Diffusion Relaxation Time Research Articles

Ultrafast dynamics of polybutadiene probed by optically heterodyne-detected optical-Kerr-effect spectroscopy

The ultrafast dynamics of polybutadiene have been studied using ultrafast optical-Kerr-effect spectroscopy. The data are compared with measurements on 1,3- and 1,4-pentadiene. The two diene derivatives have quite distinct subpicosecond dynamics, with an important contribution from an intramolecular torsional mode in the 1,4-derivative. The main part of the polymer spectral density can be assigned, by analogy with the data for 1,4-pentadiene, to intramolecular torsional motion about carbon–carbon single bonds. The picosecond diffusive orientational relaxation times of the dienes are not well described by simple hydrodynamics.

Using noise speckle pattern for the measurements of director reorientational relaxation time and diffusion length of aligned liquid crystals

A purely optical approach using noise as a perturbation source and speckle analysis is used to measure the diffusion length and the director reorientational relaxation time of an aligned nematic liquid crystal. This method gives a direct measure of the intrinsic director relaxation time without any voltage or optical driving nor nonlinear effects contrarily to previous approaches. The obtained values of the diffusion length and relaxation time are in excellent agreement with those calculated from the liquid crystal elastic and rotational viscosity constants.

Time-domain calculations of acoustic interactions with rigid porous surfaces

In previous work, a set of time-domain equations for sound propagation in a rigid porous medium, including viscous and thermal dissipation effects, was derived [Ostashev et al., J. Acoust. Soc. Am. 115, 2624 (2004)]. From those equations, time-domain counterparts to frequency-domain impedance boundary conditions (BCs) were also derived. In this paper, several approaches to computational implementation of time-domain acoustic interactions with rigid porous surfaces are discussed that are based on these equations. Most of the approaches involve convolutions between relaxation or transformed impedance functions and the acoustic wavefield variables. For these approaches, when the relaxation times for viscous and thermal diffusion in the pores (which are inversely proportional to the static flow resistivity) are large, the convolution integrals must be evaluated over many periods of the acoustic disturbance and therefore become very computationally demanding. Some example finite-difference time-domain (FDTD) calculations show the significantly increased attenuation within the porous medium resulting from the convolution terms. Computational instabilities are observed when the wave is strongly attenuated over the FDTD spatial grid interval. Alternative approaches, based on Pade and series approximations to the time-domain impedance BC, are also considered that provide more compact numerical solutions.

Diffusion-relaxation distribution functions of miscible fluids measured in grossly inhomogeneous fields

In this paper, the recently developed technique of measuring diffusion-relaxation distribution functions in grossly inhomogeneous fields was applied to the characterization of bulk fluids. The measurements were conducted in a static stray field of a superconducting magnet at a Larmor frequency of 5 MHz, relevant for ex situ nuclear magnetic resonance applications in oil-well logging or materials testing. Results are presented for samples of water and hydrocarbon oils, including a number of crude oils. The measurements indicate strong correlations between diffusion coefficients and relaxation times that are sample specific. The diffusion-relaxation correlation function provides information on the correlation between the rotational and the translational diffusion coefficients of each component of the fluid.

Adsorption kinetics of some carotenoids at the oil/water interface

The kinetic analysis of the adsorption of two carotenoids (i.e., ethyl ester of β-apo-8′-carotenoic acid and β-carotene, all trans-isomers) from n-hexane solutions at the oil/water interface is presented for several carotenoid concentrations in the oil phase. A new kinetic approach is developed and it addresses the diffusion adsorption associated with a reversible interfacial reaction, which describes the reorientation of surfactant molecules between two conformations. This approach leads to a general analytical expression that contains four physical parameters and describes with high accuracy the experimental dynamic interfacial tensions for the two carotenoids, which independently adsorb from n-hexane phase to the n-hexane/water interface. The calculations give the characteristic times for the carotenoid adsorption at the oil/water interface in terms of diffusion relaxation and kinetic relaxation times. The results explain the long time effects on the adsorption of these carotenoids at the oil/water interface. The data are in substantial agreement with the molecular structure of these carotenoids and with the earlier data recorded for cholesterol adsorption at the n-heptane/water interface. Based on these findings, we propose a molecular mechanism for the interfacial transformation of carotenoid molecules at a hydrophobic/hydrophilic interface.

Noise-enhanced stability in fluctuating metastable states.

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.

Acceleration and deceleration of dopant diffusion in a semiconductor by space and time modulation of diffusion coefficient

The integral relaxation time of dopant diffusion in a semiconductor has been analytically derived for the case of weakly space and time varying diffusion coefficient. It has been shown that the well-known integral criterion for the relaxation time is an optimal estimate of the relaxation time. The choosing of parameters of the diffusion coefficient for minimization and maximization of the relaxation time has been done. It has been demonstrated that in the case of heterostructure the most optimal structure, which accelerates the diffusion process, consists of three layers with some specific relation between diffusion coefficients of the layers. Is interesting to note, that the maximal deceleration of the diffusion process also occurs for the three layer structure, but with the opposite order of layers and different layer thickness, besides, maximal deceleration may be significantly larger than the maximal acceleration.

Analysis of emission data from O2 plasmas used for microbe sterilization

In order to study the sterilization capabilities of radio frequency driven low pressure oxygen plasmas, the radiative emission was recorded at various pressures and input powers. A distinct transition from the bright mode (primarily inductively coupled) to a dim mode (primarily capacitively coupled) was observed as the pressure was increased and/or the power decreased. The data was further analyzed to estimate the electron temperature, rotational and vibrational temperatures, and various species concentrations. Based on the diffusion and rovibrational relaxation times, it is concluded that the rotational temperatures can be assumed to be in equilibrium with the translational temperature. The ions are produced “hot” and have little time to get equilibrated with the translational temperature. It is further determined that in the bright mode, which is more effective in microbe sterilization, the translational/rotational temperatures are in the 650–850 K range, the electron temperatures are low (3.5–4.5 eV), and the concentrations of atomic O and atomic metastables are at 1 order of magnitude higher than in the dim mode.

Non-linear Model Of Time-dependent RelaxationCores For The Systems With Cross Transfer Effects

In this paper the non-linear generalization of model equations for relaxation cores with allowance for the influence of diffusion and heat relaxation times and cross transfer effects is submitted. It is proposed that physical interpretation of the non-linearity links to non-additive interaction invariants. The relaxation cores have been simulated in the form of expansion in power series of a small parameter having point of ratio between two Knudsen numbers calculated according to the characteristic space scales of elastic and inelastic molecules collisions, i.e. on Prigogine’s approach. The time relaxation of temperature and concentration field’s perturbations under the different values of small parameter has been calculated. It is established that non-linear interaction between temperature and concentration fields perturbations, initiated at different times, leads from some value of the small parameter to the phenomenon of the temporary increase of the perturbations.

Diffusive relaxation of carbon and nitrogen isotope heterogeneity in diamond: a new thermochronometer

The spatial distribution of carbon and nitrogen isotopes in diamonds provides information on mantle residence time. Diamonds with long residence at high temperature will gradually lose their initial zoning patterns due to diffusion. Using experimentally determined carbon self-diffusion coefficients and nitrogen diffusion coefficients derived from aggregation experiments, we have modeled the diffusive relaxation of zoning profiles with a spectrum of wavelengths. Carbon isotope heterogeneity will be preserved on wavelengths greater than ∼1 μm after 1 billion years’ residence at 1400 K, and on wavelengths greater than ∼200 μm after 1 million years’ residence at 2000 K. Nitrogen isotope zoning is relaxed much more slowly, with 0.1 μm zoning preserved over the age of the Earth at 1400 K and 1 μm zoning preserved after 1 million years at 2000 K. The large difference in diffusive relaxation times between carbon and nitrogen isotopes means that initially correlated carbon and nitrogen profiles will lose their correlation after sufficient diffusion of carbon has taken place. This could be used as a thermochronometer. Carbon isotope heterogeneity in diamonds associated with lower mantle mineral assemblages has significantly smaller amplitude than nitrogen isotope heterogeneity, consistent with diffusive relaxation at high temperatures in the lower mantle.

Nonstationary temperature distribution caused by bulk absorption of laser pulse

Nonequilibrium temperature is calculated and analyzed in a one-dimensional sample irradiated by a laser rectangular pulse. The general solution is obtained for arbitrary pulse duration compared with the relaxation time of nonstationary thermal diffusion (characteristic time of the problem).

The diffusion–spin relaxation time distribution function as an experimental probe to characterize fluid mixtures in porous media

The distribution function between diffusion and spin relaxation time is shown to be a powerful tool to characterize fluid mixtures in porous media. We discuss the nuclear magnetic resonance measurements using diffusion-editing sequences that were developed to measure this quantity. A recently developed two-dimensional inversion routine is used to extract the distribution function from the data. We show both theoretically and experimentally that the technique is suitable for ex situ applications in the presence of grossly inhomogeneous fields. We apply this technique to characterize sedimentary rocks saturated with oil–water mixtures. From the measured diffusion–relaxation time distribution function it is possible to quantify the oil and water saturation, to get a direct indication of the wettability of the porous media, to characterize the bulk properties of the oil and estimate the oil viscosity, and to get information about the geometrical arrangement of the fluid phases in the pore space. We have also identified effects due to susceptibility induced gradients in a sandstone and effects of strongly restricted diffusion in a limestone.

In vivo monitoring of age-related changes in rat brain using quantitative diffusion magnetic resonance imaging and magnetic resonance relaxometry

Diffusion-weighted magnetic resonance imaging (MRI) has been proven to be a sensitive diagnostic tool to examine age associated acute and chronic changes in brain tissue. The aim of our study was to examine whether there are differences in brain diffusion and transverse relaxation time between young and adult rats. In an experimental MR scanner, 24 young (age: 3 months) and 26 adult rats (age: 12 months) were examined using diffusion-weighted and transverse relaxation time (T2)-weighted MRI sequences. There were no differences in the T2 relaxation time between the two animal groups, either local or global. However, the mean apparent diffusion coefficient (ADC) within the whole brain was significantly lower (P<0.0005) in the adult animals (765±35×10−6 mm2/s) than in the young animals (829±45×10−6 mm2/s). ADC decrease was mainly found in the cerebral cortex. These results can be attributed to an activity-related or central nervous system damage-related internal water shift from the extracellular to the intracellular space without a net increase in water content in brain tissue. Our study also shows that age-related changes in diffusion should be considered when performing longitudinal studies in rats.

Translational and rotational diffusion in stretched water

We perform molecular dynamics simulations using the extended simple point charge SPC/E water model in order to investigate the dynamical behavior of supercooled-stretched water. We focus on the behavior of the translational diffusion coefficient, the orientational relaxation time, and the local hydrogen bond network. Decreasing density of pressure along an isothermal path, there is a minimum in the diffusion coefficient and a maximum in the orientational relaxation time, suggesting an initial enhancement and subsequent breakdown of the tetrahedral structure and of the hydrogen bond network as the density decreases. The analysis of the tetrahedral structure of the nearest neighbors help to clarify the relationship between the local structural changes and the system dynamics. We also find that the product of diffusion coefficient and relaxation time is nearly constant, indicating that the anomalous behavior observed in the rotational and translational diffusion arise from the same microscopic mechanism.

Relation between structural and dynamical anomalies in supercooled water

We step toward the elucidation of the relation between the structural and dynamic anomalies in supercooled water. We present the results of molecular dynamics simulations of the extended simple point charge (SPC/E) model of water for the translational and rotational diffusion and for the number of neighbors and hydrogen bonds. We find that the product of diffusion coefficient and relaxation time is nearly constant. The coupling between the two mobilities is explained in the framework of the structural anomalies.

Heterogeneous Media: Micromechanics Modeling Methods and Simulations. (Modeling and Simulation in Science, Engineering and Technology Series.)

Heterogeneous Media: Micromechanics Modeling Methods and Simulations. (Modeling and Simulation in Science, Engineering and Technology Series.)

Aqueous dimethyl sulfoxide solutions: Inter- and intra-molecular dynamics

The inter- and intra-molecular dynamics of aqueous dimethyl sulfoxide (DMSO) solutions have been measured using optical heterodyne-detected Raman-induced Kerr effect spectroscopy. Solutions were studied over the entire range of composition at 294 K. The Kerr transients characterize both the underdamped inter- and intra-molecular vibrational motions, as well as the overdamped, diffusive orientational motions. The longer diffusive relaxation time constant τ2 is assigned to DMSO reorientation, and varies strongly with mole fraction of DMSO. The shorter time constant τ1 is assigned to water reorientation, and the value of 1.0 ps is nearly invariant across the range of solution composition. The solutions deviate substantially from hydrodynamic scaling behavior, since the ratio of DMSO reorientation time constant normalized by shear viscosity τ2/η is not a linear function of mole fraction. The peak frequencies for three of five low frequency intramolecular vibrations decrease with increasing water content. Both anisotropic and isotropic Kerr transients are recorded. The isotropic Kerr transient is dominated by the partially depolarized ν10 symmetric C–S–C stretching vibration at 670 cm−1. Electronic structure calculations for isolated DMSO, perdeuterated DMSO (d6-DMSO), and water are carried out using semi-empirical (PM3), density functional (B3LYP), and MP2 methods. Basis sets up to 6-311++G(d,p) are used and vibrational frequencies are calculated within the harmonic approximation. An unusual hemispherical shape is obtained for the electrostatic potential (ESP) about the DMSO oxygen. This hemispherical ESP was consistently observed for all levels of electronic structure theory and all basis sets that were used. Calculated polarizabilities permit us to estimate the anisotropic Kerr signal for an isolated DMSO molecule to be 79 times greater than for an isolated water molecule.

Microscopic dynamics of confined supercritical water

We present the first study of the microscopic dynamics of confined supercritical water. Our results have been obtained by molecular dynamics simulations of supercritical water adsorbed inside carbon nanotubes. Water–water interactions were accounted by means of a flexible simple point charged potential whereas water–carbon interactions were modeled by Lennard-Jones forces. Diffusion coefficients and relaxation times of water molecules have been analyzed. Absorption lineshapes indicate that microscopic dynamics is dominated by a competition between confinement and thermal effects.

Composition and phase changes observed by magnetic resonance imaging during non-solvent induced coagulation of cellulose

The coagulation of cellulose from solution in N-methylmorpholine- N-oxide by water was studied by stray field magnetic resonance imaging. Changes in composition and diffusion were readily observable at different depths within the cellulose gel. It was found that the composition changed relatively quickly, due to diffusive exchange of water and solvent, such that cellulose precipitation occurred deep within the bi-phasic region of the phase diagram. The expected spinodal decomposition mechanism was supported by electron microscopic observations of the cellulose morphology. Large increases in diffusion coefficient and relaxation times were attributable to the phase separation and the progressive development of pores within the gel. Moreover, it appeared that the composition changes and evolution of morphology occurred over separate time-scales.

Brownian dynamics simulations of fluorescence fluctuation spectroscopy.

We have developed a program for the simulation of the fluorescence fluctuations as detected from highly diluted samples of (bio)molecules. The model is applied to translational diffusion and takes into account the hydrodynamic interactions. The solution concentration is kept constant by assuming periodic boundary conditions and spans here the range 0.5< C < 10 nM. We show that the fluorescence correlation functions can be accurately computed on systems of limited size (a few molecules per simulation box) by simulating for a total time approximately 100-300 times the diffusion relaxation time of the fluorescence autocorrelation function. The model is applied also to the simulation of the scanning fluorescence correlation spectroscopy (FCS) and of the photon counting histograms for the confocal collection configuration. Scanning FCS simulations of highly diluted samples (C approximately equals 0.5 nM) show anticorrelation effects in the autocorrelation functions of the fluorescence signal that are less evident for higher concentrations. We suggest here that this effect may be due to the non-uniform occupancy of the scanning area by the fluorophores.