The Influence of the Magnetic Impurity Content on the Pore Size Distribution Determination via the DDIF Technique

The pore size distribution of porous media can be determined in a completely non-invasive manner using a new nuclear magnetic resonance (NMR) technique which monitors the magnetization decay due to diffusion in internal fields (DDIF). However, using of the DDIF technique is restricted to the low-phase encoding limit when only the relaxation mode and the first-order diffusion mode are excited. In the present work the fulfillment of such a limit is verified for a progressive increase of the magnetic impurity content of the porous media. If the higher order diffusion modes are excited they lead both to a stronger attenuation of the echo signal and to the appearance of ripples in the DDIF spectra which cannot be related to a pore size distribution. The samples used in this study are porous ceramics prepared using the replication technique and the magnetic impurity is iron (III) oxide which is introduced in an increasing concentration inside the porous matrix. All NMR experiments were done on water filling such porous ceramics using a low-field instrument operating at a proton resonance frequency of 20 MHz. The average pore dimension obtained with the DDIF technique in the weak encoding limit indicates a satisfactory agreement with that observed in optical microscopy images.     

Pore sizes and pore connectivity in rocks using the effect of internal field.

A novel nuclear magnetic resonance method has been applied to several sandstone rocks to measure the pore size distribution using the magnetization decay due to diffusion in the internal magnetic field (DDIF). By comparing the results of the DDIF and Hg porosimetry experiments, a clear picture of pore connectivity emerges. The pore body diameter can be defined using the DDIF data and is found to have a clear trend as a function of porosity.     

Internal Magnetic Field Gradients in Heterogeneous Porous Systems: Comparison Between Spin-Echo and Diffusion Decay Internal Field (DDIF) Method

Two techniques used for evaluating internal magnetic field gradient (G _i), spin-echo (SE) and diffusion decay internal field (DDIF), were investigated at 9.4 T and compared in porous systems characterized by different pores size ranging from 4 to 96 μm with magnetic susceptibility difference between solid and liquid phase, \(\Delta \chi\)  ≈ 1.6 ppm. Since diffusion of a fluid in a solid porous matrix plays a role in both SE and DDIF methods, we investigated these two different methods by highlighting their dependence on characteristic parameters and length scales used to describe diffusion behavior of fluids in porous systems. Therefore, G _i behavior as a function of the dephasing length (l _g), diffusion length (l _d) and pores size (l _s) was obtained. Moreover G _i was evaluated by using both free diffusion and measured apparent diffusion coefficient of water, to quantify diffusion effect in different porous samples. This study gives more insight into the physical dynamics process to explain contrast mechanisms recently exploited by DDIF and SE applications for cancellous bone quality measurements.     

The internal magnetic field distribution, and single exponential magnetic resonance free induction decay, in rocks

When fluid saturated porous media are subjected to an applied uniform magnetic field, an internal magnetic field, inside the pore space, is induced due to magnetic susceptibility differences between the pore-filling fluid and the solid matrix. The microscopic distribution of the internal magnetic field, and its gradients, was simulated based on the thin-section pore structure of a sedimentary rock. The simulation results were verified experimentally. We show that the 'decay due to diffusion in internal field' magnetic resonance technique may be applied to measure the pore size distribution in partially saturated porous media. For the first time, we have observed that the internal magnetic field and its gradients in porous rocks have a Lorentzian distribution, with an average gradient value of zero. The Lorentzian distribution of internal magnetic field arises from the large susceptibility contrast and an intrinsic disordered pore structure in these porous media. We confirm that the single exponential magnetic resonance free induction decay commonly observed in fluid saturated porous media arises from a Lorentzian internal field distribution. A linear relationship between the magnetic resonance linewidth, and the product of the susceptibility difference in the porous media and the applied magnetic field, is observed through simulation and experiment.     

Novel NMR techniques for porous media research

Diffusion in porous media has been used as a probe of pore geometry in various NMR techniques. We will examine the effect of time-dependent diffusion in CPMG by showing that the diffusion time in CPMG is approximately the echo time, even in grossly inhomogeneous magnetic fields. Extension of the diffusion time in modified CPMG sequences is discussed. Diffusion in the susceptibility-contrast induced internal field is discussed as a means to probe pore size and pore shape. Finally, we present the general concept of two-dimensional relaxation-type experiments for study of molecules, fluids, materials and their dynamics that are characterized by spin relaxation and diffusion.     

Determining pore sizes using an internal magnetic field

A concept is proposed to measure the pore size length scale by the internal magnetic field (B_i) in porous materials. The spatial distribution of the magnetic field inhomogeneity, a result of the magnetic susceptibility contrast between the porous material and the fluid, reflects the underlying pore geometry. Diffusion in B_i causes the initial decay of magnetization. At long times, the effect of B_i saturates when the diffusion length reaches a characteristic pore size. This method is independent of surface spin relaxation in determining pore sizes. Nuclear magnetic resonance experiments on packed glass beads and sedimentary rock samples will be presented.     

MR diffusion - "diffraction" phenomenon in multi-pulse-field-gradient experiments

Using pulsed-field-gradient (PFG) experiments, the sizes of the pores in ordered porous media can be estimated from the "diffraction" pattern that the signal attenuation curves exhibit. A different diffraction pattern is observed when the experiment is extended to a larger number (N) of diffusion gradient pulse pairs. Simulations to calculate signal values from arbitrary gradient waveforms are performed for diffusion in restricted geometries using a matrix operator formalism. The simulations suggest that the differences in the characteristics of the attenuation curves are expected to make it possible to measure smaller pore sizes, to improve the accuracy of pore size measurements and potentially to distinguish different pore shapes using the N-PFG technique. Moreover, when an even number of PFG pairs is used, it is possible to observe the diffraction pattern at shorter diffusion times and measure an approximation to the average pore size even when the sample contains pores with a broad distribution of sizes.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

Comparison of two modeling approaches for highly heterogeneous porous media

The purpose of this paper is to study the acoustic behavior of highly heterogeneous, low density porous structures having a complex pore size distribution using two distinct theoretical approaches. The first approach requires the direct numerical integration of the Biot viscosity correction function. The main requirement here is a knowledge of the probability density function of the pore size, which can be achieved by an optical pore-counting technique. The fact that the observed pore size distribution in these materials could be distinctively split into two parts suggested the use of the second approach based upon the double-porosity theory by Olny and Boutin [J. Acoust. Soc. Am. 114(1), 73-89 (2003)]. The latter approach assumes a low permeability contrast between the two porous scales so that the acoustic properties could be estimated using the semi-phenomenological models of Johnson and Lafarge for the viscous and thermal dynamic permeabilities. Numerical results predicted by the two models are then compared with impedance tube experimental data showing good accuracy of the selected prediction methods.     

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.     

超声波作用下污泥水分扩散过程的数值模拟

建立了超声波作用下污泥内部水分扩散模型,利用分形理论对超声波(20 kHz)作用下污泥内部孔隙结构进行描述,探讨了超声波声能密度对污泥孔隙表面分形维数df及孔隙通道曲折度分形维数dw的影响,在此基础上建立了超声波作用下多孔介质中液体有效扩散系数的分形模型,对不同声能密度超声波辐照下污泥水分扩散过程进行了数值模拟.研究发...     

Preparation and Characterization of Poly(L-lactide-co-glycolide-co-ε-caprolactone) Scaffolds by Thermally Induced Phase Separation

Abstract

The technique of thermally induced phase separation (TIPS) is favorable for the fabrication of a porous scaffold due to a number of advantages. In this work the poly(L-lactide-co-glycolide-co-ε-caprolactone) (PLLGC) terpolymer was synthesized by melt copolymerization and porous scaffolds thereof from its solution in 1,4-dioxane were fabricated by using the TIPS method. The effects of fabrication parameters, including polymer concentration and freezing temperature, on the morphology, pore size and mechanical properties were studied. The results showed that the average pore size of the PLLGC porous scaffold increased with a decrease in PLLGC concentration and the pore size resulting from freezing at 4?°C (about 20–100?μm) was significantly larger than for other samples (20–50?μm) frozen at lower temperatures. The porosity of the scaffolds decreased with increasing PLLGC concentration or decreasing freezing temperature. On the other hand, the compressive strength of the scaffolds increased with the increase of PLLGC concentration or the decrease of freezing temperature, as would be expected. The present results can be applied in design to control the processing parameters of TIPS for a scaffold with desired pore morphology.     

Predictions of pulsed field gradient NMR echo-decays for molecules diffusing in various restrictive geometries. Simulations of diffusion propagators based on a finite element method

Pulsed field gradient NMR diffusometry is a promising tool for investigating structures of porous material through determinations of dynamic displacements of molecules in porous systems. A problem with this approach is the lack of closed analytical expressions for echo-decays in anything but idealized pore geometries. We present here an approach based on calculating the appropriate diffusion propagator by means of finite element calculations. The suggested method is quite general, and can be applied to arbitrary porous systems. The protocol for the calculations is outlined and we show results from some different cases: diffusion in confined geometries and in systems that are spatially inhomogeneous with respect to concentration.     

NMR Relaxation and Diffusion Measurements on Iron(III)-Doped Kaolin Clay

Kaolin clay samples were mixed with various amounts of Fe₂O₃ powder. The influence of this magnetic impurity on NMR relaxation and diffusion measurements on the water in this porous material was investigated. The NMR relaxation measurements showed a nearly mono-exponential decay, leading to the conclusion that the pore size distribution of the clay samples is either narrow and/or that the pores are interconnected very well. Both the longitudinal and the transverse relaxation rate depend linearly on the concentration of the Fe₂O₃ impurity. The NMR diffusion measurements revealed that the Fe₂O₃ causes internal magnetic field gradients that largely exceed the maximum external gradient that could be applied by our NMR apparatus (0.3 T/m). Additional SQUID measurements yielded the magnetization and magnetic susceptibility of the samples at the magnetic field strength used in the NMR measurements (0.8 T). A theoretical estimate of the internal magnetic field gradients leads to the conclusion that the water in the porous clay samples cannot be described by the commonly observed motional averaging regime. Probably an intermediate or a localization regime is induced by the large internal gradients, which are estimated to be on the order of 1 to 10 T/m in the pore volume and may exceed 1000 T/m at the pore surface.     

Xenon porometry: a novel method for the derivation of pore size distributions

Xenon porometry is a novel method used for characterizing porous materials by the (129)Xe nuclear magnetic resonance of xenon gas. With the method, the diffusion of gas is slowed down by immersing the material in a medium, which can be in liquid or solid state during measurements. Because of slow diffusion, the signal of a xenon atom is characteristic of the properties of only one pore, and the composite signal of all atoms represents the distribution of properties. The method is especially applicable for determining pore size distribution because the chemical shifts of two different xenon signals (one from liquid and the other from gas pockets in solid) are dependent on pore size. Therefore, the shapes of these signals represent pore size distribution function. In addition, the porosity of the material can be determined by comparing the intensities of two signals. This article focuses on describing xenon signals observed from gas pockets in a solid medium, which has turned out to be most convenient for pore size determination.     

Detection of the high eigenmodes of spin diffusion in porous media

The dynamics of spin diffusion in a fluid is governed by the Torrey-Bloch equations, and the solution is often expressed mathematically in an eigenmode expansion. We report an experimental demonstration of the excitation and detection of a wide range of eigenmodes in porous media by exploring the inhomogeneous internal magnetic field in the pore space. The nodal character of the eigenfunctions of the high eigenmodes was clearly observed. The methodology of excitation and detection of the high eigenmodes may be used to better characterize pore geometry.     

岩心孔隙介质中流体的核磁共振弛豫

弛豫时间是核磁共振研究中的一个重要参数,岩心孔隙介质流体的弛豫过程是自由流体弛豫机制、表面弛豫机制和流体的扩散弛豫机制共同作用的结果,它包含了丰富的孔隙和流体本身的信息. 弛豫时间和自扩散系数的测量及对弛豫时间的分析是核磁共振技术应用于岩心分析和石油勘测的重要内容.