Distribution Of Dielectric Relaxation Times Research Articles

Non-destructive comparative evaluation of fossil amber using terahertz time-domain spectroscopy.

Fossilized plant resins, or ambers, offer a unique paleontological window into the history of life. A natural polymer, amber can preserve aspects of ancient environments, including whole organisms, for tens or even hundreds of millions of years. While most amber research involves imaging with visual light, other spectra are increasingly used to characterize both organismal inclusions as well as amber matrix. Terahertz (THz) radiation, which occupies the electromagnetic band between microwave and infrared light wavelengths, is non-ionizing and frequently used in polymer spectroscopy. Here, we evaluate the utility of amber terahertz spectroscopy in a comparative setting for the first time by analyzing the terahertz optical properties of samples from 10 fossil deposits ranging in age from the Miocene to the Early Cretaceous. We recover no clear relationships between amber age or botanical source and terahertz permittivity; however, we do find apparent deposit-specific permittivity among transparent amber samples. By comparing the suitability of multiple permittivity models across sample data we find that models with a distribution of dielectric relaxation times best describe the spectral permittivity of amber. We also demonstrate a process for imaging amber inclusions using terahertz transmission and find that terahertz spectroscopy can be used to identify some synthetic amber forgeries.

Impedance spectroscopy and conduction mechanism of magnetoelectric hexaferrite BaFe10.2Sc1.8O19

AbstractThe dielectric relaxation and conduction properties of hexaferrite BaFe10.2Sc1.8O19 (BFSO) ceramics have been investigated by impedance spectroscopy (1 Hz‐2 GHz) at various temperatures (253‐473 K). The frequency dependence of impedance and modulus spectra of BFSO shows that its dielectric responses are thermally activated. The scaling behaviors of impedance spectra indicate that the distribution of dielectric relaxation times in BFSO is temperature independent. The frequency‐dependent conductivity spectra follow the universal‐power‐law at high temperatures but deviate slightly at low temperatures. An enormous increase in relaxation/conduction activation energies of BFSO above 413 K is also observed in both impedance and conductivity spectra. This indicates that at high temperatures, relaxation/conduction processes may be contributed mainly by the movable oxygen vacancies, whereas at low‐temperature electron hopping dominates. The conductivity fitting results further suggest that electron/oxygen vacancy‐related small polaron hopping should be the most probable conduction mechanism for BFSO.

Dielectric properties of polymer structures of the azomethine base with an inclusion of a metal center

The results of studying the temperature-frequency dependences of the dielectric parameters of metal-polymer films of poly-[CumSalpn-1,3] are presented. The dispersion of polarization characteristics has been established in the ranges of frequencies f = 102–106 Hz and temperatures T = 293–340 K. The temperature dependence of the parameter of dielectric relaxation time distribution has been obtained. The role of the temperature factor in the charge processes under study has been discussed.

DIELECTRIC PROPERTIES OF PLASMA POLYMERIZED N,N,3,5 TETRAMETHYLANILINE THIN FILMS

Plasma polymerized thin films of aluminium/thin film/aluminium configuration were deposited at room temperature by a parallel plate capacitively coupled glow discharge reactor using N,N,3,5 tetramethylaniline (TMA) as a precursor. The infrared spectroscopic analyses revealed that plasma polymerized TMA (PPTMA) films contained an aromatic ring structure with NC and CH side groups, presence of C = O was also evident. The differential thermal analysis and thermogravimetric analysis of PPTMA thin film was thermally stable up to about 505 K. The scanning electron microscopy of PPTMA thin film showed a smooth, flawless and pinhole free surface. The capacitance and ac electrical conductance of PPTMA thin films were measured as functions of frequency (100 < f < 105 Hz) and temperature (300 < T < 450 K). The electrical conductivity is more dependent on temperature in the low frequency region than that in the high frequency region. In PPTMA thin films the conduction may be dominated by hopping of carriers between the localized states at low temperatures and thermally excited at the high temperatures. The activation energies are estimated to be about 0.05 eV in the low temperature and 0.23 eV in the high temperature. Dielectric constant decreases with the increase of frequency and that decreases with the increase of temperature but dielectric loss increases with increasing frequency with a minimum in the low frequency region. The temperature-dependence of the Cole-Cole diagram shows the existence of distribution of dielectric relaxation times in the PPTMA thin films.

A broadband dielectric spectroscopy study of the relaxation properties of H-Beta-ZnS zeolite-semiconductor nanocomposite

Broadband dielectric spectroscopy was used to determine the dependences of the complex permittivity for H-Beta zeolite and H-Beta-ZnS composite in a frequency range of 10−1−105 Hz and a temperature range from −160 to +300°C. A difference in the dispersion of the real and imaginary parts of the permittivity of H-Beta-ZnS nanocomposite in comparison with initial zeolite was detected. Approximating the dielectric spectrum by the Havriliak-Negami functions made it possible to obtain the distribution of dielectric relaxation times, which contained several maxima corresponding to the relaxation transitions in both nanocomposite and initial zeolite. A new relaxation transition was observed in the nanocomposite in a temperature range of 170–230°C. The temperature dependence of the relaxation time of this transition was linearized in the Arrhenius coordinates with an activation energy of ∼2.0 eV.

Effect of Local Heterogeneity on Dielectric Relaxation Spectra in Concentrated Solutions of Poly(vinyl acetate) and Poly(vinyl octanoate)

The effect of local heterogeneity on the distribution of dielectric relaxation times was studied for concentrated solutions of poly(vinyl acetate) (PVAc) in 1-methylnaphthalene (MN) and those of poly(vinyl octanoate) (PVOc) in toluene (Tol). The half-widths A of the dielectric loss curves for the primary processes of those systems are compared with those of the PVAc/Tol system reported previously. The data indicate that A decreases in order of PVAc/Tol, PVAc/MN, and PVOc/Tol systems if compared at the same temperature T/Tg where Tg denotes the glass transition temperature of solutions. The half-width of each solution increases with decreasing temperature. The loss curve is calculated by assuming a Gaussian distribution of the local concentration Φ which results in the distribution of relaxation times g(τ). The calculated loss curves agree fairly well with the observed ones. The broadening behavior is also explained by assuming that A is proportional to the amplitude of the local concentration fluctuation ΔΦ times the slope of the Φ dependence curve of the average relaxation time r. This assumption leads to a linear relationship between A and ΔΦ/(T - T 0 ) 2 where To is the Vogel critical temperature. Using this relation, we have attempted to estimate ΔΦ. Small-angle X-ray scattering was also measured on PVAc/ MN solutions and found that the scattering intensity was lower than that for PVAc/Tol. This is consistent with the fact that A of PVAc/MN solutions is narrower than PVAc/Tol solutions.

Hydrogen induced relaxations in disordered dielectrics

In many non-crystalline or amorphous dielectrics, for example in aluminumoxide, siliconnitride, siliconoxide, or polyimide, the Kohlrausch behaviour of the time dependent polarization current j≈t−α is observed. This empirical law can be detected from the sub-microsecond range up to several thousand seconds indicating a broad distribution of relaxation times. The effect is caused by protons fluctuating in double well potentials between neighboured electronegative atoms, i. e. oxygens or nitrogens. The wells are located at the atomic shells. The transition probability or its inverse, the relaxation time, depends exponentially on the barrier height and for a tunneling transition it depends also on the distance between the wells. The barrier height increases with increasing distance. Therefore the distribution of interatomic nearest neighbour distances in the amorphous state causes the distribution of dielectric relaxation times. The model is confirmed by experiments using palladium instead of gold electrodes. The palladium absorbs hydrogen from the atmosphere and enhances the density of protons in the dielectric resulting in an increase of the polarization strength. This is shown here for thermally grown siliconoxide and electron beam evaporated aluminumoxide.

Dielectric properties of nematic liquid crystals in the ultralow frequency regime

The dielectric properties of nematic liquid crystal (4-cyano-4′-n-pentylbiphenyl: 5CB) cells in the ultralow frequency regime was investigated. A dielectric relaxation, whose relaxation time is 160 s, is observed at 303 K, and the dielectric relaxation is found to be independent of applied electric field. It is shown that the dielectric relaxation is caused by the Helmholtz double layer formed by the adsorption of impurity ions in 5CB onto the electrode surfaces of the cells, and hence the thickness of the double layer is comparable to the radius of impurity ions in 5CB. The dielectric relaxation obeys the empirical Cole-Cole circular arc law, indicating that dielectric relaxation times are distributed. The distribution of dielectric relaxation times can be explained in terms of distributed thicknesses of the Helmholtz double layer.

Primary and secondary relaxations in aliphatic alcohols: Complex dielectric permittivity spectra of 5-methyl 2-hexanol

The real and imaginary parts of the complex dielectric permittivity of 5-methyl 2-hexanol have been measured in the frequency range 10 Hz to 100 kHz and temperature range 77 K to 200 K. The results show the existence of two Arrhenius relaxation processes, assigned as α and β. It is found that these processes co-exist above the glass transition temperature, T g. However the β process persists in the glass structure with continually reduced dielectric relaxation strength and broader distribution of dielectric relaxation times with a reduction in temperature. This continues on until some 60 K below T g. Our investigation of these processes in this material and other materials already published support the glass transition theory of Johari and Goldstein that β process is generic to the glass phase of supercooled liquids. A plausible explanation of the Arrhenius nature of the α relaxation process for alcohols is also given.

Dielectric relaxation in a Rb0.30MoO3 crystal.

The dielectric relaxation frequency ${\mathrm{\ensuremath{\omega}}}_{0}$ is investigated for a ${\mathrm{Rb}}_{0.30}$${\mathrm{MoO}}_{3}$ thin sample from \ensuremath{\sim}84 K up to the vicinity of the Peierls transition by using the combined ac-dc method. ${\mathrm{\ensuremath{\omega}}}_{0}$ follows an Arrhenius behavior below \ensuremath{\sim}150 K, similar to that found in other materials. A maximum is observed in 150--160 K. An empirical formula associated with a distribution of dielectric-relaxation times was used to fit the experimental data of the combined ac-dc method.

Shear viscosity and dielectric relaxanon time of dibutyl phthalate down to glass transition temperature.

We studied the shear viscosity and the main dielectric relaxation time of dibutyl phthalate from 97°C down to −96°C (near its glass transition temperature Tg). A visco penetrometer and a dielectric spectrometer built in our laboratories allowed us to obtain experimental data in the ranges 10-10 9 Pa.s for viscosity and 1 mHz–2 MHz for dielectric relaxation time. All these data and those of different authors give viscosity and dielectric relaxation time versus temperature on twelve decades; they are well fitted by the Cohen and Grest relation. These fits obtained on a large temperature range show that there is a strong correlation between viscosity and dielectric relaxation time. Furthermore it appears that the dielectric relaxation time distribution is broadening in the vicinity of Tg.

Dielectric spectroscopy and molecular dynamics of methylene chloride CH 2Cl 2

Precise measurements of the complex permittivity of methylene chloride (CH 2Cl 2) at 293 K have been made at frequencies in the range 50–310 GHz. These, when combined with earlier results, have made possible a determination of the complex permittivity over the entire zero to THz frequency region. These results show a distribution of dielectric relaxation times. The value of the Cole-Cole distribution parameter, α, was 0.03 and that of the relaxation time, τ, was 2.07 ps. A comparison of the power absorption, A(ω), spectra of pure methylene chloride with the normalized dilute solution spectra shows that: (a) the integrated absorption intensity of the pure liquid is 20% greater than that of its dilute solution, (b) the integrated absorption intensity for the dilute solution is higher than the value calculated, using Gordon's formula, by 46%, and (c) for frequencies greater than the the frequency, 0, of maximum power absorption, A(ω) falls off as ω −2 for dilute solutions whereas for the pure polar liquid the manner in which A(ω) falls off changes from being proportional to ω −2 to ω −4, for frequencies, = (ω/2π), well in excess of 0.

Dielectric relaxation and non-linear dielectric effect in diazo compounds

Dielectric relaxation and non-linear dielectric effect measurements were carried out in 2- and 4-nitrodiazoacetophenone in p-xylene. Linear dielectric measurements have been performed in the frequency and temperature range of 0.50–36 GHz and 293–313 K, respectively. Dielectric absorption for 2-nitrodiazoacetophenone shows Debye-like behaviour, while for 4-nitrodiazoacetophenone one observes a complex curve which indicates some distribution of dielectric relaxation times. From these results information about the molecular dynamics of the dielectric relaxation is obtained.

In-source analysis of radiation curing of unsaturated polyester resin by charging current technique

The dielectric and conductive properties of unsaturated polyester (UP) resins undergo significant changes in the course of crosslinking reaction. In-source radiation curing of UP resins was studied by combining dielectric, thermal and charging current analyses. Dielectric permittivity (by stepwise changing of frequency) and charging current were measured in the course of cobalt-60 γ-irradiation at constant temperatures. The exothermic reaction could be monitored by differential thermal analysis (DTA), while the observed change of dielectric permittivity can show how the dielectric relaxation time distribution shifted through the experimental window represented by reaction temperature and by frequency range of dielectric spectrometer. The decrease in dielectric permittivity and in charging current may be mainly associated with the partial immobilization of permanent carbonyl and hydroxyl dipoles attached to the oligoester chain. The measurements of charging properties of UP resins during the curing seems very promising due to the ease with which the relaxation parameters and essential information on the molecular interactions and mobility can be derived. The electrical properties of UP resins are mainly determined by inter- and intramolecular hydrogen bonds. The shape of the charging current spectra during the curing of UP resins showed a heterogeneous nature of vitrification process. The results show that two relaxations occur: the first one is attributed to the increase in viscosity of liquid phase as oligoester chains are crosslinked prior to the gelation, and the second one to the further crosslinking in the gel phase, resulting in the vitrification of the system. The characteristic times to gelation and vitrification of UP resins in the course of radiation isothermal curing are decreasing functions of reaction temperature.

Non-exponential time behavior of electron transfer in an inhomogeneous polar medium

An analysis is made of electron transfer (ET) in a polar medium described by a distribution of dielectric relaxation times, for the case that intramolecular contributions to the ET are negligible. The generalized moment expansion is used for an approximate multi-exponential description of the non-exponential time behavior of the ET. As an example, ET in glycerol-like solvents is considered, treated by the spatially inhomogeneous model for dielectric relaxation. For this model the ET rate at long times is found to vary as τ0−1, τ0 being a dielectric relaxation time parameter, in contrast with a fractional dependence at short times.

The effect of solvent relaxation dynamics on outer-sphere electron transfer

We analyse outer-sphere electron transfer (ET) in a dielectric medium, which is characterised by a continuous distribution of dielectric relaxation times. An explicit expression for the averaged ET rate is derived in the particular case of the Davidson-Cole dielectric susceptibility function. A quantitative account of recent experimental data for ET in the Ru(phen 3) 2+ methylviologen 2+ system in glycerol is provided.

Transport properties of polymer solutions. A comparative approach

A variety of transport properties have been measured for solutions of the water soluble polymer poly(ethylene oxide)(PEO) with molecular weights ranging from 200 to 14,000, and volume fractions ranging from 0-80%. The transport properties are thermal conductivity, electrical conductivity at audio frequencies (in solutions containing dilute electrolyte), and water self-diffusion. These data, together with dielectric relaxation data previously reported, are amenable to analysis by the same mixture theory. The ionic conductivity and water self-diffusion coefficient, but not the thermal conductivity, are substantially smaller than predicted by the Maxwell and Hanai mixture relations, calculated using the known transport properties of pure liquid water. A 25% (by volume) solution of PEO exhibits an average dielectric relaxation frequency of the suspending water of one half that of pure water, with clear evidence of a distribution of relaxation times present. The limits of the cumulative distribution of dielectric relaxation times that are consistent with the data are obtained using a linear programming technique. The application of simple mixture theory, under appropriate limiting conditions, yields hydration values for the more dilute polymer solutions that are somewhat larger than values obtained from thermodynamic measurements.

Dielectric relaxation and modulus of V2O5—TeO2glasses

Abstract The dielectric behaviour of V2O5—TeO2 glasses in the composition range 10 to 80 mol.% V2O5 is reported for the temperature region 77 to 500 K and the frequency region 0.1 to 100 kHz. The variation of dielectric constant έ’ with temperature and frequency in the region where the measured a.c. conductivity approaches the d.c. conductivity indicates a bulk dielectric relaxation. The data have been analysed in terms of conventional dipolar dielectric relaxation with a distribution of dielectric relaxation times and in terms of conductivity relaxation using dielectric modulus M* = 1/e* plots. The d.c. conductivity, dielectric relaxation and conductivity relaxation have the same activation energy of 0.21–0.42 eV for decreasing V2O5 content and a frequency factor v 0 of 5 × 1010 Hz. The difference between this value and the 1012 Hz expected for phonon frequencies is attributed to a tunnelling contribution. The dielectric modulus approach is satisfactory for electronic glasses with respect to the calculat...

Numerical calculation of the dielectric relaxation time distribution function in polar liquids

A numerical method for calculation of the relaxation time distribution function based on the discrete Fourier transform of the dispersion part of the complex dielectric permittivity is developed. The time relaxation distribution function is found for water; its dispersion of relaxation times is narrow. This is explained by the presence of distorted hydrogen bonds (the Pople model).

Dielectric and thermal analysis of radiation curing of insaturated polyester resins

Radiation curing of unsaturated polyester resins were studied by combining dielectric and thermal analysis. Dielectric permitivities were measured by stepwise changing of frequency during the course of 60Co y-irradiation at constant temperature or by simultaneous change of frequency and temperature after irradiation. A continuous shift of the glass-transition of the resin and a change of the dielectric relaxation time distribution was observed as radiation crosslinking reaction proceeded. The shape of the dielectric spectrum bands indicated a heterogeneous nature of the transition which increased with increasing degree of curing. The long reaction time limiting values of the permittivity were found to be considerably higher than the unrelaxed limit showing the existence of a limiting conversion effect.