Boundary effects of molecular diffusion in nanoporous materials: A pulsed field gradient nuclear magnetic resonance study

Signatures of nanoemulsion jamming and unjamming in stimulated-echo NMR

The unjamming of elastic concentrated nanoemulsions into viscous dilute nanoemulsions, through dilution with the continuous phase, offers interesting opportunities for a pulsed-field gradient (PFG) NMR, particularly if the nanoemulsion is designed to take advantage of the nuclear specificity offered by NMR. Here, we make and study size-fractionated oil-in-water nanoemulsions using a perfluorinated copolymer silicone oil that is highly insoluble in the aqueous continuous phase. By studying these nanoemulsions using ^{19}F stimulated-echo PFG-NMR, we avoid any contribution from the aqueous continuous phase, which contains a nonfluorinated ionic surfactant. We find a dramatic change in the ^{19}F PFG-NMR decays at high field-gradient strengths as the droplet volume fraction, ϕ, is lowered through dilution. At high ϕ, observed decays as a function of field-gradient strength exhibit decay-to-plateau behavior indicating the jamming of nanodroplets, which contain ^{19}F probe molecules, in an elastic material reminiscent of a nanoporous solid. In contrast, at lower ϕ, only a simple decay is observed, indicating that the nanodroplets have unjammed and can diffuse over much larger distances. Through a comparison with bulk mechanical rheometry, we show that this dramatic change coincides with the loss of low-frequency shear elasticity of the nanoemulsion.

Pulsed field gradient NMR diffusion measurement in nanoporous materials

Labeling in diffusion measurements by pulsed field gradient (PFG) NMR is based on the observation of the phase of nuclear spins acquired in a constant magnetic field with purposefully superimposed field gradients. This labeling does in no way affect microdynamics and provides information about the probability distribution of molecular displacements as a function of time. An introduction of the measuring principle is followed by a detailed description of the ranges of measurements and their limitation. Particular emphasis is given to an explanation of possible pitfalls in the measurements and the ways to circumvent them. Showcases presented for illustrating the wealth of information provided by PFG NMR include a survey on the various patterns of concentration dependence of intra-particle diffusion and examples of transport inhibition by additional transport resistances within the nanoporous particles and on their external surface. The latter information is attained by combination with the outcome of tracer exchange experiments, which are shown to become possible via a special formalism of PFG NMR data analysis. Further evidence provided by PFG NMR concerns diffusion enhancement in pore hierarchies, diffusion anisotropy and the impact of diffusion on chemical conversion in porous catalysts. A compilation of the specifics of PFG NMR and of the parallels with other measurement techniques concludes the paper.

Diffusion in nanopores: correlating experimental findings with “first-principles” predictions

Measurement of molecular diffusion in nanoporous host materials, which are typically inhomogeneous and anisotropic, often involves an intricate web of factors and relations to be taken into account since the associated diffusivities are a function of the diffusion path of the guest molecules during a given observation time. Depending on the observation time, therefore, the result of the experimental measurement can point to completely different conclusions about the underlying diffusion phenomena. The risk of misinterpretation of the experimental data, by correlating them with irrelevant phenomena, may be reduced if there is an option to compare the data with the results of totally independent measurements. The present communication addresses this issue with reference to the particular potentials of pulsed field gradient NMR and microimaging by infrared microscopy as techniques of microscopic diffusion measurement.

Relationship between Ethane and Ethylene Diffusion inside ZIF-11 Crystals Confined in Polymers to Form Mixed-Matrix Membranes

Self-diffusivities of ethane were measured by multinuclear pulsed field gradient (PFG) NMR inside zeolitic imidazolate framework-11 (ZIF-11) crystals dispersed in several selected polymers to form mixed-matrix membranes (MMMs). These diffusivities were compared with the corresponding intracrystalline self-diffusivities in ZIF-11 crystal beds. It was observed that the confinement of ZIF-11 crystals in ZIF-11 / Torlon MMM can lead to a decrease in the ethane intracrystalline self-diffusivity. Such diffusivity decrease was observed at different temperatures used in this work. PFG NMR measurements of the temperature dependence of the intracrystalline self-diffusivity of ethylene in the same ZIF-11 / Torlon MMM revealed similar diffusivity decrease as well as an increase in the diffusion activation energy in comparison to those in unconfined ZIF-11 crystals in a crystal bed. These observations for ethane and ethylene were attributed to the reduction of the flexibility of the ZIF-11 framework due to the confinement in Torlon leading to a smaller effective aperture size of ZIF-11 crystals. Surprisingly, the intra-ZIF diffusion selectivity for ethane and ethylene was not changed appreciably by the confinement of ZIF-11 crystals in Torlon in comparison to the selectivity in a bed of ZIF-11 crystals. No ZIF-11 confinement effects leading to a reduction in the intracrystalline self-diffusivity of ethane and ethylene were observed for the other two studied MMM systems: ZIF-11 / Matrimid and ZIF-11 / 6FDA-DAM. The absence of the confinement effect in the latter MMMs can be related to the lower values of the polymer bulk modulus in these MMMs in comparison to that in ZIF-11 / Torlon MMM. In addition, there may be a contribution from possible differences in the ZIF-11/polymer adhesion in different MMM types.

PFG-NMR as a Tool for Determining Self-Diffusivities of Various Probe Molecules through H-ZSM-5 Zeolites

The understanding of major zeolite applications is partially based on diffusion of molecules inside or outside microporous networks. However, it is still a challenge to measure such phenomena. The diffusion ordered nuclear magnetic resonance spectroscopy (DOSY) technique has been reported to measure a probe molecule's diffusion inside porous solids. Pulsed-field gradient (PFG)-NMR has been used herein to measure the self-diffusivity of different probe molecules, such as neopentane, benzene, toluene and 1-dodecene with increasing dynamic diameter, respectively, on a series of H-ZSM-5 zeolites. The latter materials exhibit different crystal sizes, Si/Al ratios and the presence (or absence) of crystalline defects. In addition, shaped zeolite bodies representing industrial catalysts were compared with the afore-mentioned samples.

Intracrystalline Transport Barriers Affecting the Self-Diffusion of CH4 in Zeolites |Na12|-A and |Na12-xKx|-A

Carbon dioxide must be removed from biogas or natural gas to obtain compressed or liquefied methane, and adsorption-driven isolation of CO₂ could be improved by developing new adsorbents. Zeolite adsorbents can select CO₂ over CH₄, and the adsorption of CH₄ on zeolite |Na_12-xK_x|-A is significantly lower for samples with a high K⁺ content, i.e., x > 2. Nevertheless, we show, using ¹H NMR experiments, that these zeolites adsorb CH₄ after long equilibration times. Pulsed-field gradient NMR experiments indicated that in large crystals of zeolites |Na_12-xK_x|-A, the long-time diffusion coefficients of CH₄ did not vary with x, and the upper limit of the mean-square displacement was about 1.5 μm, irrespective of the diffusion time. Also for zeolite |Na₁₂|-A samples of three different particle sizes (∼0.44, ∼2.9, and ∼10.6 μm), the upper limit of the mean-square displacement of CH₄ was 1.5 μm and largely independent of the diffusion time. This similarity provided further evidence for an intracrystalline diffusion restriction for CH₄ within the medium- and large-sized zeolite A crystals and possibly of clustering and close contact among the small zeolite A crystals. The upper limit of the long-time diffusion coefficient of adsorbed CH₄ was (at 1 atm and 298 K) about 10^-10 m²/s irrespective of the size of the zeolite particle or the studied content of K⁺ in zeolites |Na_12-xK_x|-A and |Na₁₂|-A. The T₁ relaxation time for adsorbed CH₄ on zeolites |Na_12-xK_x|-A with x > 2 was smaller than for those with x < 2, indicating that the short-time diffusion of CH₄ was hindered.

Transport properties of hierarchical micro–mesoporous materials

This work provides an overview of different experimental techniques of diffusion measurements in porous materials and discusses transport properties of several classes of hierarchically organized micro-mesoporous materials.

Asymmetric gas mixture transport in composite membranes

The asymmetry effects in gas and electrolyte transport through composite membranes are considered. The interrelation between the kinetic theory and non-equilibrium thermodynamics description of gas mixture transport in channels is discussed. The kinetic expressions for transport and slip coefficients are given. The effect of surface forces on gas transport is discussed. A set of general equations related to gas mixture flows in capillaries and porous media is deduced. The nano-size effects in gas flows are outlined. The theoretical analysis of one-way flow effect and asymmetric separation properties of a two-layer porous membrane is given.

Tracing pore-space heterogeneities in X-type zeolites by diffusion studies

Pore-space homogeneity of zeolite NaX was probed by pulsed field gradient (PFG) NMR diffusion studies with n-butane as a guest molecule. At a loading of 0.75 molecules per supercage, a wide spectrum of diffusivities was observed. Guest molecules in the (well-shaped) zeolite crystallites were thus found to experience pore spaces of quite different properties. After loading enhancement to 3 molecules per supercage, however, molecular propagation ideally followed the laws of normal diffusion in homogeneous media. At sufficiently high guest concentrations, sample heterogeneity was thus found to be of no perceptible influence on the guest mobilities anymore.

Exploring the surface permeability of nanoporous particles by pulsed field gradient NMR

A new method to determine the surface permeability of nanoporous particles is proposed. It is based on the comparison of experimental data on tracer exchange and intracrystalline molecular mean square displacements as obtained by the PFG NMR tracer desorption technique with the corresponding solutions of the diffusion equation via dynamical Monte Carlo simulations. The method is found to be particularly sensitive in the "intermediate" regime, when the influence of intracrystalline diffusion and surface resistances of the nanoporous crystal on molecular transport are comparable and the conventional method fails. As an example, the surface permeabilities of two samples of zeolite NaCaA with different crystal sizes are determined with methane, as a probe molecule, at room temperature.

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 microm) have been measured by 1H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254-344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.

Gas Diffusion in Polycrystalline Silicalite Membranes Investigated by 1H Pulse Field-Gradient NMR

1H pulse field-gradient (PFG) spin-echo NMR was performed to measure the diffusivity of methane in a polycrystalline MFI-type silicalite membrane. Measured diffusivities decreased with an increase in the diffusion distance and converged to the constant value. This result suggests the presence of a transport barrier in the membrane. The long-time diffusivity in the membrane was 3.7 x 10(-9) m2/s, which was a factor of 3 smaller than reported values in a single crystal. The distance between the transport barriers was estimated to be much larger than 6 mum from the relationship of diffusivity with displacement. It should be noted that the estimated distances were larger than the smallest dimension of the crystals appearing in the membrane surface. Gas permeation and pervaporation tests were carried out on the same sample for which NMR measurements were taken. The estimated methane flux using measured long-time diffusivity by the permeation theory overestimated the experimental value, although it is closer to the experimental value than the value estimated using the short-time diffusivity. These results mean that the methane diffusivity in a silicalite membrane is much smaller than that in a single crystal.