Analysis of the Free Induction Decay FID

From H pulse NMR, the free induction decay (FID) with a large number of data points can be obtained. The curve fitting for the observed FIDs gives the individual T2 characteristics in the crystalline, amorphous, and interfacial phases [6-12]. Such a resolution into several components has been attempted on a broad-line spectrum of solid polyethylene (PE) [13-16], which reflect the sample morphologies. 

Generally, in order to fit the observed FID, a series of exponential functions (Eq. 8.3) are used because the distribution of dipole interaction is expressed by Lorentzian function. This is true for the solution, melt, and amorphous phases of the polymers. Actually, a PE melt with a low molecular weight (MW) exhibits a single exponential curve [17-20]. On the other hand, Weibulhan functions (Eq. 8.4) lit for the phase with partially restricted motion such as the interfacial phase [8,21]. 

For the polymeric materials, not only the dipole interactions between the nearest neighbors but also those between the proton pairs with longer distances contribute to the FID profile. Therefore, FID can be fitted by Equation 8.5 [26], 

The molecular mobility is usually discussed by T2 on the basis of BPP theory [5]. However, parameters, 1- 3 can no longer be directly compared. The mobility should be discussed by using the width of broad-line spectrum. By using these functions and the procedure, FID can be perfectly fitted without ambiguity. The obtained component ratio and integral 

In case of the FIDs with the low SIN ratio, the fitting described sometimes produces arbitrariness. To avoid this ambiguity, the explicit value determined from FID should be used. If the maximum value of FID is normalized to 1 and FID is composed of the sum of the exponentials, the area under FID can be obtained by integration as follows  

---

Recently, Neue [54] published another paper on an application of WT in dynamic NMR spectroscopy which could simplify the analysis of the free induction decay (FID) signal. Dynamic NMR spectroscopy is a technique used to measure rate parameters for a molecule [55]. The measured resonance frequencies represent the spatial coordinates of spins. Any motion, such as bond rotation and other molecular gymnastics, may change these frequencies as a function of time. The localization property of WT gives a better picture... 

---