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Spin-coated films of poly(bisphenol A carbonate) (PC) and poly(styrene- co -acrylonitrile) (SAN) doped by 4-( N , N -dimethylamino)-4′-nitrostilbene (DANS) were prepared, and their poling and depoling behaviors were investigated mainly by UV–visible absorption spectra and second-harmonic generation (SHG). The absorbance of DANS in the PC and SAN films proportionally increased with increasing its weight concentration up to 5 wt%, indicating homogeneous dissolution of DANS in the host polymers. However, above this concentration, heterogeneous structures due to DANS crystallites could be observed under a polarizing microscope. Poling of the films was performed using a triode corona discharging system. The maximum d coefficients were obtained at slightly lower poling temperature than the glass transition temperature of the corresponding dye-doped polymer. The KWW stretched exponential function could be fitted to the experimental temporal relaxation data of SHG for the SAN system. Relatively high long-term stability was observed for the PC system because of its relatively rigid backbone structure.

Objective The goal of this investigation was to assess validity of predictive models of stress relaxation in dental polymers when applied to extended master curves generated from short time experimental data by WLF time temperature superposition method. Methods The stress relaxation modulus changes with time at three different temperatures near the ambient body temperature were determined for selected mono-methacrylate (PEMA and PMMA) and dimethacrylate (bis-acryl) dental polymers. WLF time–temperature superposition procedure of logarithmic shift of the data from other temperatures to those at 37 °C was used to generate extended master curves of relaxation modulus changes with time. The extended data were analyzed for conformity to three different predictive models of stress relaxation including Maxwell, KWW stretched exponential function and Nutting's power law equation. Results Maxwell model was found to be a poor fit for the extended data in all polymers tested, but the data showed a much better fit for KWW (0.870 R 2 R 2 β in the KWW function and the fractional power exponent n in Nutting's equation were both significantly different for PEMA based system when compared to that of PMMA and bis-acryl systems. Significance The mean values of β in KWW function and power exponent n in Nutting's equation for PEMA resin is consistent with significant viscoplastic contribution to its deformation under stress unlike in PMMA and bis-acryl resin systems. This may have significant bearing for PEMA use in medium to longer term stress-bearing applications even as a temporization material.

The self-diffusion coefficient Ds of dye-labeled polystyrene chains having Mw = 3.90 × 105 g/mol and Mw/Mn < 1.10 was measured over almost 4 decades of polymer concentration in toluene solution, from 10-4 to 0.4 g/mL, by fluorescence correlation spectroscopy. In the dilute regime up to 5 × 10-3 g/mL, Ds remains practically constant. The transition to the semidilute regime is observed around 0.01 g/mL, and from 0.02 to 0.4 g/mL Ds decreases strongly with rising concentration. This decrease is well represented by a power law, Ds ∼ c-1.75, as predicted by scaling and reptation theory. As an alternative, a good fit over the whole concentration range can be obtained with a stretched exponential function, Ds = D0 exp(−15c0.65), with D0 = 2 × 10-7 cm2/s and c given in g/mL.

The dielectric relaxation in a supercooled liquid is analyzed in a model in which the liquid is composed of slowly moving molecules within clusters and fast ones between them. If the dielectric α-relaxation of molecules inside a cluster is described by a stretched exponential function then the cluster dynamics, with molecules leaving and entering the clusters, can lead to the relaxation of the system’s polarization being described by a stretched exponential function with a larger stretching exponent, that depends on the rate at which the molecules leave the clusters. The implications of this for time–temperature superposition and other properties of supercooled liquids are discussed.

The kinetics of thermal relaxation of an ensemble of photoinduced metastable electrically active B atoms in (a-Si:H):B films is studied after partial relaxation of the ensemble in the dark and under illumination of various intensities and duration. The parameters of a stretched exponential function that describes the ensemble kinetics are determined. It is found that photoinduced relaxation of metastable states manifests itself under conditions in which its rate exceeds the rate of the states’ photoinduced generation. It is shown that the variations in the relaxation-time distribution function of metastable states caused by thermal and photoinduced relaxation are similar.

Photo-induced bleaching of self-trapped holes (STH) in UV-irradiated synthetic silica has been investigated by the electron spin resonance method. We have observed two kinds of STH, STH1 and STH2 as assigned by Griscom in Ref. [D.L. Griscom, Phys. Rev. B 40 (1989) 4224]. The decay of all the spectral features was found to follow a stretched exponential function; and those features with the similar decay behavior were assigned to the same defect. The decay time obtained from the averaged fitting value for STH1 is about 4 times longer than that for STH2. Furthermore, the separated STH1 and STH2 signals have been experimentally obtained for the first time on the basis of the different decay times for each of two kinds of STHs. � 2005 Published by Elsevier B.V.

In this study, the amount of decrease in coercive field of congruent lithium niobate during repeated poling and back-poling was measured. The polarization is reversed in 300 ms and then back-poled during the rest period. The coercive field can be decreased around 1 kV/mm with a repeated poling interval of 5 s. As the interval prolonged, the poling field decrease became smaller, and a stretched exponential function is suggested for the experimental fitting resulting in a set of meaningful parameters. These values are essential for the design of high quality domain engineering.

In this work, stress-induced relaxation processes in sol-gel derived lead zirconate titanate (PZT) films with a Zr/Ti ratio of 30/70 were investigated by nanoindentation with a spherical tipped conductive indenter. The capacitance and electrical current transient flowing through the film under short-circuit conditions were measured as a function of constant nanoindentation force in the time domain. Measurements on piezoelectric films of different thickness indicated a significant mechanical clamping of the ferroelectric domains produced by the substrate. It is demonstrated that both the dielectric and electro-mechanical relaxation behavior are dependent on stress state in the film, which is affected during indentation. The relaxation of the electromechanical response is found to follow a stretched exponential function, the parameters of which are dependent on the indentation force and film thickness. On the other hand, the small signal capacitance measurement showed much slower relaxation characterized by...

The electrical conductivity of NaNO3-xAl2O 3 composites has been studied over the wide range of temperature and frequency by means of impedance spectroscopy. The real part of the frequency dependent conductivity exhibits a simple power law feature and the dimensionless frequency exponent n has been determined. The conductivity spectra show scaling behaviour when the conductivity spectra are scaled by �dcT, where T is temperature in Kelvin. The real part of dielectric permittivity shows saturation at higher frequencies and a strong dispersion at lower frequencies. The imaginary part of permittivity varies inversely with frequency, due to the presence of dc conductivity. The frequency dependent plots of M? and Z? show that the conductivity relaxation is non-Debye in nature. The Kohlrausch-Williams-Watts stretched exponential function was used to describe the modulus spectra and the stretching exponent ? is found to be temperature independent. The conductivity relaxation time has been estimated from the modulus spectra. The activation energy responsible for relaxation has been evaluated and it was found to be almost same as that of dc conductivity. ? 2005 Elsevier B.V. All rights reserved.

Time-resolved photoluminescence (PL) was performed to investigate the decay of blue–green luminescence in MCM-41 nanotubes. The PL decay exhibits a clear nonexponential profile, which can be fitted by a stretched exponential function. In the temperature range from 50 to 300 K the photogenerated carriers become thermally activated with a characteristic energy of 29 meV, which is an indication of the phonon-assisted nonradiative process. The temperature dependence of the lifetime of PL decay has been explained using a model based on the radiative recombination of localized carriers and the phonon-assisted nonradiative recombination.

Relaxation of photo-generated carriers in anatase form of crystalline titanium dioxide has ben studied by the photoconductivity measurement. Illumination of anatase crystal with UV light at 300 K has found to induce persistent enhancement in conductivity over 3000 seconds. The magnitude of the induced change is 4000 times greater than that measured in rutile crystal in the same experimental condition. The decay of the persistent photoconductivity after the termination of the UV illumination was characterized by the stretched exponential function. The excitation spectrum measurement revealed that the persistent conductivity characterized by the stretched-exponential relaxation was induced by super-band-gap excitation.

In this paper experimental results and numerical simulations of fitting exponential functions to OSL decay curves are presented. The measurements show that the OSL decay curves of single grains of a sample can vary in decay form. Despite the fact that all grains have a different OSL decay forms it appears that the OSL decay curve of their sum can be well fitted with a small number of exponential components. The simulations confirm that if the OSL decay curves of single grains consist of single exponentials with varying decay constants and intensity, the OSL decay curves of multiple-grain aliquot can be fitted with one exponential or a sum of two exponentials. The discussion is then extended to LM-OSL curves where similarly the observation of a number of first-order components may be a manifestation of the heterogeneity of the sample. In the simulations, it is also shown that a stretched exponential function may very well fit a sum of exponentials being merely an indication of the heterogeneity of the sample. It is shown that the resolution of the fit of a sum of exponentials to a decay form is limited by the intensity fluctuations. The conclusion is drawn that interpretation of the form of CW- or LM-OSL should be accompanied by complementary measurements and it should be checked that the sample is homogenous, e.g. by investigating single grains.

The relaxation properties of poly(propylene oxide) at temperatures above the glass‐transition temperature are studied by quasi‐elastic neutron scattering and molecular dynamics (MD) simulations. The contributions to the dynamic structure factor from the segmental motion and the methyl group jump rotation are separated using a threefold jump‐rotation model for the methyl side group motion, with a delta function for the distribution of relaxation times, and a stretched exponential function for the segmental motion. This simple model describes momentum transfer and time dependence of the data over a wide temperature range. The results show that with this separation, both neutron and MD data can be well described, and the analysis of both contributions is necessary in order to obtain reliable results for the segmental relaxation and rotational relaxation times at temperature above T g .

The first ever enthalpy relaxation study has been conducted of the glass transition of the bulk metallic glass forming composition Zr 65 Al 10 Ni 10 Cu 15 using differential scanning calorimetry (DSC). Both heating and cooling and isothermal annealing studies have been conducted. The glass transition temperature measured at 20 °C/min heating following a 20 °C/min cooling of 384 °C ± 2 °C agrees well with values previously published for this glass. Using the dependence of T g on heating and cooling rate, the onset T g activation energy was determined to be 120 kcal/mole ± 10 kcal/mole with the peak T g activation energy, determined by the temperature of the peak in the T g overshoot, was observed to be 98 kcal/mole ± 10 kcal/mole. Such increases in the activation energy, while not common for such transition range measurements, is consistent with this glass exhibiting non-Arrhenius enthalpy and possibly viscous relaxation rates. The heating and cooling and annealing DSC data were converted to derivative fictive temperature data and then fit to the Tool–Narayanaswamy–Moynihan–Hodge model utilizing a stretched exponential function to describe the non-exponentiality and the Tool–Narayanaswamy equation to describe the non-linearity of the relaxation. Best fit parameters for x and β were found to be 0.53 ± 0.05 and 0.79 ± 0.05, respectively. The individual fits to the data are not excellent, but the overall fit to all of the data is surprisingly good given the range of the thermal treatments given to this glass. The model fits worse, however, for the isothermal annealing data. The glass appears to anneal faster than the model predicts for relatively short anneals relatively close to the T g , but appears to anneal much slower than the model predicts for relatively long anneals relatively far from T g . These behaviors are consistent with this metallic glass exhibiting a non-Arrhenius activation energy that increases sharply with decreasing temperatures.

We use the Kardar–Parisi–Zhang equation with quenched noise in order to study the relaxation properties of driven interfaces in disordered media. For λ ≠ 0 this equation belongs to the directed percolation depinning universality class and for λ = 0 it belongs to the quenched Edwards–Wilkinson universality class. We study the Fourier transform of the two-time autocorrelation function of the interface height Ck(t', t). These functions depend on the difference of times t − t' in the steady-state regime. We find a two-step relaxation decay in this regime for both universality classes. The long time tail can be fitted by a stretched exponential function, where the exponent β depends on the universality class. The relaxation time and the wavelength of the Fourier transform, where the two-step relaxation is lost, are related to the length of the pinned regions. The stretched exponential relaxation is caused by the existence of pinned regions which is a direct consequence of the quenched noise.

The time dependence of the decay of dark electrical conductivity σ(t) from C60 crystals under air exposure was investigated at different temperatures. The decay of σ(t) can be fitted via a stretched exponential function, indicating that the diffusion of O2 in C60 crystal follows a hierarchically constrained dynamic. The diffusivity of molecular oxygen in C60 crystal is estimated using the least-square fitted time constant, and an activation energy EA=1.5eV corresponding to the diffusion process is deduced from the Arrhenius plot. The mechanism of the diffusion process is then discussed.

Fluorescence decay profiles of single DNA molecules complexed with ethidium bromides in polymer were measured by time-resolved confocal fluorescence microscopy. In contrast to other single-molecule fluorescence data reported previously, they all exhibit high nonexponentiality that can be analyzed by employing the stretched exponential function. The Kohlrausch β – τ K distributions for individual DNA–dye molecules and their physical significance are presented in the first time.

Linear viscoelastic stress relaxation and calorimetric measurements were performed on a series of mixed alkali tellurite glasses of composition 0.3([xNa2O+(1−x)Li2O])+0.7TeO2 at temperatures near and above the glass transition temperature, Tg. The stress relaxation data were well described by the stretched exponential function, G(t)=G0exp[−(t/τ)β], where τ is the relaxation time, β is the distribution of relaxation times and G0 is the high frequency modulus. The fragility, determined from the temperature dependence of τ, exhibited a minimum in the middle of the mixed alkali composition. A possible connection between the kinetic and the thermodynamic dimensions of this system was established, wherein the heat capacity change at the Tg, ΔCp(Tg), and the fragility are correlated.

Polarization relaxation was studied in Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) single crystals that show fatigue anisotropy. To excite prepoled crystals, a modest dc voltage (

Thermodynamic properties, enthalpy relaxation and fragility of a Pd43Ni10Cu27P20 bulk metallic glass-forming liquid have been investigated and the thermodynamic functions been calculated. The enthalpy relaxation from the amorphous state into the equilibrium supercooled liquid state was found to follow a stretched exponential function with the relaxation time obeying an Arrhenius law. The fragility index, calculated from the heating rate dependence of Tg, yields a value of 65. The excellent glass-forming ability of this alloy is attributed to a smaller thermodynamic driving force and larger diffusion length for crystallization than in other bulk metallic glass-forming alloys.

Lithium borosilicate (LBS) glasses of different modifier to formers ( m / f ) ratios were synthesized through sol–gel process. Structural characterisation of LBS glasses were made using XRD, FTIR and DSC techniques. XRD pattern of LBS samples showed amorphous phase for gels heat treated between 573 and 698 K and further heat treatment above 698 K showed the formation of crystalline multiphases. FTIR spectra for dried LBS gels between 338 and 443 K showed the presence of hydroxyl group on the surface of silicate and borates matrix and on heat treatment, the FTIR spectra revealed the formation of silicate and borate linkages in LBS glassy matrix. DSC curve confirmed the presence of adsorbed water molecules in LBS glassy matrix. Impedance measurements were carried out on LBS samples of different m / f ratios as a function of temperature and data were analyzed using Boukamp equivalent circuit software. The conductivity of LBS glasses at different temperatures was calculated from analyzed impedance data. Activation energy ( E a ) is obtained from Arrhenius plots of the dc conductivity and it is found to be 0.64 (±0.02) eV for high conducting sample. ac conductivity is calculated from impedance data and analyzed using Jonscher's power law (JPL) exponent (s) for m / f ratios of LBS samples at different temperatures. The power law exponent s of LBS glasses exhibited a non-linear behavior with temperature. The electric modulus data were fitted with Kohlraush–William–Watts (KWW) stretched exponential function and the modulus formalism is used to study the ionic relaxation behavior in LBS samples.

Kinetic behavior of aggregation of amyloid-beta-protein (Abeta) is represented by a stretched exponential function, F=A[1-exp(-Bt(n))]. Differences in temperature-dependence of A, B and n are studied for Abeta 1-40 and Abeta 1-42. As the temperature is lowered, parameter A is increased, parameter B is decreased and parameter n is increased in Abeta 1-40, while these parameters are less sensitive to temperature in a more hydrophobic protein Abeta 1-42. ln B is a linear function of n, which is shown by ln B = -6.34n + 3.69.

An empirical relaxation function suitable for describing the dynamics in disordered materials is presented. The function is a generalization of the stretched exponential function and based on power-law decays. The influence of parameters on the shape of the correlation function is discussed. Numerically transformed data are compared with some of the most commonly used curve–fit functions in the frequency dependent susceptibility. It is shown that a special case of the function is an approximation of the correlation function corresponding to the Cole–Cole function [K. S. Cole and R. H. Cole, J. Chem Phys. 9, 341 (1941)]. The applicability of the correlation function to describe glass transition dynamics is also discussed. Finally, it is shown that the proposed relaxation function can provide a significant improvement in the description of experimental data.

The electron transfer-induced conformational changes in cytochrome c adsorbed on electrodes have been studied with high-resolution surface plasmon resonance spectroscopy. The conformational changes in the native protein follow a stretched exponential function, exp[−( t / τ ) 0.5 ], suggesting a distribution of the activation barrier heights in the process. The measured time constants, τ , are 0.21 and 0.14 s for the oxidation and reduction, respectively. They are much slower than the electron transfer process, due to structural relaxation of the protein layer. As the concentration of guanidine hydrochloride is increased to 3 M, the conformational changes diminish, which indicates that the electron-transfer center is decoupled from the rest of the protein. After replacing the denaturant with buffer, the conformational changes re-appear but occur with much slower time constants. The slowing-down of the conformational changes may be due to the trapping of the protein in an intermediate state.

Exposure of hydrogenated amorphous silicon, a-Si:H, to light produces large-scale structural changes and increases the density of dangling Si bond defects acting as efficient carrier recombination centers. The latter is the well-studied Staebler–Wronski effect (SWE). All light-induced changes are metastable and disappear after annealing to approximately 200°C. This review focuses on one of the large-scale changes, namely that of the macroscopic density of the material. In all device quality materials, the initial stress is compressive with values typically in the range of 108–109 Pa. Exposure to light produces additional compressive stress, which can exceed 2×107 Pa. The observed change of stress is due to a change of the volume of the unsupported material and not of its elastic modulus. The relative volume change, ΔV/V, at 300 K becomes detectable at values in excess of about 10−6 after only a few photons per Si atom have been absorbed. ΔV/V saturates above 10−3, under high-intensity light after an average of more than 106 photons per Si atom have been absorbed. ΔV/V initially grows with t0.50±0.04 under CW illumination producing carrier generation rate G in the range of 1021 to a few 1023 cm−3 s−1. The approach to saturation is well fitted by a stretched exponential function with stretch exponent close to 0.5. ΔV/V is approximately proportional to G. The fastest and largest photo-expansion has been observed in the so-called “edge material” between the amorphous and microcrystalline state, produced by plasma enhanced CVD from increasingly diluted silane/hydrogen gas mixtures. The quantum efficiency of volume expansion has been observed to increase with the photon energy of the light in contrast to the SWE. No volume increase is observed in Ge rich a-Si1−xGex:H alloys and in hydrogenated microcrystalline material. Photo-expansion and the SWE show marked difference in spatial extend in the network, different evolution in time and different wavelength dependence. Hence, the two effects appear to be independent even though both involve hydrogen.

Carrier recombination dynamics in AlInGaN alloy has been studied by photoluminescence (PL) and time-resolved PL (TRPL) at various temperatures. The fast red-shift of PL peak energy is observed and well fitted by a physical model considering the thermal activation and transfer processes. This result provides evidence for the exciton localization in the quantum dot (QD)-like potentials in our AlInGaN alloy. The TRPL signals are found to be described by a stretched exponential function of exp[(-t/,tau)13], indicating the presence of a significant disorder in the material. The disorder is attributed to a randomly distributed QDs or clusters caused by indium fluctuations. By studying the dependence of the dispersive exponent beta on temperature and emission energy, we suggest that the exciton hopping dominate the diffusion of carriers localized in the disordered QDs. Furthermore, the localized states are found to have 0D density of states up to 250 K, since the radiative lifetime remains almost unchanged with increasing temperature. (C) 2003 Elsevier Science Ltd. All rights reserved.

The dynamic structure factor S ( Q , t ) measured in quasi-elastic scattering experiments ( Q being the momentum transfer) is calculated for real poly(dimethyl siloxane) (PDMS) and polyethylene (PE) chains in the molten state at high Q , where chain entanglements are irrelevant. The theoretical lineshapes, obtained within the rotational isomeric states approach, are empirically fitted with the stretched exponential function S ( Q , t )=exp[−( t / τ ) β ]. We find that the stretching exponent β increases with chain stiffness, in keeping with our previous results for coarse-grained chain models. In particular, for high molar-mass polymers PE has a somewhat larger β exponent than PDMS, in fair agreement with experimental results. Moreover, the theory predicts a marginal decrease of β with increasing temperature, due to the increased conformational flexibility. Additionally, the β exponent for PE is predicted to slightly increase in oligomers at a given T , in qualitative agreement with recent experimental results.

Quaternary InAlGaN film has been grown directly on top of low-temperature-deposited GaN buffer layer by low-pressure metalorganic vapor phase epitaxy. High-resolution X-ray diffraction and photoluminescence (PL) results show that the film has good crystal quality and optical property. Temperature-dependent PL and time-resolved PL (TRPL) have been employed to study the carriers recombination dynamics in the film. The TRPL signals can be well fitted as a stretched exponential function exp[-(t/tau)(beta)] from 14 to 250 K, indicating that the emission is attributed to the radiative recombination of excitons localized in disorder quantum nanostructures such as quantum disks originating from indium (In) clusters or In composition fluctuation. The cross-sectional high-resolution electron microscopy measurement further proves that there exist the disorder quantum nanostructures in the quaternary. By investigating the dependence of the exponential parameter beta on the temperature, it is shown that the multiple trapping-detrapping mechanism dominates the diffusion among the localized states. The localized states are considered to have two-dimensional density of states (DOS) at 250 K, since radiative recombination lifetime tau(r) increases linearly with increasing temperature. (C) 2002 Elsevier Science B.V. All rights reserved.

Purpose. To examine whether the empirical Kohlrausch-Williams-Watts (KWW) equation is applicable not only to protein aggregation but also to protein denaturation in lyophilized formulations. Lyophilized β-galactosidase (β-GA) formulations containing polyvinylalcohol and methylcellulose were used as model formulations. The possibility of predicting storage stability based on the temperature dependence of the estimated parameters of inactivation/aggregation—time constant (τ) and its distribution (β) is discussed.

The time course for the transfer of azo dyes from the microcapsule core of dioctylphthalate to the dispersing medium of methanol through a poly(ureaurethane) (PUU) membrane was measured for various average size microcapsules with a size distribution. The dye release curves are represented by a stretched exponential function C ( t )= C eq {1−exp [−( t / τ eff ) α ]}, where C ( t ) is the concentration of the dye in methanol, C eq that at the equilibrium state, and t the time. The exponent α decreased by increasing the variance of the size distribution of microcapsules. The effective time constant τ eff was expressed by τ eff = c 0 〈 R 2 〉/ κ ( α ), where 〈 R 2 〉 and κ ( α ) are the mean square of microcapsule radius and a correction for the size distribution, respectively. The characteristic proportional constant, c 0 , was determined as 2.6±0.2 min/μm 2 . From the value of the constant, the diffusion coefficient of the azo dye in the PUU membrane was evaluated as 2.6×10 −12 cm 2 /s.

Isothermal extrusion process of Zr55Cu30Al10Ni5 bulk metallic glass (BMG) has been performed at 703 K at various extrusion velocities. A simple stretched exponential function has been developed to describe the rheological properties of Zr55Cu30Al10Ni5 BMG and implemented into the finite element code to simulate the extrusion process. The simulated results are concordant with the experimental curve during the steady-state extrusion process. The extrusion at different velocities does not induce the perceptible crystallization. The supercooled liquid state (SCL) region ΔT of the extruded samples is reduced with the increase of the extrusion time.

The structural relaxation time is a measure of the molecular mobility involved in enthalpy relaxation, and thus, is a measure of the dynamics of amorphous (glassy) pharmaceutical solids that determines physicochemical properties and reactivity of drugs in amorphous formulations. In this article we describe a novel method for characterization of structural relaxation using isothermal microcalorimetry, which directly measures the rate of heat release during the relaxation processes. The structural relaxation time is then obtained from a fit of the power data to the derivative version of the Kohlrausch-Williams-Watts (KWW) equation. The relaxation times of quenched and lyophilized samples of saccharides were studied using an isothermal microcalorimeter, the Thermal Activity Monitor (TAM). In addition to the KWW derivative function, a derivative equation of the modified stretched exponential function (MSE) was employed to evaluate TAM data. The later (MSE) appeared to have numerical advantages over the KWW equation. The data demonstrate, as expected, that structural relaxation times of amorphous solids depend on a number of variables, including nature of material, temperature, moisture content, thermal history, etc. Isothermal microcalorimetry with the TAM provides a very fast and reliable way to characterize the dynamics of glassy materials, which in many respects is superior to the conventional DSC approach. To the extent stability and structural relaxation dynamics in the glass are correlated, structural relaxation parameters derived by isothermal microcalorimetry may provide data useful for rational development of stable peptide and protein formulations and for the control of their processing.

The rate of energy dissipation from Au nanoparticles to their surroundings has been examined by pump−probe spectroscopy. These experiments were performed for particles suspended in aqueous solution, with average sizes ranging from 4 to 50 nm in diameter. The results show that energy relaxation is a very nonexponential process. Fitting the data to a stretched exponential function yields a characteristic time scale for relaxation that varies from ca. 10 ps for the smallest particles examined (∼4 nm diameter) to almost 400 ps for the 50 nm diameter particles. The relaxation times are proportional to the square of the radius, but do not depend on the initial temperature of the particles (i.e., the pump laser power). For very small particles, the time scale for energy dissipation is comparable to the time scale for electron−phonon coupling, which implies that significant energy loss occurs before the electrons and phonons reach thermal equilibrium within the particle.

In this paper the dielectric relaxation behavior at high temperatures of bulk poly(vinyl acetate) and of its toluene solutions is simulated using molecular dynamics procedures and compared with experimental results obtained for these systems in a wide range of temperatures. The relaxation behavior is described by a stretched exponential function, the exponent of which lies in the range 0.5–0.6. Moreover, the temperature dependence of the mean relaxation time of the absorption is rather weak in comparison with that reported for the α relaxation of supercooled liquids near Tg.

The internal field of lithium niobate (LN) crystal defined by the offset of the ferroelectric hysteresis loop exhibits two distinct relaxation time, suggesting that it is originated from two different types of defects due to the non-stoichiometry of the crystal. The effect of defects was verified using samples of reduced defect concentration by vapor transport equilibration method. The total amount of internal field constitutes most of the coercive field of congruent LN. The inherent coercive field of stoichiometric LN was estimated to be less than 1.5 kV/mm from the internal field measurement of congruent LN by extrapolating the relaxation effect, which was found to be fit with a stretched exponential function.

Measurements of 1 H and 7 Li Nuclear Magnetic Resonance (NMR) are reported for the nanocomposite formed by the intercalation of lithium and dibutylamine in molybdenum disulfide, Li 0.1 [(C 4 H 9 ) 2 NH] y MoS 2 . The temperature dependence NMR lineshapes and spin-lattice relaxation times ( T l ) measured exhibit the qualitative features associated with the lithium motions, namely the presence of a line narrowing at 230 K. The 1 H and the 7 Li longitudinal magnetization recovery was found to be non exponential. The T l values at each temperature was determined from the fit of a stretched exponential function. An activation energy for the lithium motion E a ≈0.18 eV was extracted from the 7 Li relaxation data. The dynamical parameters obtained from the 7 Li temperature dependence relaxation data indicate the mobility of the lithium in the nanocompositeis of the same order of magnitude as those obtained in other lithium intercalation compounds.

Absorption by non-algal particles (NAP, ad) and colored dissolved organic matter (CDOM, ag) are frequently modeled by exponential functions of wavelength, either separately or as a sum. We present a new representation of NAP-plus-CDOM absorption adg based on the stretched exponential function adg(λ) = A exp{-[s(λ - λo)]β}, whose parameter β can be considered a measure of optical heterogeneity. A double exponential representation of adg can be fit extremely well by a stretched exponential for all plausible parameter combinations, despite having one fewer free parameter than a double exponential. Fitting two published compilations of in situ adg data - one at low spectral resolution (n = 5, λ = 412-555 nm) and one at high spectral resolution (n = 201, λ = 300-700 nm) - the stretched exponential outperforms the single exponential, double exponential, and a power law. We thereby conclude that the stretched exponential is the preferred model for adg absorption in circumstances when NAP and CDOM cannot be separated, such as in remote sensing inversions.

A combination of broad-band UV radiation (UV A and UV B; 250-400 nm) and a stretched exponential function (StrEF) has been utilised in efforts towards convenient and sensitive detection of fluorescent dissolved organic matter (FDOM). This approach enables accessing the gross fluorescence spectral signature of both protein-like and humic-like components in a single measurement. Commercial FDOM components are excited with the broad-band UV excitation; the variation of spectral profile as a function of varying component ratio is analysed. The underlying fluorescence dynamics and non-linear quenching of amino acid moieties are studied with the StrEF (exp(-V[Q] β )). The complex quenching pattern reflects the inner filter effect (IFE) as well as inter-component interactions. The inter-component interactions are essentially captured through the 'sphere of action' and 'dark complex' models. The broad-band UV excitation ascertains increased excitation energy, resulting in increased population density in the excited state and thereby resulting in enhanced sensitivity.

Temperature dependent diffuse reflectance spectroscopy measurements were carried out on polycrystalline samples of BaTiO3 across the tetragonal to cubic structural phase transition temperature (TP). The values of various optical parameters such as band gap (Eg), Urbach energy (Eu), and Urbach focus (E0) were estimated in the temperature range of 300 K to 480 K. It was observed that with increasing temperature, Eg decreases and shows a sharp anomaly at TP. First principle studies were employed in order to understand the observed change in Eg due to the structural phase transition. Near TP, there exist two values of E0, suggesting the presence of electronic heterogeneity. Further, near TP, Eu shows metastability, i.e., the value of Eu at temperature T is not constant but is a function of time (t). Interestingly, it is observed that the ratio of Eu (t=0)/Eu (t = tm), almost remains constant at 300 K (pure tetragonal phase) and at 450 K (pure cubic phase), whereas this ratio decreases close to the transition temperature, which confirms the presence of electronic metastability in the pure BaTiO3. The time dependence of Eu, which also shows an influence of the observed metastability can be fitted with the stretched exponential function, suggesting the presence of a dynamic heterogeneous electronic disorder in the sample across TP. First principle studies suggest that the observed phase coexistence may be due to a very small difference between the total cohesive energy of the tetragonal and the cubic structure of BaTiO3. The present work implies that the optical studies may be a sensitive probe of disorder/heterogeneity in the sample.

The non-exponential room temperature luminescence decay of colloidal quantum dots is often well described by a stretched exponential function. However, the physical meaning of the parameters of the function is not clear in the majority of cases reported in the literature. In this work, the room temperature stretched exponential luminescence decay of colloidal quantum dots is investigated theoretically in an attempt to identify the underlying physical mechanisms associated with the parameters of the function. Three classes of non-radiative transition processes between the excited and ground states of colloidal quantum dots are discussed: long-range resonance energy transfer, multiphonon relaxation, and contact quenching without diffusion. It is shown that multiphonon relaxation cannot explain a stretched exponential functional form of the luminescence decay while such dynamics of relaxation can be understood in terms of long-range resonance energy transfer to acceptors (molecules, quantum dots, or anharmonic molecular vibrations) in the environment of the quantum dots acting as energy-donors or by contact quenching by acceptors (surface traps or molecules) distributed statistically on the surface of the quantum dots. These non-radiative transition processes are assigned to different ranges of the stretching parameter β.

The aging degradation behavior of Fe-doped Lead zirconate titanate (PZT) subjected to different heat-treated temperatures was investigated over 1000[Formula: see text]h. The aging degradation in the piezoelectric properties of PZT was indicated by the decrease in piezoelectric charge coefficient, electric field-induced strain and remanent polarization. It was found that the aging degradation became more pronounced at temperature above 50% of the PZT’s Curie temperature. A mathematical model based on the linear logarithmic stretched exponential function was applied to explain the aging behavior. A qualitative aging model based on polar macrodomain switchability was proposed.

On the basis of current trends in the description of adsorption processes in complex media a conceptual analysis was made of the mechanisms of the appearance of nonexponential kinetics (stretched exponential function) in chemical reactions on a surface. A review of approaches ranging from a phenomenological description to a generalized fractal formalism is presented, and it was used to develop a model of adsorption in nonuniform media in terms of the concepts of the reaction space as a topological subject. By “geometric description” of the evolution of the surface reactions it is possible to unify the various types of effect in terms of a reaction space of required dimensionality and to establish a relationship between the parameters of macroscopic kinetics and features of the trajectory of the analyte in the nonuniform environment during its movement toward the receptor center.

Using broadband dielectric spectroscopy we investigate the changes in the conductivity relaxation times τσ observed during the physical aging of the protic ionic conductor carvedilol dihydrogen phosphate (CP). Due to the large decoupling of ion diffusion from host molecule reorientation, the ion conductivity relaxation time τσ(Tage,tage) can be directly measured at temperatures Tage below Tg for exceedingly long aging times tage till τσ(Tage,tage) has reached the equilibrium value τσ(eq)(Tage). The dependence of τσ(Tage,tage) on tage is well described by the stretched exponential function, τσ(Tage, tage) = Aexp[-((tage)/(τage(Tage)))(β)] + τσ(eq)(Tage), where β is a constant and τage(Tage) can be taken as the structural α-relaxation time of the equilibrium liquid at T = Tage. The value of τσ(eq)(Tage) obtained after 63 days long annealing of CP, deviates from the Vogel-Fulcher-Tammann-Hesse (VFTHσ) dependence of τσ(T) determined from data taken above Tg and extrapolated down to Tage. Concurrently, τage(Tage) also deviates from the Vogel-Fulcher-Tammann-Hesse (VFTHα) dependence. The results help to answer the longstanding question of whether the VFTH dependence of τσ(T) as well as the structural α-relaxation time τα(T) holds or not in the equilibrium liquid state far below Tg.

Sm2CoMnO6 samples with particle sizes ∼70 nm were synthesized by a sol-gel technique. Field cooled magnetization study exhibited a ferromagnetic transition with a Curie temperature at ∼139K. This was attributed to ferromagnetic Co2+−O−Mn4+ superexchange interaction. The results of magnetic relaxation measurements could be fitted to a stretched exponential function indicating the presence of both ferromagnetic and spin glass components in the system.

We have investigated the dynamics of confined water in a fully hydrated Na-vermiculite clay using the neutron spin-echo (NSE) technique. NSE measures the intermediate self-scattering function, i.e., the dynamics directly in the time domain. In the present experiments we performed measurements, in the time range 3–3000 ps and temperature ranging from 254 to 323 K, on the essentially two-dimensional water with a layer thickness corresponding to only two molecular layers. The data can be described by the Kohlrausch–Williams–Watts (KWW) stretched exponential function, probably indicating a broad distribution of relaxation times. The reason for the very stretched behavior of the intermediate self-scattering function IS(Q,t), particularly in the supercooled regime, is most likely that the water molecules have widely different local environments. Some water molecules are strongly interacting with the clay surfaces or the intercalated Na+ ions, whereas the remaining molecules are interacting only with other water...

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, $f(t)=f_0\exp[-(t/\tau)^\beta]$, with the exponent $\beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $T\to 0$. A relation between the specific heat and the entropy in the long time regime is found., Comment: 5 pages and 4 figures

Conventional analyses of fluorescence lifetime measurements resolve the fluorescence decay profile in terms of discrete exponential components with distinct lifetimes. In complex, heterogeneous biological samples such as tissue, multi-exponential decay functions can appear to provide a better fit to fluorescence decay data than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is essentially arbitrary and is often erroneous. Moreover, interactions, both between fluorophores and with their environment, can result in complex fluorescence decay profiles that represent a continuous distribution of lifetimes. Such continuous distributions have been reported for tryptophan, which is one of the main fluorophores in tissue. This situation is better represented by the stretched-exponential function (StrEF). In this work, we have applied, for the first time to our knowledge, the StrEF to time-domain whole-field fluorescence lifetime imaging (FLIM), yielding both excellent tissue contrast and goodness of fit using data from rat tissue. We note that for many biological samples for which there is no a priori knowledge of multiple discrete exponential fluorescence decay profiles, the StrEF is likely to provide a truer representation of the underlying fluorescence dynamics. Furthermore, fitting to a StrEF significantly decreases the required processing time, compared with a multi-exponential component fit and typically provides improved contrast and signal/noise in the resulting FLIM images. In addition, the stretched-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the resulting heterogeneity map can reveal subtle tissue differences that other models fail to show.

segments. We find that the relaxation of the correlation between neighboring chains is slower and more stretched in the polymer salt complex compared to the pure polymer. The data can, for both PPO and PPO‐LiClO4, be described by a stretched exponential function with temperature independent stretching parameters. While the relaxation times follow the macroscopic viscosity for the former, they do not for the latter. The slower relaxation in PPO‐LiClO4 compared to PPO and the failure of the viscosity scaling in PPO‐LiClO4 may be explained in terms of a temperature dependent effective molecular weight induced by cations acting as cross links between chains. We discuss the origin of the extra stretching of the relaxation in the polymer salt complex under the aspect of heterogeneity, comparing it with data in the literature. We find that the stretching to the major part is intrinsic or at most due to heterogeneities on an atomic length scale. The molecular length scale of the experiment allows for the first time a direct connection to the renewal time in the dynamic disordered hopping model for ion transport in polymer electrolytes. © 2001 American Institute of Physics. @DOI: 10.1063/1.1370073#

This article is concerned with the study of the diffusion of water molecules in a hydrogel, obtained by controlled hydration of a cross-linked polymer of sucrose and diepoxide monomers. The diffusion measurements were performed by means of 1H(NMR) nuclear magnetic resonance techniques in the fringe field of a superconductor magnet with a field gradient G≃36.3 T m−1. This large field gradient and the stimulated echo pulse sequence allows to obtain time-dependent diffusion coefficients and to observe a non-Debye feature of the relaxation attenuation function. The behavior of the diffusion follows a stretched exponential function plus a Debye term, allowing the determination of different water domains. In the long time limit the diffusion follows a long tail Levy function, whose asymptotic limit is related to the fractal dimension of the underlying polymer structure.

We introduce new techniques for obtaining single-molecule orientation images and analyzing the reorientation dynamics of single fluorescent molecules. Polarization modulation is used with confocal microscopy to measure the absorption dipole orientation and reorientation dynamics of individual dye molecules physisorbed to glass and embedded in thin, spin-cast polymer films under ambient conditions. Discrete jumps in absorption dipole orientation are observed for a significant fraction of dye molecules in all samples tested, and in all cases the distribution of first-jump times can be fitted by a stretched exponential function. A sub-population of dye molecules that is stationary on the time scale of these experiments (32 s) is observed and persists even at high excitation power. Data analysis techniques are developed for quantifying the reorientation dynamics of single molecules, and a novel method for quickly identifying rotationally mobile molecules in a scan field is introduced. A dependence of the reor...