Inversion-recovery Fourier transform

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 spectra were taken on a JEOL JNM-MH-100 (CW) spectrometer using tetramethylsilane as an internal standard. 13C spin-lattice relaxation time of the polymer was measured by the inversion-recovery Fourier transform method on a JNM-FX100 FT NMR spectrometer operating at 25 MHz. 

Ti measurements at normal probe temperatiire were made by the inversion-recovery Fourier-transform (IRFT) technique on deuteriated chloroform solutions of pristane (2,6,10,1 i -tetra-methylpentadecane) and of branched-chain/cyclic alkanes from Rexco coal tar and a Turkish asphaltite (Avgamasya). Inversion-recovery traces were recorded by using 200 cycles of the l80°-90°-PD pulse sequence with a pulse delay time (PD) of about 20s at a series of intervals, T (e.g. 1,3,5s, Figure 3). Ti values ( 0.5s) (Table IV) were measiired by plotting In(AQ-A) vs. T, where A is the equilibrium amplitude in a normal FT spectrum and A is the amplitude in an IRFT spectrum (Figure k). 

FIRFT Fast Inversion-Recovery Fourier Transform... 

Figure 2. Stacked plot of an inversion recovery Fourier transform Tj measurement of in a 4 molal...

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

A commonly used method of measuring longitudinal relaxation times in multiline spectra, almost as old as Fourier transform NMR, is the inversion recovery experiment [1] which can be schematized by the pulse sequence... 

Spin-lattice relaxation times 7j of individual nuclei (13C, H) present in a molecule can be obtained by Fourier transformation of the FID signal following a 180°, r, 90° pulse sequence. The technique is referred to as inversion-recovery method [39, 40, 41] or... 

In order to determine the content of this noncrystalline line further, we examined in more detail the behavior of the spin-lattice relaxation. Figure 5 shows the partially relaxed spectra in the course of the inversion recovery pulse sequence (180°-t-90°-FIDdd-10s)i2o with varying x values. The magnetization that was recovered for 10 s in the z direction was turned to negative z direction by 180° pulse and the magnetization recovered in z direction for varying x was measured in the xy plane under H DD. The spectra at different steps of the longitudinal relaxation were obtained by Fourier transform and are shown in Fig. 5. In these spectra the contribution from the crystalline components with Tic s of2,560 and 263 s are eliminated due to the lack of time for recovery at each pulse sequence. Therefore, we observed preferentially the relaxation process of the noncrys-... 

Other methods that have found use in measurement of T relaxation of organosilicon compounds are FIRFT (Fast Inversion Recovery combined with Fourier Transform)344,349-352 and saturation recovery353. Each of these sequences produces some dependence of the signal on a time parameter. In order to get the relaxation time, the dependence must be analysed often, a non-linear three-parameter analysis is used354. 

The signal intensity at the start of the FID is proportional to the peak height after Fourier transformation, so we could make a plot of peak height versus x delay and fit the exponential decay to a theoretical curve to measure the T2 value. This is the T2 equivalent of the inversion-recovery experiment (Section 5.8) for measurement of T. ... 

FIGURE 2.12 Determination of T, by the inversion-recovery method, (a) M is inverted by a 180° pulse at time 0. (b) After a time interval T, during which spin—lattice relaxation occurs, a 90° pulse rotates the remaining magnetization to the y (or — y ) axis, (r) The initial height of the FID or the height of a given line in the Fourier-transformed spectrum (see Chapter 3) is plotted as a function of t. Note that each point results from a separate 180°, T, 90° pulse sequence. 

Some methods take advantage of a difference in a particular property between water and the molecule to be studied. In particular, a macromolecule usually has a shorter value for proton Tt than water and a much lower diffusion coefficient. One of the oldest methods for water signal suppression is WEFT (water elimination Fourier transform), in which an inversion recovery sequence is applied (see Fig. 2.12) with r chosen to be the time that the water signal goes through zero (Tj In 2), just as in the BIRD pulse sequence. Another method makes use of the technique described in Section 9.3 to measure diffusion coefficients. 

Other approaches to elimination of the water signal have exploited the difference in relaxation times between water and the compounds of interest, and have the advantage that peaks near the solvent are unaffected. For example, WEFT (Water Eliminated Fourier Transform) NMR uses an inversion recovery pulse sequence (designed for measurement). 

We now consider the problem of determining the T s of individual lines in a multi-line high resolution spectrum. The partially relaxed Fourier transform (PRFT) method, first performed by Void, et al. (1968), works very well for this purpose. It is basically the inversion recovery sequence except that after the second pulse the partially relaxed FID is Fourier transformed to yield a partially relaxed spectrum. 

Both direct and Indirect methods have been used to measure deuterium relaxation (2) the Inversion-recovery or partially relaxed Fourier transform method Is most widely employed. 

In the last section of this review, we will discuss some of the special applications and special recent developments of Fourier transform nuclear magnetic resonance. For example, the measurements of relaxation times T, or Tj require specific pulse methods (e.g. inversion recovery for 7 )i o,i36,i37,i39.m,u7.i5j,i59.i63.i67.224)... 

The following pulse sequence is used in the inversion recovery technique a 180° pulse is followed by a time interval t, then a 90° pulse, acquisition of a FID curve, and Fourier transformation. 

To derive projection reconstruction using planar-integral data, let us first direct our attention to the FB method. Based on the FB method, recovery of the original volume image function fix, y, z) can be achieved through the inverse Fourier transform of Eq. (23),... 

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