Spin relaxation process

Woessner D E 1962 Spin relaxation processes in a two-proton system undergoing anisotropic reorientation J. Chem. Rhys. 36 1-4... 

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... 

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

A major limitation of CW double resonance methods is the sensitivity of the intensities of the transitions to the relative rates of spin relaxation processes. For that reason the peak intensities often convey little quantitative information about the numbers of spins involved and, in extreme cases, may be undetectable. This limitation can be especially severe for liquid samples where several relaxation pathways may have about the same rates. The situation is somewhat better in solids, especially at low temperatures, where some pathways are effectively frozen out. Fortunately, fewer limitations occur when pulsed radio and microwave fields are employed. In that case one can better adapt the excitation and detection timing to the rates of relaxation that are intrinsic to the sample.50 There are now several versions of pulsed ENDOR and other double resonance methods. Some of these methods also make it possible to separate in the time domain overlapping transitions that have different relaxation behavior, thereby improving the resolution of the spectrum. 

The Redfield matrix elements are defined in full analogy with the case where the conventional electron spin relaxation processes in a non-equilibrium ensemble are considered, but the rates are in general different from... 

As in Eq. (64), the electron spin spectral densities could be evaluated by expanding the electron spin tensor operators in a Liouville space basis set of the static Hamiltonian. The outer-sphere electron spin spectral densities are more complicated to evaluate than their inner-sphere counterparts, since they involve integration over the variable u, in analogy with Eqs. (68) and (69). The main simplifying assumption employed for the electron spin system is that the electron spin relaxation processes can be described by the Redfield theory in the same manner as for the inner-sphere counterpart (95). A comparison between the predictions of the analytical approach presented above, and other models of the outer-sphere relaxation, the Hwang and Freed model (HF) (138), its modification including electron spin... 

Selective inversion experiments for the determination of slow exchange rates are analogous to the saturation-transfer method in that they involve selective manipulation of one of the exchanging sites, while observing the subsequent effect on the second site as a function of time [48, 69, 70]. Chemical exchange, if present, will provide an alternative route to normal spin relaxation processes which a spin system undergoes, if perturbed at the start of an experiment. The rate of relaxation will depend on both the exchange rate k and the spin-lattice relaxation rate (Ti) (fig. 5). 

Relaxation time measurements have long been used to characterize molecular motions in solids. All nuclear spin relaxation processes are mediated by fluctuating nuclear spin interactions, with the fluctuations (generally) arising... 

Fig. 6. A spin-echo pulse sequence used to determine T2. (a) A (jt/2) pulse puts M0 into the indirection, and (b) the spin isochromats dephase with time. At a time td later, a n pulse is applied along the /-axis causing the spins to rotate through n radians (c) such that they refocus along the /-axis to form an echo at time. 2rd.(d) The decrease in magnitude of the magnetisation vector between stages (a) and (d) provides a measure of T2 [Eq. (4)]. All reversible contributions to the spin-spin relaxation process are removed by the application of the n pulse.

We have thus far considered coherent processes that take place in RPs (which in some cases been have been modulated by stochastic motion). However, the common spin-lattice and spin-spin relaxation processes familiar from magnetic resonance also come to bear on the dynamics of RPs. Typical values of Ti and T2 for small organic radicals in homogeneous solution are on the microsecond timescale and as such are rather slow relative to coherent mixing and RP diffusion. Thus, for the most part, effects of incoherent spin relaxation are not manifest in such reactions. However, for reactions in which the RP lifetime is substantially extended, for instance, by constraining the RP inside a microreactor such as a micelle (many examples in Ref. 14), relaxation effects become significant. 

Redfield limit, and the values for the CH2 protons of his- N,N-diethyldithiocarbamato)iron(iii) iodide, Fe(dtc)2l, a compound for which Te r- When z, rotational reorientation dominates the nuclear relaxation and the Redfield theory can account for the experimental results. When Te Ti values do not increase with Bq as current theory predicts, and non-Redfield relaxation theory (33) has to be employed. By assuming that the spacings of the electron-nuclear spin energy levels are not dominated by Bq but depend on the value of the zero-field splitting parameter, the frequency dependence of the Tj values can be explained. Doddrell et al. (35) have examined the variable temperature and variable field nuclear spin-lattice relaxation times for the protons in Cu(acac)2 and Ru(acac)3. These complexes were chosen since, in the former complex, rotational reorientation appears to be the dominant time-dependent process (36) whereas in the latter complex other time-dependent effects, possibly dynamic Jahn-Teller effects, may be operative. Again current theory will account for the observed Ty values when rotational reorientation dominates the electron and nuclear spin relaxation processes but is inadequate in other situations. More recent studies (37) on the temperature dependence of Ty values of protons of metal acetylacetonate complexes have led to somewhat different conclusions. If rotational reorientation dominates the nuclear and/or electron spin relaxation processes, then a plot of ln( Ty ) against T should be linear with slope Er/R, where r is the activation energy for rotational reorientation. This was found to be the case for Cu, Cr, and Fe complexes with Er 9-2kJ mol" However, for V, Mn, and... 

At this point it is necessary to relate the relaxation time for the chemical process to the spin-spin relaxation process which is always present when the system absorbs energy from the radio frequency wave. Both processes lead to broadening of the NMR absorption peak. If T, is the total relaxation time for process i, it may be estimated from T2 and x,- using the relationship... 

NMR observations basically contain spin relaxation processes which are associated with molecular motions with different specific frequencies in a given system. For quantitative measurements to determine the compositions of the system or selective measurements of particular components with different relaxation parameters, it is essential, therefore, to understand the principle of the relaxation mechanism. When our interest is focused on molecular motions, spin relaxation parameters such as spin-lattice relaxation time T, spin-spin relaxation time T2, and the nuclear Overhauser enhancement (NOE), are directly measured as a function of temperature or field frequency by using appropriate pulse sequences. Such temperature or frequency dependencies of the spin relaxation parameters are analyzed in terms of appropriate models to obtain detailed information of molecular motions with frequencies of Hz in the system. In this chapter, the basic theories and analyses... 

EPR Characteristics of Metal-Centered Radicals. Generally, electron-spin relaxation processes are much faster for metal-centered radicals compared to organic radicals (or hgand-centered radicals). Therefore, EPR spectra of metal-centered radicals are usually recorded at low temperatures (<100 K) to prevent substantial line broadening. 

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