Heterogeneous Dielectric Media Research Articles

Capacitance for fractal-like disordered dielectric slab

In this paper, we model a heterogeneous dielectric medium exhibiting fractal geometry or disordered random structures by applying non-integer dimensions to determine its capacitance between two parallel plates. The capacitance depends on the fractional dimensions of the fractal or disordered dielectric slab, which may be obtained from the theoretical fractal dimension or box-counting method. The findings are verified by CST Studio Suite (Electromagnetic field simulation software), experimental measurements, and the equivalent capacitance method. Five common types of fractals (Cantor bars/plates, Sierpinski carpet, Sierpinski triangle, Haferman carpet, and Menger sponge) and random structures are tested with good agreement. There is also an effective gain of capacitance in using less amount of dielectric materials, which may be useful in material-savings of dielectrics. This research shows a useful tool in modeling the capacitance of heterogeneous materials, where fractals and disordered structures may be commonly encountered in organic materials and any dielectrics where precision and fabrication are not perfect.

Impedance spectroscopy and magnetic studies on Co2Z ferrite sintered with SiO2 and Bi2O3 additives

Z-type (Ba3Co2Fe24O41) ferrites with Bi2O3 and SiO2 additives were prepared by solid-state reaction method. The electrical transport properties were systematically investigated and analyzed by impedance spectroscopy in the frequency range of 1 Hz to 1 MHz at different temperatures. The peak broadening in real and imaginary part of impedance spectra demonstrates the existence of multiple relaxations. Two distinct slopes of relaxation time observed represent the deviation from non-Debye type relaxation. Partially overlapped scaling behavior illustrated that the dynamic process of charge carriers was temperature dependent. The additives got segregated along the grain boundaries and exhibit their own resistance, which is verified by fitting of the Nyquist plots. This relaxation process was explained on the basis of Maxwell-Wagner effect with three heterogeneous dielectric media (grain, grain boundary and additive layer). The translatory motion of dynamic charge carriers and lattice ions is governed by small and large polaron hopping in the material. The saturation magnetization of Co2Z-Si is higher compared to Co2Z-P and Co2Z-Bi samples, due to formation of minor M-type phase.

A fast ADI algorithm for nonlinear Poisson equation in heterogeneous dielectric media

Recently, a nonlinear Poisson equation has been introduced to model nonlinear and nonlocal hyperpolarization effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated with the heterogeneous dielectric media, this Poisson model is difficult to solve numerically, particularly for large protein systems. A new pseudo-transient continuation approach is proposed in this paper to efficiently and stably solve the nonlinear Poisson equation. A Douglas type alternating direction implicit (ADI) method is developed for solving the pseudo-time dependent Poisson equation. Different approximations to the dielectric profile in heterogeneous media are considered in the standard finite difference discretization. The proposed ADI scheme is validated by considering benchmark examples with exact solutions and by solvation analysis of real biomolecules with various sizes. Numerical results are in good agreement with the theoretical prediction, experimental measurements, and those obtained from the boundary value problem approach. Since the time stability of the proposed ADI scheme can be maintained even using very large time increments, it is efficient for electrostatic analysis involving hyperpolarization effects.

A fast ADI algorithm for nonlinear Poisson equation in heterogeneous dielectric media

A nonlinear Poisson equation (NPE) has been introduced to model nonlinear and nonlocal hyperpolarisation effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due...

Achieving improved electromagnetic interference shielding performance and balanced mechanical properties in polyketone nanocomposites via a composite MWCNTs carrier

A simple and scalable melt compounding strategy is reported to prepare polyketone (POK) nanocomposites with high electrical, dielectric, EMI SE and excellent mechanical properties using poly(vinylidene fluoride) (PVDF) as a carrier of MWCNTs based on the selective distribution and migration of MWCNTs in POK/PVDF blend. The electrical percolation threshold of the POK/PVDF/MWCNT nanocomposites is only a half of that of POK/MWCNT composites due to the homogeneous dispersion of MWCNTs and the double percolation network. The enhanced dielectric performance originates from the interfacial polarization and numerous microcapacitors comprised of MWCNTs within the polymer. The EMI SE performance of the nanocomposites is significantly enhanced due to the selective localization of MWCNTs in the POK phase which provides high conductivity and heterogeneous dielectric media with multiple interfaces. Thus, this study provides possibilities to realize a high-performance polymer nanocomposites and a wider EMI shielding application potentials for POK materials via a composite MWCNTs carrier.

A GPU-based multi-level algorithm for boundary value problems

A novel geometric single-grid multi-level (GSGML) algorithm is presented for the numerical solution of boundary value problems (BVPs). The algorithm is specifically designed for parallel scalability with high occupancy of streaming processors inside many-core architectures like the Graphics Processing Unit (GPU). The algorithm consists of iterative, superposed operations on a single grid, and is composed of two full-grid routines: a restriction and a coarsened interpolation–relaxation. The restriction is a local average of scalar or vector fields, and the interpolation–relaxation is a simultaneous application of coarsened finite-difference operators and interpolations in complementary subsets of the grid. The routines are scheduled in a saw-like refining cycle. Convergence to machine precision is achieved repeating the full cycle using residuals and superposition. The algorithm is attractive for its computational simplicity and provides a competitive GPU-based fast solver for elliptic partial differential equations like the Poisson–Helmholtz equation. Applications shown in this work include the deformation of two-dimensional grids, the computation of three-dimensional streamlines for a singular trifoil-knot vortex and the calculation of three-dimensional electric potentials in heterogeneous dielectric media.

Excellent electromagnetic shield derived from MWCNT reinforced NR/PP blend nanocomposites with tailored microstructural properties

Blends of polypropylene (PP) and natural rubber (NR) with different loadings (1,3,5 &7 wt%) of multiwalled carbon nanotubes (MWCNTs) were prepared by melt blending process to design a nanocomposite with tunable electromagnetic interference (EMI) shielding performance. Scanning electron microscopy (SEM) studies show that the addition of MWCNTs changes the droplet morphology into quasi co-continuous morphology for PP/NR 80/20 (wt/wt) blend system. However there is a refinement in the co-continuous morphology of PP/NR (50/50) by the addition of MWCNTs. The effects of the blend morphology and selective localization of MWCNTs on the dielectric, electrical properties and EMI shielding performance were systematically investigated. The largely enriched dielectric performance originates from the interfacial polarization of MWCNTs within the polymer. It is understood that the shielding performance significantly enhanced due to the selective localization of MWCNTs in the NR phase that provided high conductivity and heterogeneous dielectric media with multiple interfaces. The blend nanocomposites show a shielding effectiveness of ca.29 dB at 3 GHz for 7 wt% of MWCNT loading.

Solvation and Entropic Regimes in Ion-Containing Block Copolymers

The phase behavior of ion-containing block copolymers is studied using a field-theoretic model consisting of fully mobile ions immersed in a heterogeneous dielectric medium. Two distinct thermodynamic regimes are found to emerge, resulting from the competition between ion translational entropy and solvation free energy. In the regime dominated by entropy, the disordered phase is stabilized by the addition of ions. In the regime dominated by solvation free energy, the disordered phase is destabilized, leading to a “chimney”-like channel of stable ordered phases at sufficiently large ion concentrations. The two regimes are demarcated by the parameter λB, which quantifies the variation in solvation energy upon transferring ions between different dielectric domains. Estimates of λB for experimental systems suggest that the majority of block copolymer electrolytes fall within the solvation regime.

Maxwell–Wagner polarization in grain boundary segregated NiCuZn ferrite

The present work investigates the polarization response in polycrystalline Ni0.9−yCuyZn0.1Fe1.98O4−δ (y = 0, 0.1, 0.2, 0.3, 0.4, 0.5) ferrite synthesized by solid–state reaction method. X-ray diffraction analysis confirmed cubic spinel phase formation in the calcined samples. Sintered samples contain a continuous network of CuO-rich segregation along the grain boundaries for y ≥ 0.2. Dielectric spectra showed a relaxation peak for y ≥ 0.2 in the frequency range of 1 kHz–1 MHz. This relaxation has been explained based on Maxwell–Wagner polarization considering two-layer model in connection with two heterogeneous dielectric media.

Simulation of Charged Systems in Heterogeneous Dielectric Media via a True Energy Functional

For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local polarization charge density as a dynamic variable, but such approaches require access to a true free energy functional, one that evaluates to the equilibrium electrostatic energy at its minimum. In this Letter, we derive the needed functional. As an application, we develop a Car-Parrinello MD method for the simulation of free charges present near a spherical emulsion droplet separating two immiscible liquids with different dielectric constants. Our results show the presence of nonmonotonic ionic profiles in the dielectric with a lower dielectric constant.

Flexible microfluidic normal force sensor skin for tactile feedback

Robotic applications often require robust tactile sensing capabilities on curved surfaces, such as artificial fingertips. Flexible tactile sensors could be conformally wrapped around curved digits and could enhance grip by cushioning impacts and increasing the effective contact area during grasp. Flexible microfabricated devices that use thin film or solid electrical components are susceptible to failure due to cracking and fatigue. Conductive fluids have been used as transduction media, electrical connections, and in resistance-based pressure and bend sensors. In this work, a flexible and multilayer capacitive microfluidic normal force sensor is developed with a 5×5 taxel array. The sensor uses liquid metal-filled microfluidic channels as the capacitive plates and conductive interconnects. The sensor is microfabricated using soft lithography microfabrication techniques and consists of multiple layers of PDMS microchannels filled with the liquid metal alloy Galinstan and air pockets that modify the mechanical and electrical properties of the sensor. A single taxel is calibrated for normal forces ranging from 0 to 2.5N, is shown to provide repeatable measurements of static uniaxial loads, and follows the loading and unloading phases of low-frequency dynamic loads (0.4–4Hz). The sensor prototype has a spatial resolution on the order of 0.5mm, performs reliably when wrapped around a surface having a curvature similar to that of a human finger (1.575cm−1), and has been shown to tolerate curvatures as high as 6.289cm−1. The deformable liquid capacitive plates and heterogeneous PDMS-air dielectric medium can be designed to tune the sensor's sensitivity and range. The sensor prototype provides greater sensitivity at low loads, a feature which can be exploited for robotic applications in which light touch is important.

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

This paper concerns a basic electrostatic problem: how to calculate generalized Coulomb and self-polarization potentials in heterogeneous dielectric media. In particular, with simulations of ellipsoidal semiconductor quantum dots and elongated biomacromolecules being its target applications, this paper extends the so-called three-layer dielectric models for generalized Coulomb and self-polarization potential calculation from the spherical and the spheroidal geometries to the triaxial ellipsoidal geometry. Compared to the simple steplike dielectric model, these three-layer dielectric models can overcome the mathematical divergence in the self-polarization energy by employing continuous radial dielectric functions. More specifically, in this paper, the quasiharmonic three-layer dielectric model for the ellipsoidal geometry is discussed, and the explicit analytical series solutions of the corresponding electrostatic problem are obtained in terms of the ellipsoidal harmonics. Then a robust numerical procedure working for general three-layer dielectric models is developed. The key component of the numerical method is to subdivide the transition layer of the underlying three-layer model into multiple sublayers and then in each one of them approximate the select dielectric function of the transition layer by one of the quasiharmonic functional form rather than simply by a constant value as one would normally do. As a result, the numerical method has no numerical divergence.

Bloch-wave homogenization for spectral asymptotic analysis of the periodic Maxwell operator

This paper is devoted to the asymptotic behavior of the spectrum of the three-dimensional Maxwell operator in a bounded periodic heterogeneous dielectric medium T = [−T,T]3, T > 0, as the structure period η, such that η−1 T is a positive integer, tends to 0. The domain T is extended periodically to the whole of ℝ 3, so that the original operator is understood as acting in a space of T-periodic functions. We use the so-called Bloch-wave homogenization technique which, unlike the classical homogenization method, is capable of characterizing a renormalized limit of the spectrum (called the Bloch spectrum) [6]. The related procedure is concerned with sequences of eigenvalues Λη of the resolvent of the order of the square of the medium period, which correspond to the oscillations of high-frequencies of order η−1. The Bloch-wave description is obtained via the notion of two-scale convergence for bounded self-adjoint operators, and a proof of the ‘completeness’ of the limiting spectrum is provided. The results obtained theoretically are illustrated by finite element computations.

Dielectric Spectroscopy of Metal Nanoparticle Doped Liquid Crystal Displays Exhibiting Frequency Modulation Response

Twisted nematic liquid crystal displays (TN-LCDs), doped with the nanoparticles of metal, such as Pd, Ag, or Ag-Pd, which are protected with ligand molecules, such as nematic liquid crystal, exhibit a frequency modulation (FM) electro-optical (EO) response with short response time of milliseconds (ms) or sub-ms order together with the ordinary rms voltage response. These devices are called FM/AM-TN-LCDs; they are distinct from the ordinary LCDs featured by the amplitude modulation (AM) response. The phenomena of the FM/AM LCDs may be attributed to the dielectric dispersion of a heterogeneous dielectric medium known as the Maxwell-Wagner effect. It is experimentally shown that the frequency range spreads from several tens hertz to several tens kilohertz and the spectrum is more or less centered about the dielectric relaxation frequency. We formulated a theory based on an equivalent circuit model to evaluate the dielectric relaxation frequency and the dielectric strengths; and we succeeded in explaining the dependence of the dielectric relaxation frequency on the concentration of nanoparticles and the their dielectric and electrical properties, whereas conventional theories based on electromagnetic theory are unable to explain this concentration dependence. This paper reports on the experimental results of the EO effects and the dielectric spectroscopy including the dielectric relaxation times and the dielectric strengths of nematic liquid crystal, 5CB (4-pentyl-4'-cyanobiphenyl), doped with the metal nanoparticles of I'd alone and Ag-Pd composite; and discusses how the observed dielectric relaxation frequency or dielectric relaxation time depend on the concentration of the doped nanoparticles and also their electrical and dielectric properties

Dielectric Properties of Frequency Modulation Twisted Nematic LCDs Doped with Silver Nanoparticles

Twisted nematic liquid crystal display (TN-LCD) devices, composed of nematic liquid crystal (NLC), doped with silver (Ag) nanoparticles, which are protected with the same NLC molecules of 5CB (Merck, K-15), show electrooptic characteristics that are featured by a frequency modulation and fast response. This device is called FM-TN-LCD. In this paper, we report that the frequency range in the FM-TN-LCD spreading from 40 Hz to an upper limit 2 kHz correlates with that of the dielectric dispersion of the sample cell, which is expressed analytically by the Maxwell–Wagner theory on the heterogeneous dielectric medium, where the dielectric relaxation frequency, and thus the dielectric relaxation time, are primarily governed by the electrical conductivity of the doped Ag nanoparticles.

Dielectric Properties of Frequency Modulation Twisted Nematic LCDs Doped with Palladium (Pd) Nanoparticles

Twisted nematic liquid crystal display (TN-LCD) devices, composed of nematic liquid crystal (NLC), doped with palladium (Pd) nanoparticles, which are protected with the same NLC molecules of 5CB (Merck, K-15), show electrooptic characteristics that are featured by a frequency modulation and fast response. This device is called FM-TN-LCD. In this paper, we report that the frequency range in the FM-TN-LCD spreading from tens Hz to an upper limit 1 kHz, depending on the concentration of nanoparticles, correlates with that of the dielectric dispersion of the sample cell, which is expressed analytically by the Maxwell–Wagner theory on the heterogeneous dielectric medium, where the dielectric relaxation frequency, and thus the dielectric relaxation time, are primarily governed by the electrical conductivity of the doped nanoparticles of Pd and their concentrations.

Solvent influence on conformational equilibrium in 3-nitrobenzaldehyde

Semi-empirical (PM3, AM1) and ab initio (B3LYP/6-31G(d,p)) calculations of the structure and energies of isolated 3-nitrobenzaldehyde (3-NBA) reveal that the planar trans and cis isomers are in equilibrium, with the trans being more stable by about 2.2 kJ/mol. The experimental dipole moments of 3-NBA in solvents of dielectric permittivity ε ranging from 1.9 to 25 have been determined. The increase in the mean dipole moment with increasing ε can be well explained in terms of the trans⇔ cis equilibrium and dipolar isomer–solvent interaction. The heterogeneous dielectric medium model with two concentric dielectric layers proved to be the best description for this interaction. On the other hand, the intrinsic experimental Gibbs energy for the trans⇔ cis conversion obtained from this model was higher than the quantum-chemical values. It is suggested that the quadrupolar interaction acts oppositely to the dipolar one stabilizing the more quadrupolar trans isomer.

Solvent Effect on the Gibbs Energy of Proton Transfer in the 2,6-Dichlorophenol-Triethylamine Complex

Using dipole moment measurements, the Gibbs energy ΔGPT of proton transfer in the complex of 2,6-dichlorophenol with triethylamine was determined in different solvents. The effect of solvent on ΔGPT was quantitatively discussed in terms of reaction field models for homogeneous and heterogeneous dielectric media. The specific complex–solvent interactions which, in addition to electrostatic interaction, stabilize the PT polar form of the complex is discussed as a function of the empirical parameters describing the polar and hydrogen-donating (electron-accepting) properties of the solvent.

A Dynamic Lattice Monte Carlo Model of Ion Transport in Inhomogeneous Dielectric Environments: Method and Implementation

A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielectric environments is presented. Conventional approaches using periodic boundary conditions are inefficient for nonequilibrium situations in inhomogeneous systems. Instead, the simulated system is embedded in a bigger system that determines the average electrostatic potential and the ionic concentrations at its boundaries. Two issues are of special importance: implementing the given boundary conditions in the treatment of dynamical processes at and near the boundaries, and efficient evaluation of ion−ion interaction in the heterogeneous dielectric medium during the Monte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solutions for simple geometries, and to mean field (Poisson−Nernst−Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory fails in various degrees are shown and discus...

Solvent effect on the conformational equilibrium in 3,3′-dinitrobiphenyl

Dipole moments of nitrobenzene and 3,3′-dinitrobiphenyl in nine solvents have been determined within the dielectric permittivity range 2–10. The free energy Δ G (s) conf for the conformational transoid⇋ cisoid transformation in 3,3′-dinitrobiphenyl has been determined. The observed influence of ϵ on Δ G (s) conf is quantitatively analyzed using the reaction field models of Onsager and Block-Walker for homogeneous and heterogeneous dielectric media.