Dependent Self-diffusion Coefficients Research Articles

Time dependent self-diffusion coefficient of methane molecules confined into micropores structure of a sandstone

In this work, the effect of pore structure of a sandstone on the molecular displacement of confined methane gas is analyzed. It was found that the self-diffusion coefficient of a methane molecule depends on the pore size distribution an their connectivity. In particular, the time dependent self-diffusion coefficient exhibits a maximum which is correlated with the effect of the molecular confinement. It was found that a sandstone with small pores and/or pores bad connected traps the gas more efficiently than other pores structures. This fact enable to understand the scattered values which the residual trapped gas saturation measures exhibit with different sandstones.

Concentration-dependent self-diffusion coefficients in amorphous Si1−xGex solid solutions: An interdiffusion study

Self-diffusion coefficients of Si and Ge in amorphous Si1−xGex (a-Si1−xGex) solid solutions were determined quantitatively in the temperature range of 440 °C – 460 °C by the investigation of interdiffusion in amorphous Si/Si0.52Ge0.48 multilayers using Auger electron spectroscopy sputter-depth profiling. The determined concentration dependent self-diffusion coefficients of Si and Ge in a-Si1−xGex with 0 ≤ x ≤ 0.48 at. % Ge are about ten orders of magnitude larger than in the corresponding crystalline phases, due to the inherent, excess free volume in the amorphous phase. The self-diffusion coefficient of Si (or Ge) in a-Si1−xGex increases in association with a decreasing activation enthalpy with increasing Ge concentration. This concentration dependence has been related to an overall decrease of the average bond strength with increasing Ge concentration.

Self diffusion anomaly in ferromagnetic metals: A density-functional-theory investigation of magnetically ordered and disordered Fe and Co

The temperature (T) dependent self-diffusion coefficients (D) in Fe and Co are calculated from first-principles, across the Curie temperature (Tc), employing a density functional theory approach based on a recently developed spin-wave method for modeling the paramagnetic state. Calculated results for D(T) are shown to accurately reproduce measured values for T/Tc ranging from 0.7 to 1.1, including the anomaly in the Arrhenius plot for Fe near Tc. An analysis of calculated results in Mn, Fe and Co suggests that the magnitude of the effect of magnetic disorder on D is correlated with d band filling and the transition from “weak” to “strong” ferromagnetism.

Local Structure Evolution and its Connection to Thermodynamic and Transport Properties of 1-Butyl-3-methylimidazolium Tetrafluoroborate and Water Mixtures by Molecular Dynamics Simulations

Our recently developed improved united atom force field shows a good quality to reproduce both the static and transport properties of neat ionic liquids (ILs). Combined with the TIP4P-Ew water model, the force field is used to simulate the mixture of 1-butyl-3-methylimidazolium tetrafluoroborate ([C(4)mim][BF(4)]) and water without further optimization to adjust any cross parameters. Liquid densities of the mixture are well predicted over the entire concentration range at temperatures from 298.15 to 353.15 K. Simulations also reproduce the positive values of excess volumes and excess enthalpies, as well as their increase with temperature. The simulated viscosities are in good agreement with experimental values, especially in the water-rich region. We found three distinct regions by analyzing the concentration dependent self-diffusion coefficients via Stokes-Einstein (SE) relation, indicating the mixture experiences significant microheterogeneity with the adding of water. This observation is well connected to the structure features obtained in simulations, such as radial distribution functions (RDFs), spatial distribution functions (SDFs) and water clustering analysis. At the water mole fraction (x(2)) less than 0.2, most of the water molecules are isolated in the polar cation-anion network in ionic liquids. With the increase of x(2) from 0.2 to 0.8, large water cluster forms and eventually percolates the whole system. When x(2) > 0.8, ionic liquids show a moderate degree of aggregation (with maximum around 0.9 to 0.95) before the cations and anions are fully dissolved in water.

Self diffusion in liquid aluminium

Here we report temperature dependent self-diffusion coefficients of liquid aluminium measured on absolute scale by using incoherent quasielastic neutron scattering at temperatures of 980K, 1020K, and 1060K. Aluminium self-diffusion coefficients follow an Arrhenius law with an activation energy of 280±70 meV. The Sutherland-Einstein equation relating viscosity to the diffusion coefficient well captures the temperature dependence and absolute values of the here reported aluminium self-diffusion coefficients using the covalent radius of aluminium. A comparison to published molecular dynamics simulation data helps to further narrow down the choice of the potential.

Concentration dependent self-diffusion coefficients of aqueous electrolyte solutions in bulk phase and confined in porous glasses measured by pulsed field gradient NMR

Concentration dependent self-diffusion coefficients of aqueous electrolyte solutions in bulk phase and confined in porous glasses measured by pulsed field gradient NMR

Self-Diffusion Studies in CuBTC by PFG NMR and MD Simulations

Self-diffusion and relaxation time studies of C3 to C6 hydrocarbons adsorbed in the microporous metal−organic framework CuBTC were performed by nuclear magnetic resonance (NMR) in the temperature range of 193−373 K. The presence of paramagnetic copper species in the solid CuBTC framework leads to short longitudinal (T1) and transverse (T2) relaxation times of the hydrocarbons with typical values of T1 ≲ 10 ms and T2 ≲ 3 ms. Under these conditions, pulsed field gradient (PFG) NMR self-diffusion studies could only be performed at short observation times using the primary spin echo sequence with high-intensity pulsed magnetic field gradients. The obtained temperature dependent self-diffusion coefficients were analyzed using an Arrhenius approach. The activation energies of the alkanes are in the range of 6.5−8.5 kJ/mol, increasing slightly with increasing number of carbon atoms. Significantly higher values were found for propene (13.2 kJ/mol) and 1-butene (15.0 kJ/mol). These tendencies are consistent with corresponding measurements of heats of adsorption and with data obtained in molecular dynamics (MD) simulations. The MD simulations show a strong dependence of the heat of adsorption and diffusion on loading and temperature. This is caused by the preferential adsorption of small alkanes such as propane and butane in the side pockets of the CuBTC structure at low loading and temperature.

Sodium-ion diffusion and ordering in single-crystalP2-NaxCoO2

Sodium-ion self-diffusion in $P2(\ensuremath{\gamma}){\text{-Na}}_{x}{\text{CoO}}_{2}$ has been studied using a single crystal as an electrode. Mass transport and thermodynamic properties of Na ions were measured by the potentiostatic intermittent titration technique on a single-crystal electrode with greater accuracy under well-defined diffusion geometry. Excluding the significantly slower diffusion behavior near particular Na ordered phases, average diffusion coefficients ${D}_{\text{Na}}$ are extracted to be $1.2\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }{\text{cm}}^{2}/\text{s}$ for $xg0.5$ and $4.1\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }{\text{cm}}^{2}/\text{s}$ for $xl0.5$, respectively. The existence of stable phases with special Na ordering of $x\ensuremath{\sim}0.25$, 0.33, 0.43, 0.5, 0.55, and 0.71 are verified by either the maximum or diverging signature of the $x$-dependent self-diffusion coefficients.

A new theoretical equation for temperature dependent self-diffusion coefficients of pure liquid metals

Abstract A unified equation on the viscosity of pure liquid metals (published recently by the author) is combined with the well-known Sutherland – Einstein equation to obtain a new equation for the temperature dependence of the self-diffusion coefficients of pure liquid metals. The equation does not contain new adjustable parameters. It reproduces perfectly the experimental values, measured under micro-gravity conditions for liquid Sn, Pb, In and Sb. The experimental data, obtained under normal gravity conditions appear to be equal or somewhat higher than those calculated from the present model. This is explained by the effect of gravity induced convection in the liquid.

Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium

Analytical solution for the time dependent self-diffusion coefficient of a liquid in a porous medium

Atomistic Modeling of Diffusion in Aluminum

We present molecular-dynamics simulations of self-diffusion in Al. In order to facilitate the description of elastic and vibrational properties as well as vacancy migration, an embedded-atom method potential was used in the simulations. This potential was specifically designed to reproduce the T = 0 K equation of state of Al obtained by ab initio total-energy calculations. We show that the temperature dependent self-diffusion coefficient obeys an Arrhenius law and that the resulting dynamical migration energy is slightly larger than the static migration energy obtained by using classical rate theory.

Time dependent self-diffusion coefficient of molecules in porous media

The time dependence of the self-diffusion coefficient D(t) in porous media is investigated by Monte Carlo simulation of autocorrelation functions 〈f(t)f(0)〉, where f(t) is the force of interaction between a molecule and the surface at time t. At short times, D(t) is governed by the surface population of the molecules and the probability of their return to the surface. At times t>t*, where t* is the characteristic time for the autocorrelation function to converge to zero, the apparent dynamics of the molecules is completely determined by the geometry of the surface on the length scale of D0t*, where D0 is the bulk self-diffusion coefficient. D(t) in this limit is the sum of a constant D∞=limt→∞ D(t) and a time-dependent term R̄p2/2d⋅t, where R̄p2 is the mean-squared size of an effective unit cell of the porous space and d is the dimensionality of the space. The meaning of tortuosity for self-diffusion is discussed.

Diffusion characteristics and waveguiding properties of proton-exchanged and annealed LiNbO3 channel waveguides

A discussion of the modeling of the proton exchange fabrication process is given, including a brief review of results of analytical measurements of concentration and concentration/index relation, as well as some presentation of the speculations made as to mechanisms of resulting index profiles. Discussion is then given to modeling of the exchange process itself via the ion exchange equations. The concentration profiles of protons and lithium in proton-exchanged LiNbO3 crystals measured by secondary ion mass spectroscopy are then presented. The proton concentration profiles are found to be nearly rectangular in shape. The diffusion characteristics of the ion exchange process are empirically modeled by solving the ion exchange equations with concentration dependent self-diffusion coefficients. Secondary ion mass spectroscopy (SIMS) measurements on annealed H+:LiNbO3 samples show proton and lithium concentration profiles to be Gaussian in nature. The proton and lithium concentration profiles of annealed H+:LiNbO3 samples are fit to the solutions of diffusion equations obtained from standard thermal diffusion theory. The fit has resulted in values of diffusion coefficient for protons during annealing (Dp=0.77 μm2/h). Index profiles are then calculated from these equations and are found to agree with the profiles reported elsewhere. Optical mode measurements on channel waveguides fabricated under various diffusion conditions and annealed for various times, are carried out. The mode-tailoring ability of the proton exchange process is demonstrated by fabricating low-loss single-mode channel guides (λ=0.83 μm) having channel widths as large as 6 and as small as 2.5 μm, simply by changing the diffusion conditions. Some anomalous results obtained in waveguides fabricated under extreme conditions are discussed.

Cluster expansion of the diffusion kernel of a suspension of interacting Brownian particles

We derive a cluster expansion for the wavenumber- and frequency-dependent diffusion coefficient of a suspension of interacting Brownian particles. The diffusion coefficient is expressed in terms of evolution operators of progressively increasing complexity. We expect that at low frequency only the low-order terms contribute effectively. We propose an expression for the wavenumber-dependent collective diffusion coefficient at zero frequency which involves the dynamics of only two particles. A similar expression is obtained for the wave-number dependent self-diffusion coefficient.

Zur Diffusionskinetik in Ionenaustauscherharzen Selbst-und Austauschdiffusion von Alkali-und Erdalkaliionen / The Diffusion Kinetic in Ionic Resin Exchangers. Self- and Exchange-Diffusion of Alcaliions

Abstract Heterogeneous isotope exchange rates of Na+, Ca+, Ba2+ and Sr2+ in mono-and biionic resin exchangers (Merck I) have been measured under conditions where diffusion is rate determining. For the self-diffusion of Na+, Ba2+ and Sr2+ linear Dt/r2 - f(t)-curves are obtained. Cs-isotope exchange shows non-ideal diffusion kinetics. In mixed Ba-exchangers the self-diffusion coefficients of Ba2+ and Sr2 depend on the ionic composition of the exchanger phase. Ion exchange rates have been measured for Ba/Sr2+ -exchange and its reversal. Computed curves are presented using Helfferich’s theory of ion exchange and an extended treatment with activity correction terms and concentration dependent self-diffusion coefficients. Computed and experimental curves are discussed.

Transport in two dimensions. III self-diffusion coefficient at low densities

The low density form of the generalized frequency ( s) and wavevector ( k) dependent self-diffusion coefficient D( k , s) is calculated, from which the low density forms of related quantities, e.g. the velocity autocorrelation function, are derived. Agreement is obtained with the low density kinetic theory results. A closed form expression for D( k , s) valid over a wide range of densities and times is also given, showing consistency between the asymptotic long time results, obtained previously, and the low density kinetic theory results.

Temperature dependent self-diffusion coefficient measurements of glycerol by the pulsed N.M.R. technique

(1973). Temperature dependent self-diffusion coefficient measurements of glycerol by the pulsed N.M.R. technique. Molecular Physics: Vol. 25, No. 3, pp. 735-738.