Spin reorientational relaxation process

In our description of spin reorientational relaxation processes, tensorial quantities are used for which it is necessary to know the transformation properties concerning rotation. A clear and compact formulation is obtained by replacing the cartesian components with a representation in terms of irreducible spherical components. It is known that any representation of the group of rotations can be developed into a sum of irreducible rqpre-sentations D of dimension 2/ +1. If for the description of general rotation R(U) we use the Euler angles Q = (a, p, y), this rotation will be defined by... 

The interpretation of carbon T p data is complicated by the fact that spin-spin (cross-relaxation) processes as well as rotating frame spin-lattice processes may contribute to the relaxation (40). Only the latter process provides direct information on molecular motion. For the CH and CH2 carbons of PP, the Tip s do not change greatly over the temperature interval -110°C to ambient and, as opposed to the T behavior, the CH2 carbon has a shorter T p than the CH carbon. These results suggest that spin-spin processes dominate the Tip (46). However, below ca. -115°C, the Tip s for both carbons shorten and tend toward equality. McBrierty et al. (45) report a proton Ti minimum (which reflects methyl group reorientation at KHz frequencies) at -180°C. No clear minimum is observed in the data, perhaps due to an interplay of spin-spin and spin-lattice processes. Nonetheless, it is apparent that the methyl protons are responsible for the spin-lattice portion of the Tip relaxation for CH and CH2 carbons. 

The Ti relaxation time is the time constant for magnetisation to recover on the z axis (Figure 7.3b), restoring the equilibrium Boltzmann distribution of spins. This relaxation process occurs by energy loss to the surrounding lattice (any nearby molecules) and the efficiency of the process is determined by molecular reorientations occurring near the Larmor frequency (e.g. molecular rotations and internal motions). T, is measured with the inversion-recovery (IR) or saturation-recovery (SR) pulse sequence (see Section 7.7.2). 

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

Fig. 3. Schematic representation of the topological space of hydration water in silica fine-particle cluster (45). The processes responsible for the water spin-lattice relaxation behavior are restricted rotational diffusion about an axis normal to the local surface (y process), reorientations mediated by translational displacements on the length scale of a monomer (P process), reorientations mediated by translational displacements in the length scale of the clusters (a process), and exchange with free water as a cutoff limit.

It may be appropriate to discuss the NMR findings on the /1-process in the context of results from other experimental methods. Unlike 2H NMR, the vast majority of experimental techniques are not capable of resolving slow reorientation about very small angles. In particular, several studies on the /1-process of molecular glasses may have overlooked the small-angle contribution of the majority of molecules and concluded that a small fraction of molecules is involved in the secondary relaxation process. In contrast, straightforward analysis of 2H NMR solid echo (cf. Section 3.2.1) and spin-lattice relaxation data (cf. Section 3.2.4 and in particular Ref. 115) clearly shows that essentially all molecules participate in the /1-process. However, the amplitude of the reorientation differs among the molecules. The mean... 

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... 

Von Schiitz and Wolf [29] have likewise investigated a second typical stochastic reorientation motion using NMR in molecular crystals the hindered rotation of methyl (CH3 -) groups in ten different methyl-substituted naphthalene crystals. The reorientation motions are, at not-too-low temperatures, the dominant source of nuclear spin-lathce relaxation in these highly purified molecular crystals. Only at very low temperatures do thermally-activated reorientation processes cease to play a role. The spin-lattice relaxation is then determined essentially by paramagnetic impurities. 

Conformations and Dynamic Situations.—Rotation about single bonds " and partial double bonds, carbonium-ion rearrangements, conformational processes in rings, and spin-lattice relaxation times and the mobility of organic molecules in solution have been reviewed. The proton spin-lattice relaxation of polycrystalline bicyclo[2,2,2]oct-2-ene has been measured and the enthalpy of activation or reorientational motion calculated. 

The direct NMR method for determining translational difiFusion constants in liquid crystals was described previously. The indirect NMR methods involve measurements of spin-lattice relaxation times (Ti,Ti ),Tip) [7.45]. Prom their temperature and frequency dependences, it is hoped to gain information on the self-diflPusion. In favorable cases, where detailed theories of spin relaxation exist, difiFusion constants may be calculated. Such theories, in principle, can be developed [7.16] for translational difiFusion. However, until recently, only a relaxation theory of translational difiFusion in isotropic hquids or cubic solids was available [7.66-7.68]. This has been used to obtain the difiFusion correlation times in nematic and smectic phases [7.69-7.71]. Further, an average translational difiFusion constant may be estimated if the mean square displacement is known. However, accurate determination of the difiFusion correlation times is possible in liquid crystals provided that a proper theory of translational difiFusion is available for liquid crystals, and the contribution of this difiFusion to the overall relaxation rate is known. In practice, all of the other relaxation mechanisms must first be identified and their contributions subtracted from the observed spin relaxation rate so as to isolate the contribution from translational difiFusion. This often requires careful measurements of proton Ti over a very wide frequency range [7.72]. For spin - nuclei, dipolar interactions may be modulated by intramolecular (e.g., collective motion, reorientation) and/or intermolecular (e.g., self-diffusion) processes. Because the intramolecular (Ti ) and intermolecular... 

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