Spin lattice relaxation processes description

Usually, spin-lattice relaxation experiments are performed at one or a few magnetic fields. The spectral density can thus be determined at only a few Larmor frequencies, so that a detailed analysis of its temperature variation is not possible. Here, an analysis of the spin-spin relaxation times, T, can provide further information about the spectral density, since T2 1 S2(to = 0). Often, the Cole-Davidson distribution Gco(lnT2) [34] is chosen to interpolate the relaxation around the maximum. However, one has to keep in mind that the spectral density close to Tg contains additional contributions from secondary relaxations, such as the excess wing and/or the (i-process discussed in the following sections. In Section IV.C we give an example of a quantitative description of 7) (T) at T > 7 obtained by approximating the spectral density S2(co) using dielectric data. 

Here, Hz is the Zeeman term, Hq is the quadrupolar interaction term for nuclei with 1 1, Hd is the dipolar interaction term for nuclei with 1 = 1/2, Hs is the electron shielding term and Hj is the J-coupling term. Spin relaxations will be induced by the time fluctuations of these interaction terms. For example, H spin-lattice relaxation behaviour is dominated by Hq, whereas Hq mainly determines the relaxation process of the H or magnetization in organic materials. In some cases without significant contributions from Hq and Hq, the time fluctuations of Hs and Hj also induce spin relaxation for example, the magnetization of a carbonyl carbon with a large chemical shift anisotropy relaxes due to the contribution from the time fluctuation of Hs. Nevertheless, since the main interest of polymer scientists is NMR, we focus on the description of the relaxation process in this chapter. 

Relaxation measurements provide another way to study dynamical processes over a large dynamic range in both thermotropic and lyotropic liquid crystals (see Sec. 2.6 of Chap. Ill of Vol. 2A). The two basic relaxation times of a spin system are the spin-lattice or longitudinal relaxation time 7] and the spin-spin or transverse relaxation time T2. A detailed description, however, requires a more precise definition of the relaxation times. For spin 7=1, for instance, two types of spin-lattice relaxation must be distinguished, related to the relaxation of Zeeman and quadrupolar order with rates 7j"2 and Jfg. The relaxation rates depend on spectral density functions which describe the spectrum of fluctuating fields due to molecular motions. A detailed discussion of spin relaxation is beyond the scope of this... 

The connection between this semiclassical description and the transitions between the quantum euergy levels described by Equation (2.5) can be understood, in the simple case of n 2 and n pulses applied to spin 1/2 systems, as an equalization and an inversion of populations, respectively. This means that after a nl2 or a 7t pulse, the populations are not anymore given by the thermal equilibrium expression (Equation 2.6). The return to equilibrium requires that the spin system give up some energy to the environment (generally named the lattice). This process is termed relaxation and is detailed in the next section. 

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