Characteristic Relaxation Time Research Articles

Static and dynamic properties of large polymer melts in equilibrium.

We present a detailed study of the static and dynamic behaviors of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [G. Zhang et al., ACS Macro Lett. 3, 198 (2014)], we investigate their static and dynamic scaling behaviors as predicted by theory. We find that for semiflexible chains in a melt, results of the mean square internal distance, the probability distributions of the end-to-end distance, and the chain structure factor are well described by theoretical predictions for ideal chains. We examine the motion of monomers and chains by molecular dynamics simulations using the ESPResSo++ package. The scaling predictions of the mean squared displacement of inner monomers, center of mass, and relations between them based on the Rouse and the reptation theory are verified, and related characteristic relaxation times are determined. Finally, we give evidence that the entanglement length Ne,PPA as determined by a primitive path analysis (PPA) predicts a plateau modulus,GN (0)=45(ρkBT/Ne), consistent with stresses obtained from the Green-Kubo relation. These comprehensively characterized equilibrium structures, which offer a good compromise between flexibility, small Ne, computational efficiency, and small deviations from ideality, provide ideal starting states for future non-equilibrium studies.

Cattaneo-Christov Heat Flux Model for MHD Three-Dimensional Flow of Maxwell Fluid over a Stretching Sheet.

This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.

Microporous–mesoporous carbons for energy storage synthesized by activation of carbonaceous material by zinc chloride, potassium hydroxide or mixture of them

Abstract Various electrochemical methods have been applied to establish the electrochemical characteristics of the electrical double layer capacitor (EDLC) consisting of the 1 M triethylmethylammonium tetrafluoroborate solution in acetonitrile and activated carbon based electrodes. Activated microporous carbon materials used for the preparation of electrodes have been synthesized from the hydrothermal carbonization product (HTC) prepared via hydrothermal carbonization process of d -(+)-glucose solution in H2O, followed by activation with ZnCl2, KOH or their mixture. Highest porosity and Brunauer-Emmett-Teller specific surface area (SBET = 2150 m2 g−1), micropore surface area (Smicro = 2140 m2 g−1) and total pore volume (Vtot = 1.01 cm3 g−1) have been achieved for HTC activated using KOH with a mass ratio of 1:4 at 700 °C. The correlations between SBET, Smicro, Vtot and electrochemical characteristics have been studied to investigate the reasons for strong dependence of electrochemical characteristics on the synthesis conditions of carbon materials studied. Wide region of ideal polarizability (ΔV ≤ 3.0 V), very short characteristic relaxation time (0.66 s), and high specific series capacitance (134 F g−1) have been calculated for the mentioned activated carbon material, demonstrating that this system can be used for completing the EDLC with high energy- and power densities.

Photoinduced and Thermal Relaxation in Surface-Grafted Azobenzene-Based Monolayers: A Molecular Dynamics Simulation Study.

Extensive atomistic molecular dynamics simulations have been employed to study the structure and molecular orientational relaxation of azobenzene-based monolayers grafted to a solid substrate. Systems with surface coverage of 0.6 nm(2)/molecule were investigated over a wide temperature range ranging from 298 K, where the mesogens show local ordering and the monolayer dynamics was found to be glassy, up to 700 K, where the azobenzene groups have a nearly isotropic orientational distribution, with a subnanosecond characteristic orientational relaxation time scale. Biased simulations that model single-molecule thermal excitation and conformational isomerization have been conducted to obtain insight into the mechanisms for photoinduced athermal fluidization and monolayer reorganization observed experimentally in this system. Our simulations clearly indicate that trans-cis conformational isomerization transitions of azobenzene units can lead to reorientation of mesogens and to the formation of a monolayer with strong macroscopic in-plane nematic order. While local heating created by excitation process can facilitate this process, thermal excitation alone is not sufficient to induce ordering in the monolayer. Instead, the work done by a molecule undergoing cis-trans isomerization on the cage of neighboring molecules is the key mechanism for photofluidization and orientational ordering in dMR monolayers exposed to linearly polarized light leading to relaxation dynamics that can be described in terms of higher effective temperature. The obtained simulation results are discussed in light of recent experimental data reported for these systems.

Validity of the second Fick's law for modeling ion-exchange diffusion in non-crystalline viscoelastic media (glasses)

It is shown that, in general case, the diffusion equation (or the second Fick's law) does not provide an adequate description of ion-exchange transport phenomena in viscoelastic media, including glassy or any other non-crystalline media. In this connection the general phenomenological model of ion-exchange diffusion in viscoelastic media has been developed. A theoretical analysis of the model shows that, in the case of a linear dependence of medium density on the concentration of diffusing ions, the necessary and sufficient condition of the absolute validity of the diffusion equation in viscoelastic media is Φ ≫ 1, where Φ = τD/τR is the dimensionless value (or criterion of similarity), with τD = L2/D being the characteristic time of diffusion and τR = η/G being the characteristic time of stress relaxation, where L, D, η, and G are the characteristic length of diffusion, the diffusivity, the viscosity, and the shear modulus, respectively. The value of 1/Φ characterizes the accuracy which is provided if the second Fick's law is used in the simulation of ion-exchange diffusion in viscoelastic media. We have demonstrated the applicability of this criterion experimentally. Our experimental studies on ion-exchange diffusion in an oxide glass (typical viscoelastic media) have shown that under the condition the Φ > 105 the experimental concentration profiles are close to those predicted by the second Fick's law to within an accuracy of 1%.

Real-space renormalization for the finite temperature statics and dynamics of the Dyson long-ranged ferromagnetic and spin-glass models

The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving long-ranged coupling in the region where there exists a non-mean-field-like thermal ferromagnetic–paramagnetic transition, the RG flows are explicitly solved: the characteristic relaxation time follows the critical power-law at the phase transition and the activated law with in the ferromagnetic phase. For the spin-glass model involving random long-ranged couplings of variance in the region where there exists a non-mean-field-like thermal spin-glass–paramagnetic transition, the coupled RG flows of the couplings and of the relaxation times are studied numerically: the relaxation time follows some power-law at criticality and the activated law in the spin-glass phase with the dynamical exponent coinciding with the droplet exponent governing the flow of the couplings .

Specific temperature-related features of photoconductivity relaxation in PbSnTe:In films under interband excitation

The time dependences of variations in the photoconductivity of PbSnTe:In films in the range of T ≈ 19—25 K upon interband excitation are studied. It is found that the character of conductivity relaxation after switch-off of illumination depends on the duration and intensity of the preceding illumination. In this case, the characteristic times of relaxation for various modes of illumination can differ by more than an order of magnitude. The obtained results are discussed in the context of a model assuming the presence of a quasicontinuous spectrum of capture levels in the band gap of PbSnTe:In and also a possible effect on the parameters of these levels of the ferroelectric phase transition, the temperature of which is found to be in the temperature range under study

Unsteady natural convection boundary layer heat transfer of fractional Maxwell viscoelastic fluid over a vertical plate

In classical study on viscoelastic fluids, researchers commonly ignored the effects of nonlinear convection and dealt only with the cases when the governing equations are linear. This paper presents a research on unsteady boundary layer natural convection heat transfer of Maxwell viscoelastic fluid over a vertical plate. The fractional boundary layer governing equations are firstly formulated and derived. From such derivation, the model constitutes nonlinear coupled equations with mixed time–space derivatives in the convection terms, which are solved by a newly developed finite difference method combined with an L1-algorithm. Results show that both the velocity and the temperature boundary layer manifest a short-term memory and basic relaxation time characteristics. For example, for specified velocity and temperature fractional derivative α and β, the velocity profile has a maximum, which increases and goes from a far-field region to the vertical plate as a decreasing function of α, implying a loss in velocity boundary layer thickness. But the values of such maxima behave conversely for β. More effects of the fractional order parameters α and β on velocity and temperature fields are shown graphically and analyzed in detail.

Progress in the synthesis of high performance butadiene-based elastomer for green tires

The advantages of green tires in energy saving, environmental protection and safety make it become the trend of the tire. Neodymium-based high cis -polybutadiene rubber (Nd-BR) and solution styrene-butadiene rubber (SSBR) are two important raw materials for manufacturing green tire. Situation of green tire, progress in the synthesis of Nd-BR and butadiene-based copolymer, current status of some industrialized Nd-BR and development of rare earth catalysts have been reviewed, which is helpful for the production of high-performance synthetic rubber for green tire. The main Nd-BR producers are Lanxess, Versalis, ChiMei, Kumho, Japan Synthetic Rubber, Nizhnekamskneftekhim, Goodyear, Firestone, Sibur, Synthos and Karbochem. The commercial Nd-BR products are normally divided into three grades according to the various Mooney viscosity (ML1+4100°C) of around 45, 55 and 63. Furthermore, the effect of microstructure, composition and topology on processing property, mechanical properties and dynamic mechanical properties of Nd-BR and butadiene-based copolymer were introduced. Stereo-specificity is a key factor for the performance of Nd-BR product. The results of the characteristic relaxation time ( τ ), yield stress ( T y), 300% modulus ( T 300), and T 300/ T y for various Nd-BR indicated that the increase of cis -1,4 content was benefit for the improvement of processing properties. The decrease of Δ G ʹ with an increase in cis -1,4 content indicated that Nd-BR with high cis -1,4 content of around 98.5% behaved low Payne effect, which was mainly attributed to the strong interaction between polymer and filler. Excellent processing performance means that the addition of fillers to rubber compounds are easy to scatter. These can short the mixing time and produce the highest quality product with the lowest possible cost. Nd-BR products with higher cis -1,4 content possess the superior mechanical properties and dynamic mechanical properties of BR vulcanizates, such as modulus at 300%, tensile strength, abrasion resistance, heat build-up, compression properties and rolling resistance and wet-skid resistance. Nd-BR which possesses cis -1,4 content of more than 98% has more excellent mechanical properties, dynamic mechanical properties, and is suitable for green tire as raw materials for the excellent properties such as low heat build-up, rolling power loss, compression deformation, compression ratio and abrasion loss. Long chain branched Nd-BR possesses an improved cold flow resistance, processing performance and mixing performance with the filler. High cis -1,4 butadiene/styrene elastomer and stereospecfic butadiene/styrene copolymer combine excellent performance of Nd-BR and SBR. Both mechanical performance and skid resistance ability on ice road were increased, while rolling resistance was decreased for the vulcanizates. These excellent properties of the synthetic rubbers are beneficial for manufacture of high-performance green tires.

Determining Physical Properties of the Cell Cortex

Actin and myosin assemble into a thin layer of a highly dynamic network underneath the membrane of eukaryotic cells. This network generates the forces that drive cell- and tissue-scale morphogenetic processes. The effective material properties of this active network determine large-scale deformations and other morphogenetic events. For example, the characteristic time of stress relaxation (the Maxwell time τM) in the actomyosin sets the timescale of large-scale deformation of the cortex. Similarly, the characteristic length of stress propagation (the hydrodynamic length λ) sets the length scale of slow deformations, and a large hydrodynamic length is a prerequisite for long-ranged cortical flows. Here we introduce a method to determine physical parameters of the actomyosin cortical layer in vivo directly from laser ablation experiments. For this we investigate the cortical response to laser ablation in the one-cell-stage Caenorhabditis elegans embryo and in the gastrulating zebrafish embryo. These responses can be interpreted using a coarse-grained physical description of the cortex in terms of a two-dimensional thin film of an active viscoelastic gel. To determine the Maxwell time τM, the hydrodynamic length λ, the ratio of active stress ζΔμ, and per-area friction γ, we evaluated the response to laser ablation in two different ways: by quantifying flow and density fields as a function of space and time, and by determining the time evolution of the shape of the ablated region. Importantly, both methods provide best-fit physical parameters that are in close agreement with each other and that are similar to previous estimates in the two systems. Our method provides an accurate and robust means for measuring physical parameters of the actomyosin cortical layer. It can be useful for investigations of actomyosin mechanics at the cellular-scale, but also for providing insights into the active mechanics processes that govern tissue-scale morphogenesis.

A model of axial heterostructure formation in III–V semiconductor nanowires

A kinetic model of the formation of axial heterostructures in nanocrystalline wires (nanowires, NWs) of III–V semiconductor compounds growing according to the vapor–liquid–solid (VLS) mechanism is proposed. A general system of nonstationary equations for effective fluxes of two elements of the same group (e.g., group III) is formulated that allows the composition profile of a heterostructure to be calculated as a function of the coordinate and epitaxial growth conditions, including the flux of a group V element. Characteristic times of the composition relaxation, which determine the sharpness of the heteroboundary (heterointerface), are determined in the linear approximation. A temporal interruption (arrest) of fluxes during the switching of elements for a period exceeding these relaxation times must increase sharpness of the heteroboundary. Model calculations of the composition profile in a double GaAs/InAs/GaAs axial heterostructure have been performed for various NW radii.

Relaxation time distribution obtained from a Debye decomposition of spectral induced polarization data

We have developed an alternative formulation for Debye decomposition of complex electric conductivity spectra, by recasting it into a new set of parameters with a close relationship to the continuous formulation for the complex conductivity method. The procedure determines a relaxation time distribution (RTD) and two frequency-independent parameters that modulate the complex conductivity spectra. These two parameters represent (1) the direct current contribution and (2) the conductivity range spanned by the low- and high-frequency limits. The distribution of relaxation times quantifies the contribution of each distinct relaxation process. Assuming that characteristic times with insignificant contributions can be ignored, a minimum set of characteristic relaxation times is determined. Each contribution can then be associated with specific polarization processes that can be interpreted in terms of electrochemical or interfacial parameters of mechanistic models derived from inverted parameters obtained from the proposed approach. Synthetic tests show that the procedure can fit spectral induced polarization (SIP) data and successfully retrieve the RTD. We have applied the procedure to laboratory SIP data from experiments with sand and oil mixtures undergoing microbial degradation of hydrocarbons. The RTD reveals evidence of a length scale at which a new polarization process takes place as a result of the biodegradation process.

The definition of characteristic times of plastic relaxation by dislocation slip and grain boundary sliding in copper and nickel

The behaviour of the yield strength of metals is considered from viewpoint of dynamics as a function of the limiting stress and the characteristic time of stress relaxation. Experimental curves of the static and dynamic deformation of the coarse-grained copper, microcrystalline and nanocrystalline nickel are analyzed on the basis of the relaxation model of plasticity (the integral criterion) with a constant characteristic relaxation time. The analytical expressions of the relaxation time as a function of variables that characterizes the internal structure of material are obtained from the model of dislocation slip and grain boundary sliding. The strain rate dependences of the yield strength, which are calculated with the help of both the dislocation model and the integral criterion of plasticity, are compared with the experimental data for copper and nickel in a wide range of strain rates (10−3−1011 s−1). It is shown that the proposed analytical expressions give the relaxation time, which order-of-magnitude agrees with the values obtained by fitting the results of the integral criterion. The obtained relations allow us to calculate two separate dependences of the yield strength (one for coarse-grained material, while another for nanomaterial) in Hall–Petch coordinates both for quasi-static and for high-rate deformations.

The heterogeneous energy landscape expression of KWW relaxation.

Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we obtain a general characteristic relaxation time distribution equation for the KWW function in a closed, analytic form. Analyses of numerical computation show excellent accuracy, both in time and frequency domains, in the convergent performance of the heterogeneous energy landscape expression and shunning the catastrophic truncations reported in the previous work. The stretched exponential β, closely associated to temperature and apparent correlation with one dynamic phase, reveals a threshold value of 1/2 defining different behavior of the probability density functions. Our work may contribute, for example, to in-depth comprehension of the dynamic mechanism of glass transition, which cannot be provided by existing approaches.

Structural relaxation in AgPO3 glass followed by in situ ionic conductivity measurements

The structural relaxation kinetics of a silver meta-phosphate glass (AgPO3) is investigated using a method based on the isothermal variation of its ionic conductivity over time. Samples of AgPO3 glass from the same batch were pre-annealed at 433K or 418K and then relaxed at different temperatures within this temperature range, which is close to its glass transition temperature measured by differential scanning calorimetry, TgDSC=438K. Ionic conductivity data were continuously collected by impedance spectroscopy during the isothermal relaxation process. The variation of the electrical conductivity over time is well described by the Kohlrausch expression (Φ(t)=exp[−(t/τσK)β]), in which τσK is the characteristic relaxation time and β a stretch exponent. Different values of β were found when the glass structure expanded or contracted during relaxation. In addition, viscosity values calculated by the Maxwell relationship using <τ> from conductivity data and a shear modulus taken from the literature are in accordance with the experimental viscosity measured in the same temperature range, thus validating the use of ionic conductivity to unveil glass structural relaxation.

Universal Trend of the Non-Exponential Rouse Mode Relaxation in Glass-Forming Polymers Systems: Experimental Facts, MD-Simulation Results and a Theoretical Approach Based on a Generalized Langevin Equation

ABSTRACTNowadays there are clear evidences from both experiments and MD-simulations proving that the chain Rouse modes correlation functions are non-exponential in unentangled polymer blends and also in pure polymers at low temperature (with respect to that of the glass transition Tg) even for the long wavelengths modes where local potentials and chain stiffness should not play any role. In a recent paper [S. Arrese-Igor et al, Phys. Rev. Lett.113, 078302 (2014)] it has been proposed that this non-exponential behavior depends on the ratio between the so-called Rouse time - i.e., the characteristic time of the slowest chain mode relaxation - and the time scale of the α-relaxation. This parameter is in some way ‘universal’ in the meaning that it can encode many different experimental situations. In this paper, we show that this behavior can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation (GLE) formalism and (ii) a memory function which takes into account the effect of collective dynamics on the chain dynamics of a tagged chain and which was constructed taking inspirations from the original ideas of the reptation model proposed by de Gennes.

Macro and nano scale modelling of water-water interactions at ambient and low temperature: relaxation and residence times.

The decay dynamics of ambient and low temperature liquid water has been investigated through all-atom molecular dynamics simulations, residence times calculations and time correlation functions from 300 K down to 243 K. Those simulations replicate the experimental value of the self-diffusion constant as a function of temperature by tuning the damping factor of the Langevin equation of motion. A stretched exponential function exp[-(t/τ)(β)] has been found to properly describe the relaxation of residence times calculated at different temperatures for solvent molecules in a nanodrop of free water modelled as a sphere of nanometric dimensions. As the temperature goes down the decay time τ increases showing a divergence at Ts = 227 ± 3 K. The temperature independence of the dimensionless stretched exponent β = 0.59 ± 0.01 suggests the presence of, not a characteristic relaxation time (since β≠ 1), but a distribution of decay times that also holds at low temperature. An explanation for such heterogeneity can be found at the nanoscopic level. Moreover it can be concluded that the distribution of times already reported for the dynamics of water surrounding proteins (β≤ 0.5) can not be exclusively due to the presence of the biomolecule itself since isolated water also exhibits such behaviour. The above reported Ts and β values quantitatively reproduce experimental data.

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i) the shooting method and (ii) the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.

Nonlocal heat transfer in two-dimensional Lennard–Jones crystal: Application of the molecular dynamics method

The redistribution of heat between two subsystems in the two-dimensional crystal consisting of particles interacting by means of the Lennard–Jones potential with argon parameters is considered in the frame of molecular dynamics method. Calculations of heat flux, its time derivative and kinetic temperature gradient showed that the characteristic relaxation times of the nonequilibrium flux within the nonlocal Cattaneo model at temperatures 10K<T<40K are very small (τv<10-11s) and, comparable with the time of phonons free path.

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.