Cole Dispersion Research Articles

Early-Stage Lung Tumor Detection Based on Super-Wideband Microwave Reflectometry

This paper aims to detect early-stage lung tumors in deep-seated and superficial locations, and to precisely measure the size of the detected tumor using non-invasive microwave reflectometry over a super-wideband (SWB) frequency range. Human lung phantom and lung tumors are modeled using a multi-layer concentric cylinder structure and spherical-shaped inclusions, respectively. Firstly, a study on the dielectric properties of human torso tissues is carried out over an SWB frequency range of 1–25 GHz based on the Cole–Cole dispersion model. Intensive full-wave simulations of the modeled phantom under irradiation by a custom-designed SWB antenna array are then performed. Results show that small tumor sizes from 5 mm radius in both deep-seated and superficial locations of the lung tissue can be detected based on the contrast of reflection coefficients and reconstructed images produced from backscattered signals between normal and anomalous tissues. The potential of using SWB microwave reflectometry to successfully detect the lung tumors in their early stages and at different depths of the lung tissue has been demonstrated.

A Finite Element Analysis and Circuit Modelling Methodology for Studying Electrical Impedance Myography of Human Limbs.

Electrical impedance myography (EIM) measures bioimpedance over muscles. This paper proposes a circuit-based modelling methodology originated from finite element analysis (FEA), to emulate tissues and effects from anthropometric variations, and electrode placements, on EIM measurements. The proposed methodology is demonstrated on the upper arms and lower legs. FEA evaluates impedance spectra (Z-parameters), sensitivity, and volume impedance density for variations of subcutaneous fat thickness (t f), muscle thickness (t m), and inter-electrode distance (IED), on limb models over 1Hz-1 MHz frequency range. The limbs' models are based on simplified anatomical data and dielectric properties from published sources. Contributions of tissues to the total impedance are computed from impedance sensitivity and density. FEA Z-parameters are imported into a circuit design environment, and used to develop a three Cole dispersion circuit-based model. FEA and circuit model simulation results are compared with measurements on ten human subjects. Muscle contributions are maximized at 31.25 kHz and 62.5 kHz for the upper arm and lower leg, respectively, at 4 cm IED. The circuit model emulates variations in t f and t m, and simulates up to 89 times faster than FEA. The circuit model matches subjects measurements with RMS errors and , while FEA does with and . We demonstrate that FEA is able to estimate the optimal frequencies and electrode placements, and circuit-based modelling can accurately emulate the limbs' bioimpedance. The proposed methodology facilitates studying the impact of biophysical principles on EIM, enabling the development of future EIM acquisition systems.

Preparation of a Chemically Reduced Graphene Oxide Reinforced Epoxy Resin Polymer as a Composite for Electromagnetic Interference Shielding and Microwave-Absorbing Applications

The preparation of chemically reduced graphene oxide (rGO) and the optimization of epoxy resins’ properties using micro or nanofillers are now common practices. rGO nanoparticles (60 nm) based on an epoxy resin polymer were prepared at the concentrations of 0, 1, 2, 3, 4, and 5% weight percentage with fixed 6-mm thicknesses. The dielectric properties of the composites were measured by the reflection/transmission technique in connection with a vector network analyser (VNA) at a frequency range of 8–12 GHz. The microwave absorption and shielding effectiveness properties were calculated by using the reflection S11 and transmission S21 results. The microstructure and morphology of the polymer and the rGO/cured epoxy composites were studied by field emission scanning electron microscopy (FE-SEM), Fourier-transform infrared (FT-IR) spectroscopy, and the X-ray Diffraction (X-RD) technique for characterizing crystalline materials. The dielectric and other properties of the rGO/cured epoxy composites were investigated based on the filler load and frequency. It was found that the applied frequency and the filler concentrations affected the dielectric properties of the rGO/cured epoxy composites. The results showed that the introduction of rGO particles to the composites increased their dielectric properties smoothly. The study of the dependence on frequency of both the dielectric constant ε′ and the dielectric loss ε″ showed a decrease in both quantities with increasing frequency, indicating a normal behaviour of the dielectrics. Cole–Cole plots were drawn with ε′ and ε″. A theoretical simulation in terms of the Cole–Cole dispersion law indicates that the Debye relaxation processes in the rGO/cured epoxy composites are improved due to the presence of the rGO filler. Moreover, with the addition of rGO as a filler into the Epoxy matrix, it now exhibits promise as a lightweight material for microwave absorption as well as an effective electromagnetic interference (EMI) shielding material.

Synthesis, dielectric, and microwave absorption properties of flake carbonyl iron particles coated with nanostructure polymer

Flake carbonyl iron particles (FCIPs) coated with nanostructure polymer (meth-acrylic acid-polystyrene, MAA-PS) were synthesized by dispersion polymerization using poly (vinylpyrrolidone) as stabilizer and 2, 2-azobis (isobutyronirile) as a catalytic agent. Field emission scanning electron microscope equipped with energy dispersive x-ray spectroscopy and high-resolution transmission electron microscope was used to observe its morphology of FCIPs-MAA-PS, and thermo-gravimetric analyses were employed to characterize its mass loss of polymer surface modification. Electromagnetic properties of FCIPs before and after coating were investigated by Agilent 8720ET vector network analyzer within 0.5–18 GHz. After coated with nanostructure polymer, the real part of permittivity for FCIPs/wax composite was decreased while its permeability remained nearly unchanged. Dielectric behaviors were discussed by the Cole–Cole dispersion formula. After surface modification with nanostructure polymer, reflection loss of FCIPs-MAA-PS/wax composite presented a wide absorption band and showed the minimum value of reflection loss reaching −39.4 dB when the thickness was 2.50 mm. Copyright © 2013 John Wiley & Sons, Ltd.

Assessment of carbon steel microbiologically induced corrosion by electrical impedance spectroscopy

A methodology to analyse electrochemical impedance spectroscopy (EIS) data for the study of microbiologically induced corrosion is proposed. The proposed methodology is based on the loss tangent behaviour of EIS spectra for sterile and bacteria-inoculated environments. Loss tangent parameters were obtained by fitting the EIS data to the Cole–Cole dispersion model using a genetic algorithm. Two electrochemical cells were implemented to expose carbon steel probes to sterile and inoculated media for two bacteria consortia, acid-producing bacteria (APB) and sulphate-reducing bacteria (SRB). The APB tests were exposed for 96 h and the SRB tests for 144 h. A microbial count was carried out during each experiment. The EIS spectra were measured during exposure for sterile and inoculated media. The spectra were fitted to a multi Cole–Cole dispersion model, and loss tangent parameters were obtained.

Temperature dependence of the dielectric constant of acrylic dielectric elastomer

The dielectric constant is an essential electrical parameter to the achievable voltage-induced deformation of the dielectric elastomer. This paper primarily focuses on the temperature dependence of the dielectric constant (within the range of 173 K to 373 K) for the most widely used acrylic dielectric elastomer (VHB 4910). First the dielectric constant was investigated experimentally with the broadband dielectric spectrometer (BDS). Results showed that the dielectric constant first increased with temperature up to a peak value and then dropped to a relative small value. Then by analyzing the fitted curves, the Cole–Cole dispersion equation was found better to characterize the rising process before the peak values than the Debye dispersion equation, while the decrease process afterward can be well described by the simple Debye model. Finally, a mathematical model of dielectric constant of VHB 4910 was obtained from the fitted results which can be used to further probe the electromechanical stability of the dielectric elastomers.

Graphene/polyaniline nanorod arrays: synthesis and excellent electromagnetic absorption properties

In the paper, we find that graphene has a strong dielectric loss, but exhibits very weak attenuation properties to electromagnetic waves due to its high conductivity. As polyaniline nanorods are perpendicularly grown on the surface of graphene by an in situ polymerization process, the electromagnetic absorption properties of the nanocomposite are significantly enhanced. The maximum reflection loss reaches −45.1 dB with a thickness of the absorber of only 2.5 mm. Theoretical simulation in terms of the Cole–Cole dispersion law shows that the Debye relaxation processes in graphene/polyaniline nanorod arrays are improved compared to polyaniline nanorods. The enhanced electromagnetic absorption properties are attributed to the unique structural characteristics and the charge transfer between graphene and polyaniline nanorods. Our results demonstrate that the deposition of other dielectric nanostructures on the surface of graphene sheets is an efficient way to fabricate lightweight materials for strong electromagnetic wave absorbents.

An analysis of dielectric relaxation using the fractional master equation of the stochastic Ising model

In this paper, we begin introducing some basic definitions and mathematical preliminaries of the fractional calculus theory. By using the fractional calculus technique (that is, calculus of derivatives and integrals of any arbitrary real or complex order) a solution of the fractional master equation derived from the stochastic Ising model of Glauber has been obtained and the result is applied to an analysis of the dielectric relaxation processes. From the solution of the equation, the Cole–Cole dispersion relation, KWW (Kohlrausch–William–Watts) equation and algebraic decay relaxation functions are obtained easily. Then these functions are compared with Bozdemir's earlier analysis of the stochastic Ising model.

On the FDTD Formulations for Biological Tissues With Cole–Cole Dispersion

The rationale behind several previously reported FDTD formulations for directly implementing fractional-ordered Cole-Cole models is investigated from another perspective. The explicit expressions of their numerical permittivities are derived, respectively, which makes a quantitative comparison of their modeling ability on a Cole-Cole medium possible and verifies the direct validation of these formulations clearly. Their practical performance, by evaluating implicit effective permittivities after being incorporated into a second-order or fourth-order accurate FDTD algorithm, is also illustrated for the one-dimension FDTD problem of modeling an exemplified human biological medium in order to find the potentially best one among them.

FDTD Modeling of Biological Tissues Cole–Cole Dispersion for 0.5–30 GHz Using Relaxation Time Distribution Samples—Novel and Improved Implementations

In this paper, novel finite-difference time-domain implementations of the Cole-Cole dispersion model for biological tissues, from 0.5 to 30 GHz, based on the sampling of the distribution of relaxation time, and the convolution integral formulation, are provided and verified. Moreover, shortcomings of the original relaxation time sampling implementation, with polarization formulation, were identified, and the improved polarization implementation is provided as well. These implementations are compared with the implementation utilizing the fractional derivative formulation. All compared implementations require storing the electric field and some related auxiliary quantities for only the previous time step. It is observed that, for a single-term Cole-Cole relation, relaxation time sampling implementations can provide accuracy, storage requirement, and simulation time comparable to the ones for the fractional derivative implementation. However, the latter does not exist for the more general multiterm Cole-Cole dispersion relation, for which the implementations based on the relaxation time sampling could be easily extended to.

Time domain dielectric spectroscopy of crayfish tail muscle, measured in vivo

We measured the dielectric spectra of crayfish tail muscle, in vivo, in both the time and frequency domains. We inserted a linear array of four needle electrodes (denoted 1, 2, 3 and 4) into the tail muscle. For time domain dielectric spectroscopy (TDDS), we used the MacADIOS data acquisition system to apply a voltage step of amplitude V 0 and to sample the resulting voltages across electrodes 1 and 2 and also across 3 and 4 as well as the current, I, that flowed through a series resistor during polarization and depolarization. Fourier transformation of the variation of the conductance between 2 and 3 with time yielded the capacitance and conductance spectra of the muscle from about 1 kHz down to 0.1 Hz with electrode effects presumably eliminated. A Hewlett-Packard 4192A low-frequency impedance analyzer (IA) measured directly the capacitance and conductance spectra between electrodes 2 and 3 from 100 Hz to 1 MHz. The TDDS results exhibited a strong dispersion for frequencies on the order of 10 Hz that could be characterized by a KWW response ( T∼0.1 s and β∼0.8). We modeled the IA results as a Cole–Cole dispersion with n=0.5.

Dielectric properties of aqueous glycerol and a model relating these to the properties of water

The complex permittivity of aqueous glycerol has been measured at several concentrations, at a frequency of 70 GHz and, by time domain spectroscopy, at frequencies from 0.01 to 10 GHz. The results are interpreted in terms of a single concentration-dependent Davidson–Cole dispersion. The distribution parameter β is constant at ca. 0.7 at glycerol mole fractions 1 to ca. 0.2, increasing gradually to unity as the solution is further diluted. The activation entropy rises gently up to mole fraction 0.2, then more steeply. The overall slow rise of free energy of activation results from the parallel rise of enthalpy and entropy. The single relaxation zone is taken to show that the relaxing element is common to solvent and solute. This conclusion leads to a formulation of the static permittivity of monohydric and polyhydric alcohol solutions in water and in non-polar solvents in terms of an effective concentration of an imaginary water-like reference substance having a dipole moment 8.33 × 10–30 C m (or 2.5 D) at 20 °C. The model is applied to a number of solutes for which data in water and non-polar solvents are available and to 1,4-dioxane, for which the water equivalent is negative. The model can in principle be extended to other types of solute. The resulting dipole moments relative to the reference substance are not related explicitly to the size and structure of the solute molecule. Such a correlation can only be made with the aid of extraneous evidence such as that furnished by dielectric or ultrasonic dispersion.

Dielectric Behavior of Water at Microwave Frequencies

An extensive examination of the dielectric properties of water at microwave frequencies has been made. The results have been fitted to various functions which have been derived from the Cole and Cole dispersion equation and it is concluded that the relaxation process in water is characterized by a narrow spectrum of relaxation times.