DIELECTRIC PROPERTIES OF MIXTURES OF CLAY-WATER-ORGANIC COMPOUNDS

Transcription

1 DIELECTRIC PROPERTIES OF MIXTURES OF CLAY-WATER-ORGANIC COMPOUNDS By Birsen Canan

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3 ABSTRACT The propagation of an electromagnetic wave through a material is dependent on the electrical and magnetic properties of the material. Through electromagnetic or any other geophysical techniques, the ultimate goal of a geophysicist is the identification of subsurface materials and their spatial distribution. Reaching this goal will only be possible through a complete understanding of the property behavior of different materials. For electromagnetic exploration techniques, especially for ground penetrating radar (GPR), and very early time electromagnetic (VETEM) survey techniques, the dielectric permittivity is one of most important material properties. The interpretation of VETEM requires the knowledge of both broad frequency band dielectric permittivity and conductivity for subsurface materials. In the first part of this research, the dielectric permittivities of Na- and Camontmorillonite-water mixtures were measured with respect to frequency (.3-3 MHz), concentration (12-62 %wt of clay), three different inorganic salts (NaCl, CaCl 2, and KCl), and three different molarities of the inorganic salts (.1,.1, and.1 mole/liter) for a total of 82 measurements. The frequency spectrum from 3 KHz to 3 MHz of the measured permittivities of the clay-water mixtures were characterized by a model combination of Cole-Cole and Davidson-Cole models, using the Marquardt- Levenberg least square inversion technique. Then, a volume-mixing model was sought to combine the effect of the polarization in the electrical double layer with the volume fraction of the components in the mix. For the volumetric mixing model, models suggested by Chew and Sen (1982), Chew (1984), Lyklema, et al. (1983), and Schwarz (1962) were investigated. The Schwarz model was found the best suited model for the clay-water mixtures. Lockhart (198-a) suggested the usefulness of the Schwarz model to calculate the dielectric iii

4 permittivities of clay-water mixtures between Hz frequencies. It is seen from our measured dielectric permittivity values and frequency spectrum analysis that polarization of the ions in the electrical double layer still plays an important role in the increased values of dielectric permittivities of clay-water mixtures at higher frequencies. The nonuniformity of the particle sizes along with the change in activation energies of the polarizing ions cause distributions in three relaxations. The volume-mixing model developed is for multiple relaxations based on the Schwarz model. Our results show the Schwarz model fits well to measured data for Na-montmorillonite in the frequency range between 3 KHz and 3 MHz, and for Ca-montmorillonite between 5 KHz and 3 MHz. In the second part of the research, four organic contaminants, trichloroethylene (TCE), tetrachloroethylene (PCE), ethylene glycol, and phenol, were added into the previously prepared samples of clay-water mixtures to make up a total of 216 samples, and their dielectric permittivities were measured. The frequency spectrum analysis of the dielectric permittivities of each contaminated sample is carried out by using the Cole- Davidson model parameterization via the Marquardt-Levenberg inversion technique. A comparison of the frequency spectrum of the dielectric permittivities of contaminated versus uncontaminated samples was done to see if there was any pattern to help to identify a particular organic contaminant via dielectric permittivity values of mixtures. Depending on the nature of the organic, the changes observed are: Decrease of the magnitude of dielectric permittivity and shift of the relaxation to lower frequencies for ethylene glycol and phenol, and increase in the magnitude of dielectric permittivity and shift of the relaxation toward higher frequencies for TCE and PCE contaminated samples. iv

5 TABLE OF CONTENTS Page ABSTRACT iii TABLE OF CONTENTS v LIST OF FIGURES xvi LIST OF TABLES xxxiii LIST OF SYMBOLS xxxvii ACKNOWLEDGEMENT xliv DEDICATION xlv CHAPTER-1 INTRODUCTION CHAPTER-2 BACKGROUND FOR MONTMORILLONITE AND DOUBLE LAYER Montmorillonite Clays And Their Properties Montmorillonite Structure Isomorphic Substitution And Cation Exchange Swelling Of Montmorillonite Electrical Double Layer Theory Gouy-Chapman Double Layer Model Stern s Double Layer Model Overlapping Double Layer Model Mathematical Treatment Of Double Layer xi

6 2.3.1 Diffuse Part Of The Double Layer The Inner Part Of The Double Layer Overlapping Double Layer-Modified Gouy-Chapman Model Effects Of Electrical Double Layer On The Dielectric Properties Of Clay CHAPTER-3 THEORETICAL BACKGROUND OF DIELECTRIC PHENOMENA Complex Dielectric Permittivity Relaxation Time And Distribution General Theory Of The Dielectric Permittivity Of Two Phase Disperse System Effect Of Double Layer On The Dielectric Permittivity Of Dispersed System Schwarz Model For Dielectric Permittivity Of Colloidal Suspension Dielectric Properties Of Montmorillonite Suspended In Electrolyte CHAPTER-4 CLAY ORGANIC INTERACTION Previous Studies Interaction Between TCE, PCE And Montmorillonite Interaction Between Ethylene Glycol And Montmorillonite Interaction Between Phenol And Montmorillonite The Relation Between Dielectric Properties of Organics and Montmorillonite Swelling Difficulties On Determining The Type Of Reaction On Clay xii

7 4.7 Reactions Effecting Dielectric Enhancement In Clay-Organic System 59 CHAPTER-5 LABORATORY SETUP AND TEST PROCEDURES Selection Of Materials Clays Organic Compounds Aqueous Solutions Sample Preparation Background For Fundamentals Of Transmission Line Theory Propagation Of EM Wave Through A Coaxial Line Physical Meaning Of Calibration Coefficient Laboratory Measurement System The Calibration Of The Vector Network Analyzer Dielectric Measurement Of The Samples Calculation of Dielectric Permittivity System Check And Error Analysis System Check And Data Evaluation Resonance Of The Sample Holder Entrained Air And Teflon Insert Problems With Sample Holder Description Of Typical Data Display CHAPTER-6 EXPERIMENTAL AND MODEL RESULTS OF CLAY-WATER MIXTURE Cole-Davidson Model And Marquardt-Levenberg Inversion BHS Model And Its Inversion Schwarz Model For Dielectric Permittivities Of Clay-Water Mixture 16 xiii

8 6.3.1 Application Of Schwarz Model For Clay-Water Dielectric Permittivities Surface Charge Density Particle Size And Its Distribution Mobility Of The Cations In The Stern Layer Multiple relaxation Schwarz Model For Montmorillonite Non-Uniqueness In Variables Of The Schwarz Model The Effect Of Clay Concentration DC Resistivity And The Effect Of Inorganic Salt The Effect Of The Clay Type Comparing The Schwarz Model With Measured Dielectric Permittivity Of Clay Water Mixture Discussion Of Dielectric Permittivities of Clay-Water Electrolyte Experimental Limitations In Testing The Schwarz Model CHAPTER-7 THE INFLUENCE OF ORGANICS ON DIELECTRIC PROPERTIES OF MONTMORILLONITE-WATER MIXTRURES Comparison Of Dielectric permittivities of Contaminated Samples With Blank Samples TCE and PCE Versus Blank Samples Ethylene Glycol Versus Blank Samples Phenol Versus Blank Samples Comparison Blank Samples And Contaminated Samples Together Effects of Solution Concentration And Type Of The Salt Effects of Exchangable Cations Of Clay The Effect Of The Order of Mixing Clay Water And Contaminants Discussion Of Dielectric Permittivities Of Contaminated Samples The Magnitude Of The Dielectric Permittivities Of Contaminated Samples xiv

9 CHAPTER-8 CONCLUSIONS REFERENCES CITED APPENDIX OUTLINE xv

10 LIST OF FIGURES Figure 2.1 Figure 2.2 Page Schematic representation of 2:1 type of clay minerals: (a) plan view of the tetrahedral layer, (b) cross section, (Drewer, 1988)... 8 Schematic representation of Gouy-Chapman double layer model: ion distribution in double layer, (b) electrical potential distribution when the surface is positively charged, where ψ is surface potential, and 1/κDebye screening distance, (Shaw, 1992) Figure 2.3 Schematic representation of the structure of the electrical double layer and potential distribution according to the Stern model when surface is positively charged, where ψ is the surface potential, and ψ d is the stern layer potential, ψ is the zeta potential, and (1/κ) is Debye screening distance, (Shaw, 1992) Figure 2.4 The geometry of overlapping double layers, (a) schematic representation of the equipotantial lines around two charged particles immersed in an electrolyte, (b) representation of the one-dimensional idealization of the situation in (a), (c) variation of the electrostatic potential ψ(x) with the coordinate x, whose origin is taken at the surface of the plate on the left side, d is the half distance between the two plates, (Smalley, 1994) 24 Figure 3.1 Complex dielectric permittivity curves on polar plane (a) Debye type relaxation (Böttcher, 1952), (b) Cole-Cole type relaxation (Cole and Cole 1941), (c) Davidson-Cole type of relaxation of liquid molecules (Davidson and Cole, 1951) Figure 3.2 Measured dielectric dispersion curves of an aqueous solution of hemoglobin.the curves show three separate dispersion regions. Each maximum in the ε curve corresponds a relaxation time τ = 1/ 2πfrx for each dispersion, (after Harrington and Peacocke, 1978) Figure 5.1 a, b, c Basic flow graph of a two-port network (Adams, 1969) xvi

11 Figure 5.2. a-gr9-lz5 (5 cm length, 14 mm diameter coaxial) sample holder; b-detailed view of coaxial sample holder Figure 5.2 c Scaled drawing of a teflon insert Figure 5.3 Block diagram of the dielectric permittivity measurement system.. 77 Figure 5.4 Real dielectric permittivity and log-loss tangent of air measured with four different sized sample holders (a) 5, (b) 1, (c) 15, and (d) 3 cm. These four plots show the effect of the sample holder length: Decrease in low frequency resolution with decrease in sample holder length and decrease in the frequency at resonance start appearing with increasing length. In figure (a), this frequency is about 15 KHz Figure 5.5 Figure 5.6 Figure 6.1 Figure 6.2 Figure 6.3 Dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data of SWy-2 and.1m NaCl electrolyte mixture, contaminated with TCE (sample #2) SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2) 89 STx-1 and.1m NaCl electrolyte mixture s relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when one relaxation is assumed STx-1 and.1m NaCl electrolyte mixture s relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when two relaxations are assumed STx-1 and.1m NaCl electrolyte mixture s relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when three relaxations are assumed xvii

12 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Figure 6.9 Figure 6.1 Figure 6.11 Figure 6.12 Figure 6.13 Figure 6.14 STx-1 and.1m CaCl 2 electrolyte mixture s relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when one relaxation is assumed STx-1 and.1m CaCl 2 electrolyte mixtures relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when two relaxations are assumed STx-1 and.1m CaCl 2 electrolyte mixtures relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when three relaxations are assumed STx-1 and.1m CaCl 2 electrolyte mixtures relative dielectric permittivity and log-loss tangent and their Cole-Davidson model when four relaxations are assumed The dielectric frequency spectrum of STx-1 mixed with.1m NaCl and ethylene glycol. The Cole-Davidson model and inversion were applied and the first set of Cole-Davidson parameters were generated The dielectric frequency spectrum of the same sample presented in Figure (6.8). The Cole-Davidson model and inversion were applied and the second set of Cole-Davidson parameters was generated Combined plots dielectric permittivity spectrum of the data generated using two different sets of Cole-Davidson model parameters, refer to Figures (6.8) and (6.9). Both set can give the same dielectric permittivity and log-loss tangent values above.3 MHz frequency, but not below this frequency The effect of α on the relative dielectric permittivity when all other variables of the Schwarz model are kept constant The effect of diffusion coefficient of the counterions (D) on the relative dielectric permittivity when all other variables of the Schwarz model are kept constant The effect of particle size (R) on the relative dielectric permittivity when all other variables of the Schwarz model kept constant The effect of the volume fraction of the colloidal particles (p) on the xviii

13 relative dielectric permittivity when all other variables of the Schwarz model are kept constant Figure 6.15 The linear relationship between εs and concentration function, both are dimensionless for montmorillonite water mixtures (after Lockhart, 198-a), and symbols are measurements Figure 6.16 Figure 6.17 Figure 6.18 Figure 6.19 Figure 6.2 Figure 6.21 Figure 6.22 Figure 6.23 Figure 6.24 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #1). 127 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 128 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 129 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 13) SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #1). 131 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 132 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 133 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data, and the Schwarz model and its parameters (sample #4). 134 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air xix

14 corrected data and the Schwarz model and its parameters (sample #2). 135 Figure 6.25 Figure 6.26 Figure 6.27 Figure 6.28 Figure 6.29 Figure 6.3 Figure 6.31 Figure 6.32 Figure 6.33 Figure 6.34 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 136 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #1). 137 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 138 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 139 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 14 SWy-2 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 141 SWy-2 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 142 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #1). 143 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 144 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 145 xx

15 Figure 6.35 Figure 6.36 Figure 6.37 Figure 6.38 Figure 6.39 Figure 6.4 Figure 6.41 Figure 6.42 Figure 6.43 Figure 6.44 Figure 6.45 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 146 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #1). 147 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 148 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 149 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 15 SWy-2 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #2). 151 STx-1 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 152 STx-1 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 153 STx-1 and.1m NaCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 154 STx-1 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 155 STx-1 and.1m CaCl 2 electrolyte mixture s dielectric permittivity xxi

16 spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 156 Figure 6.46 Figure 6.47 Figure 6.48 Figure 6.49 Figure 6.5 Figure 6.51 Figure 6.52 Figure 6.53 Figure 6.54 Figure 6.55 STx-1 and.1m CaCl 2 electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 157 STx-1 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 158 STx-1 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #4). 159 STx-1 and.1m KCl electrolyte mixture s dielectric permittivity spectrum including Cole-Davidson model parameters for entrained-air corrected data and the Schwarz model and its parameters (sample #3). 16 A combined plots of dielectric frequency spectrum of the samples of SWy-2 mixed with.1m NaCl, CaCl 2, and KCl electrolyte A combined plots of dielectric frequency spectrum of the samples of SWy-2 mixed with.1m NaCl, CaCl 2, and KCl electrolyte A combined plots of dielectric frequency spectrum of the samples of SWy-2 mixed with.1m NaCl, CaCl 2, and KCl electrolyte A combined plots of dielectric frequency spectrum of the samples of STx-1 mixed with.1m NaCl, CaCl 2, and KCl electrolyte A combined plots of dielectric frequency spectrum of the samples of STx-1 mixed with.1m NaCl, CaCl 2, and KCl electrolyte A combined plots of dielectric frequency spectrum of the samples of STx-1 mixed with.1m NaCl, CaCl 2, and KCl electrolyte Figure 7.1 SWy-2 and.1m NaCl electrolyte mixed blank samples Figure 7.2 SWy-2 and.1m NaCl electrolyte mixed blank samples xxii

17 Figure 7.3 SWy-2 and.1m NaCl electrolyte mixed blank samples Figure 7.4 SWy-2 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.5 SWy-2 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.6 SWy-2 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.7 SWy-2 and.1m KCl electrolyte mixed blank samples Figure 7.8 SWy-2 and.1m KCl electrolyte mixed blank samples Figure 7.9 SWy-2 and.1m KCl electrolyte mixed blank samples Figure 7.1 SWy-2,.1M NaCl electrolyte and TCE mixed samples Figure 7.11 SWy-2,.1M NaCl electrolyte and TCE mixed samples Figure 7.12 SWy-2,.1M NaCl electrolyte and TCE mixed samples Figure 7.13 SWy-2,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.14 SWy-2,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.15 SWy-2,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.16 SWy-2,.1M KCl electrolyte and TCE mixed samples Figure 7.17 SWy-2,.1M KCl electrolyte and TCE mixed samples Figure 7.18 SWy-2,.1M KCl electrolyte and TCE mixed samples Figure 7.19 SWy-2,.1M NaCl electrolyte and PCE mixed samples Figure 7.2 SWy-2,.1M NaCl electrolyte and PCE mixed samples Figure 7.21 SWy-2,.1M NaCl electrolyte and PCE mixed samples Figure 7.22 SWy-2,.1M CaCl 2 electrolyte and PCE mixed samples Figure 7.23 SWy-2,.1M CaCl 2 electrolyte and PCE mixed samples xxiii

18 Figure 7.24 SWy-2,.1M CaCl 2 electrolyte and PCE mixed samples Figure 7.25 Wy-2,.1M KCl electrolyte and PCE mixed samples Figure 7.26 SWy-2,.1M KCl electrolyte and PCE mixed samples Figure 7.27 SWy-2,.1M KCl electrolyte and PCE mixed samples Figure 7.28 Figure 7.29 SWy-2,.1M NaCl electrolyte and ethylene glycol mixed samples SWy-2,.1M NaCl electrolyte and ethylene glycol mixed samples Figure 7.3 SWy-2,.1M NaCl electrolyte and ethylene glycol mixed samples. 198 Figure 7.31 Figure 7.32 SWy-2,.1M CaCl 2 electrolyte and ethylene glycol mixed samples SWy-2,.1M CaCl 2 electrolyte and ethylene glycol mixed samples Figure 7.33 SWy-2,.1M CaCl 2 electrolyte and ethylene glycol mixed samples. 2 Figure 7.34 Figure 7.35 Figure 7.36 SWy-2,.1M KCl electrolyte and ethylene glycol mixed samples SWy-2,.1M KCl electrolyte and ethylene glycol mixed samples SWy-2,.1M KCl electrolyte and ethylene glycol mixed samples Figure 7.37 SWy-2,.1M NaCl electrolyte and phenol mixed samples Figure 7.38 SWy-2,.1M NaCl electrolyte and phenol mixed samples Figure 7.39 SWy-2,.1M NaCl electrolyte and phenol mixed samples Figure 7.4 SWy-2,.1M CaCl 2 electrolyte and phenol mixed samples xxiv

19 Figure 7.41 SWy-2,.1M CaCl 2 electrolyte and phenol mixed samples Figure 7.42 SWy-2,.1M CaCl 2 electrolyte and phenol mixed samples Figure 7.43 SWy-2,.1M KCl electrolyte and phenol mixed samples Figure 7.44 SWy-2,.1M KCl electrolyte and phenol mixed samples Figure 7.45 SWy-2,.1M KCl electrolyte and phenol mixed samples Figure 7.46 STx-1 and.1m NaCl electrolyte mixed blank samples Figure 7.47 STx-1 and.1m NaCl electrolyte mixed blank samples Figure 7.48 STx-1 and.1m NaCl electrolyte mixed blank samples Figure 7.49 STx-1 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.5 STx-1 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.51 STx-1 and.1m CaCl 2 electrolyte mixed blank samples Figure 7.52 STx-1 and.1m KCl electrolyte mixed blank samples Figure 7.53 STx-1 and.1m KCl electrolyte mixed blank samples Figure 7.54 STx-1 and.1m KCl electrolyte mixed blank samples Figure 7.55 STx-1,.1M NaCl electrolyte and TCE mixed samples Figure 7.56 STx-1,.1M NaCl electrolyte and TCE mixed samples Figure 7.57 STx-1,.1M NaCl electrolyte and TCE mixed samples Figure 7.58 STx-1,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.59 STx-1,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.6 STx-1,.1M CaCl 2 electrolyte and TCE mixed samples Figure 7.61 STx-1,.1M KCl electrolyte and TCE mixed samples xxv

20 Figure 7.62 STx-1,.1M KCl electrolyte and TCE mixed samples Figure 7.63 STx-1,.1M KCl electrolyte and TCE mixed samples Figure 7.64 STx-1,.1M NaCl electrolyte and PCE mixed samples Figure 7.65 STx-1,.1M NaCl electrolyte and PCE mixed samples Figure 7.66 STx-1,.1M NaCl electrolyte and PCE mixed samples Figure 7.67 STx-1,.1M CaCl 2 electrolyte and PCE mixed samples Figure STx-1,.1M CaCl 2 electrolyte and PCE mixed samples Figure STx-1,.1M CaCl 2 electrolyte and PCE mixed samples Figure 7.7 STx-1,.1M KCl electrolyte and PCE mixed samples Figure 7.71 STx-1,.1M KCl electrolyte and PCE mixed samples Figure 7.72 STx-1,.1M KCl electrolyte and PCE mixed samples Figure 7.73 Figure 7.74 Figure 7.75 Figure 7.76 Figure 7.77 Figure 7.78 STx-1,.1M NaCl electrolyte and ethylene glycol mixed samples STx-1,.1M NaCl electrolyte and ethylene glycol mixed samples STx-1,.1M NaCl electrolyte and ethylene glycol mixed samples STx-1,.1M CaCl 2 electrolyte and ethylene glycol mixed Samples STx-1,.1M CaCl 2 electrolyte and ethylene glycol mixed samples STx-1,.1M CaCl 2 electrolyte and ethylene glycol mixed samples xxvi

21 Figure 7.79 Figure 7.8 Figure 7.81 STx-1,.1M KCl electrolyte and ethylene glycol mixed Samples STx-1,.1M KCl electrolyte and ethylene glycol mixed Samples STx-1,.1M KCl electrolyte and ethylene glycol mixed Samples Figure 7.82 STx-1,.1M NaCl electrolyte and phenol mixed samples Figure 7.83 STx-1,.1M NaCl electrolyte and phenol mixed samples Figure 7.84 STx-1,.1M NaCl electrolyte and phenol mixed samples Figure 7.85 STx-1,.1M CaCl 2 electrolyte and phenol mixed samples Figure 7.86 STx-1,.1M CaCl 2 electrolyte and phenol mixed samples ) Figure 7.87 STx-1,.1M CaCl 2 electrolyte and phenol mixed samples Figure 7.88 STx-1,.1M KCl electrolyte and phenol mixed samples Figure 7.89 STx-1,.1M KCl electrolyte and phenol mixed samples Figure 7.9 STx-1,.1M KCl electrolyte and phenol mixed samples Figure 7.91-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.91-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.92-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range xxvii

22 Figure 7.92-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.93 Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.94-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.94-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1 and 1 MHz frequency range ) Figure 7.95-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.95-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m CaCl2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.96 Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.97-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range xxviii

23 Figure 7.97-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.98-a Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.98-b Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.99 Real relative dielectric permittivity and log-loss tangent plots of SWy-2 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.1-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.1-bReal relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.11-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.11-bReal relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.12 Real relative dielectric permittivity and log-loss tangent plots xxix

24 of STx-1 and.1m NaCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.13-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.13-bReal relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.14-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range ) Figure 7.14-b Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m CaCl2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.15 Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m CaCl 2 electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.16-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.16-b Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.17-a Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m KCl electrolyte mixed blank sample xxx

25 and TCE, PCE, ethylene glycol and phenol added samples, between.3 and 1 MHz frequency range Figure 7.17-b Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.18 Real relative dielectric permittivity and log-loss tangent plots of STx-1 and.1m KCl electrolyte mixed blank sample and TCE, PCE, ethylene glycol and phenol added samples, between 1.5 and 1 MHz frequency range Figure 7.19 Dielectric permittivity and log-loss tangent plots of the sample-1, which SWy-2 and 41 %wt ethylene glycol was mixed Figure 7.11 Dielectric permittivity and log-loss tangent plots of the sample-2, which SWy-2 and 56.6 %wt.1m KCl electrolyte was mixed ) Figure Dielectric permittivity and log-loss tangent plots of the sample-3, which.1m KCl electrolyte was mixed with sample-1. Sample-1 is the sample, which SWy-2 was mixed with ethylene glycol first. 269 Figure Dielectric permittivity and log-loss tangent plots of the sample-4, which ethylene glycol was mixed with sample-2. Sample-2 is the sample, which SWy-2 was mixed with.1m KCl electrolyte first Figure Dielectric permittivity and log-loss tangent plots of the sample-5, which SWy-2 was mixed with previously mixed ethylene glycol and.1m KCl electrolyte Figure The combined plots of dielectric permittivity and log-loss tangent of the samples-2, 3, 4, and Figure Relative real dielectric permittivities of TCE contaminated samples at 3 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of PCE contaminated samples xxxi

26 at 3 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of ethylene glycol contaminated samples at 3 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of phenol contaminated samples at 3 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of TCE contaminated samples at 1 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure 7.12 Relative real dielectric permittivities of PCE contaminated samples at 1 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of ethylene glycol contaminated samples at 3 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase Figure Relative real dielectric permittivities of phenol contaminated samples at 1 MHz frequency, open symbols for measured permittivities and filled symbols for BHS model predicted permittivities using the measured permittivities of the blank samples as one phase xxxii

27 LIST OF TABLES Page Table 5.1 Physical and Chemical data of Two Montmorillonites Table 5.2 Relative Dielectric Permittivities of Montmorillonite Table 5.3 Summary of Physical and Chemical properties of Four Organic Compounds Table 6.1 Debye screening parameters for three molarities of 1:1 and 1:2 electrolyte and κ R values for three different R (the radius of the colloidal particles) Table 6.2 Table 6.3-a Table 6.3-b Table 6.3-c Table 6.4-a Table 6.4-b Table 6.4-c Particle size distribution data on some Wyoming bentonite (Montmorillonite) The Schwarz model parameters of entrained-air corrected dielectric permittivities of SWy-2, NaCl electrolyte blank samples The Schwarz model parameters of entrained-air corrected dielectric permittivities of SWy-2, CaCl 2 electrolyte blank samples The Schwarz model parameters of entrained-air corrected dielectric permittivities of SWy-2, KCl electrolyte blank samples The Schwarz model parameters of entrained-air corrected dielectric permittivities of STx-1, NaCl electrolyte blank samples The Schwarz model parameters of entrained-air corrected dielectric permittivities of STx-1, CaCl 2 electrolyte blank samples The Schwarz model parameters of entrained-air corrected dielectric permittivities of STx-1, KCl electrolyte blank samples xxxiii

28 Table 7.1-a Table 7.1-b Table 7.1-c Table 7.2-a Table 7.2-b Table 7.2-c Table 7.3-a Table 7.3-b Table 7.3-c Table 7.4-a Table 7.4-b The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, NaCl electrolyte blank samples (first lines) and TCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, CaCl 2 electrolyte blank samples (first lines) and TCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, KCl electrolyte blank samples (first lines) and TCE contaminated sample (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, NaCl electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, CaCl 2 electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, KCl electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, NaCl electrolyte blank samples (first lines) and ethylene glycol contaminated samples (second lines). 279 The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, CaCl 2 electrolyte blank samples (first lines) and ethylene glycol contaminated samples (second lines). 28) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, KCl electrolyte blank samples (first lines) and ethylene glycol contaminated samples (second lines). 281 The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, NaCl electrolyte blank samples (first lines) phenol contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected xxxiv

29 dielectric permittivities of SWy-2, CaCl 2 electrolyte blank samples (first lines) and phenol contaminated samples (second lines) Table 7.4-c Table 7.5-a Table 7.5-b Table 7.5-c Table 7.6-a Table 7.6-b Table 7.6-c Table 7.7-a Table 7.7-b Table 7.7-c The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of SWy-2, KCl electrolyte blank samples (first lines) and phenol contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1 and NaCl electrolyte blank samples (first lines), and TCE contaminated samples (second lines) ) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, CaCl 2 electrolyte blank samples (first lines), and TCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, KCl electrolyte blank samples, (first lines), and TCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1-2, NaCl electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, CaCl 2 electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, KCl electrolyte blank samples (first lines) and PCE contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, NaCl electrolyte blank samples (first lines) and ethylene glycol contaminated samples (second lines). 291 The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, CaCl 2 electrolyte blank samples (first lines) and ethylene glycol contaminated samples (second lines). 292) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, KCl electrolyte blank samples xxxv

30 (first lines) and ethylene glycol contaminated samples (second lines). 293 Table 7.8-a Table 7.8-b Table 7.8-c Table 7.9-a Table 7.9-b The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, NaCl electrolyte blank samples (first lines) and phenol contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1, CaCl 2 electrolyte blank samples (first lines) and phenol contaminated samples (second lines) The Cole-Davidson model parameters of entrained-air corrected dielectric permittivities of STx-1-2, KCl electrolyte blank samples (first lines) and phenol contaminated samples (second lines) Relative real dielectric permittivities of SWy-2-.1M NaCl electrolyte mixture blank sample (SW1NA3), and TCE (SW1NT3), PCE (SW1NP3), ethylene glycol (SW1NE3), and phenol (SW1NF3) mixed samples at selected frequencies.. 31 Relative real dielectric permittivities of STx-1-.1M NaCl electrolyte mixture blank sample (ST1NA3), and TCE (STNTA3), PCE (STNPA3), ethylene glycol (STNEA3), and phenol (STNFA3) mixed samples at selected frequencies Table 7.1-a Relative real dielectric permittivities of SWy-2-.1M NaCl electrolyte mixture blank sample (SW1NA3), and TCE (SW1NT3), PCE (SW1NP3), ethylene glycol (SW1NE3), and phenol (SW1NF3) mixed samples at selected frequencies Table 7.1-b Relative real dielectric permittivities of STx-1-.1M NaCl electrolyte mixture blank sample (ST1NB4), and TCE (STNTB4), PCE (STNPB4), ethylene glycol (STNEB4), and phenol (STNFB4) mixed samples at selected frequencies Table 7.11-a Relative real dielectric permittivities of SWy-2-.1M CaCl 2 electrolyte mixture blank sample (SW1CA3), and TCE (SW1CT3), PCE (SW1CP3), ethylene glycol (SW1CE3), and phenol (SW1CF3) mixed samples at selected frequencies.. 35 Table 7.11-b Relative real dielectric permittivities of STx-1-.1M CaCl 2 electrolyte mixture blank sample (ST1CA3), and TCE (STCTA3), xxxvi

31 PCE (STCPA3), ethylene glycol (STCEA3), and phenol (STCFA3) mixed samples at selected frequencies Table 7.12-a Relative real dielectric permittivities of SWy-2-.1m CaCl 2 electrolyte mixture blank sample (SW1CA3), and TCE (SW1CT3), PCE (SW1CP3), ethylene glycol (SW1CE3), and phenol (SW1CF3) mixed samples at selected frequencies Table 7.12-b Relative real dielectric permittivities of STx-1-.1m CaCl 2 electrolyte mixture blank sample (ST1CA3), and TCE (STCTB3), PCE (STCPB3), ethylene glycol (STCEB3), and phenol (STCFB3) mixed samples at selected frequencies Table 7.13-a Relative real dielectric permittivities of SWy-2-.1m KCl electrolyte mixture blank sample (SW1K3), and TCE (SW1KT3), PCE (SW1KP3), ethylene glycol (SW1KE3), and phenol (SW1KF3) mixed samples at selected frequencies Table 7.13-b Relative real dielectric permittivities of STx-1-.1m KCl electrolyte mixture blank sample (ST1K3), and TCE (STKTA3), PCE (STKPA3), ethylene glycol (STKEA3), and phenol (STKFA3) mixed samples at selected frequencies Table 7.14-a Relative real dielectric permittivities of SWy-2-.1m KCl electrolyte mixture blank sample (SW1K3), and TCE (SW1KT3), PCE (SW1KP3), ethylene glycol (SW1KE3), and phenol (SW1KF3) mixed samples at selected frequencies Table 7.14-b Relative real dielectric permittivities of STx-1-.1m KCl electrolyte mixture blank sample (ST1K3), and TCE (STKTB3), PCE (STKPB3), ethylene glycol (STKEB3), and phenol (STKFB3) mixed samples at selected frequencies xxxvii

32 LIST OF SYMBOLS Symbol Terminology SI unit A Ampere C Coulomb A.s C Centigrade F Farad C.V -1 H Henry V.s.A -1 Hz Hertz cycle.s -1 J Joule kg.ms -2 K Kelvin C m meter mol Mole g-mols. 1-3 m 3 N Newton J.m -1 s Poise 1-1 kg. m -1 s -1 second T Tesla N.s.C -1.m -1 V Volt N.m.C -1 Ohm VA -1 a radius of spherical particles or hydrated ions B r Magnetic induction vector T m -2 C 1, C 2,, C n fractional contribution of each relaxation when there is n relaxationc 1 +C 2 + +C n =1 (Multiple relaxationcole-davidson model) m Unitless xxxviii

33 c Concentration of electrolyte mole m -3 c EM wave velocity in free space ( in Chapter-5) m/s D Diffusion coefficient of ions m 2 s -1 D r Displacement current Cm -2 d Distance between two charge plates Å E r Electric field vector Vm -1 e Electron charge ( x 1-19 C ) C f Frequency Hz H r Magnetic field vector T r J Cunduction current density A m -2 j D Diffusion flux A m j E Surface flux of counter ions under the influence of an applied electric field A m K a Complex conductivity of particles 1/m K i Complex conductivity of electrolyte 1/m k Boltzman constant (1.3866x ) N.m/K L Sample holder length cm N a Avagadro s number ( x1 23 ) mol -1 N ± ± n Ionic density of + and ions in any part of the double layer m -3 Ionic density of + and ions in electrolyte m -3 p Volume fraction of dispersed phase Unitless p i (p 1, p 2, p 3 )Volume fraction of each particle size Unitless Q Surface charge density on the condenser plates of a capacitor C/m 2 R Radius of disperse particles m R i (R 1, R 2, R 3 ) Radius of each particle size group m S Surface area m 2 xxxix

34 T Temperature K t Time s U Mobility of ions m 2 s -1 V -1 U Mobility of ions in free solution m 2 s -1 V -1 v EM wave velocity in any material m/s x Distance from a charged surface or point m z ± Valance of ions in an electrolyte Unitless Activation energy of counterions N.m Reduced activation energy difference between maximum and minimum activation energies required by counterions = ( max - min)/kt Unitless i ( 1, 2, 3) Reduced activation energy difference for each particle size β Distribution parameter of τ for Davidson-Cole model β 1, β 2,, β n Distribution parameters of τ 1, τ 2,.., τn for multiple relaxation Davidson-Cole model 2 Total error at the end of each inversion Unitless Unitless Unitless Unitless δ Loss angle Unitless Distribution parameter of τ for Cole-Cole model 1, 2 n Distribution parameters of τ 1, τ 2,.., τn for multiple relaxation Cole-Cole model 1/ Debye screening distance m Unitless Unitless ε Dielectric permittivity Fm -1 ε Permittivity of free space ( ) Fm -1 ε r Relative dielectric permittivity Unitless * ε r Relative complex dielectric permittivity xl

35 ε r Real part of * ε r (relative) Unitless ε r Imaginary part of ε s * ε r (relative) Static relative dielectric permittivity (or low frequency dielectric permittivity) Unitless Unitless ε High frequency relative dielectric permittivity Unitless * ε m Relative complex dielectric permittivity Unitless of the matrix in two phase mixed systems Unitless * ε w Relative complex dielectric permittivity * εr ε si Φ of water Effective relative complex dielectric permittivity of two phase mixed system (BHS model) Static relative dielectric permittivity for each particle size and fraction Volume fraction of dispersed phase (phase-2) in two phase system (BHS model) Unitless Unitless Unitless Unitless Viscosity poise 1-1 Viscosity under the influence of an external electric field poise 1-1 Debye parameter screening parameter m -1 Complex surface conductivity C 2 m 2 s -1 V -1 EM wave, wave length (Chapter-5) m Surface conductivity (independent of frequency) C 2 m 2 s -1 V -1 Magnetic permeability of free space H/m * µ r Relative complex magnetic permeability Unitless xli

36 µ r Real part of relative complex magnetic permeability µ r Imaginary part of relative complex magnetic permeability ϑ Skin depth m Unitless Unitless Resistivity (Chapter-5) -m Charge density (Chapter-2) C m -3 d Surface charge density in the diffuse layer C/m 2 s Surface charge density in the Stern layer C/m 2 Surface charge density of clay particles C/m 2 σ Change in surface charge density under the influence an applied electric field C/m 2 * σ Reduced surface charge density Unitless σ i ( 1, 2, 2 ) Surface charge density corresponding each particle size (Schwarz model) C m -2 τ, τ Relaxation time of dielectric dispersion s τ 1, τ 2,..,τ n Relaxation times for multiple relaxation s τi 1, τ2, τ3 τ Relaxation times for multiple relaxation Schwarz model dc DC conductivity of material 1/m a DC conductivity of electrolyte 1/m i DC conductivity of particles in a disperse system s 1/m Viscoelectric constant V -2 m 2 Reduced potential (e /kt) Unitless Surface potential V s Potential in the Stern layer V d Potential in diffuse layer V xlii

37 a i Potential in the electrolyte (in the Schwarz model) Potential in the particle (in the Schwarz model) Volume fraction of host medium in two phase system V V unitless ω Angular frequency (2πf ) radians s -1 xliii

38 ACKNOWLEDGMENTS This work was sponsored in part by the Air Force Office of Scientific Research, USAF, under grant/contract number F The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. This research was also partially supported by a grant from the Schlumberger foundation. I would like to express my deep appreciation to Dr. Gary Olhoeft, my advisor and mentor, for his unwavering support and believing in me even in times when I did not believe in myself. He never doubted my abilities, and he did not let me give up. I like to thank the members of my committee, Dr. Steven Pruess, Dr. Catherine Skokan, Dr. Frank Hadsell, and Dr. Bruce Honeyman, for their participation. And I would like to thank my loving and supportive, albeit impatient husband, Dr. Dave McGlone, who has been looking forward to the completion of my degree as much as I have in hopes that some day we could take our honeymoon. Also, I would like to thank my friends who have given me moral support: Dan Jones, Robert Fiore, Kristen Sneddon and Kim Oshetski. Last but not least, I thank my parents for going against the norm and teaching their daughter how to be an independent. xliv

39 DEDICATION To akir Cokun To Ouz Selvi To my Battle friend Who planted the seeds of dream. Who nourished the dream. Who made it all possible. xlv

40 1 CHAPTER-1 INTRODUCTION The majority of the top 1 contaminants ranked by EPA are organic compounds (Lucius, et al., 1992). Due to increasing levels of hazardous waste disposal, the identification and monitoring of contaminants within (or without) hazardous waste sites have become one of the most important issues in the control of related environmental problems. To detect contaminant plumes with geophysical methods requires the existence of a physical or chemical property contrast. Detection of the organic contaminants is the most difficult task for noninvasive geophysical methods at hazardous waste sites. The reasons for this difficulty are: first the low level of geophysical contrast that these contaminants provide against background soil (Olhoeft, 1992; Lucius et al., 1992), second, the concentration of contaminant considered to be of regulatory concern is around the ppm range (Olhoeft, 1992), and third, some of the physical properties such as electrical conductivity and dielectric permittivity of clay bearing soil increase drastically with the presence of water. In this high conductivity and dielectric permittivity environment, the very low level of organic contaminants make detecting them almost impossible. However, some chemical reactions, such as oxidation-reduction, polymerization, ion exchange, occur between clay and some of the organics, and can be observed via non linear complex resistivity (NLCR) measurements at low frequencies (Sadowski, 1989; King and Olhoeft, 1989; Olhoeft and King, 1991; Jones, 1997). The influence of organic contaminants on the dielectric permittivity of clay bearing soils were investigated (Kutrubes, 1986; Santamarina and Fam, 1997). Kutrubes found that volumetric-mixing model should not be used to predict the dielectric permittivity of mixtures of two

41 2 interacting phases. Santamarina and Fam showed that the mixing order in clay-waterorganic mixture makes a difference in dielectric permittivity if the organic compounds are hydrophobic compounds. Knowledge of the electrical properties of the contaminants, the contaminated soils, and the chemical interactions between them increases the probability of identifying both the contaminant type and its location (Olhoeft, 1986; Olhoeft, 1992). In order for Ground-Penetrating-Radar (GPR) to reach its full potential, a better understanding of the electrical properties of the multi-phase dielectric system is needed (Olhoeft, 1992; Powers, 1995). To interpret GPR data, calculated forward GPR models are fitted to field data to estimate subsurface electrical properties, such as material attenuation, and dielectric permittivity as a function of depth. In the interpretation of the broad frequency band EM techniques (VETEM) (Stewart, 1993; McGlone, 1996, 1997, 1998), forward and inverse models require a knowledge of the broad frequency band dielectric permittivity and the conductivity. If the relationship between effective dielectric permittivity and multiphase disperse system parameters are known, some of the information of subsurface may be extracted from the permittivity data. In dry materials and chemically non interacting mixtures, the dielectric properties are controlled by physical factors such as dielectric permittivity, grain shape, and the volume fraction of the mixture constituent (Dukhin, 1971; Hanai, 1968; Tinga, et al., 1973; Sen, et al., 1981). The majority of experimental and mathematical studies for characterization and modeling have accounted for these factors. Some researchers have observed that the effective dielectric permittivity of multiphase systems is significantly higher than of any end member of the mixture when colloidal particles are introduced into the system (Schwarz, 1962; Schwan, et al., 1962; Schurr, 1964; Dukhin and Shilov, 1974; Chew and Sen, 1982; Lyklema, et al., 1983). Colloidal particles are electrically charged by fixed or adsorbed ions and surrounded by counterions, forming an electrical double layer or ionic cloud at the electrolyte-solid

42 3 interface. The dielectric permittivity of these charged particle-electrolyte mixtures can reach several thousands in magnitude. A number of explanations have been suggested for this behavior (O Konski 196; Schwarz, 1962; Schwan, et al., 1962; Schurr, 1964; Dukhin and Shilov, 1974; Chew and Sen, 1982; Lyklema, et al., 1983; Endres and Knight, 1992). The general consensus in explaining this phenomena is that the increase in dielectric permittivity of a colloidal suspension is related to interfacial polarization, or electrochemical polarization of ion clouds around the colloidal particles. The discrepancies among the polarization mechanisms of O Konski (196), Schwarz (1962), Schurr (1964), Dukhin (1971), Chew and Sen (1982), and Lyklema et al. (1983) are due to different kinetic models of the electrochemical double layer, and also different opinions of which part of the double layer ions are polarized under an applied field. The first objective of this research is to investigate the dielectric permittivity of montmorillonite-water mixtures in light of previously suggested theories, and develop a model which can incorporate the volume fractions of the mixture component and the polarization of ions in the electrical double layer. The second objective of our research is to look into the effects of organic contaminant intrusion on the dielectric permittivity of clay-water mixtures, and to see whether chemical reactions of certain organic contaminants can be identified through the observed change in dielectric permittivity in the frequency range of 3 KHz-3 MHz. Lockhart (198-a, -b) investigated the dielectric permittivity of Na-montmorillonitewater and kaolinite-water mixtures, as examples for swelling and nonswelling clays. He suggested that Schwarz s (1962) approach to dielectric permittivity of colloidal suspensions can be used to model dielectric permittivity of clay-water mixtures. Lockhart carried out his experiments in the frequency range between 1 Hz and 1 KHz. Lockhart concluded that the ions in the Stern layer were responsible for high dielectric permittivities of clay-water mixture in that low frequency range, and at the frequencies above 1 KHz, the polarization of the ions in the Stern layer would not have any effect

43 4 on dielectric permittivities of the mixture. On the contrary, our observation is that the polarization of double layer ions is still in effect beyond 1 KHz frequencies. Raythatha and Sen (1986) developed a volumetric mixing model for dielectric permittivities of montmorillonite-water mixtures including the effect of platy structures of montmorillonite sheets. They also observed that dielectric permittivities of montmorillonite-water mixtures at mega-hertz frequencies can still be higher than what a volumetric mixing model can produce. The measured dielectric permittivities of claywater mixture (Na-montmorillonite and Ca-montmorillonite) also showed that there are multiple relaxation processes, suggesting that multiple particle size distributions might be the cause of these relaxations. The model which Lockhart (198-a, b) suggested for dielectric permittivity of claywater mixtures assumes a single relaxation caused by one particle size, and the fraction of the disperse phase was assumed to be the fraction of clay in the clay-water mixture. Lockhart also suggested that double layer polarization would be effective below 1 KHz frequencies. In this study, the model for dielectric permittivity of a clay-water mixture was developed to account for the polarization of the ions in the Stern layer along with the volume fraction of water in clay as suggested by Lockhart. Our model differs from that of Lockhart in two ways: the first, in our model, multiple particle sizes were assumed and second, the fraction of the dispersed phase was assumed to be the volume fraction of the free water in the micro capillaries. Lockhart assumed that edge to edge and edge to face orientation of the clay particles or platelets in electrolyte create a honeycomb structure resembling micro capillaries, and that these structure could be envisioned as spherical particles instead of flat disk shaped particles. After this assumption, he used the volume fraction of clay particle as the volume fraction of the disperse phase in the Schwarz model, not the volume fraction of micro capillaries. This assumption gave lower dielectric permittivity values than what were measured in the frequency range of our measurements (3 KHz to 3 MHz).

44 5 The validity of the model was tested under different conditions. These conditions are change of clay-water concentration, three different inorganic salt (NaCl, CaCl 2, and KCl) electrolytes with three different molarities of these salts (.1,.1, and.1). The influence of type of salt and their molarities on the structure of the double layer will be reviewed in Chapter 2. The assumptions for this model will be discussed in Chapters 3, and 6. Our second objective is to compare the dielectric permittivities of clay-water mixtures with those of contaminated samples. To characterize the frequency spectrum of the dielectric permittivity of clay-water and clay-water-organic mixtures, Cole-Davidson (Cole and Cole, 1941; Davidson and Cole 1952; Havriliak and Negami, 1965) parameters were calculated using the Marquardt-Levenberg non-linear least square algorithm (Marquardt, 1963; Press, et al., 1996). To see if there is a pattern between clay-water (blank) samples and those contaminated with trichloroethylene (TCE), tetrachloroethylene (PCE), ethylene glycol and phenol, their Cole-Davidson parameters were compared. The purpose of this comparison is to see if these patterns can be used in the identification of the contaminants. Before attempting to interpret the dielectric permittivities of clay-water-organic mixture s, previous studies about clay organic, and clay-water-organic reactions are reviewed in Chapter 4. The chemistry of clay-organic reactions has been extensively investigated (Theng, 1974; van Olphen, 1977; Yariv and Cross, 1979; Soma, et al, 1984 and many more); however, the swelling of clays in pure organic solvents has only been studied to a limited extent (e.g., Dowdy, and Mortland, 1968; Olejnik, et al., 1974; Brindley, 198; Murray and Quirk, 1982; Green, et al., 1983; Chen, et al., 1987; Fukushima, et al., 1988; Graber, et al., 1994). Even though the swelling of clays in water has been well studied (Foster, 1953, Norrish, 1954, Fink, et al., 1968, Odom and Low, 1978), little is known about the behavior of the clays and their interactions with water. Not much is known about the clay organic reactions in the presence of water. Most of the experimental researches for clay

45 6 organic reactions have been carried out for the clay with a single liquid mixture. For our experiments, we have chosen Na-, and Ca-montmorillonite as swelling clay, NaCl, KCl, and CaCl2 electrolytes as aqueous liquids, and ethylene glycol, tricloroethene, tetracloroethene and phenol as organics. Montmorillonite is one of the most commonly used clays as grouts and barriers for contaminant flow, and also montmorillonite is an important constituent of most natural clay systems. The chosen organics are major pollutants that have great importance in many hazardous waste site remediations. The inorganic salts used to make the aqueous electrolytes are very common in natural ground water.

46 7 CHAPTER-2 BACKGROUND FOR MONTMORILLONITE AND DOUBLE LAYER 2.1 Montmorillonite Clays And Their Properties Montmorillonite Structure The principal building elements of the clay minerals are two-dimensional arrays of silicon-oxygen tetrahedra and two-dimensional arrays of aluminum- or magnesiumoxygen-hydroxyl octahedra. The tetrahedral and the octahedral layers can be assembled in various combinations to form compound layers which are representative of the different clay minerals. The arrangement of tetrahedral and octahedral layers defines the clay mineral groups. 1:1 group minerals have one tetrahedral layer and one octahedral layer to form one sheet of clay mineral. Montmorillonites belong to the smectite clay group. This group is also called 2:1 group clay minerals because one octahedral layer is sandwiched between two tetrahedral layers to comprise one sheet of montmorillonite (Figure 2.1). A stack of ten or fifteen such sheets of montmorillonite makes up each clay particle. The space between two adjacent tetrahedral layers is called the interlayer region. The basal spacing of a clay mineral is defined as the distance from the bottom of one layer to the bottom of an adjacent layer. For the montmorillonite, the basal spacing is from 9.4 Å to 9.5 Å Isomorphic Substitution And Cation Exchange The structure of the montmorillonite group is derived from that of pyrophyllite and talc by substitution of certain atoms for other atoms. In the tetrahedral sheet, Si +4 is sometimes partly replaced by Al +3. In the octahedral sheet, there might be substitution of

47 8 (a) (b) Figure 2.1 Schematic representation of 2:1 type of clay minerals: (a) plan view of the tetrahedral layer, (b) cross section, (Drewer, 1988).