PGSE experiment

It has been known for 40 years, since the initial PGSE experiment of Stejskal and Tanner [20], that NMR is an excellent tool for measuring the statistical displacements of molecules with time, usually called diffusion. The exponential attenuation a of the PGSE signal as a function of time between the PGSE pulses is given by [21]... 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

PGSE experiments are usually conducted at fixed A(or x), varying 5 and/or G. In that case the diffusion time is relatively well-defined and nearly constants,6) ... 

Other types of PGSE experiments, including those involving alternating or sinusoidal field gradient pulses 2S), have particular applications which may be useful in polymer systems. 

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 ... 

This relationship states that the PGSE signal is precisely the power spectrum of the reciprocal lattice. This means that the PGSE experiment in the long time limit is an imaging experiment, returning not the reciprocal lattice as in k-space imaging, but the modulus squared of the reciprocal lattice [12]. 

Diffraction-like effects in PGSE experiment, which had been discussed for diffusion in both impermeable and connected structure, were experimentally confined for a sample of water-saturated, loosely packed array of monodisperse polystyrene spheres. This success suggests... 

We now consider the simple case of a spin echo in which two rectangular linear gradient pulses are applied as shown in Fig. 1. In this pulsed gradient spin-echo (PGSE) experiment, the time t used in Eq. (41) will refer to the position of the spin-echo formation. In analyzing this experiment, we will assume the weak inhomogeneous field limit and the uniform... 

Evaluation of Eq. (66) with the spectrum Eq. (83) is shown in detail in Stepisnik (1993, 1994). For the narrow pulse and the finite pulse PGSE experiment, two relatively simple closed form expressions are obtained. Figure 2 shows the fit of evaluated mean-squared displacement to the experimental data (Grinberg et al., 1987). 

Consequently, the slope of the low q echo attenuation data allows (Z (A))/. to be measured directly. This represents the simplest of all possible signal analysis in the case of the narrow gradient pulse PGSE experiment. In the study of hindered and restricted diffusion, such an analysis provides a useful guide to interdependence of length and time... 

The spatially distributed PGSE experiment provides a nice means of demonstrating diffusion anisotropy. The intensity of the image pixel depends on the local gradient g and the self-diffusion tensor as... 

Fig. 28.3. Echo attenuation curves in PGSE experiments on methanol adsorbed on organic polymeric resin crosslinked by diamagnetic Cd ions .

Figure 10 Plot of hydrod5 namic radii obtained from PGSE experiments vs. the radii calculated from crystallographic data. For compounds D, E, G, and H, the radii in the solid state were estimated using reported structures for analogous phosphine, instead of arsine. For C and J the value was calculated from...

Occasionally one can determine the diffusion coefficients for cations and anions separately, and thus determine whether they move together as ion pairs or separately as free ions. Frequently, coordination compounds in use in homogeneous catalysis possess anions such as PFg", BF4, CF3S03, or BArF , and F PGSE experiments represent an alternative and complement. 

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