Characteristic Relaxation Time Research Articles

Short time dynamics determine glass forming ability in a glass transition two-level model: A stochastic approach using Kramers’ escape formula

The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers’ transition theory, which arises in a very natural manner to calculate transition rates between wells. Then the corresponding stochastic master equation is analytically solved to find the population of metastable states. A relation between the cooling rate, the characteristic relaxation time, and the population of metastable states is found from the solution of such equation. From this, a relationship between the relaxation times and the frequency of oscillation at the metastable states, i.e., the short time dynamics, is obtained. Since the model is able to capture either a glass transition or a crystallization depending on the cooling rate, this gives a conceptual framework in which to discuss some aspects of rigidity theory, for example.

Weak ferromagnetism and short range polar order in NaMnF3 thin films

The orthorhombically distorted perovskite NaMnF3 has been predicted to become ferroelectric if an a = c distortion of the bulk Pnma structure is imposed. In order to test this prediction, NaMnF3 thin films were grown on SrTiO3 (001) single crystal substrates via molecular beam epitaxy. The best films were smooth and single phase with four different twin domains. In-plane magnetization measurements revealed the presence of antiferromagnetic ordering with weak ferromagnetism below the Néel temperature TN = 66 K. For the dielectric studies, NaMnF3 films were grown on a 30 nm SrRuO3 (001) layer used as a bottom electrode grown via pulsed laser deposition. The complex permittivity as a function of frequency indicated a strong Debye-like relaxation contribution characterized by a distribution of relaxation times. A power-law divergence of the characteristic relaxation time revealed an order-disorder phase transition at 8 K. The slow relaxation dynamics indicated the formation of super-dipoles (superparaelectric moments) that extend over several unit cells, similar to polar nanoregions of relaxor ferroelectrics.

Phase and Rheological Properties of a Curcumin‐Encapsulated Cubic Liquid Crystal

AbstractFor the purpose of encapsulating curcumin, cubic liquid crystals were constructed using a Brij 97‐NaDC (surfactant)/IPM‐PEG 400 (oil)/H2O system, at a constant Brij 97/NaDC ratio of 4:1 and varied IPM/PEG 400 ratios of 9:1, 8:2, 7:3, 6:4, 5:5, 4:6, and 3:7. The cubic liquid crystal samples, possessing a fixed surfactant/oil/water composition and different IPM/PEG 400 ratios, underwent a structure transition from Im3m to the coexistence of Im3m and Ia3d as determined by small‐angle X‐ray scattering (SAXS) measurements. SAXS and rheological investigations on the 5:5 IPM/PEG 400 ratio cubic samples suggested that the cubic liquid crystals became more stable after encapsulating curcumin in either IPM or PEG 400, as indicated by the longer characteristic relaxation time. By saturating curcumin in both IPM and PEG 400, at an IPM/PEG 400 ratio less than 5:5, higher elastic modulus, larger q value, and stronger intensity of the first scattering peak for the curcumin‐encapsulated liquid crystals were observed as compared to the corresponding curcumin‐free samples. Also, clearly different melting points for these systems were found. These results indicate a method of tailoring the stability and the temperature sensitivity of the investigated curcumin‐encapsulated cubic liquid crystals.

Application of the stretched exponential equation to sorption of mine gases and sorption induced swelling of bituminous coal

An evaluation of the ability of the stretched exponential (SE) equation to describe the sorption kinetics and the rate of expansion/contraction of hard coal in coal–carbon dioxide, coal–methane and coal–CO2/CH4 mixture systems was performed. In order to address this issue the adequate sorption experiments were carried out at high pressure by means of the volumetric method on a cubicoid solid samples. Simultaneously the kinetics of coal sorption-induced swelling were monitored. For two coals under investigation a linear and a non-linear relation between coal expansion and the amount of sorbed gas was observed. The SE equation shows a very good agreement with the sorption experimental data obtained for both coals, it is also able to accurately describe the sorption-induced-swelling of lower rank coal and the CH4-induced swelling of higher rank coal however it does not give a reasonable fit to swelling kinetics induced by sorption of CO2 and CO2\\CH4 mixtures on higher rank coal. The highest characteristic rate parameter k was found for CO2 sorption on lower rank coal, the lowest was calculated for CH4 sorption on the same coal and the values of k for higher rank coal are in between. The values of stretching parameter b for higher rank coal are greater than for lower rank coal, i.e. between 0.55 and 0.75 and <0.5, indicating a relatively narrow and a relatively broad distribution of characteristic relaxation times of sorption processes, respectively. Generally, the values of parameters k and b calculated for CO2, CH4 and CO2\\CH4 mixture sorption-induced swelling are lower for lower rank coal. The values of parameter b for swelling phenomena are not compatible with these of sorption processes.

Difference between electrostriction kinetics, and mechanical response of segmented polyurethane-based EAP

Among the key parameters, which must be taken into account for the choice of actuators used as electrical to mechanical energy converters, the response to a step function and/or the frequency dependence of this response is extremely important. For polymeric actuators and more generally for electroactive polymers, three mechanisms can be at the origin of energy losses, namely dielectric relaxations, viscoelastic relaxations and possible electrical conductivity. In a previous paper, we studied the electrical behavior of segmented polyurethanes with different weight fractions of hard (MDI-BDO) and soft (PTMO) segments. They were shown to exhibit three main mechanisms, namely, from the fastest to the slowest, a secondary or β-relaxation, the main or α-relaxation associated with the glass–rubber transition of the soft phase, and finally, their electrical conductivity. In the present work, we present the general viscoelastic response (as measured through mechanical spectrometry) of the same polyurethanes and their respective time dependent electrostriction responses, and compare it with the relaxation characteristic times of electrical and mechanical spectroscopy data.

Triple junction drag effects during topological changes in the evolution of polycrystalline microstructures

Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where grain boundary migration is steady-state. Yet, steady-state never occurs during the evolution of polycrystalline microstructures as a result of changing grain size and topological events (e.g., grain face/edge switching - “T1” process, or grain disappearance “T2” or “T3” processes). We examine the non-steady evolution of the triple junction angle in the vicinity of topological events and show that large deviations from equilibrium and/or steady-state angles occur. We analyze $∖tau$ the characteristic relaxation time of triple junction angles τ by consideration of a pair of topological events, beginning from steady-state migration. Using numerical results and theoretical analysis we predict how the triple junction angle varies with time and how τ varies with triple junction mobility. We argue that it is precisely those cases where grain boundaries are moving quickly (e.g., topological process in nanocrystalline materials), that the classical steady-state prediction of the triple junction angle about finite triple junction mobility is inapplicable and may only be applied qualitatively.

Oleofoams: Properties of Crystal-Coated Bubbles from Whipped Oleogels-Evidence for Pickering Stabilization.

Interfacially stabilized nonaqueous lipid-based foams, which we name here oleofoams, are rarely encountered as opposed to the large number of aqueous foams stabilized by molecular or particulate emulsifiers. There is no case well described in the literature with a convincing characterization of the interfacial contribution to oleofoam stability. Methods for filling this gap are described here, which reach out to a large part of the lipid phase diagram. We bring here complete evidence that lipidic crystals made of a high fraction of fully soluble monoglyceride (MG) in oil do not only adsorb at the oil-air interface but also can easily form a jammed, closely packed layer of crystals around the bubbles of a foam produced by whipping (Pickering effect). Very fine bubbles, soft textures, or firmer ones such as for shaving foams could be obtained, with a high air fraction (up to 75%), which is unprecedented. A thin, jammed layer of crystals on bubbles can cause bubbles to retain nonspherical shapes in the absence of bulk effects for times much longer than the characteristic capillary relaxation time for bare bubbles, which is actual evidence for Pickering-type interfacial stabilization. By comparing to foams obtained by depressurization, we show that whipping is necessary for bubble wrapping with a layer of crystals. The origin of high stability against Ostwald ripening at long times is also discussed. Furthermore, we show that these Pickering whipped foams have rheological properties dominated by interfacial or film contributions, which is of high interest for food and cosmetics applications because of their high moduli. This system can be considered to be a model of the crystallization behavior of MG in oil, which is similar to that in many fats. Our methods are very general in the context of lipid-based foaming, in particular, from food materials, and were used in patent applications.

Numerical simulations of Taylor anvil-on-rod impact tests using classical and new approaches

Plastic deformation of samples undergoing Taylor anvil-on-rod impact test is simulated utilising finite element method (FEM). Classical (bilinear plasticity using von Mises stress, Johnson-Cook plasticity model) plasticity models and a new plasticity model based on notion of incubation time of plastic flow initiation are employed to model dynamic deformation of tested samples. In order to verify the obtained solutions, the received predictions are compared to available experimental measurements of deformed sample shapes for two different materials (copper, aluminium) and various initial sample velocities. It is shown that bilinear von Mises plasticity model is not able to provide satisfactory coincidence between the shape of the sample boundary received in numerical simulations and in real experimental conditions. At the same time, models accounting for rate dependency of deformation are providing much more accurate results. Substitution of the concept of "dynamic" yielding stress of a material, depending on the rate of deformation by characteristic time of plastic stress relaxation provides a powerful tool for robust prediction of plastic deformation for a wide range of strain rates. The parameter of the characteristic relaxation time has a clear physical interpretation and theoretically can be evaluated from microstructural studies.

The frequency-dependent AC photoresistance behavior of ZnO thin films grown on different sapphire substrates

Zinc oxide (ZnO) thin films were grown by pulsed layer deposition under an N2 atmosphere at low pressures on a- and r-plane sapphire substrates. Structural studies using X-ray diffraction confirmed that all films had a wurtzite phase. ZnO thin films on a- and r-plane sapphire have grown with orientations along the [0002] and [112[combining macron]0] directions, respectively. Room temperature photoluminescence measurements indicate that the presence of native point defects (interstitial zinc, oxygen vacancies, oxygen antisites and zinc vacancies) is more preponderant for ZnO thin films grown on the r-plane sapphire substrate than the sample grown on the a-plane sapphire substrate. Room temperature impedance spectroscopy measurements were performed in an alternating current frequency range from 40 to 105 Hz in the dark and under normal light. An unusual positive photoresistance effect is observed at frequencies above 100 kHz, which we suggest to be due to intrinsic defects present in the ZnO thin films. Furthermore, an analysis of the optical time response revealed that the film grown on the r-plane sapphire substrate responds faster (characteristic relaxation times for τ1, τ2 and τ3 of 0.05, 0.26 and 6.00 min, respectively) than the film grown on the a-plane sapphire substrate (characteristic relaxation times for τ1, τ2 and τ3 of 0.10, 0.73 and 4.02 min, respectively).

Carbon for Energy Storage Derived from Granulated White Sugar by Hydrothermal Carbonization and Subsequent Zinc Chloride Activation

Various electrochemical methods have been applied to establish the electrochemical characteristics of the electrical double layer capacitor consisting of the activated carbon material based electrodes and 1 M triethylmethylammonium tetrafluoroborate solution in acetonitrile and 1-ethyl-3-methylimidazolium tetrafluoroborate ionic liquid as the electrolytes. Activated carbon material used for the preparation of electrodes has been synthesized from hydrochar prepared via hydrothermal carbonization process of granulated white sugar solution in H2O, followed by activation with ZnCl2 with a mass ratio of 1:4 at the temperature 700°C. High porosity and Brunauer-Emmett-Teller specific surface area (SBET = 2100 m2 g−1), micropore surface area (Smicro = 2080 m2 g−1) and total pore volume (Vtot = 1.05 cm3 g−1) have been achieved for the granulated white sugar derived carbon (GWS carbon) material. Wide region of ideal polarizability (ΔE ≤ 3.0 V), short characteristic relaxation time (0.5 s and 4.0 s), high specific series capacitance (125 F g−1 and 140 F g−1) and high energy density (39 W h kg−1 and 48 W h kg−1) have been calculated for the GWS carbon material in 1 M triethylmethylammonium tetrafluoroborate solution in acetonitrile and 1-ethyl-3-methylimidazolium tetrafluoroborate ionic liquid, respectively, demonstrating that these systems are very promising for energy storage devices.

On Cattaneo–Christov heat flux model for Carreau fluid flow over a slendering sheet

The underlying intentions of this article are to investigate the impact of non-Fourier heat flux model on the stagnation-point flow of non-Newtonian Carreau fluid. In this study, the innovative Cattaneo–Christov constitutive model is introduced to study the characteristics of thermal relaxation time. The flow is impelled by a slendering surface which is of the variable thickness. In the model, the physical mechanism responsible for homogeneous–heterogeneous reactions are further taken into account. Also, the diffusion coefficients of the reactant and auto catalyst are considered to be equal. The governing non-linear partial differential equations consisting of the momentum, energy and concentration equations are reduced to the coupled ordinary differential equations by means of local similarity transformations. The transformed ODEs are tackled numerically by employing an effective shooting algorithm along with the Runge–Kutta Fehlberg scheme. The physical characteristics of the fluid velocity, temperature and concentration profiles are illuminated with the variation of numerous governing factors and are presented graphically. For instance, our result indicates that the temperature and thermal boundary layer thickness are lower in case of Cattaneo–Christov heat flux model when compared to classical Fourier’s heat model. Meanwhile, the rate of heat transfer is significantly improved by a high wall thickness parameter and an opposite influence is found due to the thermal relaxation parameter. We further noticed that a higher value of homogeneous and heterogeneous reaction parameter corresponds to a deceleration in the concentration field and it shows an inverse relation for the Schmidt number. A correlation with accessible results for specific cases is found with fabulous consent.

Non-equilibrium critical behavior of thin Ising films

In this paper we study the non-equilibrium properties of Ising ferromagnetic films using Monte Carlo simulations by short-time dynamic method. We have found thickness dependency of critical exponents z, θ′ and β/ν. Ageing effects were observed in non-equilibrium critical behavior. Former was carried out both from high-temperature and low-temperature initial states. A characteristic time of relaxation, which diverges at a transition temperature in the thermodynamic limit, is obtained as a function of the system size and waiting time.

Interplay between viscosity and elasticity in freely expanding liquid sheets

We investigate the dynamics of freely expanding liquid sheets prepared with fluids with different rheological properties, (i) viscous fluids with a zero-shear viscosity $\eta_0$ in the range $(1-1000) \, \mathrm{mPa.s}$ and (ii) viscoelastic Maxwell fluids whose elastic modulus, $G_0$, characteristic relaxation time, $\tau$, and zero-shear viscosity, $\eta_0=G_0 \tau$, can be tuned over several orders of magnitude. The sheets are produced by impacting a drop of fluid on a small cylindrical solid target. For viscoelastic fluids, we show that, when $\tau$ is shorter than the typical lifetime of the sheet ($\sim 10$ ms), the dynamics of the sheet is similar to that of Newtonian viscous liquids with equal zero-shear viscosity. In that case, for little viscous samples ($\eta_0 <\sim 30$ mPa.s), the maximal expansion of the sheet, $d_{\rm{max}}$, is independent of $\eta_0$, whereas for more viscous samples, $d_{\rm{max}}$ decreases as $\eta_0$ increases. We provide a simple model to account for the dependence of the maximal expansion of the sheet with the viscosity that is based on an energy balance between inertia, surface tension and viscous shear dissipation on the solid target, and which accounts well for our experimental data. By contrast, when $\tau$ is longer than the typical lifetime of the sheet, the behavior drastically differs. The sheet expansion is strongly enhanced as compared to that of viscous samples with comparable zero-shear viscosity, but is heterogeneous with the occurrence of cracks, revealing the elastic nature of the viscoelastic fluid.

Dynamics of single semiflexible polymers in dilute solution.

We study the dynamics of a single semiflexible chain in solution using computer simulations, where we systematically investigate the effect of excluded volume, chain stiffness, and hydrodynamic interactions. We achieve excellent agreement with previous theoretical considerations, but find that the crossover from the time τb, up to which free ballistic motion of the monomers describes the chain dynamics, to the times W-1 or τ0, where anomalous monomer diffusion described by Rouse-type and Zimm-type models sets in, requires two decades of time. While in the limit of fully flexible chains the visibility of the anomalous diffusion behavior is thus rather restricted, the t3/4 power law predicted for stiff chains without hydrodynamic interactions is verified. Including hydrodynamics, evidence for the predicted [tln(t)]3/4 behavior is obtained. Similar good agreement with previous theoretical predictions is found for the decay of the bond autocorrelation functions and the end-to-end vector correlation. Finally, several predictions on the variation of characteristic relaxation times with persistence length describing the chain stiffness are tested.

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.

Telechelic Polymer Hydrogels: Relation between the Microscopic Dynamics and Macroscopic Viscoelastic Response.

Telechelic polymers, that is, hydrophilic polymers with hydrophobic end-groups, spontaneously form hydrogels consisting of interconnected micelles. Here we investigate the relation between the microscopic dynamics determining the connectivity, that is, the lifetime of the physical bonds and the resulting rheological properties. This is achieved by quantitatively relating the chain exchange kinetics measured by time-resolved small-angle neutron scattering (TR-SANS) and the mechanical response obtained from linear oscillatory shear measurements. The results show that the characteristic relaxation time obtained from rheology coincides exactly with TR-SANS at intermediate concentrations. The activation energy, Ea, is concentration-independent and remain exactly the same as for TR-SANS. Upon crossing the melting point, a discrete change in activation energy is observed showing the contribution from the enthalpy of fusion to the release/debridging process. The results clearly show that the mechanical response and connectivity indeed are controlled by molecular exchange processes. The relaxation time at the lowest concentration is found to be faster in rheology as compared to TR-SANS, which can be quantitatively attributed to entropic forces arising from conformational deformation of bridging chains.

Direct surface relief formation by e-beam in amorphous chalcogenide layers

Patterning processes in amorphous Se and $$\hbox {As}_{20}\hbox {Se}_{80}$$ films at short electron beam pulses (from 200 ns to 100 ms) were studied for the first time. The surface reliefs occurring as after-pulses effects were recorded and analysed. Giant hillock formation was detected at about $$200\,\upmu \hbox {s}$$ pulses while very small changes in surface morphology were observed at other pulse durations. The obtained data indicate that the strong increase in e-beam sensitivity of mechanical response (giant surface hillock formation) at about $$200\,\upmu \hbox {s}$$ is due to some resonance effect. A qualitative description is given, relating these times to the characteristic generation and relaxation time of the defects in these materials, which illuminates the process of e-beam induced structural rearrangement. The measurement has been performed at room temperature and at $$-120\,^{\circ }\hbox {C}$$ and only a 20% change in the maximal pattern height has been detected.

Experimental study on drying characteristics of wheat by low-field nuclear magnetic resonance

ABSTRACTThe characteristics of transverse relaxation time (T2) of water in wheat were studied by measuring the relaxation time of low-field nuclear magnetic resonance. Analysis of the exponential distribution of T2 revealed that wheat contains five water components. The T2 relaxation time and distribution significantly changed during drying. The dynamic characteristics of five water components during wheat drying were determined using the signal quantity of their characteristic peaks, which showed different features. Weakly chemically bound water (T22) and water ascribed to cell wall (T23) were the main source of water loss. Moreover, most T23 and extracellular water (T24) were removed during drying. Water migration between strongly chemically bound water (T21) and the other water components was bidirectional. This process was not only affected by temperature but also by wheat moisture content and proportion of the five water components. The start time of water migration advanced and growth rate of T21 at the end of drying to that before drying increased at 60, 70, and 80°C. Drying at varied temperatures should be applied according to the characteristics of five water components during the drying process. In addition, high initial temperature was found to be necessary to achieve high drying rate of T23, T24, and free water (T25). The use of drying temperature of 80°C at the early stage and then changing to 70°C reduced the heat consumption by 4.81% and increased the drying time by 9.61%.

Criteria for extensional necking instability in complex fluids and soft solids. Part I: Imposed Hencky strain rate protocol

We study the necking dynamics of a filament of complex fluid or soft solid in uniaxial tensile stretching at constant imposed Hencky strain rate $\dot\varepsilon$, by means of linear stability analysis and nonlinear (slender filament) simulations. We demonstrate necking to be an intrinsic flow instability that arises as an inevitable consequence of the constitutive behaviour of essentially any material (with a possible rare exception, which we outline). We derive criteria for the onset of necking that are reportable simply in terms of characteristic signatures in the shapes of the experimentally measured rheological response functions, and should therefore apply universally to all materials. As evidence of their generality, we numerically show them to hold in six popular constitutive models of polymers and soft glasses. Two distinct modes of necking instability are predicted. The first is relatively gentle, and sets in when the tensile stress signal first curves down as a function of the time $t$ (or accumulated strain $\epsilon=\dot\varepsilon t$) since the inception of the flow. The second is more violent, and sets in when a carefully defined `elastic derivative' of the tensile force first slopes down as a function of $t$ (or $\dot\varepsilon$). In the limit of fast flow $\dot\varepsilon\tau\to\infty$, where $\tau$ is the material's characteristic stress relaxation time, this second mode reduces to the Consid\'ere criterion for necking in solids. However we show that the Consid\'ere criterion fails to correctly predict the onset of necking in any viscoelastic regime of finite imposed $\dot\varepsilon\tau$. Finally, we elucidate the way these modes of instability manifest themselves in entangled linear polymers, wormlike micelles and branched polymers. We demonstrate four distinct regimes as a function of imposed strain rate, consistent with experimental master curves.

Magnetic relaxation phenomena in the chiral magnet Fe1−xCoxSi : An ac susceptibility study

We present a systematic study of the ac susceptibility of the chiral magnet Fe$_{1-x}$Co$_x$Si with $x$ = 0.30 covering four orders of magnitude in frequencies from 0.1 Hz to 1 kHz, with particular emphasis to the pronounced history dependence. Characteristic relaxation times ranging from a few milliseconds to tens of seconds are observed around the skyrmion lattice A-phase, the helical-to-conical transition and in a region above $T_C$. The distribution of relaxation frequencies around the A-phase is broad, asymmetric and originates from multiple coexisting relaxation processes. The pronounced dependence of the magnetic phase diagram on the magnetic history and cooling rates as well as the asymmetric frequency dependence and slow dynamics suggest more complicated physical phenomena in Fe$_{0.7}$Co$_{0.3}$Si than in other chiral magnets.