Inhomogeneous Dielectrics Research Articles

COULOMB DRAG RESISTIVITY IN DOUBLE-LAYER GRAPHENE: INHOMOGENEITY EFFECTS

We investigate Coulomb drag resistivity in a double-layer system consisting of two parallel monolayer graphene sheets. In calculations, we employ the random-phase approximation to determine the polarizability functions of the graphene layers and the frequency-dependent dielectric function of the structure, taking into account inhomogeneity effects of the background dielectric. Our numerical calculations reveal that Coulomb drag resistivity in double-layer graphene systems steadily increases with increasing temperature but quickly decreases as the interlayer separation increases. The drag resistivity between the two layers in the case of an inhomogeneous background dielectric is substantially larger than that in the case of a homogeneous one. In addition, both the value and the imbalance in carrier density in the layers lead to noticeable changes in Coulomb drag resistivity in the system. Our study results are useful in graphene-based structure applications.

Dynamic density functional theory of polymers with salt in electric fields.

We present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager's transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes.

Second-order, positive, and unconditional energy dissipative scheme for modified Poisson–Nernst–Planck equations

First-order energy dissipative schemes in time are available in literature for the Poisson–Nernst–Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that incorporate effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance. Applications in ion permeation through a 3D nanopore show that the modified PNP model, equipped with the proposed schemes, has promising applications in the investigation of ion selectivity and rectification. The proposed second-order discretization can be extended to design temporal second-order schemes with original energy dissipation for a type of gradient flow problems with entropy.

ВЛИЯНИЕ ТОЛЩИНЫ ПЛЕНОК ПОЛИДИФЕНИЛЕНФТАЛИДА НА СПЕКТР ТОКОВ ДЕПОЛЯРИЗАЦИИ МНОГОСЛОЙНЫХ СТРУКТУР

The depolarization currents of multilayer polymer films of polydiphenylene phthalide were measured using the thermally stimulated depolarization (TSD) method in the range from 170 to 400 K. The solution concentration was 2.5 and 5 wt.%. Each layer of polymer film was pre-dried at room temperature, then annealed in an oven. The number of layers of polymer film was 1, 2, 3 and 7 layers for 2.5 wt.%. and 1, 2, 3, 5 and 7 layers for 5 wt.%. The polarizing electric field strength was 2.5 × 105 V/cm. The rate of temperature change was 5 K/min. Based on experimental data, the dependence of the temperature of the position of the maximum peak of the depolarization current, the maximum values of the peaks of the depolarization currents, the values of the released charge and the activation energy of relaxation processes on the number of layers of the polymer film is shown. The temperature dependences of depolarization currents revealed two regions for a solution concentration of 2.5 wt.%. and one area for 5 wt.%. The first region is interpreted in the dipole charge approximation. The second region is explained by the presence of a wide distribution of traps occupied by injected charges. Interlayer polarization is observed in inhomogeneous dielectrics and is caused by differences in the electrical conductivity and dielectric constant of individual particles (or microparticles) of the dielectric. In such dielectrics, when an electric field is applied at the interface between its various components, charge will accumulate, which is equivalent to the creation of polarization. The results for the temperature dependences of the TSD currents of the samples showed that the total accumulated charge in the volume increases as the number of polymer layers increases. The reason for such a high concentration of trapped charges is most likely due to the presence of a wide distribution of traps occupied by injected charges. Moreover, the magnitude of the released charge is greater for samples prepared from a polymer solution with 2.5 wt. % This effect depends on the thickness of the polymer films. Namely, the thinner the films, the more charged particles penetrate the interface between the films.

Autonomous hydrogel locomotion regulated by light and electric fields.

Autonomous robotic functions in materials beyond simple stimulus-response actuation require the development of functional soft matter that can complete well-organized tasks without step-by-step control. We report the design of photo- and electroactivated hydrogels that can capture and deliver cargo, avoid obstacles, and return without external, stepwise control. By incorporating two spiropyran monomers with different chemical substituents in the hydrogel, we created chemically random networks that enabled photoregulated charge reversal and autonomous behaviors under a constant electric field. In addition, using perturbations in the electric field induced by a dielectric inhomogeneity, the hydrogel could be attracted to high dielectric constant materials and autonomously bypasses the low dielectric constant materials under the guidance of the electric field vector. The photo- and electroactive hydrogels investigated here can autonomously perform tasks using constant external stimuli, an encouraging observation for the potential development of molecularly designed intelligent robotic materials.

Theory of Doubly-Shielded Coupled Lines for Directional Couplers of Various Directivity Types With Impedance Transformation

Asymmetric coupled lines (CLs) with double shielding in an inhomogeneous dielectric medium are studied. They have specific properties that allow the creation of impedance-transforming directional couplers with a given directivity type. The proposed models and synthesis techniques take into account both electric asymmetry and dielectric inhomogeneity. Numerical simulations and measurements prove the correctness of the general theory, and the possibility of creating co-, contra-, and trans-directional couplers with impedance-transforming and phase-shifting properties. The results will be useful for finding new design solutions for next-generation microwave circuits.

An Adaptive Local Iterative Method for Fast Calculation of Electrostatic Interactions between Charged Polymers in Dielectric Inhomogeneous System

AbstractThe motion of charged polymers in the 3D dielectric inhomogeneity system is investigated using a hybrid simulation approach that combines a finite difference method with a Brownian dynamics model (FD‐BD) for the polymer chain. The interface difference scheme of the two‐dielectric model is first derived to achieve a smooth extension of the electrostatic potential values and it is verified that it has a second‐order convergence order. In addition, it is displayed that the local iteration method greatly accelerates the efficiency of calculating the electrostatic interaction forces. However, it is found that the computational efficiency improvement of the traditional local iteration is less significant (about three times) for polymer simulations such as 3D diagonal type. Therefore, a new strategy, the banded local iteration method, is proposed and the simulation results demonstrate that it can better adapt the effects of the deformation of the polymer during its motion, where the computational efficiency is increased by 29 times at most, while the relative error is controlled to less than 5.15e−4. The work can be helpful for accelerating the solution of electrostatic forces under dielectric inhomogeneity, and confer new insights into the optimization of iteration for polymer chains with different geometries in large electrostatic systems.

Complex Inhomogeneous Dielectric Target Modeling and Scattering Estimation using a Self-Designed Software

This paper presents a method to finely model the arbitrarily irregular-shaped and inhomogeneous dielectric target. The target is first geometrically divided into a set of homogeneous and isotropic tetrahedral regions. Each region is precisely matched with a set of electromagnetic parameters. As a result, this can accurately model the target which has an extremely complex dielectric constant distribution and an irregular shape. Regarding the electromagnetic scattering evaluation of the established model, the method of moments (MoM) is adopted in consideration of the coupling between these tetrahedral regions, and the total scattering is obtained by solving the matrix equation. The above two computational sections are integrated into a self-designed software. One can just input the spatial distribution of the dielectric constant and then the designed software automatically processes the target’s geometric information and meshes the target. Finally, the scattered electric field and radar cross section (RCS) of the target are output from the software. The designed software provides an effective and accurate way to study the electromagnetic scattering characteristics of the complex inhomogeneous objects.

Structural and dielectric properties of ultra-fast microwave-processed La0.3Ca0.7Fe0.7Cr0.3O3−δ ceramics

Perovskite La0.3Ca0.7Fe0.7Cr0.3O3-δ (LCFCr) is a mixed ionic and electronic conductor (MIEC) that can be employed as an electrode material in reversible solid oxide fuel cells (RSOFCs). In this work, an ultra-fast (15 ​min) one-step microwave (MW)-assisted combustion synthesis route has been developed to obtain phase pure and highly crystalline LCFCr powder. The synthesized powders exhibited a sponge-like microstructure with increased electrochemical reaction sites. Neutron thermodiffraction analysis revealed a structural transition above 500 ​°C from the room temperature (RT) orthorhombic Pnma to a rhombohedral R3c perovskite phase. The oxygen vacancy concentration was found to increase from δ ​= ​0.272(7) at RT to δ ​= ​0.333(5) at 900 ​°C. Furthermore, a 3-dimensional G-type antiferromagnetic structure was detected at RT. MW-sintering of pressed green ceramic pellets was carried out at 950 ​°C for 1 ​h, using a MW-transparent quartz fiber crucible or alternatively a SiC crucible acting as a MW-absorber. Impedance spectroscopy data on sintered ceramic pellets revealed electronic inhomogeneity as demonstrated by the occurrence of three dielectric relaxation processes associated with two grain boundary (GB)-like contributions and one bulk. The dielectric inhomogeneity encountered may be restricted to the extrinsic GB areas, which may be rather thin. More homogeneous dielectric properties of the GBs were found in the pellet that was sintered in the SiC crucible.

Dark-Exciton Driven Energy Funneling into Dielectric Inhomogeneities in Two-Dimensional Semiconductors.

The optoelectronic and transport properties of two-dimensional transition metal dichalcogenide semiconductors (2D TMDs) are highly susceptible to external perturbation, enabling precise tailoring of material function through postsynthetic modifications. Here, we show that nanoscale inhomogeneities known as nanobubbles can be used for both strain and, less invasively, dielectric tuning of exciton transport in bilayer tungsten diselenide (WSe2). We use ultrasensitive spatiotemporally resolved optical scattering microscopy to directly image exciton transport, revealing that dielectric nanobubbles are surprisingly efficient at funneling and trapping excitons at room temperature, even though the energies of the bright excitons are negligibly affected. Our observations suggest that exciton funneling in dielectric inhomogeneities is driven by momentum-indirect (dark) excitons whose energies are more sensitive to dielectric perturbations than bright excitons. These results reveal a new pathway to control exciton transport in 2D semiconductors with exceptional spatial and energetic precision using dielectric engineering of dark state energetic landscapes.

Fast Method for Accelerating Convergence of Iterative Partial Differential Equation Solvers by Changing System Matrix to Laplacian Counterpart

In this work, we find that the matrix representing the curl-curl operator in a partial differential equation solver of Maxwell’s equations can be analytically decomposed into a gradient divergence operator and a Laplacian, both of which can be constructed from the mesh information without any need for computation. The curl-curl operator can hence be replaced by the Laplacian to find the divergence-free component of the field solution. The Laplacian is positive definite and well-conditioned. As a result, the convergence of an iterative solution of Maxwell’s equations can be guaranteed, and also significantly accelerated. Based on the finding, we represent the divergence-free component of the unknown field solution by deducting its curl-free component. The curl-free component resides in the nullspace of the curl-curl operator, which is also analytically known from the mesh information no matter it is a regular grid or an unstructured mesh. After the divergence-free component is rapidly solved from a Laplacian counterpart of the original system matrix, the curl-free component can also be solved from a Laplacian matrix, and hence having fast and guaranteed convergence. The total computational cost of the proposed method is simply a small number of sparse matrix-vector multiplications. The proposed method has been successfully applied to solve ill-conditioned onchip, packaging, and antenna radiation problems at both low and high frequencies, involving both inhomogeneous dielectrics and lossy conductors. Numerical experiments have demonstrated its fast and guaranteed convergence, as well as trivial computational cost independent of problem size.

ТЕРМОФЛУКТУАЦИОННАЯ ТЕОРИЯ РАЗРУШЕНИЯ И ОЦЕНКА ДОЛГОВЕЧНОСТИ ЭЛЕКТРИЧЕСКОЙ ИЗОЛЯЦИИ СПЭ КАБЕЛЕЙ

The article is devoted to research on the creation of a method for assessing the durability ofthe main insulation of power cable lines based on the thermofluctuation theory of destruction of solids.The features of breakdown development in homogeneous and inhomogeneous dielectrics areconsidered. The problematic issues of insulating materials of power cable systems (PCS) are consideredon the basis of the development and development of non-destructive testing methods. The maincomponents that destroy the insulation of the PCS are installed. The thermofluctuation theory ofdestruction and the evaluation of the durability of electrical insulation of power cables are described.An analytical method is proposed for evaluating the processes of cellulose oxidation with the determinationof the most probable. The proposed approach to identifying the main processes of insulationdestruction allows us to present in more detail the prerequisites for the development of partial discharges(PD) in isolation and to determine measures to minimize the processes leading to the destructionof PCS insulation. The results of experiments on the study of the service life of the insulatingmaterial of aged ends of a power cable in a thermal cabinet, to determine the aging criteria, arepresented. The experimental data are interpreted from the standpoint of the thermofluctuation theory.The dependence of the increase in the temperature difference ΔT on the degree of wear of the electricalinsulating properties of the material is revealed and investigated, which makes it possible to predictits resource. The thermofluctuation theory of the destruction of insulating materials caused bythe thermofluctuation rupture of chemical bonds and the evaluation of the durability of electricalinsulation of cables made of cross-linked polyethylene are considered. It is shown that, in order tocalculate the average energy of the monomeric link of various polymer materials, it is necessary toknow: the chemical formula of the monomeric link and the values of the binding energies. In thework, the time before the breakdown of the main insulation of the PCS was determined under theaction of temperature. The model can be used in devices and systems for continuous diagnosis ofpower cables according to temperature conditions.

Far-End Crosstalk Modeling and Prediction for Stripline With Inhomogeneous Dielectric Layers (IDLs)

Far-end crosstalk (FEXT) is a critical factor that limits signal integrity performance in high-speed systems. The FEXT level is sensitive to the dielectric inhomogeneity of the stripline in fabricated printed circuit boards (PCB). The dielectric of the stripline is manufactured with multiple inhomogeneous dielectric layers (IDLs) of various resin and glass fiber bundles. A marginal difference in the dielectric permittivity of the IDLs can lead to a significant change FEXT level. In this paper, a practical FEXT modeling methodology for striplines is proposed by introducing the extraction method for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\bm{\varepsilon }}}_{\bm{r}}$</tex-math></inline-formula> of IDLs. The new stripline model is constructed with three IDLs comprised of core, prepreg, and resin pocket, to improve the model accuracy. With the cross-sectional geometry and measured S-parameters of the coupled striplines, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\bm{\ }}{{\bm{\varepsilon }}}_{\bm{r}}$</tex-math></inline-formula> of IDLs can be extracted. In addition, an analytical model to predict the FEXT polarity and magnitude of the stripline caused by the inhomogeneity is proposed targeted for pre-layout application. The proposed models have been verified using measurement. The proposed models can provide useful analysis methodology and design guidelines to mitigate the FEXT level in high-speed systems, especially for high-volume PCB tests in the pre-layout and post-layout stages.

Split dynamic mechanical relaxation of an inhomogeneous dielectric and the insights into its anomalous characteristics

The split relaxations of an inhomogeneous polymer were investigated in this paper, with special attention paid to the application of classic dynamic mechanical analysis (DMA) to inhomogeneous dielectrics. The single relaxation peak of the pristine epoxy resin split to two peaks after thermal ageing, concerning its transition toward an inhomogeneous skin-core structure. Moreover, the relaxation corresponding to the skin-layer, which only took up a small proportion in volume, anomalously dominated the entire relaxation response. The core-layer’s response was even unidentifiable when its proportion was below 65 vol%. This was found strongly correlated with the non-uniform distribution of applied stress during DMA test which kinetically affected the viscoelastic response received from the specimen. Since potential misjudgment could be induced in this case, it should be a critical issue deserving more attention.

Monte Carlo Algorithms for the Extracting of Electrical Capacitance

We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

АНТЕНА НА ОСНОВІ ГІБРИДНОЇ МЕТАЛЕВО-ДІЕЛЕКТРИЧНОЇ СТРУКТУРИ

Purpose: Nowadays, in the millimeter frequency range, the dielectric waveguides of various modifications have certain advantages over the standard metal waveguides, primarily due to the possibility of creating functional units based on them. This is due to the relative simplicity and low cost of manufacturing the dielectric waveguides and functional units using them, the high degree of their integration with active elements, the use in their manufacture of different dielectrics and polymers with a wide range of material constants and a variety of mechanical properties (in particular, some materials have a significant flexibility). After making a series of physical experiments we have found the possibility of implementing the frequency selection and radiation into free space of electromagnetic waves by a hybrid metal-dielectric structure. Design/methodology/approach: The studied electrodynamic structure belongs to the class of hybrid metal-dielectric structures. It includes a modified inverted dielectric waveguide with a periodic sequence on the dielectric plate of fifteen dielectric rods with metallized coating on one of the faces placed outwards. The structure efficiency was estimated by the voltage standing-wave ratio (VSWR) values and power attenuation in the duct. The measurements were made with the reflectometer method. To estimate the degree of electromagnetic field concentration near the rod inhomogeneities in the near zone, the mobile probe method was used. The field structures were visualized with the method of isolines. Findings: The results of a series of experimental investigations showed the possibility of matching the structure with the external waveguides in the frequency range of 26.5-32.5 GHz with the voltage standing-wave ratio (VSWR) less than 1.8. The frequency dependence of attenuation is oscillatory with clearly expressed frequency ranges with small and large attenuation values. Moreover, the dependence is almost periodic, which is typical of periodic structures. The frequency response slope in the transition zones can be quite high and reach values of 41.26 dB/GHz. The degree of concentration of the electric field near the waveguide dielectric rod and the degree of excitation of the dielectric inhomogeneities was found by directly measured electric field strength in the near zone. Measurements of energy characteristics made under the short-circuit conditions for the main guide and in the mode of matched load of the main guide showed both the ability to control the polarization characteristics and the ability to change the appearance of the pattern and its orientation in space. Conclusions: It has been experimentally proven that a hybrid metal-dielectric structure, being a modified inverted dielectric waveguide with a periodic sequence on the dielectric plate of fifteen dielectric rods with metalized coating on one of the faces placed outwards, can be effectively integrated into a standard transmission line. It is found that this structure can be matched with the external circuits in a fairly wide frequency range. It is also found that in different frequency ranges this hybrid metal-dielectric structure shows the possibility of both efficient frequency selection and radiation in free space. Antenna measurements have shown the beam pattern shape controllability. Key words: inverted dielectric waveguide, periodic sequence, voltage standing-wave ratio (VSWR), attenuation, reflectometer method, mobile probe method, directivity pattern

Analysis and Design of Inhomogeneous Dielectric Lens Antennas by using Geometrical Optics

In this paper we present a novel approach for the analysis and design of inhomogeneous lenses. The standard method of Geometrical Optics for inhomogeneous media is augmented by introducing a novel wavefront-curvature transport equation, which allows the implementation of a full electromagnetic ray tracing (i.e., vector problem including polarization) in a real 1-D fashion, namely along the ray. This opens the possibility of easy parallelization and ultra-fast analysis of inhomogeneous lenses. The design of the lens is then accomplished by resorting to a novel direct synthesis method which, by inverting the analysis problem, directly provides the refractive index spatial distribution capable to drive the rays along prescribed paths which are defined to transform the impinging field on the input surface into the target aperture distribution on the output surface of the lens.

Методы подповерхностной СВЧ томографии, основанной на применении датчиков на отрезках двухпроводной линии.

In this paper, methods of near-field microwave tomography of the subsurface structure of dielectric inhomogeneities are proposed and studied based on the use of resonance probes with pieces of twin-wire lines as sensors. In frameworks of the quasi-static approximation, the integral equation of the inverse problem that relates measured variations of the complex capacity of the resonance system of probes placed above a medium with the inhomogeneous distribution of the complex permittivity. Based on this equation, methods and algorithms of tomography and holography have been proposed and worked out that used data of 2D scanning with variable offset between the sensor wires: (a) with the fixed direction of wires of sensor; (b) in two orthogonally related directions of sensor wires; (c) with the sensor of crossed twin-wire lines. Results of the numerical simulation demonstrate the efficiency of developed algorithms of subsurface tomography and holography.

Light Confinement by Local Index Tailoring in Inhomogeneous Dielectrics

AbstractThe engineering of light confinement is a topic with a long history in optics and with significant implications for the control of light‐matter interaction. In inhomogeneous and disordered media, however, multiple scattering prevents the application of conventional approaches for the design of light fields with desired properties. This is because any local change to such a medium typically affects these fields in a non‐local and complicated fashion. Here, we present a theoretical methodology for tailoring an inhomogeneous 1D Hermitian dielectric index distribution that allows us to control the intensity profile of an incoming light field purely locally, that is, with little or no influence on the field profile outside of a designated region of interest. Strongly increasing or decreasing the light's intensity at arbitrary positions inside the medium thereby becomes possible without, in fact, changing the external reflectance or transmittance. These local modifications of the medium can thus be made undetectable to far field measurements. We apply this approach to locally control the confinement of light inside 1D materials with inhomogeneous continuous refractive index profiles and extend it to multilayer films as well as to chains of coupled micro‐resonators.

Electrification of Dielectric Satellites under the Influence of Electron Flows of the Earth\u2019s Radiation Belts

The effect of electron fluxes from the Earth’s radiation belts on satellites made of dielectric materials is studied theoretically. Spherical shaped nanosatellites of the BLITS and BLITS-M types are considered as a model. An analytical solution is obtained for the dependence of the electric field on the distance to the center of the satellite. Empirical formulas are used for the electron flux density and the track length in matter depending on the electron energy. The energy losses of incident electrons in the Debye shielding layer that surrounds the satellite, as well as the appearance of radiation conductivity in the surface layer of the dielectric, are taken into account. The reasons for the nonmonotonic dependence of the electric field on the satellite radius are established. Despite the fact that the electric field inside the satellite is smaller than the electrical breakdown threshold of the solid dielectric, it can be assumed that the dielectric micro-breakdown can occur in the surface layer of the dielectric and near inhomogeneities.