Solid-state spin-lattice relaxation rates

Solid-state spin-lattice relaxation rates in the rotating frame, Rip, contain useful information about slow motions with correlation times in the range of microseconds [146]. The measured Rjp data, however, contain the foUow-ing two relaxation pathways the spin-lattice contribution describing slow motions (Rip) and the interfering spin-spin contribution from a thermal coupling between Zeeman carbon (or nitrogen) and dipolar proton reservoirs (Rch)-... 

Strong evidence of the dominant Influence of molecular conformation on the properties of coals Is Implicit In the several data sets which show an extremum In the measured property when plotted against carbon rank. Examples are the extrema which occur In the solid state properties of mass density (22,23) and proton spin-lattice relaxation rate (24) as well as In solvent swelling and extractablllty ( ). 

Satisfaction of the third condition above depends on the rates of the spin-lattice relaxation processes between the spin sublevels. These rates are highly temperature dependent and depend also on the environment within which the molecular system is placed. In order to maintain a steady-state triplet sublevel population imbalance, the rates of spin-lattice relaxation must be slower than the rates at which the sublevels decay to the ground state. To reduce the spin-lattice relaxation rates to this level requires temperatures of the order of 4.2°K or lower, in the proper solvent. Whether or not spin-lattice processes can be "frozen" at liquid helium temperatures may even depend on the solid phase of the... 

Faster incoherent tunnelling processes can be studied by solid state NMR relaxometry [40, 41]. In these experiments the experimentally determined spin-lattice relaxation rates are converted into incoherent exchange rates. The latter are then evaluated, for example with the Bell tunnelling model described above. 

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... 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

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. 21. Temperature dependence of the rate k and time ijir of spin-lattice relaxation of state II of Pt(2-thpy)2 dissolved in n-octane. The experimental data (points) result from the emission decay times of state II, but they are corrected according to Eq. (21). The solid line represents a fit according to Eq. (22), while the broken and dotted lines give the contributions of the respective processes. The inset shows the triplet sublevels and depicts schematically the three different processes of spin-lattice relaxation. (Compare Ref. [24])...

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