Characteristic Relaxation Time Research Articles

Inelastic behavior of potassium hydrogen phthalate single crystals under ultrasonic deformation

The effect of ultrasonic deformation on the inelastic behavior of potassium hydrogen phthalate single-crystal samples with different crystallographic orientations at frequencies of ∼105 Hz has been investigated. It has been shown that the inelastic behavior of potassium hydrogen phthalate single crystals during the ultrasonic deformation is determined not by the dislocation mechanisms. It has been found that the main mechanism responsible for energy losses of mechanical vibrations in these crystals is the mechanism of ionicrelaxation polarization. The characteristic relaxation times of this process have been determined and varied in the range from 10–8 to 10–7 s.

The Static Structure and Dynamics of Cadmium Sulfide Nanoparticles within Poly(styrene‐block‐isoprene) Diblock Copolymer Melts

The static structure and dynamic behavior of cadmium sulfide nanoparticles suspended in block copolymer matrix are investigated using transmission electron microscopy, small‐angle X‐ray scattering, and X‐ray photon correlation spectroscopy. The transmission electron microscopy study shows that cadmium sulfide nanoparticles are preferentially segregated within the polyisoprene domain of a poly(styrene‐block‐isoprene) diblock copolymer. For the dynamics study, X‐ray photon correlation spectroscopy captures the relaxation process of cadmium sulfide nanoparticles. The measured characteristic relaxation time reveals that the observed dynamics are hyperdiffusive. The characteristic velocity and corresponding activation energy, which are hallmarks of a hyperdiffusive system, are determined from the relationship between the characteristic relaxation time and the wavevector.image

Correlated barrier hopping of CuO nanoparticles

The ac conduction mechanism in copper oxide nanoparticles with 8 nm size, synthesized by a precipitation method was studied by analyzing ac conductivity in the frequency range of 50 Hz–1 MHz and in the temperature range of 373–573 K. X-ray diffraction and transmission electron microscopy (TEM) were employed for the structural and morphological characterization of CuO nanoparticles. The experimental and theoretical investigations suggested that the ac conduction mechanism in CuO nanoparticles can be successfully explained by a correlated barrier hopping model, which provided reasonable values for the maximum barrier height and characteristic relaxation time. It was also found that bipolaron hopping become prominent up to a particular temperature and beyond that single polaron hopping predominates. Physical parameters such as hopping distance and density of defect states were also calculated. Photoluminescence studies confirm the presence of a surface defect in CuO nanoparticles.

Long-distance super-exchange and quantum magnetic relaxation in a hybrid metal–organic framework**Project supported by the National Natural Science Foundation of China (Grant Nos. 11227405, 51371192, and 51371193) and the Chinese Academy of Sciences (Grant No. XDB07030200).

The hybrid metal–organic framework [(CH3)2NH2]Fe(HCOO)3 with a perovskite-like structure exhibits a variety of unusual magnetic behaviors at low temperatures. While the long-distance super-exchange through the Fe-O–CH-O–Fe exchange path leads to a canted antiferromagnetic ordering at TN ∼ 19 K, a second transition of magnetic blocking develops at TB ∼ 9 K. The stair-shaped magnetization hysteresis loops below TB resemble the behaviors of resonant quantum tunneling of magnetization in single-molecular quantum magnets. Moreover, the magnetic relaxation also exhibits several features of resonant quantum relaxation, such as the exponential law with a single characteristic relaxation time, and the nonmonotonic dependence of relaxation rate on the applied magnetic field with a much faster relaxation around the resonant fields. The origin of quantum tunneling behaviors in the [(CH3)2NH2]Fe(HCOO)3 metal–organic framework is discussed in terms of magnetic phase separation due to the modification of hydrogen bonding on the long-distance super-exchange interaction.

NMR petrophysical interpretation method of gas shale based on core NMR experiment

Abstract Nuclear magnetic resonance (NMR) characteristics provide critical information to study the storage of organic shale. Based on NMR petrophysical experiment of Haynesville Shale, the response characteristics of transverse relaxation time ( T 2 ) are analyzed. According to the shape and amplitude of T 2 distribution of shale, Haynesville Shale can be categorized into two types: continuous and discontinuous T 2 spectrums. Compared with routine density porosity, NMR porosity is generally underestimated for organic shale. Therefore, the controlling factors are investigated in detail. Through constructing the correlations of NMR porosity and clay volume, total organic carbon (TOC) content, kerogen content and pyrite volumetric concentration, the pyrite and kerogen are finally regarded as dominant factors. Subsequently, a new NMR porosity correction model is proposed. Moreover, the permeability model based on NMR bin porosity is built, and water, gas and oil saturation models are also established through building some correlations between gas saturation and NMR bin porosity. NMR experiment indicates that the kerogen and adsorbed gas are located in bound fluid part of NMR T 2 distribution, and the gas storage is dominant as absorbed gas rather than free gas. The study provides a novel petrophysical interpretation method for gas-bearing shale.

Magnetic state dependent transient lateral photovoltaic effect in patterned ferromagnetic metal-oxide-semiconductor films

We investigate the influence of an external magnetic field on the magnitude and dephasing of the transient lateral photovoltaic effect (T-LPE) in lithographically patterned Co lines of widths of a few microns grown over naturally passivated p-type Si(100). The T-LPE peak-to-peak magnitude and dephasing, measured by lock-in or through the characteristic time of laser OFF exponential relaxation, exhibit a notable influence of the magnetization direction of the ferromagnetic overlayer. We show experimentally and by numerical simulations that the T-LPE magnitude is determined by the Co anisotropic magnetoresistance. On the other hand, the magnetic field dependence of the dephasing could be described by the influence of the Lorentz force acting perpendiculary to both the Co magnetization and the photocarrier drift directions. Our findings could stimulate the development of fast position sensitive detectors with magnetically tuned magnitude and phase responses.

Time of relaxation in dusty plasma model

Dust particles in plasma may have different values of average kinetic energy for vertical and horizontal motion. The partial equilibrium of the subsystems and the relaxation processes leading to this asymmetry are under consideration. A method for the relaxation time estimation in nonideal dusty plasma is suggested. The characteristic relaxation times of vertical and horizontal motion of dust particles in gas discharge are estimated by analytical approach and by analysis of simulation results. These relaxation times for vertical and horizontal subsystems appear to be different. A single hierarchy of relaxation times is proposed.

On Cattaneo–Christov heat flux in MHD flow of Oldroyd-B fluid with homogeneous–heterogeneous reactions

This paper investigates the steady two-dimensional magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid over a stretching surface with homogeneous–heterogeneous reactions. Characteristics of relaxation time for heat flux are captured by employing new heat flux model proposed by Christov. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived. Impacts of various pertinent parameters on the velocity, temperature and concentration are discussed. Analysis of the obtained results shows that fluid relaxation and retardation time constants have reverse behavior on the velocity and concentration fields. Also temperature distribution decreases for larger values of thermal relaxation time.

Rheology of PP/PP-g-MA and PP/PP-g-AA Blends and Incidence on Orientation and Crystalline Structure of Their Cast Films

The intrinsic hydrophobic character of polypropylene limits its performance in many porous membrane applications. This can be improved by hydrophilic modification of the film surface through blending with hydrophilic polymers. For producing the precursor films and, consequently, microporous membranes with the appropriate crystalline lamellar morphology, the polypropylene chains should preserve their elongated form to serve as initial nuclei for the later development of lamellar crystals. The relaxation time of the chains is the most important factor for this stage. Commercial maleic anhydride and acrylic acid grafted polypropylenes were melt blended with a polypropylene at different weight ratios. The results showed that the modifiers lowered the crystalline orientation of the blends as compared to neat polypropylene films. The effect of the modifier on the melt relaxation spectra of the blends was investigated, and a linear relationship was found between the characteristic relaxation time of the blends and their crystalline orientation function.

Investigation of the spatial structure and developmental dynamics of near-Earth plasma perturbations under the action of powerful HF radio waves

Results of numerical simulations of the near-Earth plasma perturbations induced by powerful HF radio waves from the SURA heating facility are presented. The simulations were performed using a modified version of the SAMI2 ionospheric model for the input parameters corresponding to the series of in-situ SURA–DEMETER experiments. The spatial structure and developmental dynamics of large-scale plasma temperature and density perturbations have been investigated. The characteristic formation and relaxation times of the induced large-scale plasma perturbations at the altitudes of the Earth’s outer ionosphere have been determined.

Dynamic crossover in deeply cooled water confined in MCM-41 at 4 kbar and its relation to the liquid-liquid transition hypothesis.

With quasi-elastic neutron scattering, we study the single-particle dynamics of the water confined in a hydrophilic silica material, MCM-41, at 4 kbar. A dynamic crossover phenomenon is observed at 219 K. We compare this dynamic crossover with the one observed at ambient pressure and find that (a) above the crossover temperature, the temperature dependence of the characteristic relaxation time at ambient pressure exhibits a more evident super-Arrhenius behavior than that at 4 kbar. Especially, at temperatures below about 230 K, the relaxation time at 4 kbar is even smaller than that at ambient pressure. This feature is different from many other liquids. (b) Below the crossover temperature, the Arrhenius behavior found at ambient pressure has a larger activation energy compared to the one found at 4 kbar. We ascribe the former to the difference between the local structure of the low-density liquid (LDL) phase and that of the high-density liquid (HDL) phase, and the latter to the difference between the strength of the hydrogen bond of the LDL and that of the HDL. Therefore, we conclude that the phenomena observed in this paper are consistent with the LDL-to-HDL liquid-liquid transition hypothesis.

Nonlocal damping of helimagnets in one-dimensional interacting electron systems

We investigate the magnetization relaxation of a one-dimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the one-dimensional interacting electron system, caused by slow changes of the magnetization profile. This dissipation mechanism leads to a highly nonlocal form of magnetization damping that is strongly dependent on the electron-electron interaction. Forward scattering processes lead to a spatially constant damping kernel, while backscattering processes produce a spatially oscillating contribution. Due to the nonlocal damping, the thermal fluctuations become spatially correlated over the entire system. We estimate the characteristic magnetization relaxation times for magnetic quantum wires and nuclear helimagnets.

Prediction of melt rheological properties from GPC molecular weights

The SCLAIR® solution polymerization platform produces a wide variety of ethylene-α-olefin copolymers and polyethylene homopolymers. Commercial products exhibit density and melt index values ranging from about 0.920 to 0.962 g/cm3 and 0.3–75 g/10 min respectively. Polymer molecular weight distributions can be tailored to meet a broad selection of end-use requirements. In this study, we have used a chemometric analysis approach using The Unscrambler® software to demonstrate statistical correlations between rheological properties and fundamental structural parameters for thirty-three commercial SCLAIR polyethylenes. We demonstrate that molten rheological properties such as melt index, stress exponent, zero-shear viscosity, characteristic relaxation time, cross-over modulus and frequency show good non-linear correlations with molecular weight characteristics of SCLAIR products as determined by gel permeation chromatography (GPC). We also show that, with the use of Partial Least Squares (PLS) regression techniques, most melt rheological properties can be accurately predicted on the basis of GPC data.

Formation of 2,2′-bipyridine adlayers at Sb(111)|ionic liquid + 2,2′-bipyridine solution interface

Abstract In situ scanning tunneling microscopy (STM), cyclic voltammetry and electrochemical impedance spectroscopy methods have been applied to study the adsorption of 2,2′-bipyridine (2,2′-BP) on Sb(111) single crystal electrode surface from 1-ethyl-3-methylimidazolium tetrafluoroborate + 1% 2,2′-BP solution. Influence of the Sb(111) electrode potential on the adsorption characteristics of 2,2′-BP has been demonstrated. The in situ STM data revealed that 2,2′-BP forms highly ordered patterns on the Sb(111) single crystal electrode surface. The formed dense organic adlayer decreases the dielectrical permittivity of the interface, acting as a dielectric capacitor with significantly lower characteristic relaxation time than the pure ionic liquid system.

Investigation of Water Diffusion Mechanisms in Relation to Polymer Relaxations in Polyamides

Diffusion in semicrystalline polymers is a complex phenomenon because of the existence of specific interactions (nonpolar or polar), dynamic heterogeneities, and crystalline phases. The diffusion of water in two semicrystalline polyamides (PA6,6 and PA6,10) was investigated in order to determine the diffusion mechanisms and the influence of polymer relaxations on this process. Liquid water diffusion follows a Fickian mechanism in PA6,10 and a non-Fickian or anomalous mechanism in PA6,6. Through a quasi-equilibrium experiment in dynamic vapor sorption, it is shown that this difference results from the dependence of the diffusion coefficients on water concentration. Moreover, the influence of the polymer relaxations was assessed by broadband dielectric spectroscopy. The dielectric characteristic relaxation times of the α relaxation, associated with the glass transition, and of the β relaxation, related to more local dynamics, have been measured. A simple comparison with the time scale of diffusion suggests ...

Molecular kinetic theory of strongly nonequilibrium processes of mass, momentum, and energy transfer: Local equilibrium criteria

Consequences of the complete system of transfer equations of the properties (momentum, energy, and mass) of particles and their pairs are considered under local equilibrium conditions with regard to the Bogoliubov hierarchy of relaxation times between the first and second distribution functions (DFs) and distinctions in the characteristic relaxation times of particle momentum, energy, and mass. It is found that even under the local equilibrium condition in the Bogoliubov hierarchy of relaxation times between the first and second DFs, pair correlations are maintained between all dynamic variables (velocity, temperature, and density) whose values are proportional to the gradients of transferable properties. A criterion is introduced requiring there be no local equilibrium condition upon reaching the critical value at which the description of the transfer process becomes incorrect in classical nonequilibrium thermodynamics. External forces are considered in the equations for strongly nonequilibrium processes. Along with allowing for intermolecular potentials, it becomes possible to discuss the concept of passive forces (introduced in thermodynamics by Gibbs) from the standpoint of the kinetic theory. It is shown that use of this concept does not reflect modern representations of real processes.

Predicting permeability from the characteristic relaxation time and intrinsic formation factor of complex conductivity spectra

AbstractLow‐frequency quadrature conductivity spectra of siliclastic materials exhibit typically a characteristic relaxation time, which either corresponds to the peak frequency of the phase or the quadrature conductivity or a typical corner frequency, at which the quadrature conductivity starts to decrease rapidly toward lower frequencies. This characteristic relaxation time can be combined with the (intrinsic) formation factor and a diffusion coefficient to predict the permeability to flow of porous materials at saturation. The intrinsic formation factor can either be determined at several salinities using an electrical conductivity model or at a single salinity using a relationship between the surface and quadrature conductivities. The diffusion coefficient entering into the relationship between the permeability, the characteristic relaxation time, and the formation factor takes only two distinct values for isothermal conditions. For pure silica, the diffusion coefficient of cations, like sodium or potassium, in the Stern layer is equal to the diffusion coefficient of these ions in the bulk pore water, indicating weak sorption of these couterions. For clayey materials and clean sands and sandstones whose surface have been exposed to alumina (possibly iron), the diffusion coefficient of the cations in the Stern layer appears to be 350 times smaller than the diffusion coefficient of the same cations in the pore water. These values are consistent with the values of the ionic mobilities used to determine the amplitude of the low and high‐frequency quadrature conductivities and surface conductivity. The database used to test the model comprises a total of 202 samples. Our analysis reveals that permeability prediction with the proposed model is usually within an order of magnitude from the measured value above 0.1 mD. We also discuss the relationship between the different time constants that have been considered in previous works as characteristic relaxation time, including the mean relaxation time obtained from a Debye decomposition of the spectra and the Cole‐Cole time constant.

Numerical detection of the Gardner transition in a mean-field glass former.

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

Weakly nonlinear stability analysis of polymer fibre spinning

The extensional flow of a polymeric fluid during the fibre spinning process is studied for finite-amplitude stability behaviour. The spinning flow is assumed to be inertialess and isothermal. The nonlinear extensional rheology of the polymer is described with the help of the eXtended Pom-Pom (XXP) model, which is known to exhibit a significant strain hardening effect necessary for fibre spinning applications. The linear stability analysis predicts an instability known as draw resonance when the draw ratio, $\mathit{DR}$, defined as the ratio of the velocities at the two ends of the fibre in the air gap, exceeds a certain critical value, $\mathit{DR}_{c}$. The critical draw ratio $\mathit{DR}_{c}$ depends on the fluid elasticity represented by the Deborah number, $\mathit{De}={\it\lambda}v_{0}/L$, the ratio of the polymer relaxation time to the flow time scale, thus constructing a stability diagram in the $\mathit{DR}_{c}$–$\mathit{De}$ plane. Here, ${\it\lambda}$ is the characteristic relaxation time of the polymer, $v_{0}$ is the extrudate velocity through the die exit and $L$ is the length of the air gap for the spinning flow. In the present study, we carry out a weakly nonlinear stability analysis to examine the dynamics of the disturbance amplitude in the vicinity of the transition point. The analysis reveals the nature of the bifurcation at the transition point and constructs a finite-amplitude manifold providing insight into the draw resonance phenomena. The effect of the fluid elasticity on the nature of the bifurcation and the finite-amplitude branch is examined, and the findings are correlated to the extensional rheological behaviour of the polymer fluid. For flows at small Deborah number, the Landau constant, which captures the role of nonlinearities, is found to be negative, indicating supercritical Hopf bifurcation at the transition point. In the linearly unstable region, the equilibrium amplitude of the disturbance is estimated and shows a limit cycle behaviour. As the fluid elasticity is increased, initially the equilibrium amplitude is found to decrease below its Newtonian value, reaching the lowest value for $\mathit{De}$ when the strain hardening effect is maximum. With further increase in elasticity, the material undergoes strain softening behaviour which leads to an increase in the equilibrium amplitude of the oscillations in the fibre cross-section area, indicating a destabilizing effect of elasticity in this regime. Interestingly, at a certain high Deborah number, the bifurcation crosses over from supercritical to subcritical nature. In the subcritical regime, a threshold amplitude branch is constructed from the amplitude equation.

More accurate macro-models of solid oxide fuel cells through electrochemical and microstructural parameter estimation – Part I: Experimentation

The distributed relaxation times (DRT) method has been employed in order to deconvolute the electrochemical impedance spectroscopy (EIS) measurements carried out on a Ni-YSZ|YSZ|Pr2NiO4+δ – GDC solid oxide fuel cell (SOFC). This has enabled to shed light on the diverse physicochemical processes occurring within the aforementioned cell by individuating the characteristic relaxation times of these by means of a specifically designed experimental campaign where temperature and gas compositions in anode and cathode were varied one at a time. A comprehensive equivalent circuit model (ECM) has thus been generated based on the processes observed in the DRT spectra. This ECM has proved to be instrumental for the obtainment of parameters which describe the microstructural and electrochemical properties of the SOFC when used contemporaneously with experimental results and modelling theory (described in Part II of this work).