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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Using Active Learning to Rapidly Develop Machine Learned Diffusion Coefficients of CO 2 Conversion Reagents in Metal–Organic Frameworks

Here, we used a combined molecular dynamics/active learning (AL) approach to create machine learning models that can predict the diffusion coefficient of epichlorohydrin and chloropropene carbonate, the reactant and product of a common CO 2 cycloaddition reaction, in metal–organic frameworks (MOFs). Nanoporous MOFs are effective catalysts for the cycloaddition of CO 2 to epoxides. The diffusion rates within nanoporous catalysts can control the rate of reaction as the reactants and products must diffuse to the active sites within the MOF and then out of the nanoporous material for reusability. However, the diffusion process is routinely ignored when searching for new materials in catalytic applications. Here we verified improvement during the AL process by consistently tracking metrics on the same groups of MOFs to ensure consistency. Metal identity was found to have little impact on diffusion rates, while structural features like pore limiting diameter act as a threshold where a minimum value is needed for high diffusion rates. We identified the MOFs with the highest epichlorohydrin and chloropropene carbonate diffusion coefficients which can be used for further studies of reaction energetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Influences of Hydrogen Bonding-Based Stabilization of Bolaamphiphile Layers on Molecular Diffusion within Organic Nanotubes Having Inner Carboxyl Groups

This paper reports molecular diffusion behavior in two bolaamphiphile-based organic nanotubes having inner carboxyl groups with different inner dimeters (10 and 20 nm) and wall structures, COOH-ONT 10nm and COOH-ONT 20nm , using imaging fluorescence correlation spectroscopy (imaging FCS). Here, the results were compared to those previously obtained in a similar nanotube with inner amine groups (NH 2 -ONT 10nm ). COOH-ONT 10nm , as with NH 2 -ONT 10nm , were formed from a rolled bolaamphiphile layer incorporating triglycine moieties, whereas COOH-ONT 20nm consisted of four stacks of triglycine-free bolaamphiphile layers. Imaging FCS measurements were carried out for anionic sulforhodamine B (SRB), zwitterionic/cationic rhodamine B (RB) and cationic rhodamine-123 (R123) diffusing within ONTs (1–9 µm long) at different pH (3.4–8.4) and ionic strengths (1.6–500 mM). Diffusion coefficients (D) of these dyes in the ONTs were very small (0.01–0.1 µm 2 /s), reflecting the significant contributions of molecule-nanotube interactions to diffusion. The D of SRB was larger at higher pH and ionic strength, indicating the essential role of electrostatic repulsion that was enhanced by the deprotonation of the inner carboxyl groups. Importantly, the D of SRB was virtually independent of nanotube inner diameter and wall structure, indicating the diffusion of the hydrophilic molecule was controlled by short timescale adsorption/desorption processes onto the inner surface. In contrast, pH effects on D were less clear for relatively hydrophobic R123 and RB, suggesting the significant contributions of non-Coulombic interactions. Interestingly, the diffusion of these molecules in COOH-ONT 20nm was slower than in COOH-ONT 10nm . Slower diffusion in COOH-ONT20nm was attributable to relatively efficient partitioning of the hydrophobic dyes into the bolaamphiphile layers, which was reduced in COOH-ONT 10nm due to the stabilization of its layer by polyglycine-II-type hydrogen bonding networks. These results show that, by tuning the bolaamphiphile structures and their intermolecular interactions, unique environments can be created within the nanospaces for enhanced molecular separations and reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Simulations and Experiments Reveal Effect of Nanopores on Helium Diffusion in Quartz

The diffusion properties of noble gases in minerals are widely used to reconstruct the thermal histories of rocks. In this work, we combine density functional theory (DFT) calculations with laboratory experiments to investigate controls on helium diffusion in quartz. DFT calculations for perfect α-quartz predict substantially lower activation energies and frequency factors for helium diffusion than observed in laboratory experiments, especially in the [001] direction. These results imply that no helium could be retained in quartz at Earth surface temperatures, which conflicts with observations of partial cosmogenic 3 He retention over geologic time scales. Here, we implement a model of helium diffusion in α-quartz modulated by nanopore defects that disrupt energetically favorable diffusion pathways. In this model, we find that laboratory-determined diffusivities can be most closely reproduced when a helium atom encounters ~70 nanopore sites per million interstitial sites. The results of our model indicate that diffusion of helium in natural quartz, like other noble gases in other minerals, can be significantly modulated by extended defects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Modeling the Ionic Strength Effect on Diffusion in Clay. The DR-A Experiment at Mont Terri

Solute diffusion in compacted clays depends on ionic strength through its control on the thickness of the electrical double layer (EDL) on the charged clay surfaces. In the DR-A field experiment (Mont Terri, Switzerland), synthetic porewater was circulated through a borehole for 189 days, leading to the out-diffusion of a variety of tracers into the Opalinus Clay. The borehole solution was then replaced with a higher-salinity solution for an additional 540 days, leading to the diffusion of Cs + , Ca 2+ , Mg 2+ , and Sr 2+ back into the borehole and to an increase in the out-diffusion of anions (I - , Br - ) and 3 H. The experimental results were interpreted using the CrunchClay code, which includes a mean electrostatic potential model for the EDL. The EDL corresponds to a second continuum in addition to bulk electrically neutral porewater. Species-specific diffusion (Nernst-Planck equation) occurs through both domains. A 1D radial model considered a single pore diffusion coefficient (Dp = 10-9 m2/s) for cations and 3H in the bulk porosity, and a smaller D p (3 × 10 -10 m 2 /s) for anions. Dp values in the EDL were smaller (10 -11 m 2 /s), except for Cs + and K + (5 × 10 -10 and 2 × 10 -10 m 2 /s, respectively). The model reproduced well the experimental results and showed the capability to consider temporal changes in geochemical conditions affecting the transport and retention of potentially important radionuclide contaminants (e.g., 137 Cs + , 90 Sr 2+ , 129 I - ) in underground geological nuclear waste repositories. Finally, coupled multicomponent diffusion together with the electrostatic properties of the charged surfaces are essential in the development of predictive models for ion transport in clays.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Highly Effective GeNi Alloy Contact Diffusion Barrier for BiSbTe Long-Term Thermal Exposure

A GeNi alloy diffusion barrier for contacts on bismuth antimony telluride is proposed. Multiple gold contact diffusion barriers were tested at different thermal aging conditions in air and reducing atmospheres. Among all diffusion barriers, the GeNi alloy barrier shows the best performance for bulk samples with no substantial degradation of the contact resistance, no contact color change, and no change of thermoelectric properties. We observed D Au–GeNi = (9.8 ± 2.7) × 10 –20 m 2 /s within the GeNi alloy barrier, which is 4 times smaller than D Au–BiSbTe . The presence of the initial Ge layer also proves to be effective in reducing nickel diffusion yielding D Ni–BiSbTe = (8.57 ± 0.49) × 10 –19 m 2 /s. During GeNi alloy formation, Ge diffusion into BiSbTe produces GeTe, which apparently blocks the van der Waals gaps eliminating Au and Ni fast diffusion pathways. Thermal aging of BiSbTe nanowires shows that Au and Ni diffusion degrades the thermoelectric power factor, whereas the GeNi alloy barrier sample is mostly preserved. The GeNi alloy barrier is a reliable solution to long-term thermal applications of BiTe-based materials.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Fast Diffusion of Ultrarelativistic Electrons in the Outer Radiation Belt: 17 March 2015 Storm Event

Inward radial diffusion driven by ULF waves has long been known to be capable of accelerating radiation belt electrons to very high energies within the heart of the belts, but more recent work has shown that radial diffusion values can be highly event-specific, and mean values or empirical models may not capture the full significance of radial diffusion to acceleration events. Here we present an event of fast inward radial diffusion, occurring during a period following the geomagnetic storm of 17 March 2015. Ultrarelativistic electrons up to ~8 MeV are accelerated in the absence of intense higher-frequency plasma waves, indicating an acceleration event in the core of the outer belt driven primarily or entirely by ULF wave-driven diffusion. We examine this fast diffusion rate along with derived radial diffusion coefficients using particle and fields instruments on the Van Allen Probes spacecraft mission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or “diffusive fluxes,” are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary “induced” component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. Finally, these fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Oscillation-like diffusion of two-dimensional liquid dusty plasmas on one-dimensional periodic substrates with varied widths

The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varying widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row, the diffusion is the smallest in both directions. In this study, we find that as the substrate width gradually increases to twice its initial value, the long-time diffusion of the two-dimensional dusty plasmas first increases, then decreases, and finally increases again, giving an oscillation-like diffusion with varying substrate widths. When the width increases to a specific value, the dust particles within each potential well arrange themselves in a stable zigzag pattern, greatly reducing the diffusion and leading to the observed oscillation in the diffusion with the increase in the width. In addition, the long-time oscillation-like diffusion is consistent with the number of dust particles that are hopping across the potential wells of the substrate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Anion diffusion in two-dimensional halide perovskites

Commercialization of halide perovskites in the semiconductor industry is hindered by their short-term stability. The instability of perovskites is closely interlinked with ionic diffusion. Historically, attempts to study diffusion in 2D perovskites mostly utilized electrical characterizations, but these characterizations pose a challenge in deconvoluting the impact of device architecture, interlayers, and ionic species. In this Perspective, we focus our attention on simple optical characterizations employed in the literature to investigate halide diffusion in 2D perovskites using lateral and vertical heterostructure platforms. We review the various synthesis techniques used for fabrication of halide perovskite heterostructures and discuss the qualitative and quantitative diffusion studies performed using these platforms. We discuss the numerical methods used to validate and supplement the experimental halide diffusion kinetics. Finally, we highlight the need to conduct further research on the impact of device operating conditions, lattice structure, and vacancy concentration on halide diffusion. Through this Perspective, we aim to emphasize the need of developing a comprehensive understanding of halide diffusion in perovskites for their successful deployment in optoelectronics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Proton diffusion and hydrogen/deuterium exchange in amorphous solid water at temperatures from 114 to 134 K

The reaction coefficient for hydrogen/deuterium (H/D) exchange and the diffusion of hydrated excess protons within amorphous solid water (ASW) are characterized as a function of temperature. For these experiments, water films are deposited on a Pt(111) substrate at 108 K, and reactions with pre-adsorbed hydrogen atoms produce hydrated protons. Upon heating, protons diffuse within the water, and H/D exchange occurs when they encounter D2O probe molecules deposited in the films. The time-dependent concentration of D2O is monitored with infrared spectroscopy, and it indicates the protons diffusion from the substrate and establish an equilibrium distribution prior to significant H/D exchange for temperatures 114 K ≤T≤ 134 K. By controlling the distance between the D2O molecules and the substrate, we probe the distribution of protons within the film. It decays as x−2 for the examined range of x (12–52 nm) due to the electric field that develops between the diffusing protons and their image charges in the metal substrate. This agrees with the theoretical distance scaling for the equilibrated proton concentration in a dielectric near a metal boundary. From the proton concentration and the measured D2O decay rate, a lower bound for the proton diffusion coefficient ranging from 10−20 m2/s at 114 K to 10−18 m2/s at 134 K is estimated. The diffusion coefficient has an activation energy of 0.40 eV, which is comparable to energies reported for molecular translations and rotations of H2O, suggesting they may play a critical role in the proton diffusion mechanism within ASW.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Turbulence-level dependence of cosmic ray parallel diffusion

ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Relationship between Surface Self-Diffusion and Bubble Mobility in Solids: Theory and Atomistic Simulation

Diffusion processes in solids are characterized by complex mechanisms occurring at the atomistic level. The relevant theoretical concepts are sufficiently developed in the case of the diffusion of point defects. At the same time, the diffusion of objects such as clusters of vacancies or nanometer-size cavities in the crystal lattice is described only in terms of continuous-medium approximation. This paper attempts to link the existing theory of diffusion of bubbles in a crystalline matrix with the atomistic description of the process on the basis of the molecular dynamics method. For simplicity, the diffusion of cavities in a two-dimensional Lennard-Jones lattice is considered. A controlled molecular dynamics method is proposed to speed up the direct computation of the diffusion rate of bubbles. Based on the results of simulation, a practical interpretation is given to a parameter of the continuum theory such as the rate of surface self-diffusion. The applicability range of the continuum theory is demonstrated, and principles for the refinement of the theory in the case of minimum-size bubbles are formulated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Atomic-level mechanisms of short-circuit diffusion in materials

This paper reviews the recent progress in understanding the atomic mechanisms of short-circuit diffusion along materials interfaces, such as grain and interphase boundaries, as well as lattice and interfacial dislocations/disconnections. Recent atomistic computer simulations have shown that short-circuit diffusion is dominated by collective atomic rearrangements in the form of strings and rings of mobile atoms. The process is dynamically heterogeneous in space and time and has many features in common with atomic dynamics in supercooled glass-forming liquids. We discuss examples of grain boundary, interphase boundary, and dislocation diffusion in metals and alloys, including the solute effect on the diffusion rates and mechanisms. Interphase boundaries are exemplified by Al–Si interfaces with diverse orientation relationships and atomic structures. The hierarchy of short-circuit diffusion paths in materials is reviewed by comparing the rates of grain boundary, interphase boundary, and dislocation diffusion. Future directions in the field of short-circuit diffusion in defect core regions are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

The Effect of Acetylation on Iron Uptake and Diffusion in Water Saturated Wood Cell Walls and Implications for Decay

Acetylation is widely used as a wood modification process that protects wood from fungal decay. The mechanisms by which acetylation protects wood are not fully understood. With these experiments, we expand upon the literature and test whether previously observed differences in iron uptake by wood were a result of decreased iron binding capacity or slower diffusion. We measured the concentration of iron in 2 mm thick wood sections at 0, 10, and 20% acetylation as a function of time after exposure to iron solutions. The iron was introduced either strongly chelated with oxalate or weakly chelated with acetate. The concentrations of iron and oxalate in solution were chosen to be similar to those found during brown rot decay, while the concentration of iron and acetate matched previous work. The iron content of oxalate-exposed wood increased only slightly and was complete within an hour, suggesting little absorption and fast diffusion, or only slight surface adsorption. The increase in iron concentration from acetate solutions with time was consistent with Fickian diffusion, with a diffusion coefficient on the order of 10 -16 m 2 s -1 . The rather slow diffusion rate was likely due to significant binding of iron within the wood cell wall. The diffusion coefficient did not depend on the acetylation level; however, the capacity for iron absorption from acetate solution was greatly reduced in the acetylated wood, likely due to the loss of OH groups. We explored several hypotheses that might explain why the diffusion rate appears to be independent of the acetylation level and found none of them convincing. Implications for brown rot decay mechanisms and future research are discussed.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1950

Theory of plane, symmetrical intake diffusers

The present report ties in with the investigations on the inlet diffusers by P. Ruden. The theory developed by Ruden had produced results which found excellent confirmation in wind-tunnel tests and in spite of certain still-existing defects, are technically very promising. The reasons for the new theory of the diffuser forms indicated by Ruden are twofold: first, the arguments adduced in Ruden's theory deal only with one specific operating condition, that is, a certain ratio of mean velocity within the diffuser to flying speed, while in the present report any desired velocity ratios are involved; second, a different choice of parameters and the increased possibilities of variation result in diffuser forms which cannot be reconciled at once with Ruden's theory. The first enables a theoretical check of the measurements made with Ruden's diffusers at variable velocity ratio, the second permits the calculation of diffuser types which in many respects are superior to Ruden's diffusers.

FLOW - CONFORMAL TRANSFORMATION - HODOGRAPH METHOD↗
NASA NTRS2001

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.

Non-NASA Center↗