Investigation of MWS polarization and dc conductivity in polyamide 610 using dielectric relaxation spectroscopy

Dielectric relaxation spectroscopy technique was employed to study the Maxwell–Wagner–Sillars (MWS) polarization and dc conductivity in polyamide 610. The experimental dielectric data were analyzed within the formalisms of complex permittivity and electric modulus. The results were discussed in terms of ac conductivity, MWS polarization, electrode polarization and dc conductivity. In the frequency spectra of polyamide 610, charge carriers movement resulted in high values of the dielectric permittivity. The results revealed that the motion of the polymer chains governs the charge carrier transport. Two different mechanisms for charge carrier movement showed a transition temperature located between 110 and 120 °C. The change of charge carrier movement mechanisms was resulted from the onset of the polymeric chains in the interphase between amorphous and crystalline phases.     

Variational formula for the relaxation time in the Boltzmann equation

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the Boltzmann equation, which allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility for a one-dimensional (1D) tight-binding band indicate that our analysis typically provides a better approximation than the standard RTA.     

The influence of storage time on the temperature dependence of the dc electrical conductivity of horn keratin

The direct current electrical conductivity of horn keratin was measured as a function of temperature, in the temperature range 290-480 K, with a constant heating rate, for samples stored for periods of 2-3 weeks and 5 months. The activation energy of charge conducting process was calculated. The longer storage time reduced the water content, and the electrical conductivity, but increased the activation energy at 290-320 K.     

Ac and dc electrical conductivity of polynuclear metal cluster compounds

Ac and dc electrical conductivity data are presented for two polynuclear metal cluster compounds Au₅₅(PPh)₃)₁₂Cl₆ and Pd₅₆₁Phen₃₆O₂₀₀. The temperature dependence of the low field dc conductivity increases with electrical field, the rate of increase becoming stronger with decreasing temperature. These results are compared with data for granular metal systems, and a close correspondence is observed. The conductivity is found to increase with frequency in analogy to what is observed in amorphous systems. A scaling law for low frequencies that has been recently proposed is shown to describe the data quite well.     

Mechanism of dc electrical conductivity in poly(vinyl chloride)

Dc conductivity measurements were performed as a function of temperature on unplasticized poly(vinyl chloride) and on PVC plasticized with various amounts of dioctylphthalate. The conductivity curves consist of two or three straight-line segments denoted I, II, and III with increasing of temperature. The intersection of segments I and II occurs at the glass-transition temperature T_g. The slope in region I is independent of the DOP concentration, while the slope in region II decreases slowly with an increase in the amount of DOP. No dependence of the conductivity on the molecular weight was found. From the conductivity curves, activation energies were evaluated below and above T_g. These satisfactorily coincide with those determined by dielectric loss or by electrical transient phenomena. A dc conduction mechanism is proposed based on electronic hopping favored by the micro-Brownian motions responsible for dielectric losses. These motions involve smaller chain lengths below than above T_g. The experimental results are discussed and interpreted in terms of the proposed mechanism.     

The effect of the linear charge density of carrageenan on the ion binding investigated by differential scanning calorimetry, dc conductivity, and kHz dielectric relaxation

The effect of the linear charge density of natural polyelectrolyte, carrageenan, on the ion binding to carrageenan molecules in relation to the gelation was investigated by using the dielectric relaxation spectroscopy, dc conductivity, optical rotation, and differential scanning calorimetry (DSC). Although carrageenan is an anionic polysaccharide, carrageenan molecules in the helix state at low temperatures can bind not only cation, such as potassium and cesium, but also anion, such as iodide. The dc conductivity steeply decreases just below the coil–helix transition temperature, which indicates the binding of ion to the carrageenan molecules in the helix state due to the increase of the linear charge density compared with that in the coil state. The addition of NaI promotes the helix formation, and prevents from aggregation of helices, which was suggested by the results of the dynamic shear modulus and the DSC, and resulted in an increase of the relaxation amplitude of the lowest frequency relaxation (kHz) attributed to the fluctuation of the tightly bound counter ions along the high charge density region (helix). It is concluded that binding of iodide induces (1) the increase in the amount of tightly bound counterions to carrageenan molecules and (2) the formation of non-aggregated helix.     

Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a gamma distribution or rational function approximation to its Laplace transform.     

Electrical conductivity and relaxation in mixed alkali tellurite glasses

The authors have reported the electrical conductivity and the conductivity relaxation in mixed alkali tellurite glasses of compositions of 70TeO2-xNa2O-(30-x)Li2O in the frequency range from 10 Hz to 2 MHz and in the temperature range from room temperature to just below the glass transition temperature. They have analyzed the relaxation data in the framework of different models. They have observed the mixed alkali effect in the dc and ac conductivities, the crossover frequency, and the conductivity relaxation frequency as well as in their respective activation energies in these glasses. They have also observed the mixed alkali effect in the decoupling index. The scaling property of the modulus spectra of these mixed alkali glasses shows that the conductivity relaxation in the mixed alkali tellurite glasses is independent of temperature but depends on the glass compositions.     

Relationship between the nonexponentiality of relaxation and relaxation time in the problem of glass transition

By analyzing the experimental data for various glass-forming liquids and polymers, we find that the nonexponentiality, beta, and the relaxation time, tau, are commonly related: log(tau) is an approximately linear function of 1/beta, followed in most cases by a crossover to a higher linear slope. We rationalize this relationship in the recently developed elastic approach to the glass transition. The key to the observed common relationship between beta and tau is that the two quantities are governed by the same parameter, the liquid elasticity length, d el. The increase of d el on lowering temperature increases tau and decreases beta, resulting in the observed common relationship between beta and tau. In this picture, we also discuss the crossovers of beta and tau at low temperature.     

High-temperature conductivity relaxation in undoped CdS and CdSe single crystals

The high-temperature conductivity (HTC) relaxation in CdS and CdSe single crystals, caused by a steep change of cadmium vapor pressure P_Cd, was measured. For obtaining a steep change of P_Cd improved van Doorn equipment was used. Conductivity measurements were carried out using the Van der Pauw method. It was shown that the Cd diffusion from gaseous phase into CdS and CdSe platelets leads to a conductivity time-dependence function σ(t) in the form of a sum of decreasing exponents, indicating that the rate of HTC relaxation is limited by the chemical diffusion of cadmium. A correlation between chemical and tracer-diffusion coefficients was found. Values of activation energies and preexponential factors for both types of diffusion were determined. The results are discussed using a model for transformation of Cd^··_i into V^··_S,Se previously proposed by Chern and Kröger for chemical self-diffusion in CdTe.     

Acoustic relaxation and ionic conductivity of oxyethylene aliphatic polyionenes

Polyionenes composed of oxyethylene and aliphatic hydrocarbon units were studied by differential scanning calorimetry, wide-and small-angle X-ray scattering, and dielectric spectroscopy. These polymers are characterized by the variation of T _g with the concentration of ionic centers. Polyionenes with short ethylene oxide segments are amorphous; however, as the average number of monomer units in the oxyethylene segments increases to 20, a crystalline structure typical of poly(ethylene oxide) is formed. Oxyethylene-aliphatic polyionenes are microphase-separated systems. Polyionenes from this series are characterized by a high ionic conductivity, which increases with an increase in the concentration of ionic sites—the conductivity at room temperature is 10^?5–10^?4 Ω^?1 cm^?1. By means of acoustic spectroscopy, it was found that the isotherms of the ultrasound absorption (frequency domain) and ultrasound speed had two dispersion regions. The mechanism of the dispersions was associated with the softening of the quasi-lattice produced by cationic sites and with the motion of chain segments connecting these sites, The speed of sound in polyionene is abnormally high (1800–2100 m/s) for polymers, a result which is due to a high level of intermolecular interactions.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

dc Proton conductivity at low‐frequency in Nafion conductivity spectrum probed by time‐resolved SAXS measurements and impedance spectroscopy

The electric transport properties of Nafion membranes are investigated by impedance spectroscopy (IS) and correlated with small angle X‐ray scattering (SAXS). Detailed IS measurements in a wide range of temperature and frequencies (f) allowed separating contributions from different charge carriers in Nafion. At controlled relative humidity and temperature, Nafion IS spectrum exhibits at T > 160 °C two distinct frequency‐independent conductivities occurring at high f ～ 10⁶ Hz and low f < 10^?2 Hz. Such IS measurements were combined with time‐dependent SAXS measurements under applied dc electric potential, which provided compelling evidence that the low‐f dc conductivity is related to the motion of protons via ion‐hopping in hydrated Nafion membranes. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 822–828     

Dielectric relaxation time of polymers

The temperature dependence of the dielectric relaxation time of amorphous polymers can be described quite satisfactorily by an expression derived from the theory of the relaxation time for local conformational transitions in a polymer chain. This theory was recently developed using the Kramers theory of the rate constant together with the free-volume theory.     

Nonlinear relaxation patterns in the Cahn-Hilliard equation: an exact solution

We consider the 1-D Cahn-Hilliard equation with the order parameter v and derive an equation for a modified order parameter g such that g'=v'. The new equation allows for separation of variables. This yields exact solutions for v expressed in terms of generalized hypergeometric functions. These solutions have an infinite gradient at their zeros and the first three derivatives of zero at their extrema. The amplitude of these patterns decreases as the inverse square root of time. It is suggested that the phenomenon of compartmentalization of evolving structures typically observed in evolutionary models of the Cahn-Hilliard type is a manifestation of relaxation patterns similar to those derived in this paper.     

A new equation for the thermal conductivity of organic compounds

This work presents a wide literature survey of the available data of the experimental thermal conductivity data of organic liquids. The experimental data were collected for 136 compounds belonging to the following families: refrigerants, alkanes, alkenes, aromatics, cycloalkanes, cycloalkenes, ethers, esters, ketones, carboxylic acids, and alcohols. The experimental data were regressed with the most reliable semi-empirical correlating methods existing in the literature and a reliable set of 4,584 experimental data was finally selected. The influence of several physical parameters on the thermal conductivity calculation is discussed and a new equation to represent the thermal conductivity of organic liquids at atmospheric pressure for temperatures below normal boiling point and at saturation for temperatures above the normal boiling point is presented. To minimize the deviation between the predictions and the experimental data and to find the optimal coefficients for the proposed equation, a statistical analysis was performed. The resulting equation is simple and is able to predict the thermal conductivities with low deviations for the major part of the collected data for the studied families.     

Limitations of the relaxation time approach to desorptton

Calculating all one- and two-phonon contributions in fourth order to the isothermal desorption time, the validity of the relaxation time approach, and the adequacy of second-order perturbation theory to localized physisorption kinetics are examined. Explicit criteria are tested in numerical results.     

Structure-dependent band dispersion in epitaxial anthracene films

The intermolecular band dispersion related to the highest occupied molecular orbital of epitaxial anthracene multilayer films on single-crystalline Bi(0001) has been measured using angle-resolved ultraviolet photoelectron spectroscopy. By comparing the dispersion to that of anthracene multilayers on Cu(110) [F. Bussolotti, Y. Yamada-Takamura, and R. Friedlein, Phys. Rev. B 80, 153402 (2009)], it is shown how the transfer integrals and the difference in on-site energies depend on lattice parameters and how this, in turn, affects the band curvature along high-symmetry directions.