Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

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.     

Determination of water self-diffusion coefficient in complex food products by low field 1H PFG-NMR: comparison between the standard spin-echo sequence and the T1-weighted spin-echo sequence

In 1990, Van Den Enden et al. proposed a method for the determination of water droplet size distributions in emulsions using a pulsed-field-gradient nuclear magnetic resonance (PFG-NMR) T1-weighted stimulated-echo technique. This paper describes both the T1-weighted spin-echo sequence, an improved method based on this earlier work, and, the standard PFG spin-echo sequence. These two methods were compared for water self-diffusion coefficient measurement in the fatty protein concentrate sample used as a 'cheese model.' The transversal and longitudinal relaxation parameters T1 and T2 were determined according to the temperature and investigated for each sample; fat-free protein concentrate sample, pure anhydrous milk fat, and fatty protein concentrate sample. The water self-diffusion in fat-free protein concentrate samples followed a linear behavior. Consequently, the water self-diffusion coefficient could be easily characterized for fat-free protein concentrate samples. However, it seemed more complicated to obtain accurate water self-diffusion in fatty protein concentrate samples since the diffusion-attenuation data were fitted by a bi-exponential function. This paper demonstrates that the implementation of the T1-weighted spin-echo sequence, using the different T1 properties of water and fat phases, allows the accurate determination of water self-diffusion coefficient in a food product. To minimize the contribution of the 1H nuclei in the fat phase on the NMR echo signal, the fat protons were selectively eliminated by an additional 180 degrees pulse. This new method reduces the standard errors of diffusion data obtained with a basic spin-echo technique, by a factor of 10. The effectiveness of the use of the T1-weighted spin-echo sequence to perform accurate water self-diffusion coefficients measurement in fatty products is thus demonstrated.     

Constant time steady gradient NMR diffusometry using the secondary stimulated echo

A pulse sequence producing a second stimulated echo is suggested for the compensation of relaxation and residual dipolar interaction effects in steady gradient spin echo diffusometry. Steady field gradients of considerable strength exist in the fringe field of NMR magnets, for instance. While the absolute echo time of the second stimulated echo is kept constant throughout the experiment, the interval between the first two radiofrequency pulses is augmented leading to a modulation of the amplitude of that second stimulated echo by self-diffusion only. The unique feature of this technique is that it is of a single-scan/single-echo-signal nature. That is, no reference signals neither of the same pulse sequence nor of separate experiments are needed. The new method was tested with poly(ethylene oxide) melts and proved to provide reliable data for (time dependent) self-diffusion coefficients down to the physical limit (D approximately 10(-15)m(2)/s) when flip-flop spin diffusion starts to become effective.     

核磁共振中多量子相干扩散行为的理论表述和计算机模拟

改进了Warren所提出的CRAZED脉冲序列以研究分子间多量子相干的扩散过程 ,讨论了利用核磁共振测量分子内和分子间多量子相干表观自扩散系数的理论表述 ,采用粒子的随机行走模型模拟其扩散行为 .在短脉冲近似和长脉冲梯度场两种实验条件下 ,分别获得了因扩散引起的不同相干阶数的相对信号衰减强度随梯度场脉冲间隔时间的变化曲线 ,由此得到分子内多量子相干和分子间多量子相干的表观扩散率与溶液分子扩散系数的关系 .还将计算机模拟结果与理论预测进行分析和比较 ,发现二者能很好地吻合 .研究结果表明 ,分子间多量子相干的表观扩散率与常规的分子内多量子相干的表观扩散率明显不同 ,因此 ,分子间多量子相干的表观扩散率可能提供一种新的核磁共振成像的对比度机理     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Spectral separation of gaseous fluorocarbon mixtures and measurement of diffusion constants by F gas phase DOSY NMR

Diffusion-ordered (DOSY) NMR techniques have for the first time been applied to the spectral separation of mixtures of fluorinated gases by diffusion rates. A mixture of linear perfluoroalkanes from methane to hexane was readily separated at 25 °C in an ordinary experimental setup with standard DOSY pulse sequences. Partial separation of variously fluorinated ethanes was also achieved. The constants of self-diffusion of a set of pure perfluoroalkanes were obtained at pressures from 0.25 to 1.34 atm and temperatures from 20 to 122 °C. Under all conditions there was agreement within 20% of experimental self-diffusion constant D and values calculated by the semiempirical Fuller method.     

Self-Diffusion Measurements by Pulsed-Gradient Multiple-Spin-Echo Imaging

A new method is described which allows the spatial distribution of the self-diffusion coefficient over a sample to be determined in a single NMR imaging experiment. This technique combines NMR imaging principles with the pulsed-field-gradient multiple-spin-echo (PGMSE) method. Two basic forms of the pulse sequence for PGMSE imaging have been devised and image intensity as a function of the diffusion-gradient strength is given. The effects of the imaging gradients on the additional diffusion attenuation of image intensities are considered. Finally, the preliminary experimental verification of the PGMSE imaging technique is illustrated by measuring the diffusion coefficient for doped water using the version of the pulse sequence in which all of the 180° radiofrequency pulses are not slice-selective.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Deuterium stimulated-echo-type PGSE NMR experiments for measuring diffusion: application to a liquid crystal.

The accessibility of molecular self-diffusion coefficients in anisotropic materials, such as liquid crystals or solids, by stimulated-echo-type (2)H PGSE NMR is examined. The amplitude and phase modulation of the signal in the stimulated-echo-type sequence by the static quadrupole coupling during the encoding/decoding delays is suppressed by adjusting the pulse flip angles and the phase cycle. For nuclei that experience both nonnegligible quadrupole and dipole couplings, the application of magic echoes during the evolution periods of stimulated echo is demonstrated as a helpful technique in the case of slow diffusion. These findings are demonstrated by experimental results in the thermotropic liquid crystal of partially deuterated 8CB. The obtained diffusion coefficients are also compared to data obtained by a (1)H homonuclear-decoupling-type PGSE NMR method in the same material.     

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.     

2-d ESR diffusion coefficient imaging with the projection reconstruction method

The static gradient spin echo (SGSE) of the conduction electron spins in a quasi-one dimensional organic conductor is analyzed by simulation and for a microstructured (fluoranthene)(2)PF(6) single crystal. It is shown that useful two-dimensional magnetic resonance images of the diffusion coefficient (mobility) D can be obtained from pixel-by-pixel analysis of the signal decay with pulse separation tau, adopting the projection reconstruction (PR) method for signal generation.     

在辐射阻尼存在下有效横向弛豫时间T*2的快速测定

利用CPMG自旋回波技术,通过一连串180°脉冲抑制辐射阻尼效应,让磁化矢量经过横向弛豫T₂过程大幅度衰减后再检测回波信号的线宽,该方法可直接获得有效横向弛豫时间T*₂,并可在CPMG测试T₂值的同时进行. 另外,当饱和恢复法用于估计T*₂值时,信号检测必须使用小角度脉冲.所有结果已进行了实验验证.     

Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

Double-quantum-filtered NMR signals in inhomogeneous magnetic fields

The possibility of exciting and detecting proton NMR double-quantum coherences in inhomogeneous static and radiofrequency magnetic fields was investigated. For this purpose specialized pulse sequences which partially refocus the strongly inhomogeneous evolution of the spin system and generate double-quantum buildup and decay curves were implemented on the NMR MOUSE (mobile universal surface explorer). The theoretical justification of the method was developed for the simple two-spin-1/2 system. The performances of the same pulse sequences were also tested on a solid-state high-field NMR spectrometer. It was shown that DQ decay curves have a better signal-to-noise ratio in the initial time regime than DQ buildup curves. The double-quantum buildup and decay curves were recorded for a series of cross-linked natural rubber samples. These curves give access to quantitative values of the ratio of proton total residual dipolar couplings which are in good agreement with those measured in homogeneous fields. A linear dependence of these ratios on the sulfur-accelerator content was found.     

Measurement of One-Dimensional Spatially Resolved Self-Diffusion Coefficients and Longitudinal Relaxation Times with a Single B1 Gradient

A very simple experimental setup, involving a single coil for generating a radiofrequency field gradient, enables one to determine the self-diffusion coefficient and the longitudinal relaxation time along the gradient axis. This is accomplished by a two-dimensional experiment involving three gradient pulses. The first part of the sequence includes two pulses of identical duration separated by an evolution interval which, by proper phase cycling, encodes longitudinal magnetization according to translational diffusion. The last pulse is incremented for purposes of spatial encoding.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites--water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by ¹H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.     

Self-diffusion coefficient by single-sided NMR

It is presented a novel method for the measure of the self-diffusion coefficient. The method exploits the fixed gradient of an open magnet, as that used in single-sided NMR, and it does not use prior information on T(2). The approach presented in this paper can be practiced also on the fringe field of superconducting magnets and it is based on the construction of the ratios between echoes taken at different interpulses separation in a Carr-Purcell-Meiboom-Gill pulse sequence. The determination of the self-diffusion coefficient facilitates the estimate of T(2) because the transverse relaxation results almost influenced by the molecular diffusion effect, also at the shorter interpulses time, when it is measured in field strongly inhomogeneous.     

液态纯铁自扩散系数研究

液态金属固有的良好导热性能和很好的流动性能,逐渐受到了工程领域越来越多的重视。但由于液相扩散系数的测量困难,目前未见液态纯铁的自扩散系数报道。本文以液态纯铁正则系综为研究对象,采用分子动力学模拟方法对其自扩散系数进行了模拟分析,研究结果表明液态纯铁自扩散系数随温度增加呈现出了较大的变化,应用自扩散系数与温度存在的Arrhenius关系拟合出了液态纯铁的自扩散系数经验公式,进一步获得了液态纯铁原子的平均自由程计算关系式。