Frequency Dependence Of Dielectric Permittivity Research Articles

New insights into understanding the defect structures and relationship of frequency dependences of dielectric permittivity and ac conductivity of CaCu3Ti4O12

In view of the inconclusive defect structure of CaCu3Ti4O12 (CCTO) ceramics, a defect model has been proposed in this investigation underlying the results of the previous works and updated knowledge in the literature papers concerning the band structure, charge transfer between Cu and Ti ions, and processing of CCTO. This model is capable of explaining why CCTO grain interior becomes semiconductive and grain and domain boundaries are insulating, and the grain-boundary resistance would dramatically drop due to the effect of sintering temperature/time and dopants. The ac conductivity of undoped and CaSiO3-doped CCTO associated with electrical charge carrier motion was investigated as a function of frequency at different temperatures. In order to identify the physical entity, the frequency dependence of ac conductivity at different temperatures is further characterized by the peak frequencies of the frequency dependence of the imaginary part of impedance (Z″) and electrical modulus (M″). The related physical entity has been specified by the activation energy and s value of power-law equation. It is suggested that each region cannot be specified by a unique physical entity; instead, it is a transition between relaxations of the related physical entity as the frequency increases. The electron hopping inside percolation clusters containing local polarized clusters of the related physical entity with the main contribution to the ac conductivity may determine the corresponding dielectric permittivity of each region.

Room temperature structural, dielectric, and conductivity properties of AlxCd1-xFe2O4 ferrites

The purpose of this study is to investigate dielectric and conduction mechanisms in accordance with composition at room temperature. In this study, AlxCd1-xFe2O4 ferrites with different stoichiometric rates (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) were prepared through co-precipitation method. The precipitated powder was sintered at 800 °C for 8 h to form the pure spinel ferrite nanoparticle. The formation of the cubic spinel phase has been demonstrated by X-ray diffraction analysis. The resulting powder was shown to be nanosized. Experiments were performed at room temperature in the frequency range of 20 Hz to 10 MHz. Frequency-dependent dielectric permittivity and dielectric loss for all examined samples exhibit the dielectric relaxation phenomenon explained by the Maxwell-Wagner polarization. Dielectric constant, AC conductivity, and dielectric loss decreased with increasing frequency. Dielectric constant, dielectric loss, and AC conductivity decreased along with increasing stoichiometric ratio x = 0 to 0.5. However, deviations in the intermediate values were observed, and the values of 0.2 were between 0 and 0.1 and the values of 0.3 were between 0.4 and 0.5. The impedance analysis explained the role of grains and grain boundaries within prepared samples. As a result, it was found that the relaxation process was compatible with the Cole-Cole model.

In Situ Measurement of Dielectric Permittivity and Electrical Conductivity of CoCl2/BaCl2 Doped PVDF Composite at Elevated Temperature

This work describes the synthesis and in situ characterization of polyvinylidene fluoride (PVDF) composite films doped with different weight percentage of CoCl2/BaCl2. The solution casting method was used for fabrication of composite films. XRD and SEM were used to analyse the surface morphology of PVDF composite films which confirms the formation of β and α phase predominately. The XRD spectra confirm the reduction in intensities of some peaks associated with α and β phase’s pre dominantly with the insertion of dopants. Dielectric permittivity and ac conductivity of the PVDF composites were measured at elevated temperature. The frequency dependence of dielectric permittivity and ac conductivity behaviour of PVDF composites with different weight percentage of Co/Ba fillers were investigated. The results reveal that the addition of Co/Ba to the host Polymer PVDF affects the dielectric permittivity and conductivity of PVDF composite. The results further reveals that the annealing influences the overall crystallization process and various phases of doped PVDF composite which in turn may affect the piezoelectric behaviour, which is prerequisite for sensing and actuator application of these PVDF composites. Thus the behaviour of sensors and devices based on doped PVDF composite can be predicted at elevated temperature. This study focused to understand the interaction between PVDF and Co/Ba dopants at elevated temperature.

On fractional modeling of viscoelastic foams

Empiric models have been introduced to describe frequency dependence of dielectric permittivity. Simple exponential models are often not satisfactory, while advanced non-exponential models (usually referred as “anomalous relaxation”) are commonly required to better explain experimental observations of complex systems. For viscoelastic materials, the so-called fractional derivatives models are powerful for both dynamic and loss moduli prediction. In this paper, the analysis of the main models used in the characterization of dielectric and viscoelastic materials such as five-parameter fractional Zener model and empiric Havriliak–Negami model are analysed. The fractional shape parameters describing the symmetric and asymmetric broadening of the complex modulus don't have the same influence in low and high frequencies. In contrast to the five-parameter Zener model, the empiric model asymmetry parameter has an influence on complex modulus at low frequencies comparing to the loss modulus peak frequency. A no resonance technique based on a forced vibrations procedure is used to investigate the frequency dependent complex shear modulus of a polyurethane foam, not influenced by its fluid phase, in the range 0.1–500 Hz. It is shown that the Havriliak–Negami model can predict the frequency dependence for a wide frequency range.

Optimization of physicochemical and dielectric features in the conductive copolymers of aniline and 2-aminophenol

The current exploration emphasizes improving the solubility and thermal characteristics of the homopolymers–polyaniline and poly-2-aminophenol via copolymerization technique with simultaneous optimization of conductivity and dielectric behavior. Poly (aniline-co-2-aminophenol) copolymers with varying monomers compositions have been synthesized using chemical oxidative copolymerization technique. The copolymers showed considerable improvement of solubility in organic solvent compared to the unsubstituted polyaniline. Morphology of these copolymers was characterized by powdered-XRD and FESEM measurements. The studies revealed improved crystallinity in the copolymers compared to poly-2-aminophenol homopolymer. All the copolymers possess porous network with different degrees of aggregated nanoparticles blended with nanoflake structures. The copolymers also exhibited appreciable thermal stability over the homopolymers inferred from DSC measurements. The variation of frequency-dependent conductivity and dielectric permittivity of these different copolymers were further investigated and correlated with grain size distribution and varying proportions of oligoaniline segments in the polymer backbone of poly-2-aminophenol.

On the Physical Meaning of Disperse Parameters of Frequency Dependence of Dielectric Permittivity in the Havriliak–Negami Model

This paper is devoted to an analysis of the frequency dispersion of dielectric permittivity in order to establish the physical meaning of the dispersion parameters α and β in the Havriliak–Negami model. It is found that parameter α is associated with the spectrum broadening of relaxation time τ. Examples with the appearance of a dispersion with parameter α of about 0.4 and 0.7 are presented. A conclusion is drawn that disorder creates a broadening of the relaxation times. Dispersion parameters α and β are introduced to preserve the unified relaxation time. The possibility of the analysis of experimental results on the basis of the Debye model in order to obtain the relaxation time distribution and determine parameters α and β according to the log(τHN/τ) chart is shown.

Role of ferrite phase on the structure, dielectric and magnetic properties of (1-x) KNNL/x NFO composites ceramics

In the present paper, we studied, ferroelectric/ferrite composite materials, with different ferrite compositions, prepared by solid state sintering method in one step. Lead-Free Sodium Potassium Lithium Niobate (KNNL) as ferroelectric and Nickel Ferrite (NFO) as ferrite material (1-x) KNNL-xNFO with different compositions was prepared. Structural analysis was carried out by X-ray diffraction spectra of the composite, which exhibits Bragg’s peaks corresponding to both perovskite and spinel phase. Raman scattering spectra demonstrates the characteristic phonon modes corresponding to mixed phase of perovskite and spinel phase. X-ray photoelectron spectroscopy (XPS) was carried out to investigate the chemical state of composites and Ni was found in mixed state. Frequency dependent dielectric permittivity and dielectric loss at different temperature exhibits the dielectric relaxation phenomenon explained by Maxwell-Wagner polarization, which is thermally activated polaron hopping for 3d- electrons and holes of mixed valanced Fe and Ni. The value of dielectric permittivity and loss increases with increasing temperature and NFO concentration. Room temperature magnetic hysteresis curve exhibits remnant magnetization (Mr) and coercive field value to increase with increasing ferrite composition, a typical nature of the soft magnetic materials.

Graphene may help to solve the Casimir conundrum in indium tin oxide systems

We reconsider the long-explored problem that the magnitude of the measured Casimir force between an Au sphere and an indium tin oxide (ITO) film decreases significantly with no respective changes in the ITO dielectric permittivity required by the Lifshitz theory. Two plausible resolutions of this conundrum are discussed: the phase transition of an ITO film from metallic to dielectric state and the modification of a film surface under the action of UV light. To exclude the latter option, we propose an improvement in the experimental scheme by adding a graphene sheet on top of an ITO film. The formalism is developed allowing precise calculation of the Casimir force between an Au sphere and a graphene sheet on top of ITO film deposited on a quartz substrate. In doing so Au, ITO, and quartz are described by the frequency-dependent dielectric permittivities and real graphene sheet with nonzero mass-gap parameter and chemical potential by the polarization tensor at nonzero temperature. Numerical computations performed both before and after the phase transition resulting from the UV treatment show that the presence of graphene leads to only a minor decrease in the drop of the Casimir force which remains quite measurable. At the same time, in the presence of graphene the guess that an observed drop originates from the modification of an ITO surface by the UV light breaks down. Similar results are obtained for the configuration of two parallel plates consisting of a graphene sheet, an ITO film and a quartz substrate. The proposed experiments involving additional graphene sheets may help in resolution of the problems arising in application of the Lifshitz theory to real materials.

Electrodynamics of ferroelectric films with negative capacitance

We construct a comprehensive theory of the electrodynamic response of ferroelectric ultra-thin films containing periodic domain textures (PDT) with 180{\deg} polarization-oriented domains. The focal point of the theory is the negative-capacitance phenomenon which naturally arises from the depolarization field induced by PDT. We derive frequency-dependent dielectric permittivity related to the PDT dynamics across the entire frequency range. We find the resonance mode of domain oscillations in the THz spectral band and the singular points in the phase of the reflected THz beam that are intimately related to the negative capacitance. Our findings provide a platform for the THz negative capacitance-based optics of ferroelectric films and for engineering the epsilon-near-zero plasmonic THz metamaterials.

Effect of space charge on dielectric and magneto-dielectric behaviors in Ba0.85Ca0.15Zr0.1Ti0.9O3/La0.67Sr0.33MnO3 heterostructure

The Ba0.85Ca0.15Zr0.1Ti0.9O3/La0.67Sr0.33MnO3 (BCZT/LSMO) heterostructures were deposited on LaAlO3 (111) substrates through radio-frequency magnetron sputtering technique. Dielectric behaviors as a function of frequency, temperature and magnetic field were investigated. The frequency dependence of dielectric permittivity exhibited apparent relaxation behavior. The corresponding activation energy estimated from Arrhenius plot was 2 meV. Abnormal point at 120 K was detected from the real part of dielectric permittivity vs temperature plot and magnetodielectricity (MD) vs temperature plot simultaneously, which refer to rhombohedral to orthorhombic phase transition in BCZT. A maximum of 20 percent was obtained in MD-temperature pattern, indicating obvious magneto-electric (ME) coupling. The dielectric permittivity relaxation phenomena as well as magneto-dielectric effect can be ascribed to the role of space charges, which arise at interface of BCZT and LSMO owing to lattice mismatch. The dependence of magneto-dielectric on temperature results from the variation of lattice mismatch degree induced by phase transition of BCZT.

Nonperturbative theory of atom-surface interaction: corrections at short separations

The nonperturbative expressions for the free energy and force of interaction between a ground-state atom and a real-material surface at any temperature are presented. The transition to the Matsubara representation is performed, whereupon the comparison is made with the commonly used perturbative results based on the standard Lifshitz theory. It is shown that the Lifshitz formulas for the free energy and force of an atom-surface interaction follow from the nonperturbative ones in the lowest order of the small parameter. Numerical computations of the free energy and force for the atoms of He and Na interacting with a surface of an Au plate have been performed using the frequency-dependent dielectric permittivity of Au and highly accurate dynamic atomic polarizabilities in the framework of both the nonperturbative and perturbative theories. According to our results, the maximum deviations between the two theories are reached at the shortest atom-surface separations of about 1 nm. Simple analytic expressions for the atom-surface free energy are derived in the classical limit and for an ideal-metal plane. In the lowest order of the small parameter, they are found in agreement with the perturbative ones following from the standard Lifshitz theory. Possible applications of the obtained results in the theory of van der Waals adsorption are discussed.

Effect of ethylene carbonate plasticizer on agar-agar: NH4Br-based solid polymer electrolytes

Proton-conducting polymer electrolytes based on biopolymer, agar-agar as the polymer host, ammonium bromide (NH4Br) as the salt and ethylene carbonate (EC) as the plasticizer have been prepared by solution casting technique with dimethylformamide as solvent. Addition of NH4Br and EC with the biopolymer resulted in an increase in the ionic conductivity of polymer electrolyte. EC was added to increase the degree of salt dissociation and also ionic mobility. The highest ionic conductivity achieved at room temperature was for 50 wt% agar/50 wt% NH4Br/0.3% EC with the conductivity 3.73 × 10−4 S cm−1. The conductivity of the polymer electrolyte increases with the increase in amount of plasticizer. The frequency-dependent conductivity, dielectric permittivity (e′) and modulus (M′) studies were carried out.

Issues and hints about UV-optical measurements of (Ba1-xSrx)TiO3 nano-powder synthesized by sol-gel method

The lead free perovskite ferroelectric nano-powder (Ba1-xSrx)TiO3 (x = 0.0, 0.025, 0.05, 0.075 and 0.1) have been synthesized by using Sol-gel method. The main issue of measurement the UV-optical properties of the ceramics can be shortened into the solubility of the powder inside a suitable solution. The present study reports an overview for how to solve this problem and the technique has been illustrated in-details in the experimental section. The crystalline and the microstructure of the investigated samples were observed employing X-ray diffraction (XRD) and scanning electron microscope (SEM) equipped with an energy-dispersive X-ray (EDAX) analyzer respectively. The thermal analysis of the pure calcined powder was performed by using differential thermal analysis (DTA). The single phase powder and ceramics were detected by using XRD, where the phase obtained by calcined and sintered the samples at 1000 and 1200 °C for 3 h respectively. The patterns were observed matched with BaTiO3 perovskite tetragonal structure with absence of any detectable for the secondary phases. The particle size of the ceramics was observed decreased with increasing the concentration of Sr ions owing to the different ionic radius between Ba2+ (1.36 Å) and Sr2+ (1.19 Å). The characterization of the electrical properties for the sintered pellets within the temperature range (30–270 °C) were performed by dielectric spectroscopy method. The temperature and frequency dependences of dielectric permittivity (ԑr) and diffused phase transition (DPT) showed the changes in the character of the ferroelectric-paraelectric (FE–PE) phase transition.

Extended Jaya's Algorithm for Optimal Design of Broadband Layered Microwave Absorbing Structures

Layered microwave absorbing structures (MASs) for the suppression of electromagnetic signals are important due to their broadband frequency response. However, optimization of such structures is difficult because several design variables are involved. A method for the efficient design of broadband, layered, magneto-dielectric MASs is based on analytical modeling of the frequency-dependent complex dielectric permittivity ( ${\mathbf \varepsilon_{r}}$ ) and magnetic permeability ( ${\mu} _{r}$ ). The use of an efficient, extended Jaya's algorithm for optimization results in highly feasible values of ${\mathbf \varepsilon_{r}}$ and ${\mu} _{r}$ based on optimal Debye parameters for a specific reflection loss (RL) and a −10 dB absorption bandwidth. The optimization is carried out in the X-band for both single- and dual-layer MASs. Deeper insight is obtained by optimizing RL with and without constraints on absorber layer coating thickness. The results show the effectiveness of the optimization for the design of MASs for practical applications.

Dielectric spectroscopy analysis using viscoelasticity-inspired relaxation theory with finite element modeling

We demonstrate the formulation of frequency-dependent dielectric permittivity by superposition of Debye functions inspired by viscoelastic relaxation theory. With multiple relaxation times and permittivity strength, a viscoelastic Prony Series is adapted to construct an expression of dielectric permittivity for polymer dielectric materials, which can be successfully matched with experimental data. We then develop a finite element modeling approach with explicit microstructure dispersion and inclusion of filler-matrix interphase using functionalized silica-epoxy nanocomposite samples as a testbed. The interphase relaxation behavior is expressed using the bulk polymer properties modified by frequency and magnitude shift factors that adjust the shape of the simulated dielectric spectrum to mimic changes in relaxation time due to the polymer/filler interaction. Finally, the influence of interphase thickness and dispersion state is investigated with parametric studies. It is found that total interphase area in the composite has a critical influence over the composite property, and by varying interphase layer and dispersion within a reasonable range, as much as 20% difference can be obtained in the simulated composite property. Our simulation results provide insights into the underlying relaxation mechanism in the interfacial region.

Structural and dielectric properties of the fluorite-type LaxCe1−xO2−δ ceramics

High density (95–97%) Lax () ceramics were tested for structural and dielectric properties. Dense microstructure and controlled phase-purity were obtained for all the -doped samples. A surprising three-fold increase was noticed in the frequency dependent dielectric permittivity behavior for the ceramic, associated with the space-charge polarization at grain boundaries or inhomogeneous microstructure of the ceramic. High resistivity (∼108 Ωm) at room temperature was noticed for the ceramics (at 100 Hz). Hopping of electrons within the oxygen vacancies were noted as the main transport mechanism; strong localization of charge carriers were noticed at high frequencies. The temperature dependent ac-resistivity analysis (T) provides strong evidence for Mott’s variable range hopping process of charge carriers, between the localized states with an average hopping length of RH of 3 nm and hopping energy of WH of 0.67 eV. Moreover, the effect of grains and grain boundaries on the correlation between ac-conductivity and angular-frequency ω has been discussed in detail.

Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements

Dimensional analysis was performed to understand the physics of ionic dispersion in reservoir rocks and to identify the factors influencing the cation exchange capacity (CEC) of these rocks. Dimensional analysis revealed the existence of a general relation independent of the unit system between two dimensionless groups denoted as the cationic dispersion number [Formula: see text] and the conductivity number [Formula: see text]. The former group [Formula: see text] stands for the ratio of the CEC to the electrical double-layer dispersion. The latter group [Formula: see text] represents the ratio of the low-frequency ionic conductivity to the high-frequency electronic polarization. Complex dielectric permittivity measurements on 121 water-saturated sandstone and carbonate rock samples were used to validate the dimensionless groups. In retrospect, dimensional analysis was useful in identifying variables influencing the CEC of hydrocarbon rocks. In particular, these variables consist of rock porosity [Formula: see text], specific surface area, and five other parameters of the Cole-Cole function, which describes the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz. The Cole-Cole function parameters are [Formula: see text], which is a characteristic relaxation time; [Formula: see text] is the so-called spread parameter; [Formula: see text] is the real DC conductivity of water-saturated rocks; and [Formula: see text] and [Formula: see text], which are the real numbers representing the static and the high-frequency dielectric permittivities of the water-saturated rock, respectively. A general regression neural network (GRNN) model was developed to predict the CEC of shaly sandstones and carbonate rocks as a function of the variables identified by the dimensional analysis as essential in predicting the CEC. The CEC prediction capability of the GRNN model has been tested with a blind data set, and it has been compared with the CEC prediction capability using a nonlinear regression model developed in this study and using a linear regression model available in the literature. The GRNN model outperformed both of these empirical models. With the GRNN model, it is possible to obtain reliable quantitative estimates of the CEC of shaly sandstone and carbonate rocks using nondestructive frequency-dependent dielectric permittivity measurements that are rapid, economic, and accurate. In return, accurate and fast estimates of the CEC are useful in many petroleum engineering applications. They can be used to identify clay types and can also be used to quantify the volume of hydrocarbon in shaly sands using well-log resistivity data. The results of this study represent a major advantage for formation evaluation, wellbore stability analysis, and designing stimulation jobs.

Improved Dielectric Properties of Polyvinylidene Fluoride Nanocomposite Embedded with Poly(vinylpyrrolidone)-Coated Gold Nanoparticles.

A novel nanocomposite dielectric was developed by embedding polyvinylpyrrolidone (PVP)-encapsulated gold (Au) nanoparticles in the polyvinylidene fluoride (PVDF) polymer matrix. The surface functionalization of Au nanoparticles with PVP facilitates favorable interaction between the particle and polymer phase, enhancing nanoparticle dispersion. To study the effect of entropic interactions on particle dispersion, nanocomposites with two different particle sizes (5 and 20 nm in diameter) were synthesized and characterized. A uniform particle distribution was observed for nanocomposite films consisting of 5 nm Au particles, in contrast to the film with 20 nm particles. The frequency-dependent dielectric permittivity and the loss tangent were studied for the nanocomposite films. These results showed the effectiveness of PVP ligand in controlling the agglomeration of Au particles in the PVDF matrix. Moreover, the study showed the effect of particle concentration on their spatial distribution in the polymer matrix and the dielectric properties of nanocomposite films.

Experimental investigation of the dielectric properties of soil under hydraulic loading

An experimental set-up was developed in order to determine the coupled hydraulic, dielectric and mechanical properties of granular media under hydraulic loading. The set-up consisted of a modified column for permeability tests involving a flow meter and pressure transducers along the sample to quantify the hydraulic gradient. A newly developed open-ended coaxial probe allowed the measurement of the frequency dependent dielectric permittivity of the material under test. The shear strength of the sample within the column was measured using a conventional vane shear device. In this paper, the overall set-up is introduced with focus on the open-ended coaxial probe. The design and calibration of the probe are introduced in detail. A numerical study showed that the sensitive cylindrical volume of the probe was approximately 150 mm in diameter with a depth of 65 mm. An investigation with glass beads showed that the set-up allowed the parameterization of the hydraulic, mechanic and dielectric parameters of granular materials under the influence of vertical flow. A satisfactorily good correlation between porosity and the real part of the dielectric permittivity was detected. The critical hydraulic gradient defining the transition of a fixed bed of particles to fluidization was characterized by a sharp peak in the evolution of the hydraulic conductivity and could easily be determined from the measurements. The shear strength of the material under test reduces linearly with increasing hydraulic gradient. Future investigations will be carried out to provide the required parameterizations for experimental and numerical investigations of the internal erosion of granular media.

Orientational Mobility in Dendrimer Melts: Molecular Dynamics Simulations

We have simulated the melt of poly(carbosilane) dendrimers using atomistic models and have reproduced the effect predicted by the analytical theory; i.e., orientational autocorrelation functions of a segment from the same layer (numbered from periphery) are practically identical and do not depend on dendrimer size. The frequency dependences of the dielectric and NMR relaxation were obtained and studied in detail. The main contribution to the maxima of these dependences is given by the pulsation process. It leads to a shift of the maxima to low frequencies for the core segment in comparison with the maxima for peripheral segments. The contribution of local reorientation can also be significant, and in some cases this contribution manifests as an additional maximum. The nontrivial scaling laws in the frequency dependences of dielectric permittivity and NMR relaxation rate averaged over all layers of a dendrimer macromolecule are found. A similar scaling law is observed in the experiments on NMR relaxation b...