Pulsed Field Gradient Nuclear Magnetic Resonance Measurements Research Articles

Complementary Mass Transport Investigations in Open-Cell Foams: Full-Field Computational Fluid Dynamics Simulation with Random-Walk Microscopic Particle Tracking and Methane Nuclear Magnetic Resonance Displacement Measurements

Numerical simulation can provide detailed understanding of mass transport within complex structures. For this purpose, numerical tools are required that can resolve the complex morphology and consider the contribution of both convection and diffusion. Solving the Navier–Stokes equations alone, however, neglects self-diffusion. This influences the simulated displacement distribution of flow especially in porous media at low Péclet numbers (Pe < 16) and in near-wall regions where diffusion is the dominant mechanism. To address this problem, this study uses μCT-based computational fluid dynamics (CFD) simulations in OpenFOAM coupled with the random-walk particle tracking (PT) module disTrackFoam and cross-validated experimentally using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) measurements of gas flow within open-cell foams (OCFs). The results of the multi-scale simulations—with a resolution of 130–190 µm—and experimental PFG NMR data are compared in terms of diffusion propagators, which are microscopic displacement distributions of gas flows in OCFs during certain observation times. Four different flow rates with Péclet numbers in the range of 0.7–16 are studied in the laminar flow regime within 10 and 20 PPI OCFs, and axial dispersion coefficients were calculated. Cross-validation of PFG NMR measurements and CFD-PT simulations revealed a very good matching with integral differences below 0.04%, underpinning the capability of both complementary methods for multi-scale transport analysis.

Charge Transport and Glassy Dynamics in Blends Based on 1-Butyl-3-vinylbenzylimidazolium Bis(trifluoromethanesulfonyl)imide Ionic Liquid and the Corresponding Polymer.

Charge transport, diffusion properties, and glassy dynamics of blends of imidazolium-based ionic liquid (IL) and the corresponding polymer (polyIL) were examined by Pulsed-Field-Gradient Nuclear Magnetic Resonance (PFG-NMR) and rheology coupled with broadband dielectric spectroscopy (rheo-BDS). We found that the mechanical storage modulus increases with an increasing amount of polyIL and is a factor of 10,000 higher for the polyIL compared to the monomer (= Pa at 100 rad s−1 and 298 K). Furthermore, the ionic conductivity of the IL is a factor higher than its value for the polymerized monomer with S cm−1 at K. Additionally, we found the Haven Ratio ( obtained through PFG-NMR and BDS measurements to be constant around a value of for the IL and blends with 30 wt% and 70 wt% polyIL. These results show that blending of the components does not have a strong impact on the charge transport compared to the charge transport in the pure IL at room temperature, but blending results in substantial modifications of the mechanical properties. Furthermore, it is highlighted that the increase in might be attributed to the addition of a more mobile phase, which also possibly reduces ion-ion correlations in the polyIL.

New Technique for Evaluating Fracture Geometry and Preferential Orientation Using Pulsed Field Gradient Nuclear Magnetic Resonance

Summary In-situ evaluation of fracture tortuosity (i.e., pore geometry complexity and roughness) and preferential orientation is crucial for fluid flow simulation and production forecast in subsurface water and hydrocarbon reservoirs. This is particularly significant for naturally fractured reservoirs or postacid fracturing because of the strong permeability anisotropy. However, such downhole in-situ characterization remains a challenge. This study presents a new method for evaluating fracture tortuosity and preferential orientation based on the pulsed field gradient (PFG) nuclear magnetic resonance (NMR) technique. Such an approach provides diffusion tortuosity, τd, defined as the ratio of bulk fluid diffusion coefficient to the restricted diffusion coefficient in the porous media. In the PFG NMR technique, the magnetic field gradient can be applied in different directions, and therefore anisotropy in diffusion coefficient and τd can be evaluated. Three 3D printed samples, characterized by well controlled variable fracture tortuosity, one fractured sandstone, and three acidized carbonate samples with wormhole were used in this study. PFG NMR measurements were performed using both 2- and 12-MHz NMR instruments to obtain τd in the three different principal directions. The results obtained from the NMR measurements were compared with fracture tortuosity and preferential orientation determined from the microcomputed tomography (micro-CT) images of the samples. The results showed that τd increases as the fracture tortuosity and pore geometry complexity increases, showing good agreement with the image-based geometric tortuosity values. Moreover, the lowest τd values were found to coincide with the preferential direction of fracture surfaces and wormhole body for a given sample, whereas the maximum τd values correspond to the nonconnected pathway directions. These results suggest that the implantation of directional restricted diffusion measurements on the NMR well logging tools would offer a possibility of probing tortuosity and determining preferential fluid flow direction via direct downhole measurements.

Concentration-Dependent Solvation Structure and Dynamics of Aqueous Sulfuric Acid Using Multinuclear NMR and DFT.

Sulfuric acid is a ubiquitous compound for industrial processes, and aqueous sulfate solutions also play a critical role as electrolytes for many prominent battery chemistries. While the thermodynamic literature on it is quite well-developed, comprehensive studies of the solvation structure, particularly molecular-scale dynamical and transport properties, are less available. This study applies a multinuclear nuclear magnetic resonance (NMR) approach to the elucidation of the solvation structure and dynamics over wide temperature (-10 to 50 °C) and concentration (0-18 M) ranges, combining the 17O shift, line width, and T1 relaxation measurements, 33S shift and line width measurements, and 1H pulsed-field gradient NMR measurements of proton self-diffusivity. In conjunction, these results indicate a crossover between two regimes of solvation structure and dynamics, occurring above the concentration associated with the deep eutectic point (∼4.5 M), with the high-concentration regime dominated by a strong water-sulfate correlation. This description was borne out in detail by the activation energy trends with increasing concentration derived from the relaxation of both the H2O/H3O+ and H2SO4/HSO4-/SO42- 17O resonances and the 1H self-diffusivity. However, the 17O chemical shift difference between the H2O/H3O+ and H2SO4/HSO4-/SO42- resonances across the entire temperature range is nevertheless strikingly linear. A computational approach coupling molecular dynamics simulations and density functional theory NMR shift calculations to reproduce this trend is presented, which will be the subject of further development. This combination of multinuclear, dynamical NMR, and computational methods, and the results furnished by this study, will provide a platform for future studies on battery electrolytes where aqueous sulfate chemistry plays a central role in the solution structure.

Effect of hydrate anti-agglomerants on water-in-crude oil emulsion stability

Under high-pressure and low-temperature conditions, gas hydrate shells may form and grow at the interface of water droplets in water-in-oil emulsions. Such hydrate formation can enable downstream agglomeration and slurry viscosification, thus increasing the risk of hydrate blockage. Therefore, emulsion stability represents a critical parameter in understanding this overall flow behaviour. In this study, the impact of three common and widely-used industrial anti-agglomerants from three different suppliers (AA-1, AA-2 and AA-3—exact composition is commercially sensitive) on 30 wt% water-in-oil (W/O) emulsion stability was investigated. Bench-top nuclear magnetic resonance (NMR) pulsed field gradient (PFG) methods were used to measure the droplet size distributions (DSDs) of the W/O emulsions as a complement to bottle stability test. In the absence of hydrate anti-agglomerants, based on visual observation, 85% of the original W/O emulsion remained after 10 h. In the presence of AA-1 and AA-2, 94% of the original emulsion was retained; in contrast, AA-3 acted to destabilise the emulsion with only 64% of the original emulsion visually evident after 10 h. These results were substantiated by PFG NMR measurements which showed substantial changes in droplet size as a function of sample height for the W/O emulsion formulated with AA-3. Interestingly the W/O emulsion formulated with AA-1, while very stable, was characterised by comparatively very large water droplets, indicative of a complex multiple water-in-oil-in-water (W/O/W) emulsion microstructure. AA-2 forms stable emulsion with small droplets of water dispersed in the oil phase. Our results provide insight into a wide range of potential impacts of AA addition on an industrial crude oil pipeline, in which AA-1 resulted in a complex W/O/W multiple emulsion, AA-2 behaved as an emulsifier and AA-3 behaved as a demulsifier.

Diffusion in Nanoporous Materials: Novel Insights by Combining MAS and PFG NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) allows recording of molecular diffusion paths (notably, the probability distribution of molecular displacements over typically micrometers, covered during an observation time of typically milliseconds) and has thus proven to serve as a most versatile means for the in-depth study of mass transfer in complex materials. This is particularly true with nanoporous host materials, where PFG NMR enabled the first direct measurement of intracrystalline diffusivities of guest molecules. Spatial resolution, i.e., the minimum diffusion path length experimentally observable, is limited by the time interval over which the pulsed field gradients may be applied. In “conventional” PFG NMR measurements, this time interval is determined by a characteristic quantity of the host-guest system under study, the so-called transverse nuclear magnetic relaxation time. This leads, notably when considering systems with low molecular mobilities, to severe restrictions in the applicability of PFG NMR. These restrictions may partially be released by performing PFG NMR measurements in combination with “magic-angle spinning” (MAS) of the NMR sample tube. The present review introduces the fundamentals of this technique and illustrates, via a number of recent cases, the gain in information thus attainable. Examples include diffusion measurements with nanoporous host-guest systems of low intrinsic mobility and selective diffusion measurement in multicomponent systems.

Unexpected Diffusion Anisotropy of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc).

Metal-organic frameworks are promising materials for energy-efficient gas separations, but little is known about the diffusion of adsorbates in materials featuring one-dimensional porosity at the nanoscale. An understanding of the interplay between framework structure and gas diffusion is crucial for the practical application of these materials as adsorbents or in mixed-matrix membranes, since the rate of gas diffusion within the adsorbent pores impacts the required size (and therefore cost) of the adsorbent column or membrane. Here, we investigate the diffusion of CO2 within the pores of Zn2(dobpdc) (dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. The residual chemical shift anisotropy for pore-confined CO2 allows PFG NMR measurements of self-diffusion in different crystallographic directions, and our analysis of the entire NMR line shape as a function of the applied field gradient provides a precise determination of the self-diffusion coefficients. In addition to observing CO2 diffusion through the channels parallel to the crystallographic c axis (self-diffusion coefficient D∥ = (5.8 ± 0.1) × 10-9 m2 s-1 at a pressure of 625 mbar CO2), we unexpectedly find that CO2 is also able to diffuse between the hexagonal channels in the crystallographic ab plane (D⊥ = (1.9 ± 0.2) × 10-10 m2 s-1), despite the walls of these channels appearing impermeable by single-crystal X-ray crystallography and flexible lattice MD simulations. Observation of such unexpected diffusion in the ab plane suggests the presence of defects that enable effective multidimensional CO2 transport in a metal-organic framework with nominally one-dimensional porosity.

Quantification of porous microstructures in partially frozen drops using magnetic resonance techniques

Nuclear magnetic resonance (NMR) measurements were shown to be able to non-invasively quantify the microstructure formed following freeze-concentration of (2mm diameter) drops composed of a range of aqueous solutions (sucrose, fructose, coffee solution and NaCl). Specifically the surface-to-volume ratio and tortuosity of the resultant porous ice structures were uniquely quantified using pulsed field gradient (PFG) NMR measurements of restricted self-diffusion of the remaining unfrozen solution. These measurements were performed as a function of both solute concentration and freezing temperature. Validation was achieved via random walk self-diffusion simulations on SEM micrograph images of fracture planes through selected drops. Reasonably good agreement was produced between the NMR measurements and these simulations. A rapid version of the PFG measurement method was subsequently used to enable quantitative microstructure evolution measurements during the drop freezing process, as well as during subsequent ripening of the porous ice structure.

Dynamics and role of rosin acid molecules for preparation of well-dispersed CaCO3 colloidal suspensions

We studied the dynamics and role of rosin acid molecules for the preparation of well-dispersed calcium carbonate (CaCO3) colloidal aqueous suspensions. We investigated a quantitative determination method of the amounts of free diffused surfactant molecules in H2O particle dispersion using the pulsed field gradient nuclear magnetic resonance (PFG-NMR). The diffusion phenomena of rosin acid surfactant molecules in a CaCO3 aqueous dispersion were directly observed using the PFG-NMR method. It was clearly found that the observed diffusion of rosin acid surfactant molecules was attributed to the micelle-like agglomerated rosin acid molecules in the CaCO3 aqueous dispersion using PFG-NMR method. Large amounts of rosin acid molecules were strongly bound onto CaCO3 particles, contributing to the well-dispersed primary size of CaCO3 in colloidal secondary particles. The free diffused micelle-like agglomerated rosin acid molecules were found to play an important role in maintaining the stability of the CaCO3 in a dispersion of colloidal secondary particles. The CaCO3/rosin acid secondary particles were estimated to be larger than submicron size using dynamic light scattering (DLS). The structure of the CaCO3/rosin acid secondary particle observed by scanning transmission electron microscopy under extremely low pressure supported the results from PFG-NMR and DLS measurements. The well-dispersed primary CaCO3 particles were found to be surrounded by a large amount of rosin acid surfactant molecules. The observed zeta potentials of this secondary particle dispersion were between −70 and −60 mV, indicating again that the CaCO3 was covered with rosin acid. The PFG-NMR method is found to be a powerful tool to investigate the role of surfactant molecules for preparation of well-dispersed colloidal suspensions.

Aggregation behavior and intermicellar interactions of cationic Gemini surfactants: Effects of alkyl chain, spacer lengths and temperature

The aggregation behavior of the cationic Gemini surfactants C m H 2 m +1N(CH 3) 2(CH 2) S (CH 3) 2 N C m H 2 m +1,2Br − with m = 12, 14 and s = 2, 4 were studied by performing surface tension, electrical conductivity, pulsed field gradient nuclear magnetic resonance (PFG-NMR), and cyclic voltammetry (CV) measurements over the temperature range 298 K to 323 K. The critical micelle concentration (CMC), surface excess ( Г max), mean molecular surface area ( A min), degree of counter ion dissociation ( α), and the thermodynamic parameters of micellization were determined from the surface tension and conductance data. An enthalpy–entropy compensation effect was observed and all the plots of enthalpy–entropy compensation exhibit excellent linearity. The micellar self-diffusion coefficients ( D m ) and intermicellar interaction parameters ( k d ) were obtained from the PFG-NMR and CV measurements. These results are discussed in terms of the intermicellar interactions, the effects of the chain and spacer lengths on the micellar surface charge density, and the phase transition between spherical and rod geometries. The intermicellar interaction parameters were found to decrease slightly with increasing temperature for 14–4–14, which suggests that the micellar surface charge density decreases with increasing temperature. The mean values of the hydrodynamic radius, R h , and the aggregation number, N agg, of the Gemini surfactants’ m–4– m micelles were calculated from the micellar self-diffusion coefficient. Moreover, the N agg values were calculated theoretically. The experimental values of N agg increase with increases in the chain length and are in good agreement with both previous results and our theoretical results.

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

AbstractDiffusion of gases in polymers below the glass transition temperature, Tg, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [13C]O2 diffusion in polymer films at 298 K are performed. Data obtained in polymers with Tg above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below Tg is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below Tg requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010

Observing Diffusive Exchange between Surfactant and Aqueous Domains in Detergents

Nuclear magnetic resonance (NMR) two-dimensional relaxation correlation experiments have been used to study an industrially relevant formulation of surfactant multilamellar vesicles (MLVs) in an aqueous solution. By correlating transverse T2 relaxation measurements before and after a storage interval, diffusive exchange of water molecules between domains can be observed. Two average exchange times of 0.04 and 0.83 s were determined by solving the one-dimensional Fredholm integral form of a model for region-to-region exchange. Diffusion coefficients for the restricted and free water fractions within the mixture determined via chemically selective pulsed field gradient (PFG) NMR measurements allowed exchange distances of 6.2 and 81 microm to be determined from the exchange times. These exchange distances are associated with the average MLV diameter and speculatively with the size of MLV clusters, respectively.

Electrical conductivity and translational diffusion in the 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid

Broadband dielectric and terahertz spectroscopy (10(-2)-10(+12) Hz) are combined with pulsed field gradient nuclear magnetic resonance (PFG-NMR) to explore charge transport and translational diffusion in the 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid. The dielectric spectra are interpreted as superposition of high-frequency relaxation processes associated with dipolar librations and a conductivity contribution. The latter originates from hopping of charge carriers on a random spatially varying potential landscape and quantitatively fits the observed frequency and temperature dependence of the spectra. A further analysis delivers the hopping rate and enables one to deduce--using the Einstein-Smoluchowski equation--the translational diffusion coefficient of the charge carriers in quantitative agreement with PFG-NMR measurements. By that, the mobility is determined and separated from the charge carrier density; for the former, a Vogel-Fulcher-Tammann and for the latter, an Arrhenius temperature dependence is obtained. There is no indication of a mode arising from the reorientation of stable ion pairs.

Molecular Exchange through the Vesicle Membrane of Siloxane Surfactant in Water/Glycerol Mixed Solvents

The effect of glycerol on the permeability of vesicle membranes of a siloxane surfactant, the block copolymer polyethyleneoxide-b-polydimethylsiloxane-polyethyleneoxide, (EO)15-(DMS)15-(EO)15, was studied with freeze-fracture transmission electron microscopy (FF-TEM) and pulsed-field gradient nuclear magnetic resonance (PFG-NMR) spectroscopy. The FF-TEM results show that, in pure water, the surfactant can form small vesicles with diameters of less than 25 nm, as well as a few multilamellar vesicles with diameters larger than 250 nm. Gradual substitution of water with glycerol to a glycerol content of 40% leads to significant structural transformations: small vesicles are gradually swollen, and large multilamellar vesicles disappear. A glycerol content of 60% results in the complete disintegration of the vesicles into membrane fragments. PFG-NMR measurements indicate that the vesicle membrane does not represent an effective barrier for water molecules on the NMR time scale; hence, the average residence time of water in the encapsulated state is below tau b = 2 ms. In contrast, the average residence time of glycerol molecules in the encapsulated state can be as large as tau b = 910 ms. The permeability of the vesicle membrane increases with increasing glycerol concentration in the solvent: At a concentration of 40%, the residence time tau b is lowered to approximately 290 ms. After vesicle destruction at higher glycerol concentrations, a small glycerol fraction is still bound by membrane fragments that are formed after the disintegration of the vesicles.

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

When analyzingT2 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 theT2 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 theT2 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.

Study of Dispersion in Packed Chromatographic Columns by Pulsed Field Gradient Nuclear Magnetic Resonance

Pulsed field gradient nuclear magnetic resonance (PFGNMR) allows the direct determination of the average value of the axial and transverse apparent dispersion coefficient in a packed bed over a certain volume of this bed. From these data, the dependence of the local value of the height equivalent to a theoretical plate (HETP) of a chromatographic column on the fluid velocity can be measured accurately. The results are shown to be exactly accounted for by the Giddings equation. The PFGNMR measurements are made over a very short period of time. Hence they give the value of the HETP averaged over a limited volume of packing and a short time. This value is markedly smaller than the one afforded by the classical methods of chromatography and which is derived from the width of the distribution of the residence time of a small sample. The difference is explained by systematic variations of the local mobile-phase velocity across the column. PFGNMR techniques also allow the determination of the tortuosity of the column packing in the absence of flow. Their results confirm that the apparent dispersion experienced by a molecule is a function of the duration of the observation, until the tortuosity of the packing is completely felt. The values obtained agree very well with those derived from classical chromatography determinations.