Measurement of diffusion coefficients in polystyrene using xenon-129 NMR

A sample of polystyrene beads, 18 μm in diameter, has been sealed in an NMR tube under 10 atm of xenon gas. Two dimensional,¹²⁹Xe NMR spectra show cross peaks between the resonances corresponding to xenon in the free gas and the sorbed state, indicating that appreciable exchange occurs during the mixing time of the NMR experiment. Selective saturation of the free gas resonance attenuates the integrated intensity of the sorbed xenon resonance as a function of saturation time, thus allowing the accurate measurement of the exchange rates between the gas and the sorbed states. A model has been developed using a slightly modified form of Crank’s treatment of diffusion in a sphere which allows for the accurate determination of the diffusion coefficient for xenon in the sorbed state. The diffusion coefficient for xenon in polystyrene at 25°C is determined to be 2.9·10^?9 cm²/s.     

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter.     

129Xe NMR studies of the dynamics of xenon in siliceous ZSM-12 zeolite

The adsorption of xenon in siliceous zeolite ZSM-12 has been studied by static, magic angle spinning and 2D-EXSY¹²⁹Xe NMR. Anisotropic lines were observed with parameters dependent on the Xe loading and the temperature of the experiment. The observed dependence of the isotropic chemical shift is at variance with the predictions of the mean-free-path model, which casts further doubt on the applicability of this model to the interpretation of Xe NMR data in porous systems. Based on the continuous changes of anisotropic parameters with the loading, we conclude that there are several adsorption sites for xenon in the pores. A qualitative model for the distribution and rapid exchange of the xenon atoms between several sites is discussed. The observed lines arise from a dynamic average of the chemical shift tensors for the different types of site weighted by their populations. 2D-EXSY spectra show two kinds of slow exchange of Xe: (a) particle to particle and, (b) particle to interparticle gas phase.     

Analysis of porosity in porous silicon using hyperpolarized 129Xe two-dimensional exchange experiments

The porosity in porous silicon was characterized using hyperpolarized (HP) xenon as a probe. HP xenon under conditions of continuous flow allows for the rapid acquisition of xenon NMR spectra that can be used to characterize a variety of materials. Two-dimensional exchange spectroscopy (EXSY) (129)Xe NMR experiments using HP xenon were performed to obtain exchange pathways and rates of xenon mobility between pores of different dimensions within the structure of porous silicon and to the gas phase above the sample. Pore sizes are estimated from chemical shift information and a model for pore geometry is presented.     

Pore-Structure Determinations of Silica Aerogels byXe NMR Spectroscopy and Imaging

Silica aerogels represent a new class of open-pore materials with pore dimensions on a scale of tens of nanometers, and are thus classified as mesoporous materials. In this work, we show that the combination of NMR spectroscopy and chemical-shift selective magnetic resonance imaging (MRI) can resolve some of the important aspects of the structure of silica aerogels. The use of xenon as a gaseous probe in combination with spatially resolved NMR techniques is demonstrated to be a powerful, new approach for characterizing the average pore structure and steady-state spatial distributions of xenon atoms in different physicochemical environments. Furthermore, dynamic NMR magnetization transfer experiments and pulsed-field gradient (PFG) measurements have been used to characterize exchange processes and diffusive motion of xenon in samples at equilibrium. In particular, this new NMR approach offers unique information and insights into the nanoscopic pore structure and microscopic morphology of aerogels and the dynamical behavior of occluded adsorbates. MRI provides spatially resolved information on the nature of the flaw regions found in these materials. Pseudo-first-order rate constants for magnetization transfer among the bulk and occluded xenon phases indicate xenon-exchange rate constants on the order of 1 s⁻¹for specimens having volumes of 0.03 cm³. PFG diffusion measurements show evidence of anisotropic diffusion for xenon occluded within aerogels, with nominal self-diffusivity coefficients on the order ofD= 10⁻³cm²/s.     

Combined Reduced 4D C Exchange and H Spin Diffusion Experiment for Determining the Length Scale of Dynamic Heterogeneities

A multidimensional static solid-state NMR experiment is described that combines 13C exchange sequences with 1H spin diffusion. It realizes a spatial correlation of different reorientation rates. By means of this experiment the length scale of dynamic heterogeneities can be measured directly. The pulse sequence and phase cycle as well as the experimental setup procedure and data analysis are described in detail. It complements the previous letter on this subject where a brief report of the main results were presented (U. Tracht et al., 1998, Phys. Rev. Lett. 81, 2727). Application of this experiment to an amorphous polymer in the supercooled state yields a length scale of immobile regions of about 3 nm.     

Lithium dynamics in LiMn2O4 probed directly by two-dimensional (7)Li NMR

LiMn2O4 has been studied using magic-angle-spinning nuclear magnetic resonance (MAS NMR). 1D MAS NMR shows three Li resonances assigned to different crystallographic sites. At low temperatures an extra peak appears, indicating charge ordering of Mn3+ and Mn4+. Direct observation of the lithium dynamics was possible using rotor-synchronized 2D exchange NMR. A millisecond time scale exchange of lithium starts around 285 K between the 8a and the 16c site. At 380 K lithium even starts to hop between more than two sites. The activation energies and Li jump rates are derived and are in agreement with those determined macroscopically.     

Probing proteins in solution by (129)Xe NMR spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by (129)Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia "Frontiers of NMR in Molecular Biology VI", Jan. 9--15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 "Optical Polarization and Xenon NMR of Materials", June 28--30, 2000, Sestri Levante, Italy, p. 46).     

Xenon NMR measurements of permeability and tortuosity in reservoir rocks

In this work we present measurements of permeability, effective porosity and tortuosity on a variety of rock samples using NMR/MRI of thermal and laser-polarized gas. Permeability and effective porosity are measured simultaneously using MRI to monitor the inflow of laser-polarized xenon into the rock core. Tortuosity is determined from measurements of the time-dependent diffusion coefficient using thermal xenon in sealed samples. The initial results from a limited number of rocks indicate inverse correlations between tortuosity and both effective porosity and permeability. Further studies to widen the number of types of rocks studied may eventually aid in explaining the poorly understood connection between permeability and tortuosity of rock cores.     

Probing Proteins in Solution by Xe NMR Spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by ¹²⁹Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia “Frontiers of NMR in Molecular Biology VI”, Jan. 9–15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 “Optical Polarization and Xenon NMR of Materials”, June 28–30, 2000, Sestri Levante, Italy, p. 46).     

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.     

129Xe NMR study of the homogeneity and the size distribution of small sodium metal particles in NaY zeolite

NaY zeolite samples loaded with sodium metal by vapor phase deposition have been investigated using¹²⁹Xe NMR spectroscopy. At low sodium concentration, the¹²⁹Xe NMR spectrum showed three resonance lines which clearly indicate the existence of distinct domains in the zeolite sample. Such an observation suggests that the diffusion of the xenon atoms into each domain only occurs with respect to the NMR time scale (2.9 ms). As the sodium concentration increases, observation of a single broad line indicate a macroscopic homogenization of the system. The shift of this line is explained in part due to a paramagnetic interaction between the xenon atoms and the unpaired electrons of particles containing an odd number of sodium atoms. The linewidth is due to the distribution of the local magnetic fields partially averaged by the rapid motion of the xenon atoms and to the statistical distribution of the sodium particles in the supercage cavities. The paramagnetic interaction vanishes with the oxidation of the sample leading to a narrowing and a shift of the line to higher magnetic fields.     

Sensitivity enhancement by exchange mediated magnetization transfer of the xenon biosensor signal

Hyperpolarized xenon associated with ligand derivatized cryptophane-A cages has been developed as a NMR based biosensor. To optimize the detection sensitivity we describe use of xenon exchange between the caged and bulk dissolved xenon as an effective signal amplifier. This approach, somewhat analogous to 'remote detection' described recently, uses the chemical exchange to repeatedly transfer spectroscopic information from caged to bulk xenon, effectively integrating the caged signal. After an optimized integration period, the signal is read out by observation of the bulk magnetization. The spectrum of the caged xenon is reconstructed through use of a variable evolution period before transfer and Fourier analysis of the bulk signal as a function of the evolution time.     

Surface effects on liquid crystals constrained in nanoscaled pores investigated by field cycling NMR relaxometry and Monte Carlo simulations

Proton relaxation rates of nematic liquid crystals confined in nanoporous cavities were measured in a broad frequency range with the help of field cycling nuclear magnetic resonance relaxometry. The shape of relaxation dispersion curves in confined materials strongly deviates from the behavior in bulk, both above and below the bulk isotropization temperature. A strong increase in relaxation rates, exceeding by two orders of magnitude that of the bulk sample, is observed in the range of a few kilohertz. Relaxation rates in bigger pores decreased. Experimental findings are interpreted in terms of surface-induced orientational order and diffusion between sites with different orientations of local directors. With the aid of Monte Carlo simulations, two processes affecting low-frequency relaxation could be identified: (a) exchange losses of molecules from the surface-ordered phase to the bulk-like phase, and (b) Reorientations Mediated by Translational Displacements, which dominate the long-time scale and account for the recovery of correlation in molecular orientations as molecules probe different surface sites. It is shown that the width of the oriented layer may strongly affect the slope of dispersion curves and that cross-over between plateau and power law dispersion regimes shifts towards lower frequencies for bigger pores.     

MAS NMR studies of carbon-13 spin exchange in durene

One- (1-D) and two-dimensional (2-D) carbon-13 NMR exchange measurements in powder samples of isotopically normal durene under magic angle spinning (MAS) are reported. The experiments include rotor synchronized 2-D exchange (RS2DE), 1-D magnetization transfer (MT) and time reverse ODESSA (tr-ODESSA). The latter two experiments were performed as a function of several external parameters, including proton decoupling field during mixing time, sample spinning rate and partly, of temperature. The effects of these parameters on the spin exchange induced by spin diffusion and by chemical, or physical exchange, is discussed. Spin exchange between all types of carbons in the durene molecules occurs on the time scale of seconds. From the dependence of the spin exchange rate on the external parameters it is concluded that the process is dominated by spin diffusion. On the basis of these results an upper limit of 10(-16) cm2 s(-1) can be set for the self-diffusion constant in crystalline durene.     

Product operator analysis of the influence of chemical exchange on relaxation rates

Measurements of chemical-exchange processes by NMR are widely used to obtain valuable information about molecular dynamics and structure. Here, a computational method is introduced to assess the influence of chemical exchange on spin relaxation rates. The method is based on the inclusion of a random exchange process in product operator calculations on a microscopic level. This product operator approach can be applied to estimate exchange contributions when using sophisticated pulse sequences that cannot be easily described analytically. The method applies to the full range of exchange times measurable by NMR and can incorporate interference effects between exchange and other processes such as scalar coupling. To demonstrate its utility, simulated relaxation data were compared with theoretical predictions of spin-locking and Carr-Purcell spin-echo sequences with hard and adiabatic pulses, using different time scales for a two-site chemical-exchange process. Finally, simulations were used to examine a system in which a second random process is superimposed on a simple two-site exchange process. The method was found to provide a simple and robust tool to analyze pulse sequences and equations commonly used to study exchange-induced relaxation.     

The exchange of hydrogen ions and of water molecules near the active site of cytochrome c

Three-pulse electron-spin-echo envelopes have been measured for frozen solution samples of horse heart ferric cytochrome c both before and after exchange against D₂0. The deuterium modulation pattern was enhanced relative to modulation patterns due to coupled ¹⁴N nuclei by dividing the envelope obtained with the nondeuterated sample into the envelope obtained with the deuterated sample. Measurements of the modulation depth were made by fitting single cycles of a decaying waveform having the free deuterium NMR period to early portions of the experimental quotient waveform. The observed modulation depth was compared with the depth calculated theoretically from X-ray crystallographic data. The good agreement obtained in this comparison demonstrates the reliability of the electron-spin-echo method as a means of studying the distance and/or distribution of exchangeable hydrogen nuclei in the vicinity of sufficiently well-characterized protein metal-ion active sites.     

129Xe and131Xe NMR of xenon on silica surfaces at 77 K

Little is known about¹²⁹Xe NMR spectral features and spin-lattice relaxation behavior, and the dynamics of xenon atoms, for xenon adsorbed on solid surfaces at cryogenic temperatures (≤77 K), where exchange with gas-phase atoms is not a significant complication. We report¹²⁹Xe NMR experiments at 9,4 T that provide such information for xenon adsorbed onto the hydroxylated surface of a number of microporous silica samples at 77 K. A convenient design for these cryogenic experiments is described. Dynamics of surface-adsorbed xenon atoms on the time scale of seconds can be observed by¹²⁹Xe NMR hole-burning experiments; much slower dynamics occurring over hours and days are evidenced from changes with time of the¹²⁹Xe NMR chemical shifts. The peak maxima occur in the region ca. 180–316 ppm, considerably downfield of¹²⁹Xe shifts previously reported on surfaces at higher temperatures, and closer to the shift of xenon bulk solid (316.4±1 ppm). The¹²⁹Xe spin-lattice relaxation timesT ₁ range over five orders of magnitude; possible explanations for both nonexponential relaxation behavior and extremely shortT ₁ values (35 ms) are discussed. Preliminary¹³¹Xe and¹H NMR results are presented, as well as a method for greatly increasing the sensitivity of¹²⁹Xe NMR detection at low temperatures by using closely-spaced trains of rf pulses.     

NMR study of the dissolution of laser-polarized xenon

NMR of laser-polarized xenon is used to probe the dissolution behaviour of the noble gas in different liquids. The dissolution and self-relaxation rates are extracted via a macroscopic model, and comparison of the decay rate of the xenon magnetization in deuterated and non-deuterated solvent pairs allows the determination of the pure dipole-dipole contribution to relaxation. A transient convective effect, tentatively assigned to the xenon concentration gradient, is observed and characterized by diffusion encoding MRI experiments. The flow of xenon penetrates inside the solvent near the walls of the NMR tube, the longitudinal images showing a “” shape, the transverse ones a “O” shape. This convection effect has implications for delivery conditions of laser-polarized xenon in continuous flow experiments and magnetic resonance imaging. Received 29 April 2002 / Received in final form 26 July 2002 Published online 22 October 2002 RID="a" ID="a"e-mail: hdesvaux@cea.fr RID="b" ID="b"URA CNRS/CEA 331