Spin-lattice relaxation processes

After B, is turned off, nuclei can change their nuclear spin orientations through two types of relaxation processes. Spin-lattice (longitudinal) relaxation (governed by relaxation time 7, ) involves the return of the nuclei to a Boltzmann distribution. Spin-spin (transverse) relaxation (governed by relaxation time 72 or 7 ) involves the dephasing of the bundled nuclear spins. Normally 7 < T2 < 7,. 

The methods by which excited nuclei return to their ground state and by which the Boltzmann equilibrium is reestablished are called relaxation processes. In NMR systems there are two principal types of relaxation processes spin-lattice relaxation and spin-spin relaxation. Each occurs as a first-order rate process and is characterized by a relaxation time, which governs the rate of decay. 

The spin-lattice relaxation is enabled via spin-orbital coupling involving a phonon process. Spin-lattice relaxation time (tsl) is temperature dependent. Generally speaking, tsl becomes smaller on increasing the temperature. One can distinguish three types of spin-lattice relaxation processes [103] ... 

Since the total number of nuclei N = N, + Np,itia evident from equation (1) that (N — N ), and hence the intensity of the n.m.r. signal, is proportional to N. Typically, the excess population in the -state is 1 10 . Application of the appropriate radiofrequency field induces both upward and downward transitions, but the former predominate. The observed signal indicating energy absorption would quickly be saturated (iVp = iV ) but for a non-radiative process, spin-lattice relaxation, by which the Boltzmann distribution can be continuously re-established. Spin-lattice relaxation times, that is the time required for a collection of nuclei to return to the Boltzmann distribution after perturbation, varies according to the type of nucleus (e.g., etc.) and, for a... 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

If the two sites exchange with rate k during the relaxation, tiien a spin can relax either tlirough nonnal spin-lattice relaxation processes, or by exchanging witli the other site, equation (B2.4.45) becomes (B2.4.46). 

The decay of M to Mo is called longitudinal relaxation (because it is parallel with the field Ho), it is identical with the spin-lattice relaxation described earlier. The rate constant for this process is therefore l/T,. The decay of M, and My is... 

Methods of disturbing the Boltzmann distribution of nuclear spin states were known long before the phenomenon of CIDNP was recognized. All of these involve multiple resonance techniques (e.g. INDOR, the Nuclear Overhauser Effect) and all depend on spin-lattice relaxation processes for the development of polarization. The effect is referred to as dynamic nuclear polarization (DNP) (for a review, see Hausser and Stehlik, 1968). The observed changes in the intensity of lines in the n.m.r. spectrum are small, however, reflecting the small changes induced in the Boltzmann distribution. 

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

Appendix Spin-Lattice Relaxation Processes References... 

In this section, the characteristics of the spectra displayed by the different types of iron—sulfur centers are presented, with special emphasis on how they depend on the geometrical and electronic structure of the centers. The electronic structure is only briefly recalled here, however, and interested readers are referred to the excellent standard texts published on this topic (3, 4). Likewise, the relaxation properties of the centers are described, but the nature of the underlying spin-lattice relaxation processes is not analyzed in detail. However, a short outline of these processes is given in the Appendix. The aim of this introductory section is therefore mainly to describe the tools used in the practical applications presented in Sections III and IV. It ends in a discussion about some of the issues that may arise when EPR spectroscopy is used to identify iron-sulfur centers. 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

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