Solids spin-lattice relaxation times

The small term is due to the broadening caused by the magnetic field inhomogeneity. In solids, spin-lattice relaxation time, T is much longer... 

Different solid-state NMR techniques CPMAS NMR, the second moment of the signal, the spin-lattice relaxation time in the rotating frame T p) were combined to reach the conclusion that in the case of por-phine H2P the double-proton transfer is followed by a 90° rotation within the crystal (see Scheme 2). 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Quantitative solid state 13C CP/MAS NMR has been used to determine the relative amounts of carbamazepine anhydrate and carbamazepine dihydrate in mixtures [59]. The 13C NMR spectra for the two forms did not appear different, although sufficient S/N for the spectrum of the anhydrous form required long accumulation times. This was determined to be due to the slow proton relaxation rate for this form. Utilizing the fact that different proton spin-lattice relaxation times exist for the two different pseudopolymorphic forms, a quantitative method was developed. The dihydrate form displayed a relatively short relaxation time, permitting interpulse delay times of only 10 seconds to obtain full-intensity spectra of the dihydrate form while displaying no signal due to the anhydrous... 

Fig. 30. Hydrogen spin lattice relaxation time T, in a-Si H against temperature for flake samples removed from their substrate (solid line) and for a-Si H on quartz substrates two weeks after deposition (triangles). The circle data points are for the quartz substrate samples ten months after deposition. The magnitude of the 40 K minimum of T, is inversely portional to the number of H2 molecules contributing to the relaxation process (Van-derheiden et al., 1987). 

In solids, the coupling between the spins is much larger than their coupling with the lattice. The spin-lattice relaxation time is therefore very long (a few minutes) compared with the spin-spin relaxation time. It was soon realized that, to a first approximation, the evolution of many-spin systems towards equilibrium... 

Fig. 13. Predicted magnetic field dependence of the electron spin lattice relaxation time. Solid line pseudorotation model dashed line spin dynamics calculation. Reproduced with permission from Odelius, M. Ribbing, C. Kowalewski, J. J. Chem. Phys. 1996,104, 3181-3188. Copyright 1996 American Institute of Physics.

Fig. 1. Magnetic field dependences of the proton spin-lattice relaxation time of water in Bioran B30 and Vycor glasses at temperatures above 27°C and below the temperature where the non-surface water freezes ( —25°C and —35°C). The solid lines represent the power law in the Larmor frequency with an exponent of 0.67 (34).

Adsorbed water was observed to have a large effect on the F spin-lattice relaxation time for fluorine-doped aluminas in the dilute and intermediate concentration range of fluorine (0.3-8 wt. % F). An increase in Ti by a factor of 2 to 3 was observed in these samples when adsorbed water was removed from the solid by heating between 200-300°. The effect was completely reversible addition of oxygen-free water back to the solid resulted in recovery of the original (shorter) relaxation time. This effect was observed by the measurement of the in phase and ir/2 out of phase components of the dispersion derivative at resonance dx /6Ho at high rf power, from which effective values of Ti may be calculated 46). Values of Ti were also obtained by saturation of the resonance absorption derivative. 

Figure 2. Fluorine NMR relaxation times for a sample of Linde molecular sieve 13X containing about 6.6 molecules of SFg per cage O, spin lattice relaxation time , spin-spin relaxation time T2 characterized by exponential decay V and A, T2 characterizedby two relaxation times ticked O, decay as r2. Solid lines are theory to the left of 10Z/T = 6 based on molecular diffusion to the right of 10Z/T controlled by Tu. For dashed lines see text (20)...

Solid-state NMR suffers from two persistent problems (1) low abundance and/or sensitivity of the observed nucleus, and (2) long spin-lattice relaxation times Tx. Both can be remedied with the help of a double-resonance technique known as cross-polarization (CP) (21). 

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