Representation Of Permittivity Research Articles

Dielectric Study of Tetraalkylammonium and Tetraalkylphosphonium Levulinate Ionic Liquids.

Broadband dielectric spectroscopy in a broad temperature range was employed to study ionic conductivity and dynamics in tetraalkylammonium- and tetraalkylphosphonium-based ionic liquids (ILs) having levulinate as a common anion. Combining data for ionic conductivity with data obtained for viscosity in a Walden plot, we show that ionic conductivity is controlled by viscosity while a strong association of ions takes place. Higher values for ionic conductivities in a broad temperature range were found for the tetraalkylphosphonium-based IL compared to its ammonium homolog in accordance with its lower viscosity. Levulinate used in the present study as anion was found to interact and associate stronger with the cations forming ion-pairs or other complexes compared to the NTf2 anion studied in literature. In order to analyze dielectric data, different fitting approaches were employed. The original random barrier model cannot well describe the conductivity especially at the higher frequencies region. In electric modulus representation, two overlapping mechanisms contribute to the broad low frequencies peak. The slower process is related to the conduction mechanism and the faster to the main polarization process of the complex dielectric permittivity representation. The correlation of the characteristic time scales of the previous relaxation processes was discussed in terms of ionic interactions.

An Approximation of 2-D Inverse Scattering Problems From a Convex Optimization Perspective

We present a two-step strategy to solve an inverse scattering problem in 2-D geometry. The first step approximates the inverse scattering as a convex optimization problem and provides an estimation of the total field inside the domain under investigation without <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge or tuning parameters. In the second step, the previously estimated total field is used to reconstruct the unknown contrast permittivity, which is represented by a superposition of level-1 Haar wavelet transform basis functions. Subject to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\ell _{1}}$ </tex-math></inline-formula> -norm constraints of the wavelet coefficients, a least absolute shrinkage and selection operator (LASSO) problem that searches for the global minimum of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\ell _{2}}$ </tex-math></inline-formula> -norm residual is exploited by accounting for the sparsity of the wavelet-based permittivity representation. Numerical results are presented to assess the effectiveness of the proposed formulation against objects with relatively small electric size. Finally, the approach is validated against experimental data.

Comparative analysis of dielectric, shear mechanical and light scattering response functions in polar supercooled liquids

The studies of molecular dynamics in the vicinity of liquid–glass transition are an essential part of condensed matter physics. Various experimental techniques are usually applied to understand different aspects of molecular motions, i.e., nuclear magnetic resonance (NMR), photon correlation spectroscopy (PCS), mechanical shear relaxation (MR), and dielectric spectroscopy (DS). Universal behavior of molecular dynamics, reflected in the invariant distribution of relaxation times for different polar and weekly polar glass-formers, has been recently found when probed by NMR, PCS, and MR techniques. On the other hand, the narrow dielectric permittivity function ε*(f) of polar materials has been rationalized by postulating that it is a superposition of a Debye-like peak and a broader structural relaxation found in NMR, PCS, and MR. Herein, we show that dielectric permittivity representation ε*(f) reveals details of molecular motions being undetectable in the other experimental methods. Herein we propose a way to resolve this problem. First, we point out an unresolved Johari–Goldstein (JG) β-relaxation is present nearby the α-relaxation in these polar glass-formers. The dielectric relaxation strength of the JG β-relaxation is sufficiently weak compared to the α-relaxation so that the narrow dielectric frequency dispersion faithfully represents the dynamic heterogeneity and cooperativity of the α-relaxation. However, when the other techniques are used to probe the same polar glass-former, there is reduction of relaxation strength of α-relaxation relative to that of the JG β relaxation as well as their separation. Consequently the α relaxation appears broader in frequency dispersion when observed by PCS, NMR and MR instead of DS. The explanation is supported by showing that the quasi-universal broadened α relaxation in PCS, NMR and MR is captured by the electric modulus M*(f) = 1/ε*(f) representation of the dielectric measurements of polar and weakly polar glass-formers, and also M*(f) compares favorably with the mechanical shear modulus data G*(f).

Granular Permittivity Representation in Extremely Near-Field Light–Matter Interaction Processes

Light-matter interaction processes are significantly affected by surrounding electromagnetic environment. Dielectric materials are usually introduced into an interaction picture via their classical properties, e.g. permittivity, appearing in constitutive relations. While this approach was proven to be applicable in many occasions, it might face limitations when an emitter is situated very close to a material boundary. In this case nonlocal extend of a quantum wave function of an emitter becomes comparable with a distance to a boundary and a lattice constant of a material. Here a semi-classical model, taking into account material's granularity, is developed. In particular, spontaneous emission process in the vicinity of flat boundaries is considered. The material boundary is divided into a pair areas - far zone is modeled as a continuous phase, while the near zone next to a nonlocal emitter is represented with a discrete array of polarizable particles. This array resembles optical properties of the continuous phase under the standard homogenization procedure. Local field effects were shown to lead orders of magnitude corrections to spontaneous emission rates in the case of sub-nanometer emitter-surface separation distances. The developed mesoscopic model enables addressing few aspects of local field corrections in quite complex scenarios, where quantum ab initio techniques yet face challenges owing to involved computational complexity. The developed method could be utilized for designs of quantum sources and networks, enhanced with structured electromagnetic environment.

Variable-Temperature Measurements of the Dielectric Relaxation Spectroscopy in 0.1 SiO2-0.2 Cao-0.2 Na2O-0.5 P2O5 Bioactive Glass Materials

Bioactive glasses with chemical composition 0.1 SiO2-0.2 CaO-0.2 Na2O-0.5 P2O5 have been prepared. The dielectric properties of the samples were measured in the frequency range from 100 Hz to 1 MHz and temperatures range from 100 to 370 K (Tg ≈ 400 K). The obtained data were analysed by the means of dielectric permittivity representation and modelled using the Havriliak–Negami equation. Various relaxation parameters were calculated with accuracy. Furthermore, investigation of the temperature dependence of their relaxation time using the Vogel– Tammam–Fulcher (VTF) model shows the weak interaction between alkali ions constituents and molecular networkformers for temperatures up to the glass transition.

Geometrical Description in Binary Composites and Spectral Density Representation

In this review, the dielectric permittivity of dielectric mixtures is discussed in view of the spectral density representation method. A distinct representation is derived for predicting the dielectric properties, permittivities ε, of mixtures. The presentation of the dielectric properties is based on a scaled permittivity approach, , where the subscripts e, m and i denote the dielectric permittivities of the effective, matrix and inclusion media, respectively [Tuncer, E. J. Phys.: Condens. Matter 2005, 17, L125]. This novel representation transforms the spectral density formalism to a form similar to the distribution of relaxation times method of dielectric relaxation. Consequently, I propose that any dielectric relaxation formula, i.e., the Havriliak-Negami empirical dielectric relaxation expression, can be adopted as a scaled permittivity. The presented scaled permittivity representation has potential to be improved and implemented into the existing data analyzing routines for dielectric relaxation; however, the information to extract would be the topological/morphological description in mixtures. To arrive at the description, one needs to know the dielectric properties of the constituents and the composite prior to the spectral analysis. To illustrate the strength of the representation and confirm the proposed hypothesis, the Landau-Lifshitz/Looyenga (LLL) [Looyenga, H. Physica 1965, 31, 401] expression is selected. The structural information of a mixture obeying LLL is extracted for different volume fractions of phases. Both an in-house computational tool based on the Monte Carlo method to solve inverse integral transforms and the proposed empirical scaled permittivity expression are employed to estimate the spectral density function of the LLL expression. The estimated spectral functions for mixtures with different inclusion concentration compositions show similarities; they are composed of a couple of bell-shaped distributions, with coinciding peak locations but different heights. It is speculated that the coincidence in the peak locations is an absolute illustration of the self-similar fractal nature of the mixture topology (structure) created with the LLL expression. Consequently, the spectra are not altered significantly with increased filler concentration level—they exhibit a self-similar spectral density function for different concentration levels. Last but not least, the estimated percolation strengths also confirm the fractal nature of the systems characterized by the LLL mixture expression. It is concluded that the LLL expression is suitable for complex composite systems that have hierarchical order in their structure. These observations confirm the finding in the literature.

Analysis of hybrid EM wave absorber using thin corrugated dielectric lossy sheet based on equivalent permittivity representation

AbstractThe 10‐m and 3‐m semianechoic chambers are in widespread use for the electromagnetic compatibility (EMC). The hybrid EM wave absorber consisting of the sintered ferrite tiles and the dielectric lossy materials has been usually used for these semianechoic chambers. In the past, Suetake, Naito, and Shimizu's studies played a key part in providing the basis for the hybrid EM wave absorber. The reflectivity of the hybrid EM wave absorber can be calculated from the multilayered approximate structure. In particular, each layer occupied partly by the dielectric lossy materials can be replaced by the homogeneous plate having the equivalent relative complex permittivity, which is determined through the synthesized capacitance model in the large wavelength range. But, there was a problem that the equivalent relative complex permittivity differs with the process of the synthesized capacitance model.We propose a new method which can be applied to the equivalent relative complex permittivity by the finite difference method (FDM). Moreover, the reflectivity of the hybrid EM wave absorber using the thin corrugated dielectric lossy sheet is calculated and measured. As a result, it is confirmed that the measured reflectivity agrees with the calculation one. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(7): 12–20, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10082

A new representation of permittivity versus temperature for alkanols of the same chain length

The alkanols of three carbon length have been studied by dielectric methods during many years and they do not obey any theoretical model. These substances have the same chain length and have one, two or three dipoles per molecule, so their ability to form hydrogen bridges changes from one substance to other, and one can obtain information by comparative studies. In previous works, we have measured the thermal dependence of permittivity of these substances and analysed the results with an empirical modification of the Onsager equation. Now we shall analyse and compare the results using a different representation. In this representation, the data shows straight lines, whose slopes depend on the quantity of dipoles of each molecule encouraging the high quality of the fittings obtained with the three substances, and also that they behave in the same dielectric way with the rise of temperature.

Modelling electromagnetically induced transparency media using the finite-difference time-domain method

Time-domain electromagnetic modelling of complex structures which include both non-dispersive media and media exhibiting electromagnetically induced transparency (EIT) require a general, robust calculation method such as finite-difference time-domain (FDTD). We propose a complex-valued, exact two-pole representation of the permittivity of a three-level system which is suitable for integration into the FDTD algorithm via the auxiliary differential equation method. Our calculation model confirmed reported results which were calculated with an approximate representation of the EIT permittivity. Additionally, propagation calculations which mimic slow light experiments were performed. A major advantage of our representation is the ease with which changes in the control field Rabi frequency can be implemented by using a time-dependent permittivity.

A linear representation of permittivity versus temperature data for pure alcohols

In previous works, permittivity of some pure aliphatic alcohols was measured as a function of temperature and, together with data from the literature, was fitted with an empirical modification of Onsager equation. This representation is complicated because one has to solve the Onsager quadratic equation and then fit the experimental values. Here a new set of data is used in a different representation, with the inverse of the temperature, and a straight line is obtained for each sample. The slopes of these lines are not coincident with those calculated with Onsager or Kirkwood–Fröhlich models, and one can evaluate the differences between the experimental and theoretical values. This is a very simple and clear representation and the good quality of the linear fits attained with the two sets of our measurements and data from several authors is encouraging. A qualitative explanation of the differences observed with the theoretical values is offered.

Analyses for a dipolar relaxation in the featureless dielectric spectrum, and a comparison between the permittivity, modulus and impedance representations

The apparently featureless permittivity, Iµ′, and loss, Iµ″, spectra of a nylon 12 polymer have been analysed to reveal its dipolar relaxation process and dc conductivity. Two other representations of the data, namely electric modulus and impedance, have been examined for their suitability in cases where overwhelmingly large contributions from electrode impedance and dc conductivity mask the dipolar relaxation process. In these two representations, the shape of the spectra of the relevant quantities could be fitted to a distribution of conductivity relaxation times, but when the parameters obtained from such fittings were used to calculate Iµ′ and Iµ″, large discrepancies between the calculated and measured quantities became obvious. Thus, modulus and impedance representations seem unsuitable for the analysis of the dielectric data. Critical examination demonstrated that unique and reliable information is obtained only when the dielectric data were analysed in permittivity representation and interfacial (electrode/sample) effects taken into account. The permittivity representation seems preferable to the other two representations.

Dielectric Relaxation Studies of Annealed Short Side Chain Perfluorosulfonate Ionomers

Annealing of dry, short side chain Na + -perfluorosulfonate ionomers at a submelting temperature above the ionic cluster glass transition results in increased order and more structural cohesion in the matrix and disruption of order in the clusters as seen by DSC. Hydrative capacity increases with increased annealing. Electrical impedance studies show how the permittivity representation of data is most useful for studying long-range ion motions while admittance is better suited for detecting cluster-confined motions. A cluster-associated peak was rationalized as shifting to lower frequencies with increase in temperature/time of annealing due to an increase in hydrated cluster size

Barrier effects on ionic conductivity and dielectric response of Tl(NbTe)O 6

Complex impedance measurements in the frequency range 10-10 7 Hz and at temperatures ranging between 298 K and 800 K have been performed on Tl(NbTe)O 6 powder samples. Complex impedance plots are strongly affected by grain boundaries. An analysis of the dielectric response in the permittivity representation allows to distinguish between bulk and barrier contributions.