Relaxation Distribution Function Research Articles

Reinvestigation of conducting properties of Ca-doped barium titanate

Relaxation processes of Ba1−xCaxTiO3 ceramics with x = 0.05, 0.10 and 0.23 Ca contents were studied by combining the dielectric modulus and complex impedance experiments. Use of both methods permits an exploration of relaxation processes in both time and frequency domains, including relaxation distribution function at low and high frequency relaxation regions (grain and grain boundary). From an analysis using the complex impedance formalism, the predominant time distribution relaxation function turns out to be a Cole-Cole type, whereas from the dielectric modulus formalism it is described by non-Debye relaxation functions. While activation energies derived from the dielectric modulus formalism are characteristic of doubly-ionized oxygen vacancies (0.85–1.00 eV), they are from the complex impedance approach expressed as a typical electronic conduction (1.2–1.5 eV). It was identified that the impedance formalism describes well the relaxation in the low frequency regime with similar activation energy derived from the Jonscher power law (1.1–1.4 eV). The present study highlights the potential of using both impedance and dielectric modulus formalisms to identify and quantify non-Debye relaxation process and conducting properties in mixed electronic-ionic conductors.

A Novel Approach to Estimate Electrothermal Aging of Epoxy–Alumina Nanocomposites Using Dielectric Relaxation Current Analysis

In this article, an advanced technique is applied to estimate the aging state of epoxy–alumina nanocomposite insulation. For this purpose, several epoxy–alumina nanocomposite samples are prepared in the laboratory. Samples are undergone into artificial electrothermal aging conditioning up to duration of 600 h. After each 100-h instant, the relaxation current is measured under 1-kV/mm dc stress through the developed experimental setup in the laboratory. From the experimentally measured current data, relaxation frequency distribution (RFD) function of the test samples is computed. Based on the relaxation distribution function, two aging sensitive parameters are evaluated. In order to correlate these two aging sensitive parameters with the aging state of insulation, two empirical relationships are proposed based on the experimental investigation. The effectiveness of these two empirical relationships is validated with the laboratory prepared epoxy nanocomposites (EPNCs) insulation having a definite aging state. The experimental investigation shows that the proposed method can effectively be applied for estimating the aging state of nanocomposites insulation used in real-life high-voltage equipment.

Molecular dynamics and composition of crude oil by low-field nuclear magnetic resonance.

Nuclear magnetic resonance (NMR) techniques are widely used to identify pure substances and probe protein dynamics. Oil is a complex mixture composed of hydrocarbons, which have a wide range of molecular size distribution. Previous work show that empirical correlations of relaxation times and diffusion coefficients were found for simple alkane mixtures, and also the shape of the relaxation and diffusion distribution functions are related to the composition of the fluids. The 2D NMR is a promising qualitative evaluation method for oil composition. But uncertainty in the interpretation of crude oil indicated further study was required. In this research, the effect of each composition on relaxation distribution functions is analyzed in detail. We also suggest a new method for prediction of the rotational correlation time distribution of crude oil molecules using low field NMR (LF-NMR) relaxation time distributions. A set of down-hole NMR fluid analysis system is independently designed and developed for fluid measurement. We illustrate this with relaxation-relaxation correlation experiments and rotational correlation time distributions on a series of hydrocarbon mixtures that employ our laboratory-designed downhole NMR fluid analyzer. The LF-NMR is a useful tool for detecting oil composition and monitoring oil property changes. Copyright © 2016 John Wiley & Sons, Ltd.

One- and two-dimensional spin correlation of complex fluids and the relation to fluid composition

Many natural fluids, including crude oils, are complex mixtures of molecules with a broad range of sizes and chemical properties. In such systems, the molecular dynamics is complex and the relaxation and diffusion behavior cannot be described by a single relaxation time or diffusion coefficient. Nevertheless, low field NMR relaxation and diffusion measurements have become powerful tools for the study of such fluids. The complexity can be overcome by analyzing the measurements in terms of one- and two-dimensional distribution functions. The one-dimensional relaxation and diffusion distribution functions are directly related to the composition of the fluids. We also show that from the analysis of the shape of the relaxation and diffusion decay, it is possible to predict the temperature dependence of viscosity. Two-dimensional distribution functions probe further aspects of the molecular dynamics. The correlation between T1 and T2 relaxation behavior can be used to detect the presence of slow motion and to probe the aggregation of molecules into supermolecular structures. Diffusion–relaxation distribution functions give information about the chemical composition of the fluid. Beaucoup de fluides naturels, en particulier les huiles lourdes, sont des mélanges complexes de molécules possédant une large distribution de tailles et de propriétés chimiques. Dans ces systèmes, la dynamique des molécules est complexe et le comportement de relaxation et de diffusion ne peut pas se décrire par un simple temps de relaxation ou coefficient de diffusion. Néanmoins, la relaxation RMN à bas champ et les mesures de diffusion sont devenus des outils puissants pour étudier de tels fluides. On peut contourner la complexité en analysant les mesures en termes de fonctions de distributions à une et deux dimensions. Les fonctions de distribution de relaxation et de diffusion à une dimension sont directement reliées à la composition des fluides. On montre également que l'analyse de la forme des déclins de relaxation et de diffusion permet de prédire la dépendance en température de la viscosité. Les fonctions de distribution à deux dimensions permettent de suivre d'autres aspects de la dynamique moléculaire. Les corrélations entre les comportements de relaxation T1 et T2 peuvent être utilisés pour détecter des mouvements lents et mettre en évidence l'agrégation des molécules en structures supramoléculaires. Les corrélations entre les fonctions de distribution de diffusion et de relaxation donnent enfin des informations sur la composition chimique des fluides étudiés.

Modeling of the dynamic mechanical properties of the coagent reinforced row hydrogenated poly(butadiene-co-acrylonitrile) (HNBR) and the morphology of coagent nanodispersions in HNBR matrix

Coagents are typically used for crosslinking of synthetic elastomers and are ordinarily used to achieve excellent properties of the crosslinked products. Dynamic mechanical properties of two different types of reinforcing coagents and not cured hydrogenated poly(butadiene-co-acrylonitrile) compounds were investigated and modeled. The function of zinc dimethacrylate (ZDMA) inverted with loading in the mixtures from filler-like (up to 13 phr) into plasticizer-like behavior (over 13 phr). Nevertheless, trimethylolpropane trimethacrylate (TMPTMA) as a reinforcing substrate exhibited a reinforcing effect during the glass transition and plateau region throughout the investigated loading range. Morphology evolved during processing changed in parallel with the results obtained from dynamical mechanical analysis (DMA) of the blends. Both in the case of ZDMA and TMPTMA micro- and nano-phases evolved during mixing. The volume fractions of the particles under 100 nm in ZDMA and TMPTMA blends ranged from 16 to 89 %. Dynamic mechanical properties were modeled using a continuous relaxation distribution function, Williams-Landel-Ferry (WLF) equation and the modified Guth-Gold equation. The measured dynamic mechanical properties of not cured compounded elastomers containing coagents/fillers are of a great importance in connection with processing operations, which could be designed with aid of the proposed model.

Influence of morphology on the dynamic mechanical properties of hydrogenated acrylonitrile butadiene elastomer/coagent nanodispersions

AbstractCoagents are vinyl monomers that react with free radicals formed by peroxide dissociation and are either grafted to elastomer chains or homopolymerized within a segregated phase to form a crosslinked network. The initial phase distribution within the elastomer matrix is of great importance for the final user properties of a composite material. In this study, the morphology of blends of each of three different coagents, that is, zinc dimethacrylate (ZDMA), N,N′‐m‐phenylene dimaleimide (HVA‐2), and trimethylolpropane trimethacrylate (TMPTMA) on a reinforcing substrate with dicumyl peroxide and hydrogenated acrylonitrile butadiene elastomer after processing was investigated with scanning electron microscopy. The morphology that evolved during processing was then compared to the results obtained from dynamic mechanical analysis (DMA) of the blends. Dynamic mechanical properties were modeled with a continuous relaxation distribution function, the Williams–Landel–Ferry equation, and the modified Guth–Gold equation. In the case of ZDMA and TMPTMA, a microphase and a nanophase evolved during processing, whereas the HVA‐2 phase in the blends remained well segregated. The volume fraction of the particles under 100 nm in ZDMA and TMPTMA blends ranged from 79 to 89%. The DMA results revealed the reinforcing effect of ZDMA and TMPTMA during the glass‐transition and in the plateau region, whereas HVA‐2 exhibited plasticizer‐like behavior. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

NMR Characterization of complex fluids by diffusion–relaxation distribution functions

NMR Characterization of complex fluids by diffusion–relaxation distribution functions

Quantitative characterization of food products by two-dimensional D– [formula omitted] and [formula omitted]– [formula omitted] distribution functions in a static gradient

We present new NMR techniques to characterize food products that are based on the measurement of two-dimensional diffusion– T 2 relaxation and T 1 – T 2 relaxation distribution functions. These measurements can be performed in magnets of modest strength and low homogeneity and do not require pulsed gradients. As an illustration, we present measurements on a range of dairy products that include milks, yogurt, cream, and cheeses. The two-dimensional distribution functions generally exhibit two distinct components that correspond to the aqueous phase and the liquid fat content. The aqueous phase exhibits a relatively sharp peak, characterized by a large T 1 / T 2 ratio of around 4. The diffusion coefficient and relaxation times are reduced from the values for bulk water by an amount that is sample specific. The fat signal has a similar signature in all samples. It is characterized by a wide T 2 distribution and a diffusion coefficient of 10 −11 m 2 / s for a diffusion time of 40 ms, determined by bounded diffusion in the fat globules of 3 μm diameter.

Molecular weight effects on the glass transition of gelatin/cosolute mixtures.

The structural properties of four gelatin fractions in mixture with sucrose and glucose syrup have been investigated extensively using small deformation dynamic oscillation. The total level of solids was 80%, the number average molecular weight of the protein ranged from 29.2 to 68 kD, and the temperatures were between 60 and -60 degrees C. Remarkably, the nature of the time and temperature dependence on the viscoelastic functions of all samples could be reduced to master curves using horizontal shift factors. The construction of master curves indicates a common mechanism of structure formation, which, in accordance with the synthetic polymer literature, comprises the rubbery zone, glass transition region, and glassy state. Application of Ferry's free-volume formalism and Rouse theory suggests that there is no change in the thermodynamic state of materials during vitrification, with changes in molecular weight simply introducing shifts in the time scale and temperature range of contributions to viscoelasticity. The thermorheological simplicity allowed development of the concept of "rheological" Tg. This was defined as the point between free-volume phenomena of the polymeric backbone occurring in the glass transition region and an energetic barrier to rotation required for local chain rearrangements in the glassy state. Mechanical relaxation and retardation distribution functions were calculated, thus obtaining values for the effective friction coefficient per monomer unit of the protein. It appears that the local friction coefficient is governed by a linear relationship between fractional free volume and the decreasing molecular weight of the protein, which introduces additional voids due to molecular ends.

Quantitative Measurement of Two-Dimensional Distribution Functions of Diffusion and Relaxation in Grossly Inhomogeneous Fields

We demonstrate the quantitative extraction of multidimensional distribution functions in the presence of grossly inhomogeneous fields. Examples are shown for diffusion— T 2 distribution functions and T 1− T 2 distribution functions. The pulse sequences consist of an initial editing sequence followed by a long series of nominal 180° pulses. They are designed such that the kernels describing the relationships between the distribution functions and the measured data are separable. The required phase cycling is discussed. We analyze in detail the extra spin dynamics effects due to the strong field inhomogeneities including the effects on diffusion and relaxation. A recently developed algorithm is used to invert the data and extract stable multidimensional distribution functions in an efficient manner. We present examples for several applications of this new technique. Diffusion–relaxation distribution functions can be used for fluid identification and for the characterization of pore geometry of porous media based on the effects of restricted diffusion. We have also determined T 1− T 2 distribution functions of water saturated sedimentary rock and find excellent agreement with previous measurements performed in homogeneous fields.

Application of tikhonov regularization to dipole glass relaxation function

Relaxation distribution function g(τ) was derived from the experimental data of dielectric measurements by use of the Tikhonov regularization method of solving for the inverse solution of the integral transform defining the relaxation time distribution g(τ) in the dipole glass system undergoing the glass freezing. The distribution function g(τ) allows to calculate the average or effective relaxation time (τ). The temperature dependence of (τ) was studied in DRADP-x (x = 0.4) dipole glass and found to follow the Vogel-Fulcher law of glass freezing with the static freezing temperature T 0≃16.5K.

Segmental mobilities in an athermal diblock copolymer melt far above T g by incoherent neutron scattering

We report on incoherent elastic and quasielastic neutron scattering from a symmetric poly(isoprene-1,2 butadiene) (PIP-PVE) almost athermal diblock copolymer at different wave vectors Q in the range 0.18 to 1.8 Å−1. A fixed window temperature scan between 20 K and 300 K revealed the presence of segmental dynamics above 200 K and hence line shape analysis of the incoherent quasielastic spectra Sinc(Q,ω) was performed at high temperatures far above the single glass transition Tg(=221 K) to obtain the characteristic time scales. A two step nonexponential relaxation function was found adequate to describe consistently Sinc(Q,ω) with the faster relaxation time being comparable with the segmental relaxation time in bulk PIP at similar Q. This dynamic incompatibility may arise from dynamic heterogeneities as a consequence of composition fluctuations. The observation of a bimodal relaxation distribution function in PIP–PVE with low Tg contrast at temperatures far above the single Tg emphasizes the role of the intramolecular correlations due to chain connectivity.

Relaxation strength and distribution function of an internal friction peak

A procedure based on the mechanical properties of a modified anelastic element (MAE) has already been developed to get a functional dependence of the real and imaginary components of the dynamical modulus or compliance. The MAE is essentially a standard anelastic element except for its characteristic time, which depends on the frequency. The analysis of this dependence provides an analytical description of not only the dynamical properties but also the distribution function. In this work it is shown that the procedure can be extended to internal friction peaks, yielding not only the parameters of the distribution function but also the relaxation strength. This procedure is applied to various materials and the results are compared with a previous method proposed in the literature.

Local motions in a microphase-separated poly(styrene-b-methylphenylsiloxane) diblock copolymer melt

The segmental dynamics in the microregions of a microphase-segregated poly(styrene-b-methylphenylsiloxane) (P(S-b-MPS)) with M n =59.000 and PS fraction f PS =0.22 were selectively studied by depolarized light scattering and dielectric spectroscopy over the temperature range -20 to +110°C. About 50% of the material was found to partition in PS-rich and PMPS-rich environments with orientational dynamics very similar to that of the pure homopolymers. Below the high T g , the segemental relaxation with in the PS microregion displays a weaker temperature dependence and the relaxation distribution function becomes narrower, as compared to those of PS homopolymer

Viscoelastic behavior of polyhydroxyether

Abstract The present investigation reports the determination of viscoelastic behavior and the relaxation distribution function of polyhydroxyether (PHE) over an extended time scale by reducing the stress-strain curves to the unit strain rate followed by their shifts to a reference temperature along a line of unit slope. The polyhydroxyether was synthesized from bisphenol A and epichlorohydrin. The stress-strain measurements were carried out at different temperatures and at different strain rates using solution-cast films of PHE and the Instron tensile testing machine.

Relaxation Distribution Function of Intracellular Dielectric Zones as an Indicator of Tumorous Transition of Living Cells

The response decay data of living cells subject to electric polarization is associated with their relaxation distribution function (RDF) and can be determined using the inverse Laplace transform method. A new polynomial, involving a series of associated Laguerre polynomials, has been used as the approximating function for evaluating the RDF, with the advantage of avoiding the usual arbitrary trial values of a particular parameter in the numerical computations. Some numerical examples are given, followed by an application to cervical tissue. It is found that the average relaxation time and the peak amplitude of the RDF exhibit higher values for tumorous cells than normal cells and might be used as parameters to differentiate them and their associated tissues.

Interrelations between relaxation distribution functions and apparent activation energy of flow

Starting from both the three-dimensional diagram of viscoelastic properties in the reciprocal temperature — log frequency — space and the time-temperature interrelation via apparent activation energy of flow, the possibility of theoretical interpretation of the isochronal behaviour is demonstrated, in analogy to the isothermal one. The determinative apparent activation energy of local flow is related with the relaxation spectra over the entire range of validity of the time-temperature superposition principle. Thus a theoretical background is offered for the method recommended before for the evaluation of the apparent activation energy of flow, which is applicable to calculate both isotherm and isochrone shift factors.

Study of Optical Relaxation and Inhomogeneous Distribution Function of Impurity Organic Molecules by Site‐Selective Laser Spectroscopy

AbstractSite‐selective excitation of luminescence and hole burning in the absorption spectra are used for a study of the electronic and vibrational relaxations and inhomogeneous distribution function for coproporphyrin III molecules in solid ethanol and n‐octane matrices in the temperature range from 3.2 to 26 K. From the structural luminescence spectra obtained at the site‐selective excitation the vibrational frequencies of coproporphyrin in the ground and excited electronic states are measured. The temperature broadening of the homogeneous, purely electronic zero‐phonon line investigated by hole burning is mainly determined by the two‐phonon Raman scattering of low‐frequency phonons with the effective frequency 35 cm−1 while its residual width at 0 K results from the anharmonicity of the matrix vibrations. The pure dephasing time T obtained from the homogeneous, purely electronic zero‐phonon linewidths changes from 17.6 to 53.0 ps at T = 3.5 K to 2.8 ps at T = 25 K. The phase relaxation time T2 measured from the homogeneous linewidth of the vibronic level in the excited electronic state is equal to 2.4 ps at T = 3.5 K.

Changes in capacitance of amorphous Se:As alloy films during structural relaxation below the glass transition temperature

Reversible hysteresis behavior of capacitance and ac conductance of amorphous Se:As alloy films (alloy range 0–4% As) below the glass transition temperature (Tg) is observed when measurements are carried out at fixed frequency in the temperature scan mode over an experimental range encompassing Tg. In this measurement mode, annealing effects which follow either cycling or film formation by evaporation can be continuously monitored, via film capacitance, as the film undergoes kinetically arrested isothermal relaxation toward a quasistable state. Arsenic addition to amorphous Se alters many of its physical properties. For example, in a previous study of the same series of films, it was found that both the dielectric increment measured just above their respective Tg ’s and the widths of the associated relaxation distribution function varied significantly with composition. In the present study, dielectric and thermodynamic measurements indicate that arsenic addition to amorphous Se significantly slows the rate of structural relaxation near room temperature (?15 K below respective Tg ’s). However, it is found that the shape of the capacitance relaxation function, associated in this case with structural relaxation below Tg, is relatively insensitive to alloy composition. The changes in room temperature relaxation, reflected in capacitance measurements, can in fact be adequately accounted for, phenomenologically, solely in terms of the shift in Tg induced by arsenic alloying. It is suggested (1) that dielectric relaxation in the melt above Tg and structural relaxation during annealing below Tg are controlled by a different set of dynamic processes or (2) progressive arsenic alloying skews the relaxation distribution function so that the very low frequency-spectral components which dominate relaxation below Tg remain unaffected.

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).