Nearly-free induction decay

Studying moderately thin samples, the molecular time constants can be directly obtained from the experimental data without the need of computer simulations. This situation is termed nearly-free induction decay (NFID) which is related to the case of free induction decay in very thin samples. Some numerical results are depicted in Fig. 1. A specific experimental situation is considered with resonant, weak input pulses of Gaussian shape and duration tp (FWHM) and two values of the normalized propagation length, ai 0.2 and aJl 1. Here a denotes the conventional absorption coefficient at the maximum of the absorption band. The intensity of the transmitted pulse is evaluated from Maxwell-Bloch equations for homogeneous line broadening. 

In many of these descriptions of lineshapes, chemical exchange line-shapes are treated as a unique phenomenon, rather than simply another example of relaxation effects on lineshapes. This is especially true for line-shapes in the intermediate time scale, where severe broadening or overlapping of lines may occur. The complete picture of exchange lineshapes can be somewhat simplified, following Reeves and Shaw [13], who showed that for two sites, the lineshape at coalescence can always be described by two NMR lines. This fact can be exploited to produce a clarified picture of exchange effects on lineshapes and to formulate a new method for the calculation of exchange lineshapes [16, 23]. This method makes use of the fact that lineshapes, even near coalescence, retain Lorentzian characteristics [13] (fig. 3). These lines, or coherences, are each defined by an intensity, phase, position, and linewidth, and for each line in the spectrum, the contribution of that particular line to the overall free induction decay (FID) or spectrum can be calculated. 

Figure 7. Free-induction decay line shapes for H4Os4(CO)i2 near 100°K and room temperature. The lack of complete symmetry in the line shape may be caused by a probe impurity signal located slightly to the left of the spectra s...

Figure 8. Free-induction decay line shapes for H4Ru4(CO)i2 near 120°K and room temperature. The sharp peak located slightly left of the center in the room-temperature spectrum (and the asymmetry in the lower temperature spectrum) is caused partially by probe impurities.

Spin-lattice relaxation times for the protein protons were measured using the 90°-t-90° pulse sequence. Free induction decay amplitude was measured 15-20 microsec after the end of the second pulse by averaging 30 repetitions. To obtain the obvious double exponential relaxation behavior from the water protons, the first pulse of a 180°-t-90° sequence was attenuated so that the 180° pulse width was about 55 microsec while the second pulse remained near 4 microsec. Experimental considerations led us to believe the errors for the protein Ti values and the slow component of the water Ti curve are about 5% although linear least squares fits indicate better precision. 

Figure 33 shows the time dependence of the diffusivities of the reactant molecules (cyclopropane) and of the product molecules (propene) as well as of their relative amount, as determined by an analysis of the contributions of both molecular species to the NMR signal following the first tt/2 pulse (free induction decay) under reaction conditions (208]. The diffusivities of these reactant and product molecules happen to be quite close to each other, so there is no essential change in the diffusivity of either of the components with increasing reaction time. It is remarkable that this result may be predicted already on the basis of PFG NMR measurements at lower temperatures (i.e., far away from reaction conditions), where both diffusivities are also found to be nearly identical and independent of the composition (208]. In such a case the self-diffusivity should apparently coincide with the coefficient of counterdiffusion. 

More sophisticated NMR techniques have been also applied to measure the crystallinity in PVA cryogels [58]. For instance, pulsed mixed magic-sandwich echo sequences have been applied in a low-field NMR spectrometer [58]. This kind of pulse sequence provides near-quantitative refocusing of the rigid contribution to the initial part of proton free induction decay [58], allowing for a more quantitative determination of crystallinity in these gels. The results so obtained essentially confirm those shown in Fig. 10. 

The method used to excite the nuclei and achieve resonance must clearly be capable of covering all of the Larmor frequencies in the sample. This is achieved in the Fourier transform (FT) method by simultaneously exciting all the Larmor frequencies by application of a pulse (short burst) of rf signal (Bj) at or near all vqS, which results in the equalization of the populations of the nuclear spin energy levels. Equilibrium spin populations are reestablished in a free-induction-decay (FID) process following the rf pulse. The vector diagram in Fig. 20.5 can be used to visualize the effect of the rf pulse (61) on the nuclear spins and their subsequent FID to equilibrium. 

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