The dotted and dash-dotted lines indicate the two relaxation peaks due to adsorbed water polarization and interfacial pDOÌar1ZzafiOT\.... Results of the local dielectric measurement and
Dielectric properties in low frequency range 33
Interfacial pOlariZAtiOT -. cọ TH nề 34
The occurrence of an individual interfacial polarization depends on two factors One is the spatial scale of the polarization The smaller the scale is, the higher relaxation frequency material has Such as, electrode polarization normally has much lower relaxation frequency whose scale is in proportion to the distance of two electrodes, than that of double layer (MHz, Raythatha & Sen, 1986) with polarization scale of particle size Because charges accumulation is the cause of the interfacial polarization, the other factor involves the mobility of the charge carrier The mobility of ions in aqueous electrolyte is given in order: H* > Li* > Na* > K* > NH," > Rb* >
Cs* > Ca** With higher counterion mobility (conductivity), the electrochemical relaxation frequency moves up toward a higher frequency For instance, the stern layer has much lower relaxation frequency (100 Hz, Raythatha & Sen, 1986), and the dielectric constant of clay suspension is reduced substantially upon exchanging Na* ions with Ca**, or with relatively large, less mobile, organic cations (Raythatha & Sen, 1986) Here, the use of counterion denotes that the mobility of ions is hindered by interfacial interaction
Accordingly, when interfacial phenomena are caused by the change of surface physical properties, it will become the origins of additional polarizations Like adsorbed water, the restricted bound ions adjacent to the inclusion surface will raise stern layer polarization and become sensitive to temperature since their thermal agitation may overcome energy barriers on the surface and move to the neighboring well (Santamarina et al., 2001) Similarly, double layer may also polarize when relative displacement takes place between the counterion clouds and the charged inclusions This phenomenon was firstly proposed for colloid particles which were suspended in electrolyte and analytically modeled by Schwarz (1962) and Chew & Sen (1982) The presence of electrolyte, such as alkali metal chlorides solution that are often used as “background” electrolytes for controlling ionic strength in the study of the mixture conductivity and permittivity, and high inclusion concentration can weaken the double layer polarization because (1) displaced ions are replaced by the diffusion of ions into and out of the bulk solution, and (2) ions in the double layer can move from one particle to a neighboring particle in response to the applied
Chapter 2 Literature Review and Background electric field (Santamarina et al., 2001) However, as a trade-off, surface conduction prevails over particles, and leads to conductivity enhancement.
Electrode polarization (EP) - cà He 36
Electrode polarization, which takes place at the interface of two different materials in the process of measurement, essentially belongs to the category of interfacial polarization In the definition of interfacial polarization, the discrepancy between the two materials often pertains to their permittivity However, in the description of electrode polarization, charge carrier is usually used to explain the cause of this polarization, such as the electrodes placed in electrolyte, where charge can freely move in the former while the later contains unbound charge carriers — ions
~ as a dielectric continuum Subject to electric force formed by the pair of anode and cathode electrodes, ions flows to electrodes with opposite charge Since the ions can not penetrate the electrode surface, they accumulate in the form of a charge cloud and, at the interface, a double layer comes into being, whose state is controlled by two opposite interactions: electric attraction and ion diffusion (coming from concentration gradients) The impeded ionic motion depends on the duration of time for which the field maintains its direction before being reversed When undergoing alternating field, counterions travelling to the electrode at each half-cycle can be retarded by ionic mobility (ionic friction coefficient) in host material (Scott et al., 2000), and the interplay of the two factors results in the frequency dependence of charge cloud thickness (Paul & Kaler, 1997), which affects the strength of electrode polarization At the low frequency, stable double layer forms for enough time allows ions accumulation to an equilibrium state towards ionic diffusion In EM properties measurement, the presence of double layer screens the applied field and must hamper the proper analysis of slow relaxation processes (Wiibbenhorst & van Turnhout, 2000) While, at a higher frquency, dynamic thinner double layer associated with diminished EP is formed For system in extremely high frequency, it is impossible to generate a counterion layers, where EP becomes negligible
Since the dielectric spectroscopy is often obscured by EP due to the avoidless insertion of the electric measurement system, many efforts have been done to model this phenomenon-the charges redistribution in field The direct and simple method is phenomenological equivalent circuit, such as a capacitor and a resistor in series However, more theoretical modelling was put forward to overcome the disadvantage of equivalent circuit due to neglecting frequency dependence of electrical components An aw? decay of dielectric permittivity observed in experiments was successively built up in a model for parallel plate (Cirkel et al., 1997) that has taken charge conservation and ion diffusion into account Furthermore, theorectical and sysmatic analysis (Scott et al., 2000) was extended to dynamic ac system by introducing zeta potential-the dc potential at electrode-electrolyte interface.
Dielectric properties in high frequency range 37
In the microwave region, the loss due to de conductivity of free charge carriers is small and relaxation due to interfacial polarization no longer occurs (Hoekstra & Doyle, 1971) It is expected, at the high frequency range, that the interfacial polarization, including electrode polarization, double layer polarization, will diminish with the augment of exciting frequency in that the formation of induced
“dipoles” can not follow the step of field Such that only orientational, ionic and electronic polarizations are left to govern dielectric properties, and among which, the orientational polarization predominates the apparent permittivity For loss portion,
Chapter 2 Literature Review and Background the loss factor approaching orientation peak prevails over the ohmic conductivity loss (Eq 2.12) - the primary obstacle to precise energy loss application Consequently, most of the interference upon the interpretation of measured permittivity is filtered and it becomes easy to investigate the material dielectric properties.
Relevance of electromagnetic properties to soil characteristics
Fabric arrangement by DC COTIUCfIVIẨY HHằ Hưng Hee 40
In this research, the mechanical and electromagnetic (EM) wave based techniques, because of the nondestructive nature, are jointly used to characterize the soil behavior with particular emphasis on the clay behavior from understanding the sedimentation process to revealing the sediment features Because of the complexity involved in the EM-wave based measurement, a focus is also put on solving the testing related difficulties at different frequency ranges The thesis is organized in seven chapters and a brief description of each of them is as follows
Chapter 2 presents a critical review of the fundamentals regarding polarization, different polarization mechanisms in the single component material as well as in the mixture, and the mixing rules and its applications for geomaterials
Chapter 3 addresses the techniques involve in the measurement of a broad-band dielectric spectrum, ranging from kHz to GHz, using the open-ended coaxial probe
In each measurement frequency range, the focus is put on the formulation of the aperture admittance model which is associated with the measured aperture reflection coefficient or impedance The calibration also relies on the admittance model The verification of the testing techniques is provided by testing the liquid with known dielectric spectrum
Chapter 4 makes use of the measurement techniques mentioned in Chapter 3 to explore the dielectric spectrum of the kaolinite sediments ranging from kHz to GHz.
A Broadband Permittivity Measurement Technique: Theory
Introduction 47
The dielectric properties of materials, such as soils, are often studied over a wide frequency range from Hz and GHz in view of engineering applications or material characterization needs (Santamarina et al, 2001) Various techniques/methods have been used individually or together for the measurements across a broad frequency band, such as time domain reflectometry techniques (TDR), transmission methods, reflection techniques, resonant phenomena, and parallel plate capacitors (Fellner-Feldegg, 1969; von Hippel, 1995; Shang et al., 1999) Among them, the open-ended coaxial probe integrated with the reflection techniques has been widely used not only in geotechnical engineering related researches (Santamarina et al., 2001; Fam & Dusseault, 1998; Cho et al., 2004), but also in various industrial and scientific applications (Blackham & Pollard, 1997; Gershon et al., 1999; Pournaropoulos & Misra, 1997; Schwan, 2000; Nelson & Bartley, 1998, 2002; Fear et al., 2003) The particular advantages of using this method are that it allows non-destructive measurements over a broad frequency band, sets relatively minor limitations on the shape and configuration of the test materials, has no special requirement for sample preparations, and is suitable for in situ, in vivo, and in vitro measurements (Nyshadham et al., 1992; Pournaropoulos & Misra, 1997; Fear et al.,
2003) Furthermore, a small-sized probe allows the assessment of local dielectric
Chapter 3_ A Broadband Permittivity Measurement Technique: Theory and Experimental Verifications of a saturated soil sample (Dong & Wang, 2005) This feature, the small size of the probe, also permits the sensor to be buried in the sample for long-term monitoring without significant perturbations Considering these advantages, especially the potential of a broadband measurement, an open-ended coaxial probe with a small diameter of 2.2 mm (Fig 3.1) is selected as a sensor to explore permittivity measurements from kHz to GHz, which is the main objective of this paper
The paper begins by revisiting the aperture admittance models, followed by explaining the model formulation, measurement principle, and associated calibration for testing permittivity in a range of frequencies The operating frequency is separated into three different ranges, i.e., high frequency (HF, 500 MHz ~ 20 GHz), medium frequency (MF, 10 MHz ~ 1 GHz), and low frequency (LF, | kHz ~ 15 MHz) Verification of different aperture admittance models and associated measurement techniques are provided by experiments on pure ethanol and methanol as well as on sodium chloride (NaCl) solutions of different concentrations A broadband dielectric spectrum of kaolinite slurry measured by the proposed techniques is also presented and analyzed.
Aperture admittance models 48 3.3 The high-frequency measurement (HF, 500 MHz ~ 20 GHZ) .s.0s000e000 50
As shown in Fig 3.2, an open-ended coaxial probe is generally modeled as a coaxial aperture opening on an infinite ground plane in contact with a semi-infinite material under test (MUT) In order to fulfill the assumption of an infinite ground plane, a conductive flange is often utilized In the configuration illustrated in Fig 3.2, the electromagnetic (EM) wave traveling along the coaxial line is partially reflected back while it meets the discontinuity at the probe end; therefore the associated reflection coefficient 7; which is typically measured by a network analyzer can be expressed as
1 Z,+Z, IUY,+1/Y, 1+¥,/¥, I+, where Z, is a lumped impedance that is related to the EM field distribution around the probe aperture (¥, is the correspondent aperture admittance), Zo is the characteristic impedance of the coaxial line (50 © in general), and Ÿ¿ is called the normalized aperture admittance By matching the EM fields around the aperture, the normalized aperture admittance Y, under the assumption that only the dominant transverse EM wave mode (TEM mode) is considered over the coaxial opening can be given as (Misra, 1987; Blackham & Pollard, 1997):
1 = ak ma where a cylindrical coordinate system (7, @, z) is used with the unprimed coordinates representing the source point (z < 0 regime) and the primed one representing the field points (z > 0 regime); km = AK m & Mo)”; R = (r’ +r?-2rr'cos@)'"; ke = O(Ke& Mo)": j=(-1)'*; wis the angular frequency; ô’ằ, is the complex relative permittivity of the MUT, ô is the relative permittivity of the dielectric material filling the coaxial line (the filling material is assumed lossless and homogeneous); & and / are the permittivity and permeability of free space; a and b are the inner and outer radii of the coaxial line, respectively The aperture admittance model, i.e Eq 3.2, imposes the complex relative permittivity of the MUT xằ relating to the aperture admittance
Y, and thus the reflection coefficient J; by Eq 3.1 This relation is the basic principle of the permittivity measurement and therefore a reliable and accurate measurement over a broad frequency band relies on precisely formulating the aperture admittance model In the following discussion, the adopted models based on the analytical
Chapter 3 A Broadband Permittivity Measurement Technique: Theory and Experimental Verifications solution (Eq 3.2) are described in detail for the HF, MF, and LF measurements
3.3 The high-frequency measurement (HF, 500 MHz ~ 20 GHz)
The definite integral of Eq 3.2 does not provide an easy solution An alternative is thus adopted, i.e., the use of a Taylor series expansion (Blackham & Pollard, 1997) The normalized aperture admittance Y;, becomes
1.2 2 4 3 5 rẻ dy i] yk, Aol Ste ha 7k, In(b/a) 2 24 6 120 where J, = ƒ ƒ ƒ R"? cos(¢)dédrdr’ bb7 (n = 1, 2, 3, ) aa0
Similarly, the aperture admittance Ÿ; 1s given by where Zp is the characteristic impedance of the coaxial line: z=+L=-L #2 mÊ, ly 2z Ý£¿kK 1 4a (3.5)
Blackham & Pollard (1997) use only the first 28 items of this series in the aperture admittance model and replace the parameter /,, with J,,:
For satisfactory results, the measured frequency should be less than or equal to L10/(K'm)² GHz The parameters @, ỉ, and # optimize the match between actual admittance (Eq 3.2) and approximation (Eq 3.3) These parameters are determined by measuring materials with known permittivities This approximation method can generally be applied up to the aforementioned frequency limit.
~20 GHz for a coaxial line with b = 3 mm Note that the upper frequency bound increases with decreasing sizes of the coaxial line
The coaxial probe used in this study, however, is without a conductive flange to function as the infinite ground plane (see Fig 3.1 and Fig 3.2) Thus, the issue is how a model derived for a probe with a flange can be applied to a probe without one Zheng & Smith (1991) compare experiments using these two kinds of probes and conclude that both probes can deliver results in close agreement Furthermore, numerical simulations of the EM field around the probe aperture (for the one without a flange) indicate that the field located in the z = 0 plane (i.e., corresponding to the ground plane in Fig 3.2) merely has a very small magnitude, less than -30 dB (Hagl et al., 2003) That is, most of the EM fields still converge to the probe end even without the help of the conductive flange Thus, Eq 3.3 still can serve as a suitable aperture admittance mode] for a probe without a flange Besides, the minor discrepancy due to the fringe fields in the z < 0 regime can be adjusted using the parameters a, £, and y
3.3.2 Calibration of the measurement system
Because of systematic errors, the reflection coefficient measured by a network analyzer I, differs from that at the probe aperture [ This drawback can be improved by calibration through the model shown in Fig 3.3 According to the model, an S-parameter matrix can cause these two reflection coefficients to be related by
Chapter 3 A Broadband Permittivity Measurement Technique: Theory and Experimental Verifications different standards: a short circuit, an open circuit (by air), and a reference load (typically by reference liquids such as deionized/distilled water, ethanol, and methanol) Thus, the S parameters, S,; (directivity), S:2S2; (reflection tracking), and S22 (source mismatch) in Eq 3.7, are determined Note that except for the perfect short termination (zero impedance) where the reflection coefficient is -1, the determination of reflection coefficients for air and reference liquids requires calculations involving the aperture admittance model In this study, a commercial software package (Agilent Technologies, model number 85070E) is used to integrate the aperture admittance model with the corresponding calibration While a reference liquid, e.g deionized water is chosen as the calibration standard, the Cole-Cole function is used to provide the spectral information The function is
1+(7@7)Z 1+(7œz)Z ca (3.8) where ô is the complex relative permittivity; ô and x” are the real and the imaginary parts, respectively; Tis the relaxation time; @is the distribution parameter; A, and ko are the relative permittivity at @ >> @.i and @ AG = (3.27) where | and 2 denote the two relaxation processes due to adsorbed water polarization and interfacial polarization, respectively The fitting parameters are also indicated in the figure Note that A implicitly includes the dielectric constant arising from free water polarization; it can be used to estimate the water content (Topp et al., 1980) and deduce the void ratio (Dong & Wang, 2005) The adsorbed water polarization occurs at fi = 1.3 MHz, and the relaxation strength is Ak2 = 94.16 The large distribution parameter, Q = 0.681, indicates a wide distribution of relaxation time The interfacial polarization takes place at f,.: = 57.5 kHz and the relaxation strength is
Effects of pH-induced Structure on the Dielectric Properties
Introduction 75
Electromagnetic techniques have been widely used for in-situ testing to obtain subsurface information (Topp et al., 1984; Davis & Annan, 1989; Binley et al., 2002), and for laboratory experiment to enhance understanding of soils (Lockhart, 1980a,
Dielectric permittivity measurement is widely employed to assess geomaterial properties due to its ability to provide a comprehensive dielectric spectrum This spectrum encompasses frequencies from Hertz to Giga Hertz and reveals distinct polarization mechanisms Bulk water molecules exhibit orientational polarization at ~ GHz, while bound water molecules adsorb onto clay surfaces and undergo polarization at ~ MHz Additionally, spatial polarization, consisting of double layer polarization and Maxwell-Wagner polarization, is observed at radio frequencies.
Chapter 4 Effects of pH-induced Structure on the Dielectric Properties of Kaolinite Sediment frequency A detailed review of different polarization mechanisms can be found in Santamarina et al (2001) The measured permittivity owing to bulk water polarization is pertinent to the water content or porosity The permittivity arising from bound water polarization is very much dependent on the surface characteristics of clay particles Fabric packing, to a certain extent, can enhance spatial polarization The DC conductivity reflects the scalar and vector characteristics of the pore
Clay behavior is intimately related to the properties of the pore fluid This is due to the charged surfaces and the associated interparticle forces In kaolinite, the fluid pH influences the surface charges and therefore various fabric associations are developed accordingly (Wang & Siu, 2006) We anticipate that the features of clay-water mixtures {i.e., clay sediment) with various fabric associations to be manifested as different permittivity spectra However, the relevant study is not sufficient and the behavior remains unconcluded Hence, this study is aimed for the revelation about the link between the properties of clay sediment with different structures and the characteristics appear in the corresponding dielectric spectrum This paper begins with a brief introduction of the pH effect on the surface charges of kaolinite and associated fabric formations The data processing procedures follow with particular emphasis on how to remove electrode polarization for the purpose of finding DC conductivity and identifing multiple relaxation spectra over a wide frequency range The measured permittivity spectra in clay-water mixtures of different structures, which are manipulated by changing the pore-fluid pH, are discussed in terms of different polarization mechanisms from high to low frequency: free water polarization, bound water polarization, and spatial polarization In addition, the DC conductivity of clay sediment and the supernatant liquid are jointly considered in the data interpretation.
pH effects on surface charges and associated fabric formations
The total charges of a particle arise from two sources: (1) negative permanent structural charges due to isomorphic substitutions or broken bonds in minerals, and (2) charges due to the binding of H+ or OH-, which can be positive or negative.
(iii) the adsorbed ion charge within the stern layer, Arern (Stumm, 1992; Sposito,
In this context, changing the pH can result in a positive or negative @ and even a zero @, where the pH value is considered as the point of zero charge (PZC) The PZC is very close to the isoelectric point (IEP) but not identical due to the entrapment of diffused ions within the shear plane (Sposito, 1998) In kaolinite, edge and face sites have different PZC and IEP Also, edge surfaces are more sensitive to pH than face surfaces (Jepson, 1984; Zhou & Gunter, 1992; Ma & Eggleton, 1999) When the pH value is less than the isoelectric point of the edge TEPeage, negatively charged faces and positively charged edges promote the structure of face-to-edge (EF) flocculation, which ultimately can form voluminous sediment As the pH is greater than [EPeage, all the face and edge sites are negatively charged so that double layer repulsion prevails between particles, and dispersed and deflocculated structures are preferred in the suspension These particles, however, are able to slide and roll over each other to form dense sediment which exhibits a structure like face-to-face (FF) aggregation.
Material and sample preparation 77
Speswhite kaolin is used in this study It is composed of 47 % SiOz and 38 % Al,03; the specific gravity and surface area (BET) are 2.6 and 14 m’/g, respectively;
Chapter 4 Effects of pH-induced Structure on the Dielectric Properties of Kaolinite Sediment
Ltd., UK) The isoelectric point at the edge site, IEPegge, is around 5 (Wang & Siu, 2006) Pretreatment is applied to the kaolinite powder to remove excess salts and impurities This procedure is completed by washing six times using deionized water that has a DC conductivity, Opc, less than 1 uS/cm 10 grams of the pretreated powder is mixed with de-ionized water to form a clay suspension, which has a total volume of 45 mL The suspension is adjusted to different pH values by adding different amounts of dilute hydrochloric acid (HCl) and sodium hydroxide (NaOH) The target pH is monitored using a pH meter, OAKION Benchtop pH/Conductivity/TDS 510 meter Finally, these different pH suspensions are allowed to settle about 6 months; during this period, the samples are sealed and isolated from any environmental disturbance Fig 4.2 shows the final formation of the samples where sediments of different volumes owing to different fabric associations are readily seen.
Experimental details 78
Fig 4.3 shows the experimental setup The open-ended coaxial probe (Agilent 85070E) used here for permittivity measurement holds a slim form with an outside diameter of 2.2 mm and a length of 200 mm For measurements from 10 MHz to 3 GHz, a network analyzer (Agilent Technologies E5070B; operating frequency ranges
The reflection coefficient at the probe tip is determined using a frequency range of 300 kHz to 3 GHz Conversely, impedance measurements within the range of 1 kHz to 15 MHz are conducted using a precision impedance analyzer (Agilent Technologies 4294A), operating within a frequency range of 40 Hz to 40 MHz.
~ 110 MHz) The measured reflection coefficient and impedance are used to derive the complex permittivity of the specimens The details of the measurement technique can be found in Chapter 3 The coaxial probe and the connecting cable between the probe and the analyzer must remain undisturbed after calibration to minimize errors arising from their movement Therefore, a lab jack is used to lift the samples up to access the probe instead of moving the probe downward to the samples during testing Any air pockets, which can lead to significant errors, are carefully removed from the probe tip before testing
The skin depth of the electromagnetic wave determines the spatial measurement range of the probe This range is relevant to the required sample size and the insertion depth of the probe with respect to the sample, which are crucial to the measurement accuracy The range can be quantified by the method similar to Hoshina et al (2001) This method is based on the principle that measured dielectric constant x’ (or the reflection coefficient) can be changed while a conductive plate interferes the detective range of the probe, which can be carried out using the testing configuration shown in Fig 4.4 In testing the backward and forward effective ranges, permittivity is continuously measured when a conductive metal plate is gradually moved towards the probe tip The measurement is implemented in ethanol at the frequency of 3 GHz Likewise, in testing the radial effective range, permittivity is constantly recorded while a copper bar with a cone-shaped cavity inside, which serves as the changeable conductive boundary, is gradually pulled away from the probe Fig 4.5 shows the results that the effective range of the probe is 2.0 mm, 2.0 mm and 2.1 mm in the forward, backward, and radial directions, respectively The larger permittivity change in response to the interference of the metal plate as shown in Fig 4.5a implies that the forward effective range has a stronger effect on the measurement Based on the results as shown in Fig 4.5 and considering that the skin depth of the electromagnetic wave is related to the permittivity and conductivity of the specimen as well as the testing frequency, an effective measurement range is
Chapter 4 Effects of pH-induced Structure on the Dielectric Properties of Kaolinite Sediment ensured with a penetration depth of more than 15 mm for the backward effective range and 5 mm for the radial and forward effective ranges
The permittivity measurement is carried out both on the overlying fluid (i.e., the supernatant liquid) and the kaolinite sediment The measurement of permittivity in supernatant liquid is aimed at removing electrode polarization and identifying the DC conductivity The measurement of permittivity in the sediment is the main focus for this study and discussed in detail below In order to minimize any possible disturbance, the probe is inserted as slow as possible and a time interval of at least 10 minutes is allowed to recover from any minute perturbations before testing The measurement temperature for all the tests is around 20 C.
Data processing procedures 80 1 Measurement In the supernatant ]1QuU1d -+ cv xxx 80 2 Measurement In the sedimernt - - - ng g9 5k km 81
4.5.1 Measurement in the supernatant liquid
Fig 4.6 demonstrates that the two kinds of polarization take place in the supernatant liquid in the measurement from | kHz to 3 GHz One is the orientational polarization of water molecules in an electrolyte, which exhibits a relaxation frequency around 19 GHz The polarization characteristics of these water molecules are very close to those of bulk water when the electrolyte concentration is low (Stogryn 1971) The other is the inevitable electrode polarization (EP), which arises from the electrical double layer between the metal electrode surface and the ionic solution This polarization overwhelms at low frequencies, and, as shown in Fig 4.6, the magnitude of the dielectric constant ô’ reaches the order of 4 at 1 kHz The measured ô’ from different polarization mechanisms is accumulated towards lower frequencies; therefore, for instance, the value of A’ at 1 kHz includes the contribution from orientational polarization of water molecules (or simply called bulk-water polarization) and electrode polarization
The measured relative loss factor K’meq is from (i) the polarization loss ô” and (ii) the DC conductivity Opc:
Eo where & is the permittivity of the free space (= 8.854x10°!? F/m) and wis the angular frequency Thus, within a certain frequency range where the measured x” due to the electrode and orientational polarization losses are minimized, the DC conductivity of the supernatant liquid can be derived using Eq 4.2 The frequency range used here for this derivation is from 1 MHz to 15 MHz as indicated in Fig 4.6
The derived Onc, following Eq 4.2, assembles the solid line in Fig 4.6 This solid line gradually deviates from and is higher than the data points of measured xk” when the frequency is lower than ~ 10° Hz This behavior is attributed to the prevailing electrode-polarization loss, which, hinders the ionic conduction Similar observations can be found in a TDR measurement by Hager & Domszy (2004) In this context, the measured x” is a net result of these two competing processes and it is difficult to differentiate their individual contribution Thus, for measurements in the clay sediment, the losses due to electrode polarization and DC conductivity are identified together as a whole (to be discussed next)
4.5.2.1 Identify the spectra of electrode polarization and DC conductivity Electrode polarization (EP) and DC conductivity have to be identified and removed from the measured dielectric spectrum of the sediment prior to further analyses because of their overwhelming effects Electrode polarization depends on
Chapter 4 Effects of pH-induced Structure on the Dielectric Properties of Kaolinite Sediment the surface characteristics of the electrode such as topography, areas, reactive functional groups, and chemical interactions with the sample being tested (Cirkel et al., 1997; Scott et al., 2000; Feldman Yu et al., 2001) No simple techniques are widely accepted to correct electrode polarization because of the complexities involved Elimination of electrode polarization in this study is implemented by subtraction of the associated responses that are estimated from the reference spectra The reference spectra are constructed using the same probe to test fluid with different
DC conductivities In the following discussions, the procedures involved to identify the spectrum of electrode polarization and the DC conductivity are described in detail
First, the measured ô’ and x” of all the supernatant samples, ranging from 1 kHz to 15 MHz, are assembled to form two 3-D meshes in the Opc-f-K" and Opc-f-K space as presented in Fig 4.7 The DC conductivity in the figure, as previously described, is derived by Eq 4.2 using the measured x’ ranging from 1 MHz to 15 MHz and the meshes are generated by bi-cubic interpolation from all the measured data points Second, find the corresponding point of the measured ô” in the sediment at the frequency of 1 kHz along the Opc-k” curve which is indicated by an arrow in Fig 4.7a From this point, a virtual plane that is perpendicular to the axis of the DC conductivity is extended to intersect the 3-D mesh This intersection gives the following information: (j) the DC conductivity of the sediment and (ii) the x” spectrum (i.e., the projection on the f-ô” plane) which is a lump sum of the losses due to electrode polarization and DC conductivity Third, in Fig 4.7b, locate the corresponding point of the DC conductivity that is obtained from the second step (i.e., following the vertical dash line) From this point, again, draw a virtual plane that is perpendicular to the conductivity axis The intersection with the 3-D mesh in the
Opc-f-K' space renders the x’ spectrum (i.e., the projection on f-ô’ plane) which consists of the contribution from both electrode and bulk water polarization (see Fig
6 for details) After the contribution from the associated bulk water polarization is subtracted, the ô’ spectrum of electrode polarization can be obtained Note that this processing procedure implicitly assumes: (i) electrode polarization depends only on
DC conductivity, which, in principle, is the base of the so-called substitution method used in calibrating the EP influence (Feldman Yu et al., 2001); and (ii) apart from the loss due to electrode polarization, any other polarization loss has minor input to the measured ô” at 1 kHz
After the ô’ spectrum due to electrode polarization and the x” spectrum arising from the losses of electrode polarization and DC conductivity are identified, they can be removed from the measured results as a correction Fig 4.8 presents those corrected data and associated multiple relaxation spectra Guided by the finding in Ishida et al (2000), the complex dielectric spectrum K (0) can be described as a superposition of three Cole-Cole relaxation spectra:
1+(727„)” 1+(7/ỉ7,” +(77)” where the subscripts w, b and s stand for the relaxation processes occurring at high, intermediate, and low frequencies, respectively; A is the permittivity due to ionic and electronic polarization; Axis the relaxation strength; Tis the relaxation time; and a(0 < a@< 1) is the Cole-Cole parameter related to the distribution of the relaxation time These three relaxation processes from high to low frequencies corresponds to bulk water, bound water, and spatial polarization, respectively
Chapter 4 Effects of pH-induced Structure on the Dielectric Properties of Kaolinite Sediment
The parameters of the three Cole-Cole relaxation spectra (1.e., Ax, 7 @) are determined by curve fitting to the corrected data With the aid of the nonlinear least-square method using the Gauss-Newton algorithm, the best fit is obtained by two steps in which Eq 4.4 and Eq 4.5 are involved:
Kg (O) Kea (Q,) 2 44 cư mea ares) eo i=]
A= where subscript cal and mea denote the fitted results using Eq 4.3 and the measured data, respectively; asterisk signifies complex numbers; and y is the residual error The relaxation strength at low frequency is about 2 ~ 3 orders larger than the relaxation strengths at high and intermediate frequencies Therefore, the curve fitting has to start in a logarithmic scale (i.e., using Eq 4.4) to get the initial value of these parameters Guided by these initial values, an optimized adjustment of the fitting parameters continues in a linear scale using Eq 4.5
The kaolinite sediments with various fabric associations yield different permittivity spectra The following discussions of spectrum features and their relevance to sediment properties follow the sequence: free water polarization, bound water polarization, spatial polarization, and the DC conductivity
The kaolinite sediment porosity, derived from the sediment volume, exhibits a distinct transition around pH 5, corresponding to the isoelectric point of the edge site Consequently, when pH < 5 (Group A), face-to-edge flocculation dominates, resulting in voluminous sediments Conversely, at pH > 5 (Group B), edge-to-face flocculation prevails, leading to more compact sediments.
5 (Group B), face-to-face aggregation leads to dense sediment
The measured dielectric constant ô’.g at high frequency (‘eg = AKy+) reveals the same trend as sediment porosity: the value of ~ 60 is obtained in Group A samples and a lower value, ranging from 51 to 56, is measured in Group B samples (Table 4.1) This observation can be attributed simply to the fact that bulk water exhibits much larger polarizability (a = 78.3 at 25 “C from Nyshadham et al., 1992) than kaolinite does (x = 5.1 from Robinson, 2004) and, therefore, polarization of bulk water in the sediment pores dominates the measured x’,g, i.e., greater porosity, greater water content and higher ô’. For completeness, the relaxation time, 7, and the Cole-Cole parameter, @ of bulk water at 25 ‘, which are similar to the measured results at high frequency, are also listed in Table 4.1 as a reference This, again, suggests that the main polarization mechanism at this measurement frequency range is bulk water polarization