The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations

q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, δ, is comparable to the diffusion time, Δ. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Δ/δ, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Δ/δ  1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long δ the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Δ/δ  1 the diffraction peaks are shifted to even higher q-values, even when δ is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Δ/δ  1.     

A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R(1), R(2), and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and quantify the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the internal motions experienced by the residues which are used to quantify the diffusion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data corresponding to isotropic, axially symmetric anisotropic, and fully asymmetric anisotropic rotational diffusion, as well as experimental NMR data. We compare the Bayesian statistical approach with a widely used method for extracting tumbling parameters using both synthetic and experimental data. While it can be difficult to separate the effects of chemical exchange from rotational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalent standard analysis.     

The effect of experimental parameters on the signal decay in double-PGSE experiments: negative diffractions and enhancement of structural information

Double pulsed gradient spin echo (d-PGSE) experiment has been recently suggested for detecting microscopic anisotropy in macroscopically isotropic samples. This sequence is complex and has many variables, including, intra alia, combinations of directions and amplitudes of the pulsed gradients, diffusion times in each of the encoding periods and the mixing time period. The effect of these experimental parameters of the d-PGSE sequence was studied in an array of water filled microcapillaries of micron diameters. We found that negative diffractions occur, as indeed predicted by recently published simulations. We also found differential effects of prolongation of the mixing time between collinear and orthogonal d-PGSE experiments. The d-PGSE experiment in the collinear direction perpendicular to the long axis of the cylinder exhibited a marked dependence on the mixing time, while the orthogonal d-PGSE experiment exhibited no such dependence at all. Interestingly, one of the most important predictions by the simulations was that the d-PGSE sequence could potentially discriminate between compartments of different sizes better than the single PGSE (s-PGSE) and it seems that our experimental results indeed corroborate these predictions.     

15N spin diffusion rate in solid-state NMR of totally enriched proteins: the magic angle spinning frequency effect

As demonstrated by means of the one-dimensional solid-state MAS exchange experiment (CODEX), the rate of the proton driven spin diffusion between backbone (15)N nuclei in totally enriched protein depends strongly on the magic angle spinning (MAS) frequency: spin diffusion at MAS frequency 16 kHz is about 4-5 times slower as compared to that at MAS frequency 1 kHz which is due to the averaging of the homo- and hetero-nuclear dipolar interactions by MAS. It is important that even at the highest MAS frequencies used in our experiments the spin diffusion rate is comparable or larger than typical values of the spin-lattice relaxation rates of backbone nitrogens in solid proteins. Thus, the precise quantitative analysis of (15)N T(1)'s in totally enriched solid proteins may lead to wrong quantitative results. On the other hand, the effectiveness of the (15)N-(15)N correlation and structure determination experiments making use of (15)N-(15)N distances can be increased by decreasing the MAS frequency as far as possible, which is counter intuitive to the commonly applied fast MAS conditions in order to reduce the dipolar-broadened line widths for increased spectral resolution.     

转动传能中的量子干涉--干涉角和转动量子数的关系

沙国河等人在CO(A1∏(v=0)~e3∑-(v=1))体系与He,Ne和Ar碰撞诱导转动传能中首次观测到了量子干涉效应,并测量了干涉度。从理论上进一步研究原子-双原子分子体系碰撞诱导转动传能中量子干涉效应与转动量子数以及能量间隔的关系是十分必要的。我们考虑长程相互作用势,应用一级玻恩近似和直线轨迹近似,分别计算了CO(A1∏(v=0)~e3∑-(v=1))体系和He,Ne,Ar碰撞诱导转动传能中不同转动量子数以及不同能量间隔下的干涉角,得到了干涉角随转动量子数和能量间隔的变化趋势。这些结果对设计、分析这种类型的实验有一定的指导意义。     

Superheating and supercooling of vortex matter in a Nb single crystal: direct evidence for a phase transition at the peak effect from neutron diffraction

We report the first observation of a striking history dependence of the structure function of vortex matter in the peak effect regime in a Nb single crystal by using small angle neutron scattering combined with in situ magnetic susceptibility measurements. Metastable phases of vortex matter, supercooled vortex liquid and superheated vortex solid, have been identified. We interpret our results as direct structural evidence for a first-order vortex solid-liquid transition at the peak effect.     

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

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

A computer experiment on the deviation from the Bragg law and the widths of diffraction patterns in perfect crystals

New analytical expressions were recently derived for the deviation for the Bragg law and for the width of diffraction patterns in perfect crystals. This letter presents the results of a computer experiment leading to the evaluation of these two quantities as a function of the incidence angle for the Ge 220 reflection of CuKα₁ radiation. The comparison of the obtained data with the old and the new expressions certainly confirm the validity of the new ones.     

The effects of experimental parameters in the thermal diffusivity measurements of oriented polymer films using mirage effect: Computer simulation

Computer simulations have been carried out to study the effects of the experimental parameters when the mirage method has been applied to thermal diffusivity measurements of oriented polymer films. The parameters under study are the thermal diffusivity of the fluid surrounding the sample, the modulation frequency and the radius of the heating beam, the height and the radius of the probe beam, and the sample thickness and thermal diffusivity. Proposals for the optimum parameter values to maximize the measurement sensitivity for the sample diffusivity are made and the difficulties arising from the low diffusivity of the samples are described. It is also concluded that because the thermal properties of the fluid surrounding the sample have a strong contribution to the mirage signals, the signals do not include any simple feature corresponding to the sample diffusivity. Therefore it should be determined from the entire measurement data using regression methods.     

Magnetorefractive effect in nanocomposites: Dependence on the angle of incidence and on light polarization

The polarization and angular dependences of the magnetorefractive effect (MRE) in metal-insulator nanocomposites in reflection and transmission geometries have been calculated in terms of the high-frequency, spin-dependent tunneling mechanism. The MRE exhibits a weak polarization and angular response at small angles of incidence. The MRE in reflection and transmission starts to grow strongly with increasing angle of incidence. The MRE in reflection in nanocomposites with metal contents corresponding to the insulating phase near the percolation threshold reaches the largest values with p-polarized light at an angle of incidence close to the Brewster angle. The results of the calculation are in a qualitative agreement with experimental data.     

Gas diffusion in zeolite beds: PFG NMR evidence for different tortuosity factors in the Knudsen and bulk regimes

We present molecular dynamics simulations in the micro-canonical ensemble of a Lennard-Jones model of nitrogen confined in realistic models for saccharose-based carbons developed in our previous work. We calculate the velocity autocorrelation function and mean-squared displacement, and the self-diffusivities from the latter. We observe that the self-diffusivity increases with temperature and exhibits a maximum with loading or adsorbate density. To the best of our knowledge, a maximum in self-diffusivities has not been observed in molecular dynamics simulations of fluids confined in slit pores.Received: 1 January 2003, Published online: 30 October 2003PACS: 61.43.Gt Powders, porous materials - 68.43.Jk Diffusion of adsorbates, kinetics of coarsening and aggregation - 82.75.Fq Synthesis, structure determination, structure modeling     

Gas diffusion in zeolite beds: PFG NMR evidence for different tortuosity factors in the Knudsen and bulk regimes

Self-diffusion of ethane in beds of zeolite NaX is studied using Pulsed Field Gradient (PFG) NMR. The ethane diffusivities were measured for displacements, which are orders of magnitude larger than the size of individual crystals. These diffusivities were compared with those, calculated using simple gas kinetic theory. The results of the comparison indicate that for the same bed of NaX crystals the apparent tortuosity factor in the Knudsen regime ( i.e. when molecule-solid collisions dominate) is significantly larger than that in the bulk regime ( i.e. when molecule-molecule collisions dominate). This finding is attributed to the more pronounced geometrical trapping by the pore structure of the zeolite bed in the Knudsen than in the bulk regime.     

The influence of water content on the 23Na and 31P NMR spectral parameters in solid Na-DNA

23Na and 31P MAS NMR spectra and spin-lattice relaxation times in a solid sample of Na-DNA were measured under very carefully controlled conditions of relative ambient humidity. The observed substantial changes of the NMR parameters are related to the water-induced transitions between the different molecular configurations of DNA, with the transition between A- and B-DNA occurring in the 30-60% range of relative humidity. Our work demonstrates that the previously measured NMR parameters are in error because the relative humidity of the system had not been controlled, rendering the results irreproducible.     

The value of B K from the experimental data on CP violation in K mesons and up-to-date values of CKM matrix parameters

The difference between the quantity induced by box diagram and the experimentally measured value of ɛ is determined and used to obtain the value of ∈ with high precision. Present-day knowledge of CKM matrix elements (including B-factory data) allows us to obtain from the SM expression for the value of parameter B _K : B _K =0.89±0.16. It turns out to be very close to the result of vacuum insertion, B _K =1. The text was submitted by the authors in English.     

Effect of the parameters on diffraction efficiency after thermal fixing for reflection geometry hologram storage in LiNbO3:Fe

For reflection geometry hologram storage in LiNbO₃:Fe, we have shown that the diffraction efficiency increases with doping level and thickness of storage material monotonically. When the acute angle between reference and z-axis is large enough for getting a relative small Bragg angle that is needed for angle multiplexing, smaller angle does good to diffraction efficiency after thermal fixing. And for absorption coefficient, there is an appropriate value responding to optimal diffraction efficiency after thermal fixing and we develop a theoretical model that predicts achievable diffraction efficiency after thermal fixing as a function of crystal thickness, doping level, acute angle between reference and z-axis and absorption coefficient. We compare this model with experiment results and get a good agreement.     

Tracer diffusion measurements in solid lithium: a test case for the comparison between NMR in static and pulsed magnetic field gradients after upgrading a standard solid state NMR spectrometer

This paper reports on the upgrading of a standard solid state NMR spectrometer, which has been used in combination with a field variable 7 T cryomagnet, to a low-cost combined SFG and PFG NMR spectrometer. Both methods are applied to solid lithium as a simple test case. The results show that under the given conditions SFG NMR and PFG NMR can provide tracer diffusion coefficients for 7 Li diffusion down to about 10(-14) and 10(-13) m2/s, respectively. SFG and PFG NMR are complementary methods. The paper demonstrates advantages and disadvantages of each method with a concrete example and why it is desirable to be able to apply both methods to the same sample.