Characteristic Relaxation Time Research Articles

Strain rate relaxation of normal and thrust faults in Italy

We find that geodetic strain rate (SR) integrated with the knowledge of active faults points out that hazardous seismic areas are those with lower SR, where active faults are possibly approaching the end of seismic cycle. SR values estimated from GPS velocities at epicentral areas of large historical earthquakes in Italy decrease with increasing elapsed time, thus highlighting faults more prone to reactivation. We have modelled an exponential decrease relationship between SR and the time elapsed since the last largest earthquake, differencing historical earthquakes according to their fault rupture style. Then, we have estimated the characteristic times of relaxation by a non-linear inversion, showing that events with thrust mechanism exhibit a characteristic time (∼ 990 yr) about three times larger than those with normal mechanism. Assuming standard rigidity and viscosity values we can infer an average recurrence time of about 600 yr for normal faults and about 2000 yr for thrust faults.

Atomistic simulations of cavitation in a model polyethylene network

A molecular-level understanding of cavitation in polymer networks upon imposition of mechanical stress is still lacking. Molecular Dynamics simulations of crosslinked amorphous Polyethylene (PE) were conducted in order to study cavitation as a function of the prevailing stress. We first show that the characteristic relaxation times related to tube confinement and chain connectivity can be obtained by examining the mean square displacement of middle chain monomers. Then, we present a methodology for predicting the cavitation strength and understanding its dependence on cohesive interactions and entropic elasticity. Our simulations show that experimental observations and predictions of continuum mechanics analysis, which relate the critical stress for cavitation to the Young’s modulus of the rubber, are in agreement with the observed tensile triaxial stress below which a pre-existing cavity cannot survive in a cavitated sample.

RETRACTED: Protein dynamics by neutron scattering

Neutron scattering techniques represent a powerful tool for characterizing both the structure and dynamical properties of bio-systems, for example, proteins and membranes interacting with their solvents. In this paper, Elastic Neutron Scattering (ENS) data collected at the Institut Laue-Langevin (Grenoble, France) on dry and D2O hydrated lysozyme by varying hydration level are presented, and compared with previously published data on the same protein system, also with the addition of bio-protectants. The data have been collected with three different spectrometers, i.e. IN13, IN10 and IN4. This set of ENS data gives direct access to the temperature behavior of both (i) the Mean Square Displacement (MSD) and (ii) the characteristic system relaxation time. As a result, an explicative hypothesis on the relationship between the so-called "protein dynamical transition" (PDT) and the "fragile-to-strong dynamical crossover" (FSC) is formulated. Furthermore, by taking into proper account the effect of the finite instrumental energy resolution of the used spectrometers, the vibrational MSD of dry and hydrated lysozyme is calculated. The vibrational MSD of the lysozyme in the dry state resulted to be higher than the one in the hydrated state; the latter reaches the former at a temperature value of T=220K that corresponds to the temperature at which the FSC occurs. As a result, a cage effect resulting from the hydration water on the protein surface is hypothesized and subsequently linked to the FSC.

Electron-ion relaxation time dependent signal enhancement in ultrafast double-pulse laser-induced breakdown spectroscopy

We investigated the emission properties of collinear double-pulse compared to single-pulse ultrafast laser induced breakdown spectroscopy. Our results showed that the significant signal enhancement noticed in the double pulse scheme is strongly correlated to the characteristic electron-ion relaxation time and hence to the inter-pulse delays. Spectroscopic excitation temperature analysis showed that the improvement in signal enhancement is caused by the delayed pulse efficient reheating of the pre-plume. The signal enhancement is also found to be related to the upper excitation energy of the selected lines, i.e., more enhancement noticed for lines originating from higher excitation energy levels, indicating reheating is the major mechanism behind the signal improvement.

Thermodynamics and mechanics of photochemcially reacting polymers

We develop a thermodynamics and mechanics theory for polymers that when irradiated with light, undergo photochemical reactions that alter their macromolecular structure, e.g., by bond breaking and/or reformation, and in turn affect their mechanical and physical behavior. This emerging class of highly-engineered active materials shows great promise for myriad applications and is a subset of a broader class of polymers with covalent bonds that can be dynamically tuned with various environmental stimuli. We formulate a general thermodynamic and kinetic framework to model the complex photochemical–thermal–mechanical coupling in these materials. Our theory considers the behavior of a polymer that is subjected to the combination of mechanical and thermal loading while simultaneously irradiated by light with multiple frequency components and directions. We introduce an approach to model the photochemical reactions that can change the network topology, resulting chemical species transport, heat conduction and finite deformation. We describe the interaction of the material with light via a radiometric description and show how it can be linked to a full electromagnetic treatment when appropriate and if desired. Our approach is sufficiently general to permit the modeling of various materials that operate via different photochemical reaction mechanisms. After formulating the general theory, we specialize it to a polymer that when irradiated with light undergoes a series of photochemical reactions that cause chain scission and reformation which continuously rearrange the polymer network into a stress-free configuration. Based on the operant physical mechanisms we develop a constitutive model using a polymer chain decomposition and evolution approach to track the molecular structure changes during simultaneous irradiation and mechanical loading. In the special case of isothermal conditions with monochromatic and unidirectional irradiation, we recover a previous model based on intuitive ad-hoc assumptions and thus put it on strong thermodynamic footing. Finally we use our model to simulate the behavior of a polymer that is biaxially stretched and then irradiated with light from one side. We simulate the process and emphasize the spontaneous bending that occurs due to inhomogeneous photoinduced stress relaxation. From our theory, we obtain an analytical expression of a characteristic time for photo-induced stress relaxation in terms of the dominating system parameters.

Transients in Porous Media: Exact and Modelled Time-Domain Green's Functions

Time domain responses of porous media have been studied by some authors, but generally the possible descriptions have been given in the frequency domain. The aim of this paper, limited to materials with rigid skeleton considered as equivalent fluids, is to compare the descriptions by Johnson-Allard ($JA$%) as well as by Pride-Lafarge ($PL$) with i) some analytical, approximate formulas, based upon asymptotic high frequency expansion ; ii) the exact formula by Zwikker and Kosten for the case of cylindrical pores. The paper starts with a short summary of the statement of the different general full frequency models ($JA$ and $PL).$ The Green function in the time domain is shown to exhibit interesting properties of materials. In particular the maximum response depends on one dimensionless parameter only, which is denoted $\xi $ and is the ratio of the travelled distance to the product of the \textquotedblleft frozen\textquotedblright\ sound speed and a characteristic viscous relaxation time. The distance $\xi $ is related to a time domain Stokes number. The numerical computation of the Green function is done by FFT, with some precautions, because of the importance of the higher frequencies on the response shape. The $PL$ description is shown to be the best full frequency general model, but some discrepancies with the exact model appear at short times or short distances. When the distance $\xi $ increases from zero, the asymptotic expansion shows that the maximum of the Green function decreases first as $1/\xi ^{2}$, then exponentially.

Shear rheology of water/glycerol monostearate crystals in canola oil dispersions interfaces

2.0% or 3.0% wt glycerol monostearate (GMS) was put into canola oil (CO) at 70°C, and the dispersions were cooled down to 30°C (cooling rate of 1.0 or 10.0°C/min), in order to obtain GMS crystals in CO dispersions (CDx,y). Particle size, shape, and crystallinity index of CDx,y was determined. Water/oil interfaces were prepared and the shear rheological response of the adsorbed layers was studied at different ageing times. In all the cases, the interfaces exhibited creep compliance-time dynamics, whose experimental data fitted well a model represented by a Hookean spring in series with two Kevin–Voigt elements, providing two characteristic relaxation times. The fast relaxation time was related to the rearrangement of a rigid disordered layer of crystals adsorbed at the interface taking place at small time scales (about 2s) as a consequence of the applied shear; while the slow relaxation time was related to further GMS crystals adsorption from the interface vicinity, which induced a slower rearrangement and reconfiguration of crystals at the interface in the face of shear disturbances. Model parameters values with respect to ageing time showed that the water/oil interface reached an equilibrium state after about 5–7h for higher GMS concentration.

Nanoconfined segmental dynamics in miscible polymer blend nanocomposites: the influence of the geometry of nanoparticles

The influence of nanoconfinement on segmental relaxation behavior of poly(methyl methacrylate) and poly(styrene-ran-acrylonitrile) miscible blend and its nanocomposites with spherical and layered nanoparticles have been investigated. Dynamic mechanical analysis was employed to examine the effect of geometry of nanoparticles on the temperature dependence and relaxation function breadth of segmental dynamics (α-relaxation) in the glass transition region. The maxima of the loss modulus curves were used to fit to the Vogel–Fulcher–Tamman equation to describe the temperature dependence of the characteristic relaxation times. Furthermore, the T g-normalized semi-logarithmic Arrhenius plots (fragility plots) were exploited to indicate the changes in cooperative segmental motions across the glass transition. The master curves for relaxation modulus were also constructed for each sample as a function of time using the time–temperature superposition principle. The investigated nanocomposites showed a narrower segmental dispersion in the glass transition region compared to the neat systems. The relaxation modulus master curves were fitted by the Kohlrausch–Williams–Watts (KWW) function. It was observed that the distribution parameter of segmental relaxation time increased with addition of nanoparticles which was correlated with a decrease in fragility index. In addition, the increase of the KWW distribution parameter (β KWW) for spherical silica nanocomposites was less than that for nanocomposites prepared with layered silicates (organoclay).

Microfluidic extensional rheometry using a hyperbolic contraction geometry

Microfluidic devices are ideally suited for the study of complex fluids undergoing large deformation rates in the absence of inertial complications. In particular, a microfluidic contraction geometry can be utilized to characterize the material response of complex fluids in an extensionally-dominated flow, but the mixed nature of the flow kinematics makes quantitative measurements of material functions such as the true extensional viscosity challenging. In this paper, we introduce the ‘extensional viscometer-rheometer-on-a-chip’ (EVROC), which is a hyperbolically-shaped contraction-expansion geometry fabricated using microfluidic technology for characterizing the importance of viscoelastic effects in an extensionally-dominated flow at large extension rates (\(\lambda \dot \varepsilon _a \gg 1\), where \(\lambda \) is the characteristic relaxation time, or for many industrial processes \(\dot \varepsilon _a \gg 1\) s\(^{-1}\)). We combine measurements of the flow kinematics, the mechanical pressure drop across the contraction and spatially-resolved flow-induced birefringence to study a number of model rheological fluids, as well as several representative liquid consumer products, in order to assess the utility of EVROC as an extensional viscosity indexer.

Spatial and temporal effects upon deposition of particles onto thin films of silicon dioxide produced using high-energy deposition processes

The interaction of deposited atoms with a silicon dioxide film is simulated for the case of using high-energy processes for the deposition of optical nanocoatings. The method of molecular dynamics with a classical force field is used for describing the interaction between the atoms. The characteristic time of fast relaxation of the kinetic energy of the deposited atom and the characteristic depth of its penetration into the film are estimated. It is shown that the angular distribution of the velocities of the deposited atoms is significant for the formation of a coating.

A cone-partitioned plate rheometer cell with three partitions (CPP3) to determine shear stress and both normal stress differences for small quantities of polymeric fluids

Edge fracture hampers the measurement of the two normal stress differences N1 and N2 in a cone-partitioned plate rheometer with two partitions (CPP2). A third nonmeasuring partition has therefore been added, solely to shield off edge fracture (CPP3). The partial normal forces on the inner two partitions are much better balanced than on the CPP2. The new partitioned plate rheometer cell has been downsized to fit an MCR300. Potentially, N1 and N2 can now be obtained for all rheometric tests that can be performed with that rheometer. This publication reports on the technical features of the CPP3 cell. Step shear-rate tests in the range 0.1 < Wi < 3 and a strain of γ = 40 have been performed with a poly(dimethyl siloxane) (PDMS) standard to proof the rheometric functionality. The characteristic relaxation time of the PDMS is comparable to the axial response time, in spite of a cone angle of 0.15 rad. This means that transient normal force data are affected by instrument compliance. Steady state N1 and N2 however are measured correctly. N1 compares with data from a CPP2 and the MCR300, but can be determined with much less polymer. The scattering of the steady state second normal stress difference N2 is substantially reduced compared to the CPP2. A critical evaluation of the pros and cons of the CPP3 is given, based on the results of this study.

A quasi-static algorithm that includes effects of characteristic time scales for simulating failures in brittle materials

When the brittle heterogeneous material is simulated via lattice models, the quasi-static failure depends on the relative magnitudes of [Formula: see text], the characteristic releasing time of the internal forces of the broken elements and [Formula: see text], the characteristic relaxation time of the lattice, both of which are infinitesimal compared with [Formula: see text], the characteristic loading period. The load–unload (L–U) method is used for one extreme, Telem ≪ Tlattice, whereas the force–release (F–R) method is used for the other, Telem ≫ Tlattice. For cases between the above two extremes, we develop a new algorithm by combining the L–U and the F–R trial displacement fields to construct the new trial field. As a result, our algorithm includes both L–U and F–R failure characteristics, which allows us to observe the influence of the ratio of [Formula: see text] to [Formula: see text] by adjusting their contributions in the trial displacement field. Therefore, the material dependence of the snap-back instabilities is implemented by introducing one snap-back parameter γ. Although in principle catastrophic failures can hardly be predicted accurately without knowing all microstructural information, effects of γ can be captured by numerical simulations conducted on samples with exactly the same microstructure but different γs. Such a same-specimen-based study shows how the lattice behaves along with the changing ratio of the L–U and F–R components.

Time-resolved optical response of all-oxide YBa2Cu3O7/La0.7Sr0.3MnO3proximitized bilayers

We present femtosecond pump--probe spectroscopy studies of time-resolved optical reflectivity of all-oxide YBa${}_{2}$Cu${}_{3}$O${}_{7}$/La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ (YBCO/LSMO) superconductor/ferromagnet (S/F) bilayers consisting of a 100-nm-thick YBCO base layer and either 10 or 35 nm LSMO cap thickness. At temperatures far below the YBCO superconducting transition ${T}_{C}$, samples with a 10 nm F overlayer show a photoresponse that is similar to, but faster than, pure-YBCO, 100-nm-thick reference samples, while close to ${T}_{C}$ and above (up to \ensuremath{\sim}160 K) we observe a signature of both the electronic and spin response that cannot be interpreted as an incoherent sum of contributions from the two layers. The photoresponse of the S/F structures with the 35-nm LSMO layer always qualitatively follows that of the pure LSMO, but with a shorter relaxation time. In all cases, the YBCO/LSMO nonequilibrium dynamics can be modeled using a generalized multitemperature model, which is a superposition of the dynamics of the three-temperature models that are used to describe the superconductor and ferromagnet subsystems, respectively. The long term of the photoresponse signal of the S/F bilayer can be well fitted with the two characteristic relaxation times.

The possibility of using femtosecond IR spectroscopy to determine the composition of molecules in the gas phase

The possibility of using one method of femtosecond laser spectroscopy, IR pump-probe, is considered for analyzing the molecular composition of gas. The measured intramolecular relaxation time of the vibrational energy is proposed as an individual characteristic of molecules. A number of compounds of different classes having the molecular chromophore group C=O are investigated. It is shown that the characteristic relaxation times of the corresponding analytical signals in the resonant exciting of C=O vibrations are significantly different for different molecules (ten or more), making it possible to identify molecules in mixtures by means of temporal selection. The linear dependence of the analytical signal on the vapor pressure of the investigated compounds and the energy fluence of the exciting radiation is revealed. It is shown that the analytical signal is not dependent on the pressure of the buffer gas (nitrogen) up to 1 atm.

Extremely Slow Spin Relaxation in a Spin-Unpolarized Quantum Hall System

Cyclotron spin-flip excitation in a ν=2 quantum Hall system, being separated from the ground state by a slightly smaller gap than the cyclotron energy and from upper magnetoplasma excitation by the Coulomb gap [S. Dickmann and I. V. Kukushkin, Phys. Rev. B 71, 241310(R) (2005); L. V. Kulik, I. V. Kukushkin, S. Dickmann, V. E. Kirpichev, A. B. Van'kov, A. L. Parakhonsky, J. H. Smet, K. von Klitzing, and W. Wegscheider, Phys. Rev. B 72, 073304 (2005)] cannot relax in a purely electronic way except only with the emission of a shortwave acoustic phonon (k~3×10(7)/cm). As a result, relaxation in a modern wide-thickness quantum well occurs very slowly. We calculate the characteristic relaxation time to be ~1 s. Extremely slow relaxation should allow the production of a considerable density of zero-momenta cyclotron spin-flip excitations in a very small phase volume, thus forming a highly coherent ensemble-the Bose-Einstein condensate. The condensate state can be controlled by short optical pulses (~1 μs), switching it on and off.

Surface Characterization of Supercapacitor Electrodes after Long-Lasting Constant Current Tests

TOF-SIMS, FIB-SEM, XPS and electrochemical methods have been used for the characterization of physical properties and chemical composition of microporous carbide derived carbon electrodes, prepared from TiC at 950 ºC (noted as TiC-CDC) after 40000 charge/discharge cycles. Some changes in surface chemical composition of TiC-CDC electrodes and Al current collectors has been established including partial dissolution of Al from positively charged electrode and deposition of Al onto the negatively charged TiC-CDC electrode surface. The values of gravimetric energy (taking into consideration the active TiC-CDC material weight only) calculated before and after constant current charge/discharge cycling tests at cell voltage 3.4 V were quite similar (35 and 34 W h kg-1, respectively). At starting moment the gravimetric power was practically 1.4 times higher (195 kW kg-1, 146 kW dm-3) than that calculated after 40000 charge/discharge cycles (144 kW kg-1, 104 kW dm-3). The characteristic relaxation time constant (0.94 and 1.23 s, respectively) increases somewhat in accordance with the decrease of power density during long-lasting cycling at higher cell voltage range from 0.2 to 3.4 V.

Four-component united-atom model of bitumen

We propose a four-component united-atom molecular model of bitumen. The model includes realistic chemical constituents and introduces a coarse graining level that suppresses the highest frequency modes. Molecular dynamics simulations of the model are carried out using graphic-processor-units based software in time spans in order of microseconds, which enables the study of slow relaxation processes characterizing bitumen. This paper also presents results of the model dynamics as expressed through the mean-square displacement, the stress autocorrelation function, and rotational relaxation. The diffusivity of the individual molecules changes little as a function of temperature and reveals distinct dynamical time scales. Different time scales are also observed for the rotational relaxation. The stress autocorrelation function features a slow non-exponential decay for all temperatures studied. From the stress autocorrelation function, the shear viscosity and shear modulus are evaluated, showing a viscous response at frequencies below 100 MHz. The model predictions of viscosity and diffusivities are compared to experimental data, giving reasonable agreement. The model shows that the asphaltene, resin, and resinous oil tend to form nano-aggregates. The characteristic dynamical relaxation time of these aggregates is larger than that of the homogeneously distributed parts of the system, leading to strong dynamical heterogeneity.

Associating and rheological behaviors of fluorinated cationic guar gum in aqueous solutions

The fluorinated cationic guar gum (FCGG) was prepared with cationic guar gum (CGG) and fluorinated reactive monomer (FAM). FAM was synthesized from isophorone diisocyanate and 2,2,3,4,4,4-hexafluoro-1-butanol. The molecular structure, associating and rheological behaviors of FCGG were studied by the FT-IR, 19F NMR, X-ray diffraction, dynamic rheometer and fluorescence spectroscopy, respectively. The results show that FAM is successfully incorporated into CGG. With the increased degree of substitution (DS), the crystallinity is reduced from 3.01 to 0.67% and the characteristic relaxation time is changed significantly from 0.10 to 3.3s. At low shear rates (<20s−1), the viscosity of FCGG solution increases with the increase of shear rates. The bigger the DS, the higher the apparent viscosity. The viscosity retention factor of FCGG can reach 126.97% at 30°C and 51.33% at 60°C, respectively. The data indicate that FCGG has much better heat resistance.

Glassy Dynamics of Protein Methyl Groups Revealed by Deuteron NMR

We investigated site-specific dynamics of key methyl groups in the hydrophobic core of chicken villin headpiece subdomain (HP36) over the temperature range between 298 and 140 K using deuteron solid-state NMR longitudinal relaxation measurements. The relaxation of the longitudinal magnetization is weakly nonexponential (glassy) at high temperatures and exhibits a stronger degree of nonexponentiality below about 175 K. In addition, the characteristic relaxation times deviate from the simple Arrhenius law. We interpret this behavior via the existence of distribution of activation energy barriers for the three-site methyl jumps, which originates from somewhat different methyl environments within the local energy landscape. The width of the distribution of the activation barriers for methyl jumps is rather significant, about 1.4 kJ/mol. Our experimental results and modeling allow for the description of the apparent change at about 175 K without invoking a specific transition temperature. For most residues in the core, the relaxation behavior at high temperatures points to the existence of conformational exchange between the substates of the landscape, and our model takes into account the kinetics of this process. The observed dynamics are the same for dry and hydrated protein. We also looked at the effect of F58L mutation inside the hydrophobic core on the dynamics of one of the residues and observed a significant increase in its conformational exchange rate constant at high temperatures.

Fast Dynamics and Relaxation of Colloidal Drops during the Drying Process Using Multispeckle Diffusing Wave Spectroscopy

The fast dynamics generated by the Brownian motion of particles in colloidal drops, and the related relaxation during drying, which play key roles in suspension systems, were investigated incorporating multispeckle diffusing wave spectroscopy (MSDWS). MSDWS equipment was implemented to analyze the relaxation properties of suspensions under a nonergodic and nonstationary drying process, which cannot be elucidated by conventional light scattering methods, such as dynamic light scattering and diffusing wave spectroscopy. Rapid particle movement can be identified by the characteristic relaxation time, which is closely related to the Brownian motion due to thermal fluctuations of the particles. In the compacting stage of the drying process, the characteristic relaxation time increased gradually with the drying time because the particles in the colloidal drop were constrained by themselves. Moreover, variations of the initial concentration and particle size considerably affected the complete drying time and characteristic relaxation time, producing a shorter relaxation time for a low concentrated suspension with small particles.