Physical mechanisms responsible for the relaxation time distribution in disordered dielectrics

The relaxation time distribution function F(τ) is calculated in the framework of the random-field theory. The function F(τ) is expressed through the distribution function f(E) of a random electric field E with due regard for the derived dependence of the relaxation time τ on the electric field. The distribution function F(τ) is calculated in terms of the statistical theory within the random-field approximation. The nonlinear random-field contributions and spatial effects of correlations between randomly distributed electric dipoles are taken into account. The calculations are performed for a mixed ferroelectric glassy phase in which the short-range and long-range polar orders coexist. It is demonstrated that the inclusion of nonlinear contributions of the random field leads to an asymmetric relaxation time distribution function F(τ), whereas allowance made only for the linear random-field contributions results in a symmetric function F(τ). A comparison of the calculated functions F(τ) with empirical functions derived from the Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-Williams-Watts (KWW), and Havriliak-Negami (HN) laws for the dielectric response shows that these laws correspond to disordered systems in which the long-range and short-range orders coexist. Different forms of the function F(τ) are determined by either linear (the CC law) or nonlinear (the DC, KWW, and HN laws) contributions of the random field.     

Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Whereas the first part of this paper dealt with the relaxation in the β-regime, this part investigates the final relaxation (α-relaxation) of a simulated polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of ideal mode-coupling theory (MCT). The temperature range covers the onset of a two-step relaxation behaviour down to a temperature merely 2% above . We monitor the incoherent intermediate scattering function as well as the coherent intermediate scattering function of both a single chain and the melt over a wide range of wave numbers q. Upon approaching the coherent α-relaxation time of the melt increases strongly close to the maximum q _max of the collective static structure factor S_q and roughly follows the shape of S_q for q q _max. For smaller q-values corresponding to the radius of gyration the relaxation time exhibits another maximum. The temperature dependence of the relaxation times is well described by a power law with a q-dependent exponent in an intermediate temperature range. Deviations are found very close to and far above , the onset of which depends on q. The time-temperature superposition principle of MCT is clearly borne out in the whole range of reciprocal vectors. An analysis of the α-decay by the Kohlrausch-Williams-Watts (KWW) function reveals that the collective KWW stretching exponent and KWW relaxation time show a modulation with S_q. Furthermore, both incoherent and coherent KWW times approach the large-q prediction of MCT already for q > q _max. At small q, a q^-3 power law is found for the coherent chain KWW times similar to that of recent experiments.     

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T _g , the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T _g , revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.     

Continuous distribution of relaxation times during mechanical relaxation of fully-stabilized zirconia

The internal friction (IF) was measured for ZrO₂ doped with 10 mol% Y₂O₃ polycrystals and single crystals before aging. The degree of the temperature shift with the frequency change δ(1/T?) was examined in order to determine if one or both parameters in the Arrhenius's equation contribute to the occurrence of the continuous distribution of relaxation times (τ). A continuous distribution is derived only from the continuous distribution of the pre-exponential factor (τ ₀), while the activation energies (H?) for τ are constant in two peaks. The peak fitting was carried out using some conventional distribution functions, i.e., the RCSI model, and some famous functions for dielectric relaxation. The IF curves can be fitted quite well by the Kohlrousch–Williams–Watts (KWW) equation with reasonable parameters. The orientation factor (Γ) dependence of the relaxation of the reciprocal torsional modulus (δG ^?1) is a linear function relative to Γ in both peaks. When the H for τ of both peaks of the poly- and single crystals was compared, the polycrystalline results should be considered average values of the single-crystalline results. Therefore, the single-crystalline IF peaks also consist of two peaks and the parameters (the relaxation strength and H?) obtained by the peak fitting are valid. A continuous distribution of τ is derived only from the continuous distribution of τ ₀ and the distribution function is the KWW equation.     

Linear relaxation processes governed by fractional symmetric kinetic equations

The fractional symmetric Fokker-Planck and Einstein-Smoluchowski kinetic equations that describe the evolution of systems influenced by stochastic forces distributed with stable probability laws are derived. These equations generalize the known kinetic equations of the Brownian motion theory and involve symmetric fractional derivatives with respect to velocity and space variables. With the help of these equations, the linear relaxation processes in the force-free case and for the linear oscillator is analytically studied. For a weakly damped oscillator, a kinetic equation for the distribution in slow variables is obtained. Linear relaxation processes are also studied numerically by solving the corresponding Langevin equations with the source given by a discrete-time approximation to white Levy noise. Numerical and analytical results agree quantitatively.     

Dielectric permittivity and electric modulus of polyethylene oxide (PEO)-LiClO4 composite electrolytes

Dielectric permittivity and conductivity relaxation in polyethylene oxide (PEO)-LiClO₄ salt polymer electrolytes have been investigated for different lithium ion concentrations. We have observed that imaginary modulus spectra exhibit asymmetric maxima with peak-width much broader than that of the Debye peak and are skewed toward the high frequency sides of the maxima. The charge carriers for the electrolyte having higher lithium salt concentration relax much faster than that for other electrolytes and produces higher conductivity. The modulus data have been fitted using non-exponential Kohlrausch-Williams-Watts (KWW) function φ(t). We have observed that the value of the non-exponential parameter (β) is fairly low and nearly constant for different salt concentrations. The low value of β suggests a wide distribution of non-exponential relaxation times. Using the scaling of modulus data we have observed that the relaxation dynamics of charge carriers in these PEO-Li salt based electrolytes is independent of temperature and salt concentration.     

Microscopic theory of heterogeneity and nonexponential relaxations in supercooled liquids.

Recent experiments show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999)]. Such heterogeneity is expected from the random first order transition theory of the glass transition. Using a microscopic approach based on this theory, we derive a relation between the departure from Debye relaxation as characterized by the beta value of a stretched exponential response function, phi(t) = e(-(t/tau(KWW))beta), and the fragility of the liquid. The beta value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.     

Transient chaos in quantum and classical mechanics

Bogolubov's classical example of statistical relaxation in a many-dimensional linear oscillator is discussed. The relation of the discovered relaxation mechanism to quantum dynamics as well as to some new problems in classical mechanics is considered.     

Finite-difference time-domain simulation of ultrashort pulse propagation incorporating quantum-mechanical response functions

A semiclassical implementation of the finite-difference time-domain method is used to simulate coherent linear propagation of ultrashort mid-infrared pulses through optically dense samples of isotropically diluted liquid water. Bloch equations for the density matrix are used as a simple model of the O--H oscillator relaxation, and the algorithm is extended to other response functions. Sensitivity of the field to the form of the response function is demonstrated, and the results are compared with experimentally determined electric fields in the same media [Rev. Sci. Instrum. 73, 2227 (2002)].     

Glass transition and enthalpy relaxation of polyphosphate compounds

The glass transition behaviour of polyphosphate compounds such as di- and tri- polyphosphates used as food additives and ATP, ADP existing in biosystems, were investigated by using DSC. From the DSC heating curves of the frozen solutions, the glass transition temperatures of the maximum freeze concentrated solutions, Tg', were determined. It was found that Tg's for polyphosphates are relatively high. The lyophilized tripolyphosphates, ATP and ADP also showed the glass transition at a relatively high temperature, depending on the moisture content. In addition, the enthalpy relaxation behaviour of glassy ATP and ADP was examined and analyzed by using the Kohlrausch-Williams-Watts (KWW) and the Vogel-Fulcher-Tammann (VFT) equations. Judging from the parameters of the KWW and VFT equations, the amorphous states of ATP and ADP were suggested to be more fragile than trehalose and sucrose.     

Coupling of the relaxation and resonant elements in the autonomous chaotic relaxation oscillator (ACRO)

If a harmonic oscillator is embedded in a relaxation oscillator, the resulting system may behave like an autonomous chaotic relaxation oscillator (ACRO). The discharge transient of the relaxation oscillator excites sinusoidal oscillations in the harmonic oscillator and these sinusoids affect when the next discharge occurs. This can lead to chaotic intervals in the oscillator periods. A simple electronic model of the ACRO is studied over a wide range of parameters using numerical, analytic, and experimental techniques. The dynamics of the ACRO is found to be determined by three parameters: (1) tuning, (2) coupling, and (3) damping. Complex, intermittent outputs can always be inhibited by increasing the damping of the harmonic oscillator. For weak damping, strong coupling yields chaotic periods. With weak damping and weak coupling, complex behavior only occurs if the relaxation oscillator is tuned near a resonance of the harmonic oscillator. A new path to chaos, called a disruption bifurcation, is the source for intermittency in the ACRO. This bifurcation occurs when the amplitude of internal resonances is excited to the degree that existing limit cycles are disrupted.     

Glass transitions and dynamics in thin polymer films: dielectric relaxation of thin films of polystyrene

The glass transition temperature T(g) and the temperature T(alpha) corresponding to the peak in the dielectric loss due to the alpha process have been simultaneously determined as functions of film thickness d through dielectric measurements for polystyrene thin films supported on glass substrate. The dielectric loss peaks have also been investigated as functions of frequency for a given temperature. A decrease in T(g) was observed with decreasing film thickness, while T(alpha) was found to remain almost constant for d>d(c) and to decrease drastically with decreasing d for d相似文献   

Structural relaxation in polyethylene in the presence of silver oxide investigated by positron-lifetime spectroscopy

Structural relaxation in high-density virgin polyethylene and silver oxide doped polyethylene has been investigated using positron annihilation lifetime technique at 30 °C and 100 °C ageing temperatures. The ortho-positronium (o-Ps) pick-off lifetime and its intensity show no changes with isothermal ageing time for the virgin sample at 30 °C. In the case of the doped sample at 30 °C, the o-Ps intensity shows exponential relaxation in the short-time range. At 100 °C, the o-Ps lifetime remains almost constant, whereas the o-Ps intensity exhibits an exponential character in the virgin and doped samples, which can be fitted with exponential decay curves. The relaxation times have been evaluated from the structural relaxation function constructed using o-Ps intensity values, and the stretching exponent has been estimated using the Kohlrausch–Williams–Watts (KWW) function. Positron results indicate that the stretching exponent seems to be temperature dependent. PACS 78.70.Bj     

Linear and nonlinear resonance features of an erbium-doped fibre ring laser under cavity-loss modulation

The continuous-wave output of a single-mode erbium-doped fibre ring laser when subjected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the dynamical study of these resonances shows that the behaviour of the system exhibits features of a nonlinear damped oscillator under harmonic modulation. These nonlinear dynamical features, including harmonic and subharmonic resonances, have been studied experimentally and analysed with the help of a simple time-domain and frequency-domain information obtained from the output of the laser. All the studies are restricted to the modulation frequency lying in a regime near the relaxation oscillation frequency.     

Pure odd-order oscillators with constant excitation

In this paper the excited vibrations of a truly nonlinear oscillator are analyzed. The excitation is assumed to be constant and the nonlinearity is pure (without a linear term). The mathematical model is a second-order nonhomogeneous differential equation with strong nonlinear term. Using the first integral, the exact value of period of vibration i.e., angular frequency of oscillator described with a pure nonlinear differential equation with constant excitation is analytically obtained. The closed form solution has the form of gamma function. The period of vibration depends on the value of excitation and of the order and coefficient of the nonlinear term. For the case of pure odd-order-oscillators the approximate solution of differential equation is obtained in the form of trigonometric function. The solution is based on the exact value of period of vibration. For the case when additional small perturbation of the pure oscillator acts, the so called ‘Cveticanin's averaging method’ for a truly nonlinear oscillator is applied. Two special cases are considered: one, when the additional term is a function of distance, and the second, when damping acts. To prove the correctness of the method the obtained results are compared with those for the linear oscillator. Example of pure cubic oscillator with constant excitation and linear damping is widely discussed. Comparing the analytically obtained results with exact numerical ones it is concluded that they are in a good agreement. The investigations reported in the paper are of special interest for those who are dealing with the problem of vibration reduction in the oscillator with constant excitation and pure nonlinear restoring force the examples of which can be found in various scientific and engineering systems. For example, such mechanical systems are seats in vehicles, supports for machines, cutting machines with periodical motion of the cutting tools, presses, etc. The examples can be find in electronics (electromechanical devices like micro-actuators and micro oscillators), in music instruments (hammers in piano), in human voice producing folds (voice cords), etc.     

Dynamics of driven Brownian inverted oscillator

In this paper, we derive the quantum Langevin equation for a driven Brownian inverted oscillator in the framework of the Heisenberg picture for the Caldeira-Leggett model. We describe the influence of an arbitrary time-dependent force on an open inverted oscillator dynamics. We take into account environment through the integral operator of relaxation and the force correlation function. The resulting behavior of the system is represented as a combination the time evolution of the position expectation and the variance, being induced simultaneously by spreading the wave packet and the chaotic Brownian motion. We discuss the possibility of stabilization of an open inverted oscillator, when applying external alternating force.