Fourier transform, pulsed-field gradient

Molecular self-diffusion coefficients are experimentally easily accessible and can be measured accurately with various techniques. However, the Fourier transform pulsed field gradient spin-echo NMR (FT PGSE NMR) approach has during the last decade proved to be superior to other approaches for several reasons. In this technique the displacement of nuclear spins in a controlled magnetic field gradient is monitored, and the contributions of different components are resolved by Fourier transformation of the NMR signal (spin echo). 

All standard pulse sequences for these experiments include some mechanism for selecting xH-X pairs and suppressing the other XH signals (phase cycling and/or pulsed field gradients, see below). As a further advantage, residual signal intensity of protons not bound to X (because of imperfect suppression) will not lead to a cross peak in the xH,X plane after Fourier transformation, but merely contribute to axial peaks at the spec-... 

Abbreviations D, self-diffusion coefficient ge, gradient-echo IR, inversion recovery IRFT, inversion recovery fourier transform MRS, magnetic resonance spectroscopy PD, proton density PFGSE, pulsed field gradient spin echo se, spin-echo. 

The NMR technique for measuring self-diffusion in liquids was first reported in 1965390, and its variant for multicomponent mixtures became available with the introduction of the Fourier transform. Wider use had to wait until pulsed field gradients became generally... 

In a 2D experiment one or more scans are acquired with a delay tl that is incremented in subsequent acquisitions to generate a time domain tl. The time domain tl in conjunction with the acquisition time domain t2 generates a 2D data set that upon double Fourier transform gives a 2D spectrum. In a very simplified view all 2D experiments can be described as series of ID experiments but in practise the situation is rather more complicated because to achieve quadrature detection in both dimensions phase cycling or pulse field gradients must be used. Consequently the processing of 2D data sets depends upon the detection mode and the experimental setup. 

Spectral studies such as Fourier transform infrared/attenuated total reflectance (FTIR/ATR) analysis, solid-state or pulse field gradient (PFG) nuclear magnetic resonance (NMR), x-ray diffraction (XRD) or small angle x-ray scattering (SAXS) analysis, and Raman study are basically the characterization methods for hybrid/ composite membranes. Sometimes, the multiple spectral analyses are necessary to better understand the structure-property relationship for a kind of composite polyelectrolytes. 

Fig. 1.10 Soft rf pulses (left) in the shape of a sine (sin x/x) function, and their Fourier transforms (right), being equivalent to the excited slice in the presence of a constant magnetic field gradient. The well defined sine function (top) produces an excitation that is a slice...

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