Nuclear spin relaxation rate, temperature dependence

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. 

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]. 

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... 

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... 

Spin dynamics studies in poly pyrrole-perchlorate (PPy-CIO4) have been performed by Devreux and Lecavellier [8]. At first, observation of the Overhauser effect proved the existence of a direct dynamic coupling between electronic and nuclear spins [104]. The frequency dependence of the proton relaxation rate is shown in Fig. 5.19. The data can be fitted with Ti" a for temperatures r < 150 K. For T > 150 K, the data deviate from 1-D diffusion behavior. They also cannot be fitted with the law of a pseudo-one-dimensional diffusion [Eq. (10)] with the introduction of a cutoff frequency o>c. Instead, they can be accounted for by taking the spectral density... 

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. 

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... 

Abstract Spatially-resolved NMR is used to probe antiferromagnetism in the vortex state of nearly optimally doped high-rc cuprate H2Ba2CuC>6+a (Tc = 85 K). The broadened 205Tl-spectra below 20 K and the temperature dependence of the enhanced nuclear spin-lattice relaxation rate 205 Tfl at the vortex core region indicate clear evidences of the antiferromagnetic order inside the vortex core ofTl2Ba2Cu06+J. 

Let us finally also mention here the results of proton nuclear relaxation time 7 measurements on TEA(TCNQ)2 [53,54], From the frequency dependence of 7, it is deduced that the spin motion is a nearly one-dimensional diffusion. Moreover, the temperature dependence of the on-chain spin diffusion rate shows a quite remarkable feature while it is thermally activated below 220 K, it suddenly becomes temperature independent above 220 K. 

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