Diffusion transport

Non-evaporable getter (NEG) materials have become an integral part of many ultrahigh vacuum environments mainly due to their unique surface properties which are able to achieving extreme-high vacuum conditions of the order of 10 −12 mbar and lower. NEG materials have to be " activated " after exposure to atmospheric gases. Activation is performed by heating the getter to appropriate temperature in order to remove the adsorbed gas molecules/ atoms (mainly oxygen and carbon) from the getter surface to get atomically clean metal surface of getter alloy. Main mechanism of removal of oxygen and carbon is diffusion from the surface layer into the bulk. The elements in getter alloy shall have high diffusivity and high solubility for oxygen and carbon. Diffusion of oxygen gas has been studied for pure metals, but for getter alloys there is almost no data available. At low temperature the diffusion length may be only of the order of few nm so we used surface sensitive analytical te...

Diffusion Fundamentals 12 (2010) 77 © M. Achimovičová Fund. One of the authors (V.Š.) thanks the Deutsche Forschungsgemeinschaft for supporting his work in the framework of the Priority Program "Crystalline Nonequilibrium Phases" (SPP 1415).

Crystallites of zeolite LSX with a diameter of about 10 µm are shown to allow the simultaneous investigation of intracrystalline mass transfer phenomena of water molecules and lithium ions in hydrated zeolite Li-LSX by NMR diffusometry. By MAS NMR spectroscopy with the 1 H and 6 Li nuclei, the water molecules and lithium ions are found to yield two signals, a major and a minor one, which may be attributed to locations in the sodalite cages and the supercages, respectively. By 1 H and 6 Li exchange spectroscopy the mean residence times in the sodalite cages at 373 K are found to be about 150 ms for the water molecules and about 40 ms for the lithium cations . As to our knowledge, PFG NMR measurements of cation diffusion in zeolites have never been performed. Whilst, under the given experimental conditions, the water diffusivity at 373 K could be determined to be of the order of 2.5 × 10 -10 m 2 s -1 or even larger, the diffusivity of the lithium ions in the same sample and at the same temperature was found to be (2.0 ± 0.8) × 10 -11 m 2 s -1 . This yields to a Haven factor of about 10 for the ion conductivity in the zeolite Li-LSX. The new options provided by the high-intensity device for PFG NMR diffusion measurement applied in this study for the measurement of the intracrystalline diffusion of both the cations and the guest molecules in zeolite Li-LSX, in purposeful combination with the information accessible by PFG MAS NMR and two-dimensional MAS NMR spectroscopy, have all potentials for opening new routes for a deeper understanding of the dynamic processes in host-guest systems under the involvement of exchangeable cations. Figure 1: Water and ion diffusion in the package of zeolite crystallites.

Determining the composition of solid materials is of high interest in areas such as material research or quality assurance. There are several modalities at disposal with which various parameters of the material can be observed, but of those only magnetic resonance imaging (MRI) or computer tomography (CT) offer a non-destructive determination of material distribution in 3D. A novel non-destructive imaging method is Magnetic Particle Imaging (MPI), which uses dynamic magnetic fields for a direct determination of the distribution of magnetic materials in 3D. With this approach, it is possible to determine and differentiate magnetic and nonmagnetic behaviour. In this paper, the first proof-of-principle measurements of magnetic properties in solid environments are presented using a home-built traveling wave magnetic particle imaging scanner.

The effects of molecular exchange processes on the two-dimensional (2D) NMR T2-T2 distributions obtained by Laplace inversion were studied by numerical simulations. The Monte–Carlo technique is used to generate free random walks of a large number of molecules within space regions characterized by different relaxation times. Molecular exchange processes are considered during CPMG encoding periods as well as during the storage period, τstore. Systematic simulations were performed as function of NMR parameters like the storage period, τstore and geometric or physical system properties.

For many applications such as advanced energy storage systems, chemical sensors or electrochromic devices fast ionic conduction plays an important role. In many cases, see e.g., Refs. [1-3], nanocrystal-line ceramics with crystallite diameters smaller than 50 nm show an enhanced ion conductivity compared to their coarse-grained counterparts, i.e., single crystals or materials with µm-sized particles. This observation can be explained by their large fraction of structurally disordered interfacial regions providing fast migration pathways for the ions [2,3]. Mechanical treatment of µm-sized particles in a high-energy ball mill represents a simple technique to obtain large quantities of a nanocrystalline material. In addition to that it is also possible to synthesize ceramics directly by ball milling [3]. In many cases this leads to metastable, non-equilibrium compounds which cannot be prepared following conventional synthesis methods [4,5]. In the present paper, BaLiF 3 , the only kno...

The role of nanocrystalline materials in addressing the current challenges in energy storage has attracted large attention. Besides nanostructured B-type TiO 2 [1], being the fifth polymorph of titanium dioxide, Li intercalated nanocrystalline rutile is considered to act as a potential anode in inherently safe secondary Li ion batteries. In contrast to its coarse-grained counterpart, which is electrochemical-ly inactive, nanocrystalline Li x TiO 2 (rutile) shows a high capacity, high rate performance, and good cycleability when used as an electrode material [2] demonstrating that nanostructuring is a promising strategy to meet the high power and high energy density requirements for Li-based energy storage devices. The advantages of nano-electrodes over those composed of micrometer-sized bulk materials are due to their shorter lengths for both electronic and Li + transport, a higher electrode-electrolyte contact area, and a much better compensation of the strain arising during Li + i...

The experimental and theoretical study of the co-adsorption and co-diffusion of several gases through a microporous solid and the instantaneous (out of equilibrium) distribution of the adsorbed phases is particularly important in many fields, such as gas separation, heterogeneous catalysis, purification of confined atmospheres, reduction of exhaust emissions contributing to global warming, etc. The original NMR imaging technique used gives a signal characteristic of each adsorbed gas at each instant and at each level of the solid and therefore the distribution of several gases in competitive diffusion and adsorption. But it does not allow to determine separately the inter-and intra-crystallite quantities. A new fast and accurate analytical method for the calculation of the coefficients of co-diffusing gases in the intraand inter-crystallite spaces of microporous solid (here ZSM 5 zeolite) is developed, using high-performance methods (iterative gradient methods of residual functional minimization and analytical methods of influence functions) and mathematical coadsorption models, as well as the NMR spectra of each adsorbed gas in the bed. These diffusion coefficients and the gas concentrations in the inter-and intra-crystallite spaces are obtained for each position in the bed and for different adsorption times.

Nitrogen adsorption (B.E.T. method) is the most commonly applied technique to measure the specific surface area (SSA) of active pharmaceutical ingredient (API) and excipient powders. The major limitation of the B.E.T. method is the requirement of large sample amounts for low surface area materials. Since the majority of APIs and excipients used in the pharmaceutical industry exhibit low surface areas this greatly limits the utility of the general B.E.T. method for pharmaceutical applications. The aim of this work was to evaluate the applicability of an alternative method for measuring SSA of API and excipients by inverse gas chromatography (IGC). With this technique, the SSA was measured in situ by injections of a single solute (suitable nonpolar probe) of increasing concentrations at constant temperature using finite dilution (IGC-FC). The solutes used for this investigation were n-alkanes: hexane, heptane, and octane. A model material, spherical glass beads, was selected to develo...

A number of random processes in various fields of science is described by phenomenological equations of motion containing stochastic forces, the best known example being the Langevin equation (LE) for the Brownian motion (BM) of particles. Long ago Vladimirsky (1942) in a little known paper proposed a simple method for solving such equations. The method, based on the classical Gibbs statistics, consists in converting the stochastic LE into a deterministic equation for the mean square displacement of the particle, and is applicable to linear equations with any kind of memory in the dynamics of the system. This approach can be effectively used in solving many of the problems currently considered in the literature. We apply it to the description of the BM when the noise driving the particle is exponentially correlated in time. The problem of the hydrodynamic BM of a charged particle in an external magnetic field is also solved.

A multi-pulsed free-induction NMR experiment is described theoretically for spins diffusing within a cylindrical capillary. The characteristic time for the particles to move on a distance of the capillary diameter is smaller or comparable to the time interval between the applied 90° rf pulses and the relaxation times entering the Bloch equations. In this case the spin diffusion is restricted and the classical solutions of these equations for unbounded media are not applicable. We have calculated the mean magnetization in the cross-section of the capillary after any of the rf pulses and found the induced NMR signal within the Bloch-Torrey-Stejskal theory for spins reflected at boundaries. The problem is extended by considering a possible macroscopic (plug and Poiseuille) flow of the fluid inside a capillary. It is found that with the increase of the rf pulse number, the maxima of the observed signals do not decay to zero but converge to a nonzero value. The proposed theory thus seems to be suitable for the description of experiments on systems rapidly relaxing due to diffusion and flow.

A multi-pulsed free-induction NMR experiment is described theoretically for spins diffusing within a cylindrical capillary. The characteristic time for the particles to move on a distance of the capillary diameter is smaller or comparable to the time interval between the applied 90° rf pulses and the relaxation times entering the Bloch equations. In this case the spin diffusion is restricted

Traditional bead-spring models of the polymer dynamics are based on the Einstein theory of the Brownian motion (BM), valid only at the times much larger than the particle´s relaxation time. The reason is in neglecting the inertial and memory effects in the dynamics. In the present work we use a generalized theory of the BM to build models of the dynamics of flexible polymers in dilute solution. The equations of motion for the polymer segments include the friction force that follows from the linearized Navier-Stokes hydrodynamics. It has a form of a memory integral. To get a correct description of the short-time dynamics, inertial effects are included into the consideration. For negligible hydrodynamic interactions (HI) between the beads the motion of the polymer center of mass is not influenced by internal forces within the chain and has been considered exactly. Then we include the HI into the description of motion of chains, which are assumed Gaussian in equilibrium. Analytical sol...

An experimental and theoretical study of the dehydration of natural gas using microporous silica beds for motor fuel technology in extreme winter climates is described. Analytical solutions to the problem of non-isothermal adsorption and desorption are based on Heaviside's operational method and Laplace integral transformation. Experimental and modeling distributions of moisture and temperatures of gas at the inlet and outlet of the silica beds for each adsorption-desorption phase at different times are presented. The distribution of moisture within the beds for the full dehydration-regeneration cycle is determined. Keywords Natural gas dehydration, diffusion of adsorbed gas, adsorption and desorption of gases, modeling, Heaviside's operational method, Laplace integral transformation.

Using the Fluctuation Theorem (FT), we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical ensemble. Using a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.

We present the first results of the magnetic field dependence of the longitudinal nuclear magnetic relaxation of anion-cation pair of ionic liquids (Li + -ionogels) confined within a silica-like mesoporous matrices designed for lithium batteries. These results are in favour of a very-correlated dynamical motion of the anion-cation pair within the solid and disordered silica matrix.

The characteristics (surface-to-volume ratio, pore radius, diffusion, surface relaxation strength, tortuosity) of a porous system composed of a fluid confined in unconsolidated glass beads were obtained by Pulsed Gradient Stimulated Echo (PGSTE) NMR using two different probe molecules, benzene and water, respectively. The measurements were carried out on a low field NMR instrument operating at 20 MHz proton frequency. Using a 13-interval pulse sequence, the effective diffusion coefficient D of a fluid (water and benzene, respectively) confined in a porous material (unconsolidated glass beads) was measured as a function of the square-root of diffusion time tD (Fig. 1). The limiting diffusion coefficient D0 and the surface-to-volume S/V-ratio were determined from Eq. 1 [1] where D0 equals the bulk diffusion. The ratio between D0 and the limiting diffusion D∞ at long diffusion time is termed the tortuosity factor Γ(= D0/D∞) and is an important matrix parameter D(tD) =− 4 9 √ π D 0 S V ...

1. Introduction Molecular beam epitaxy has become an important tool to prepare ultrathin films and nanostructures in nonequilibrium states that show novel properties distinctly different from the equilibrium bulk phases. Theoretically, the question arises how to relate the structural characteristics of the growing material to the incoming flux and temperature-dependent surface diffusion constants. This question is fairly well understood for one-component systems. By contrast, only few theoretical studies were devoted to the growth of binary alloy nanostructures, despite of the large interest in this field from the experimental and technological viewpoint. In this communication we present detailed kinetic Monte Carlo simulations of growing nanoclusters within a binary alloy model that allows arbitrary diffusion moves of atoms within an active zone near the cluster surface. Our model is designed to describe fcc-type alloys under growth in the (111) direction. The main motivation came ...

1. Introduction In order to improve catalyst activity and selectivity for diffusion-limited reactions within porous heterogeneous catalysts it is necessary to understand the interrelationship between pore structure and mass transport. In particular, an accurate knowledge of the pellet pore size distribution is essential. However, current techniques for analysing nitrogen adsorption isotherms (such as the BJH and NLDFT methods), and cryoporometry melting curves, make unfounded assumptions concerning the thermodynamic independence of differently-sized pores within complex pore networks. Hence, potential pore-pore interaction effects leading to cooperative cascades of advanced adsorption, or advanced melting, in sorption and cryoporometry experiments respectively, are not taken into account. For example when analysing gas adsorption data, a potential discrepancy of a factor of two, between estimated and actual pore sizes, would be anticipated from employing the wrong meniscus geometry ...

The modelling of electro-diffusion in the multicomponent system in open space and time domains has been only recently addressed and made numerous applications in biology, fuel cells, electrochemical sensors and reference electrodes possible. In this work we show the numerical simulations of electrical potential over time and resulting electrochemical impedance spectra of ion-selective membrane electrodes (ISE's). The numerical results are obtained by use of the coupled Nernst-Planck, Poisson and continuity equations (forming the NPP model). The equations are solved by means of the finite difference method, the Rosenbrock solver with the use of Matlab (by MathWorks) platform. The potential-time response of the ISEs in open-and closed-circuit conditions as a function of varying heterogeneous rate constants, ionic concentrations and membrane thickness are computed. The potential-time response to small-current perturbation is applied for simulations of the impedance spectra. The results obtained show that the membrane with Nernstian response presents only one capacitive arc in the impedance spectra, related to conductivity and dielectric properties of the membrane material. Non-Nernstian behaviour is related to slow ionic transport through the membrane|solution interfaces and is manifested by the appearance of an additional (capacitive) arc between the highfrequency bulk and the low-frequency (Warburg) arcs. The presented approach directly relates the diffusivities in the membrane and the interface properties (heterogeneous rate constants determining the transport across interfaces) to the characteristic properties of the impedance spectra (characteristic radial frequencies). It is concluded that the Matlab platform allows solving the NPP problem and simulating the non-linear effects in electrodiffusion in a convenient way.

We define the volume density and basing on the Euler’s and Lagrange theorems derive the volume continuity equation. These fundamental formulae define the volume fixed frame of reference in the multicomponent, solid and liquid solutions. The volume velocity is a unique frame of reference for all processes namely, the mass diffusion, charge transport, heat flow, etc. No basic changes are obligatory in the foundations of linear irreversible thermodynamics except recognizing the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the use of the Navier-Lamé equation of mechanics of solids. Proposed modifications of Navier-Lamé and energy conservation equations are self-consistent with the literature for solid-phase continua dating back to the classical experiments of Kirkendall and their interpretation by Darken. We do show that when Darken constraints are used the general formul...

We study molecular diffusion in (linear) nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore walls and the molecules. In this paper we present in full detail the algorithm, which we used in our previous studies, where we showed complete equivalence of self-(or tracer-) and transport diffusion.

Comparing the rates of molecular diffusion in porous materials under different regimes of measurement may provide valuable information about the underlying mechanisms. After quite generally explaining the benefit of such a procedure, we refer to a case which in the last few years has raised controversial discussion within the community, viz. the comparison of diffusion phenomena in pores of varying roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. In our studies, the coefficients of self-and transport diffusion are found to be in satisfactory agreement, which contradicts previous literature data. A number of effects which might becloud this relationship are discussed. regimes of measurement may provide valuable information about the underlying mechanisms. After quite generally explaining the benefit of such a procedure, we refer to a case which in the last few years has raised controversial discussion within the community, viz. the comparison of diffusion phenomena in pores of varying roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. In our studies, the coefficients of self-and transport diffusion are found to be in satisfactory agreement, which contradicts previous literature data. A number of effects which might becloud this relationship are discussed.

1. Introduction Molecular beam epitaxy has become an important tool to prepare ultrathin films and nanostructures in nonequilibrium states that show novel properties distinctly different from the equilibrium bulk phases. Theoretically, the question arises how to relate the structural characteristics of the growing material to the incoming flux and temperature-dependent surface diffusion constants. This question is fairly well understood for one-component systems. By contrast, only few theoretical studies were devoted to the growth of binary alloy nanostructures, despite of the large interest in this field from the experimental and technological viewpoint. In this communication we present detailed kinetic Monte Carlo simulations of growing nanoclusters within a binary alloy model that allows arbitrary diffusion moves of atoms within an active zone near the cluster surface. Our model is designed to describe fcc-type alloys under growth in the (111) direction. The main motivation came ...