Gas diffusion in zeolite beds: PFG NMR evidence for different tortuosity factors in the Knudsen and bulk regimes

We present molecular dynamics simulations in the micro-canonical ensemble of a Lennard-Jones model of nitrogen confined in realistic models for saccharose-based carbons developed in our previous work. We calculate the velocity autocorrelation function and mean-squared displacement, and the self-diffusivities from the latter. We observe that the self-diffusivity increases with temperature and exhibits a maximum with loading or adsorbate density. To the best of our knowledge, a maximum in self-diffusivities has not been observed in molecular dynamics simulations of fluids confined in slit pores.Received: 1 January 2003, Published online: 30 October 2003PACS: 61.43.Gt Powders, porous materials - 68.43.Jk Diffusion of adsorbates, kinetics of coarsening and aggregation - 82.75.Fq Synthesis, structure determination, structure modeling     

The DOSY Toolbox: A new tool for processing PFG NMR diffusion data

The DOSY Toolbox is a free programme for processing PFG NMR diffusion data (sometimes loosely referred to as DOSY data), distributed under the GNU General Public License. NMR data from three major manufacturers can be imported and all processing is done in a user-friendly graphical user interface. The Toolbox is completely free-standing in the sense that all necessary basic processing of NMR data (e.g., Fourier transformation and phasing) is catered for within the programme, as well as a number of methods specific to DOSY data (e.g., DOSY and SCORE). The programme is written in MATLAB^® and as such can be run on any platform, but can also run independent of MATLAB^® in a free-standing compiled version for Windows, Mac, and Linux.     

A PFG NMR experiment for translational diffusion measurements in low-viscosity solvents containing multiple resonances

Pulsed gradient simulated-echo (PGSE) NMR diffusion measurements provide a facile and accurate means for determining the self-diffusion coefficients for molecules over a wide range of sizes and conditions. The measurement of diffusion in solvents of low intrinsic viscosity is particularly challenging, due to the persistent presence of convection. Although convection can occur in most solvent systems at elevated temperatures, in lower viscosity solvents (e.g., short chain alkanes), convection may manifest itself even at ambient laboratory temperatures. In most circumstances, solvent suppression will also be required, and for solvents that have multiple resonances, effective suppression can likewise represent a substantial challenge. In this article, we report an NMR experiment that combines a double-stimulated echo PFG approach with a WET-based solvent suppression scheme that effectively and simultaneously address the issues of dynamic range and the deleterious effects of convection. The experiment described will be of general benefit to studies aimed at the characterization of diffusion of single molecules directly dissolved in low-viscosity solvents, and should also be of substantial utility in studies of supramolecular assemblies such as reverse-micelles dissolved in apolar solvents.     

An improved method for suppressing protein background in PFG NMR experiments to determine ligand diffusion coefficients in the presence of receptor

In NMR diffusion experiments to study ligand-protein binding equilibria, the spectral background due to broad protein resonances can contribute significantly to the measured ligand signal intensity resulting in erroneous binding affinities. One method to suppress the protein spectral background involves coupling a CPMG pulse train before or after the BPPSTE pulse sequence to allow for differential T(2) relaxation of the broad protein resonances. Here, we present an improved method, the Gradient Phase Encoded Spin-lock (GraPES) experiment that integrates the relaxation filter into the diffusion period. Compared with sequential CPMG-BPPSTE pulse sequences, GraPES offers effective suppression of the protein background with improved signal-to-noise ratios and shorter experiment times.     

Enhanced (13)C PFG NMR for the study of hydrodynamic dispersion in porous media

PFG NMR methods are frequently used as a means of probing both coherent and incoherent molecular motions of fluids contained within heterogeneous porous media. The time scale over which molecular displacements can be probed in a conventional PFG NMR experiment is limited by the relaxation characteristics of (1)H - the nucleus that is typically observed. In multiphase systems, due to its sensitivity to susceptibility gradients and interactions with surfaces,(1)H signal is frequently characterized by rapid T(1) and T(2) relaxation. In this work, a heteronuclear approach to PFG NMR is demonstrated which allows the study of molecular displacement over extended time scales (and, consequently, length scales) by exploiting the longer relaxation time of (13)C. The method presented employs the DEPT technique of polarization transfer in order to enhance both the sensitivity and efficiency of (13)C detection. This hybrid coherence transfer PFG technique has been used to acquire displacement propagators for flow through a bead pack with an observation time of up to 35 s.     

Two-dimensional PFG NMR for encoding correlations of position, velocity, and acceleration in fluid transport

A generalized approach to obtain two-dimensional maps of spatial particle coordinates and their derivatives with respect to time by PFG-NMR employing multiple gradient pulses is presented. A sequence of n magnetic field gradient pulses makes it possible, after independent stepping of each pulse and subsequent Fourier transformation, to plot the spin density distribution in coordinate space at n times and along the respective directions of the gradient pulses. In particular, two gradient pulses of effective area k(1) and k(2) separated by a time interval Delta lead to a plot of the combined two-time probability density, W(2)(r(1), 0; r(2), Delta), to find a particle at a coordinate r(1) at t = 0 and at r(2) at t = Delta. A conventional experiment for measuring transport properties by simultaneous stepping of the gradients under the condition k(1) = -k(2) is equivalent to a projection onto the secondary diagonal in the [r(1), r(2)] plot. The main diagonal represents an average position between the two timepoints t = 0 and t = Delta, so that a rotation of the coordinate plot by an angle of 45 degrees allows one to correlate the displacement R = r(2) - r(1) with the averaged position r parallel to the gradient direction. While an average velocity during the time interval Delta can be defined as &vmacr; = R/Delta, an extension toward acceleration and higher order derivatives is straightforward by modification of the pulse sequence. We discuss this concept by application to flow through a circular and a narrowing pipe (confusor), respectively, the experimental results of which are compared to numerical simulations. Copyright 2000 Academic Press.     

Long-range diffusion in beds of nanoporous particles: pitfalls and potentials

Owing to the recent progress in the area of hardware and software of the pulsed field gradient NMR technique, molecular transport in real-life zeolite systems, such as zeolite beds and particles of formulated fluid catalytic cracking (FCC) catalysts, can be investigated in detail. These studies have revealed a number of important features of molecular transport in zeolites, which are reviewed in the present paper. In particular, the anomalous character of intracrystalline diffusion in MFI-type zeolites, dependence of the tortuosity factor in zeolite beds on diffusion regime and the role of various modes of diffusion in transport limitations arising for catalytic reactions in FCC catalysts will be discussed.     

Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick’s law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.     

Combining PFG and CPMG NMR measurements for separate characterization of oil and water simultaneously present in a heterogeneous system

When analyzingT ₂ relaxation time curves from an ordinary Carr-Purcell-Meiboom-Gill (CPMG) experiment in a multicomponent system, where internal magnetic field gradients broaden the line widths significantly, there is very little direct information regarding the mobility of the components and on the type of environment experienced by each component. Compared to a standard CPMG experiment, a combination of pulsed field gradient (PFG) methods with the CPMG experiment will increase the amount of information that is obtainable from the nuclear magnetic resonance (NMR) experiment on a system of components differing significantly in molecular mobility. We propose a method for achieving separate measurements of theT ₂ attenuation of two components simultaneously present within a sample, and we believe it to be generally valid for any system in which the components differ significantly in molecular mobility. The two components could be oil and water in porous rock, or fat and water in a biological tissue, where a separation of theT ₂ attenuations for the two components will add insight to the study of the systems. In order to verify the method we made use of a sample containing a mixture of oil and water in two separate bulk phases, and compared the results with PFG-CPMG experiments performed on samples containing oil or water only, respectively. The method was applied to systems containing glass spheres immersed in water and oil, and it was possible to obtain information about the physical environment of the components which otherwise is not easily obtainable. The method presented here is therefore presumably applicable to whole rock cores or tissue samples.     

Effects of surface roughness on self- and transport diffusion in porous media in the Knudsen regime

The effect of surface roughness on Knudsen diffusion in nanoporous media is investigated by means of dynamic Monte Carlo simulations in three-dimensional rough fractal pores. These simulations yield new insight and explain a number of apparent inconsistencies by revealing a striking difference between the roughness dependence of transport diffusion and gradientless (self- or tracer) diffusion. Both analytical and simulation results show a significant roughness dependence of self-diffusion in the Knudsen regime. Transport diffusion, on the other hand, is roughness independent, as the fluxes do not depend on the detailed residence time and molecular trajectories.     

PFG NMR measurements of flow through porous media: effects of spatial correlations of the magnetic field and the velocity field

Used for a long time for diffusion studies, PFG NMR techniques are now widely used to study flow through porous media. We discuss here the effects of the magnetic field inhomogeneities and the finite gradient pulse duration in this case. We propose a statistical model based on spatial correlations of the magnetic field and velocity field and as far as we can, we draw practical conclusions on the PFG NMR measurements conditions.     

Analysis of the transport coefficients for simple dense fluids: The diffusion and bulk viscosity coefficients

The analysis of transport coefficients based on the modified Enskog theory (MET), discussed in a previous publication, has been extended to include the self-diffusion coefficient (D) and the bulk viscosity coefficient (η_v). Specifically, calculated values according to the MET are compared with experiment over the range for which data are available. Fluids considered are argon, nitrogen and methane. Agreement between theory and experiment for densities less than about twice the critical density (ρ_c) is generally within about 10%. However, much of the data was taken at densities well in excess of 2_ρc in which case agreement is still not unsatisfactory. Deviations exceeding 10% between theoretical and experimental self-diffusion coefficients were observed for densities in the approximate range 0.9 ? _ρ/ρc ? 2.0. It is possible that these deviations are due to long range correlated molecular motions which are not present in the MET. The sound absorption is also briefly considered. Finally, the behavior of η_v and D at low densities is discussed.     

TRAPDOR double-resonance and high-resolution MAS NMR for structural and template studies in zeolite ZSM-5

A combination of ²⁷Al magic-angle spinning (MAS)/multiple-quantum (MQ) MAS, and ²⁷Al–{¹⁴N} TRAnsfer of Population in DOuble-Resonance (TRAPDOR) nuclear magnetic resonance (NMR) was used to study aluminium environments in zeolite ZSM-5. ²⁷Al–{¹⁴N} TRAPDOR experiments, in combination with ¹⁴N NMR were employed to show that the two tetrahedral peaks observed in the ²⁷Al MAS/3Q-MAS spectra of as-synthesized ZSM-5 are due to aluminium atoms occupying crystallographically inequivalent T-sites. A ¹³C–{²⁷Al} TRAPDOR experiment was used to study the template, tetrapropyl ammonium bromide (TPABr), in the three-dimensional pore system of ZSM-5. The inequivalency of the methyl groups of TPA was observed in the ¹³C–{²⁷Al} TRAPDOR spectra of as-synthesized ZSM-5 and the motion of the methyl end of the propyl chain appeared to be more restricted in the sinusoidal channel than in the straight channel.     

High temperature NMR in vanadium: Electron paramagnetism and atomic diffusion effects

We present preliminary results on Knight shift T₁ and T₂ measurements between 300 and 1700 K. We have observed the motional narrowing due to the self diffusion as well as a strong quadrupolar contribution to T₁ due to the diffusion of interstitial gases. K varies from 0.58 to 0.63%. This temperature dependence is shown to be mainly due to an intrinsic temperature effect. The high temperature Korringa like behaviour of T₁ with T₁T = 1.05 sec. K is explained in terms of the temperature dependence of the d spin contribution.     

NMR evidence for the coexistence of order-disorder and displacive components in barium titanate

A quadrupole coupling induced 47Ti and 49Ti satellite background which transforms into well-defined satellite lines below T(c) in the ferroelectric phase has been observed in the cubic phase of an ultrapure BaTiO3 single crystal. The results demonstrate the coexistence of a displacive and order-disorder component in the phase transition mechanism and tetragonal breaking of the cubic symmetry due to biased Ti motion between off-center sites in the paraelectric phase above T(c).