Multiplicity of dielectric relaxation times of dispersed ice microcrystals

Summary The multiplicity of relaxation times of the dielectric relaxation of water molecules in dispersed ice microcrystals has been studied by means of the thermally stimulated depolarization (TSD) current method. Using several experimental techniques offered by the TSD method we have shown that the relaxation mechanism is characterized by a continuous distribution of relaxation times with both the activation energy.W and the pre-exponential factorτ ₀ in the Arrhenius equation being distributed parameters. A linear relationship has been found to exist betweenW and lnτ ₀. The dielectric behaviour of ice emulsions has been found to resemble strongly in some aspects that of HF-doped ice and ice samples with high concentrations of crystal imperfections. The multiplicity of relaxation times has been explained by the interaction of intrinsic ionic defects with water molecules. Work supported in part by the Greek Ministry of Research and Technology.     

Investigating the dielectric properties of potassium iodate polycrystals

Linear and nonlinear dielectric properties of KIO₃ polycrystalline samples are investigated. It is shown that linear dielectric permittivity ε' displays four anomalies corresponding to phase transitions in KIO₃. Anomalies of third-harmonic coefficient γ_3ω are observed at temperatures of 113, 263, and 345 K, corresponding to phase transitions between KIO₃ ferroelectric phases. It is established that the third-harmonic coefficient responsible for the nonlinearity of dielectric properties displays no anomalies during the transition to the paraelectric phase of KIO₃ at approximately 485 K. Possible reasons for there being no such anomaly are discussed.     

Continuous distribution of relaxation times during mechanical relaxation of fully-stabilized zirconia

The internal friction (IF) was measured for ZrO₂ doped with 10 mol% Y₂O₃ polycrystals and single crystals before aging. The degree of the temperature shift with the frequency change δ(1/T?) was examined in order to determine if one or both parameters in the Arrhenius's equation contribute to the occurrence of the continuous distribution of relaxation times (τ). A continuous distribution is derived only from the continuous distribution of the pre-exponential factor (τ ₀), while the activation energies (H?) for τ are constant in two peaks. The peak fitting was carried out using some conventional distribution functions, i.e., the RCSI model, and some famous functions for dielectric relaxation. The IF curves can be fitted quite well by the Kohlrousch–Williams–Watts (KWW) equation with reasonable parameters. The orientation factor (Γ) dependence of the relaxation of the reciprocal torsional modulus (δG ^?1) is a linear function relative to Γ in both peaks. When the H for τ of both peaks of the poly- and single crystals was compared, the polycrystalline results should be considered average values of the single-crystalline results. Therefore, the single-crystalline IF peaks also consist of two peaks and the parameters (the relaxation strength and H?) obtained by the peak fitting are valid. A continuous distribution of τ is derived only from the continuous distribution of τ ₀ and the distribution function is the KWW equation.     

Reconstruction of the distribution function of relaxation times for 7CB and 7OCB liquid crystals from dielectric spectra

A technique for reconstructing the distribution function of relaxation times from the dielectric spectra measured over a wide range of frequencies is proposed and tested using 7CB and 7OCB liquid crystals as examples. The objective function, which is the sum of the squares of the differences between the calculated and measured permittivities, is minimized with the Mathcad program package. It is demonstrated that, in the case of parallel orientation of the molecular director with respect to the polarization of the ac electric field, the distribution function of relaxation times is consistent with the Debye relaxation model; however, there are insignificant deviations in the short-time interval corresponding to the high-frequency portion of the dielectric spectrum. For perpendicular orientation of the director, the distribution function of relaxation times exhibits specific features that are most pronounced for the 7OCB liquid crystal and probably reflect intramolecular motions of the rigid core and fragments of the alkyl chain.     

Spectral distribution of relaxation times in spin glasses

Recent neutron scattering measurements on spin glasses show that the dynamics of the spin systems can be best described in terms of wide spectral distribution of relaxation times evolving continuously with decreasing temperature but which is devoid of any critical behaviour, either speeding up or slowing down, at any finite temperature including the spin glass “freezing temperature T_sg”. It is argued that the latter temperature itself is dependent on the time constant of measurement for all spin glasses in general; the observed variation with frequency being less pronounced in some systems than others owing to some special characteristics of their spin dynamics such as, for example, the presence of parallel channels of rapid relaxation provided by the Korringa coupling in metallic spin glasses. The neutron scattering measurements presented here enable us to propose plausible forms for the density of relaxation times of the spin system and to show that the logarithmic frequency dependence of the freezing temperature observed in low frequency ac susceptibility measurements follows naturally from a uniform density of relaxation times at these frequencies.     

Determination of the two dimensional distribution of the attempt relaxation times and activation energies from temperature dependence of dielectric dispersion

We present a method for numerical calculation of two dimensional distributions of the attempt relaxation times and activation energies from the temperature dependence of the experimental dielectric permittivity dispersion. We introduce empirical attempts to account for broad and/or asymmetric dispersions with the idea of using a weighted collection of Debye relaxation times. Then we present a modification of the aforementioned idea including attempt relaxation time and activation energy using the Arrhenius law, which significantly complicates the computation of the aforementioned distribution. Incorporating the activation energy and the attempt relaxation time into the equation transforms the discretized matrix equations into tensor equations. We rework the tensor equations into simpler matrix equations, thus permitting us to solve the presented discretized integral equation by using existing Least Distance Problem solving methods. Also, we present a regularization method and a way to choose the regularization parameter based on a best fit criterion. In the end we discuss the method showing some simulated results and experimental results. We then point out some problems involved in the calculations and propose methods to reduce their significance.     

Non-markovian properties of dielectric relaxation in liquids

Statistical molecular memory is investigated in dielectric relaxation in a liquid medium. A new method of closing the infinite chain of kinetic equations for the time correlation function is proposed, and used to obtain an equation permitting the calculation of the smallest-order memory functions. The spectrum of the non-Markovian parameter obtained indicates that dielectric relaxation in liquid CH₃I is a significantly non-Markovian process.Kazan' State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 27–31, October, 1995.     

Structural study of aqueous solutions of tetrahydrofuran and acetone mixtures using dielectric relaxation technique

The complex permittivity, static dielectric constant and relaxation time for tetrahydrofuran-water and acetone-water mixtures have been determined at 0°, 10°, 25° and 35°C using time domain reflectometry technique (TDR). The behaviour of relaxation time of the mixture shows a maxima for the mixture with 30% of water by volume. This suggests that the tendency to form cluster between water and solute molecule is maximum for this mixture. The excess permittivity for both tetrahydrofuran-water mixture and acetone-water mixtures, are found to be negative. The Kirkwood correlation factor has been determined at various concentrations of water. Static dielectric constant for the mixtures have been fitted well with the modified Bruggeman model. The values of the Bruggeman parametera for tetrahydrofuran is found to be more than the corresponding value for acetone.     

Measurement of longitudinal relaxation times using surface coils

The poor B₁ field homogeneity associated with surface coils reduces the effectiveness of inversion-recovery techniques for determination of T₁ relaxation times. This paper presents a variation of the saturation-recovery T₁ experiment which introduces periodic phase shifts in the saturating irradiation to achieve rapid and effective saturation of the sample magnetization, thereby avoiding the complications of B₁ field inhomogeneity. Comparison of the presented technique with the inversion-recovery technique utilizing a composite inverting pulse and alternating phase acquisition is provided. A discussion of the relative merits of each technique is presented.     

Phenomenological approach on wave propagation in dielectric media with two relaxation times

In this paper dielectric phenomena with two relaxation times are discussed. By assuming a sinusoidal form for induction vector D a sinusoidal electric field is generated and it depends on unknown phenomenological coefficients whose expressions together to their numerical values as functions of frequency are obtained. Moreover, electromagnetic wave propagation is analysed obtaining wave vector as function of the aforementioned coefficients. The results are applied to a Vinylidene Chloride-Vinyl Chloride (VDC-VC) to test the applicability of the model.     

Cole-Davidson dielectric relaxation as a self-similar relaxation process

An effort has been undertaken to understand the nature of one type of non-exponential relaxation, namely Cole-Davidson relaxation. Toward this end, a model of relaxation as a self-similar process is proposed. An equation containing operators of fractional integration and differentiation is obtained and solved, which the relaxation function obeys in this case. Fiz. Tverd. Tela (St. Petersburg) 39, 101–105 (January 1997)     

Fe掺杂CaCu3Ti4O12陶瓷的介电性能与弛豫特性研究

采用固相反应法制备了CaCu3Ti4-xFexO12(0≤x≤0.2)陶瓷,通过x射线衍射、扫描电子显微镜、介电频谱和阻抗谱等手段研究了Fe对CaCu3Ti4O12陶瓷的结构和介电性能的影响.研究发现:CaCu3Ti4-xFexO12陶瓷在x取值范围内形成了连续固溶体.随着Fe含量x的增加,晶粒半导性逐渐消失,介电常数减小.当x≤0.04时,在106-108和103-104 Hz频率范围存在介电弛豫行为I和介电弛豫行为Ⅱ,高频介电弛豫行为I与陶瓷内的晶界阻挡层有关,而低频介电弛豫行为Ⅱ与陶瓷表面层发生的界面极化有关.在CaCu3Ti3.99Fe0.01O12陶瓷的高温频谱中,观察到了第三个介电弛豫行为Ⅲ,它与局域电荷的跃迁有关,利用阿列纽斯关系式得到此过程的热激活能0.78 eV.     

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).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 37–40, March, 1982.     

Investigation of the dielectric properties of polymer composite films with a ferroelectric filler using the bridge and thermal noise methods

Thin films of composite polymers based on polyvinylidenfluoride (PVDF), with ferroelectric fillers of No-Zr-Ti-Pb (NZTP-l) were used to study the dielectric properties of the composites; specifically, we obtained the temperature dependence of the dielectric permittivity at various frequencies at various contents of filler piezoceramic in the polymers. Measurements were conducted using the bridge method and with the thermal noise method. In the studies with the bridge method, the range of the frequencies was 25 Hz-1 MHz; in the studies with the thermal noise method, the frequencies varied from 1 to 100 kHz.     

Microstructure and dielectric properties of granular composite films

This paper reviews some of the recent progress in understanding the relationship between the microstructure and the d c and optical properties of composites. By focusing on two unique characteristics of metal-insulator composites — the percolation threshold and the optical dielectric anomaly — it is demonstrated that the concept of a ‘structural unit’ arises naturally as a means for incorporating the microstructural information in the calculation of the effective dielectric function ̄ for an inhomogeneous system. A theory based on a statistical consideration of two types of structural unit is shown to result in values for ̄ in excellent agreement with observed data.     

Loss tangent (internal friction) for high relaxation strengths and a lognormal distribution of relaxation and retardation times

Summary The loss tangent (internal friction) is evaluated numerically for a lognormal distribution of retardation or relaxation times and high relaxation strengths. It is shown that the loss tangent peak becomes more asymmetrical and the peak width, at half-maximum, decreases as the relaxation strength increases, dropping down to values corresponding to a Debye peak at very large relaxation strengths. Furthermore, the asymmetry of the peak can be used to establish if the lognormal distribution is in the retardation or in the relaxation spectrum. Finally, a procedure which can be used to obtain the relaxation strength, the geometrical parameter of the distribution and the average retardation or relaxation time, from the experimental loss tangentvs. frequency curves, is described. This procedure is applied to actual experimental data reported in the literature for polystyrene. The authors of this paper have agreed to not receive the proofs for correction.     

Segmental relaxation in semicrystalline polymers: A mean-field model for the distribution of relaxation times in confined regimes

The effect of confinement in the segmental relaxation of polymers is considered. On the basis of a thermodynamic model we discuss the emerging relevance of the fast degrees of freedom in stimulating the much slower segmental relaxation, as an effect of the constraints at the walls of the amorphous regions. In the case that confinement is due to the presence of crystalline domains, a quasi-Poissonian distribution of local constraining conditions is derived as a result of thermodynamic equilibrium. This implies that the average free-energy barrier F for conformational rearrangement is of the same order of the dispersion of the barrier heights, ( F) , around F . As an example, we apply the results to the analysis of the -relaxation as observed by dielectric broad-band spectroscopy in semicrystalline poly(ethylene terephthalate) cold-crystallized from either an isotropic or an oriented glass. It is found that in the latter case the regions of cooperative rearrangement are significantly larger than in the former.