Distribution Of Time Constants Research Articles

Dielectric relaxation in 91%Pb(Zn1∕3Nb2∕3)O3–9%PbTiO3 single crystal at low temperature

The temperature dependent dielectric response of ⟨001⟩-oriented 91%Pb(Zn1∕3Nb2∕3)O3–9%PbTiO3 single crystal has been studied at various frequencies. A dielectric relaxation process with a broad distribution of time constant has been observed below 180K. The peak temperature of the dielectric loss can be fitted well with Volger–Fulcher relation. We assume this relaxation process can be attributed to the freezing of ferroelectric macrodomain walls induced by the pinning of point defects.

Microrheology of Human Lung Epithelial Cells Measured by Atomic Force Microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus ( G *( ω)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1–100 Hz) and at different loading forces (0.1–0.9 nN) with atomic force microscopy. G *( ω) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G′( ω) increased with frequency following a power law with exponent ∼0.2. The loss modulus G″( ω) was ∼2/3 lower and increased similarly to G′( ω) up to ∼10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G′( ω) and G″( ω). G *( ω) conformed to the power-law model with a structural damping coefficient of ∼0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.

Low-frequency noise study in electron devices: review and update

Low-frequency noise or flicker noise has been found in many systems and has become a hot research topic for more than eight decades. It was believed that there exists a common origin of this kind of noise for different systems. The common origin theories were shook as more experiments on electron devices were conducted. For electronic system, it is easier to produce samples with different noise behaviors via different fabrication processes, measurement conditions such as temperature, stressing, biasing etc. More and more studies suggest that if there is a common regime for the low-frequency noise, it must be mathematical rather than physical ones. These mathematical processes give rise to 1/ f spectrum could be due to the distribution of time constant in spatial or energy-wise and the non-linear transformation of Gaussian signal. This paper presents a historical review on the development of low-frequency noise study in electron devices and the recent progresses in the understanding and modeling are updated.

Photoinduced birefringence at low temperatures in Langmuir–Blodgett films of azobenzene-functionalized copolymers

The temperature dependence has been investigated for the photoinduced birefringence in Langmuir–Blodgett (LB) films from the azocopolymer 4-[ N-ethyl- N-(2-hydroxyethyl)]amino-2′-chloro-4′-nitroazobenzene (MMA-DR13) mixed with cadmium stearate. The build-up and relaxation of the birefringence in the range from 20 to 296 K were fitted with a Kohlrausch–Williams–Watts (KWW) function, with a β-value of 0.78–0.98 for the build-up and 0.18–0.27 for the decay. This is consistent with a distribution of time constants for the kinetics of the birefringence processes. The maximum birefringence increased with increasing temperature up to 120 K because the free volume fluctuation also increased with temperature. Above 120 K, the birefringence decreased with temperature as thermal diffusion dominates. In the latter range of temperature, an Arrhenius behavior is inferred for both build-up and decay of birefringence. In each case two activation energies were obtained: 0.8 and 5 kJ/mol for the build-up and 10 and 30 kJ/mol for the decay. The energies for the build-up are much lower than those associated with motion of the polymer chain, which means that the dynamics is governed by the orientation of the chromophores. For the decay, local motion of lateral groups of the polymer chains becomes important as the activation energies are within the range of γ-relaxation energies.

Electroanalytical features of non-uniformly doped conducting poly-3-(3,4,5-trifluorophenyl)thiophene films

Specially prepared, thin poly-3-(3,4,5-trifluorophenyl)thiophene, PTFPT, films were shown to possess stable p- and, most importantly, n-doping in TEABF4/sulfolane (SF) solutions. Electrodes comprising PTFPT films were studied by cyclic voltammetry (CV), potentiostatic intermittent titration (PITT), and electrochemical impedance spectroscopy (EIS). A detailed analysis of the shape of the time-dependent current transients during PITT characterization of the PTFPT electrodes has been performed. The non-uniform character of the PTFPT film doping was proved. Plots of dlog|I(t)|/dlog tvs.t/τd were found to be useful for understanding the response of potentiostatic transients. The Cottrell time domain during potentiostatic transients was found to be very narrow, reflecting the drastic effect of the Ohmic potential drops (mainly across the film's bulk) on the semi-infinite diffusion current transient at the shortest times, and a wide distribution of the diffusion time constants. PITT and EIS characterizations provided converging results with respect to the relevant diffusion time constants and the non-uniform character of PTFPT film doping in the SF solution. EIS measurements were found to be very useful for the determination of diffusion time constants, as they allow more effective separation of the medium frequency, Warburg response from the Ohmic and the kinetic high-frequency responses.

Pressure-volume curves in acute respiratory distress syndrome: clinical demonstration of the influence of expiratory flow limitation on the initial slope.

The presence of an initial segment with a low compliance on the static pressure-volume (PV) curve in patients with acute respiratory distress syndrome (ARDS) indicates that some lung compartments do not initially receive insufflated gas. We tested the hypothesis that an uneven distribution of time constants, producing a "slow compartment," was in part responsible for the change in compliance between the initial and the intermediate segment of the PV curve. In 16 patients with ARDS submitted to mechanical ventilation in volume-controlled mode with a supportive respiratory rate of 15 breaths/minute, we constructed the static PV curve on the first day of respiratory support and determined the intrinsic positive end-expiratory pressure (PEEPi4) during a prolonged end-expiratory pause (4 seconds). We also measured the volume of a "slow compartment" during a prolonged expiration (> 6 seconds), and determined an external PEEP (PEEPe) suppressing PEEPi4. Among the 16 patients studied, 11 exhibited a low inflection point, associated with a "slow compartment" of 172 +/- 83 ml, responsible for a PEEPi4 of 3 +/- 2 cm H2O. Conversely, the five remaining patients had a linear PV curve, associated with a minimal "slow compartment" of 28 +/- 10 ml, responsible for a negligible PEEPi4. We observed that individual slopes of the initial segment of the PV curve were inversely and significantly correlated with the proportion of the "slow compartment" (r = -0.85). We concluded that the shape of the inspiratory PV curve in ARDS might be dependent on the presence of a "slow compartment," and demonstrated that a low external PEEP appeared sufficient to achieve a substantial mechanical improvement in clinical practice.

Extension of the measurement model approach for deconvolution of underlying distributions for impedance measurements

Electrochemical impedance spectra frequently reveal the influence of distributions of activation or relaxation processes, but methods for extracting information concerning these distributions are not well developed. Complex non-linear weighted regression of Voigt elements was applied to synthetic impedance data to identify the influence of stochastic noise and incomplete frequency ranges on the ability to resolve the expected distribution. The method was also applied to analysis of impedance data for heat-separated human stratum corneum. Regression of a Voigt series was found to provide a convenient way to identify a distribution of relaxation time constants corresponding to a given experimental spectrum. While the presence of stochastic noise reduces the number of Voigt elements that can be resolved, the parameters trace the same profile for the distribution of time constants. The technique should be particularly useful for experimental systems for which no deterministic model is available.

Noise Sources in Polycrystalline Silicon Thin-Film Transistors

ABSTRACTSources for low frequency noise in polycrystalline silicon thin-film transistors are analytically investigated. The grain boundary is modeled as symmetric Schottky barrier and a new device equation for current conduction in thin-film transistors is presented. At lower currents where barrier height is large enough to provide necessary distribution of time constants for 1/f noise, the number fluctuation via barrier height modulation at the grain boundary is found to be the main noise generation mechanism. At higher currents, mobility and diffusivity fluctuation are found to be dominant

Rare-earth dependence of photoinduced chain-oxygen ordering inRBa2Cu3O7−x(x≈0.3)investigated by Raman scattering

We investigated a set of oxygen-deficient $R{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ $(x\ensuremath{\approx}0.3)$ ceramic samples with Raman spectroscopy under resonant conditions for the defect-induced Cu-O chain related modes at 230 and 600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Emphasis was laid on the frequency and intensity of the modes for different rare-earth atoms, and especially on their dependence under illumination. The modes display photoinduced bleaching for all R, including the nonsuperconducting $R=\mathrm{Pr}.$ The dynamics of their bleaching following a temperature quench indicates similar complex relaxation processes for all samples. A simple stretched exponential with a common $\ensuremath{\beta}=0.36\ifmmode\pm\else\textpm\fi{}0.04$ and a distribution of time constants ranging from 50 to 1400 s describes our data well. We discuss our results in connection to photoinduced chain-oxygen ordering in oxygen-deficient superconductors.

Generation- Recombination Noise in Amorphous Semiconductors

ABSTRACTWe examine different approaches to the analysis of noise in amorphous hydrogenated silicon associated with trapping and generation – recombination processes, which appear to predict very different noise spectra. In one approach the broad noise spectrum observed is assumed to be composed of a distribution of Lorentzian noise spectra, each associated with traps at a given energy depth, with appropriate weighting according to the energy distribution of characteristic time constants. This latter weighting is taken to mirror the energy distribution of states in the gap. This represents a linear superposition of the (weighted) contribution from individual trapping levels, each with its own characteristic time constant. This approach thus assumes that each trap level is an independent source of fluctuation in free carrier number, unaffected by the presence of other traps in the material. At first sight this assertion seems plausible, since in the multi-trapping situation envisaged, cross-correlation effects must be very small. However, the presence of several groups of traps, or, in the limit, a continuum, results in a distribution of characteristic time constants, which is not a simple linear superposition of the time constants for each level. Thus the assertion that a flat density of states, or a region which is flat, such as the top of a broadened level, results in a region of 1/f slope in the noise spectrum, may not be valid. We present an alternative model in which the distribution of time constants is appropriately incorporated, and compare the predictions of this model with the ‘superposition’ approach, using computed noise spectra.

Excitability properties of motor axons in patients with spontaneous motor unit activity

OBJECTIVESMeasures of nerve excitability provide information about biophysical properties of peripheral axons in disease states. One measure, the strength duration time constant (τSD), was previously reported to be prolonged in...

Electrical Conductivity and Dielectric Dispersion Phenomena of Concentrated TiO2 Suspensions

The complex conductivity of concentrated TiO2 suspensions (up to 50 vol%) was measured over a large frequency range (1 MHz–1.8 GHz), as a function of grain volume content. These measurements highlight relaxation phenomena in the intermediate frequency range, which are associated with the dispersed powder. These phenomena were previously noted in O'Brien's theoretical developments. A quantitative data analysis was made, in terms of time constant distribution, using the CONTIN software, from Provencher. As a result, a complex process is highlighted, including two main mechanisms in different ranges of time constants. Particularly, we showed good agreement between the higher frequency mechanism and the O'Brien theory. From Dukhin's λ ratios, which are ratios of grain surface to bulk electrolyte conductances, we calculated the electrolyte conductivity as a function of powder concentrations. At higher powder concentrations, these values are different from those measured with centrifuged liquids.

Electrical characterization of aluminous cement at the early age in the 10 Hz–1 GHz frequency range

A CFA cement from Lafarge prepared at 20°C, 100% relative humidity, and with water-to-cement weight ratio (W/C)=0.4, has been tested electrically between 10 Hz–1 MHz and 1 MHz–1 GHz. The samples have been measured at 20°C and 50% relative humidity from 8 h up to 150 h after mixing the water with the cement. For the first frequency range, the results presented here focus on the effect of the chemical nature of the electrode on the electrical response of the cement. Different electrode materials, namely, silver, gold or an indium–gallium mix, have been investigated. Silver leads to a major contribution of the cement–electrode interface to the global electrical response. This effect is less pronounced with gold and indium–gallium. Concerning the higher frequency range, measurements between 1 MHz and 1 GHz enable the evolution of the interface between cement and water during hydration to follow. An analysis of electrical data, namely, the permittivity and the conductivity, has been carried out using a procedure based on a continuous distribution of time constants. The corresponding relaxation frequencies are presented and related to the state of water inside the cement material. A comparison of the electrical behaviour between a cement and a silico-aluminous ceramic, in which water is not as reactive as in a cement, is also discussed.

Uniform bunch formation by RF voltage modulation with a band-limited white signal

Uniform bunch formation by RF voltage modulation with a band-limited white signal is proposed to relax the space-charge effects in proton synchrotrons. A unique feature of this method is to increase the bunching factor without the longitudinal emittance blow-up, in principle. The beam dynamics is discussed based on the diffusion equation and computer simulations. The temporal evolution, time constant and equilibrium distribution are derived.

Multiple measures of axonal excitability: a new approach in clinical testing.

From measurements of nerve excitability and the changes in excitability produced by nerve impulses and conditioning currents, it is possible to infer information about the membrane potential and biophysical properties of peripheral axons. Such information cannot be obtained from conventional nerve conduction studies. This article describes a new method that enables several such measurements to be made on a motor nerve quickly and reproducibly, with minimal operator intervention. The protocol measures stimulus-response behavior using two stimulus durations (from which the distribution of strength-duration time constants can be estimated), threshold electrotonus to 100-ms polarizing currents, a current-threshold relationship (indicating inward and outward rectification), and the recovery of excitability following supramaximal activation. The method was tested on 30 healthy volunteers, stimulating the median nerve at the wrist and recording from the abductor pollicis brevis. The results were comparable with previously published normal data, but the recordings took less than 10 min. The convenience and brevity of the new method make it appropriate for routine clinical use.

Luminescence decay kinetics of Ge related center in silica

Detailed measurements of luminescence decay kinetics in Ge doped silica fiber have been carried out for different excitation energies from 3 to 7.7 eV and luminescence detection energy from 2 to 4eV. The decay kinetics of luminescence is rather well approximated by an exponent. A distribution of time constants over the range 90–130 μs in decay exponential approximation is pointed out. This distribution is due to structural non-equivalencey of Ge centers in the disordered glass structure. At 10 K the life time increases up to 150–450 μs, and it is explained as influence of zero-field splitting of the triplet state. The spectra of luminescence and its excitation also are affected by inhomogeneous broadening. The excitation with photons above 6.4 eV causes appearance of thermally stimulated luminescence also.

Distribution of time constants for tunneling through a one-dimensional disordered chain

The dynamics of electronic tunneling through a disordered 1D chain of finite length is considered. We calculate distributions of the transmission coefficient T, Wigner delay time and, $\tau_\phi$ and the transport time, $\tau_t=T\tau_\phi$. The central bodies of these distributions have a power-law form, what can be understood in terms of the resonant tunneling through localised states.

The use of regularization methods in the deconvolution of underlying distributions in electrochemical processes

Many problems in electrocatalysis involve distribution of adsorption energies. Similarly, electrochemical impedance spectroscopy often involves distributed elements. Such problems are described by Fredholm integral equations and the underlying distribution functions may be solved using regularization techniques. A software package developed recently was used to determine the distribution function and the regularization parameters. Our studies show that it is relatively easy to obtain the adsorption energy distribution functions in simple cases. Comparison of the hydrogen adsorption on polycrystalline and monocrystalline (531) platinum shows similarities in the adsorption energies on both surfaces. Continuous (constant phase element) and discontinuous (fractal model) time constant distribution functions in the impedance were well reproduced, but in the more complex case (porous electrode) the method is more limited.

Magnetic properties of pulverized titanomagnetite, Fe2.4 Ti0.6 O4 : effect of thermal fluctuations

SUMMARY The magnetic properties of titanomagnetite, Fe 2.4 Ti 0.6 O 4 , pulverized in a ball mill for times between 3.5 and 78 hr form a consistent picture if the material is treated as monodomain particles of decreasing size progressively subject to thermal fluctuations. The magnetic observations are made over a range of characteristic measurement times: 10’3 s (susceptibility measurement), 1 s (coercive force measurement) and 104 s (viscous decay of remanence). The magnetic viscosity coeYcient first rises then falls as pulverization proceeds. This is ascribed to a distribution of time constants in the assemblage of particles, the maximum viscosity occurring when the value of the time constant at the peak in the distribution, in zero field, is the same as the characteristic measurement time. The application of a field equal to the coercive force shifts the distribution so that the peak corresponds to the characteristic time of the coercive force measurement. The position of the corresponding zero-field peak can readily be calculated from the observed coercive force and the uniaxial anisotropy constant derived from hysteresis loop parameters. This shows that the calculated zero-field peak position for the degree of pulverization at which the maximum viscosity occurs is the same as the viscous decay measurement time. At maximum pulverization time, and therefore smallest particle size, the peak in the zero-field time constant distribution is five orders of magnitude bigger than the characteristic time of susceptibility measurement, which can be satisfactorily interpreted in terms of only a few per cent of the particle assemblage being aVected by thermal fluctuations. The observed eVectiveness of thermal fluctuations requires that the pulverized particles contain nanocrystals, in size about two orders of magnitude smaller than the particle envelope. The presence of the nanocrystals is supported by transmission electron microscope and X-ray line broadening observations.

A time-domain method for the analysis of thermal impedance response preserving the convolution form

The study of the thermal behavior of complex packages such as multichip modules (MCMs) is usually carried out by measuring the so-called thermal impedance response, that is: the transient temperature after a power step. From the analysis of this signal, the thermal frequency response can be estimated, and consequently, compact thermal models may be extracted. We present a method to obtain an estimate of the time constant distribution underlying the observed transient. The method is based on an iterative deconvolution that produces an approximation to the time constant spectrum while preserving a convenient convolution form. This method is applied to the obtained thermal response of a microstructure as analyzed by finite element method as well as to the measured thermal response of a transistor array integrated circuit (IC) in a SMD package.