Slow spin relaxation

K.K.P. Srivastava, A Mossbauer study of slow spin relaxation of paramagnetie Fe in MgCOj. J. Phys. C. Solid State Phys. 16, 1137-1139 (1983)... 

Slow spin relaxation of optically polarized atoms... 

Dehmelt, H. G. (1957). Slow spin relaxation of optically polarized sodium atoms. 

The crystal field interaction gives rise to an energy splitting into a number of Kramers doublets. In the case of high-spin Fe " with spin S = 5/2, there are three Kramers doublets, each of which give rise to separate contributions in the Mossbauer spectra of samples with slow paramagnetic relaxation. For 1 = 0 and a = 0, they can be labeled l/2), 3/2) and 5/2). 

In paramagnetic materials, the relaxation frequency is in general determined by contributions from both spin-lattice relaxation and spin-spin relaxation. Spin-lattice relaxation processes can conveniently be studied in samples with low concentrations of paramagnetic ions because this results in slow spin-spin relaxation. Spin-spin relaxation processes can be investigated at low temperatures where the spin-lattice relaxation is negligible. Paramagnetic relaxation processes have... 

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

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... 

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

Also spin-lattice relaxation times T and spin-spin relaxation times T2 were measured as a function of pressure on different selectively deuterated DPPC (at C2, Cg and Ci3, respectively) by Jonas and co-workers (Fig. 14). The spin-latticed relaxation time T is sensitive to motions with correlation times tc near Uo i e., motions with correlation times in the range from 10 to 10 " s. In comparison with Ti, the spin-spin relaxation time T 2 is more sensitive to motions with correlation times near (e qQlh), i.e., in the intermediate to slow range (10 " to 10 s). The Ti and T2 values obtained showed characteristic changes at various phase transition pressures, thus indicating abrupt changes... 

Fig. 3. Variation of the completely reduced dipole-dipole spectral density (see text) for the model of a low-symmetry complex for S = 3/2. Reprinted from J. Magn. Reson., vol. 59,Westlund, RO. Wennerstrom, H. Nordenskiold, L. Kowalewski, J. Benetis, N., Nuclear Spin-Lattice and Spin-Spin Relaxation in Paramagnetic Systems in the Slow-Motion Regime for Electron Spin. III. Dipole-Dipole and Scalar Spin-Spin Interaction for S = 3/2 and 5/2 , pp. 91-109, Copyright 1984, with permission from Elsevier.

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