Spin-echo diffusion experiments

The parameter to be measured in spin-echo diffusion experiments is the amplitude A of the echo. Its magnitude depends 3) on the spin-spin relaxation time T2 and on the diffusion coefficient D. For an SGSE experiment employing a 90°-t-180° rf pulse sequence in the presence of a steady field gradient of magnitude G0 4),... 

E.D. von Meerwall, "Interpreting Pulsed-gradient Spin-echo Diffusion Experiments in Polydisperse Specimens," J. Mag. Reson.. 50 409-416 (1982). 

For the spin-echo diffusion-relaxation experiment, they showed... 

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

Figure 2.7.2 illustrates two implementations of the diffusion-relaxation experiment using the pulsed field gradient. In the first implementation, a spin-echo... 

In an experiment, tcp is to be varied systematically to obtain the 2D data matrix. For the spin-echo and stimulated-echo based sequences, molecular diffusion causes signal decay in the first segment, thus both are called diffusion-editing sequences. 

Modem NMR diffusion measurements are all based on the Stejskal-Tanner (S-T) pulsed field gradient spin-echo experiment [174] in which a gradient pulse is... 

Figure 2. Spin-echo -NMR spectra from a diffusion experiment with a cubic phase of dDAVP (10%), MO (60%) and 2H20 (40%). Temperature 40 C, t=20 ms, A=24 ms, g=l 19 gauss/cm and 8=1.0,2.0..., 9.0 ms. The inset shows the aromatic region originating from dDAV P at a higher amplification. Also shown is the pulse sequence used in the NMR-diffusion method (see text for details).

Several NMR pulse sequences have been developed for measuring the diffusion coefficient. The most successful and currently used experiment is the modified spin-echo experiment (PGSE) proposed by Stejskal in 1967.62 As the echo signal is due to the transversal components of magnetic moments, the echo attenuation normalized for the attenuation due to relaxation can be written as63 ... 

Three analytical expressions for the spin-echo intensity as a function of the gradient in a pulsed field gradient NMR experiment for spins diffusing in a sphere with reflecting walls are reinvestigated. It is found that none of the published formulas are completely correct. By numerical comparisons the correct formula is found. 

Because T2 tends to be longer for molecules of lower molecular weight, spin-echo experiments tend to be very sensitive to contamination by light, diffusing impurities often found in polymer preparations. Care must be taken to remove these 32) to avoid inviting misinterpretation of experimental data. 

The PGSE experiment can detect the presence of two or more diffusivities in the species at resonance. The intensity of the spin echo is a function of the duration 8, magnitude G and the time A between the applied magnetic field gradient pulses ... 

One particular model of a biological system is a set of barriers in an otherwise homogeneous medium. If diffusion is observed over a short enough time, very little of the substance experiences the effect of the barriers, and the observed motion is characteristic of the medium alone. As the time of observation is extended, more of the substance is reflected at barriers and thus, its total displacement is less than would have been the case without the barrier bringing about less attenuation of the PG spin-echo [48, 49]. From an analysis of such data one can, in principle, obtain information on the geometry of the domains in which restricted diffusion occurs information on cell size, droplet size distribution [50] etc. 

The attenuation of spin echo in a standard PGSE diffusion experiment, described by equation (16), may be written in complex number notation as... 

Diffusions NMR spectroscopy (e.g. PGSE = Pulsed Gradient Spin Echo STE = Stimulated Echo DOSY = Diffusion Ordered Spectroscopy) is a straightforward and accurate method for determination of the self-diffusion coefficient of a molecule. Its principal use in dendrimer chemistry is for size determination of dissolved dendrimers since the self-diffusion coefficient is directly correlated with the hydrodynamic radius of the molecule via the Stokes-Einstein equation [24]. Although one-dimensional and multidimensional diffusion NMR experiments can thus make an important contribution to structural characterisation of dendrimers, they have been used comparatively rarely until recently [25, 26]. 

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