Pore diameter mapping using double pulsed-field gradient MRI and its validation using a novel glass capillary array phantom

Double pulsed-field gradient (d-PFG) MRI can provide quantitative maps of microstructural quantities and features within porous media and tissues. We propose and describe a novel MRI phantom, consisting of wafers of highly ordered glass capillary arrays (GCA), and its use to validate and calibrate a d-PFG MRI method to measure and map the local pore diameter. Specifically, we employ d-PFG Spin-Echo Filtered MRI in conjunction with a recently introduced theoretical framework, to estimate a mean pore diameter in each voxel within the imaging volume. This simulation scheme accounts for all diffusion and imaging gradients within the diffusion weighted MRI (DWI) sequence, and admits the violation of the short gradient pulse approximation. These diameter maps agree well with pore sizes measured using both optical microscopy and single PFG diffusion diffraction NMR spectroscopy using the same phantom. Pixel-by-pixel analysis shows that the local pore diameter can be mapped precisely and accurately within a specimen using d-PFG MRI.     

Microstructural features assessment of different waterlogged wood species by NMR diffusion validated with complementary techniques

Wood is a hygroscopic, multi-scale and anisotropic natural material composed of pores with different size and differently oriented. In particular, archaeologically excavated wood generally is waterlogged wood with very high moisture content (400%–800%) that need to have a rapid investigation at the microstructural level to obtain the best treatment with preservative agents. Time-dependent diffusion coefficient D(t) quantified by Pulse Field Gradient (PFG) Nuclear Magnetic Resonance (NMR) techniques provides useful information about complex porous media, such as the tortuosity (τ) describing pore connectivity and fluid transport through media, the average-pore size, the anisotropic degree (a_n). However, diffusion NMR is intrinsically limited since it is an indirect measure of medium microstructure and relies on inferences from models and estimation of relevant diffusion parameters. Therefore, it is necessary to validate the information obtained from NMR diffusion parameters through complementary investigations. In this work, the structures of five waterlogged wood species were studied by PFG of absorbed water. D(t) and τ of water diffusing along and perpendicular to vessels/tracheids main axes together with relaxation times and a_n were quantified. From these parameters, the pore sizes distribution and the wood microstructure characterization were obtained. Results among wood species were compared, validated and integrated by micro-imaging NMR (μ-MRI), environmental-scanning electron-microscope (ESEM) images, wood dry density and imbibition times measurement of all woods. The work suggests that a_n vs τ rather than the estimated pore size diversifies and characterize the different wood species. As a consequence diffusion-anisotropy vs tortuosity could be an alternative method to characterize and differentiate wood species of waterlogged wood when high resolution images (μ-MRI and ESEM) are not available. Moreover, the combined use of D(t) and micro-MRI expands the scale of dimensions observable by NMR covering all the interesting length scales of wood.     

Diffusion studies in confined nematic liquid crystals by MAS PFG NMR

Pulsed field gradient (PFG) NMR and magic-angle spinning (MAS) NMR have been combined in order to measure the diffusion coefficients of liquid crystals in confined geometry. Combination of MAS NMR with PFG NMR has a higher spectroscopic resolution in comparison with conventional PFG NMR and improves the application of NMR diffusometry to liquid crystals. It is found that the confinement of the liquid crystal 5CB in porous glasses with mean pore diameters of 30 and 200 nm does not notably change its diffusion behavior in comparison with the bulk state.     

Molecular mobility and transport in polymer membranes and polyelectrolyte multilayers

Polyelectrolyte multilayers prepared by the layer-by-layer technique provide an efficient way to generate planar structures of tailored surface charge and hydrophobicity, which are used as membranes for pervaporation. The use of polyelectrolyte multilayers to form the membrane permits tailoring the surface charge of the membrane and, thus, selectivity; at the same time, it reduces fouling of the membrane by adsorption of organic matter. Pulsed field gradient (PFG) nuclear magnetic resonance has been used to investigate the diffusion of probe molecules into polymer systems. Evaluation of the apparent diffusion coefficient in porous poly(amide) results in a pore size of 4 microm, as found in electron micrographs. For the pore size obtained for polyelectrolyte multilayers, no equivalent pores could be found in microscopy. Propagators for the diffusion of propanol and propanol-water mixture into multilayers reveal that there might be selective interaction of probe molecules with the polyelectrolyte system.     

A tensor approach to double wave vector diffusion-weighting experiments on restricted diffusion

Previously, it has been shown theoretically that in case of restricted diffusion, e.g. within isolated pores or cells, a measure of the pore size, the mean radius of gyration, can be estimated from double wave vector diffusion-weighting experiments. However, these results are based on the assumption of an isotropic orientation distribution of the pores or cells which hampers the applicability to samples with anisotropic or unknown orientation distributions, such as biological tissue. Here, the theoretical considerations are re-investigated and generalized in order to describe the signal dependency for arbitrary orientation distributions. The second-order Taylor expansion of the signal delivers a symmetric rank-2 tensor with six independent elements if the two wave vectors are concatenated to a single six-element vector. With this tensor approach the signal behavior for arbitrary wave vectors and orientation distributions can be described as is demonstrated by numerical simulations. The rotationally invariant trace of the tensor represents a pore size measure and can be determined from three orthogonal directions with parallel and antiparallel orientation of the two wave vectors. Thus, the presented tensor approach may help to improve the applicability of double wave vector diffusion-weighting experiments to determine pore or cell sizes, in particular in biological tissue.     

Evidence of microphase separation in controlled pore glasses

The phase separation of a mixture of water and isobutyric acid (iBA) confined in the pore space of Controlled Pore Glass (CPG) 10-75 has been studied by ¹H NMR relaxometry and ¹H-pulsed field gradient (PFG) diffusion measurements. For an acid-rich mixture (mass fraction 54 wt% iBA), evidence of a phase separation process in the pores was obtained, which occurs in a temperature window between 32 and 39 °C, as indicated in the PFG data by an anomalous temperature dependence of the diffusion coefficient and in the relaxation data by a bi-exponential magnetization decay. The phase separation temperature of the mixture in the pore is slightly lower than in the bulk mixture of the same composition (41 °C) and extends over a finite temperature range. A qualitative model of the phase separation process in the pores is developed, which assumes a temperature-dependent domain-like structure of the liquid below the phase transition temperature and a breakdown of these domains upon reaching the transition temperature.     

The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, δ, is comparable to the diffusion time, Δ. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Δ/δ, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Δ/δ  1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long δ the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Δ/δ  1 the diffraction peaks are shifted to even higher q-values, even when δ is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Δ/δ  1.     

固体核磁共振技术在甲醇制烯烃反应中的应用

甲醇制烯烃过程是由非石油路线生成低碳烯烃的重要途径之一.分子筛因具备独特的孔结构和可调变的酸性质,而成为甲醇制烯烃过程的核心催化剂.固体核磁共振(NMR)是鉴定物质结构、阐释催化反应机理的强有力的工具,在甲醇制烯烃的研究中被广泛应用.本文主要总结了近年来利用原位固体NMR、多维多核NMR、脉冲梯度场NMR等固体NMR技术研究甲醇制烯烃反应机理取得的重要进展.原位固体NMR可以在真实反应条件下监测催化反应中反应物、中间体和产物的动态演变过程;多维多核NMR可以在不破坏催化剂结构情况下确定反应中间体结构信息,特别是¹²⁹Xe NMR可以很灵敏探测反应中催化剂的孔道结构变化;脉冲梯度场NMR可用于测定孔道内分子的扩散系数,阐明分子筛的扩散机制.     

Computer simulation of the spin-echo spatial distribution in the case of restricted self-diffusion

This article concerns the question of a proper stochastic treatment of the spin-echo self-diffusion attenuation of confined particles that arises when short gradient pulse approximation fails. Diffusion is numerically simulated as a succession of random steps when motion is restricted between two perfectly reflecting parallel planes. With the magnetic field gradient perpendicular to the plane boundaries, the spatial distribution of the spin-echo signal is calculated from the simulated trajectories. The diffusion propagator approach (Callaghan, "Principles of Nuclear Magnetic Resonance Microscopy," Oxford Univ. Press, Oxford, 1991), which is just the same as the evaluation of the spin-echo attenuation by the method of cumulant expansion in the Gaussian approximation, with Einstein's approximation of the velocity correlation function (VCF) (delta function), agrees with the results of simulation only for the particle displacements that are much smaller than the size of the confinement. A strong deviation from the results of the simulation appears when the bouncing rate from the boundaries increases at intermediate and long gradient sequences. A better fit, at least for intermediate particle displacements, was obtained by replacing the VCF with the Oppenheim--Mazur solution of the Langevin equation (Oppenheim and Mazur, Physica 30, 1833--1845, 1964), which is modified in a way to allow for spatial dependence of particle displacements. Clearly, interplay of the correlation dynamics and the boundary conditions is taking place for large diffusion displacements. However, the deviation at long times demonstrates a deficiency of the Gaussian approximation for the spin echo of diffusion inside entirely closed pores. Here, the cumulants higher than the second one might not be negligible. The results are compared with the experiments on the edge enhancement by magnetic resonance imaging of a pore.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

Structural and dynamic properties of polyoxyethylene sorbitan monooleate micelle in water dispersion studied by pulsed field gradient NMR

The diffusion phenomenon of a nonionic surfactant, polyoxyethylene sorbitan monooleate (POE-SMO), micelle in aqueous solution was investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR) with a high gradient strength of 17.4 T/m at the diffusion timet _d varied from 3 to 300 ms. This high gradient strength allowed us to measure the slow self-diffusion coefficient of POE-SMO micelle, and the short diffusion time below 10 ms showed the restricted diffusion of the micelle. At the shortt _d the self-diffusion of the micelle was restricted and the restricted sizes were 1.8, 1.5, and 0.8 μm for the POE-SMO concentration of 100, 200 and 300 mM, respectively, and 0.6 μm for the POE-SMO only. The possible reason of this restriction was assumed to be the formation of a spatial network or a micellar clustering. Furthermore, a proton exchange between water molecule and surfactant OH group on the micelle surface was proposed. With respect to this proposal, the residence time of the proton at the micelle surface and the thickness of the surface were investigated from proton self-diffusion coefficients by PFG NMR.     

Separation of velocity distribution and diffusion using PFG NMR

Pulsed field gradient (PFG) NMR is applied to investigate flow processes. In this case the NMR signal experiences phase modulation due to flow and signal attenuation due to the distribution of velocities. The velocity distribution consists of one part originating from diffusion and of a second part, the distribution of the directed motion. The usual PFG-experiment in which the gradient strength is incremented cannot distinguish between both. Incrementing velocity at constant gradient strength keeps the contribution from diffusion constant but changes the absolute width of the velocity distribution. So the signal is attenuated again, but only due to the distribution of the directed motion. The phase modulation as a signature of flow is not affected by this strategy, because velocity and gradient strength are Fourier conjugated. The key advantage of this approach is the possibility of measuring very low velocities, which only cause a very slight phase modulation that is easily covered by diffusion. The method is discussed here for very slow flow in a rheometer cell.     

Measuring small compartments with relatively weak gradients by angular double-pulsed-field-gradient NMR

NMR diffusion–diffraction patterns observed in compartments in which restricted diffusion occurs are a useful tool for direct extraction of compartment sizes. Such diffusion–diffraction patterns may be observed when the signal intensity E_(q,?) is plotted against the wave-vector q (when q = (2π)^− 1γδG). However, the smaller the compartment sizes are, the higher are the q-values needed to observe such diffractions. Moreover, these q-values should be achieved using short gradient pulses requiring extremely strong gradient systems. The angular double-pulsed-field gradient (d-PFG) NMR methodology has been proposed as a tool to extract compartment sizes using relatively low q-values. In this study, we have used single-PFG (s-PFG) NMR and angular d-PFG NMR to characterize the size of microcapillaries of about 2 ± 1 μm in diameter. We found that these microcapillaries are characterized by relatively strong background gradients that completely masked the effects of the microscopic anisotropy (μA) of the sample, resulting in a completely unexpected E(φ) profile in the angular d-PFG NMR experiments. We also show that bipolar angular d-PFG NMR experiments can largely suppress the effect of these background gradients resulting in the expected E(φ) profile from which the compartment dimensions could be obtained with relatively weak gradient pulses. These results demonstrate that the above methodology provides a quick, reliable, non-invasive means for estimating small pore sizes with relatively weak gradients in the presence of large magnetic susceptibility.     

Determination of pore space shape and size in porous systems using NMR diffusometry. Beyond the short gradient pulse approximation

The influence of finite length gradient pulses on NMR diffusion experiments on liquids confined to diffuse between two parallel planes is investigated. It is experimentally verified that the pore size decreases when determined using finite gradient pulses if the results are analyzed within the short gradient pulse approximation. The results are analyzed using the matrix formulation. The observed minima in the echo decay profiles are considerably less sharp than theoretical analysis would indicate and we suggest that this is due to the presence of a distribution of pore sizes in the sample. In addition, effects due to the presence of background gradients are discussed. It is argued that effects due to the finite length gradient pulses are relatively minor and in realistic applications the effects due to inhomogeneities in pore sizes and effects due to background gradients will constitute more serious problems in pore size determinations by means of NMR diffusometry.     

Radiation sintering of magnesia: Pore structure studies

Co⁶⁰ γ-ray irradiation of a nonequilibrium surface of magnesium oxide produced tremendous effects on both the extent of the surface area, and on the pore structure. In all cases investigated incompletely decomposed crystals showed appreciable lowering of surface area which indicated activated sintering of the material. The pores present are mainly wide, but with a very narrow distribution of their sizes. Their most probable hydraulic radius is about 10 Å. Upon irradiation sintering is accompanied by widening of pores, and a second group of pores showed its appearance in the pore size distribution curves. These effects seem to be associated with the presence of traces of the volatile component of the parent material, and in particular with the presence of traces of water vapor. Irradiation of the completely decomposed material produced no changes in surface area or pore structure.

The role played by water vapor in accelerating the sintering of magnesia is discussed and possible explanations are given for the effects of irradiation. Dual effects of water vapor might lead to the sintering acceleration of magnesia; chemisorption of OH groups which create cation vacancy on the surface leading to activated surface diffusion, and oxygen bridging between two adjacent/or opposite OH groups particularly in narrow pores, leading to their blocking.     

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.     

Composite Pulsed Field Gradients with Refocused Chemical Shifts and Short Recovery Time

An improved self-compensating pulsed field gradient (PFG) technique that combines antiphase gradient pairs with broadband frequency-modulated 180° pulses is proposed. The antiphase gradient pairs lead to superb system recovery. In addition, evolution under chemical shift and heteronuclearJcoupling are refocused during the PFG, making it appear effectively instantaneous. This new approach makes it possible to obtain high-resolutionphase-sensitive2D spectra for the PFG version of many experiments such as COSY, DQF-COSY, and HSQC without adding extra compensating delays or pulses. While reasonable suppression of unwanted magnetization is achieved, this method also gives satisfactory retention of desired signals. As a bonus, the field-frequency lock is not perturbed during the experiments.     

Measurement of hyperpolarized gas diffusion at very short time scales

We present a new pulse sequence for measuring very-short-time-scale restricted diffusion of hyperpolarized noble gases. The pulse sequence is based on concatenating a large number of bipolar diffusion-sensitizing gradients to increase the diffusion attenuation of the MR signal while maintaining a fundamentally short diffusion time. However, it differs in several respects from existing methods that use oscillating diffusion gradients for this purpose. First, a wait time is inserted between neighboring pairs of gradient pulses; second, consecutive pulse pairs may be applied along orthogonal axes; and finally, the diffusion-attenuated signal is not simply read out at the end of the gradient train but is periodically sampled during the wait times between neighboring pulse pairs. The first two features minimize systematic differences between the measured (apparent) diffusion coefficient and the actual time-dependent diffusivity, while the third feature optimizes the use of the available MR signal to improve the precision of the diffusivity measurement in the face of noise. The benefits of this technique are demonstrated using theoretical calculations, Monte-Carlo simulations of gas diffusion in simple geometries, and experimental phantom measurements in a glass sphere containing hyperpolarized (3)He gas. The advantages over the conventional single-bipolar approach were found to increase with decreasing diffusion time, and thus represent a significant step toward making accurate surface-to-volume measurements in the lung airspaces.     

Correlated displacement-T2 MRI by means of a Pulsed Field Gradient-Multi Spin Echo Method

A method for correlated displacement-T2 imaging is presented. A Pulsed Field Gradient-Multi Spin Echo (PFG-MSE) sequence is used to record T2 resolved propagators on a voxel-by-voxel basis, making it possible to perform single voxel correlated displacement-T2 analyses. In spatially heterogeneous media the method thus gives access to sub-voxel information about displacement and T2 relaxation. The sequence is demonstrated using a number of flow conducting model systems: a tube with flowing water of variable intrinsic T2's, mixing fluids of different T2's in an "X"-shaped connector, and an intact living plant. PFG-MSE can be applied to yield information about the relation between flow, pore size and exchange behavior, and can aid volume flow quantification by making it possible to correct for T2 relaxation during the displacement labeling period Delta in PFG displacement imaging methods. Correlated displacement-T2 imaging can be of special interest for a number of research subjects, such as the flow of liquids and mixtures of liquids or liquids and solids moving through microscopic conduits of different sizes (e.g., plants, porous media, bioreactors, biomats).     

Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations

Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors’ orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.