FID curve

Most molecules examined by NMR have more than just two sets of nuclei, each set with a different frequency (Av ). Furthermore, each set has its own relaxation times (T and T2), and usually there are different numbers of nuclei within each set. These factors combine to give complex digital FID curves consisting of n data points (usually in the thousands), numbered from 0 to n- 1. 

With regard to point (2) mentioned earlier, because of its linearity, the FFT imparts noise as unaltered from the time domain to the frequency domain. Moreover, the FFT has no possibility of separating noise from the true signal. In an attempt to improve resolution, one tries in vain to increase the total acquisition time, but for longer signals, noise becomes the major content to the encoded signals or free induction decay (FID) curves. 

A FID curve of polyvinyl chloride polymer formulation yielded four peaks corresponding to a pesticide (79°), a plasticizer (179°), a stabilizer (275°), and the polyvinyl chloride (438°). 

In these experiments, oxidation of acetaldehyde with a gas phase concentration of 100 ppm was studied. Using the catalysts in this study, acetaldehyde is oxidized without any side reactions of importance. Only the HC-FID curves are shown, since the conversion curves for the continuous FID instrument and the gas chromatograph coincide. The light-off temperatures for acetaldehyde oxidation are higher than for ethanol oxidation. This means that if acetaldehyde is formed it is more difficult to eliminate than unbumed ethanol. 

FIGURE 3.16 (a) An FID curve for the hydrogens in acetone (time domain) (b) the appearance of the FID when the decay is removed (c) the frequency of this sine wave plotted on a frequency chart (frequency domain). 

The line shapes shown in Fig. lb are determined by Fourier transforming the FID curves shown in Fig. la. Although some subtle differences can be seen in the two FIDS, they are quite similar. The FID curves of Fig. la are both composed of two components an exponential decay at long times, which transforms to a narrow Lorentzian line in the frequency domain (Fig. 1 b), and a Gaussian shape at short times, which transforms to a Gaussian line in frequency. 

Figure 2. Gas chromatographic curves for volatiles. Key Curve 1, standard mix in water of less than 1% each of methanol, ethanol, diethyl ether, and acetone flushed with He, trapped and tested on Poropak Q as were the fermentation gases (FID) Curve 2, gas phase of eight-day fermentation trapped and tested as described in text (FID) Curve 3, collected and counted GC effluents (see text) Curve 4, standard mix of 0.1% each methanol, ethanol, acetone, and acetic acid and Curve 5, water phase of fermentation.

According to eqns 15..3U and 15.32 the intensity of the maxima in the FID curve decays exponentially as Therefore Tz corresponds to the time at which the intensity has been reduced to l/e of the... 

Fourier Transform NMR. In Fourier transform NMR (FTNMR), a repetitive radio frequency (RF) pulse is applied in order to excite all of the nuclei of the particular nuclear species being studied. The sum of the free induction decay (FID) curves from each pulse is analyzed by a Fourier transform method in order to generate the familiar frequency domain spectra. Fundamentally, parameters such as the frequency, intensity, application time of the appropriate RF pulse, and time intervals between these pulses are important variables when using this technique. The principle of the pulsed Fourier transform technique can be found in books covering the fundamental concepts of NMR spectroscopy (58,59). 

Now consider a two-spin system. We can think of the magnetization vector of an AX spin system with /= 0 as consisting of two parts, one formed by the A spins and the other by the X spins. When the 90° pulse is applied, both magnetization vectors are tipped into the perpendicular plane. However, because the A and X nuclei precess at different frequencies, they induce two signals in the detector coils, and the overall FID curve may resemble that in Fig. 13.24a. The composite FID curve is the analog of the struck bell emitting a rich tone composed of all the frequencies at which it can vibrate. 

The problem we must address is how to recover the resonance frequencies present in a free-induction decay. We know that the FID curve is a sum of oscillating functions, so the problem is to analyze it into its component frequencies by carrying out a Fourier transformation. When the signal in Fig. 13.24a is transformed in this way, we get the frequency-domain spectrum shown in Fig. 13.24b. One Hne represents the Larmor frequency of the A nuclei and the other that of the X nuclei. 

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. 

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