Confinement effects on dipolar relaxation by translational dynamics of liquids in porous silica glasses

Confinement-enhanced Li+ ion dynamics in an ionic liquid-based electrolyte in porous material

While Ionic Liquids (IL) are promising liquid electrolyte components for Li-ion batteries due to their high electrochemical stability and low volatility and flammability, unfavorable Lithium-anion clusters lead to poor Li+ transport properties such as low transference numbers. A confinement of ILs in nanoporous materials could overcome these problems, based on altered structural and dynamic properties of the confined ILs. We investigate the coordination and the Li+ dynamics in an IL/Li-salt mixture of 1-butyl-1-methylpyrrolidinium bis(trifluormethyl-sulfonyl)imide (Pyr14TFSA) and LiTFSA and reveal in how far the confinement has positive or negative effects on ion clustering in the electrolyte. To this end, the electrolyte is confined in mesoporous silica SBA-15 (pore diameter 8 nm or 4 nm) or the metal-organic framework (MOF) ZIF-8 (pore diameter 1.16 nm). Raman spectra elucidate the Li-anion coordination and the interaction of the ions with the walls. Temperature-dependent 7Li spin relaxation rates, analyzed within the model of Bloembergen, Purcell and Pound (BPP), allow statements on the local Li+ environment, the local Li+ dynamics and its activation. In the SBA-15 materials the Li+ coordination is unchanged with persisting Li-TFSA clusters. Furthermore, the local dynamics of Li+ is reduced upon confinement, as expected due to geometrical restrictions. At the same time, however, both structural and dynamic parameters do not show a pronounced dependence on the pore size. Surprisingly, upon confinement in ZIF-8 Li+ displays faster local dynamics and a more asymmetric environment in comparison to the bulk electrolyte. The enhanced dynamics is accompanied by a reduced coordination to TFSA-, suggesting the breakup of Li-TFSA clusters. Differences between the porous materials are attributed to the nature of the wall surface, as Raman spectra suggest that in SBA-15 the TFSA- ion is preferentially interacting with the pore walls, whereas in ZIF-8 the Pyr14+ ion is immobilized by the pore walls. These results demonstrate a strong influence of internal interfaces on IL structure and dynamics and bear potential for further tailoring ion dynamics.

Fluids and Electrolytes under Confinement in Single-Digit Nanopores

Confined fluids and electrolyte solutions in nanopores exhibit rich and surprising physics and chemistry that impact the mass transport and energy efficiency in many important natural systems and industrial applications. Existing theories often fail to predict the exotic effects observed in the narrowest of such pores, called single-digit nanopores (SDNs), which have diameters or conduit widths of less than 10 nm, and have only recently become accessible for experimental measurements. What SDNs reveal has been surprising, including a rapidly increasing number of examples such as extraordinarily fast water transport, distorted fluid-phase boundaries, strong ion-correlation and quantum effects, and dielectric anomalies that are not observed in larger pores. Exploiting these effects presents myriad opportunities in both basic and applied research that stand to impact a host of new technologies at the water-energy nexus, from new membranes for precise separations and water purification to new gas permeable materials for water electrolyzers and energy-storage devices. SDNs also present unique opportunities to achieve ultrasensitive and selective chemical sensing at the single-ion and single-molecule limit. In this review article, we summarize the progress on nanofluidics of SDNs, with a focus on the confinement effects that arise in these extremely narrow nanopores. The recent development of precision model systems, transformative experimental tools, and multiscale theories that have played enabling roles in advancing this frontier are reviewed. We also identify new knowledge gaps in our understanding of nanofluidic transport and provide an outlook for the future challenges and opportunities at this rapidly advancing frontier.

Nuclear spin relaxation as a probe of zeolite acidity: a combined NMR and TPD investigation of pyridine in HZSM-5

The relative surface affinities of pyridine within microporous HZSM-5 zeolites are explored using two-dimensional ¹H nuclear magnetic resonance (NMR) relaxation time measurements. The dimensionless ratio of longitudinal-to-transverse nuclear spin relaxation times T₁/T₂ is shown to exhibit strong sensitivity to the silica/alumina ratio (SAR) of these zeolites, which is indicative of material acidity. This trend is interpreted in terms of increased pyridine surface affinity with decreasing SAR. Temperature programmed desorption (TPD) analysis corroborates this observation, revealing a distinct increase in the heat of desorption associated with adsorbed pyridine as a function of decreasing SAR. A direct correlation between NMR and TPD data suggests NMR relaxation time analysis can be a valuable tool for the non-invasive characterisation of adsorption phenomena in microporous solids.

Water and Ion Dynamics in Confined Media: A Multi-Scale Study of the Clay/Water Interface

This review details a large panel of experimental studies (Inelastic Neutron Scattering, Quasi-Elastic Neutron Scattering, Nuclear Magnetic Resonance relaxometry, Pulsed-Gradient Spin-Echo attenuation, Nuclear Magnetic Resonance Imaging, macroscopic diffusion experiments) used recently to probe, over a large distribution of characteristic times (from pico-second up to days), the dynamical properties of water molecules and neutralizing cations diffusing within clay/water interfacial media. The purpose of this review is not to describe these various experimental methods in detail but, rather, to investigate the specific dynamical information obtained by each of them concerning these clay/water interfacial media. In addition, this review also illustrates the various numerical methods (quantum Density Functional Theory, classical Molecular Dynamics, Brownian Dynamics, macroscopic differential equations) used to interpret these various experimental data by analyzing the corresponding multi-scale dynamical processes. The purpose of this multi-scale study is to perform a bottom-up analysis of the dynamical properties of confined ions and water molecules, by using complementary experimental and numerical studies covering a broad range of diffusion times (between pico-seconds up to days) and corresponding diffusion lengths (between Angstroms and centimeters). In the context of such a bottom-up approach, the numerical modeling of the dynamical properties of the diffusing probes is based on experimental or numerical investigations performed on a smaller scale, thus avoiding the use of empirical or fitted parameters.

The3He nuclear magnetic relaxation in nematically ordered Al2O3aerogels: effects of4He and nitrogen pre-plating

The results of³He gas pulsed NMR spin-lattice relaxation study in high-porosity (84.9%-97.9%) nematically ordered Al₂O₃aerogels at 1.5 and 4.2 K are presented. The linear dependence ofT₁on gas pressure is observed in aerogels that are pre-plated by helium-4. Nitrogen pre-plating prior to helium-4 pre-plating weakly decreases the³He gas spin-lattice relaxation rate. A few possible mechanisms plausibly involved in³He nuclear magnetic relaxation in aerogels are considered. The suggested nuclear spin-lattice relaxation model due to some magnetically 'dirty' aerogel fibers allows to estimate the effective mean free path of³He atoms in aerogel.

Chromatographic NMR spectroscopy: the effect of hollow silica microspheres on magnetic field inhomogeneities and resonance lineshapes

We provide a description of the line broadening phenomenon observed in chromatographic NMR spectra with hollow silica microspheres.

Advances in the Interpretation of Frequency-Dependent Nuclear Magnetic Resonance Measurements from Porous Material

Fast-field-cycling nuclear magnetic resonance (FFC-NMR) is a powerful technique for non-destructively probing the properties of fluids contained within the pores of porous materials. FFC-NMR measures the spin-lattice relaxation rate R 1 ( f ) as a function of NMR frequency f over the kHz to MHz range. The shape and magnitude of the R 1 ( f ) dispersion curve is exquisitely sensitive to the relative motion of pairs of spins over time scales of picoseconds to microseconds. To extract information on the nano-scale dynamics of spins, it is necessary to identify a model that describes the relative motion of pairs of spins, to translate the model dynamics to a prediction of R 1 ( f ) and then to fit to the experimental dispersion. The principles underpinning one such model, the 3 τ model, are described here. We present a new fitting package using the 3 τ model, called 3TM, that allows users to achieve excellent fits to experimental relaxation rates over the full frequency range to yield five material properties and much additional derived information. 3TM is demonstrated on historic data for mortar and plaster paste samples.

Direct Correlation between Adsorption Energetics and Nuclear Spin Relaxation in a Liquid-saturated Catalyst Material

The ratio of NMR relaxation time constants <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>T</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> provides a non-destructive indication of the relative surface affinities exhibited by adsorbates within liquid-saturated mesoporous catalysts. In the present work we provide supporting evidence for the existence of a quantitative relationship between such measurements and adsorption energetics. As a prototypical example with relevance to green chemical processes we examine and contrast the relaxation characteristics of primary alcohols and cyclohexane within an industrial silica catalyst support. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>T</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>/</mml:mo> <mml:msub><mml:mi>T</mml:mi> <mml:mn>2</mml:mn></mml:msub> </mml:mrow> </mml:math> values obtained at intermediate magnetic field strength are in good agreement with DFT adsorption energy calculations performed on single molecules interacting with an idealised silica surface. Our results demonstrate the remarkable ability of this metric to quantify surface affinities within systems of relevance to liquid-phase heterogeneous catalysis, and highlight NMR relaxation as a powerful method for the determination of adsorption phenomena within mesoporous solids.

Theoretical investigation of heterogeneous wettability in porous media using NMR

It is highly important to understand the heterogeneous wettability properties of porous media for enhanced oil recovery (EOR). However, wettability measurements are still challenging in directly investigating the wettability of porous media. In this paper, we propose a multidimensional nuclear magnetic resonance (NMR) method and the concept of apparent contact angles to characterize the heterogeneous wettability of porous media. The apparent contact angle, which is determined by both the wetting surface coverage and the local wettability (wetting contact angles of each homogeneous wetting regions or wetting patches), is first introduced as an indicator of the heterogeneous wettability of porous media using the NMR method. For homogeneously wetting patches, the relaxation time ratio T1/T2 is employed to probe the local wettabiity of wetting patches. The T2 - D is introduced to obtain the wetting surface coverage using the effective relaxivity. Numerical simulations are conducted to validate this method.

Multiscale nuclear magnetic relaxation dispersion of complex liquids in bulk and confinement

The nuclear magnetic relaxation dispersion (NMRD) technique consists of measurement of the magnetic-field dependence of the longitudinal nuclear-spin-lattice relaxation rate 1/T₁. Usually, the acquisition of the NMRD profiles is made using a fast field cycling (FFC) NMR technique that varies the magnetic field and explores a very large range of Larmor frequencies (10 kHz < ω₀/(2π) <40 MHz). This allows extensive explorations of the fluctuations to which nuclear spin relaxation is sensitive. The FFC technique thus offers opportunities on multiple scales of both time and distance for characterizing the molecular dynamics and transport properties of complex liquids in bulk or embedded in confined environments. This review presents the principles, theories and applications of NMRD for characterizing fundamental properties such as surface correlation times, diffusion coefficients and dynamical surface affinity (NMR wettability) for various confined liquids. The basic longitudinal and transverse relaxation equations are outlined for bulk liquids. The nuclear relaxation of a liquid confined in pores is considered in detail in order to find the biphasic fast exchange relations for a liquid at proximity of a solid surface. The physical-chemistry of liquids at solid surfaces induces striking differences between NMRD profiles of aprotic and protic (water) liquids embedded in calibrated porous disordered materials. A particular emphasis of this review concerns the extension of FFC NMR relaxation to industrial applications. For instance, it is shown that the FFC technique is sufficiently rapid for following the progressive setting of cement-based materials (plasters, cement pastes, concretes). The technique also allows studies of the dynamics of hydrocarbons in proximity of asphaltene nano-aggregates and macro-aggregates in heavy crude oils as a function of the concentration of asphaltenes. It also gives new information on the wettability of petroleum fluids (brine and oil) embedded in shale oil rocks. It is useful for understanding the relations and correlations between NMR relaxation times T₁ and T₂, diffusion coefficients D, and viscosity η of heavy crude oils. This is of particular importance for interpreting T₁, T₂, 2D T₁-T₂ and D-T₂ correlation spectra that could be obtained down-hole, thus giving a valuable tool for investigating in situ the molecular dynamics of petroleum fluids. Another domain of interest concerns biological applications. This is of particular importance for studying the complex dynamical spectrum of a folded polymeric structure that may span many decades in frequency or time. A direct NMRD characterization of water diffusional dynamics is presented at the protein interface. NMR experiments using a shuttle technique give results well above the frequency range accessible via the FFC technique; examples of this show protein dynamics over a range from fast and localized motions to slow and delocalized collective motions involving the whole protein. This review ends by an interpretation of the origin of the proton magnetic field dependence of T₁ for different biological tissues of animals; this includes a proposal for interpreting in vivo MRI data from human brain at variable magnetic fields, where the FFC relaxation analysis suggests that brain white-matter is distinct from grey-matter, in agreement with diffusion-weighted MRI imaging.

Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments

Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions. These fluctuate due to translational displacements and to a lesser degree also by rotational reorientations in the short-range limit. The analysis of the inter-molecular proton spin-lattice relaxation rate thus permits one to evaluate self-diffusion variables such as the diffusion coefficient or the mean square displacement on a time scale from nanoseconds to several hundreds of microseconds. Numerous applications to solvents, plastic crystals and polymers will be reviewed. The technique is of particular interest for polymer dynamics since inter-molecular spin-lattice relaxation diffusometry bridges the time scales of quasi-elastic neutron scattering and field-gradient NMR diffusometry. This is just the range where model-specific intra-coil mechanisms are assumed to occur. They are expected to reveal themselves by characteristic power laws for the time-dependence of the mean-square segment displacement. These can be favorably tested on this basis. Results reported in the literature will be compared with theoretical predictions. On the other hand, there is a second way for translational diffusion phenomena to affect the spin-lattice relaxation dispersion. If rotational diffusion of molecules is restricted, translational diffusion properties can be deduced even from molecular reorientation dynamics detected by intra-molecular spin-lattice relaxation. This sort of scenario will be relevant for adsorbates on surfaces or polymer segments under entanglement and chain connectivity constraints. Under such conditions, reorientations will be correlated with translational displacements leading to the so-called RMTD relaxation process (reorientation mediated by translational displacements). Applications to porous glasses, protein solutions, lipid bilayers, and clays will be discussed. Finally, we will address the intriguing fact that the various time limits of the segment mean-square displacement of polymers in some cases perfectly reproduce predictions of the tube/reptation model whereas the reorientation dynamics suggests strongly deviating power laws.

Explicit calculation of nuclear-magnetic-resonance relaxation rates in small pores to elucidate molecular-scale fluid dynamics

Nuclear-magnetic-resonance (NMR) spin-lattice (T_{1}^{-1}) and spin-spin (T_{2}^{-1}) relaxation rate measurements can act as effective nondestructive probes of the nanoscale dynamics of ^{1}H spins in porous media. In particular, fast-field-cycling T_{1}^{-1} dispersion measurements contain information on the dynamics of diffusing spins over time scales spanning many orders of magnitude. Previously published experimental T_{1}^{-1} dispersions from a plaster paste, synthetic saponite, mortar, and oil-bearing shale are reanalyzed using a model and associated theory which describe the relaxation rate contributions due to the interaction between spin ensembles in quasi-two-dimensional pores. Application of the model yields physically meaningful diffusion correlation times for all systems. In particular, the surface diffusion correlation time and the surface desorption time take similar values for each system, suggesting that surface mobility and desorption are linked processes. The bulk fluid diffusion correlation time is found to be two to five times the value for the pure liquid at room temperature for each system. Reanalysis of the oil-bearing shale yields diffusion time constants for both the oil and water constituents. The shale is found to be oil wetting and the water T_{1}^{-1} dispersion is found to be associated with aqueous Mn^{2+} paramagnetic impurities in the bulk water. These results escalate the NMR T_{1}^{-1} dispersion measurement technique as the primary probe of molecular-scale dynamics in porous media yielding diffusion parameters and a wealth of information on pore morphology.

Nuclear-magnetic-resonance relaxation due to the translational diffusion of fluid confined to quasi-two-dimensional pores

Nuclear-magnetic-resonance (NMR) relaxation experimentation is an effective technique for nondestructively probing the dynamics of proton-bearing fluids in porous media. The frequency-dependent relaxation rate T_{1}^{-1} can yield a wealth of information on the fluid dynamics within the pore provided data can be fit to a suitable spin diffusion model. A spin diffusion model yields the dipolar correlation function G(t) describing the relative translational motion of pairs of ^{1}H spins which then can be Fourier transformed to yield T_{1}^{-1}. G(t) for spins confined to a quasi-two-dimensional (Q2D) pore of thickness h is determined using theoretical and Monte Carlo techniques. G(t) shows a transition from three- to two-dimensional motion with the transition time proportional to h^{2}. T_{1}^{-1} is found to be independent of frequency over the range 0.01-100 MHz provided h≳5 nm and increases with decreasing frequency and decreasing h for pores of thickness h<3 nm. T_{1}^{-1} increases linearly with the bulk water diffusion correlation time τ_{b} allowing a simple and direct estimate of the bulk water diffusion coefficient from the high-frequency limit of T_{1}^{-1} dispersion measurements in systems where the influence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surface-to-bulk desorption rates for a thin pore. G(t) is found to decorrelate when spins move from the surface to the bulk, display three-dimensional properties at intermediate times, and finally show a bulk-mediated surface diffusion (Lévy) mechanism at longer times. The results may be used to interpret NMR relaxation rates in hydrated porous systems in which the paramagnetic impurity density is negligible.

Model for the interpretation of nuclear magnetic resonance relaxometry of hydrated porous silicate materials

Nuclear magnetic resonance (NMR) relaxation experimentation is an effective technique for probing the dynamics of proton spins in porous media, but interpretation requires the application of appropriate spin-diffusion models. Molecular dynamics (MD) simulations of porous silicate-based systems containing a quasi-two-dimensional water-filled pore are presented. The MD simulations suggest that the residency time of the water on the pore surface is in the range 0.03-12 ns, typically 2-5 orders of magnitude less than values determined from fits to experimental NMR measurements using the established surface-layer (SL) diffusion models of Korb and co-workers [Phys. Rev. E 56, 1934 (1997)]. Instead, MD identifies four distinct water layers in a tobermorite-based pore containing surface Ca2+ ions. Three highly structured water layers exist within 1 nm of the surface and the central region of the pore contains a homogeneous region of bulklike water. These regions are referred to as layer 1 and 2 (L1, L2), transition layer (TL), and bulk (B), respectively. Guided by the MD simulations, a two-layer (2L) spin-diffusion NMR relaxation model is proposed comprising two two-dimensional layers of slow- and fast-moving water associated with L2 and layers TL+B, respectively. The 2L model provides an improved fit to NMR relaxation times obtained from cementitious material compared to the SL model, yields diffusion correlation times in the range 18-75 ns and 28-40 ps in good agreement with MD, and resolves the surface residency time discrepancy. The 2L model, coupled with NMR relaxation experimentation, provides a simple yet powerful method of characterizing the dynamical properties of proton-bearing porous silicate-based systems such as porous glasses, cementitious materials, and oil-bearing rocks.

Nuclear magnetic resonance relaxometry of water in two and quasi-two dimensions

Molecular dynamics (MD) and Monte Carlo (MC) methods are used to determine the spin-pair correlation function G(*)(t) for the diffusion of bulk water in three dimensions (3D) and pore water in two dimensions (2D) and quasi-two dimensions (Q2D). The correlation function is required for the determination of the nuclear magnetic resonance spin-lattice and spin-spin relaxation times T(1) and T(2). It is shown that the analytic form of the powder-average correlation function, introduced by Sholl [Sholl, J. Phys. C: Solid State Phys. 7, 3378 (1974)] for the diffusion of spins on a 3D lattice, is of general validity. An analytic expression for G(*)(t) for a uniform spin fluid is derived in 2D. An analytic expression for the long-time behavior of G(*)(t) is derived for spins diffusing on 3D, 2D, and Q2D lattices. An analytic correction term, which accounts for spin pairs outside the scope of the numerical simulations, is derived for 3D and 2D and shown to improve the accuracy of the simulations. The contributions to T(1) due to translational and rotational motion obtained from the MD simulation of bulk water at 300 K are 7.4 s and 10±1 s, respectively, at 150 MHz, leading to an overall time of 4.3±0.4 s compared to the experimental value of 3.8 s. In Q2D systems, in which water is confined by alpha-quartz surfaces to thicknesses of 1-5 nm, T(1) for both translational and rotational relaxation is reduced due to the orientation and adsorption of spins at the surfaces. A method of parametrizing the MC lattice-diffusion simulations in 3D, 2D, and Q2D systems is presented. MC results for G(*)(t) for 3D and 2D systems are found to be consistent with an analytic uniform fluid model for t~/>40 ps. The value of TT(1) for translational diffusion obtained from the MC simulation of bulk water is found to be 4.8 s at 15 MHz. G(*)(t) obtained from MC simulations of Q2D systems, where water is confined by hard walls, is found to execute a distinct transition from 3D to 2D behavior. The T(1) is found to be similar to the 3D bulk water result at all pore thicknesses.

Dynamics of Liquids in Confined Geometries

An overview of several NMR studies of liquids in confined geometries is presented. First, the NMR relaxation rates, 1/T1, 1/T1ρ , and 1/T2 were measured for several molecular liquids confined to porous silica glasses with pore radii in the range from 12 Å to 100 Å as a function of temperature, pore size, and frequency. The experimental relaxation data were interpreted in terms of bulk, surface, and topological contributions using the following expression:

where 1/Tib and 1/Tis are the bulk and the surface layer relaxation rates, ε is the thickness of the surface layer, R is the pore radius, and Ai(ω) represents the pure topological effect.

Second, the pressure effects on the dynamics of the confined liquid of acetonitrile-d3 were also investigated. Third, the natural abundance of 13C spin lattice relaxation rates for CS2 confined to porous silica glasses provided information about confinement effects on the angular momentum behavior of this simple liquid.

Temperature-induced hydrophobic-hydrophilic transition observed by water adsorption

The properties of nanoconfined and interfacial water in the proximity of hydrophobic surfaces play a pivotal role in a variety of important phenomena such as protein folding. Water inside single-walled carbon nanotubes (SWNTs) can provide an ideal system for investigating such nanoconfined interfacial water on hydrophobic surfaces, provided that the nanotubes can be opened without introducing excess defects. Here, we report a hydrophobic-hydrophilic transition upon cooling from 22 degrees C to 8 degrees C via the observation of water adsorption isotherms in SWNTs measured by nuclear magnetic resonance. A considerable slowdown in molecular reorientation of such adsorbed water was also detected. The observed transition demonstrates that the structure of interfacial water could depend sensitively on temperature, which could lead to intriguing temperature dependences involving interfacial water on hydrophobic surfaces.

Water dynamics in ionomer membranes by field-cycling NMR relaxometry

The dynamic behavior of water within two types of ionomer membranes, Nafion and sulfonated polyimide, has been investigated by field-cycling nuclear magnetic relaxation. This technique, applied to materials prepared at different hydration levels, allows the proton motion on a time scale of microseconds to be probed. The NMR longitudinal relaxation rate R(1) measured over three decades of Larmor angular frequencies omega is particularly sensitive to the host-water interactions and thus well-suited to study fluid dynamics in restricted geometries. In the polyimide membranes, we have observed a strong dispersion of R(1)(omega) following closely a 1/square root omega law in a low-frequency range (correlation times from 0.1 to 10 micros). This is indicative of a strong interaction of water with "interfacial" hydrophilic groups of the polymeric matrix (wetting situation). Variations of the relaxation rates with water uptake reveal a two-step hydration process: solvation and formation of disconnected aqueous clusters near polar groups, followed by the formation of a continuous hydrogen bond network. On the contrary, in the Nafion we observed weak variations of R(1)(omega) at low frequencies. This is typical of a nonwetting behavior. At early hydration stages, R(1)(omega) evolves logarithmically, suggesting a confined bidimensional diffusion of protons in the microsecond time range. Such an evolution is lost at higher swelling where a plateau related to three-dimensional diffusion is observed.

Water dynamics in ionomer membranes by field-cycling NMR relaxometry

The dynamic behavior of water within two types of ionomer membranes, Nafion and sulfonated polyimides, has been investigated by field-cycling nuclear magnetic relaxation. This technique, applied to materials prepared at different hydration levels, allows to probe the proton motion on a time scale of the microsecond. The NMR longitudinal relaxation rate R(1) measured over three decades of Larmor angular frequencies omega is particularly sensitive to the host-water interactions and thus well suited to study fluid dynamics in restricted geometries. In the polyimide membranes, we have observed a strong dispersion of R(1)(omega) following closely a 1/sqrt[omega] law in a low-frequency range (correlation times from 0.1 to 10 micros). This is indicative of a strong interaction of water with "interfacial" hydrophilic groups of the polymeric matrix (wetting situation). On the contrary, in the Nafion, we observed weak variations of R(1)(omega) at low frequency. This is typical of a nonwetting behavior. At early hydration stages, the proton-proton inter-dipolar contribution to R(1)(omega) evolves logarithmically, suggesting a confined bidimensional diffusion of protons in the microsecond time range. Such an evolution is lost at higher swelling where a plateau related to 3D diffusion is observed.

Phase Diagram and Glass Transition of Confined Benzene

We used differential scanning calorimetry, neutron scattering, and proton NMR to investigate the phase behavior, the structure, and the dynamics of benzene confined in a series of cylindrical mesoporous materials MCM-41 and SBA-15 with pore diameters, d, between 2.4 and 14 nm. With this multitechnique approach, it was possible to determine the structure and, for the first time to our knowledge, the density of confined benzene as a function of temperature and pore size. Under standard cooling rates, benzene partially crystallizes in SBA-15 matrixes (4.7 <or= d <or= 14 nm) but not in MCM-41 (2.4 <or= d <or= 3.5 nm). Structure factors of the confined phases were recorded at different temperatures and compare to those of the bulk. The confined liquid has the same structure as the bulk above the bulk melting point. In SBA-15, the confined crystals are defective and have the same structure as the bulk. In MCM-41, the liquid undergoes a glass transition at low temperature regardless of the cooling rate or the thermal history of the sample. The density as a function of temperature was measured by neutron scattering contrast matching, and the glass transition temperatures were determined from the density versus temperature curves. The pore size dependence of T(g) does not show any evidence of finite size effects. A temperature versus pore diameter phase diagram of confined benzene is proposed combining liquid, supercooled liquid, crystal states, and glassy states. NMR relaxation time measurements showed that the dynamics of the confined liquids are slower than those of the bulk above its melting point. In the partially crystallized samples, the liquid and the crystal have the same relaxation times. The activation energies of reorientation motions in the confined phases, determined from spin lattice relaxation times, are smaller than the bulk ones.

Spin-lattice NMR relaxation by anomalous translational diffusion

A model-free theoretical framework for a phenomenological description of spin-lattice relaxation by anomalous translational diffusion in inhomogeneous systems based on the fractional diffusion equation is developed. The dependence of the spin-lattice relaxation time on the size of the pores in porous glass Vycor is experimentally obtained and found to agree well with our theoretical predictions. We obtain nonmonotonic behavior of the translational spin-lattice relaxation rate constant (it passes through a maximum) with the variation of the parameter referring to the extent of inhomogeneity of the system.

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.

Molecular dynamics of tert-butyl chloride confined in CPG studied by NMR

The molecular dynamics of tert-butyl chloride (TBC) confined to Controlled Pore Glass matrices of 25 and 7.5 nm were investigated by measuring NMR linewidths, lineshapes, and 1H and 2H spin--lattice relaxation times. The behaviour of confined TBC can be explained assuming that the guest molecules form two distinct phases; the surface-affected phase, composed of molecules located at the pore surface, and the bulk-like phase located at the centre of the pores. The bulk-like component of confined TBC, at the temperatures corresponding to the phase III, is characterized by two dynamically different subphases.

Surface nuclear magnetic relaxation and dynamics of water and oil in granular packings and rocks

Low field proton nuclear spin-relaxation at variable magnetic field strength and temperature provides surface dynamical parameters such as surface diffusion coefficients, activation energies, time of residence and coefficient of surface affinity. These parameters were extracted from measurements on grain packs and natural oil-bearing rocks. On grain packs, we show first that changing the amount of surface paramagnetic impurities leads to striking different relationships between the pore-size and the relaxation times T1 and T2. These relationships are well supported by fast-diffusion (surface-limited) or slow-diffusion relaxation models. Surface relaxivity parameters rho1 and rho2 are deduced from the pore size dependence in the fast-diffusion regime. Then, we evidence the frequency and temperature dependence of the surface relaxivity rho1 by field cycling NMR relaxation and relevant theoretical models. The typical frequency dependence found allows an experimental separation of the surface and bulk microdynamics in granular packings and petroleum rocks and the determination of the above mentioned surface dynamical parameters. Finally, we present the first field cycling nuclear spin relaxation experiments performed in water/oil saturated petroleum rocks. We believe that these experiments give new information about the surface localization of these two saturating liquids in pores.

Surface nuclear magnetic relaxation and dynamics of water and oil in macroporous media

Proton nuclear spin-relaxation studies on water- or oil-saturated granular packings and limestone rocks allow estimating surface molecular dynamical parameters. Measurements were performed at various conditions of temperature, magnetic field strengths, and pore size. We show by low field NMR relaxation that changing the amount of surface paramagnetic impurities leads to striking different pore-size dependences of the relaxation times T1 and T2 of liquids in pores. These dependences are well supported by surface-limited or diffusion-limited relaxation models. Surface relaxivity parameters rho(1) and rho(2) are deduced from the pore-size dependence in the surface-limited regime. We evidence the frequency and temperature dependence of the surface relaxivity rho(1) by field cycling NMR relaxation and relevant theoretical models. The typical frequency dependence found allows an experimental separation of the surface and bulk microdynamics in porous media. Several surface dynamical parameters, such as diffusion coefficients, activation energies, time of residence, and coefficient of surface affinity, were therefore determined. The methods presented here give a powerful analysis of the surface microdynamics of confined liquids, which can be applied to the study of oil-bearing rocks.

High-resolution magnetic relaxation dispersion measurements of solute spin probes using a dual-magnet system

The magnetic field dependence of the nuclear spin-lattice relaxation rate provides a detailed report of the spectral density functions that characterize the intra- and intermolecular fluctuations that drive magnetic relaxation. We have addressed the difficult sensitivity and resolution problems associated with low magnetic field strengths by using two magnets in close proximity and shielded from each other. The sample is stored in the high magnetic field, pneumatically driven to the variable satellite field, then returned to the high field for detection at high resolution. A magnetic shield effectively decouples the two magnets so that varying the satellite field strength has minimal effect on the field strength and shim of the high field magnet. The disadvantage of the sample-shuttle magnet-pair system is the restriction imposed on the relaxation times by the finite shuttle times. Experiments not described here have shown this rate maximum to be about 20 s(-1) for most practical solutions. However, we demonstrate here that the sensitivity gains over switched-current magnet systems permit characterization of solute inter- and intramolecular dynamics over the time scale range from tens of microseconds to less than a picosecond. This range permits investigation of a number of crucial chemical dynamics questions, while high sensitivity permits examination of a variety of solute spins. Representative data are presented for (1)H, (111)Cd, and (7)Li.

Translational diffusion of liquids at surface of microporous materials: new theoretical analysis of field cycling magnetic relaxation measurements

1H spin-lattice relaxation rates of several aprotic polar liquids on calibrated microporous chromatographic glass beads that have paramagnetic ion impurities are recorded over magnetic field strengths using a field-switched magnetic relaxation dispersion spectrometer. The typical bilogarithmic magnetic field dependence of these rates supports quantitatively our theory of nuclear paramagnetic relaxation and gives the translational diffusion at the surface of nanopores. Our results demonstrate that magnetic relaxation dispersion at low magnetic field strengths in high surface area heterogeneous systems may be quantitatively understood in terms of the parameters of the spatial confinement and the local translational dynamics.

Magnetic cross-relaxation and chemical exchange between microporous solid and mobile liquid phases

Nuclear magnetic spin-lattice relaxation rates are reported as a function of magnetic field strength, pH, and temperature for water protons in Sephadex gels. The water proton rates report the relaxation profile characteristic of the solid at high pH values. At lower pH values, the relaxation rate is limited by a slow chemical exchange process that makes the relaxation rate independent of magnetic field at low field strengths. In cases where the proton exchange rate does not limit the total relaxation rate, the magnetic field dependence of the relaxation rate is given by a power law of the type R = Av-B, where B is 0.75 except at pH 11 where the data are better represented with B = 0.5. The exchange events important for the water proton relaxation are represented as a two-stage process in which water within the pores of the gel exchanges protons and magnetization with the solid spin system rapidly compared with the rate at which the water within the pores exchanges with the bulk water phase.

Quenched molecular reorientation and angular velocity in nanopores

A theoretical treatment shows how the orientational dependent and spin rotation relaxation rates of a confined nonpolar liquid depend on the average pore size. Experimental nuclear relaxation data on carbon disulfide and cyclohexane in a set of calibrated porous glasses support the theory.

Nuclear relaxation of liquids in confinements

We study theoretically the effects of geometrical confinement on the dipolar relaxation of a non-interacting liquid in porous media. Application to the 1H relaxation of methylcyclohexane liquid in porous silica glasses is given. The case of an interacting liquid is considered by molecular dynamics simulations. Geometrical confinement and surface interaction lead to similar frequency behaviour of relaxation rates according to the layering of local density and anisotropy of the molecular mobility.

Characterisation of wetting heterogeneities in sandstone rocks by MRI

MRI is applied to the visualisation of wetting heterogeneities evidenced by water proton T1 contrast at 0.1 T. Water saturated Fontainebleau sandstone samples were examined either in their original water-wet condition, or after silanation. T1, T2Hahn, and T2CPMG were measured for several porosities. T1 and T2CPMG of hydrophobic samples are both twice longer than those of hydrophilic ones. This good contrast allows us to observe wetting heterogeneities in T1-profiles and T1-weighted images.