Microscopic Relaxation Time Research Articles

Structural and microscopic relaxations in a colloidal glass

The aging dynamics of a colloidal glass has been studied by multiangle dynamic light scattering, neutron spin echo, X-ray photon correlation spectroscopy and molecular dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q(-2). The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q(-2)-dependence in the early stages of aging, to a Q(-1)-dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition.

A quantum relaxation-time approximation for finite fermion systems

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

Critical phenomena in dynamical Ising-typed thin films by effective-field theory

The stationary state solutions of the Ising-typed thin films with different layers in the presence of an external oscillatory field are examined within the effective-field theory. The study focuses on the effects of external field frequency and amplitude on the overall behavior. Particular attention is paid on evolution of the special point with dynamic field frequency corresponding to critical temperature of the three-dimensional infinite bulk system where the surface and modified exchange parameters are of no importance. Some findings such as surface enhancement phenomenon and effect of thickness on the dynamic process are introduced together with some other well known characteristics. An attempt is made to explain the relations between the competing time scales (intrinsic microscopic relaxation time of the system and the time period of the external oscillatory field) and frequency dispersion of the critical temperature coordinate of the special point.

Dielectric Behaviors of Typical Benzene Monosubstitutes, Bromobenzene and Benzonitrile

The dielectric behaviors of typical benzene monosubstitutes, bromobenzene (Br-Bz) and benzonitrile (NC-Bz), were investigated up to 3 THz in the pure liquid state over a temperature range from 10 to 60 °C to understand differences in molecular motions of these simple, planar molecules bearing rather different electric dipole moments: 1.72 and 4.48 D for Br-Bz and NC-Bz in gaseous state, respectively. Temperature dependence of spin-lattice relaxation time (T(1)) for (13)C NMR and viscosities for these liquids were also determined to obtain information for molecular motions. Moreover, depolarized Rayleigh scattering (DRS) experiments were carried out for both liquids at 20 °C to determine frequency dependencies of optical susceptibilities up to 8 THz directly relating to rotational motions of their molecular planes. Most Br-Bz molecules rotate freely over a temperature range examined, showing a Kirkwood correlation factor close to g(K) ∼ 1.0 at dielectric Debye-type relaxation times (ca. 18 ps at 20 °C) essentially identical to microscopic (dielectric) relaxation times evaluated from T(1)(13)C NMR data. A small amount of Br-Bz molecules forms dimeric intermolecular associations in an antiparallel configuration of dipole moments. On the other hand, NC-Bz molecules form stable dimers in the antiparallel dipole configuration at a population much higher than that of Br-Bz because of a markedly greater dipole moment than that of Br-Bz. A major dielectric relaxation mechanism for NC-Bz found at ca. 70 ps at 20 °C results from the dissociation process of dimers with a lifetime longer than a rotational relaxation time, observable as a minor dielectric relaxation mechanism at ca. 12 ps at 20 °C, of individual monomeric NC-Bz molecules without the formation of dimers. The formation of stable dimers in an antiparallel configuration is responsible for the observed small g(K) values, ca. 0.5, and disagreement between major (or minor) dielectric relaxation times and microscopic dielectric relaxation times over the entire temperature range examined.

Hysteretic response characteristics and dynamic phase transition via site dilution in the kinetic Ising model

The decay of the hysteresis loop area of the system, which is obeying a site diluted kinetic Ising model, is considered by the disorder parameter using the effective field theory analysis. The exhibition focuses on the understanding of external field frequency, amplitude and the site concentration dependency of the hysteresis loop area for several powerful treatments. Important characteristics of the hysteretic response, such as frequency dispersion, effect of domain nucleation phenomenon on the dynamic process etc. has been introduced together with well known other characteristics. An attempt has been made to explain the relations between the competing time scales (intrinsic microscopic relaxation time of the system and the time period of the external oscillatory field) and the shape of the response. As a result of the detailed investigations, existence of essentially three, particularly four types of dispersion curves have been propounded.

Dielectric Behavior of Some Small Ketones as Ideal Polar Molecules

The dielectric behaviors of some small symmetric ketone molecules, including acetone, 3-pentanone, cyclopentanone, 4-heptanone, and cyclohexanone, were investigated as a function of temperature (T) over a wide frequency range from 50 MHz (3.14 × 10(8) s(-1), in angular frequency) to 3 THz (1.88 × 10(13) s(-1)). The temperature dependencies of the rotational diffusion times (τ(r)) determined using (17)O NMR spin-lattice relaxation time (T(1)) measurements and viscosities of the ketones were also examined. The obtained temperature dependencies of the parameters for the ketones were compared with those of ideal polar molecules, which obey the Stokes-Einstein-Debye (SED) relationship without the formation of intermolecular dimeric associations and without orientational correlations between dipoles (molecular axes), that is, free rotation. Kirkwood correlation factors (g(K)) of only acetone and 3-pentanone were close to unity over a wide temperature range, whereas those of other ketones were obviously less than unity. These results revealed that no correlations exist between the rotational motions of dipoles in acetone and 3-pentanone, as expected in ideal polar molecules. However, other ketones exhibited orientational correlations in their dipoles because of dipole-dipole interactions via antiparallel configurations. Furthermore, because acetone and 3-pentanone satisfied the SED relationship and because their microscopic dielectric relaxation times (τ(μ)), which were calculated from the determined dielectric relaxation times (τ(D)) via the relationship τ(μ) = τ(D)g(K)(-1), were identical to 3τ(r) and were proportional to Vη(k(B)T)(-1) over the wide temperature range examined, where V, k(B), and η represent the effective molecular volume, Boltzmann's constant, and the viscosity of the liquid molecules, respectively, these two ketone molecules behave as ideal polar molecules. In addition, other ketones not significantly larger than acetone and 3-pentanone in molecular size likely form dimeric intermolecular associations with antiparallel cyclic configurations, which demonstrates the g(K) values less than unity.

The Influence of the Rigidity of a Carbon Nanotube on the Structure and Dynamics of Confined Methanol

In this paper, we compare the behavior of liquid methanol confined by an open-ended single-walled nanotube (SWCNT) under four different simulation conditions by using the molecular dynamics (MD) simulations technique. The first model is a rigid and fixed SWCNT with all its carbon atoms fixed at their initial positions; the second is a flexible and fixed SWCNT with its centre-of-mass fixed at the center of the MD box and with the carbon–carbon bond potential applied; the third is a rigid and floating SWCNT, and the fourth is the most realistic flexible and floating SWCNT model — without fixed atoms and with bond potential. The microscopic structure and transport properties of bulk methanol confined by the four different SWCNTs were analyzed. No changes in the radial distribution functions of the hydrogen bond between MeOH molecules are found, and the self-diffusion constant and microscopic dipole relaxation time are essentially unaffected by the confinements. In spite of the flexible/rigid or fixed/floating ð15; 15Þ SWCNT model used, the structure and transport properties of confined MeOH are found to be very close in all the simulated cases. We conclude that using the approximation of rigid or/and fixed SWCNT does not lead to any systematic errors in properties of the confined liquid. The results show that simulations using rigid carbon nanotubes provide a reliable description of molecular diffusion and other solvent properties in a variety of applications, such electro-chemical devices, membranes and sensors that rely on these properties.

Dynamic Signatures of Microphase Separation in a Block Copolymer Melt Determined by X-ray Photon Correlation Spectroscopy and Rheology

The relationship between structure and dynamics in a polystyrene-polyisoprene block copolymer melt in the vicinity of the order−disorder transition was studied by small-angle X-ray scattering (SAXS), X-ray photon correlation spectroscopy (XPCS), and rheology. Rheological measurements on the disordered state indicate the presence of a fast process arising from the relaxation of polyisoprene chains and a slow process resulting predominantly from the relaxation of concentration fluctuations. In contrast, XPCS measurements of the disordered phase are dominated by diffusion of micelles. Time-resolved SAXS, XPCS, and rheology experiments on samples quenched from disorder-to-order reveal the existence of two regimes. While the microscopic relaxation time, measured by XPCS, increases after all of the quenches, SAXS and rheological signatures of ordering are only seen when the quench depth exceeds a critical value of 10 °C. For quenches 5 °C below the order-to-disorder transition temperature, no changes in the SAXS profiles and rheological properties are observed on experimental time scales. It is evident that nucleation barriers preclude the formation of the ordered phase during shallow quenches. The time-resolved rheology measurements enable estimation of the nucleation barriers that are responsible for the observations in the shallow quench regime.

Viscous hydrodynamics with bulk viscosity – uncertainties from relaxation time and initial conditions

Bulk viscosity suppresses elliptic flow ν 2 , as does shear viscosity. It can thus not be neglected when extracting the shear viscosity from elliptic flow data. We here explore uncertainties in the bulk viscous contribution to viscous ν 2 suppression that arise from presently uncontrolled uncertainties in the initial value of the bulk viscous pressure and its microscopic relaxation time.

Observation of superspin-glass behavior inFe3O4nanoparticles

The aging and memory effects of ${\text{Fe}}_{3}{\text{O}}_{4}$ nanoparticles have been studied using a series of zero-field-cooled (ZFC) and field-cooled magnetization measurements at various aging protocols. The genuine ZFC magnetization after the ZFC procedure with a single stop and wait process shows an aging dip at the stop temperature on reheating. The depth of the aging dip is dependent on the wait time. The frequency dependence of the ac magnetic susceptibility is indicative of critical slowing down at a freezing temperature ${T}_{f}$ $(=30.6\ifmmode\pm\else\textpm\fi{}1.6\text{ }\text{K})$. The relaxation time $\ensuremath{\tau}$ is described by a power-law form with a dynamic critical exponent $x$ $(=8.2\ifmmode\pm\else\textpm\fi{}1.0)$ and a microscopic relaxation time ${\ensuremath{\tau}}_{0}$ $[=(1.33\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{s}]$. The ZFC-peak temperature decreases with increasing magnetic field $(H)$, forming a critical line with an exponent $p=1.78\ifmmode\pm\else\textpm\fi{}0.26$, close to the de Almeida--Thouless exponent $(p=3/2)$. These results indicate that the superspin-glass phase occurs below ${T}_{f}$.

Effective Temperatures and Activated Dynamics for a Two-Dimensional Air-Driven Granular System on Two Approaches to Jamming

We present experiments on several distinct effective temperatures in a granular system at a sequence of increasing packing densities and at a sequence of decreasing driving rates. This includes single-grain measurements based on the mechanical energies of both the grains and an embedded oscillator, as well as a collective measurement based on the Einstein relation between diffusivity and mobility, which all probe different time scales. Remarkably, all effective temperatures agree. Furthermore, mobility data along the two trajectories collapse when plotted vs effective temperature and exhibit an Arrhenius form with the same energy barrier as the microscopic relaxation time.

Causal relativistic hydrodynamics for viscous fluids**Work supported by the US Department of Energy under grant DE-FG02-01ER41190.

We report on recent results from VISH2+1, a code that solves the relativistic Israel–Stewart equations for causal viscous hydrodynamics for heavy-ion collisions with longitudinal boost invariance. We find that even ‘minimal’ shear viscosity η/s = ℏ/(4π) leads to a large reduction of elliptic flow compared to ideal fluid dynamics. We explore systematically the sensitivity of this reduction to the equation of state, system size, initial conditions and the microscopic relaxation time in different formulations of the Israel–Stewart equations.

Creep and relaxation functions of a heterogeneous viscoelastic porous medium using the Mori-Tanaka homogenization scheme and a discrete microscopic retardation spectrum

In this paper the macroscopic creep and relaxation functions of a heterogeneous viscoelastic porous medium are derived by using Mori-Tanaka homogenization scheme. Analytical and semi-analytical solutions can then be determined with a parametric number of heterogeneous phases embedded in a viscoelastic matrix whose behavior is described with a parametric number of analogical units. Under some simplifying assumptions, a solution strategy is presented in order to make explicit how the microscopic retardation and relaxation times of the viscoelastic matrix control the distribution of the retardation and relaxation times of the homogenized medium.

Water Diffusion in a Synthetic Hectorite Clay Studied by Quasi-elastic Neutron Scattering

We present a quasi-elastic neutron scattering study of water dynamics confined in a model clay system, a synthetic hectorite with Na+ compensating counterions. As shown by water adsorption gravimetry and neutron/X-ray diffraction, the clay system has, unlike its natural counterparts, very well-defined swelling characteristics, with a clear appearance of a monohydrated and a bihydrated state. This simplifies to a great extent neutron scattering analysis and interpretation. Initially, microscopic relaxation times as well as long-range self-diffusion coefficients for water in Na-hectorite at ambient temperature are determined using the time-of-flight (TOF) and neutron spin echo (NSE) neutron scattering techniques, applying a simple model of isotropic (three-dimensional) translational diffusion. Results from the two techniques are in excellent agreement, giving diffusion coefficient of approximately 1.5 × 10-10 m 2 s-1 and 4.5 × 10-10 m 2 s-1 for the monohydrated and bihydrated state, respectively. Concentrat...

Simulations of aging and plastic deformation in polymer glasses

We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation time scales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that the entire distribution of relaxation times scales identically with age. Despite large changes in mobility, we observe comparatively little structural change except for a weak logarithmic increase in the degree of short-range order that may be correlated with an observed decrease in aging with increasing load.

Relation between macroscopic and microscopic dielectric relaxation times in water dynamics

AbstractA simplified derivation for the ratio of macroscopic to microscopic relaxation times of polar liquids is based on the Mori‐Zwanzig projection‐operator technique, with added statistical assumptions. We obtain several useful forms for the lifetime ratio, which we apply to the dynamics of liquid water. Our theoretical single‐molecule relaxation times agree with the second Debye relaxation times as measured by frequency‐domain dielectric spectroscopy of water and alcohols. From the theory, fast relaxation modes couple to the Debye relaxation time, τd, through very large water clusters, and their temperature dependence is similar to that of τd. Slower modes are localized to smaller water clusters and exhibit weaker temperature dependence. This is exemplified by the lifetime ratios measured by time‐domain dielectric spectroscopy and optical Kerr effect spectroscopy, respectively.

Density of states and group velocity of electrons inSiO2calculated from a full band structure

The full band structure of SiO 2 has been determined in order to calculate parameters that are necessary for the description of carrier transport. Ah initio calculations of the density of states and group velocity for theconduction bands of SiO 2 are worked out as a function of energy. Four different crystal structures of SiO 2 are investigated, which are known to be built up by the same fundamental unit, namely, the SiO 4 tetrahedron: they are the α- and β-quartz and the α- and β-cristobalite. All of them are polymorphs of silica. The conduction bands are calculated by means of two different techniques: the Hartree-Fock method and density-functional theory. The different features of the two methods are examined. Eight energy bands are used to calculate the density of states and group velocity for the energies of interest. Based on such calculations, the relevant scattering mechanisms have been modeled to determine the microscopic relaxation times. This in turn allows for the solution of the Boltzmann transport equation in the coordinate and energy space, which eventually leads to the calculation of macroscopic quantities such as carrier concentration, average velocity, and average energy. Examples are given of calculated electron mobility and average energy, along with comparisons with experimental results available in the literature.

Hierarchy of dielectric relaxation times in water

This work presents a simple model, which allows us to obtain the relation between macroscopic and microscopic dielectric relaxation times in water on the basis of the Zwanzig–Mori formalism for the time correlation functions. In the model it is supposed that water consists of areas, so-called clusters, the size of which are defined by the dipoles spatial correlation radius. The macroscopic dielectric relaxation time of a sample is the relaxation time of the cluster polarization. The obtained relation between macroscopic and microscopic dielectric relaxation times contains the parameters depending on the cluster shape and structure. Such an approach is valid for the associated liquids having one macroscopic relaxation time only. As to systems with the wide distribution of relaxation times this approach demands generalization.

Photophysics of a Bridged 7-Diethylamino-4-methyl-coumarin C102: Studying the Hydrogen Bonding Effect by Time Resolved Stimulated Emission

The time-resolved stimulated emission of a 7-diethylamino-4-methyl-coumarin dye, Coumarin 102 (C102), was investigated in polar and hydroxylic solvents. Analysis of these spectroscopic measurements using semiempirical solvent polarity scales (ET(30), Kamlet and Taft) showed that the stabilization of the excited singlet state is mainly governed by dipolar and hydrogen bonding interactions. This particuliar behavior was reflected by a good adequacy between the present measured solvation times and the microscopic (or molecular) relaxation times related to both the Debye relaxation time τD (dielectric continuum model) and the Kirkwood factor gk, which expresse the degree of short range order in the liquid. These data were compared with the ones obtained for thioxanthone via pump−probe experiments and other data available in the literature.

On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system size, whereas the time scale for relaxation to equilibrium depends on microscopic dynamics. To illustrate this, we also look at deterministic and stochastic versions of the Ehrenfest model with a distribution of microscopic relaxation times.