Diffusive diffraction measurements in porous media: effect of structural disorder and internal magnetic field gradients

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.

Diffusive diffraction phenomenon observed by PGSE NMR technique in a sugar-based low-molecular-mass gel

The paper presents the diffusive diffraction phenomenon observed by the single-pulse-gradient spin-echo (s-PGSE) NMR technique in a real porous material: a gel composed of low-molecular-mass gelator methyl-4,6-O-(p-nitrobenzylidene)-α-D-glucopyranoside and toluene. Thanks to this phenomenon, we can probe the true microstructure (not xerogel) in which the toluene diffuses. To analyze the measured diffusion-diffraction pattern, we employed a composite bicompartmental model that superimposes restricted diffusion in small cavities of the gel matrix within the bundles of crossing fibers, with free diffusion in large and unconfined compartments between the bundles of crossing fibers. For restricted diffusion a pore-hopping formalism was applied. The observation of the diffraction pattern and its analysis leads to the conclusion that the pores, in the slow diffusing compartment of studied gel are ordered, at least locally, and relatively monodisperse with a size of 64 μm. Moreover, the restricting walls formed by the crossing fibers are perpendicular to the direction of the diffusion gradient.

Overcoming apparent susceptibility-induced anisotropy (aSIA) by bipolar double-pulsed-field-gradient NMR

Double-Pulsed-Field-Gradient (d-PFG) MR is emerging as a powerful new means for obtaining unique microstructural information in opaque porous systems that cannot be obtained by conventional single-PFG (s-PFG) methods. The angular d-PFG MR methodology is particularly important since it can utilize the effects of microscopic anisotropy (μA) and compartment shape anisotropy (csA) in the E(ψ) profile at the different t(m) regimes to provide detailed information on compartment size and eccentricity. An underlying assumption is that the PFGs that are imparted to weigh diffusion are the only gradients present; however, in realistic systems and especially where there are randomly oriented anisotropic pores, susceptibility effects may induce strong internal gradients. In this study, the effects of such internal gradients on E(ψ) plots obtained from angular d-PFG MR and on microstructural information that can be obtained from s-PFG and d-PFG MR were investigated. First, it was found that internal gradients induce a bias in the s-PFG MR results, thus creating an anisotropy that is not related to microstructure, termed apparent-Susceptibility-Induced-Anisotropy (aSIA). We then show that aSIA effects are also manifest in different ways in the angular d-PFG MR experiment in controlled phantoms and in realistic systems such as quartz sand, emulsions, and biological systems. The effects of aSIA in some cases completely masked the effects of μA and csA; however, we subsequently show that by introducing bipolar gradients to the d-PFG MR (bp-d-PFG), the effects of aSIA can be largely suppressed, restoring the E(ψ) plots that are expected from the theory along with the microstructural information that it conveys. We conclude that when specimens are characterized by strong internal gradients, the novel information on μA and csA that is manifest in the E(ψ) plots can indeed be inferred when bp-d-PFG MR is used, i.e. when bipolar gradients are applied.

Observation of restricted diffusion in the presence of a free diffusion compartment: single- and double-PFG experiments

Theoretical and experimental studies of restricted diffusion have been conducted for decades using single pulsed field gradient (s-PFG) diffusion experiments. In homogenous samples, the diffusion-diffraction phenomenon arising from a single population of diffusing species has been observed experimentally and predicted theoretically. In this study, we introduce a composite bi-compartmental model which superposes restricted diffusion in microcapillaries with free diffusion in an unconfined compartment, leading to fast and slow diffusing components in the NMR signal decay. Although simplified (no exchange), the superposed diffusion modes in this model may exhibit features seen in more complex porous materials and biological tissues. We find that at low q-values the freely diffusing component masks the restricted diffusion component, and that prolongation of the diffusion time shifts the transition from free to restricted profiles to lower q-values. The effect of increasing the volume fraction of freely diffusing water was also studied; we find that the transition in the signal decay from the free mode to the restricted mode occurs at higher q-values when the volume fraction of the freely diffusing water is increased. These findings were then applied to a phantom consisting of crossing fibers, which demonstrated the same qualitative trends in the signal decay. The angular d-PGSE experiment, which has been recently shown to be able to measure small compartmental dimensions even at low q-values, revealed that microscopic anisotropy is lost at low q-values where the fast diffusing component is prominent. Our findings may be of importance in studying realistic systems which exhibit compartmentation.

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.

Diffusion processes in homogeneous and phase-separated binary fluid mixtures

Diffusion processes in dynamically asymmetric binary fluid mixtures made of monodisperse polystyrene (PS) and a rodlike nematogen molecule (5CB) are studied by pulsed-field gradient spin echo NMR in the vicinity of the phase-separation/phase-dissolution temperature. The phase-separation process and the loss of mobility of polymer chains at Tg take place simultaneously evidencing the strong effect of elasticity on the sample morphology. Below the instability point of the mixture, two self-diffusion coefficients, named Dfast and Dslow, are observed and assigned to mobile molecules i) dissolved in the polymeric matrix and ii) phase-separated in isolated or interconnected domains, respectively. The temperature dependence of Dfast exhibits an Arrhenius-like behaviour when the mixture is submitted to a slow cooling rate whereas a Vogel-Fulcher-Tamman-Hesse law is obeyed for deep quenches. These results show the dynamic heterogeneities existing in the PS/5CB system below the UCST. Characteristic length scales are estimated from modelling echo attenuation curves exhibiting diffraction-like patterns.