of these correlations inferred from the preceding discussion. As such, the evidence does not support for these associated liquids the result of Kivelson and Keyes (46) that a factor g should give the relation of times x with and without correlations. The comparison is, however, a bit unfair as the model of molecular reorienting units in a Brownian dynamical environment used by the authors would seem ill suited to the present problem. Similar behavior of the primary x^ relaxation has been reported by Bertolini et al. (47) for ethanol and 2-propanol solutions with added water, to mole fraction 0.5 for the first two and 0.15 for the last, at frequencies from 0.47 to 1.87 or 3.75 GHz. They represented their data for a single x^ relaxation decreasing with X. However, plots of e' versus toe" for their reported values give indications of higher Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 frequency deviations, particularly at temperatures of 0°C and -26°C, similar to ours which are more evident because of the wider frequency range. An original objective of this work, to test the conjecture that a microemulsion interface composed of water and 1-butanol might rea sonably be expected to exhibit a relaxation at ca 1 GHz, has been rea lized in the sense that our most nearly comparable bulk system, of equimolar water in 1-propanol has a primary relaxation at a comparable but higher frequency of 1.6 GHz. The existence of faster secondary relaxation in the bulk solutions may also have a counterpart for the interfacial layer, but present evidence is too meager to decide the question. The second principal result of this work, which was not anticipaged, was the finding of a need for at least a second relaxation of increasing amplitude and nearly constant relaxation time T 2 = 22 ± 3 ps, about three times that of pure water (8.3 ps at 25°C) but equal to that for a secondary relaxation of the neat alcohol. This has been found for several alcohols at various temperatures and frequencies. Early results of Girard and Abadie (48) for 1-octanol at room tempera ture indicate T2 = 40 ps, for example, with similar values for other alcohols .from work of Brot (49). For 1-propanol, measurements by Davidson and Cole (44) at low temperatures (-130 to - 150°C) showed such a relaxation in detail, but at much lower frequencies, and also a third still smaller and faster relaxation. Garg and Smyth (50) found a similar behavior at temperature 20, 40, and 60°C with derived values of T 2 estimated to give T2=20ps at 25°C, in agreement with our results (Their value t^=390 ps is, however, considerably larger than Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. t ^=320 ps from our and other more recent work). There is little doubt of the existence of smaller, fast relaxa tion processes in alcohols in addition to the primary one, but their molecular origins have been a subject of considerable conjecture and debate for many years. Two quite different kinds of mechanism proposed with numerous variations are changes in hydrogen bonding, either to.a new neighbor or within hydrogen bonded "chains" on the one hand (51), (52),(53), or to reorientations of unbounded, singly, and multiply bonded molecular complexes on the other (54) (55). An extensive dis cussion of the pros and cons for the several alcohols which have been studied is beyond the scope of this paper, but can be found in the Bottcher-Bordewijk treatise (56). In the present context, we suggest that the relaxation with T^ unchanged from the value for the neat 1-propanol but increasing specta cularly in amplitude an addition of up to 0.75 mole fraction of water is not to be explained in terms of reorientations of whole.molecules of either kind, much less any well defined, long lived aggregate. Rather, one needs to consider possibilities for reorientation of hydrogen bonding hydroxyl groups of either species constrained by local "struc ture" but not by necessity for appreciable displacements of attached alkyl groups. Even cursory study of space filling models of hydrogen bonded chains suggests plausible conformational changes and shifts in hydrogen bonding which could meet such requirements, with no obvious preferred candidates. Adequate computer simulations can be extremely useful for such purposes, as shown by the work of Helfand (57) for the simpler conformational dynamics of single polymer chains, but would seem to be enormously more complex for any straightforward study Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 of mixtures of transiently hydrogen bonded chains. Finally, we suggest two related propositions. The first is that, although we have been able to represent the present results reasonably well by a sum of two distinct Debye relaxation functions, there is no justification for supposing that either describes a simple dynamical process rather than sums or combinations of processes with nearly the same characteristic times on a logarithmic scale. Indeed, our data for solutions with mole fraction X from 0.5 to 0.75 give and T 2 different by less than the factor five sometimes cited as the minimum for resolving two Debye functions of the same amplitude, as each has width of e" at half height of 1.1 decades. Second, it should be possible to improve the definition of the processes, the faster ones especially, by measurements to higher fre quencies and at lower temperatures. It seems feasible to raise the upper frequency limit to 10 GHz even for water with £g = 80 by simple changes in cell design and in calibration of residuals in the TDR in strumentation (39), while measurements at 0°C and below should reduce the frequency ranges of dispersion by a factor of two or more. These further mesurements have not yet been possible because of time limita tion, but are planned for future work. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 CHAPTER IV MICROWAVE INTERFEROMETRIC DETERMINATION OF COMPLEX DIELECTRIC PROPERTIES INTRODUCTION This chapter, describes the design, construction, operation and testing of an apparatus which extends our measurement capabilities to 23.45 GHz. The device shown in block diagram form in Figure (24) is based on apparatti described by Straiton and Saxton et al. (60). and Tolbert (58),Schwarz (59), The device is essentially a microwave transmis sion type bridge circuit which measures the phase and amplitude change experienced by an electromagnetic wave as it traverses a sample speci men . The phase and amplitude shifts are converted into 8 and a, which are the imaginary and real parts of the complex propagation con stant, y = a + j3, from which e*, the complex dielectric constant is determined: Y = a + j B = jw(y * e * ) 2 where U* = yQ = 1 = permeability of sample material e* = e'-ie" A complete set of relations between a, 6, and e* is presented in Appendix B. EXPERIMENTAL The liquid sample is contained in a teflon cell consisting of an adjustable piston in cylinder arrangement shown in Figure (25). The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •SOURCE - KLYSTRON O REFERENCE LEVEL SET ATTENUATOR SPLITTER' y -ISOLATOR TRANSMITPHASE ANGLE - SLOTTED LINE S.L. SAMPLEMETERRECEIVE-ATTENUATION PA ATTENUATION Figure 24. Microwave Transmission Interferometer for the Determination of Complex Dielectric Constants at 23.45 GHz o M Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MICROWAVE SIGNAL AIR TEFLONPISTON *'0" RING RIM SEAL JQUID FEED TEFLON-CYLINDER LIQUID SAMPLE SPACE- 3/2 CELL SECTION AIR* / Figure 25. Sectional View of Variable Pathlength Teflon Sample Cell Used in the Determination of £* of Liquids by Microwave Interferometry 63 cell thickness is adjustable to allow for phase and amplitude measure ments as a function of sample thickness. The procedure involves bal ancing precision attenuator, PA, and slotted line, SL, for a minimum signal without the sample present. Then small increments of sample are introduced into the cell by turning the four cell positioning screws. Typically a distance of .05 inch = .1270 cm was used which cor responds to one complete turn of each of the 20 thread per inch screws. Micrometer measurements before and after were used to verify the ac curacy of this technique. procedure is repeated. sured. Upon introduction of the sample the balancing Typically, 9 such increments of sample are mea Plots of amplitude and phase versus pathlength are then con structed. The slopes of these graphs, determined with the aid of lin ear regression, yield a a n d A L i n decibels/cm and phase angle/cm res At spectively. It should also be noted that lensed horns were employed. Horn separation was 6 inches and the beam was focused down to a 1 inch spot size 3 inches away from each horn. way between the horns. A The sample was positioned mid sample calculation may be found in Appendix B. RESULTS AND DISCUSSION Figures (26) and (27) show the results of the determination of ag and AL respectively for 1-propanol, ethanol, acetone and water from inAt cremental sample length phase and amplitude measurements. It should be noted that this variable pathlength method is applied to account for the effects of reflections at the principle dielectric interfaces, i.e. air/teflon, teflon/sample, sample/teflon and teflon/air. The reflec tions come about as a direct result of the change in dielectric constant which occurs at each interface. Since the reflections are to a first Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o O 04 S138I03Q o o O 26. o Figure O Determination of a From WATER Variable Pathlength Attenuation Data ACETONE 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0001 X wd 'U IH S 3SVHd Figure 27. 2400 r Determination of AL From Variable Pathlength Phase Shift Data 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 approximation functions of the individual interfaces, measurement at multiple pathlengths can be used to subtract out their effect. Another reason for incremental measurements has to do with phase angle ambi guity. The slotted line section SL in Figure(24) is the recombining element for the interferometer. Waves from the source (reference) enter at the top while the received signals (signals which have passed through the sample) enter at the bottom. The interference patterns which result are detected by a movable probe (59), (61). of measurement is 0-180°. The range This means that phase shifts such as 45°, 45 + 180 = 225° or 45 + 360 = 405° would appear the same to SL. The incremental method precludes the possibility of such ambiguity by keeping the incremental phase shifts well below 180°. Resonance Effects. Another source of error which arises in these measurements is due to resonance effects. This is due to the interaction between sample specimen and both receive and transmit horns. To counteract this ef fect a variation of the 1/4 wavelength technique described by Little, et al. (62) and Epstein (63) has been applied. This technique in volves phase and attenuation measurements with the sample at a fixed position. The procedure is repeated with the sample displaced i wave length towards the transmit horn. The average of these two readings for both phase and amplitude are taken as the data pair at each fixed sample pathlength. Near Field Free Space Wavelength Correction Factor. The last aspect to be dealt with arises from the effect of wave diffraction. This occurs in closely coupled Transmit/Receive setups Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 such as the one employed here. The phenomenon was originally described by Kerns and Dayhoff (64) and Baird (65) and is of importance in the microwave interferometric determination of the free space velocity of electromagnetic energy (light). The phenomenon acts to lengthen the effective free space wavelength which occurs in the focused region be tween the closely spaced receive and transmit horns. X = KX e o where XQ = c/F c = Free Space Velocity of Light F = Frequency K = Xq = Nondiffracted Free Space Wavelength of Light Xg = Effective Wavelength used in Calculation of £* (See Appendix B) Diffraction Correction Constant Using an approximation technique Bussey (66) has estimated a value of K = 1.025. A value of 1.020 was chosen for this study as it produced values of e* (see other workers. a movable Table 4) in best agreement with observations A more exact of determination ofXgmight bemade with probe connected to a micrometer drive. The probe could be moved between the two horns (Figure 24) in the vicinty of the sample. This is a free space analog of a slotted line where the distance be tween two successive voltage minima gives i Xg(61). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Table 4. Dielectric Properties of Standard Liquids Determined by Micro wave Interferometry at 23.45 GHz Sample Temp 1-Propanol 24.0°C 9.74 .530 3.42 .87 3.35 .80 Ethanol 24.5°C 17.09 .665 4.18 1.70 4.25 1.69 7.37 17.5 7.4 36.90 32.5 35.1 Acetone 24.7°C Water 22.0°C a^db/cm 35.75 119.8 AL/At e’ 2.03 17.85 3.33 33.28 e" e’lit e"lit Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 CHAPTER V APPLICATIONS The following is a brief listing of applications of electromag netic properties measurement techniques which might be of interest to chemical engineers. Perl (67),(68) has applied the technique of Microwave Absorption Spectroscopy (69), (70), (31) to the determination of oil and water saturations in porous sandstone rocks. This apparatus allows observa tion of the two phase flow process in the rocks during enhanced oil re covery experiments. Doughty (71) applied a microwave resonance technique at 9.5 GHz to the determination of water content in oil-water emulsions. His technique does not, however, take into account the difference in di electric properties of the two basic emulsion types which has been described in Chapter II of the present study. Of interest, however, is his use of a resonant cavity with sample tube holes drilled in the narrow side of the cavity. In this manner the sample cuts across an electric field whose intensity varies with distance. This allows a larger sample tube to be employed,3 mm x 2 mm, outer and inner dia meter (compared to the perturbation set-up described in the present study). This might be more useful in a flow monitoring scheme. Prausnitz et al (72) have presented a numerical model for the prediction of vapor-liquid equilibrium compositions from fundamental properties measurements. The most important of these basic proper ties is the vapor phase second virial coefficient which itself is re lated to the dipole moment. These dipole moments are usually Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 determined by measurement of the dielectric constant of the gas (73). It is of interest to note that, at present, Prausnitz’s model relies on calculated dipole moments. He has found large discrepancies in the case of polar associating molecules such as water, methanol, acetic acid, etc. Currently he uses an association parameter (n) to bring his model calculations in line with experimental observations. Dielectric studies may serve to quantify such vapor phase associations. Indeed, the determination of chemical structure has been the primary goal of most studies of dielectric phenomena; Debye (1), Smyth (73). More recently, Cole et al.(74),(75) has described a method for the determination of second virial coefficients from dielectric measure ments. The difference between dielectric properties of water, oil, and rock have been used in a novel determination of absorbed water-inoil reservoirs (Rau, (76)). This data, which improves the deter mination of reservoir oil saturation, provides information critical to the drilling of successful (not dry) oil wells. Ellerbruch (77) presented a microwave method for the measure ments of densities and flow rates for cryogenic materials such as Hydrogen and Nitrogen as liquids or slushes, using resonant cavity and microwave doppler techniques respectively. Changes in dielectric constant might occur in chemical reactions affording a means by which reaction product compositions or rates could be determined nondestructively and noninvasively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 CHAPTER VI SUMMARY AND FUTURE WORK This chapter has been set-up with respect to the separate investi gations presented in Chapters II, III, and IV. Chapter II Dielectric Properties of Emulsions It would be of interest to investigate the effects of particle size in such dispersed phase systems. Here, the low frequency (Mega Hertz) range may provide more information as the interfacial polariza tion effect is quite strong there and may exhibit a greater sensitivity to drop size. The effect of surfactant type and concentration should also be examined. It is possible that e* of the interfacial layer for 0/W macroemulsions is sufficiently different from its W/0 counterpart to explain the difference in dielectric properties of these two basic macroemulsion types (2), (5). With regards to this it may be possible to generate dilute (<10%) surfactant free W/0 type dispersion using a neutral bouyancy oil phase such as the CCl^/oil mixture (9) described in this chapter. Sonication would be the recommended dispersion tech nique for creating submicron or micron size droplets. Chapter III 1-Propanol/Water Solution The dielectric study described in this chapter was performed over the range of 50-7800 MHz (0.05-7.8 GHz). The TDR apparatus employed in this study utilizes an open circuit coaxial transmission line as a test cell and hence was limited to measurements of e'<20 at Ca 5 GHz. This limited the study to solutions containing less than .75 mole Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 fraction watar (Ca .55 weight fraction). The model developed to de scribe the mixture dielectric properties, a two time constant Debye type representation, required fitting 4 parameters to the data over the range of frequencies investigated. It would be useful then to examine these mixtures in the resonance apparatus at 9.5 GHz and the transmis sion apparatus described in Chapter IV at 23.45 GHz. These apparatti do not have such upper bounds on their measurement capabilities and the data might be useful in extending the fit to higher frequencies while also testing the resonability of such a two time constant hy potheses. With regards to another application Brost and Davis (31) have used isopropanol/water mixtures to simulate the microwave absorption properties of water-oil mixtures commonly found in porous media oil re covery experiments. They have attempted to use such solutions to cali brate the porous media itself. Their plots of microwave attenuation vs. wt% alcohol exhibited a slight nonlinearity at 9.5 GHz and a gross nonlinearity at CA 24 GHz. They had assumed that the alcohol/water mixture absorption would be linear with alcohol content. This is in direct conflict, however, with our results presented in this chapter which suggests a very high degree of interaction between the alcohol and water molecules in such mixtures which was not seen to vary linearly with weight fraction. It would, therefore, be of further interest to characterize the dielectric properties of such mixtures at typical core flooding frequencies (9.5 and 23.5 GHz). Such information would be useful in our lab where a microwave attenuation core flooding appa ratus has become a standard tool for the investigation of multiphase flow and recovery processes in porous media enhanced oil recovery Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 experiments. Perl (67). Chapter IV Microwave Transmission Interferometry at 23.45 GHz This apparatus differs from those described in the previous chap ters in that it is capable of measuring large samples and can in prin ciple be applied to measurements in a porous medium. As it stands now, however, the technique requires data as a function of pathlength (sample thickness). This data is then used in a simple iterative solu tion to the complex dielectric constant of a sample assuming a plane electromagnetic wave in an infinite medium with no reflections or in teractions between the sample and container boundaries (see Appendix B). A mathematical technique developed by Richmond (78) and Bussey and Richmond (79) does, however, allow in principle for the direct calculation of £ ' and £". The method, a digitally implimented recur sive technique, simply carries through the exact solution to the field equations across each dielectric interface i.e. air/sample, thru sample, sample/air etc. A drawback to this procedure, however, is its inability to account for resonance effects which arise from interactions between the transmit horn and sample front face, and the receive horn and sample back face. In the present study these effects are averaged out by the r wavelength method (62),(63) described in this chapter, and this might be a useful approach if the exact equation method is attempted. The data acquisition procedure for this experiment is rather tedi ous and time consuming. It requires manual balancing of a precision attenuator and phase measuring device (micrometer fitted slotted line section of waveguide). Also, the determination of phase shift can be ambiguous as the slotted line range is from 0-180°. Hence, a true Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 reading of 45° could also be 45° + 180° = 225° or 45° + 360° = 405° etc. In the present study, this was accounted for by the introduction of small increments of sample liquid into the variable path length cell. The problem of data acquisition and phase angle ambiguity might be solved simultaneously be replacing the precision attenuator and slotted line with a computerized Automatic Network Analyser (ANA). This device also known as a signal analyser, is phase locked and capable of re solving phase and attenuation changes of Ca .1° and .1 db respectively. It also has the advantage of stepped frequency operation. This fea ture can allow the direct determination of unambiguous phase shifts by noting the phase shift differences at two or more frequencies. This fractional phase shift can then be used to back calculate the total, true phase shift. Also, as this device is computer controlled it is amenable to on line data processing. This would be useful if the re cursive digital technique described above is adopted. Also worthy of mention is a Universal Microwave Phase-Measuring System developed by Ernst (80) for use in plasma diagnostic applications. This system uses a single sideband with suppressed carrier (SSBSC) (80) method for de tecting microwave phase changes and can measure phase shifts of up to 20 it radians (3600°) unambiguously. Summary This thesis is concerned with the application of microwave diag nostic techniques of interest to chemical engineers. The techniques described herein use electromagnetic methods to determine concentrations and emulsion types, particularly in solutions or dispersions where water is one of the components. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 These electronic determinations can be made rapidly, nondestructively and 'in some cases, noninvasively. The electronic measurements also lend themselves to interfacing in a computer process control scheme. It should also be noted that the dielectric techniques de scribed herein have been devised to take the place of wet chemical and optical microscopy techniques and also provide an electronic means of monitoring multiphase flow within a porous media. Highlighted in this work is: 1) A dielectric method for the simultaneous determination of macroemulsion type and water content using a microwave resonance dielectrometer; 2) A study which characterized the broadband dielectric pro perties of 1 -propanol/water solutions using the technique of Time Domain Reflectrometry (TDR) and; 3) Complete description of the design, construction and opera tion of a K-Band (23.46 GHz) Microwave Transmission Inter ferometer for the determination of complex dielectric pro perties of liquids or solids such as porous media. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 APPENDIX A STANDARDS USED IN THE PERTURBATION STUDY OF CHAPTER II AND SAMPLE CALCULATIONS Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 Standards Used in the Perturbation Study of Chapter II The values of e' and e" for the liquid standards used in the micro wave resonant cavity standard reference calibration procedure were chosen as follows: Methanol: Debye dispersion parameters suggested by Poley (82) as reported by Buckley Sflid Maryott (83) were used to calculate e' and e" from e * = e' - ie" = using eg = 32.8, Acetone: + (es-eoo)/(l-(iujT)1-a A.l = 5.62 and T = 48.8 x 10- ^2 sec and a = 0.0 e 1 and e" were determined by interpolation of the data of Smyth et al (84) as reported in Reference 83. Water: e' and e" were calculated from Equation A.l using Cole- Cole (85) dispersion parameters based on a regression analysis of existing data by Mason et al (8 6 ) and Grant et al (87) as suggested by Hasted (45), ( 88 ). The parameters used were: e t = 78.96, e = 4.22, S oo = 8.46 x 10-1 2 sec and a = 0.013. Sample Calculation for the Resonance Dielectrometer Ex. acetone at 9.505 GHz Refer to Figures 2 and 3 on Pages 11 and 13 respectively. First we rewrite equations 2.2 and 2.3 noting the following re lationships. V = total volume = length x width x height i.e. V = LWH v = interior volume of glass capillary tube in cavity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 kg = rnr/L = 7ir/(15.285 cm) kQ = 2irF/c = 2tt 9.505 x 10 9 Hz/3 x 10 10 cm/sec Substituting these relationships into equation 2.2 for e' and equation 2.3 and 2.7 for e" we obtain e* = Ci) -11*11 /u\ U (TTr H) (k /k )2 = (i)(W/irr2 )(k /k )2 AL + 1 g O o n A.l Inserting numerical values for the constants above we obtain (W=.9 inch): e" = (i)(3800.75)AL + 1 A.4 The cavity is first adjusted to obtain resonance with an empty sample tube bynoting the maximum dip below the baseline. points are thencalculated using equations 2 .1 a The and2 .1 b (page 2power 1 2 ). For acetone at 9.505 GHz the empty resonance dip, dbg = 6.35 db and the sample dip, dbg = 3.75 db from which: (dbe )| = 2.11, (dbg )^ = 1.48 A.5 the moveable short position is varied between the % power values from which the following results were obtained (L2_Li)s = -0114 cm A*6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 (L,2~L^)e = .0080 cm A.7 (L2+Ll V 2 = 1*72450 A .8 A.9 (L2+Ll V 2 = 1*73520 cm Now using A .6 and A.7 in A.3, and A .8 and A.9 in A.4 we obtain e’ = 21.33 e" = 3.23 Voltage Ratio Calculation of e" From equation 2.8 R s = .649, R e = .481 e" = (i)(3800.75)(.008)(.649-.481)/(1-.649) = 3.64 The value of the empty tube Q-factor in A.7, was determined by repetitive measurement. This value was, therefore, known to a greater accuracy (± .0001 cm) and the voltage ratio technique was employed throughout this work for the determination of e" hence ( e ' - l ^ = 20.33 and = 3.64 are the measured values obtained using the perturbation approximation. These values must now be corrected using the procedure outlined on page 19, by equation 2.11 and the constants in Table 5. (e'-l)c = .9259(20.33) + .3920 = 19.22 (e")c = (3.64)(19.22)/(20.33) = 3.44 the final corrected values are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 £ 1 = 20.22 e" = 3.44 Smyth (73) found s' = 20.1 and e" = 3.41 Simultaneous Determination of Emulsion Type and Water Content From Dielectric Measurements on Unknown Emulsion Using the Calibration Curves in Chapter II 1. Given an unknown emulsion with e*=13.0 and e"=6.5 at 11.003 determine type and water content. tangent e 'V e ’ = 0 . 5 . GHz, We first calculate the loss We see from Figure (14) that this cor responds to a 0/W type emulsion. Once the emulsion type has been determined we find from Figure 12 or from Figure 13 that this corresponds 2. to a fractional water content of 0.3. Given the measured values of e ? and e" = 10,3 at 11.003 GHz, respectively, we first calculate the loss tangent e 'V e ' = 0 . 3 . We see from Figure 14 that this corresponds to a W/0 type emul sion. Again, once the emulsion type has been identified one may use either Figure 12 or 13 to determine the fractional water content of 0.3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 5. Standard Liquid Reference Calibration Data for the Microwave Resonance Dielectrometer Frequency (GHz) 8.193 (e ’- D p («• Sample Methanol 8.85 8.34 Acetone 21.35 19.23 Water 72.76 65.45 9.505 1 )T £"p e"x (E1-■Dp 11.003 (*•- -1 )T E"p e"t (£'--l)p (C- _1)T E"p e"T 9.70 9.34 7.58 7.48 9.0 8.34 6.56 6.81 3.32 2.99 19.90 19.10 3.6 3.41 19.40 18.93 3.74 3.83 27.14 66.71 62.18 32.6 29.75 61.49 58.39 34.37 32.11 30.0 7.6 Correction Eqn 2.11 Constants Slope, a .8975 .9259 .9452 Intercept, b .1538 .3920 .3690 Correlation Coefficient Avg. Error, Back Calculations for 3 Standards .99991 £'=±1.1% £'=±1 .1% £'=±1.6% e"=± 2 .0 % e"=±2.5% e "=3.4% Calibration Line (e'-l)T = P = Perturbation Measurement Value, (e'-l) + b T = True, Standard Reference Value 7.41 82 APPENDIX B DIELECTRIC EQUATIONS FOR THE INTERFEROMETER DESCRIBED IN CHAPTER IV Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MICROWAVE TRANSMISSION EQUATIONS TRANSMISSION EQUATIONS Phase constant due to the sample 3s = eo \ P is given bySchwarz (59) ((1 + ((1 + (£"/£')2 )i )/2)i A.l which for the sake of Brevity will be rewritten as A.2 where A is everything to the right of the radical in Equation A.l but the interferometer measures 3 s - 3 = o m A.3 hence S m +3 o =3 v/e' A o * A.A where 3 m = 2 3 g(AL/At) A.5 Adding Equations A.4 and A.5 and rearranging the result we obtain 6? = but (1/A + 2 6 g(AL/At)/ 6 0 A )2 A .6 3 = » A = 1.597 cm as determined by slotted line measureg Ag g ments of the distance, d, between successive minima, i.e. Ag = 2 d So'f1 o but here we must substitute A for A (Baird (65)) to account for Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 diffraction effects arising from the close placement of the receive and transmit horns. We note also the following relationships A where K e e = AK o e = diffraction factor at 23.45 GHz Xq = C/F = 3 x 1010/(23.45 x 109 ) = 1.279 cm With these substitutions Equation A .6 then becomes (using Kg = 1.02 as described in Chapter IV) e' = (1/A + (1.634)(AL/At)/A)2 A.7 where AL/At is the slope of the phase versus distance plot (see Figure 27) in cm of slotted line micrometer travel per unit sample pathlength, cm/cm For e" Schwarz (59) gives e" = 2a 8s/eo2 = 2je' (ag) A AQ/(8.686)(2Tr) which at 23.45 GHz and substituting Ag for Aq becomes A ( .0478) where ^ A .8 is the slope of attenuation versus distance plot (see Fig ure 26) in decibels per unit sample pathlength, db/cm. It is of interest to notice the non zero Y intercept for the attenuation plots, particularly those for water and acetone. This phenomenon is due to reflection at the two liquid/teflon interfaces. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 Determination of ot^ and 8 ^ As discussed above, 8 g is determined from equation A.3 and A.5. The phase angle, AL, and attenuation determined at each path length as follows: 1. Adjust level set to desired maximum attenuation, 2. Balance bridge for minimum by adjusting slotted line SL and precision attenuator PA without the cell. might be 40 db and .350 cm. Typical readings, In this example 40 db is now the maximum sample attenuation that can be measured. 3. Insert empty cell between horns. tion. Readjust phase and attenua Typical readings would be 39.4 db and .4827 cm. This means the cell has a loss of .6 db and a phase angle of .1327 cm. Just as a matter of interest the teflon thickness is .495 cm and this yields k k = .1327/.495 which when inserted into At equation A.7 (A^l.O) yields £* =2.07,the dielectric constant of the pure teflon. 4. Move cell 1/4 wavelength towards transmit Horn by insertion of shims. In this work (.96)(l/4) A0 wavelength was employed Redo the determination of AL and db as in Step 3. 5. Average AL of Step 3 and 4 to obtain AL to be plotted in Figure 27. Do the same with the values of attenuation for Figure (26). 6 . Determine AL and a At from the slope of the phase data versus s pathlength and attenuation vs pathlength. In this study, the best straight line through the data was determined by linear regression.Typical correlation coefficients exceeded .99 on AL/At and .98 on a . s Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 7) Setting k^, the free space wavelength correction factor equal to 1 , 0 2 as discussed in the chapter,calculate using equations A.7 and A. 8 . e' and e" Note that the two equations are coupled and require an Iterative Solution. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 BIBLIOGRAPHY (1) Debye, P., Polar Molecules, The Chemical Catalogue, New York, 1929. (2) Clausse, M., "Dielectric Properties of Emulsions and Related Systems", in Encyclopedia of Emulsion Technology. Vol. 1, Chap. 3, Sec. C, P. Becher, ed., 1980. (3) Foster, K.R., Epstein, B.R., Jenin, P.C. and MacKay, R.A., "Di-slectric Studies on Nonionic Microemulsions", J. Colloid Inter face Sci.. Vol. 8 8 , P. 233, 1982. (4) Epstein, B.R., Foster, K.R. and MacKay, R.A., "Microwave Dielectric Properties of Ionic and Nonionic Microeraulsions" J. Colloid Interface S ci.. Vol. 95, P. 218-227, 1983. (5) Hanai, T., "Electrical Properties of Emulsions", in Emulsion Science, P. Sherman ed., Academic Press, London and New York, P. 353-478, 1968. (6 ) Sillars, R.W., "The Properties of a Dielectric Containing SemiConducting Particles of Various Shapes", sJ. Institution of Electrical Engineers, Vol. 80, P . 378-394, 1937. 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C hem. Phys., Vol. 23, P. 493, 1955. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 (41) Heston, W.M., Hennelly, E.J. and Smyth, C.P., "Dielectric Con stants, Viscosities, Densities, Refractive Indexes, and Dipole Moment Calculations for Some Organic Halides", J. Am. Chem. Soc., Vol. 72, P. 2071, 1950. (42) Levesque, D., Weiss, J.-J. and Oxtoby, D.W., "A Molecular Dynam ics Simulation of Rotational and Vibrational Relaxation in Liquid HC1", J. Chem. Phys.. Vol. 79, P. 917, 1983. (43) Rahman, A. and Stillinger, F.H., "Molecular Dynamics Study of Liquid Water", J. Chem. Phys.. Vol. 55, P. 3336, 1971. (44) Davidson, D.W. and Cole, R.H., "Dielectric Relaxation in Glycerol, Propylene Glycole, and n-Propanol", J^. Chem. Phys., Vol. 19, P. 1484-1490, 1951. (45) Hasted, J.B., "Aqueous Dielectrics". Chapman and Hall, Ch. 3, P. 89, 1973. (46) Knelson, D., and Keyes, T., "Unified Theory of Orientational Relaxation", J. Chem. 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