Permittivity Model Research Articles

Permittivity Modeling in Electrolyte PC-SAFT

Permittivity Modeling in Electrolyte PC-SAFT

Artificial Intelligence Using FFNN Models for Computing Soil Complex Permittivity and Diesel Pollution Content

Soil pollution caused by hydrocarbons, such as diesel, poses significant risks to both human health and the ecosystem. The evaluation of soil pollution and various soil engineering applications often relies on the analysis of complex permittivity, encompassing parameters such as dielectric constant and dielectric loss. Various computational models, including theoretical physics-based models, mixture theory models, statistical empirical models, and artificial neural network (ANN) models, have been explored for computing soil complex permittivity and predicting water and pollutant content. Theoretical models require detailed data that is often unavailable, and thus have limited applicability. Mixture models tend to underestimate soil characteristics due to inaccuracies in permittivity estimation of soil phases. While empirical models are widely used, their applicability is restricted to specific soil types, datasets, and locations. ANN models offer promising predictions, accommodating nonlinear phenomena and allowing for missing information and variables. In this study, capacitive electromagnetic electrode sensors were utilized to determine the complex permittivity of soil contaminated with varying levels of diesel at different moisture levels. Theoretical mixture, empirical, and Feed Forward Neural Network (FFNN) models were employed to compute the permittivity of polluted soil based on its phases and to predict the level of diesel pollution. A comparison of these modeling approaches revealed that the FFNN model exhibited the best performance. The ANN model demonstrated superior performance metrics, including a high correlation coefficient and lower mean square error. Specifically, the correlation coefficients for the FFNN model were 0.9942 for training samples, 0.9967 for validation samples, and 0.9977 for test samples. Additionally, the ANN model yielded the lowest mean square error compared to the other three models. Doi: 10.28991/CEJ-2024-010-09-018 Full Text: PDF

A New Metric for the Comparison of Permittivity Models in Terahertz Time-Domain Spectroscopy

A New Metric for the Comparison of Permittivity Models in Terahertz Time-Domain Spectroscopy

Microwave enhanced demulsification of metal ion extraction emulsions: From permittivity modeling to proof of concept for solvent extraction processes

The demulsification by microwaves of liquid-liquid systems for metal recycling was experimentally and numerically investigated. Strongly ionic aqueous phases with high conductivities and typical organic phases, both representative of industrial ones, were used. Experimental microwave demulsification was achieved in both the W/O and O/W systems at the laboratory scale showing the rapidity and the efficiency of the process. The dielectric properties of these representative emulsions were measured and modeled using the permittivities measured in the separate phases and the phase fractions. Taking into account the direction of the emulsion, permittivities were predicted over a wide range of frequencies, along with microwave penetration depths in the whole range of phase fractions. Numerical simulations of the electric field distribution and penetration depths calculations at several frequencies demonstrated that microwave heating is relevant and possible in both W/O and O/W dense packed emulsions, which should rapidly lead to demulsification, including on a large industrial scale.

A permittivity-conductivity joint model for hydrate saturation quantification in clayey sediments based on measurements of time domain reflectometry

Hydrate saturation (Sh) is one of the key parameters for resource assessment of hydrate reservoirs and production optimization of natural gas. There are still significant challenges in determining the Sh in clayey formations. Both dielectric and resistivity logging tools have been used for identifying and evaluating hydrate-bearing formations; however, there is little work on a joint analysis and modelling of the permittivity and resistivity for quantifying the Sh. To bridge the knowledge gap, we have proposed a novel permittivity-conductivity (P–C) joint approach based on TDR (time domain reflectometry)-derived parameters (i.e., apparent permittivity Ka and bulk conductivity σdc) in this work. The proposed P–C joint approach can provide a theoretical basis for the joint interpretation of dielectric and resistivity geophysical measurements on hydrate-bearing formations in the field. First, the basic theory for deriving the Ka and σdc from the TDR responses of hydrate-bearing sediments was formulated based on the dielectric polarization and electrical conduction mechanisms. Second, an experimental campaign was carried out including the development of experimental system, calibration of TDR probe and design of experimental scheme. Third, the influences of hydrate saturation, clay mineralogy and clay content on the TDR responses of unconsolidated sediments were examined. Then the Ka and σdc were related to Sh respectively, and finally a novel P–C joint model for the quantification of Sh in clayey sediments was established and verified. It has been demonstrated that: (1) the Ka of the clayey samples with hydrates decreases almost linearly with an increasing clay content up to 20 %, while the σdc of the smectite-bearing samples decreases nonlinearly in contrast to the linear trend for illite; (2) the power-law mixing formula incorporating an empirical exponent is a preferable permittivity model for hydrate-bearing clayey sediments due to its merits of empirical and theoretical nature, while the Simandoux equation is effective to account for the clay effects on the conductivity of hydrate-bearing sediments with smectite and illite; (3) the P–C joint model can be established by utilizing the porosity of hydrate-bearing sediments as a bridge parameter between Ka and σdc. The variation behavior of Ka and σdc with different types and contents of clay minerals can be explained by the difference of the amount of bound water and swelling effects between the illite-bearing and smectite-bearing samples. The proposed P–C joint model outperforms the standalone permittivity-based and conductivity-based models especially for the clayey cases. The root-mean-squared errors of the P–C joint models are 7.339, 2.930 and 2.065 % for the clean-sand samples, clayey samples with illite and smectite, respectively.

Comparison of the Casimir force between SiC plates with different permittivity models: Lorentz model and Palik data

Accurate calculation of Casimir forces is essential for the development of micro- and nanoelectromechanical systems. Silicon carbide (SiC) is an excellent material for fabricating microsensors due to its high durability, high stiffness, and low thermal expansion. The permittivity of the SiC could be characterized by the Lorentz model or the Palik data. However, the influence of the two models of calculating permittivity on the Casimir force has not been discussed. In this work, we calculate the Casimir force between SiC plates by the Lorentz model and the Palik data, respectively. The Casimir force calculated by the Lorentz model could be 4 times greater than the Palik data for SiC at a gap distance of 10 nm. The difference of the permittivity in the ultraviolet lead to different Casimir forces. This work demonstrates the difference between the two models of permittivity for calculating the SiC-based Casimir force, and provides a reliable base for more accurate Casimir force calculations.

Advancing noninvasive and nondestructive root phenotyping techniques: A two-phase permittivity model for accurate estimation of root volume

Noninvasive and nondestructive root phenotyping techniques under field conditions are needed to advance plant root science. Soil electrical parameters including capacitance and resistance hold potential to meet this need, although their specific ability to detect roots remains uncertain. In this study, we developed a two-phase root and soil permittivity model at high frequency enabling accurate and noninvasive prediction of root volume. The validation calculation showed that the two-phase model successfully predicts root volume with a minimal error of less than 1 % under the control conditions with roots placed in wet soil and water. Furthermore, we demonstrated that the high-frequency bulk soil capacitance when integrated into an empirical model, can accurately estimate root volume for summer maize (Zea mays L.) in both the field (root mean square error (RMSE) = 1.52 cm3) and in root washing-free measurement applications in the absence of soil (RMSE = 0.36 cm3). When the empirical relationship between high-frequency bulk soil capacitance and root volume is not adequate, the two-phase model can be used to calibrate the empirical model. To this end, a series of soil pot experiments with winter wheat (Triticum aestivum L.) showed that the measurement accuracy can be fundamentally improved. These results highlighted the effectiveness of the two-phase permittivity model, making high-frequency bulk soil capacitance a reliable method for in situ measurement of root volume. It is anticipated that the availability of new equipment for measuring high-frequency soil electrical parameters will lead to widespread adoption of this root phenotyping technique in the future.

THE EFFECT OF MOISTURE CONTENT ON ELECTRICAL PROPERTIES OF SELECTED SOFTWOODS; CEDAR, JUNIPER, AND PINE

Natural woods as a raw material have been taking a considerable interest topic by industries such as the forest industry, furniture manufacturing, and nowadays suitable electronics. One of the most essential steps of manufacturing for those industry purposes is RF heating/drying of raw wood material nowadays. However, knowing the electrical properties, such as the dielectric constant of wood-based material before processing is tremendously important. It is well-known that the moisture content and density levels of material directly affect the dielectric properties. Moisture and density conditions are different in each material because it’s related directly to the absorption and affection of material towards moisture sources. Therefore, in this study of wood material under varying conditions, proper empiric models have been generated to express this relationship. This study is based on three different softwood specimens widely used in the forest industry. The dielectric properties were determined in the frequency range of 2.17 GHz-6.0 GHz as a function of moisture content and density for wood species. Each measurement contains 500 raw data points; a vector network analyzer collected 49,500 S-parameter data. Each wood specimen consists of six samples; the average of data obtained from these samples was considered as a dielectric measure for the examined wood specimen. The proposed empiric models have RMSE better than 0.05 for the relation between loss tangent and density, while the proposed empiric models for dielectric permittivity have better than 0.90 with density relation, which is considered an acceptable ratio for model generation.

A thermodynamic approach to analyzing relative permittivity and solvent mole fraction models, and application to SN1 reactions.

The standard methods for analyzing solvent effects on chemical reactions largely include linear free energy relations that relate kinetic and spectroscopic terms to solvent interactive parameters. The number of these parameters has grown over the years in order to make linear free energy techniques more accurate and cover a wider range of reaction systems. However, even with the myriad of parameters, the details of specific reaction systems make the application of these techniques sometimes unreliable. On the other hand, a thermodynamic approach provides a more precise analysis, and has proven particularly useful for reactions in multi-component solvent systems. In this article we present the mathematical formalism for relating the activation free energy to the bulk thermodynamic properties for a binary (cosolvent) system. We then use this thermodynamic approach, coupled with selected solvent models, to analyze the hydrolysis rates of tert-butyl chloride in the acetonitrile/water solvent system under iso-mole fraction, isodielectric, and isothermal conditions. These analyses allow us to differentiate and quantify bulk electrostatic effects and the effects of close-range solute-solvent interactions.

Methods and tools for assessing the accuracy of composite property models

Property modeling is essential for optimal application and efficient design of new composite materials. Although numerous models of composite properties are available in the literature, there is a lack of rigorous validation of these models. This paper introduces a freely distributed collection of experimental data on the electrical and dielectric properties of composites and an open-source program package for modeling and testing composite property models. The software provides a quantitative estimation of prediction accuracy, making it a valuable tool for assessing the quality of a composite model. The paper demonstrates the use of the proposed tools to estimate two-phase models of composite electrical conductivity that account for the filler shape. The results of this test showed that the examined models failed to simulate the shape of the filler. Also, the article gives an example of the comparison of three-phase models of relative permittivity of composites with fitting parameters. In addition, the study presents the analysis of errors in the approximation of experimental data by the model, as well as recommendations on methods and selection of criteria for evaluating the quality of models.

Numerical calculation of thermoreflectance coefficient of c-Si for wavelengths of 200–800 nm and temperatures of 300–500 K

In this paper, the thermoreflectance (TR) coefficient of c-Si is numerically calculated over the wavelength range of 200–800 nm and the temperature range of 300–500 K using a complex permittivity model that considers interband transitions and free carriers. The calculated results are in good agreement with literature values, and it is found that the temperature dependence of the TR coefficient is almost negligible at wavelengths above 500 nm. On the other hand, in the wavelength range of 200–500 nm, the TR coefficient depends strongly on the wavelength, and the temperature stability also changes significantly depending on the wavelength. This suggests that the wavelength of the probe light for TR measurement should be appropriately selected to realize high sensitivity and temperature stability, considering the constraints of the optical system and the temperature range of the sample.

Permittivity Model Selection Based on Size and Quantum-Size Effects in Gold Films

The article is focused on optical properties of nanostructures containing spherical gold nanoparticles of various radii. We explore correlation between the particle radius and the choice of permittivity model applied to describe optical absorption spectra of gold granules. The experiments show splitting of the absorption band of granular gold films to form a second absorption peak. The first peak is associated with the phenomenon of plasmon resonance, while the second one reflects quantum hybridization of energy levels in gold. Quantum effects are shown to prevail over size effects at a granule diameter of about 5-6 nm. The Mie theory gives a rigorous solution for the scattered electromagnetic field on a sphere taking into account optical properties of the latter, however, it does not specify the criteria for selecting a model to calculate dielectric permittivity. Both calculations and experiments confirm the limiting diameter of gold nanoparticles where the Hampe-Shklyarevsky model is applied. Meanwhile, this model is still unable to predict the splitting of the plasma absorption band. The data presented in the article can be used for a predetermined local field enhancement in composite media consisting of a biolayer and metal nanoparticles. The conducted research provides a deeper understanding of the influence of a terahertz high-intensity electromagnetic field localized in the space on quantum dots.

The SSR Brightness Temperature Increment Model Based on a Deep Neural Network

The SSS (sea surface salinity) is an important factor affecting global climate changes, sea dynamic environments, global water cycles, marine ecological environments, and ocean carbon cycles. Satellite remote sensing is a practical way to observe SSS from space, and the key to retrieving SSS satellite products is to establish an accurate sea surface brightness temperature forward model. However, the calculation results of different forward models, which are composed of different relative permittivity models and SSR (sea surface roughness) brightness temperature increment models, are different, and the impact of this calculation difference has exceeded the accuracy requirement of the SSS inversion, and the existing SSR brightness temperature increment models, which primarily include empirical models and theoretical models, cannot match all the relative permittivity models. In order to address this problem, this paper proposes a universal DNN (deep neural network) model architecture and corresponding training scheme, and provides different SSR brightness temperature increment models for different relative permittivity models utilizing DNN based on offshore experiment data, and compares them with the existing models. The results show that the DNN models perform significantly better than the existing models, and that their calculation accuracy is close to the detection accuracy of a radiometer. Therefore, this study effectively solves the problem of SSR brightness temperature correction under different relative permittivity models, and provides a theoretical support for high-precision SSS inversion research.

Dielectric Spectroscopy Shows a Permittivity Contrast between Meningioma Tissue and Brain White and Gray Matter-A Potential Physical Biomarker for Meningioma Discrimination.

The effectiveness of surgical resection of meningioma, the most common primary CNS tumor, depends on the capability to intraoperatively discriminate between the meningioma tissue and the surrounding brain white and gray matter tissues. Aiming to find a potential biomarker based on tissue permittivity, dielectric spectroscopy of meningioma, white matter, and gray matter ex vivo tissues was performed using the open-ended coaxial probe method in the microwave frequency range from 0.5 to 18 GHz. The averages and the 95% confidence intervals of the measured permittivity for each tissue were compared. The results showed the absence of overlap between the 95% confidence intervals for meningioma tissue and for brain white and gray matter, indicating a significant difference in average permittivity (p ≤ 0.05) throughout almost the entire measured frequency range, with the most pronounced contrast found between 2 GHz and 5 GHz. The discovered contrast is relevant as a potential physical biomarker to discriminate meningioma tissue from the surrounding brain tissues by means of permittivity measurement, e.g., for intraoperative meningioma margin assessment. The permittivity models for each tissue, developed in this study as its byproducts, will allow more accurate electromagnetic modeling of brain tumor and healthy tissues, facilitating the development of new microwave-based medical devices and tools.

Nonlocal Hydrodynamic Model with Viscosive Damping and Generalized Drude–Lorentz Term

The response of plasmonic metal particles to an electromagnetic wave produces significant features at the nanoscale level. Different properties of the internal composition of a metal, such as its ionic background and the free electron gas, begin to manifest more prominently. As the dimensions of the nanostructures decrease, the classical local theory gradually becomes inadequate. Therefore, Maxwell’s equations need to be supplemented with a relationship determining the dynamics of current density which is the essence of nonlocal plasmonic models. In this field of physics, the standard (linearized) hydrodynamic model (HDM) has been widely adopted with great success, serving as the basis for a variety of simulation methods. However, ongoing efforts are also being made to expand and refine it. Recently, the GNOR (general nonlocal optical response) modification of the HDM has been used, with the intention of incorporating the influence of electron gas diffusion. Clearly, from the classical description of fluid dynamics, a close relationship between viscosive damping and diffusion arises. This offers a relevant motivation for introducing the GNOR modification in an alternative manner. The standard HDM and its existing GNOR modification also do not include the influence of interband electron transitions in the conduction band and other phenomena that are part of many refining modifications of the Drude–Lorentz and other models of metal permittivity. In this article, we present a modified version of GNOR-HDM that incorporates the viscosive damping of the electron gas and a generalized Drude–Lorentz term. In the selected simulations, we also introduce Landau damping, which corrects the magnitude of the standard damping constant of the electron gas based on the size of the nanoparticle. We have chosen a spherical particle as a suitable object for testing and comparing HD models and their modifications because it allows the calculation of precise analytical solutions for the interactions and, simultaneously, it is a relatively easily fabricated nanostructure in practice. Our contribution also includes our own analytical method for solving the HDM interaction of a plane wave with a spherical particle. This method forms the core of calculations of the characteristic quantities, such as the extinction cross-sections and the corresponding components of electric fields and current densities.

A Modified MLC-Based Microwave Sensing System for Retrieving Permittivity of Liquid Samples

A modified magnetic-LC (MLC)-based microwave sensing system is proposed in this manuscript. The proposed microwave sensing system consists of the modified MLC resonator and the active RF circuits. The modified MLC resonator is evolved from a traditional MLC resonator, and the density of electrical field for the modified MLC resonator is increased significantly than traditional one. And, the more concentrated electrical field can improve the sensitivity of retrieving real permittivity. The RF detection circuits is composed of a low noise amplifier (LNA), a bandpass filter (BPF), and an envelope detector. The operating principle of proposed sensing system can be illustrated as follows: Assuming that the signal generator produces a RF signal with a fixed frequency of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , then the RF signal passes through the passive resonator, the magnitude and phase of original RF signal will be changed. Then, the BPF can suppress the out-of-band spurious signals, and make the desired RF signal cleaner. Next, the modulated RF signal is demodulated by envelope detector, and after demodulation, the direct current (DC) output voltage can be measured by multimeter. As known, the DC output voltage will be altered by loading liquid under tests (LUTs) with different permittivity, a mathematical model for DC output voltage and real permittivity can be established. The permittivity of LUTs with different volume fractions of water can be predicted by the established mathematical model. In measurement, the proposed sensing system shows an average sensitivity of about 55.35 mV/(per unit ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ′) in detecting ethanol-water mixed solution with different volume fractions of water, which is several times higher than the other designed ones. The proposed M-MLC-based microwave sensing system is a good candidate in the application of characterizing liquid samples.

A Calibrated Permittivity Modeling Approach for Cross-Area Path Loss Prediction

A Calibrated Permittivity Modeling Approach for Cross-Area Path Loss Prediction

Effect of the DC-bias electric field on the phase transition characteristics in PMN ceramics

Relaxor ferroelectrics play an important role for technological applications, mainly for using in the fabrication of actuators, transducers and sensors. Therefore, there has been an increasing interest of the scientific community in the investigation of the physical properties of such system in order to better elucidate the observed intriguing and unsolved phenomena. In this work, relaxor Pb(Mg1/3Nb2/3)O3 (PMN) ceramic system was prepared and the dielectric properties have been studied in details as a function of frequency, temperature and magnitude of the DC-bias electric field. Results reveal that the temperature dependence of the dielectric permittivity can be successfully described in the whole analyzed temperature range (100–400 K) by using a macroscopic statistical model, which describe the dielectric response in relaxor systems with diffuse phase transition (DPT). By using this phenomenological model, the temperature and DC-bias electric field dependences of the dielectric permittivity have been also revisited, from the analysis of the DPT behavior, promoting a careful discussion on the nature of the phase transition in relaxors materials. The calculated sizes of the polar nanoregions (PNRs) suggest the development of a structural disorder in the studied system, which promote the high diffuse ferroelectric transition as the amplitude of the DC-bias electric field increases.

Measurement of Time Dependent Reflection, Transmission, and Absorption in Laser Driven Silicon and GaAs Switches for 250 GHz Radiation.

The reflectance and transmittance of Si and GaAs wafers irradiated by a 6 ns pulsed, 532 nm laser have been studied for s- and p-polarized 250 GHz radiation as a function of laser fluence and time. The measurements were carried out using precision timing of the and signals, allowing an accurate determination of the absorptance where . Both wafers had a maximum reflectance above 90% for a laser fluence . Both also showed an absorptance peak of ~50% lasting ~2 ns during the risetime of the laser pulse. Experimental results were compared with a stratified medium theory using the Vogel model for the carrier lifetime and the Drude model for permittivity. Modeling showed that the large absorptance at the early part of the rise of the laser pulse was due to the creation of a lossy, low carrier density layer. For Si, the measured and were in very good agreement with theory on both the nanosecond time scale and the microsecond scale. For GaAs, the agreement was very good on the nanosecond scale but only qualitatively correct on the microsecond scale. These results may be useful for planning applications of laser driven semiconductor switches.

Electronic-Based Model of the Optical Nonlinearity of Low-Electron-Density Drude Materials

Low-electron-density Drude (LEDD) materials such as indium tin oxide (ITO) are receiving considerable attention for their combination of CMOS compatibility, unique epsilon-near-zero (ENZ) behavior, and giant ultrafast nonlinear thermo-optic response. However, current understanding of the electronic and optical response of LEDD materials is limited due to the simplistic modeling that extends only the known models of noble metals without considering the interplay among the lower electron density, relatively high Debye energy, and the nonparabolic band structure. We bridge this knowledge gap and provide a complete understanding of the nonlinear electronic-thermal-optical response of LEDD materials. In particular, we rely on state-of-the-art electron dynamics modeling, as well as a time-dependent permittivity model for LEDD materials under optical pumping within the adiabatic approximation. We find the electron temperature may reach values much higher than realized before, even exceeding the Fermi temperature, in which case the effective chemical potential dramatically decreases and even becomes negative, thus, transient giving the material some characteristics of a semiconductor. We further show that the nonlinear optical response of LEDD materials originating from the changes to the real part of the permittivity is associated with changes of the population. This resolves the argument about the rise time of the permittivity, showing that it is instantaneous. In this vein, we show that referring to the LEDD permittivity as having a Kerr or ``saturable'' nonlinearity is unsuitable since its permittivity dynamics is absorptive rather than nonresonant and does not originate from population inversion. Finally, we analyze the probe-pulse dynamics and unlike previous work, we obtain a quantitative agreement with the results of recent experiments.