Characteristic Relaxation Time Research Articles

Anomalous Brownian motion of colloidal particle in a nematic environment: effect of the director fluctuations

As recently reported [Turiv T. et al., Science, 2013, Vol. 342, 1351], fluctuations in the orientation of the liquid crystal (LC) director can transfer momentum from the LC to a colloid, such that the diffusion of the colloid becomes anomalous on a short time scale. Using video microscopy and single particle tracking, we investigate random thermal motion of colloidal particles in a nematic liquid crystal for the time scales shorter than the expected time of director fluctuations. At long times, compared to the characteristic time of the nematic director relaxation we observe typical anisotropic Brownian motion with the mean square displacement (MSD) linear in time $\tau$ and inversly proportional to the effective viscosity of the nematic medium. At shorter times, however, the dynamics is markedly nonlinear with MSD growing more slowly (subdiffusion) or faster (superdiffusion) than $\tau$. These results are discussed in the context of coupling of colloidal particle's dynamics to the director fluctuation dynamics.

Relaxation and phase-transition characteristics of relaxor ferroelectric potassium lithium niobate

The electric modulus relaxations were considered to be coupled phenomena between the polarization fluctuations due to local symmetry breaking and ionic hopping through nearest neighbor sites. The Nb-rich potassium lithium niobate (K5.595Li3.125Nb11.28O30) crystals exhibited a ferroelectric diffused phase transition around the dielectric maximum temperature Tmax = 350. The electric modulus relaxations were characterized by using the Cole-Davidson distribution of the electric modulus relaxation times at frequencies ranging from 100 Hz to 1 MHz. Although the lattice constants along the a-axes and the c-axes and the tetragonal unit cell volume showed linear expansions with increasing temperature T, the axial ratio c/a decreased with increasing T at temperatures below the Burn’s temperature TB. The dielectric relaxation accompanied the high ionic conduction in the temperature range above T. The ac conductivity σ'(ω) was analyzed by using the formulae, where ωO is the crossover frequency. It was considered that a double-Arrhenius behavior of the dc conductivity σdc at temperatures around the Burn’s temperature TB was suspected of thermally activated motions in the random distribution of oxygen vacancies and lithium ions. The ac universality could result in a disordered configuration of the mobile ions, i.e., the dc conductivity at temperatures above TB. The slow relaxations of the nano-sized polar regions may contribute to the dc conductivity σdc at temperatures below TB. The characteristic relaxation time τCD showed a change in activation energy from 1.08 eV to 0.80 eV at temperatures around TB. The scaling factor increased in proportion to (TB − T) at TTB, but was almost constant at T >TB, where e'∞ is the high frequency dielectric constant and T is the temperature in Kelvin.

Single-shot T1 mapping of the corpus callosum: a rapid characterization of fiber bundle anatomy.

Using diffusion-tensor magnetic resonance imaging and fiber tractography the topographic organization of the human corpus callosum (CC) has been described to comprise five segments with fibers projecting into prefrontal (I), premotor and supplementary motor (II), primary motor (III), and primary sensory areas (IV), as well as into parietal, temporal, and occipital cortical areas (V). In order to more rapidly characterize the underlying anatomy of these segments, this study used a novel single-shot T1 mapping method to quantitatively determine T1 relaxation times in the human CC. A region-of-interest analysis revealed a tendency for the lowest T1 relaxation times in the genu and the highest T1 relaxation times in the somatomotor region of the CC. This observation separates regions dominated by myelinated fibers with large diameters (somatomotor area) from densely packed smaller axonal bundles (genu) with less myelin. The results indicate that characteristic T1 relaxation times in callosal profiles provide an additional means to monitor differences in fiber anatomy, fiber density, and gray matter in respective neocortical areas. In conclusion, rapid T1 mapping allows for a characterization of the axonal architecture in an individual CC in less than 10 s. The approach emerges as a valuable means for studying neocortical brain anatomy with possible implications for the diagnosis of neurodegenerative processes.

Bridging time-scales: Grain boundary sliding constitutive law from atomistics

Grain boundary sliding is the key deformation and damage mechanism for high temperature deformation of crystalline materials impacting, thus, applications ranging from nuclear reactors to aircrafts. Despite decades of research—theoretical and experimental—a definitive atomistic understanding of this phenomenon has been elusive. The primary bottleneck is the fact that conventional molecular dynamics can only address pico-to-nano seconds of material physics while the characteristic relaxation times for creep phenomena (including grain boundary sliding) are several orders of magnitude slower. In this letter, we use a fresh approach based on a recently developed potential energy surface sampling method that allows us to bridge long time scales and, for the first time, develop a physically reasonable constitutive law. Our results show a dramatic improvement over what can be gleaned from conventional molecular dynamics and provide insights on the relative merits of existing theories of grain boundary sliding. Our simulations (based on a prototypical metal, Al) answer important questions such as (i) is there a threshold stress for grain boundary sliding?, (ii) what is the form of constitutive law for grain boundary sliding? and others.

Effect of a constant magnetic field on dislocation anharmonicity in silicon

The effect of constant magnetic fields on dislocation anharmonicity of p-type silicon single crystals with a conductivity of 6 Ω cm has been studied. It has been found that preliminary exposure of dislocation silicon (with a dislocation density of 104–106 cm−2) to a constant magnetic field (B = 0.7 T, t = 30 min) at room temperature causes a change in the nonlinear fourth-order elastic modulus βd. The observed changes are associated with the dynamics of magnetosensitive complexes of structural defects and, hence, with the changes in the length of the vibrating dislocation segment. Based on the dynamics of βd(t) after sample exposure to a magnetic field, the conclusion is made about an increase in the vibrating dislocation segment length Ld by 30%, and the characteristic relaxation times of observed effects are estimated.

The influence of ultrahigh molecular weight polyacrylonitrile on the copolymerization of acrylonitrile with itaconic acid and on the rheological properties of the resulting polyacrylonitrile solutions

In this study, a series of ultrahigh molecular weight polyacrylonitrile (UHMWPAN)/dimethylsulfoxide dilute solutions were produced and they were used afterwards as reaction medium for the synthesis of copolymers of acrylonitrile with itaconic acid by solution polymerization. The influence of UHMWPAN was investigated on the copolymerization and on the rheological behavior of the copolymer solutions. It was found that the presence of UHMWPAN was greatly influential on the copolymerization and the rheological behavior of the solutions. Compared with the polyacrylonitrile solution without UHMWPAN, Mη and η increased significantly. The results of shear rheological measurements indicated that the existence of UHMWPAN increased the characteristic relaxation time of polyacrylonitrile solutions. What is more, the polyacrylonitrile solutions containing UHMWPAN exhibited much more evident strain-hardening behavior than the solution without UHMWPAN. It was thus determined that polyacrylonitrile solutions containing a small amount of UHMWPAN are suitable for dry-jet wet spinning and can provide enhanced properties in the preparation of high-performance polyacrylonitrile precursor fiber.

ВПЛИВ ПРОСТОРОВОЇ ІЗОМЕТРІЇ НАНОНАПОВНЮВАЧІВ НА ВЛАСТИВОСТІ НАНОКОМПОЗИТІВ НА ОСНОВІ ПОЛІСТИРОЛУ

Методом диференційної скануючої калориметрії досліджені нанокомпозити (НК) на основі атактичного полістиролу (ПС) та карбонанотрубок (КНТ) та НК основі ПС та аеросилу (АЕ)з масовим вмістом нанонаповнювача w від 0,5% до 5,0%. Виявлено різний характер впливу високоанізометричних наночастинок КНТ та ізометричних сферичних наночастинок АЕ на теплофізичні, релаксаційні властивості та термодинаміку формування нанокомпозитів. Встановлено, що екстремальний характер поведінки теплофізичних та термодинамічних властивостей ПС/КНТ при w = 0,5…1,0% є результатом переходу ізольованих нанотрубок в агрегати частинок КНТ. Значна адгезія аеросилу до ПС приводить до монотонної зміни термодинамічних властивостей нанокомпозитів та збільшення характеристичних часів релаксації у всьому діапазоні складів.

Asymmetric Director Structures and Ions in the Measurement of the Flexoelectric Sum (e1 + e3)

Hybrid Aligned Nematic (HAN) devices filled with highly ionic liquid crystal materials screen out the internal bias due to surface polarization, making it possible to determine the flexoelectric sum, e1 + e3. A transient change is observed in the device response due to differing polarities of an external offset applied to an AC signal, with a time constant similar to the characteristic ion relaxation time in the material. Assuming ions screen out the internal bias, data-theory fits in the low frequency, low voltage perturbative regime gives a value of /verte1 + e3/vert = 10 pCm−1 for the standard commercial eutectic E70 nematic liquid crystal mixture.

Magnetic nanoparticle motion in external magnetic field

A set of equations describing the motion of a free magnetic nanoparticle in an external magnetic field in a vacuum, or in a medium with negligibly small friction forces is postulated. The conservation of the total particle momentum, i.e. the sum of the mechanical and the total spin momentum of the nanoparticle is taken into account explicitly. It is shown that for the motion of a nanoparticle in uniform magnetic field there are three different modes of precession of the unit magnetization vector and the director that is parallel the particle easy anisotropy axis. These modes differ significantly in the precession frequency. For the high-frequency mode the director points approximately along the external magnetic field, whereas the frequency and the characteristic relaxation time of the precession of the unit magnetization vector are close to the corresponding values for conventional ferromagnetic resonance. On the other hand, for the low-frequency modes the unit magnetization vector and the director are nearly parallel and rotate in unison around the external magnetic field. The characteristic relaxation time for the low-frequency modes is remarkably long. This means that in a rare assembly of magnetic nanoparticles there is a possibility of additional resonant absorption of the energy of alternating magnetic field at a frequency that is much smaller compared to conventional ferromagnetic resonance frequency. The scattering of a beam of magnetic nanoparticles in a vacuum in a non-uniform external magnetic field is also considered taking into account the precession of the unit magnetization vector and director.

Vibrational non-equilibrium in the hydrogen–oxygen reaction. Comparison with experiment

A theoretical model is proposed for the chemical and vibrational kinetics of hydrogen oxidation based on consistent accounting of the vibrational non-equilibrium of the HO2 radical that forms as a result of the bimolecular recombination H+O2 → HO2. In the proposed model, the chain branching H+O2 = O+OH and inhibiting H+O2+M = HO2+M formal reactions are treated (in the terms of elementary processes) as a single multi-channel process of forming, intramolecular energy redistribution between modes, relaxation, and unimolecular decay of the comparatively long-lived vibrationally excited HO2 radical, which is able to react and exchange energy with the other components of the mixture. The model takes into account the vibrational non-equilibrium of the starting (primary) H2 and O2 molecules, as well as the most important molecular intermediates HO2, OH, O2(1Δ), and the main reaction product H2O. It is shown that the hydrogen–oxygen reaction proceeds in the absence of vibrational equilibrium, and the vibrationally excited HO2(v) radical acts as a key intermediate in a fundamentally important chain branching process and in the generation of electronically excited species O2(1Δ), O(1D), and OH(2Σ+). The calculated results are compared with the shock tube experimental data for strongly diluted H2–O2 mixtures at 1000 < T < 2500 K, 0.5 < p < 4 atm. It is demonstrated that this approach is promising from the standpoint of reconciling the predictions of the theoretical model with experimental data obtained by different authors for various compositions and conditions using different methods. For T < 1500 K, the nature of the hydrogen–oxygen reaction is especially non-equilibrium, and the vibrational non-equilibrium of the HO2 radical is the essence of this process. The quantitative estimation of the vibrational relaxation characteristic time of the HO2 radical in its collisions with H2 molecules has been obtained as a result of the comparison of different experimental data on induction time measurements with the relevant calculations.

Rheological Indicators for Environmental Stress Cracking Resistance of Polyethylene

Abstract Most studies on environmental stress cracking resistance (ESCR) of polymers have focused on performing mechanical tests in the solid state. In this work, investigations in the melt state were carried out, to identify potential melt indicators for a relative measure of ESCR. A normalized characteristic relaxation time (λN), obtained from dynamic shear experiments, was established as a valid measure of ESCR of linear low density polyethylene, where a large content of short chain branches is present. In addition, the melt strain hardening coefficient (MSHC), obtained from extensional rheological methodologies, was found to be another potential and reliable indicator of ESCR. An inverse correlation between MSHC and ESCR was observed, indicating an inverse relationship between ESCR and chain extensibility in the melt. Furthermore, a new factor called “melt hardening stiffness (mHS)” was developed from the slope of a stress vs. Hencky strain obtained from a Sentmanat extensional rheometer. mHS was found to be another promising indicator of ESCR obtained from rheological studies conducted in this work.

An Evaluation of Coulomb Stress Changes from Earthquake Productivity Variations in the Western Gulf of Corinth, Greece

Spatial and temporal evolution of the stress field in the seismically active and well-monitored area of the western Gulf of Corinth, Greece, is investigated. The highly accurate and vast regional catalogues were used for inverting seismicity rate changes into stress variation using a rate/state-dependent friction model. After explicitly determining the physical quantities incorporated in the model (characteristic relaxation time, fault constitutive parameters, and reference seismicity rates), we looked for stress changes across space and over time and their possible association with earthquake clustering and fault interactions. We focused our attention on the Efpalio doublet of January 2010 (M = 5.5 and M = 5.4), with a high aftershock productivity, and attempted to reproduce and interpret stress changes prior to and after the initiation of this seismicity burst. The spatial distribution of stress changes was evaluated after smoothing the seismological data by means of a probability density function (PDF). The inverted stress calculations were compared with the calculations derived from an independent approach (elastic dislocation model) and this comparison was quantified. The results of the two methods are in good agreement (up to 80 %) in the far field, with the inversion technique providing more robust results in the near field, where they are more sensitive to the uncertainties of coseismic slip distribution. It is worth mentioning that the stress inversion model proved to be a very sensitive stress meter, able to detect even small stress changes correlated with spatio–temporal earthquake clustering. Data analysis was attempted from 1975 onwards to simulate the stress changes associated with stronger earthquakes over a longer time span. This approach revealed that only M > 5.5 events induce considerable stress variations, although in some cases there was no evidence for such stress changes even after an M > 5.5 earthquake.

Quantifying Dynamic Processes in Reactive Materials: An Extended Burn Tube Test

AbstractA common method for measuring the reactivity of rapidly deflagrating materials has been to loosely pack a desired mixture into an approx. 10 cm long×3 mm diameter acrylic tube, ignite the material on one end, and report the observed self‐propagating flame velocity through the material. While this method can yield qualitative information, linking this to quantitative intrinsic properties, such as particle burn time, has remained challenging. In this work, we significantly redesign the traditional burn tube experiment. Between 25 and 250 mg of nanocomposite aluminum/copper oxide (Al/CuO) thermite is loosely packed into the capped end of a 1.8 m long tube, and the remainder of the tube is left unfilled. The material is ignited using a hot wire, resulting in a steadily‐propagating luminous front, which extends part, or all, of the way down the length of the tube. We suggest the behavior is a result of “reactive entrainment”, which occurs when the reaction time scale becomes longer than the characteristic momentum relaxation time scale. When this criterion is met, and when there are significant pressure gradients present or produced during the reaction, material will be entrained by the gases before and/or during the reaction; a behavior very different from conventional thermites, which use larger particle sizes. The effect of sample mass and tube diameter on propagation velocity is investigated, and we find a linear scaling with mass and a power law scaling with tube radius (r−1.3) between 1.56 and 4.76 mm radii. For several conditions, we observe the reaction complete; defined by the distance where the propagation velocity decreases to a fixed fraction of its steady value. The ratio of quench distance to propagation velocity was found to approach a constant value of 3.29±0.70 ms, which we suggest is the burn time of the Material. For the range of masses studied in this work, the burn time was found to be independent of mass, implying that it is an intrinsic particle burn time. We expect other quantitative information can be deduced from this experiment, so long as the chosen sample mass and tube dimensions allow one to observe the full extent of reaction.

Hydrodynamic Perspective on Asphaltene Agglomeration and Deposition

In this work, we propose a detailed numerical model for asphaltene agglomeration and deposition, as induced by a resolved turbulent liquid carrier phase flow, in which transport, breakup, and re-entrainment are also taken into account. Asphaltene phase separation is represented by the appearance of adhesive primary particles, which bond upon collision and act as a precursor to agglomerate formation. Deposition is considered using a novel approach in the context of agglomerate structure resolving simulations: the attractive particle–wall interaction is modeled by a damped harmonic oscillator, whereas the deceleration of depositing particles occurs with a characteristic relaxation time. In the absence of deposition, agglomeration and breakup give rise to a statistical steady state. Universal scaling relations, valid for a large range of Reynolds numbers, accurately predict the mean agglomerate mass in this steady state. We show that the shape of the agglomerates is insensitive to the breakup mechanism considered and that the fractal dimension is similar to experimental values reported in the literature for asphaltenes. It is found that the properties of the agglomerates change when two-way coupling is considered instead of one-way coupling, but not when large-eddy simulations are conducted instead of direct numerical simulations. When particle–wall interactions are included, deposition predominantly occurs close to the region where asphaltene phase separation takes place. The morphology of the deposit layer is shown to depend upon the local concentration and the mobility of the deposited particles; we also present how these features depend upon the parameters of the deposition model.

Translational diffusion of water inside hydrophobic carbon micropores studied by neutron spectroscopy and molecular dynamics simulation.

When water molecules are confined to nanoscale spacings, such as in the nanometer-size pores of activated carbon fiber (ACF), their freezing point gets suppressed down to very low temperatures (∼150K), leading to a metastable liquid state with remarkable physical properties. We have investigated the ambient pressure diffusive dynamics of water in microporous Kynol ACF-10 (average pore size ∼11.6Å, with primarily slit-like pores) from temperature T=280 K in its stable liquid state down to T=230 K into the metastable supercooled phase. The observed characteristic relaxation times and diffusion coefficients are found to be, respectively, higher and lower than those in bulk water, indicating a slowing down of the water mobility with decreasing temperature. The observed temperature-dependent average relaxation time 〈τ〉 when compared to previous findings indicate that it is the width of the slit pores-not their curvature-that primarily affects the dynamics of water for pore sizes larger than 10 Å. The experimental observations are compared to complementary molecular dynamics simulations of a model system, in which we studied the diffusion of water within the 11.6 Å gap of two parallel graphene sheets. We find generally a reasonable agreement between the observed and calculated relaxation times at the low momentum transfer Q(Q≤0.9Å(-1)). At high Q, however, where localized dynamics becomes relevant, this ideal system does not satisfactorily reproduce the measurements. Consequently, the simulations are compared to the experiments at low Q, where the two can be best reconciled. The best agreement is obtained for the diffusion parameter D associated with the hydrogen-site when a representative stretched exponential function, rather than the standard bimodal exponential model, is used to parametrize the self-correlation function I(Q,t).

Dynamic rheological behavior of two LDPE/HDPE binary blending melts

The dynamic rheological behaviors are measured by small amplitude oscillatory shear on a rotational rheometer for two low-density polyethylene/high-density polyethylene blends: LDPE 2102TN26/HDPE 5306 and LDPE2102TN26/HDPE8916. The composition dependence of zero shear viscosity as well as characteristic relaxation time of the two blends deviate the log addition rule, indicating the two blends are immiscible. Two emulsion models Palierne’s model and Bousmina’s model are used to fit the storage modulus-frequency data, the results indicate the two blends are immiscible except at the 90/10(LDPE/HDPE) weight ratio.

Constitutive relations for viscoelastic materials under thermorelaxation transition

A mathematical model of the mechanical behavior of viscoelastic bodies in a complex stress state under thermorelaxation transition is considered. The constructed constitutive equations allow one to describe the relations between the stress and strain tensors over a wide temperature interval including temperatures of relaxation transition. It is assumed that the characteristic relaxation times of the isotropic homogeneous polymer in a highly elastic state are much shorter than the characteristic times of external forces, which makes it possible to describe its behavior using the elastic model. In the glassy state, the behavior of the polymer is described in the framework of linear viscoelasticity. It is also assumed that the process of glass transition is accompanied by the formation of new intermolecular bonds, each being unstressed at the time of its appearance. It has been shown that the obtained constitutive relations of the hereditary type do not violate the second law of thermodynamics. A finite element procedure based on the stepwise integration has been developed and applied for solving quasi-stationary boundary value problems in mechanics of vitrifying polymers. The numerical technique is generalized to the case of taking into account the viscoelastic properties of the material in the glassy state. The validity of the physical and numerical models has been verified in the experiments, in which the residual stresses in the cylindrical EDT-10 epoxy resin specimens subject to non-uniform cooling are determined by the split ring method and polarization-optical method. It has been shown that the results of calculations agree well with the experimental data.

Supercapacitors Based on Mixture of Room Temperature Ionic Liquids Containing Specifically Adsorbed Iodide Anions

The influence of 5 wt% addition of 1-ethyl-3-methylimidazolium iodide (EMImI) in 1-ethyl-3-methylimidazolium tetrafluoroborate (EMImBF4) on the melting point, bulk conductivity and electrochemical properties of the ionic liquid mixture as an electrolyte in electrical double layer capacitor (EDLC) has been studied using cyclic voltammetry, electrochemical impedance spectroscopy, constant current charge-discharge and constant power discharge methods. The specific conductivity decreased from 13.6 mS cm-1 to 12.8 mS cm-1 and the melting point increased from 17°C to 19.5°C by adding 5 wt% of EMImI into EMImBF4. Noticeable increase in specific capacitance up to 245 F g-1 at 1.0 V, specific energy (36.7 Wh kg-1) and specific power values has been established. Thus, EDLC based on EMImBF4 + EMImI mixture demonstrated nearly 50% higher stored charge value than EDLC without EMImI addition. However, only minor increase in characteristic relaxation time constant from 1.45 s to 1.48 s for EDLC based on I- adsorption effect has been established.

Relaxation mechanism of plastic deformation and its justification using the example of the sharp yield point phenomenon in whiskers

The generality of the dynamic approach to a wide range of problems of the continuum mechanics, including deformation at the rates determining quasi-static deformation conditions has been demonstrated using the example of deformation of cadmium and copper whiskers. The sharp yield point phenomenon has been analyzed in terms of the theory of dislocations and phenomenological integrated criteria of plasticity. It has been shown that the characteristic relaxation times used in these criteria, regardless of the applied model of plasticity, reflect essential properties of the very deformation process itself.

Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence

AbstractWe study unconfined homogeneous turbulence with a destabilizing background density gradient in the Boussinesq approximation. Starting from initial isotropic turbulence, the buoyancy force induces a transient phase toward a self-similar regime accompanied by a rapid growth of kinetic energy and Reynolds number, along with the development of anisotropic structures in the flow in the direction of gravity. We model this with a two-point statistical approach using an axisymmetric eddy-damped quasi-normal Markovian (EDQNM) closure that includes buoyancy production. The model is able to match direct numerical simulations (DNS) in a parametric study showing the effect of initial Froude number and mixing intensity on the development of the flow. We further improve the model by including the stratification timescale in the characteristic relaxation time for triple correlations in the closure. It permits the computation of the long-term evolution of unstably stratified turbulence at high Reynolds number. This agrees with recent theoretical predictions concerning the self-similar dynamics and brings new insight into the spectral energy distribution and anisotropy of the flow.