Mathematical modeling of the multimodal distributions of elastomer relaxation spectra using the family of Pearson curves

An approach to the mathematical modeling of elastomer relaxation spectra obtained via acoustic spectroscopy is presented. The solving of Pearson differential equations is the basis for the calculated dependences. The solutions to the equations describe the frequency and temperature distribution of the mechanical loss tangent. The form of the distribution is estimated from selected statistical moments of the experimental relaxation spectra and the mechanical loss tangent.     

Dielectric relaxation and ac conductivity of double perovskite oxide Ho2ZnZrO6

Double perovskite oxide holmium zinc zirconate Ho₂ZnZrO₆ (HZZ) is synthesized by solid state reaction technique under a calcination temperature of 1100 °C. The crystal structure has been determined by powder X-ray diffraction, which shows monoclinic phase at room temperature. The variation of dielectric constant (ε′) and loss tangent (tan δ) with frequency is carried out assuming a distribution of relaxation times. The frequency corresponding to loss tangent peak is found to obey an Arrhenius law with activation energy of 89.7 meV. The frequency-dependant electrical data are analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary electric modulus shows the temperature-independent nature of the distribution of relaxation times. Nyquist plots are drawn to identify an equivalent circuit and to know the bulk and interface contributions.     

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.     

AC conductivity and dielectric relaxation in Ba(Sm1/2Nb1/2)O3 ceramic

The complex perovskite oxide a barium samarium niobate (BSN) synthesized by solid-state reaction technique has single phase with cubic structure. The scanning electron micrograph of the sample shows the average grain size of BSN∼1.22 μm. The field dependence of dielectric response and loss tangent were measured in the temperature range from 323 to 463 K and in the frequency range from 50 Hz to 1 MHz. The complex plane impedance plots show the grain boundary contribution for higher value of dielectric constant in the low frequency region. An analysis of the dielectric constant (ε′) and loss tangent (tan δ) with frequency was performed assuming a distribution of relaxation times as confirmed by the scaling behaviour of electric modulus spectra. The low frequency dielectric dispersion corresponds to DC conductivity. The logarithmic angular frequency dependence of the loss peak is found to obey the Arrhenius law with an activation energy of 0.71 eV. The frequency dependence of electrical data is also analyzed in the framework of conductivity and electric modulus formalisms. Both these formalisms show qualitative similarities in relaxation times. The scaling behaviour of imaginary part of electric modulus M″ and dielectric loss spectra suggest that the relaxation describes the same mechanism at various temperatures in BSN. All the observations indicate the polydispersive relaxation in BSN.     

Efficiency of paramagnetic relaxation enhancement in off-resonance rotating frame

Transferring from laboratory frame to off-resonance rotating frame for the (1)H spin can compensate the relaxivity loss for paramagnetic agents at the magnetic field strength higher than 3 Tesla and enhance water relaxation rate constant significantly. A comprehensive theory for calculating the relaxation rate constants in the off-resonance rotating frame is described. This theory considers the contributions from both inner shell and outer shell water. The derived relaxation rate constants and relaxation enhancement efficiency as a function of the magnetic field strength and the effective field parameters are directly correlated to the structures, dynamics and environments of paramagnetic agents. To validate the theoretical predictions, we have measured the relaxation enhancement efficiency for a series of macromolecule conjugated gadolinium chelates at 9.4 Tesla. The experimental results confirmed the theoretical predictions. The theory also predicts the relaxation enhancement for T(2)-type paramagnetic agents at high magnetic fields. Promising fields of applications include situations where T(1)- or T(2)-type paramagnetic agents are used for labeling molecular/cellular events.     

Determining the relaxation polarization parameters in dielectrics with high electrical conductivity

In dielectrics with high steady leakage of conductivity, the frequency–temperature dependences of the dielectric loss tangent generally allow us to determine the relaxation time and activation energy of relaxation process only when they are strong. With weak relaxation processes, there are no extrema in the frequency dependence of the dielectric loss tangent. In such cases, the parameters of the relaxation processes are initially determined from the frequency behavior of the imaginary parts of the electrical module or impedance. However, the frequency dependences of these quantities when there is electrical conduction can contain three extrema. Identifying the maxima associated with relaxation polarization therefore requires additional research.     

Dielectric relaxation,modulus behavior and thermodynamic properties in [N(CH3)3H]2ZnCl4

[N(CH₃)₃H]₂ZnCl₄ has been analyzed by X-ray powder diffraction patterns, differential scanning calorimetry and impedance spectroscopy. The [N(CH₃)₃H]₂ZnCl₄ hybrid compound is obtained by slow evaporation at room temperature and found to crystallize in the orthorhombic system with Pnma space group. Five-phase transitions at low temperature were detected by differential scanning calorimetry measurements. The analysis of Nyquist plots has revealed the contribution of three electrically active regions corresponding to the bulk mechanism, distribution of grain boundaries and electrode processes. The dielectric relaxation is described by a non-Debye model. The study of the dielectric constants ?′, ?″ and loss tangent tan (δ) with frequency exhibits a distribution of relaxation times. The complex modulus plots have confirmed the presence of grains and grain boundaries as well as a non-Debye type of relaxation in the material. Thermodynamic parameters such as the free energy for dipole relaxation ΔF, the enthalpy ΔH and the change in entropy ΔS have been determined with the help of the Eyring theory.     

Proton spin relaxation in 2-chloroacrylontirile by double resonance

Nuclear magnetic double resonance experiments were performed on the strongly coupled two-proton system (AB) in 2-chloroacrylontirile to study the spin relaxation processes. The single resonance parameters of the AB spectrum are (operating frequency 100 MHz): |vA - vB|=9.85±0.1 Hz and J _AB=2.8±0.1 Hz. Frequency-sweep double resonance spectra were obtained by irradiating each of the four transitions at different strengths of irradiation in the range 0.015 Hz to 2.35 Hz. These spectra were analysed by using the ‘Bloch approximation’ in the rotating frame for the ‘high’ irradiation strengths and the ‘simple line’ approximation for the ‘low’ irradiation strengths. The analysis showed that the proton relaxation in this molecule can be described by interaction with isotropic random fields of nearly equal strengths at the two nuclei with no appreciable correlation between them. Internal dipole-dipole interaction is not a significant mechanism (at room temperature). It is shown that for analysing ‘low’ irradiation spectra the choice of certain functions of intensity changes would lead to a marked distinction between the different relaxation mechanisms.     

Dielectric relaxation and AC conduction of an AgTlSe2 semiconductor in the solid and liquid states

Measurements of the dielectric properties of AgTlSe₂ in the solid and liquid states were carried out in a wide range of frequencies and temperatures. The material displayed dielectric dispersion, and a loss peak was observed. Cole-Cole diagrams have been used to determine the distribution parameter (a) and the molecular relaxation time (). The process of dielectric relaxation (loss) and ac conduction was attributed to the correlated barrier hopping model suggested by Elliott for amorphous solids, where two carriers simultaneously hop over a barrier between charged defectD ⁺ andD ^– states.     

Viscoelastic characterization of compacted pharmaceutical excipient materials by analysis of frequency-dependent mechanical relaxation processes

A newly developed method for determining the frequency-dependent complex Young's modulus was employed to analyze the mechanical response of compacted microcrystalline cellulose, sorbitol, ethyl cellulose and starch for frequencies up to 20 kHz. A Debye-like relaxation was observed in all the studied pharmaceutical excipient materials and a comparison with corresponding dielectric spectroscopy data was made. The location in frequency of the relaxation peak was shown to correlate to the measured tensile strength of the tablets, and the relaxation was interpreted as the vibrational response of the interparticle hydrogen and van der Waals bindings in the tablets. Further, the measured relaxation strength, holding information about the energy loss involved in the relaxation processes, showed that the weakest material in terms of tensile strength, starch, is the material among the four tested ones that is able to absorb the most energy within its structure when exposed to external perturbations inducing vibrations in the studied frequency range. The results indicate that mechanical relaxation analysis performed over relatively broad frequency ranges should be useful for predicting material properties of importance for the functionality of a material in applications such as, e.g., drug delivery, drug storage and handling, and also for clarifying the origin of hitherto unexplained molecular processes.     

Transverse relaxation mechanisms in articular cartilage

Relaxation rates in the rotating frame (R1rho) and spin-spin relaxation rates (R2) were measured in articular cartilage at various orientations of cartilage layer to the static magnetic field (B0), at various spin locking field strengths and at two different static magnetic field strengths. It was found that R1rho in the deep radial zone depended on the orientation of specimens in the magnet and decreased with increasing the spin locking field strength. In contrast, R1rho values in the transitional zone were nearly independent of the specimen orientation and the spin locking field strength. Measurements of the same specimens at 2.95 and 7.05 T showed an increase of R1rho and most R2 values with increasing B0. The inverse B0 dependence of some R2 values was probably due to a multicomponent character of the transverse magnetization decay. The experiments revealed that the dominant T1rho and T2 relaxation mechanism at B0 < or = 3 T is a dipolar interaction due to slow anisotropic motion of water molecules in the collagen matrix. On average, the contribution of scalar relaxation due to rapid proton exchange in femoral head cartilage at 2.95 T is about 6% or less of the total R1rho at the spin locking field of 1000 Hz.     

Determination of the electron relaxation rates in paramagnetic metal complexes: applicability of available NMR methods

Four different approaches for determining the electron relaxation rates in paramagnetic metallo-proteins are investigated, using a paramagnetic Ni2+ complex of a protein as an example. All four approaches rely on the determination of the longitudinal paramagnetic relaxation enhancements, R1p, of the 1H nuclei and the backbone 15N nuclei. Three of the methods utilize the field dependence of the R1p rates. It is found that the applicability of each of these methods depends on whether the fast-motion condition, omegaS2tau2<1, applies to the electron relaxation, omegaS being the Larmor frequency of the electron spin S and tau the correlation time of the electron relaxation. If the fast-motion condition is fulfilled, the electron relaxation rate can be obtained from the ratio of the R1p rates of one or more protons at two magnetic field strengths (method A). On the other hand, if the fast-motion condition does not apply, more elaborate methods must be used that, in general, require a determination of the R1p rates over a larger range of magnetic field strengths (method C). However, in the case of paramagnetic metal ions with relatively slow electron relaxation rates only two magnetic field strengths suffice, if the R1p rates of a hetero nucleus are included in the analysis (method B). In the fourth method (method D), the electron relaxation is estimated as a parameter in a structure calculation, using distance constraints derived from proton R1p rates at only one magnetic field strength. In general, only methods B and C give unambiguous electron relaxation rates.     

环氧树脂高温分子链松弛与玻璃化转变特性

环氧树脂是电力设备中广泛应用的一种绝缘材料, 其介电性能受到分子链运动特性的影响. 本文制备了直径为50 mm、厚度为1 mm的环氧树脂试样, 采用差示扫描量热仪和宽频介电谱仪测试了环氧树脂的玻璃化转变温度和介电特性. 实验结果表明, 环氧树脂的玻璃化转变温度为105 ℃, 在玻璃化转变温度以上, 高频段出现了由分子链段运动造成的松弛过程, 低频段出现了由载流子在材料中迁移造成的直流电导过程. 发现环氧树脂不同尺寸分子链段的松弛时间不同, 其松弛时间分布较宽, 计算得到了分子链段在不同温度下的松弛时间分布特性. 分子链松弛峰频率和直流电导随温度的变化关系服从Vogel-Tammann-Fulcher公式. 拟合实验结果得到分子链松弛峰频率和直流电导的Vogel温度和强度系数. 由Vogel温度计算得到了与差示扫描量热测试结果一致的玻璃化转变温度, 约为102 ℃. 结果表明玻璃化转变温度以上环氧树脂的自由体积增大, 分子链段有足够的空间来响应外电场从而产生分子链松弛极化, 载流子有足够的能量在材料中迁移形成电导.     

Ionic conduction mechanism and relaxation studies of NaNbAlP<Subscript>3</Subscript>O<Subscript>12</Subscript> compound

The Na superionic conductor (NASICON) NaNbAlP₃O₁₂ compound was prepared by the conventional solid-state reaction method. The formation of single-phase material was confirmed by X-ray diffraction studies, and it was found to be a hexagonal phase at room temperature. The electrical conductivity was measured in the frequency range from 200 Hz to 5 MHz and temperatures between 573 and 773 K using impedance spectroscopy technique. The obtained results were analyzed by fitting the experimental data to the equivalent circuit model. The analysis of Nyquist plots has revealed the contribution of three electrically active regions corresponding to the bulk mechanism, distribution of grain boundaries, and electrode processes. Besides, the frequency dependence of the conductivity is interpreted in terms of Jonscher’s law. Temperature dependence of the power law exponent s strongly suggests that the non-overlapping small polaron tunneling (NSPT) model is the dominant transport process. The variation of the imaginary part of the complex modulus as a function of angular frequency at several temperatures shows a double relaxation peak suggesting the presence of grains and grain boundaries in the sample. An analysis of the dielectric constants ε″ and loss tangent tan (δ) with frequency shows a distribution of relaxation times.     

Spectral estimation of NMR relaxation

In this paper, spectral estimation of NMR relaxation is constructed as an extension of Fourier Transform (FT) theory as it is practiced in NMR or MRI, where multidimensional FT theory is used. nD NMR strives to separate overlapping resonances, so the treatment given here deals primarily with monoexponential decay. In the domain of real error, it is shown how optimal estimation based on prior knowledge can be derived. Assuming small Gaussian error, the estimation variance and bias are derived. Minimum bias and minimum variance are shown to be contradictory experimental design objectives. The analytical continuation of spectral estimation is constructed in an optimal manner. An important property of spectral estimation is that it is phase invariant. Hence, hypercomplex data storage is unnecessary. It is shown that, under reasonable assumptions, spectral estimation is unbiased in the context of complex error and its variance is reduced because the modulus of the whole signal is used. Because of phase invariance, the labor of phasing and any error due to imperfect phase can be avoided. A comparison of spectral estimation with nonlinear least squares (NLS) estimation is made analytically and with numerical examples. Compared to conventional sampling for NLS estimation, spectral estimation would typically provide estimation values of comparable precision in one-quarter to one-tenth of the spectrometer time when S/N is high. When S/N is low, the time saved can be used for signal averaging at the sampled points to give better precision. NLS typically provides one estimate at a time, whereas spectral estimation is inherently parallel. The frequency dimensions of conventional nD FT NMR may be denoted D₁, D₂, etc. As an extension of nD FT NMR, one can view spectral estimation of NMR relaxation as an extension into the zeroth dimension. In nD NMR, the information content of a spectrum can be extracted as a set of n-tuples (ω₁, … ω_n), corresponding to the peak maxima. Spectral estimation of NMR relaxation allows this information content to be extended to a set of (n + 1)-tuples (λ, ω₁, … ω_n), where λ is the relaxation rate.     

Glass transitions and dynamics in thin polymer films: dielectric relaxation of thin films of polystyrene

The glass transition temperature T(g) and the temperature T(alpha) corresponding to the peak in the dielectric loss due to the alpha process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in T(g) was observed with decreasing film thickness, while T(alpha) was found to remain almost constant for d>d(c) and to decrease drastically with decreasing d for d相似文献   

Influence of the moment of inertia of the pendulum on the internal friction (loss tangent) measured by free decay

Summary The internal friction (loss tangent) of solids is normally measured, as a function of temperature, with a torsion pendulum operating in free decay. Curves of the internal friction and the oscillation frequency, against temperature, are obtained at various moments of inertia, to extract the parameters characteristic of the relaxation process (relaxation time and strength). In all these experiments only the temperature is considered as an independent variable and the moment of inertia of the pendulum is mainly used to shift the internal friction peaks in the temperature scale. It is pointed out in the paper that the moment of inertia is also an independent variable which can be used to determine, with high accuracy, if the measured peak is of the Debye type or not. A new torsion pendulum, with continuously variable moment of inertia is presented, which allows measurements of the partial derivative of the internal friction and the oscillation frequency with respect to the moment of inertia, at constant temperature. Finally, some measurements of the Snoek relaxation in Nb-O alloys are presented, to show the applicability of the concepts developed in the paper. The authors of this paper have agreed to not receive the proofs for correction.     

Determination of the Maier-Saupe strength parameter from dielectric relaxation experiments: a molecular dynamics simulation study

Molecular dynamics simulations have been performed to investigate the rotational motion in the nematic and isotropic phases of a model mesogenic system in which the interactions between the molecules are represented by the Gay-Berne potential. First-rank end-over-end rotational relaxation times, analogous to those measured using dielectric relaxation spectroscopy for real mesogens with a longitudinal electric dipole, have been determined as a function of temperature and density. The relaxation times at temperatures throughout the nematic region are found to be larger than the values extrapolated from the isotropic phase to the same temperature. The simulation results are compared with the extended Debye theory for dielectric relaxation in the nematic phase. This relates the reduction in the relaxation rate to the retardation factor which depends on the Maier-Saupe strength parameter, and in turn is defined uniquely by the second-rank orientational order parameter. The simulations indicate that the retardation factor at constant strength parameter is density dependent, a feature neglected in the relaxation theory. We compare the simulation results where possible with experiment.     

Cross correlations in the longitudinal relaxation of strongly coupled spins

A generalized set of magnetization modes for quantifying cross-correlation contributions to longitudinal relaxation in strongly coupled spin systems is described in this paper. Such a set of modes (called longitudinal multiple-quantum modes) is used to unravel cross-correlation information in strongly coupled systems, where the strength of the J coupling tends to obscure such effects. The applicability of such methods is demonstrated for a small molecule which exhibits some strong coupling effects even at high magnetic field strengths. The contribution of "remote" cross correlations to the longitudinal relaxation of strongly coupled spins is detailed. Copyright 2000 Academic Press.     

Phenomenological theory of structural relaxation based on a thermorheologically complex relaxation time distribution

The aim of this work is to explore the consequences on the kinetics of structural relaxation of considering a glass-forming system to consist of a series of small but macroscopic relaxing regions that evolve independently from each other towards equilibrium in the glassy state. The result of this assumption is a thermorheologically complex model. In this approach each relaxing zone has been assumed to follow the Scherer-Hodge model for structural relaxation (with the small modification of taking a linear dependence of configurational heat capacity with temperature). The model thus developed contains four fitting parameters. A least-squares search routine has been used to find the set of model parameters that fit simultaneously four DSC thermograms in PVAc after different thermal histories. The computersimulated curves are compared with those obtained with Scherer-Hodge model and the model proposed by Gómez and Monleón. The evolution of the relaxation times during cooling or heating scans and also during isothermal annealing below the glass transition has been analysed. It has been shown that the relaxation times distribution narrows in the glassy state with respect to equilibrium. Isothermal annealing causes this distribution to broaden during the process to finally attain in equilibrium the shape defined at temperatures above T _g .