Nuclear longitudinal relaxation, functional

The functional form of the nuclear longitudinal relaxation immediately suggests that the contact contribution can provide the values of the contact coupling constant and of 72e = Tso, provided that the lifetime, xm, is longer than T e- No information on the field dependence of electron relaxation can be achieved. On the contrary the functional form of transverse nuclear relaxation contains a non-dispersive term, Tig. The latter, as we have seen for the dipolar contribution, increases with increasing the field (Fig. 3), and therefore the nuclear contact transverse relaxation also increases with increasing the field. Its measurement is thus informative on the t value. 

The information content of nuclear longitudinal relaxation measurements in both paramagnetic and diamagnetic systems can be greatly increased by performing such measurements as a function of the magnetic field. For paramagnetic species, the reason is apparent from the functional form of the equations discussed in Chapter 3 and from the relevant experimental data, reported in Chapter 5. The field dependence of a relaxation rate is called relaxation dispersion, and is abbreviated as NMRD. In principle, NMRD would be helpful for any chemical system, but practical limitations, as will be shown, restrict its use, with a few exceptions, to water protons. 

The mobility of proton containing molecules in foods can be investigated by the acquisition of Nuclear Magnetic Resonance Dispersion (NMRD) profiles that report about the changes in the H-spin-lattice or longitudinal relaxation rate (Ri=l/Ti) as function of the applied magnetic field strength. 

The fundamental requirement for longitudinal relaxation of a proton nucleus is a time dependent magnetic field fluctuating at the Larmor frequency of the nuclear spin. In the fast motion limit, the frequency distribution of the fluctuating magnetic fields associated with the molecular motion, i.e. the spectral density function J(a)), has, in the simplest case, a Lorentzian shape, as described by Eq. (1), and is characterized by the correlation time xc ... 

Under conditions of proton decoupling there are two relaxation parameters of general interest the longitudinal relaxation time, and NOE, the nuclear Over-hauser enhancement. The third relaxation parameter, T2 or spin-spin relaxation time is not readily measurable for in decoupled systems. Both and NOE are directly related to the transition probabilities associated with nuclei changing energy levels. However, their functional dependence on transition probabilities differs and they can therefore be used in combination to resolve ambiguities. NOE has been found to be a very sensitive measure of mobility of carbon atoms of proteins and to provide reliable qualitative measures of the state of carbon atoms [3]. 

Fig. 2.2.8 Pulse sequences for measurement of Ti relaxation times by (a) saturation recovery and (b) inversion recovery. The effect of the pulse sequences is illustrated in terms of the vector model of the nuclear magnetization and by graphs showing the evolution of the longitudinal magnetization M, as a function of ti.

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