Wide Range Of Relaxation Times Research Articles

Dynamics of non-equilibrium concentration fluctuations during free-diffusion in highly stratified solutions of glycerol and water.

We investigate the non-equilibrium fluctuations occurring during free diffusion between two solutions of glycerol and water with various concentration differences. The non-linearity of the system, determined by the strong stratification of the sample, requires introducing an interpretation model able to characterize the dependence of the correlation properties of the non-equilibrium fluctuations on the local thermophysical variables of the system. The proposed model allows us to characterize the dynamics of non-equilibrium fluctuations in the presence of a wide range of relaxation times determined by the strong stratification of the sample, at variance with the cumulant methods commonly used in dynamic light scattering experiments, which work well in the presence of a moderate dispersion of relaxation times.

Multiscale Analysis of Segmental Relaxation in PC/PETg Multilayers: Evidence of Immiscible Nanodroplets

This work highlights the influence of layer thicknesses on glass transition and molecular mobility in polycarbonate (PC) and poly(ethylene terephthalate glycol) (PETg) multilayered films obtained by the layer-multiplying coextrusion process. By combining modulated temperature scanning calorimetry (MT-DSC) and dielectric relaxation spectroscopy (DRS) measurements, the average values of the cooperative rearranging region (CRR) size in a wide range of relaxation times and temperatures have been calculated. The size reduction from micro- to nanoscale is accompanied by a significant deviation of the structural and dynamical properties compared to the bulk. Furthermore, we have evidenced significant differences in PETg and PC behaviors: PETg plays the role of a “hard-confined” polymer, while PC behaves as a “free-confined” polymer, implying opposite variations of the glass transition temperature. The determination of the relaxation parameters for each individual polymer has been possible even for very low layer thicknesses (below 10 nm), for which the multilayer structure is not observed. This result shows that even when PETg and PC are brought into very intimate contact, they maintain their own structural behavior and segmental relaxation, suggesting the formation of immiscible nanodroplets when the multilayer structure disappears.

Prediction of Li-ion battery capacity degradation considering polarization recovery with a hybrid ensemble learning model

Polarization recovery is a phenomenon that significantly affects the capacity degradation behavior of lithium-ion battery (LIB). In this study, we demonstrated that capacity fluctuation during fading was highly correlated with polarization recovery through micro-Roman and rate performance tests. A series of aging experiments with a wide range of relaxation times (0.08 h to 200 h) were developed to analyze the effects of polarization recovery on discharge capacity. The experimental dataset includes 30,696 charge-discharge cycles under various conditions based on LiFePO4/graphite and LiNi0.8Co0.15Al0.05O2/graphite battery cells. Here, a hybrid ensemble learning model (HEL) was proposed to achieve accurate predictions while considering polarization recovery. Multiple highly correlated stress factors of polarization recovery were identified and then utilized as the input data of HEL. Our analysis shows that HEL is capable of precisely capturing capacity degradation with fluctuations due to polarization recovery, the implication of which is critical to the advancement of lifetime management in battery energy storage applications.

Why the Cox–Merz rule and Gleissle mirror relation work: A quantitative analysis using the Wagner integral framework with a fractional Maxwell kernel

In this work, we mathematically derive the conditions for which empirical rheometric relations such as the Cox–Merz rule and Gleissle mirror relationship are satisfied. We consider the Wagner integral constitutive framework, which is a special limiting case of the Kaye–Bernstein Kearsley Zapas (K-BKZ) constitutive equation to derive analytical expressions for the complex viscosity, the steady shear viscosity, and the transient stress coefficient in the start-up of steady shear. We use a fractional Maxwell liquid model as the linear relaxation modulus or memory kernel within a non-linear integral constitutive framework. This formulation is especially well-suited for describing complex fluids that exhibit a broad relaxation spectrum and can be readily reduced to the canonical Maxwell model for describing viscoelastic liquids that exhibit a single dominant relaxation time. To incorporate the nonlinearities that always become important in real complex fluids at large strain amplitudes, we consider both an exponential damping function as well as a more general damping function. By evaluating analytical expressions for small amplitude oscillatory shear, steady shear, and the start-up of steady shear using these different damping functions, we show that neither the Cox–Merz rule nor the Gleissle mirror relation can be satisfied for materials with a single relaxation mode or narrow relaxation spectrum. We then evaluate the same expressions using asymptotic analysis and direct numerical integration for more representative complex fluids having a wide range of relaxation times and nonlinear responses characterized by damping functions of exponential or Soskey–Winter form. We show that for materials with broad relaxation spectra and sufficiently strong strain-dependent damping the empirical Cox–Merz rule and the Gleissle mirror relations are satisfied either exactly, or to within a constant numerical factor of order unity. By contrast, these relationships are not satisfied in other classes of complex viscoelastic materials that exhibit only weak strain-dependent damping or strain softening.

Explicit and viscosity-independent immersed-boundary scheme for the lattice Boltzmann method.

Viscosity independence of lattice-Boltzmann methods is a crucial issue to ensure the physical relevancy of the predicted macroscopic flows over large ranges of physical parameters. The immersed-boundary (IB) method, a powerful tool that allows one to immerse arbitrary-shaped, moving, and deformable bodies in the flow, suffers from a boundary-slip error that increases as a function of the fluid viscosity, substantially limiting its range of application. In addition, low fluid viscosities may result in spurious oscillations of the macroscopic quantities in the vicinity of the immersed boundary. In this work, it is shown mathematically that the standard IB method is indeed not able to reproduce the scaling properties of the macroscopic solution, leading to a viscosity-related error on the computed IB force. The analysis allows us to propose a simple correction of the IB scheme that is local, straightforward and does not involve additional computational time. The derived method is implemented in a two-relaxation-time D2Q9 lattice-Boltzmann solver, applied to several physical configurations, namely, the Poiseuille flow, the flow around a cylinder towed in still fluid, and the flow around a cylinder oscillating in still fluid, and compared to a noncorrected immersed-boundary method. The proposed correction leads to a major improvement of the viscosity independence of the solver over a wide range of relaxation times (from 0.5001 to 50), including the correction of the boundary-slip error and the suppression of the spurious oscillations. This improvement may considerably extend the range of application of the IB lattice-Boltzmann method, in particular providing a robust tool for the numerical analysis of physical problems involving fluids of varying viscosity interacting with solid geometries.

Dynamic Heterogeneity and Cooperative Length Scale at Dynamic Glass Transition in Glass Forming Liquids

Understanding the evolution of the cooperative molecular mobility as a function of time and temperature remains an unsolved question in condensed matter research. However, recently great advances have been made within the framework of the Adam–Gibbs theory on the connection between cooperatively rearranging regions, or dynamic heterogeneities, i.e., domains of the supercooled liquid whose relaxation is highly correlated. The growth of the size of these dynamic domains is now believed to be the driving mechanism for different experimental parameters like relaxation times and viscosity of supercooled liquid approaching the glass transition. Recent studies have shown the evolution of cooperative motions in supercooled liquids using different experimental tools and models. In this work, broadband dielectric spectroscopy and modulated temperature differential scanning calorimetry were carried out on six different amorphous glass-forming systems in order to scan a wide range of relaxation times and temperatures...

A Direct Solver for Initial Value Problems of Rarefied Gas Flows of Arbitrary Statistics

AbstractAn accurate and direct algorithm for solving the semiclassical Boltzmann equation with relaxation time approximation in phase space is presented for parallel treatment of rarefied gas flows of particles of three statistics. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to capture the time evolution of the discretized velocity distribution function in physical space and time. The method is developed for two space dimensions and implemented on gas particles that obey the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Computational examples in one- and two-dimensional initial value problems of rarefied gas flows are presented and the results indicating good resolution of the main flow features can be achieved. Flows of wide range of relaxation times and Knudsen numbers covering different flow regimes are computed to validate the robustness of the method. The recovery of quantum statistics to the classical limit is also tested for small fugacity values.

Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations

We discuss implicit-explicit (IMEX) Runge--Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We consider both the case of easy invertible collision operators and the challenging case of Boltzmann collision operators. We give sufficient conditions in order that such methods are asymptotic preserving and asymptotically accurate. Their monotonicity properties are also studied. In the case of the Boltzmann operator the methods are based on the introduction of a penalization technique for the collision integral. This reformulation of the collision operator permits us to construct penalized IMEX schemes which work uniformly for a wide range of relaxation times avoiding the expensive implicit resolution of the collision operator. Finally, we show some numerical results which confirm the theoretical analysis.

Using hierarchical memory to calculate friction force between fractal rough solid surface and elastomer with arbitrary linear rheological properties

An algorithm for calculating the force of friction between a fractal rough solid surface and a model elastomer with arbitrary linear rheological properties has been developed based on the method of dimensionality reduction with application of a hierarchically organized memory. Using this method, it is possible to calculate the friction force between an elastomer and a solid surface with experimentally determined topography, taking into account both the broad spectrum of wave vectors (ranging from nanometers to centimeters) for real surfaces and the wide range of relaxation times (from nanoseconds to seconds).

Exponential Runge–Kutta Methods for Stiff Kinetic Equations

We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a nonequilibrium part and are exact for relaxation operators of BGK type. For Boltzmann-type kinetic equations they work uniformly for a wide range of relaxation times and avoid the solution of nonlinear systems of equations even in stiff regimes. We give sufficient conditions in order that such methods are unconditionally asymptotically stable and asymptotic preserving. Such stability properties are essential to guarantee the correct asymptotic behavior for small relaxation times. The methods also offer favorable properties such as nonnegativity of the solution and entropy inequality. For this reason, as we will show, the methods are suitable both for deterministic as well as probabilistic numerical techniques.

Single-Molecule Pump-Probe Detection Resolves Ultrafast Pathways in Individual and Coupled Quantum Systems

We report the first experimental study of individual molecules with femtosecond time resolution using a novel ultrafast single-molecule pump-probe method. A wide range of relaxation times from below 100 up to 400 fs is found, revealing energy redistribution over different vibrational modes and phonon coupling to the nanoenvironment. Addressing quantum-coupled molecules we find longer decay times, pointing towards inhibited intramolecular decay due to delocalized excitation. Interestingly, each individual system shows discrete jumps in femtosecond response, reflecting sudden breakup of the coupled superradiant state.

The use of transient electric birefringence to characterize the conformation of DNA in solution, the mechanism of DNA gel electrophoresis, and the structure of agarose gels

Abstract Two small, 153 base-pair (bp) DNA restriction fragments, one of which migrates anomalously slowly during electrophoresis in polyacrylamide gels, have been characterized by transient electric birefringence (TEB). The decay of the birefringence of the anomalously slowly migrating fragment is faster than that of the normal fragment under a variety of buffer conditions, suggesting that the anomalous fragment is stably bent or curved in free solution. Reversing field experiments suggest that both the anomalous and normal DNA fragments orient in the electric field by a slow induced dipole mechanism. Birefringence relaxation times have also been measured for three DNA molecules embedded in agarose gels of various concentrations. The embedded DNA molecules become oriented in the electric field, just as in free solution. If the median pore diameter of the gel is approximately twice as large as the apparent end-to-end length of the DNA in solution, the relaxation times of the embedded DNA molecules are unaffected by the presence of the gel, indicating that the DNA retains its usual wormlike coil conformation in the gel matrix. However, as the end-to-end length of the DNA approaches the median pore diameter of the gel, the DNA molecules become stretched out and elongated in the electric field, leading to a repetitive, or end-on, mode of migration during electrophoresis. The relaxation times of the stretched DNA molecules scale as the 2.8 power of molecular weight, in reasonable agreement with reptation theories. The structure of agarose gels has also been characterized by TEB. The long, low voltage electric fields used for pulsed field gel electrophoresis (PFGE) cause extensive orientation of the agarose gel fibers. A wide range of relaxation times is observed after the field is removed, corresponding to the orientation of gel fibers up to 22 μm in length. The sign of the birefringence is variable, indicating that the gel fibers can be oriented in different directions in different parts of the gel. Surprisingly, the sign of the birefringence reverses upon field reversal, suggesting that the gel fibers change their direction of orientation in reversing electric fields. This anomalous orientation behavior is not observed for chemically crosslinked polyacrylamide gels. The apparent orientation and reorientation of agarose gel fibers in rapidly reversing electric fields may lead to ‘dynamic pores’ in the gel matrix, facilitating the migration of very large DNA molecules during PFGE.

Nano-scale medium-range order in semiconducting glassy chalcogenides

Comprehensive X-ray diffraction studies of bulk glassy g-(As2S3)0.95In0.05, g-(As2S3)0.95(GaSb)0.05 and g-(As2S3)0.56I0.44 samples reveal a large-scale medium-range ordering with correlation lengths up to ∼ 50 Å. The In- or Ga-doped glasses are considered non-homogeneous media containing a discrete hierarchy of metal enriched nanoclusters embedded in a metal-depleted g-As2S3 matrix. In this qualitative model, the observed additional optical absorption band, as well as the surprising phenomenon of stable optical anisotropy in g-As2S3:In, are explained. Large amounts of I atoms produce a more flexible medium-range order superstructure which may be easily rearranged by photoexcitation. This is the reason for the strong photoinduced metastable optical anisotropy in g-As2S3:I with a rather wide range of relaxation times.

Memory effects in the self-diffusion of interacting Brownian particles

We study the time-dependent self-diffusion coefficient for suspensions of interacting, spherical Brownian particles. The self-diffusion coefficient exhibits memory effects with a wide range of relaxation times and a long-time tail. An approximate description of the time dependence involving a small number of parameters is proposed. We test the approximation for an exactly solvable model in which the particles interact via a square step or well potential and show that it works satisfactorily.

Kinetics of Diabatic and Adiabatic Electron Exchange in Organic Systems Comparison of Theory and Experiment

AbstractThe rate constants ket of electron self exchange between neutral molecules and the corresponding radical ions, measured by ESR line broadening, are discussed for seven organic ϕ‐systems in 18 aprotic solvents of a wide range of relaxation times, τL (0.2 < τL/ps < 10), and polarities, γ(0.05 < γ 0.53) in terms of the theoretical approaches of Marcus and Sumi and of Jortner and Bixon, both valid for comparable magnitudes of inner and outer reorganization energies. (γ = < γ = 1/n2‐1/ε; n = refractive index; ε = dielectric constant.) The electron transfer is diabatic for four substituted p‐phenylenediamines, it is adiabatic relaxation overdamped for tetracyanoquinodimethane (TCNQ), tetrathiafulvalene (TTF) and tetracyano‐ethylene (TCNE). By changing the solvents no transition between both mechanisms is found. To explain the results, the reactants are represented by ellipsoids. Their centre to centre distance in the transition state is derived from slopes of lnket τL γ−1/2 vs. γ (for adiabatic reactions) or of Infketγ1/2 vs. γ (for diabatic reactions). The mutual orientation of the reactants follows the minimum of electrostatic energy. The resonance splitting V for this orientation, calculated from the overlap integrals agrees well for all systems with the observed diabatic or adiabatic behaviour of the reaction, except for TCNE. The resonance splitting and the equilibrium constant of the precursor complex are derived experimentally from the temperature dependence of the electron transfer rate constant ket. Negative association energies of the complex are due to ion‐dipole interactions of the reactants. An additional reorganization term is observed for the aliphatic TCNE system in ethereal solvents. To describe the experiments quantitatively, both theories used are nearly equivalent.

Mechanical properties of Bacillus subtilis cell walls: effects of removing residual culture medium

Experiments are described in which the tensile strength, the initial (Youngs') modulus, and other mechanical properties of the bacterial cell wall were obtained as functions of relative humidity (RH) in the range of 20 to 95%. These properties were deduced from tensile tests on bacterial thread, a fiber consisting of many highly aligned cells of Bacillus subtilis, from which residual culture medium had been removed by immersion in water. Reasons are given to support the idea that the mechanical properties of bacterial thread relate directly to those of the cylinder wall and that they are not influenced by septa, cytoplasm, or the thread assembly. The data show that the cell wall, like many other heteropolymers, is visco-elastic. When dry, it behaves like a glassy polymer with a tensile strength of about 300 MPa and a modulus of about 13 GPa. When wet, its behavior is more like a rubbery polymer with a tensile strength of about 13 MPa and a modulus of about 30 MPa. Thus, the cell wall is stronger than previously reported. Walls of this strength would be able to bear a turgor pressure of 2.6 MPa (about 26 atm). The dynamic behavior suggests a wide range of relaxation times. The way in which mechanical behavior depends strongly on humidity is discussed in terms of possible hydrogen bond density and the ordering of water molecules. Cell walls in threads containing residual culture medium TB are, except at low RH, 10 times more flexible and about 4 times less strong. All of their mechanical properties appear to vary with change in RH in a manner similar to those of walls from which the culture medium has been washed, but with a downshift of about 18% RH.

Macroscopic quantum interference and superconducting glass state in YBa2(Cu1−xFex)3O7−δ

Macroscopic quantum phenomena and superconducting glass state have been observed simultaneously in a random system of linked Josephson junctions in lumps of suitable high temperature superconducting ceramics Y-Ba-Cu-O. This multiply connected Josephson medium was used for radio-frequency SQUID operation at temperatures up to 90 K. The effect of nonergodic glass state on SQUID behaviour readily was observed. The presence of a wide range of relaxation times in glass state leads to an appreciable noise of 1/f type in the SQUID output signal at f ≲ 103 Hz.

Dynamics of photoinduced isomerization of azobenzene moieties in liquid‐crystalline polymers

AbstractForced Rayleigh scattering was used to investigate the dynamics of photoinduced isomerization of azobenzene involved in reversible holographic information storage. The studies were performed with statistical liquid‐crystalline side‐group copolymers having different concentrations of the dye, in a copolymer forming no mesophase and in a physical mixture of the dye in a liquid‐crystalline side‐group homopolymer. Two relaxation processes were found in the glassy state of these polymers, the faster one being distributed over a wide range of relaxation times ascribed mainly to reorientational relaxation of the dye as well as the glassy matrix. The second is a single exponential, ascribed to the relaxation of azobenzene back to its trans conformation. The two processes could be assigned through a control experiment using an irreversibly isomerizing dye. The results of a calculation of the angular dependence of azobenzene isomerization was compared with the experiment, in order to judge the influence of the anisotropic matrix on the relaxation process.

Thermoluminescent relaxation of stable systems

The Kohlrausch relaxation function (or the stretched exponential function) is compared in detail with a kinetic model for isothermal temperature stimulated luminescent decay based on a Gaussian distribution of activation energies. In each case the reactivity rate is assumed to follow an Arrhenius form (or the Randall-Wilkins form) s exp(- E/kT). Use of the Gaussian distribution has been found to give a good accounting of observed experimental results. The present investigation is primarily meant to determine the uniqueness of such fits to experimental data. As appropriate for this purpose, the controlling parameters of the two relaxation functions are forced into equivalence by an imposed normalization. The normalization point is selected for a critical time to best reveal the differences between the two time dependent relaxation functions. Although the resulting two decay functions are not rendered completely identical, close numerical agreement over a wide range of relaxation times and activation energy distribution widths is found. The similarity in the widths of the corresponding energy distributions is found to be the main reason for this close agreement. Exact features of the activation energy distribution are important only in the very short and very long time periods of the relaxation process. Recovering the activation energy distribution from experimentally measured data is discussed in detail.

The contrast-to-noise in relaxation time, synthetic, and weighted-sum MR images.

The contrast-to-noise ratio (CNR) in three types of computed MR images is compared in a computer simulation. The original data consist of two spin-echo or two saturation-recovery images. Each pair of images is used to generate a relaxation time image, a synthetic image at arbitrary echo or repetition time, and an image which is a weighted sum of the original images. The CNR produced by these three methods is compared for signals spanning a wide range of relaxation times. In every comparison an optimally weighted sum produces the highest CNR that is statistically attainable. The CNR in the optimum synthetic image equals this bound only if contrast reversal does not occur in the original images. The CNR in relaxation time images is always less than the statistical bound and can be less than the CNR in the original images.