Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR

Monitoring the Conformational Changes of the Aβ(25-35) Peptide in SDS Micelles: A Matter of Time

Alzheimer's disease is a neurodegenerative disease characterized by the formation of amyloid plaques constituted prevalently by amyloid peptides. Due to the well-known challenges related to the study in solution of these peptides, several membrane-mimicking systems such as micelle constituted by detergent-i.e., DPC and SDS-have been deeply investigated. Additionally, the strategy of studying short fragments instead of the full-length peptide turned out to be advantageous in exploring the structural properties of the different moieties in Aβ in order to reproduce its pathologic effects. Several studies reveal that among Aβ fragments, Aβ(25-35) is the shortest fragment able to reproduce the aggregation process. To enrich the structural data currently available, in the present work we decided to evaluate the conformational changes adopted by Aβ(25-35) in SDS combining CD and NMR spectroscopies at different times. From the solved structures, it emerges that Aβ(25-35) passes from an unordered conformation at the time of the constitution of the system to a more ordered and energetically favorable secondary structure at day 7, which is kept for 2 weeks. These preliminary data suggest that a relatively long time affects the kinetic in the aggregation process of Aβ(25-35) in a micellar system, favoring the stabilization and the formation of a soluble helix conformation.

Microsized Pore Structure Determination in EPDM Rubbers Using High-Pressure 129Xe NMR Techniques

Microsized pore parameters, such as pore size and distance between pores in a series of model EPDM rubbers, were determined in situ under the pressure of 500 psi using ¹²⁹Xe nuclear magnetic resonance (NMR) techniques: spin-lattice (T₁) and spin-spin (T₂) relaxation measurements, pulsed-field gradient (PFG) NMR, and two-dimensional exchange spectroscopy (2D EXSY). The T₁/T₂ (≫1) ratio for the xenon confined in the pores is larger than that for nonconfined free xenon. This suggests that almost the entire pore surface interacts with xenon atoms like a closed pore. While these pores still connect each other through very narrow diffusion/exchange channels, it is possible to observe the echo decay in PFG-NMR and cross-peaks in 2D EXSY. The results show that both diffusion (D_pore ≈ 2.1 × 10^-10 m²/s) and exchange (exchange rate, τ_exch = a few tens of milliseconds) of xenon between a pore within the material and outer surface are prolonged. The exchange distances (l), which correspond to the xenon gas penetration depth, were estimated to be 70-100 μm based on the measured diffusion coefficients and exchange rate (1/τ_exch). NMR diffraction analysis reveals that pore size (a) and pore distance (b) are on the order of magnitude of micrometers and tens of micrometers, while the diffusion coefficients of xenon gas in the diffusion channels (D_eff) are about 10^-8 m²/s. Overall, this study suggests that the pores with a few micrometers connected through very narrow flowing channels with the length of several tens of micrometers are developed 70 to 100 μm below the rubber surface. Furthermore, the overall steady-state diffusion of xenon is slower, approximately 2 orders of magnitudes, than the diffusion in the channel between the pores. The pore and exchange distances correlated with the composition of rubbers showed that the properties of EPDM rubber as a high-pressure gas barrier could be improved by reducing the size of cracks and the depth of gas penetration by the addition of both carbon black and silica fillers.

The origin of a large apparent tortuosity factor for the Knudsen diffusion inside monoliths of a samaria–alumina aerogel catalyst: a diffusion NMR study

The contribution from surface diffusion into the apparent tortuosity factor can be separated for light gases in a porous catalyst.

MAG-PGSTE: a new STE-based PGSE NMR sequence for the determination of diffusion in magnetically inhomogeneous samples

A new stimulated echo based pulsed gradient spin-echo sequence, MAG-PGSTE, has been developed for the determination of self-diffusion in magnetically inhomogeneous samples. The sequence was tested on two glass bead samples (i.e., 212-300 and <106 microm glass bead packs). The MAG-PGSTE sequence was compared to the MAGSTE (or MPFG) (P.Z. Sun, J.G. Seland, D. Cory, Background gradient suppression in pulsed gradient stimulated echo measurements, J. Magn. Reson. 161 (2003) 168-173; P.Z. Sun, S.A. Smith, J. Zhou, Analysis of the magic asymmetric gradient stimulated echo sequence with shaped gradients, J. Magn. Reson. 171 (2004) 324-329; P.Z. Sun, Improved diffusion measurement in heterogeneous systems using the magic asymmetric gradient stimulated echo (MAGSTE) technique, J. Magn. Reson. 187 (2007) 177-183; P. Galvosas, F. Stallmach, J. Kärger, Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios, J. Magn. Reson. 166 (2004) 164-173, P. Galvosas, PFG NMR-Diffusionsuntersuchungen mit ultra-hohen gepulsten magnetischen Feldgradienten an mikroporösen Materialien, Ph.D. Thesis, Universität Leipzig, 2003, P.Z. Sun, Nuclear Magnetic Resonance Microscopy and Diffusion, Ph.D. Thesis, Massachusetts Institute of Technology, 2003] sequence and Cotts 13-interval [R.M. Cotts, M.J.R. Hoch, T. Sun, J.T. Marker, Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems, J. Magn. Reson. 83 (1989) 252-266] sequence using both glass bead samples. The MAG-PGSTE and MAGSTE (or MPFG) sequences outperformed the Cotts 13-interval sequence in the measurement of diffusion coefficients; more interestingly, for the sample with higher background gradients (i.e., the <106 microm glass bead sample), the MAG-PGSTE sequence provided higher signal-to-noise ratios and thus better diffusion measurements than the MAGSTE and Cotts 13-interval sequences. In addition, the MAG-PGSTE sequence provided good characterization of the surface-to-volume ratio for the glass bead samples.

Heterogeneity of polyelectrolyte diffusion in polyelectrolyte-protein coacervates: a 1H pulsed field gradient NMR study

Proton pulsed field gradient (PFG) NMR was used to study the diffusion of poly(diallyldimethylammonium chloride) (PDADMAC) in coacervates formed from this polycation and the protein bovine serum albumin (BSA). Application of high (up to 30 T/m) magnetic field gradients in PFG NMR measurements allowed probing the diffusion of PDADMAC on a length scale of displacements as small as 100 nm in coacervates formed at different pH's and ionic strengths, i.e., conditions of varying protein-polycation interaction energy. Studies were carried out for a broad range of diffusion times and corresponding values of the mean square displacements. Several ensembles of PDADMAC polycations with different diffusivities were observed in the measured range of diffusion times. The existence of these ensembles and the pattern of their changes with increasing diffusion time support the hypothesis about the microscopic heterogeneity of PDADMAC-BSA coacervates and also provide evidence for the dynamic disintegration and reformation of dense domains.

Dynamic Nuclear Polarization of Amyloidogenic Peptide Nanocrystals: GNNQQNY, a Core Segment of the Yeast Prion Protein Sup35p

Dynamic nuclear polarization (DNP) permits a approximately 10(2)-10(3) enhancement of the nuclear spin polarization and therefore increases sensitivity in nuclear magnetic resonance (NMR) experiments. Here, we demonstrate the efficient transfer of DNP-enhanced (1)H polarization from an aqueous, radical-containing solvent matrix into peptide crystals via (1)H-(1)H spin diffusion across the matrix-crystal interface. The samples consist of nanocrystals of the amyloid-forming peptide GNNQQNY(7-13), derived from the yeast prion protein Sup35p, dispersed in a glycerol-water matrix containing a biradical polarizing agent, TOTAPOL. These crystals have an average width of 100-200 nm, and their known crystal structure suggests that the size of the biradical precludes its penetration into the crystal lattice; therefore, intimate contact of the molecules in the nanocrystal core with the polarizing agent is unlikely. This is supported by the observed differences between the time-dependent growth of the enhanced polarization in the solvent versus the nanocrystals. Nevertheless, DNP-enhanced magic-angle spinning (MAS) spectra recorded at 5 T and 90 K exhibit an average signal enhancement epsilon approximately 120. This is slightly lower than the DNP enhancement of the solvent mixture surrounding the crystals (epsilon approximately 160), and we show that it is consistent with spin diffusion across the solvent-matrix interface. In particular, we correlate the expected DNP enhancement to several properties of the sample, such as crystal size, the nuclear T(1), and the average (1)H-(1)H spin diffusion constant. The enhanced (1)H polarization was subsequently transferred to (13)C and (15)N via cross-polarization, and allowed rapid acquisition of two-dimensional (13)C-(13)C correlation data.

Profiles with microscopic resolution by single-sided NMR

A single-sided NMR sensor to produce depth profiles with microscopic spatial resolution is presented. It uses a novel permanent magnet geometry that generates a highly flat sensitive volume parallel to the scanner surface. By repositioning the sensitive slice across the object one-dimensional profiles of the sample structure can be produced with a space resolution better than 5 microm. The open geometry of the sensor results in a powerful testing tool to characterize arbitrarily sized objects in a non-destructive way.

Restricted diffusion and release of aroma molecules from sol-gel-made porous silica particles

The aim of the current study is to predict the release kinetics of organic molecules entrapped in sol-gel-made silica particles using both pulsed field gradient-nuclear magnetic resonance (PFG-NMR) techniques and model calculations to describe restricted diffusion. The macroscopic release profile of aroma molecules from sol-gel-made particles is measured directly by UV-VIS spectroscopy, while the release kinetics are calculated by the Crank equation. The microscopic restricted pore diffusion coefficient of the aroma molecules in the Crank equation is obtained in situ by pulsed field gradient (PFG) magic angle spinning (MAS) nuclear magnetic resonance (NMR). Furthermore, restricted pore diffusion coefficients obtained by model calculations are in agreement with those measured by PFG-MAS-NMR, indicating the potential of the latter for characterization and screening of encapsulation formulations. Measured and calculated release profiles agree within experimental error.

Restricted diffusion in silica particles measured by pulsed field gradient NMR

The restricted diffusion coefficient of water through porous silica is measured by pulsed field gradient (PFG) NMR as a function of loading in order to develop a model for self-diffusion at full pore filling in sol-gel-made porous silica particles. This model describes the pore or intraparticle diffusion coefficient as a function of particle porosity, tortuosity, and the steric hindrance applied on the molecules by the pore space. The particle morphology is characterized by nitrogen adsorption and an appropriate tortuosity model is chosen in comparison with literature data. To characterize the material, NMR relaxation and diffusion studies at different degrees of pore filling were carried out in relation to the silica/water adsorption isotherm.

Diffusion in porous building materials with high internal magnetic field gradients

Measuring the water diffusivity in porous building materials with NMR is hindered by the presence of large internal magnetic field gradients originating from magnetic impurities (Fe). To investigate the diffusion of water in these materials, a stimulated echo NMR technique is applied. A new analytical equation for the long-time signal decay in the presence of spatially varying internal field gradients is derived. This equation is experimentally confirmed by measurements on representative materials with large internal gradients (fired-clay brick and sintered crushed glass) and a material with very small internal gradients (glass filter). The diffusivity is determined in the long time limit, where it is constant and limited by the tortuosity of the pore structure. Tortuosities of different samples derived from the NMR data show an excellent agreement with the macroscopic tortuosities measured by electrochemical impedance spectroscopy. The developed technique can also be applied in unsaturated media, during e.g., drying, water absorption, and concentration changes. The characteristic length scales of the internal field fluctuations estimated from the model are compared with the structural length scales, whereas the magnitude of these fluctuations is compared with results of macroscopic magnetization measurements.

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.

Effect of internal gradients in the nuclear magnetic resonance measurement of the surface-to-volume ratio

We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with [B(t)-B(0)](2), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t). Diffusion takes place while the field is on, so that the spins precess as they diffuse, in contrast to the simpler problem of purely classical diffusion considered in [P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)] which is applicable only to the ideal pulsed-field gradient experiment. We compute the short-time asymptotic form of F(t) and find that it depends on the surface-to-volume ratio (S/V) of the pore space as well as on the average of the gradients over the bounding surface. In a system with nonuniform gradients that vary faster near the surface than in the bulk, as for internal susceptibility fields, this gradient surface average may be much larger than the gradients in the bulk, significantly enhancing the apparent S/V. We discuss the application of our results to the widely used Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence as well as proposing a modification of it, which we term "padded" CPMG, that may be preferable in systems with significant surface relaxation. We indicate how each sequence can be used to probe the internal fields.

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

Self-diffusion of ethane in beds of zeolite NaX is studied using Pulsed Field Gradient (PFG) NMR. The ethane diffusivities were measured for displacements, which are orders of magnitude larger than the size of individual crystals. These diffusivities were compared with those, calculated using simple gas kinetic theory. The results of the comparison indicate that for the same bed of NaX crystals the apparent tortuosity factor in the Knudsen regime ( i.e. when molecule-solid collisions dominate) is significantly larger than that in the bulk regime ( i.e. when molecule-molecule collisions dominate). This finding is attributed to the more pronounced geometrical trapping by the pore structure of the zeolite bed in the Knudsen than in the bulk regime.

Background gradient suppression in pulsed gradient stimulated echo measurements

Pulsed gradient spin echo (PGSE) experiments can be used to measure the probability distribution of molecular displacements. In homogeneous samples this reports on the molecular diffusion coefficient, and in heterogeneous samples, such as porous media and biological tissue, such measurements provide information about the sample's morphology. In heterogeneous samples however background gradients are also present and prevent an accurate measurement of molecular displacements. The interference of time independent background gradients with the applied magnetic field gradients can be removed through the use of bipolar gradient pulses. However, when the background gradients are spatially non-uniform molecular diffusion introduces a temporal modulation of the background gradients. This defeats simple bipolar gradient suppression of background gradients in diffusion related measurements. Here we introduce a new method that requires the background gradients to be constant over coding intervals only. Since the coding intervals are typically at least an order of magnitude shorter than the storage time, this new method succeeds in suppressing cross-terms for a much wider range of heterogeneous samples.

Structure-mobility relations of molecular diffusion in nanoporous materials

Depending on the measuring conditions, pulsed field gradient (PFG) NMR measurements of molecular diffusion in beds of nanoporous particles may provide information about the propagation rate of guest molecules in both the intra- and interparticle spaces, as well as through the interface between them. Recent progress in both PFG NMR instrumentation and computational techniques have initiated studies of novel aspects in each of these areas, which are reviewed in this communication. They concern the possibility of multicomponent diffusion measurements with ultra-high pulsed field gradients, the peculiarities of molecular diffusion in channel networks, the determination of the surface-to-volume ratio of nanoporous particles and the dependence of the tortuosity factor of long-range diffusion on the diffusion mode in the intercrystalline space.

PFG NMR and internal magnetic field gradients in plant-based materials

In this contribution, it is demonstrated that inner magnetic field gradients can seriously affect the results of stimulated echo PFG NMR experiments on plant-based materials even if there is no notable content of paramagnetic substances. Such effects could be observed both in experiments on water in pharmaceutical grade cellulose powder materials and on eggplant fruit tissue. In both cases, it was observed that the effects of internal magnetic field gradients led to different relative values of the diffusion coefficient compared to values obtained with a gradient-compensating pulse sequence.

Fractal geometry of surface areas of sand grains probed by pulsed field gradient NMR

Pulsed field gradient NMR self-diffusion studies of water were used to determine surface-to-volume ratios and specific surface areas of the grains forming a glacial sand deposit. Both quantities exhibit a noninteger power-law dependence as a function of the diameters of the grains. The associated fractal dimensions of the surface area ( D(s)) and of the pore volume ( D(v)) are found to be D(s)-D(v) = -0.70+/-0.05 and D(s) = 2.20+/-0.05. The results demonstrate that NMR studies with native pore fluids are suitable to investigate the fractal nature of natural, unconsolidated porous materials.