Nuclear spin relaxation rate, temperature

By the same experimental technique, the temperature dependence of the nuclear spin relaxation rates was investigated for the radical cations of dimethoxy- and trimethoxybenzenes [89], The rates of these processes do not appear to be accessible by other methods. As was shown, l/Tfd of an aromatic proton in these radicals is proportional to the square of its hyperfine coupling constant. This result could be explained qualitatively by a simple MO model. Relaxation predominantly occurs by the dipolar interaction between the proton and the unpaired spin density in the pz orbital of the carbon atom the proton is attached to. Calculations on the basis of this model were performed with the density matrix formalism of MO theory and gave an agreement of experimental and predicted relaxation rates within a factor of 2. 

Petrov et al. have presented a variable temperature solid-state NMR investigation of cryptophane-Exhloroform and cryptophane-Erdichlorometh-ane inclusion complexes.The line shapes and nuclear spin relaxation rates were analysed in terms of the distribution of C-D bond orientations and the time scale of the guest dynamics. It was found that encaged chloroform produces broad spectra, and that its reorientation is relatively slow with a correlation time of 0.17 ps at 292 K. In contrast, the line shapes of encaged dichloromethane were narrow and the motion of this guest molecule was fast with a correlation time of 1.4 ps at 283 K. The NMR data were complemented by an X-ray diffraction study of the cryptophane-E dichloro-methane structure, which was utihsed in the analysis of the NMR parameters. 

As opposed to the previous examples, the rate of the pair substitution BRi BR2 BR3 can be varied by neither the reactant concentrations nor the solvent polarity because it is intramolecular and only involves neutral species. However, the ratio of polarizations of corresponding protons in Pi and P2 exhibits a pronounced temperature dependence, " which is shown in Fig. 9.8 and can be explained in the following way. Ideally, these opposite polarizations should have exactly equal magnitudes, but their ratio deviates from 1 if nuclear spin relaxation in the paramagnetic intermediates is taken into account. Biradicals with nuclear spin states that slow down intersystem crossing of BRi live longer, so their nuclear spins suffer a stronger relaxation loss. 

The dynamic characteristics of adsorbed molecules can be determined in terms of temperature dependences of relaxation times [14-16] and by measurements of self-diffusion coefficients applying the pulsed-gradient spin-echo method [ 17-20]. Both methods enable one to estimate the mobility of molecules in adsorbent pores and the rotational mobility of separate molecular groups. The methods are based on the fact that the nuclear spin relaxation time of a molecule depends on the feasibility for adsorbed molecules to move in adsorbent pores. The lower the molecule s mobility, the more effective is the interaction between nuclear magnetic dipoles of adsorbed molecules and the shorter is the nuclear spin relaxation time. The results of measuring relaxation times at various temperatures may form the basis for calculations of activation characteristics of molecular motions of adsorbed molecules in an adsorption layer. These characteristics are of utmost importance for application of adsorbents as catalyst carriers. They determine the diffusion of reagent molecules towards the active sites of a catalyst and the rate of removal of reaction products. Sometimes the data on the temperature dependence of a diffusion coefficient allow one to ascertain subtle mechanisms of filling of micropores in activated carbons [17]. 

Fig. 101. Left Near-ZF (i.e., a small LF is applied to suppress relaxation effects from nuclear moments) pSR spectra in YjMojO, stated as polarization (A(0 divided by the instrumental asymmetry, A, ), at various temperatures. The inset shows the early time behavior tar below the glass transition temperature (Dunsiger et al. 1996a). Right Near-ZF muon spin relaxation rate 1/T, as a function of temperatuie in TbjTijO,. The inset shows representative pSR spectra, all of which exhibit exponential relaxation. From Gardner et al. (1999).

When using the temperature dependence of the nuclear spin-spin or nuclear spin-lattice relaxation rate to study molecular motion, as is the case with the surface diffusion we are dealing with here, there exist soolled strong and weak collision limits. Different mathematical relationships are needed to describe these limits. Consider the nuclear spin-spin relaxation rate (1 / T2) as measured by a conventional Hahn-echo pulse sequence, and suppose that Aa> is the amplitude of the local field fluctuation responsible for relaxation. Also assume that r is the correlation time for the motion, say a jump, which causes the local field to fluctuate. The strong collision limit is defined such that... 

It is known (Blumberg 1960, Tse and Hartmann 1968, McHenry et al. 1972) that the kinetics (308) is typical for disordered systems in which a strong inhomogeneous NMR line broadening takes place and nuclear spin diffiision is hampered due to the Larmor frequencies differences of the nuclear spins located in the neighbouring crystal lattice sites. In such systems the nuclear spins at low temperatures relax directly via paramagnetic centers, well coupled with phonons. When paramagnetic centers with 5 = are randomly distributed in a crystal lattice, the nuclear spin-lattice relaxation rate is determined as follows ... 

In the previous section we have seen how the hyperfine fields of localized electron spins at chain ends can be interpreted in terms of the temperature and pressure dependence of A cham- Let us now consider the time-dependent properties of these states as revealed by fluctuations of the hyperfine fields. Such fluctuations lead to a strong mechanism for relaxation of the nuclear spins. The rate for spin-lattice relaxation is given by... 

The temperature-dependance of the nuclear-spin relaxation in our very porous amorphous materials is qualitatively the same as in most of the explored classical glasses. . s. In the latters, the relaxation rates behave as T o+ ), with a lying between 0.1 and 0.5. As showed by previous studies, the faster ionic conductor the glass is, the faster the relaxation. When compared to non ionic-conducting amorphous materials, our oxydes present particularly short relaxation times. 

N-protonation the absolute magnitude of the Ad values is larger than for Af-methylation <770MR(9)53>. Nuclear relaxation rates of and have been measured as a function of temperature for neat liquid pyridazine, and nuclear Overhauser enhancement has been used to separate the dipolar and spin rotational contributions to relaxation. Dipolar relaxation rates have been combined with quadrupole relaxation rates to determine rotational correlation times for motion about each principal molecular axis (78MI21200). NMR analysis has been used to determine the structure of phenyllithium-pyridazine adducts and of the corresponding dihydropyridazines obtained by hydrolysis of the adducts <78RTC116>. 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

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