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A gas model of diffusion in liquid metals is presented. In this model, ions of liquid metals are assumed to behave like the molecules in a dense gas. Diffusion coefficient of solute is discussed with reference to its mass, ionic size, and pair potential. The model is applied to the case of solute diffusion in liquid silver. An attempt was made to predict diffusion coefficients of solutes with reasonable accuracy.
The reaction between Al2O3 and alpha2-Ti3Al was studied with a series of Al2O3/alpha2-Ti3Al multiphase diffusion couples annealed at 900, 1000 and 1100 C. The diffusion-paths were found to strongly depend on alpha2- Ti3Al(O) composition. For alloys with low oxygen concentrations the reaction involved the reduction of Al2O3, the formation of a gamma-TiAl reaction-layer and diffusion of Al and O into the alpha2-Ti3Al substrate. Measured concentration profiles across the interaction-zone showed "up-hill" diffusion of O in alpha2-Ti3Al(O) indicating a significant thermodynamic interaction between O and Al, Ti or both. Diffusion coefficients for the interstitial O in alpha2-Ti3Al(O) were determined independently from the interdiffusion of Ti and Al on the substitutional lattice. Diffusion coefficients are reported for alpha2-Ti3Al(O) as well as gamma-TiAl. Interpretation of the results were aided with the subsequent measurement of the activities of Al, Ti and O in alpha 2-Ti3Al(O) by Knudsen effusion-cell mass spectrometry.
Polymer networks with dynamic covalent bonds have been investigated for their self-healing ability, recyclability, and potential as more sustainable materials. Recent results have indicated that in some cases, bond exchange can enhance the transport of penetrants in dense networks, pointing to their potential for separations of membranes. Here, imine dynamic bonds in ethylene oxide (EO) networks with precise linker lengths were synthesized to investigate the transport of N,N′-bis(2,5-di-tert-butylphenyl)-3,4,9,10-perylenedicarboximide (BTBP), a large, anisotropic dye molecule. Networks with mesh sizes smaller than, comparable to, and greater than the size of the penetrant axes were investigated to probe the effects of bond exchange and network confinement on transport. Mesh sizes, which ranged from 0.5 to 1.62 nm, were determined from shear rheology, glass transitions by calorimetry, and probe diffusion coefficients by fluorescence recovery after photobleaching. Permanent networks with identical EO chain lengths were prepared as control samples, and up to a 3 orders of magnitude increase in diffusion coefficient is observed in the dynamic systems for short linkers containing 13 backbone atoms. The longest linkers with 71 backbone atoms show no difference between the permanent and dynamic networks. Linkers shorter than 11 backbone atoms, corresponding to a mesh size smaller than the penetrant small axis, diffusion is no longer observable on the experimental time scale, indicating a sharp cutoff attributed to the precise linkers and narrow mesh size distribution. The dynamic imine exchange time scales were compared to the diffusive hopping times of penetrants and indicate that exchange can occur during a diffusive displacement. Furthermore, these findings provide insights into the factors affecting penetrant transport in dense polymers and inspire the development of next-generation selective polymer membranes.
This innovative software estimates rotational diffusion coefficients of particles from X-ray photon correlation spectroscopy (XPCS) data of monodispersed particle systems. It is the first method capable of extracting rotational diffusion information from three-dimensional particle systems using XPCS. Using the angular-temporal cross-correlation of the XPCS images, this software is able to estimate the rotational diffusion coefficients with only a few percent relative errors while requiring minimal prior knowledge of particle structures. This software enhances XPCS analysis capabilities, allowing researchers to study translational and rotational Brownian dynamics of particles in suspension across various temporal and spatial scales.
The results of the spatial distribution of cosmic ray density, gradients, and anisotropy obtained on the basis of the numerical solution of the anisotropic diffusion equation with an account of solar wind velocity change depending on the latitudinal angle theta of the form U=u sub oe sup alpha theta and the diffusion coefficient depending on the spatial coordinates and the particle rigidity are presented. It is shown that the increase of the solar wind velocity and the diffusion coefficient with heliolatitude leads to gradient distributions that are in accord with experimental data observed in space. The results of the energetic spectrum of 11 and 22-year cosmic ray variations obtained with an account of direction of the general magnetic field of the Sun are presented are given.
Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set Omega of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability P(X) that crack penetration depth exceeds X is expressed as a functional integral over Omega of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather nonrestrictive assumptions, the integral is reduced to solving a diffusion-type equation. A new characteristic of fracture process, 'crack diffusion coefficient', is introduced. An illustrative example is then considered where the integration is reduced to solving an ordinary differential equation. The effect of the crack diffusion coefficient and of the magnitude of strength fluctuations on probability density of crack penetration depth is presented. Practical implications of the proposed model are discussed.
We consider the effect of oblique EMIC waves on relativistic electron scattering in the outer radiation belt using simultaneous observations of plasma and wave parameters from CRRES. The main findings can be s ummarized as follows: 1. In 1comparison with field-aligned waves, int ermediate and highly oblique distributions decrease the range of pitc h-angles subject to diffusion, and reduce the local scattering rate b y an order of magnitude at pitch-angles where the principle absolute value of n = 1 resonances operate. Oblique waves allow the absolute va lue of n > 1 resonances to operate, extending the range of local pitc h-angle diffusion down to the loss cone, and increasing the diffusion at lower pitch angles by orders of magnitude; 2. The local diffusion coefficients derived from CRRES data are qualitatively similar to the local results obtained for prescribed plasma/wave parameters. Conseq uently, it is likely that the bounce-averaged diffusion coefficients, if estimated from concurrent data, will exhibit the dependencies similar to those we found for model calculations; 3. In comparison with f ield-aligned waves, intermediate and highly oblique waves decrease th e bounce-averaged scattering rate near the edge of the equatorial lo ss cone by orders of magnitude if the electron energy does not excee d a threshold (approximately equal to 2 - 5 MeV) depending on specified plasma and/or wave parameters; 4. For greater electron energies_ ob lique waves operating the absolute value of n > 1 resonances are more effective and provide the same bounce_averaged diffusion rate near the loss cone as fiel_aligned waves do.
Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.
Gelling the electrolyte in lithium–sulfur (Li–S) batteries provides advantages in terms of safety and mitigating polysulfide shuttling leading to reduced side reactions and dendrite growth on the anode side. In the current study, organic and ceramic crosslinkers have been used to improve the entrapment of polysulfides and prevent them from shuttling to the anode side. However, the performance of gel electrolytes is still far from being on par with liquid electrolytes in terms of raw capacity. The discharge curves exhibit an extended first plateau for gel electrolyte batteries compared to liquid electrolytes, showing that polysulfides are better trapped in the gel system. Yet, in the conversion of soluble polysulfides into insoluble polysulfides, the second plateau was delayed. Qualitative and quantitative analysis of the polysulfide diffusion in the liquid electrolyte and gel electrolyte systems were also conducted to predict the relative diffusivity ratio between the liquid electrolyte and gel electrolyte for simulation. To probe what happens at the end of the discharge, where the mass transport in the gel electrolyte appears to be slow, a modified discharge procedure was used where the cell is first paused after discharge and then discharged a second time before recharging normally. Coin cell tests for two gel electrolytes in addition to liquid electrolyte show up to 7% capacity recovery after the pause, which indicates that the diffusion of species during the pause is responsible for the failure recovery. Additionally, the recovery is higher for gel electrolytes compared to liquid, for higher C-rates, and for longer pause times. To better understand this behavior, a Li–S numerical model with mass transport limited reactions was used to examine the polysulfide diffusion coefficients expected in different electrolyte systems. The model is able to reproduce the trends seen in experiments and yields a higher recovery for smaller Li 2 S 4 diffusion coefficients, suggesting that insufficient Li 2 S 4 mass transport is responsible for failure at the end of discharge. By identifying the effect that gel electrolytes have on the state of the battery during discharge using both experimental and simulation methods, this work is a step towards leveraging the advantages of gel electrolytes and mitigating their weaknesses.
The radial diffusion equation with synchrotron losses is solved by the Laplace-transform method for near equatorially mirroring relativistic electrons. The evolution of a power-law distribution function is found, and the characteristics of synchrotron burnoff are stated in terms of explicit parameters for an arbitrary diffusion coefficient of a specific form. The peaking of the 10.4-cm volume emissivity from Jupiter at an L shell of about 1.8 provides an estimate of the diffusion coefficient in the radiation belts; one value is suggested as the appropriate modification, for an equatorial field strength of 4.2 G, of the Birmingham et al. (1974) result. Nonsynchrotron losses are included phenomenologically; from the phase-space densities reported by McIlwain and Fillius (1975), the particle lifetime is estimated. Asymptotic forms for the distribution in the strong synchrotron loss regime are provided.
Because of the presence of multiple ion species in the Io plasma torus, whistler mode noise can be converted to ion cyclotron waves via a polarization reversal process at the local crossover frequency. Using whistler mode intensity measurements in the Jovian magnetosphere from Voyager 1, the pitch-angle diffusion rates that would occur if the noise is converted to ion cyclotron waves is estimated. Typical pitch-angle diffusion coefficients range from 0.000001/sec for protons resonating near the equator to 0.0001/sec for 10-keV O(+) ions resonating at high latitudes. Although complete bounce averaged diffusion coefficients have not yet been computed, preliminary estimates indicate that the energetic ion precipitation caused by these waves may be able to account for the EUV auroral emissions at the foot of the torus field lines.
In this work, we present dynamical and morphological studies on poly(dimethylsiloxane) (PDMS)-based bottlebrush polymers in solution. A combination of small-angle neutron scattering (SANS), pulsed field gradient nuclear magnetic resonance (PFG NMR), and neutron spin echo (NSE) spectroscopy was used to identify structural changes inherent in changing the side-chain length while keeping the backbone constant. These morphological changes are mirrored in the diffusion coefficient determined by PFG NMR, resulting in two coefficients for the elongated and one for the more spherical sample. Faster motions are tracked by NSE using the advantage of time- and length-scale resolutions with the diffusion coefficient predetermined by PFG NMR. Hereby, the sample with short side chains relaxes like wormlike micelles considering the longitudinal direction, whereas the dynamics along the radial extension shows a much stronger Q-dependence as known from any theory. The dynamical behavior within the blob region, covered with the more spherical sample, follows the predictions of Zimm as well as of Zilman and Granek (ZG).
Oxygen self diffusion coefficients were determined in single crystal alpha-Al2O3 using the gas exchange technique. The samples were semi-infinite slabs cut from five different boules with varying background impurities. The diffusion direction was parallel to the c-axis. The tracer profiles were determined by two techniques, single spectrum proton activation and secondary ion mass spectrometry. The SIMS proved to be a more useful tool. The determined diffusion coefficients, which were insensitive to impurity levels and oxygen partial pressure, could be described by D = .00151 exp (-572kJ/RT) sq m/s. The insensitivities are discussed in terms of point defect clustering. Two independent models are consistent with the findings, the first considers the clusters as immobile point defect traps which buffer changes in the defect chemistry. The second considers clusters to be mobile and oxygen diffusion to be intrinsic behavior, the mechanism for oxygen transport involving neutral clusters of Schottky quintuplets.
We present the first calculations of the heavy flavor diffusion coefficient using lattice QCD with light dynamical quarks corresponding to a pion mass of around 320 MeV. For temperatures 195 MeV< 𝑇 <352 MeV, the heavy quark spatial diffusion coefficient is found to be significantly smaller than previous quenched lattice QCD and recent phenomenological estimates. The result implies very fast hydrodynamization of heavy quarks in the quark-gluon plasma created during ultrarelativistic heavy-ion collision experiments.
Jovian electron intensity in the energy range 2-7 MeV was measured along the trajectory of Pioneer 11 up to 16 deg heliographic latitude. These electrons have crossed the average direction of the interplanetary magnetic field, propagating normal to the solar equatorial plane, and their intensity continues to be modulated by corotating interaction regions over this latitude range. From these data, the electron diffusion coefficient perpendicular to the equatorial plane (K2 = 2 x 10 to the 20th sq cm/s) was derived to within a factor 2 using a three-dimensional diffusion-convection model and the values of the parallel and perpendicular diffusion coefficients in the solar equatorial plane (Ky = 5 x 10 to the 22nd sq cm/s, K2 = 10 to the 21st sq cm/s, respectively), which had previously successfully described Jovian electron propagation near the equatorial plane from 1 to about 10 AU. These results indicate that the Jovian electron intensity may be very low at high solar latitudes.
Two triglycine sulphate crystals were grown from an aqueous solution in Spacelab 3 aboard a Space Shuttle. Using a diffusion coefficient of 0.00002 sq cm/s, a computerized simulation gave reasonable agreement between experimental and theoretical crystal sizes and interferometric lines in the solution near the growing crystal. This diffusion coefficient is larger than most measured values, possibly due to fluctuating accelerations on the order of .001 g (Earth's gravity). The average acceleration was estimated to be less than .000001 g. At this level, buoyancy driven convection is predicted to add approx. 20 percent to the steady state growth rate. Only very slight distortion of the interferometric lines was observed at the end of a 33 hr run. It is suggested that the time to reach steady state convective transport may be inversely proportional to g at low g, so that the full effect of convection was not realized in these experiments.
Two triglycine sulphate crystals were grown from an aqueous solution on the Spacelab 3 mission. Using a diffusion coefficient of 0.00002 sq cm/sec, a computer simulation gave reasonable agreement between experimental and theoretical crystal sizes and interferometric lines in the solution near the growing crystal. This diffusion coefficient is larger than most measured values, possibly due to fluctuating accelerations on the order of 0.001 g. The average acceleration was estimated to be less than 10 to the -6th g. At this level buoyancy-driven convection is predicted to add approximately 20 percent to the steady-state growth rate.
The diffusion coefficients of D and Li were calculated in amorphous, glassy Li+D mixtures for various concentrations of D in lithium over the temperature range 100–1000 K. The densities of the mixtures as a function of temperature were also determined. The diffusion coefficients were obtained by the analysis of the mean-squared displacement using molecular dynamics with ReaxFF, a reactive force field. In conclusion, the diffusion and density data obtained for Li+D mixtures were compared with the available experimental and calculated data reported in the literature.