Pulsed field gradient NMR study of anomalous diffusion in a lecithin-based microemulsion

Self-diffusion measurements in microemulsion systems composed of a naturally occurring soybean lecithin mixture, an aqueous phase, either water or a 1% aqueous PDADMAC solution, and isooctane were accomplished by pulsed field gradient (PFG) 1H NMR spectroscopy at oil dilution lines of low and intermediate water/lecithin ratios. The concentration-dependent diffusion data reveal water-in-oil (W/O) reverse micellar aggregates with dimensions on the nanometer scale being slightly smaller at low water content. With increasing micellar volume fractions, both hydrodynamic as well as direct interactions between particles significantly slow aggregate diffusion. The surfactant mean square displacements (msd's) in dilute and concentrated polymer-free systems studied as a function of diffusion time (20-1000 ms) are characterized by a crossover from Gaussian diffusion, due to slow aggregate motion, to anomalously enhanced diffusion, due to fast surface-bulk surfactant exchange at intermediate times revealing weak, barrier-controlled adsorption behavior. Upon addition of the polycation PDADMAC, the diffusion characteristics change to exclusively superdiffusive behavior with surfactant msd scaling with time as t(3/2) over the entire time range studied. This is caused by surfactant molecules performing Levy walks along the surface of reverse micelles mediated by the dilute bulk. The bulk-mediated surface diffusion is a consequence of the diffusion-controlled micelle-bulk exchange dynamics induced by interactions of PDADMAC with surfactant headgroups.     

Diffusion of methane and carbon dioxide in carbon molecular sieve membranes by multinuclear pulsed field gradient NMR

Carbon molecular sieve (CMS) membranes are promising materials for energy efficient separations of light gases. In this work, we report a detailed microscopic study of carbon dioxide and methane self-diffusion in three CMS membrane derived from 6FDA/BPDA(1:1)-DAM and Matrimid polymers. In addition to diffusion of one-component sorbates, diffusion of a carbon dioxide/methane mixture was investigated. Self-diffusion studies were performed by the multinuclear (i.e., (1)H and (13)C) pulsed field gradient (PFG) NMR technique which combines the advantages of high field (17.6 T) NMR and high magnetic field gradients (up to 30 T/m). Diffusion measurements were carried out at different temperatures and for a broad range of the root-mean-square displacements of gas molecules inside the membranes. The diffusion data obtained from PFG NMR are compared with the corresponding results of membrane permeation measurements reported previously for the same membrane types. The observed differences between the transport diffusivities and self-diffusion coefficients of carbon dioxide and methane are discussed.     

Application of pulsed field gradient NMR with high gradient strength for studies of self-diffusion in lipid membranes on the nanoscale

This work demonstrates the feasibility of noninvasive studies of lipid self-diffusion in model lipid membranes on the nanoscale using proton pulsed field gradient (PFG) NMR spectroscopy with high (up to 35 T/m) gradient amplitudes. Application of high gradients affords for the use of sufficiently small diffusion times under the conditions when the width of the gradient pulses is much smaller than the diffusion time. As a result, PFG NMR studies of partially restricted or anomalous diffusion in lipid bilayers become possible over length scales as small as 100 nm. This length scale is important because it is comparable to the size of membrane domains, or lipid rafts, which are believed to exist in biomembranes. In this work, high-gradient PFG NMR has been applied to study lipid self-diffusion in three-component planar-supported multibilayers (1,2-dioleoyl- sn-glycerol-3-phosphocholine/sphingomyelin/cholesterol). The degree of lipid orientation in the bilayers was determined with (31)P NMR. A special insert was designed to mechanically align the multibilayer stack at the magic angle with respect to the direction of the constant magnetic field to address the detrimental effects of proton dipole-dipole interactions on the NMR signal. This insert is an alternative to the conventional method of magic angle orientation of lipid membranes, the goniometer probe, which is not compatible with commercial high-gradient coils because of the lack of space in the magnet bore. Macroscopic orientation of the multibilayer stacks using the insert was confirmed with (1)H NMR spectroscopic studies and the comparison of results obtained from identical experiments using a goniometer probe for orientation. Diffusion studies were carried out at three different constant magnetic field strengths ( B 0) over a range of temperatures and diffusion times. The measured diffusivities were found to be in agreement with the data obtained previously by techniques that are limited to much larger length scales of diffusion observation than high-gradient PFG NMR.     

Pivotal steps towards quantification of molecular diffusion coefficients by NMR.

Using nuclear magnetic resonance (NMR) spectroscopy with a pair of pulsed field gradients (PFGs), Stajeskal and Tanner successfully measured molecular diffusion coefficients in solution in 1965. This method has since been used extensively in various applications, especially after the PFG was implemented in commercial NMR probes. Due to the nonuniformity of the PFG and radio frequency (RF) fields, molecules distributed throughout the sample experience different PFG and RF fields and contribute unevenly to the measured diffusion coefficients, resulting in considerable errors in conventional NMR diffusion experiments. By selective excitation of a central sample region with an offset-independent adiabatic inversion pulse and a PFG, a uniform RF field can be assumed, and the PFG can be represented as a linear approximation. Under these conditions, the molecules diffuse as if they were all experiencing the same effective gradient g(e), leading to a Gaussian signal decay as a function of the PFG strength. Quantitative measurement of molecular diffusion coefficients is therefore made possible. From the diffusion coefficient of a 90 % H(2)O/10 % D(2)O sample, it is convenient to calibrate g(e) with a Java program. In a similar way the nonlinearity of the PFG can be corrected.     

The role of mesopores in intracrystalline transport in USY zeolite: PFG NMR diffusion study on various length scales

PFG NMR has been applied to study intracrystalline diffusion in USY zeolite as well as in the parent ammonium-ion exchanged zeolite Y used to produce the USY by zeolite steaming. The diffusion studies have been performed for a broad range of molecular displacements and with two different types of probe molecules (n-octane and 1,3,5-triisopropylbenzene) having critical molecular diameters smaller and larger than the openings of the zeolite micropores. Our experimental data unambiguously show that, in contrast to what is usually assumed in the literature, the intracrystalline mesopores do not significantly affect intracrystalline diffusion in USY. This result indicates that the intracrystalline mesopores of USY zeolite do not form a connected network, which would allow diffusion through crystals only via mesopores.     

In situ study on molecular diffusion phenomena in nanoporous catalytic solids

As an omnipresent phenomenon in nature, diffusion is among the rate-determining processes in many technological processes. This is in particular true for catalytic conversion in nanoporous materials. We provide a critical review of the possibilities of exploring diffusion phenomena over microscopic dimensions in such media by direct experimental observation. By monitoring the probability distribution of molecular displacements as a function of time, the pulsed field gradient technique of NMR (PFG NMR) records the rate of molecular re-distribution. By varying the observation time, PFG NMR is thus able to trace even hierarchies of transport resistances as occurring, e.g., in catalyst particles in the form of binder-compacted assemblages of zeolite crystallites. Alternatively, and complementary to this information, interference microscopy (IFM) and IR microscopy (IRM) are able to follow the evolution of intracrystalline concentration profiles during uptake and release. This allows, in particular, an accurate quantification of the transport resistances on the surface of the individual crystallites and of the probability that reactant molecules from the gas phase, upon colliding with the external surface, are able to penetrate through such "surface barriers" into the crystal bulk phase. Being able to distinguish between different molecular species, IRM is able to record the evolution of intracrystalline concentration profiles even during multi-component adsorption and catalytic reactions (169 references).     

Unexpectedly low translational mobility of methane and tetrafluoromethane in the large-pore molecular sieve VPI-5

Molecular diffusion of methane and tetrafluoromethane in the microporous material VPI-5 was studied by pulsed field gradient nuclear magnetic resonance (PFG NMR) and NMR exchange experiments. The translational mobility of both molecules in VPI-5 was found to be at least two orders of magnitude smaller than in ZSM-5. This is surprising since the channels in VPI-5 are about two times as wide as those in ZSM-5. The surprisingly small translational mobility in VPI-5 could be caused by a more complete stabilization effect or by single-file diffusion. The intracrystalline mean life time of methane in VPI-5 directly measured in the NMR tracer exchange experiments was found to be in satisfactory agreement with the value estimated on the basis of the PFG NMR data on translational mobility for ordinary intracrystalline diffusion. It must be ruled out, therefore, that molecular transportation over length scales of the order of the crystallite dimensions is controlled by single-file diffusion.     

Diffusion of molecules confined in semipenetrable nanoscale carriers probed by pulsed field gradient NMR

Diffusion of three low-molecular-weight compounds cyclohexane (CX), benzene (BZ), and chloroform (CL) preferentially confined in the cores of nanoscale carriers was probed by pulsed field gradient (PFG) NMR methods. The carriers were monolayer micelles of sodium dodecyl sulfate (SDS), bilayer micelles of poly(hexyl methacrylate)-block-(acrylic acid) (M2), and trilayer micelles of poly(2-ethylhexyl methacrylate)-block-(methyl methacrylate)-block-(acrylic acid) (M3) in D(2)O at 300 K. Although the radius of the confinement space was 10(-)(8) m or lower, the course of the PFG signal attenuation in pulsed gradient spin-echo or stimulated echo experiments under varied diffusion time corresponds to apparently unrestricted diffusion, which is slowed down compared to that of the compound dissolved in D(2)O. Analysis using approximate relations reveals that the response of the system to PFG NMR consists of three independent components, namely (i) diffusion of the carrier as a whole, (ii) hindered escape of a confined molecule and its diffusion in the medium, and (iii) diffusion of the molecules dissolved in the medium. If process ii is fast enough, exchange of the compound between the carrier and the medium includes the influence of iii as a component of a monoexponential PFG decay; otherwise, two sets of signals are observed with different diffusion responses, or biexponential PFG is observed. According to the results of this study, the only barrier of the diffusion of the inspected compounds CX, BZ, and CL out of their confinement in the carriers SDS or M2 is a thermodynamic one, that is, the resistance of the saturated solution to accept surplus molecules of the solute. In a three-layer micelle M3, the additional polymer sheet around the confinement area forms an additional diffusion barrier for CX, however. The study shows that PFG NMR, though unable to observe directly restricted diffusion on the nanoscale, can be useful in studying systems designed, for example, for a controlled release of low-molecular-weight substances.     

Translational diffusion of macromolecular assemblies measured using transverse-relaxation-optimized pulsed field gradient NMR

In structural biology, pulsed field gradient (PFG) NMR spectroscopy for the characterization of size and hydrodynamic parameters of macromolecular solutes has the advantage over other techniques that the measurements can be recorded with identical solution conditions as used for NMR structure determination or for crystallization trials. This paper describes two transverse-relaxation-optimized (TRO) (15)N-filtered PFG stimulated-echo (STE) experiments for studies of macromolecular translational diffusion in solution, (1)H-TRO-STE and (15)N-TRO-STE, which include CRINEPT and TROSY elements. Measurements with mixed micelles of the Escherichia coli outer membrane protein X (OmpX) and the detergent Fos-10 were used for a systematic comparison of (1)H-TRO-STE and (15)N-TRO-STE with conventional (15)N-filtered STE experimental schemes. The results provide an extended platform for evaluating the NMR experiments available for diffusion measurements in structural biology projects involving molecular particles with different size ranges. An initial application of the (15)N-TRO-STE experiment with very long diffusion delays showed that the tedradecamer structure of the 800 kDa Thermus thermophilus chaperonin GroEL is preserved in aqueous solution over the temperature range 25-60 °C.     

Temperature driven annealing of perforations in bicellar model membranes

Bicellar model membranes composed of 1,2-dimyristoylphosphatidylcholine (DMPC) and 1,2-dihexanoylphosphatidylcholine (DHPC), with a DMPC/DHPC molar ratio of 5, and doped with the negatively charged lipid 1,2-dimyristoylphosphatidylglycerol (DMPG), at DMPG/DMPC molar ratios of 0.02 or 0.1, were examined using small angle neutron scattering (SANS), (31)P NMR, and (1)H pulsed field gradient (PFG) diffusion NMR with the goal of understanding temperature effects on the DHPC-dependent perforations in these self-assembled membrane mimetics. Over the temperature range studied via SANS (300-330 K), these bicellar lipid mixtures exhibited a well-ordered lamellar phase. The interlamellar spacing d increased with increasing temperature, in direct contrast to the decrease in d observed upon increasing temperature with otherwise identical lipid mixtures lacking DHPC. (31)P NMR measurements on magnetically aligned bicellar mixtures of identical composition indicated a progressive migration of DHPC from regions of high curvature into planar regions with increasing temperature, and in accord with the "mixed bicelle model" (Triba, M. N.; Warschawski, D. E.; Devaux, P. E. Biophys. J.2005, 88, 1887-1901). Parallel PFG diffusion NMR measurements of transbilayer water diffusion, where the observed diffusion is dependent on the fractional surface area of lamellar perforations, showed that transbilayer water diffusion decreased with increasing temperature. A model is proposed consistent with the SANS, (31)P NMR, and PFG diffusion NMR data, wherein increasing temperature drives the progressive migration of DHPC out of high-curvature regions, consequently decreasing the fractional volume of lamellar perforations, so that water occupying these perforations redistributes into the interlamellar volume, thereby increasing the interlamellar spacing.     

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

Diffusion of gases in polymers below the glass transition temperature, T_g, 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 T_g 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 T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g 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     

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.     

How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance

Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived.     

Diffusion properties of liquid crystal-based microemulsions

Microscopic diffusion processes in thermotropic 5CB liquid crystals (LC) with imbedded surfactant-stabilized water microemulsions are studied using pulsed field gradient nuclear magnetic resonance (PFG NMR). The experiments are performed in a temperature range around the isotropic-nematic transition temperature of the LC. The temperature dependence of the diffusivities of the liquid crystal and surfactant molecules remains almost unchanged in the whole temperature range studied. With varying water content, the diffusivities of the surfactant molecules are found to be almost invariable, indicating that the surfactant diffusivities remain essentially unaffected by whether a microemulsion is formed or the surfactant molecules diffuse as individual species. At the same time, the formation of the microemulsion is found to be crucial for the macroscopic separation of the mixture into LC- and surfactant-rich phases.     

Anomalous penetrant diffusion as a probe of the local structure in a blend of poly(ethylene oxide) and poly(methyl methacrylate)

Pulse field gradient (PFG) NMR measurements have been made to study the diffusion of diethyl ether in blends of poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA). The blends have 10–30 wt % PEO, a composition range within which these materials are amorphous glasses. The diffusion of diethyl ether through the blends is quite rapid, with diffusion constants in the range of 10^?7 to 10^?8 cm²/s. In PFG NMR experiments, the apparent diffusion constant depends on the timescale over which diffusion is observed. The values decrease to a plateau as the time increases, this being the signature of tortuous diffusion. Tortuous diffusion is usually observed in heterogeneous systems in which there are regions that support fast diffusion and regions that support slow diffusion or act as barriers. In these blends, PEO is known to undergo rapid segmental motion typical of a rubbery state well below the glass transition, whereas the segmental motion of PMMA is slower by many orders of magnitude. Mobile PEO provides a pathway for the diffusion of structurally similar diethyl ether, whereas solid‐like PMMA acts as a barrier. The size of the domains can be estimated either from a lattice model or from equations for tortuous diffusion. Micrometer sizes are indicated that are unexpectedly large, given the size of the polymer chains and the size of the concentration fluctuations, both of which are thought to be in the tens of nanometers. The lattice model and the equations for tortuous diffusion assume a random dispersion of impenetrable or less penetrable objects. This may not be the appropriate morphology for the diffusion pathway. Recently, large sizes have been indicated by PFG NMR experiments, in which a penetrant is thought to diffuse in a curvilinear fashion. In these blends, the pathway for diethyl ether is along the PEO backbone. A plot of the logarithm of the mean‐square displacement versus the logarithm of time has a slope of about 0.6, close to the value of 0.5 for pure curvilinear diffusion. Exponents with values in this range can also be associated with diffusion in a fractal space, which, in this situation, still consists of mobile PEO. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1053–1067, 2004     

Transport Phenomena in Nanoporous Materials

Diffusion, that is, the irregular movement of atoms and molecules, is a universal phenomenon of mass transfer occurring in all states of matter. It is of equal importance for fundamental research and technological applications. The present review deals with the challenges of the reliable observation of these phenomena in nanoporous materials. Starting with a survey of the different variants of diffusion measurement, it highlights the potentials of “microscopic” techniques, notably the pulsed field gradient (PFG) technique of NMR and the techniques of microimaging by interference microscopy (IFM) and IR microscopy (IRM). Considering ensembles of guest molecules, these techniques are able to directly record mass transfer phenomena over distances of typically micrometers. Their concerted application has given rise to the clarification of long‐standing discrepancies, notably between microscopic equilibrium and macroscopic non‐equilibrium measurements, and to a wealth of new information about molecular transport under confinement, hitherto often inaccessible and sometimes even unimaginable.     

Predicting gas transport in formed zeolite adsorbents from NMR studies

The self-diffusion of nitrogen, methane, and carbon monoxide within a 5A zeolitic adsorbent has been examined with use of pulsed field gradient (PFG) NMR. In all cases, the diffusion process is well-described by a refined version of the long-range diffusion model (LRDM), adapted here for use with pelletized adsorbents, which uses exclusively adsorbent porosity and isotherm data as inputs. Correlation of the experimental data with this model yields tortuosity factors that are characteristic of the adsorbate and reflect the longer diffusive path a molecule must take due to the winding nature of the pore structure. It is demonstrated that the diffusion model can be used to accurately predict the diffusion coefficients for a ternary gas mixture within a 5A zeolite. To fully characterize the diffusive process, the surface excess on the PFG NMR samples has been obtained by a novel gas-phase NMR technique that is well-suited for measuring pure and multicomponent isotherms.     

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.     

Studies on supramolecular gel formation using DOSY NMR

Herein, we present the results obtained from our studies on supramolecular self‐assembly and molecular mobility of low‐molecular‐weight gelators (LMWGs) in organic solvents using pulsed field gradient (PFG) diffusion ordered spectroscopy (DOSY) NMR. A series of concentration‐dependent DOSY NMR experiments were performed on selected LMWGs to determine the critical gelation concentration (CGC) as well as to understand the behaviour of the gelator molecules in the gel state. In addition, variable‐temperature DOSY NMR experiments were performed to determine the gel‐to‐sol transition. The PFG NMR experiments performed as a function of gradient strength were further analyzed using monoexponential DOSY processing, and the results were compared with the automated Bayesian DOSY transformation to obtain 2D plots. Our results provide useful information on the stepwise self‐assembly of small molecules leading to gelation. We believe that the results obtained from these experiments are applicable in determining the CGC and gel melting temperatures of supramolecular gels. Copyright © 2015 John Wiley & Sons, Ltd.     

The Potentials of Pulsed Field Gradient NMR for Investigation of Porous Media

PFG NMR self-diffusion studies provide information on the translational mobility of fluid molecules. Since in porous media the diffusion path of fluid molecules in the pore space is affected by interaction with the pore wall, PFG NMR measurements are sensitive to structural peculiarities of the confining porous medium. The pore space properties which can be investigated depend on length scales set by the PFG NMR experiment in respect to the typical size of the structural feature studied. Based upon these length scales, an interpretation pattern for PFG NMR self-diffusion studies in porous media is given. PFG NMR self-diffusion studies in macro- and microporous systems such as sedimentary rocks and zeolite crystallites, respectively, are reviewed.