Spin diffusion relaxation mechanisms

The minimum in the spin-lattice relaxation time is more difficult to account for. It cannot be attributed to the onset of the diffusional motion, because the jump frequency does not match the Larmor frequency at the temperature where diffusion becomes important. For this reason it is necessary to postulate an additional kind of motion in the lithium-vanadium bronze—a side-to-side jumping from one side of the channel to the other. In the structure there are sites on both sides of the channel roughly 2 A. apart which are equivalent but only one of which is occupied to fulfill stoichiometry. This kind of motion should start at a lower temperature than the above diffusion and lead to a correlation frequency that matches the Larmor frequency at the spin-lattice time minimum. Because of modulation of quadrupolar interaction, side-to-side motion could provide an effective spin-lattice relaxation mechanism. 

As discussed in section 6.3, relaxation times of solid polymers are not only determined by dynamic phenomena. There may exist a contribution from the static mechanism of spin diffusion. The probability for a flip-flop between two opposite 1/2 spins having the same precession frequency is a decreasing function of the distance between the spins. Moreover, for heterogeneous solids, the spin diffusion mechanism manifests itself in a particular way. When two proton populations have different spin temperatures at a given time, they will tend to a common spin temperature by spin diffusion. (The mechanism is described in more detail in chapter 7). Such a situation occurs during a Ti( H) or determination in a heterogeneous system. For example,... 

Director fluctuations are however not the only spin-lattice relaxation mechanism in nematics. Translational self-diffusion of nematic molecules modulates the inter-molecular nuclear dipole-dipole interactions and induces - as first emphasized by Vilfan, Blinc and Doane [36], another contribution... 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

Some measurements have been made of self diffusion in pure ethylene and in ethylene-sulfur hexafluoride mixtures (22), but these measurements were made very close to the critical temperature and up to pressures of only about 100 bar. Proton spin-lattice relaxation times (T.) of ethylene have been measured at temperatures from 0°C to 50°C and pressures up to about 2300 bar (13). The relaxation time values were -M0—50 sec for much of the region studied. Several relaxation mechanisms contribute to this long relaxation time and make both the measurement and analysis of the relaxation times very difficult. For these reasons, we decided to limit our study to the measurement of the self-diffusion coefficient in supercritical ethylene (60. 

The spin-lattice relaxation time 7] as a function of temperature T in liquid water has been studied by many researchers [387-393], and in all the experiments the dependence T (T) showed a distinct non-Arrhenius character. Other dynamic parameters also have a non-Arrhenius temperature dependence, and such a behavior can be explained by both discrete and continuous models of the water structure [394]. In the framework of these models the dynamics of separate water molecules is described by hopping and drift mechanisms of the molecule movement and by rotations of water molecules [360]. However, the cooperative effects during the self-diffusion and the dynamics of hydrogen bonds formation have not been practically considered. 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

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