Deuteron spin-lattice relaxation

In the theory of deuteron spin-lattice relaxation we apply a simple model to describe the relaxation of the magnetizations T and (A+E), for symmetry species of four coupled deuterons in CD4 free rotators. Expressions are derived for their direct relaxation rate via the intra and external quadrupole couplings. The jump motion between the equilibrium positions averages the relaxation rate within the same symmetry species. Spin conversion transitions couple the relaxation of T and (A+E). This mixing is included in the calculations by reapplying the simple model under somewhat different conditions. The results compare favorably with the experimental data for the zeolites HY, NaA and NaMordenite [6] and NaY presented here. Incoherent tunnelling is believed to dominate the relaxation process at lowest temperatures as soon as CD4 molecules become localized. 

Mayer, C., G. Grobner, K. Muller, K. Weisz, and G. Kothe (1990) Orientation-dependent deuteron spin-lattice relaxation times in bilayer membranes characterization of the overall hpid motion. Chem. Rhys. Lett. 165, 155-161. 

Tropolone is easily deuterated and the Sj-Sq fluorescence excitation spectrum of jet-cooled TRN(OD) was reported by Sekiya et al. [40]. The observed doublet separation, DS = 2 cm 1, is near the 2.2 cm value reported by Alves and Hollis [22], and about 10% of the value observed for TRN(OH). Presently the only available experimental estimate for the ZP tunneling splitting of Sq TRN(OD) is Ao <0.17 cm 1 [80] obtained using a chloroform solvent and NMR spectroscopy to measure the deuteron spin-lattice relaxation time. 

Figure 5.13 shows the dependence on pressure, for various temperatures, of the rotational and translational molecular mobility for trifluoromethane. Rotational mobility is characterized by the deuteron spin-lattice relaxation time, Tj, and translational mobility is characterized by the self-diffusion coefficient. In all nonpolar liquids, and also in most polar liquids, changes in temperature and pressure have a stronger influence upon the translational mobility than upon the rotational mobility. 

Figure 8. Temperature and pressure dependence of the deuteron spin-lattice relaxation time in glycerol-df. Key , 1 bar A, 2000 bar and O, 4000 bar. (Reproduced, with permission, from Ref. 16. Copyright 1971, American Institute...

The deuteron spin-lattice relaxation rates R, where j labels the position of the deuteron in the alkyl chains, were found to decrease monotonically along the chains of mesogens [8.7, 8.15-8.17]. The spin-lattice relaxation rates in liquid crystals were also found to follow the same trend [8.18, 8.19]. These observations may be accounted for by a model that considers the contributions made to the rotations within the molecule and reorientation of the whole molecule. Beckmann et al. [8.7] found that a model of superimposed rotations is consistent with a monotonic decrease of relaxation rates along the pentyl chain of 5CB-di5 (Fig. 8.2). 5CB will be used as a model liquid crystal. 

It has been clear for some years that internal motions are important in determining nuclear spin relaxation in liquid crystals. This mechanism has been neglected in the early theories [8.27-8.29] proposed to explain nuclear spin relaxation in ordered mesophases. Recently, large quantities of experimental data were collected [8.7, 8.11, 8.15, 8.30, 8.31] in liquid crystal phases to give spectral densities for the different nuclear sites in the molecules. This led to the development of the theoretical models described in previous sections, which aim at treating internal motions in ordered mesophases. Thus far, only several liquid crystals has been studied in detail to examine the relaxation effects of internal motions. Beckmann et al. [8.7] were first to apply the superimposed rotations model (Section 8.21) to account for the site dependence of the deuteron spin-lattice relaxation rates at 30.7 MHz in the pentyl chain of 5CB. The spectral densities were calculated in the fast motion limit to give equations like Eq. (8.15). Since only the spin-lattice relaxation rate see Eq. (5.40)]... 

At low fields, proton and especially deuteron spin-lattice relaxation times of viscous polymer systems may easily fall short of a millisecond. That is, coming from the large polarization field of typically 0.5 T, relaxation fields that can be as low as 10 T must be reached and settled and stabilized with a desired accuracy of better than 10% within a total passage time in the order of one millisecond. The short settling time is a stringent condition which is not easy to fiilfill practically. Likewise the passage from the relaxation field to the detection field should occur in a transition time of the same order. In particular, the detection flux density needed for magnetic resonance must be hit and reproduced with an accuracy of about 10" in subsequent transients. 

Figures 28, 29, 30, 31, 32, 33, and 34 show a series of typical spin-lattice relaxation dispersion curves. The technique has been applied to melts, solutions, and networks of numerous polymer species. As experimental parameters, the temperature, the molecular weight, the concentration, and the cross-link density were varied. For control and comparison, the studies are partly supplemented by rotating-frame spin-lattice relaxation data and, of course, by high-field data of the ordinary spin-lattice relaxation time. Furthermore, the deuteron spin-lattice relaxation was employed for identifying the role different spin interactions are playing for relaxation dispersion.

Fig. 36a, b. Deuteron spin-lattice relaxation times of deuterated polyethyleneoxide (PEG) (a) and polybutadiene (PB) (b) as a function of the frequency [156]... 

Fig. 45a, b. Frequency dependence of the deuteron spin-lattice relaxation time of perdeuterated PEG confined in 10-nm pores of solid PHEMA at 80 °C (a) and in bulk melts (b) [95, 185]. The dispersion of the confined polymers verifies the law Ti (X M° ft)° at high frequencies as predicted for limit (II)de of the tube/reptation model (see Table 1). The low-frequency plateau observed with the confined polymers indicates that the correlation function implies components decaying more slowly than the magnetization relaxation curves, so that the Bloch/Wangsness/Redfield relaxation theory [2] is no longer valid in this regime. The plateau value corresponds to the transverse relaxation time, T2, for deuterons extrapolated from the high-field value measured at 9.4 T... 

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