Pressure-driven molecular dynamics simulations of water transport through a hydrophilic nanochannel

ABSTRACT

Transport of fluids inside porous materials is relevant to many fields of application. Non-equilibrium molecular dynamics simulation is a powerful technique to explore fluid transport through porous media at the molecular scale. In this work, we compared two commonly used methods for studying pressure-driven transport. The first method was based on the application of an external force field on each fluid particle. The second method made use of two movable walls, acting as pistons, so as to generate transport. These two methods were used to study water transport inside a cylindrical hydrophilic silica nanopore. Several pressure differences were considered from 20 bar to 1000 bar. The results were compared to the theoretical Poiseuille fluid flow. No significant difference was found between the two methods. However, a substantial water flow enhancement was observed compared with the theoretical flow. Both the structural and dynamical properties of water remained unaffected by the applied pressure difference.     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

低场核磁共振：弛豫和扩散的多维实验

近年来，低场核磁共振日益展示其在弛豫与扩散测量中的有效应用。在材料研究领域，诸如催化剂的研制、水泥的水化、岩石及土壤中的液体输运等，以及地质勘探和医疗诊断学中的人体组织性质的表征方面，核磁共振的弛豫与扩散测量都十分重要。特别是此技术在多维度方法方面的发展，大大促进了其在多孔材料方面的应用。多孔材料在人们生活的环境中无所不在，其微结构（微米级至毫米级）对于其性质和应用方面，具有决定性的作用。该文概述低场核磁共振的弛豫及扩散的多维度技术的基本原理、核磁共振方法学及其应用的若干关键性进展。     

Correlation functions for inhomogeneous magnetic field in random media with application to a dense random pack of spheres

In porous media subject to applied magnetic field, the internal field arises out of susceptibility contrast of the constituents. We have examined the spatial inhomogeneity of the internal fields in a random pack of spheres using numerical computation. We find that the pair-correlation function of the internal field (K2) is a close approximation to the structure factor of the material, thus K2 can be used to characterize pore geometry. The magnetic length scale LambdaM exhibited in K2 is shown to be related to the fluid transport in the medium.     

Fast-field-cycling NMR: Applications and instrumentation

Magnetic field cycling in nuclear magnetic resonance (NMR) experiments has been used since the early days of NMR. Originally such time-dependent magnetic field experiments were motivated to study cross relaxation, spin system thermodynamics and indirect detection of quadrupolar resonance. The first apparatus used mechanical or pneumatic systems to shoot the sample between two magnets, the typical “flying time” being a few hundreds of milliseconds. As a natural evolution of the experimental technique and the need to extend its application to samples with higher relaxation rates, faster magnetic field switching devices were developed during the last years. Special electric networks combined with sophisticated air core magnets allowed one to switch magnetic fields between zero and fields of the order of 0.5 T in a few milliseconds. Today we refer to this new generation of instruments as “fast-field-cycling” devices. The technique has been successfully used during the last years to obtain information on the molecular dynamics and order in different materials, ranging from organic solids, metals, polymers, liquid crystals, porous media to biological systems. At present it is also turning to be an important tool for the design of contrast agents for magnetic resonance imaging. Fast field cycling was mainly oriented toT ₁ relaxometry as a unique technique offering a dynamic window of several decades, ranging from few kilohertz to several megahertz. However, there exist less conventional applications of the technique that can also provide relevant information concerning molecular dynamics, structure and molecular order. In this article we will briefly deal with basic aspects of the technique, its evolution, present-day relevant applications and the last improvements concerning specialized instrumentation.     

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.     

Molecular mobility in fixed-bed reactors investigated by multiscale NMR techniques

The complex problem of a fixed-bed reactor consisting of catalytically active particles provides an exceptional opportunity of combining a wide range of NMR methods which have become available over time as tools to probe porous media. This work demonstrates the feasibility of different NMR techniques for the investigation of the intra- and interparticle pore space over length scales from nanometers up to centimeters. Many industrially relevant cracking reactions leave a coke residue on the inner surface of the porous catalyst particles so that the active sites become inaccessible to the reactants. Moreover, the pore space shrinks due to the formation of coke, thereby hindering molecular transport. The presence of the coke residue and its influence on the mobility of adsorbed fluid molecules are probed by 129Xe spectroscopy, NMR cryoporometry, relaxation dispersion measurements, and investigations of the reduced diffusivity in the intraporous space. The voids surrounding the random arrangement of catalyst pellets represent another pore space of much larger dimensions, the properties of which can be more directly investigated by mapping the fluid density and the velocity distribution from velocity-encoded imaging. Propagator representations averaged over large sample volumes are discussed and compared to velocity images obtained in selected axial slices of the reactor.     

Transport of a cathodic arc plasma in a straight, magnetized duct

Measurements are presented of the transport of a supersonic, cathodic-arc plasma through a straight, magnetized duct. These measurements are compared to previous work on curved ducts, in order to illuminate the effect of duct curvature on the transport. The axial ion flux through the straight duct decays as ions are lost to the walls. This decay is exponential, with a scale length of seven duct radii; this is two to three times longer than in most experiments on curved ducts. The scale length is independent of the magnetic field strength for fields from 5-40 mT. (For this range of magnetic fields, the electron Larmor radius varies from 0.03-0.003 duct radii; while the ion Larmor radius varies from 4-0.5 duct radii.) This differs from previous experiments with curved ducts, where the attenuation length generally increases with magnetic field. Also in contrast to experiments on curved ducts, biasing the duct wall to positive voltages similar to the ion energy produces only a slight decrease in the ion losses to the wall. The observed scale length for ion loss and its independence from the magnetic field strength are in quantitative agreement with a plasma fluid simulation. Differences in plasma transport through straight and curved ducts are discussed     

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.     

固态高分子体系多尺度分子运动的核磁共振研究

固体核磁共振技术是研究固态高分子材料中结构和分子动力学的一种非常重要和有效的手段. 该技术的一个重要特点是可以通过合理的实验方法,实现对研究体系中从低频(Hz)到中频(kHz)乃至高频(MHz)范围内分子运动的观测. 因此,固体核磁共振技术非常适合研究高分子体系中各类不同尺度分子运动. 该文首先简要介绍核磁共振研究分子运动的基本原理和方法,以及固态高分子体系的结构和分子动力学特点,然后结合固态高分子体系中的一些例子对核磁共振在固态高分子多尺度分子运动方面的一些研究成果展开讨论.     

Effect of impermeable interfaces on apparent diffusion coefficient in heterogeneous media

It is known that the short-time behavior of the diffusion coefficient, which is measurable by nuclear magnetic resonance (NMR), provides an estimate of the specific surface of porous samples filled with an NMR-detectable fluid. This method is not directly applicable to the exploration of structure of impermeable restrictions in mixtures such as living tissues, in which the inherent microscopic structure in the bulk medium results in the same pattern of the temporal dynamics of the diffusion coefficient as the impermeable restrictions studied. Here, an approach to describe diffusion and the boundary effect in heterogeneous media is developed in the framework of a cumulant expansion of the NMR signal. The leading term of this expansion is determined by the velocity autocorrelation function which is expressed in terms of properties of microscopic transport in the medium. Given these properties, the apparent diffusion coefficient as measured by NMR can be found by a straightforward integration. Calculations are performed in one spatial dimension.     

Slow dynamics of embedded fluid in mesoscopic confining systems as probed by NMR relaxometry

Mesoscopic media such as porous materials or colloidal dispersions strongly influence the dynamics of the embedded fluid. In the strong-adsorption regime, it was recently proposed that the effective surface diffusion on flat surface is anomalous and exhibits long-time pathology, enlarging the time domain of the embedded-fluid dynamics towards the low-frequency regime. An interesting way to probe such a slow interfacial process is to use the field-cycling NMR relaxometry. This technique is used here to probe the fluid dynamics in two types of interfacial systems: i) a colloidal glass made of thin and flat particles; ii) a fully saturated porous media, the Vycor glass. Experimental results are critically compared to either a simple theoretical model of NMR dispersion involving elementary steps of the fluid dynamics near an interface (loops, trains, tails) or Brownian-dynamics simulations performed inside 3D reconstructions of these confined systems.Received: 1 January 2003, Published online: 14 October 2003PACS: 76.60.Es Relaxation effects - 61.43.Gt Powders, porous materials - 82.70.Dd Colloids     

Quantum mechanical and molecular mechanical simulation approaches bridging length and time scales for simulation of interface reactions in realistic environments

Computer-assisted design of functional materials requires methods that are able to simultaneously describe these with the necessary accuracy at the relevant time and length scales. One such possibility is the combination of classical interatomic force fields with density-functional based tight-binding (DFTB), an efficient and accurate quantum method. We employ this combination to study porous silicon dioxide functionalized with imidazole, which is used as an additive to polymer electrolyte membranes (PEM) for fuel cells applications. We analyze the water density and the dynamics of the functional groups at different temperatures by molecular dynamics simulation, whereas we calculate DFTB free energy barriers for proton transport reactions within the functionalized surface at different water contents. Combining both results, a macroscopic picture of the proton diffusion is drawn. Furthermore, we simulate the adsorption reactions of different components of an epoxide adhesive system on gamma alumina, using a direct coupling of DFTB and classical modeling. This yields direct chemical insight, how water and excess protons at the interface weaken the adhesion between epoxy polymers and natively oxidized aluminium.     

NMR 1D-imaging of water infiltration into mesoporous matrices

It is shown that coupling nuclear magnetic resonance (NMR) 1D-imaging with the measure of NMR relaxation times and self-diffusion coefficients can be a very powerful approach to investigate fluid infiltration into porous media. Such an experimental design was used to study the very slow seeping of pure water into hydrophobic materials. We consider here three model samples of nuclear waste conditioning matrices which consist in a dispersion of NaNO₃ (highly soluble) and/or BaSO₄ (poorly soluble) salt grains embedded in a bitumen matrix. Beyond studying the moisture progression according to the sample depth, we analyze the water NMR relaxation times and self-diffusion coefficients along its 1D-concentration profile to obtain spatially resolved information on the solution properties and on the porous structure at different scales. It is also shown that, when the relaxation or self-diffusion properties are multimodal, the 1D-profile of each water population is recovered. Three main levels of information were disclosed along the depth-profiles. They concern (i) the water uptake kinetics, (ii) the salinity and the molecular dynamics of the infiltrated solutions and (iii) the microstructure of the water-filled porosities: open networks coexisting with closed pores. All these findings were fully validated and enriched by NMR cryoporometry experiments and by performing environmental scanning electronic microscopy observations. Surprisingly, results clearly show that insoluble salts enhance the water progression and thereby increase the capability of the material to uptake water.     

Hyperfine interaction studies of amorphous materials using NMR

Through hyperfine interactions the electronic structure of amorphous materials can be investigated by NMR. Furthermore, the local character of these interactions makes them adequate to study the local environment and the local symmetry around the probe nuclei through the measurement of hyperfine fields and electric field gradients. We review recent NMR studies of amorphous metals from the following two points of view: (1) Electronic structure: Knight shifts and spin relaxation times in paramagnetic materials and hyperfine fields in ferromagnetic materials. (2) Local amorphous structure: topological and chemical short-range order. Emphasis will be given to the comparisons between amorphous materials and corresponding crystalline materials.     

Random-walk technique for simulating NMR measurements and 2D NMR maps of porous media with relaxing and permeable boundaries

We revisit random-walk methods to simulate the NMR response of fluids in porous media. Simulations reproduce the effects of diffusion within external inhomogeneous background magnetic fields, imperfect and finite-duration B(1) pulses, T(1)/T(2) contrasts, and relaxing or permeable boundaries. The simulation approach consolidates existing NMR numerical methods used in biology and engineering into a single formulation that expands on the magnetic-dipole equivalent of spin packets. When fluids exhibit low T(1)/T(2) contrasts and when CPMG pulse sequences are used to acquire NMR measurements, we verify that classical NMR numerical models that neglect T(1) effects accurately reproduce surface magnetization decays of saturated granular porous media regardless of the diffusion/relaxation regime. Currently, analytical expressions exist only for the case of arbitrary pore shapes within the fast-diffusion limit. However, when fluids include several components or when magnetic fields are strongly inhomogeneous, we show that simulations results obtained using the complete set of Bloch's equations differ substantially from those of classical NMR models. In addition, our random-walk formulation accurately reproduces magnetization echoes stemming from coherent-pathway calculations. We show that the random-walk approach is especially suited to generate parametric multi-dimensional T(1)/T(2)/D NMR maps to improve the characterization of pore structures and saturating fluids.     

Hole-burning NMR in strongly inhomogeneous fields

Different pulse sequences for frequency-selective NMR in the highly inhomogeneous fields of single-sided NMR are explored. A modified Hahn-echo is used to burn a hole in the spectrum of the detected echo. The hole diminishes following molecular dynamics on the scale of the echo time. Preliminary experiments were performed on pure water and natural rubber with the NMR-MOUSE. The results demonstrate the feasibility of hole burning to study slow molecular dynamics by mobile NMR in strongly inhomogeneous magnetic fields.     

Porous media characterization by PFG and IMFG NMR

Fully and partially filled with tridecane quartz sand was studied by different NMR techniques. The set of NMR experiments was carried out to obtain information about porous media geometry and fluid localization in it in case of partially filled porous space. The study was done using three NMR approaches: pulse field gradient NMR (PFG NMR), DDif experiment and tau-scanning experiment. The possibility to use all three approaches to study porous media properties even at the high resonance frequency is shown together with complementarity of the given by them information. Thus, first two approaches give information about porous sizes and geometry, at the same time tau-scanning experiment allows us to obtain information about distribution of internal magnetic field gradients in the porous space and draw conclusions about fluid localization in it.