Consequences of Restricted Defect Diffusion on NMR and Dielectric Relaxation

Nuclear magnetic and dielectric relaxation formulas are given for a model of limited diffusion of defects. The limitation is introduced by the assumption of fixed reflecting barriers on both sides of the defect. The diffusion process is assumed to be one-dimensional and continuous. The effect of the finite length of the defects is included in the presented treatment.

On the Reconstruction of NQR Nutation Spectra in Solids with Powder Geometry

In single crystals the NQR nutation frequency depends on the relative orientation of the coil and the quadrupole axes. In powders the nutation lineshape is a superposition of spectra from the randomly oriented single crystals, so that powder patterns appear in such experiments if the recon­struction is performed by the Fourier transform method. In this paper an alternative reconstruction method of nutation spectra is suggested making use of the Hankel Transform. In this way the nutation spectra are simplified. Singularities arising with experiments for the determination of the asymmetry parameter η can easily be resolved. In the particular case of an axially symmetric quadrupolar tensor and a homogeneous radiofrequency field one can reduce the powder pattern to a single line without heterogeneous broadening with respect to orientation. Further improvement o f the nutation spectra can be achieved by taking advantage of the maximum entropy method, which strongly reduces apodisation and noise problems. Applications of the new data manipulation techniques to N Q R imaging methods published elsewhere and 2D zero-field N Q R spectroscopy are reported.

Molecular Dynamics of Monomer, Oligomer, and Polymer Liquids in Porous Media: A Field-Cycling Nmr Relaxometry and NMR Field-Gradient Diffusometry Study

The molecular dynamics of fluids in porous media has been studied using field-cycling NMR relaxometry and NMR field-gradient diffusometry. The frequency dependences of the 1H and 2H spin-lattice relaxation times T1 of various liquids in porous glass reveal weak and strong adsorption behaviour depending on the polarity of the adsorbates. Correlation times eight orders of magnitude longer than in bulk have been observed. The T1 dispersion moreover reflects geometrical details of the matrix in a length scale three orders of magnitude longer than the adsorbate molecules. The mean-square displacements of adsorbate molecules on the surface are only one order of magnitude less than in bulk. The global diffusivity is reduced by tortuosity and porosity effects. The observed phenomena may be explained by bulk-mediated surface diffusion, i.e., Lévy walks. The dynamics of polymer chains much longer than the pore size is characteristicly different from that in bulk melts. There is evidence that the reptation mechanism explains at least a part of the phenomena observed for the porous matrix in contrast to findings with bulk polymer melts.

Fluctuations, exchange processes, and water diffusion in aqueous protein systems: A study of bovine serum albumin by diverse NMR techniques

Experimental frequency, concentration, and temperature dependences of the deuteron relaxation times T(1) and T(2) of D(2)O solutions of bovine serum albumin are reported and theoretically described in a closed form without formal parameters. Crucial processes of the theoretical concept are material exchange, translational diffusion of water molecules on the rugged surfaces of proteins, and tumbling of the macromolecules. It is also concluded that, apart from averaging of the relaxation rates in the diverse deuteron phases, material exchange contributes to transverse relaxation by exchange modulation of the Larmor frequency. The rate limiting factor of macromolecular tumbling is determined by the free water content. In a certain analogy to the classical free-volume theory, a "free-water-volume theory" is presented. There are two characteristic water mass fractions indicating the saturation of the hydration shells (C(s) approximately 0.3) and the onset of protein tumbling (C(0) approximately 0.6). The existence of the translational degrees of freedom of water molecules in the hydration shells has been verified by direct measurement of the diffusion coefficient using an NMR field-gradient technique. The concentration and temperature dependences show phenomena indicating a percolation transition of clusters of free water. The threshold water content was found to be C(c) (w) approximately 0.43.

Spin-lattice relaxation dispersion in polymers: dipolar-interaction components and short- and long-time limits

The Mori-Zwanzig projection operator technique was employed to derive the effective Hamiltonian for spin-segment coupling. The fluctuations of this operator are responsible for spin-lattice relaxation in polymer chains. In detail, dipolar interaction of spins is rigorously analyzed by components representing fluctuations of the Kuhn segment end-to-end vectors and local fluctuations on a length scale shorter than the root mean square Kuhn segment length. The former correspond to the usual coarse-grain picture of polymer chain mode theories. It is shown that these non-local chain modes dominate proton spin-lattice relaxation dispersion of flexible polymers at frequencies up to about 10(8)Hz. A corresponding evaluation of experimental data for polybutadiene melts is presented.

Molecular exchange dynamics in partially filled microscale and nanoscale pores of silica glasses studied by field-cycling nuclear magnetic resonance relaxometry

Nuclear magnetic spin-lattice relaxation experiments have been performed in partially filled porous glasses with wetting and nonwetting fluids. The frequency dependence of the spin-lattice relaxation rate in Vycor (4 nm pores) and VitraPOR #5 (1 microm pores) silica glasses was studied as a function of the filling degree with the aid of field-cycling NMR relaxometry. The species of primary interest were water ("polar") and cyclohexane ("nonpolar"). Spin-lattice relaxation was examined in the frequency range from 1 kHz to 400 MHz with the aid of a field-cycling NMR relaxometer and an ordinary 400 MHz NMR spectrometer. Three different mobility states of the fluid molecules are distinguished: The adsorbed state at the pore walls, the bulklike liquid phase, and the vapor phase. The adsorbate spin-lattice relaxation rate is dominated by the "reorientation mediated by translational displacements" (RMTD) mechanism taking place at the adsorbate/matrix interface at frequencies low enough to neglect rotational diffusion of the molecules. The experimental data are analyzed in terms of molecular exchange between the different mobility states. Judged from the dependence of the spin-lattice relaxation rates on the filling degree, limits for slow and fast exchange (relative to the RMTD time scale) can be distinguished and identified. It is concluded that water always shows the features of slow exchange irrespective of the investigated pore sizes and filling degrees. This is in contrast to cyclohexane which is subject to slow exchange in micrometer pores, whereas fast exchange occurs in nanoscopic pores. The latter case implies that the vapor phase contributes to molecular dynamics in this case at low filling degrees while it is negligible otherwise.

Molecular dynamics of n-dodecylammonium chloride in aqueous solutions investigated by 2H NMR and 1H NMR relaxometry

Molecular dynamics in n-dodecylammonium chloride/water solutions for concentrations of 34 and 45 wt% was studied by 2H NMR and by 1H NMR dispersion of spin-lattice relaxation in the 2 kHz-90 MHz frequency range. The system exhibits a number of lyotropic liquid crystalline phases, which differ in symmetry and involve motions characterized by a wide frequency scale. The analysis of 2H NMR lineshapes of selectively deuterated DDACl molecules gave us an evidence for local trans-gauche conformational changes in the chains, whereas the dispersion of spin-lattice relaxation times T1 explored by fast field cycling method revealed fast local motions, translational diffusion and collective molecular dynamics of the chains. In particular, we have found that the order director fluctuation mechanism in smectic and nematic phases dominates spin-lattice relaxation below 1 MHz and that local motions and translational diffusion are responsible for the spin-lattice relaxation in the higher Larmor frequency range.

Apparent low-field spin-lattice dispersion in the smectic-A mesophase of thermotropic cyanobiphenyls

Proton field-cycling spin-lattice relaxometry T1 of the smectic-A mesophase in cyanobiphenyls revealed the presence of steep dispersions in the low-frequency regime. We clearly show that the strong dispersion characteristic of smectic organizations cannot be attributed to the collective molecular dynamics (order director fluctuations), as it is usually interpreted. We present two independent experimental evidences: the dependence of the dispersion with the slew rate of the magnetic field cycle and the dependence of the dispersion with the presence and power of an ultrasonic field.

Rayleigh-Bénard percolation transition study of thermal convection in porous media: numerical simulation and NMR experiments

Thermal convection was studied as a function of the porosity in random-site percolation model objects in a Rayleigh-Bénard configuration. NMR velocity mapping experiments and numerical simulations using the finite-volume method are compared. Velocity histograms were evaluated and can be described by power laws in a wide range. The maximum velocity as a function of the porosity indicates a combined percolation/Rayleigh-Bénard transition.

Surface effects and dipolar correlations of confined and constrained liquids investigated by NMR relaxation experiments and computer simulations

Local order and molecular dynamics of liquids near surfaces strongly deviate from the behavior in the bulk. This in particular refers to liquid crystals above the bulk isotropization temperature. Transverse relaxation data of 5CB examined in porous glasses with different pore sizes are reported. A strong pore size effect was found. For the interpretation, a simple diffusion-adsorption computer simulation was carried out. Molecules can diffuse from the isotropic bulk part of the pore fluid to the ordered surface layer and vice versa. The residual dipolar correlation function is characterized by a slowly decaying tail owing to repeated returns of molecules to the surface. At each return the molecular orientation correlation is recovered as far as the surface sites visited have orientations correlated to the initial site. That is, molecular orientation is controlled by the "reorientation mediated by translational displacement" process considered in previous papers.

Flow through percolation clusters: NMR velocity mapping and numerical simulation study

Three- and (quasi-)two-dimensional percolation objects have been fabricated based on Monte Carlo generated templates. The object size was up to 12 cm (300 lattice sites) in each dimension. Random site, semicontinuous swiss-cheese, and semicontinuous inverse swiss-cheese percolation models above the percolation threshold were considered. The water-filled pore space was investigated by nuclear magnetic resonance (NMR) imaging and, after exerting a pressure gradient, by NMR velocity mapping. The spatial resolutions of the fabrication process and the NMR experiments were 400 microm and better than 300 microm, respectively. The experimental velocity resolution was 60 microm/s. The fractal dimension, the correlation length, and the percolation probability can be evaluated both from the computer generated templates and the corresponding NMR spin density maps. Based on velocity maps, the percolation backbones were determined. The fractal dimension of the backbones turned out to be smaller than that of the complete cluster. As a further relation of interest, the volume-averaged velocity was calculated as a function of the probe volume radius. In a certain scaling window, the resulting dependence can be represented by a power law, the exponent of which was not yet considered in the theoretical literature. The experimental results favorably compare to computer simulations based on the finite-element method (FEM) or the finite-volume method (FVM). This demonstrates that NMR microimaging as well as FEM/FVM simulations reliably reflect transport features in percolation clusters.

Flow, diffusion, and thermal convection in percolation clusters: NMR experiments and numerical FEM/FVM simulations

Percolation objects were fabricated based on computer-generated, two- or three-dimensional templates. Random-site, semi-continuous swiss cheese, and semi-continuous inverse swiss-cheese percolation models above the percolation threshold were considered. The water-filled pore space was investigated by NMR imaging and, in the presence of a pressure gradient, NMR velocity mapping. The fractal dimension, the correlation length, and the percolation probability were evaluated both from the computer-generated templates and the corresponding NMR spin density maps. Based on velocity maps, the percolation backbones were determined. The fractal dimension of the backbones turned out to be smaller than that of the complete cluster. As a further relation of interest, the volume-averaged velocity was calculated as a function of the probe volume radius. In a certain scaling window, the resulting dependence can be represented by a power law the exponent of which was not yet considered in the theoretical literature. The experimental results favorably compare to computer simulations based on the finite-element method (FEM) or the finite-volume method (FVM). Percolation theory suggests a relationship between the anomalous diffusion exponent and the fractal dimension of the cluster, i.e., between a dynamic and a structural parameter. We examined interdiffusion between two compartments initially filled with H2O and D2O, respectively, by proton imaging. The results confirm the theoretical expectation. As a third transport mechanism, thermal convection in percolation clusters of different porosities was studied with the aid of NMR velocity mapping. The velocity distribution is related to the convection roll size distribution. Corresponding histograms consist of a power law part representing localized rolls, and a high-velocity cut-off for cluster-spanning rolls. The maximum velocity as a function of the porosity clearly visualizes the percolation transition.

Diffusion measurements with the aid of nutation spin echoes appearing after two inhomogeneous radiofrequency pulses in inhomogeneous magnetic fields

Nutation echoes are generated by radiofrequency (RF) pulses with an inhomogeneous amplitude, B(1) = B(1)(r), in inhomogeneous magnetic fields, B(0) = B(0)(r). The two gradients of strengths G(1) and G(0), respectively, must be aligned in parallel for a maximum echo signal. After two RF pulses, two echoes appear at times tau(a) = 2 tau(1) + tau(2) + (G(1)/G(0))tau(1) and tau(b) = 2 tau(1) + tau(2) + 2(G(1)/G(0))tau(1), where tau(1) is the RF pulse duration and tau(2) the interpulse interval. It is shown that these echoes can favorably be employed for the determination of self-diffusion coefficients even in the poor experimental situation one often faces in low-resolution or low-field NMR. The signal intensity is comparable to that of ordinary Hahn echoes. Diffusion coefficients and spin-lattice relaxation times can be evaluated from the same experimental data set if both nutation echoes are recorded. Test experiments are in good agreement with literature data. Applications of the technique to "inside out" NMR, well logging NMR, surface coil NMR, toroid cavity NMR, etc., are suggested.

The nutation spin echo and its use for localized NMR

A suitably matched combination of unidirectional gradient pulses of the radio frequency amplitude B(1) and of the main magnetic field B(0) produces an unconventional type of spin echo, the nutation echo. The echo signal becomes volume selective if the gradients to be matched are inhomogeneously distributed in space. An example is a combination of a constant B(0) gradient and the inhomogeneous B(1) gradient of a surface coil. We suggest a method for localized NMR on this basis. Nutation echoes can also be used to map the spatial distribution of B(1) gradients of an arbitrary radio frequency coil geometry with the aid of a small probe sample. Copyright 2000 Academic Press.

Segment diffusion and flip-flop spin diffusion in entangled polyethyleneoxide melts: A field-gradient NMR diffusometry study

Chain dynamics in melts of entangled polyethyleneoxide melts has been investigated using fringe field nuclear magnetic resonance diffusometry. As already demonstrated in our previous work, intermolecular flip-flop spin diffusion strongly influences spin echo attenuation for long diffusion times and high molecular weights. The experimental data have been evaluated taking this phenomenon quantitatively into account. Predictions of the reptation model for the correspondingly modified time and molecular weight dependences of the effective segment diffusion coefficient are presented and compared with experimental results. While the ordinary Rouse model totally fails to explain the experimental data, a satisfactory qualitative description is provided on the basis of the tube/reptation model. However, the fitted parameter values turned out to be inconsistent with known properties of this polymer. This in particular refers to the mean squared chain end-to-end distance divided by the molecular weight, for which neutron-scattering values are available in the literature. Relative to those results, the value evaluated from our NMR diffusometry data on the basis of the tube/reptation model turned out to be much too large.

Two-pulse nutation echoes generated by gradients of the radiofrequency amplitude and of the main magnetic field

A two-pulse NMR nutation spectroscopy scheme is suggested that leads to a new type of spin echoes. The amplitude of the radiofrequency (RF) pulses as well as the external magnetic field are assumed to be subject to gradients G(1) and G(0), respectively, in the same but otherwise arbitrary direction. Multiple echoes are predicted and observed at times k(G(1)/G(0))tau(1) and tau -/+ k(G(1)/G(0))tau(1) (k = 1, 2, 3, ...) after the second RF pulse, where tau(1) represents the radiofrequency pulse duration, and tau is the spacing of the RF pulses. Based on these echoes, a method for diffusion measurements is proposed that simultaneously provides the spin-lattice relaxation time and the self-diffusion coefficient.

Diffusion measurements using the nonlinear stimulated echo

The nonlinear stimulated echo that is generated by a sequence of three radiofrequency pulses, 90 degrees-tau(1)-90 degrees-tau(2)-45 degrees, in high magnetic fields (or at low temperatures) in the presence of pulsed or steady field gradients can be applied for measurements of the diffusion coefficient. Corresponding test experiments are reported. Steady gradients can be used without knowledge of the relaxation times. Remarkably the attenuation of the nonlinear stimulated echo by diffusion is substantially stronger than in the case of the ordinary stimulated echo.

Low-frequency molecular dynamics studied by spin-lock field cycling imaging

Spin-lock adiabatic field cycling imaging (SLOAFI) relaxometry was shown to be a useful technique for obtaining a fast study of spin-lattice relaxation dispersion in the rotating frame. The aim of the present article is to describe some technical aspects of the experiment in more detail, while showing simple examples that can be compared with laboratory frame relaxation. We also present here a general discussion of the equations for an off-resonance experiment used to analyze low-frequency molecular dynamics.

Propagator representation of anomalous diffusion: the orientational structure factor formalism in NMR

The radial Fourier transform for the isotropic space with a fractal dimension is discussed. The moments of diffusive displacements with non-Gaussian propagators arising as solutions of fractional diffusion equations are calculated. The Fourier propagator is applied to NMR correlation and spectral density functions in context with the orientational structure factor formalism. It is shown that the low-frequency molecular fluctuations of liquids in porous media with strong or forced adsorption at surfaces are due to reorientations mediated by translational displacements caused by surface diffusion of the adsorbate molecules. In terms of this formalism, field-cycling NMR experiments provide information on the static and dynamic fractal dimensions related to surface diffusion. The experimental results for liquids in porous silica glass can be explained by a surface fractal dimension df=2.5, where the mean squared displacement scales as <r(2)(t)> proportional, variantt(2/dw) with dw=1 (ballistic transport), if the surface population can exchange with the bulklike phase in the pores, and with dw=2, if the bulklike phase is frozen. The former dynamics is interpreted in terms of bulk-mediated surface diffusion.

Surface fractals probed by adsorbate spin-lattice relaxation dispersion

Spin-lattice relaxation of strong adsorbates confined in disordered structures such as porous silica glass is treated on the basis of a relaxation mechanism due to "reorientation mediated by translational displacements." In such a situation the low-frequency spin-lattice relaxation dispersion beyond the regime where local reorientations dominate reflects molecular dynamics as well as the surface geometry on a length scale longer than 1 nm. It is shown that the power law frequently observed for the spin-lattice relaxation dispersion in porous media can be traced back to surface fractality. The fractal properties of rough surfaces and the statistics governing surface displacements enter explicitly in the expression for the dipolar correlation function. The surface fractal dimension can thus be evaluated from the low-frequency spin-lattice relaxation dispersion accessible by field-cycling NMR relaxometry.

PRAWN: mixing sequences for selective heteronuclear J cross polarization

In this work, we present a family of pulse sequences for selective heteronuclear J cross-polarization (JCP), which we have developed especially for indirect 13C imaging using JCP, for example in the CYCLCROP environment. The sequences are straightforward to implement and operate reliably. Results of an average Hamiltonian analysis are given for the basic sequence, which we term PRAWN (pulsed rotating frame transfer sequence with windows). It is shown experimentally that the pulse sequence, which operates efficiently with low RF duty cycles down to a few percent, has a useful tolerance range to absolute Hartmann-Hahn mismatch and generates coherence transfer spectra in close correspondence with the JCP average Hamiltonian. Computer simulation of the performance of the basic sequence on a heteronuclear spin-(1/2) AX system is also presented. The mismatch compensation of PRAWN may be markedly enhanced further by issuing a pi pulse to each spin halfway through the basic PRAWN train and in phase quadrature to it. A simple analysis of this modified sequence, PRAWN-pi, is given under conditions of mismatch and off-resonance irradiation.

A new formalism for the evaluation of order-fluctuation modes in liquid crystals from field-cycling NMR-relaxometry data

A numerical procedure is presented which permits one to derive a formal distribution of collective fluctuation modes from experimental field-cycling NMR-relaxometry data of an ordered system. The purpose is to distinguish true order-fluctuation modes from local reorientation mechanisms. The evaluation scheme is demonstrated using simulated as well as experimental data. Applications serving the elucidation and characterization of modified or limited director fluctuation modes as they occur with liquid crystals in pores or with lyotropic systems are discussed. Test experiments have been carried out with a potassium laurate system.

Molecular dynamics and order of microconfined liquid crystals

A new technique based on the dipolar-correlation effect was applied in combination with field-cycling-relaxometry to study ordering effects and slow director fluctuations in a nematic liquid crystal confined in porous glasses. Both methods demonstrate a strong influence of geometrical confinements on the distribution of director fluctuation modes. The mean-squared fluctuation estimated from the dipolar-correlation effect decreases exponentially with decreasing pore diameter. The critical mean pore size for the onset of bulk behaviour was found to be of the order of 120 nm. Frequency dependences of spin-lattice relaxation times exhibit sudden sharp deviations from the square root law at frequencies below the MHz-range. These changes are assumed to reflect the lack of long wavelength fluctuations in the spectrum of director fluctuation modes due to finite pore sizes.

Diffusion and relaxation in interface layers of crystals in nanoporous glass

Below the freezing point, experimental data provide evidence for the existence of a non-frozen interface layer (NFL) between the crystal in the pore and the pore walls. The molecules in this layer are effectively confined in a quasi-two-dimensional space that forces them to reorient when moving along the curved pore surface. Through this relaxation mechanism, the translational mobility in the unfrozen phase reveals itself in a pronounced frequency dependence of the spin-lattice relaxation time. The experimentally observed drop of the self-diffusion coefficients by more than one order of magnitude below the phase transition can be interpreted in terms of geometric restrictions as well as interactions with the surface.

Field-cycling NMR relaxometry of molecules undergoing Lévy walks at the surface of fine particles and porous glass

Slow surface dynamics of solvents confined in the pore space of porous glass and fineparticles was studied by proton field-cycling relaxometry. Molecular reorientations mediated by translational displacements are shown to be an important low-frequency T1-relaxation mechanism in porous media at low nuclear magnetic resonance (NMR) frequencies in the strong adsorption limit. This is revealed by the pronounced T1-dispersion in this case while a flat one is observed for weak adsorption. The following nanoporous materials were examined in this respect: fineparticles of ZnO,-TiO2, porous glass. Silanized surfaces lead to a somewhat steeper T1-dispersion of non-polar cyclohexane than the native, i.e. polar, surfaces. On the other hand, there is no strong influence of the surface groups on the T1(omega) slope of (polar) acetone. The results are discussed with reorientations mediated by translational displacements enhanced by Lévy walks on the surface.

Multiple nonlinear stimulated echoes

Three-pulse sequences in the presence of magnetic field gradients at high magnetic fields produce multiple nonlinear stimulated echoes (NOSE) at times ntau1 after the third pulse, where n is an integer and tau1 the interval between the first two pulses. These phenomena are due to the demagnetizing field produced by the spatial modulation of the nuclear magnetization arising in the sample after the first two pulses. The theory is presented and compared with experiments. The dependence of the NOSE amplitudes on the flip angles and on the pulse intervals is described. Implications for multidimensional NMR experiments based on sequences of three or more pulses in the presence of field gradients are discussed.