Lattice Relaxation Processes

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). 

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. 

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. 

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... 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

Ammonium alums undergo phase transitions at Tc 80 K. The phase transitions result in critical lattice fluctuations which are very slow close to Tc. The contribution to the relaxation frequency, shown by the dotted line in Fig. 6.7, was calculated using a model for direct spin-lattice relaxation processes due to interaction between the low-energy critical phonon modes and electronic spins. 

In a metal, there are excited states for electrons that lie below the ionization energy. This can be conceived as an electron in a "conduction band" and a "hole" that interact so that the combination is neutral but not of lowest energy. Such an excited state is called an exciton. Excitons may move by diffusion of the electron-hole pair or by transfer of a molecular exciton to another molecule. Reversion of the exciton to a lower energy state may be slow enough for the lifetime to be longer that of lattice relaxation processes. 

Fig. 14. A scheme of the spin-lattice relaxation process together with spin diffusion. A and are two kind of spins in the component polymers A and B. Its assumed that 7) of A is much shorter than that of B.

The spin-lattice relaxation process is usually exponential. Theoretically, the effect of spin-diffusion, characterized by the coefficient D (order of 1(T12 cm2 s 1), has an influence on T, relaxation times when ix > L2/D, where Lis the diffusion path length. NMR studies of model systems f6r rubber networks, based on a styrene-butadiene-styrene block copolymer (SBSy, in which styrene blocks act as a crosslink for polybutadiene rubber segments of known and uniform length, indicate that spin diffusion operating between PS and PB phases causes a lowering of Tg for the PS component in SBS (as compared to the pure PS) and hindering of the motion of the PB component (as compared to the pure PB)51). 

The spin-lattice relaxation process, designated 7 (also termed longitudinal relaxation), varies widely for different types of carbon atoms. 

High-spin tetrahedral or pseudo-tetrahedral (C2v) [Co(X)2(PR3)2] (R = alkyl, aryl X = Cl-, Br-) complexes are easily prepared from CoX2 and PR3 in hot EtOH (Table 36). Addition of a large cation can lead to the isolation of the [Co(X)3(PR3)]- anion, and [Co(X)(PMe3)4](BPh4) has been isolated (Table 36). Crystal structures are available (Table 35). Care must be taken to avoid ligand oxidation, especially for R = aryl. [Co(X)2(PR3)2] and (NB<)[Co(X)3(PR3)] have ESR and NMR characteristics consistent with a fast spin-lattice relaxation process (Tj 6 x 10 3 s- )450 and use of... 

Based upon the current theories of CIDEP and CIDNP, we propose that in many photochemical systems the primary photochemical reaction of the excited triplet state contributes to magnetic polarization via the triplet mechanism. The secondary reaction of the polarized primary radicals may transfer their initial polarization to the "secondary radicals" provided that the radical reactions can compete with the radical spin-lattice relaxation process (59,97). On the other hand, secondary reactions of the primary radical pair or the uncorrelated F pair contribute to polarization by the radical-pair mechanism. A general scheme showing the possible and simultaneous operations of both the... 

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... 

If the symmetry increases or decreases drastically, the spin-lattice relaxation process is fast, or the optical pumping is not successful in producing large spin alignment, the above rules would not be as definite. 

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] ... 

These components will oscillate as a function of t]. The resultant Z-magnetizations will be in a nonequilibrium state and spin-lattice relaxation processes will work toward equilibrium. For the case of protons relaxation is primarily dipolar via other protons, this non-equilibrium magnetization will then be redistributed by mutual spin flip to other protons. The final 90° pulse monitors the extent of magnetization transfer. The 2D experiment samples all degrees of magnetization transfer as it increments t]. ... 

The magnitude and sign of the enhancement in liquids depend upon the spin lattice relaxation processes in the solution, and these are dependent upon the molecular motions and interactions present in the solution. In order to understand the spin lattice relaxation processes in these systems it is first convenient to consider the mechanism for a diamagnetic system of nuclei of spin quantum number I=. ... 

The principle is quite simple. The MW field is switched on with a variable delay x after the laser flash. The amplitude of the transient signal plotted as a function of x renders the decay of the spin-polarized initial magnetization towards its equilibrium value. This method is preferred over the TREPR technique at low MW power (see equation (bl.15.31)) since the spin system is allowed to relax in the absence of any resonant MW field in a true spin-lattice relaxation process. The experiment is carried out by adding a PIN diode MW switch between the MW source and the circulator (see figure Bl.15.4, and set between a pair of isolators. Since only low levels of MW power are switched (typically less than 1 W), as opposed to those in ESE and FT EPR, the detector need not be protected against high incident power levels. 

The important point to get out of all this is that since the nuclear spin-lattice relaxation processes usually depend on the the existence of molecular motion to generate a randomly varying magnetic field or EFG, we can get valuable information about these motions from the relaxation rates. 

This does not at all mean that the majority of the spin-lattice relaxation processes in nature are exponential. It is just that much NMR is done on samples in which most of the interactions which give rise to non-exponential effects are absent or else the non-exponentiality is ignored for one reason or another. The spin-lattice relaxation time T is defined only for exponential processes. Therefore, any scheme for deter-... 

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