Hydrogen nuclei relaxation

The first successful nuclear magnetic resonance (NMR) measurements were made by E. M. Purcell et al. at Harvard, and F. Bloch et al at Stanford, independently in 1946. They observed the proton ( H) signal of the hydrogen nucleus of samples of paraffin wax (solid) and water (liquid), respectively. Their success in observing the proton signal was based on using samples in which the relaxation time was short. 

Conradi and Norberg (1981) assume that the rate t is that for a quadru-polar nucleus relaxing via two-phonon Raman processes. This assumption affects primarily the low temperature behavior of Tf, but not the value of T, at the minimum or its frequency dependences at low and high temperatures, which are determined by the ratio (Wh/ o) and the Tq dependence of Eq. (12) for coqT c 1 and coqT 1, respectively. The term provides a rate below which the relaxation is no longer dominated by rapid spin diffusion to the molecular hydrogen sites. The fits of Conradi and Norberg (1981) to the data of Carlos and Taylor (1980) are shown in Fig. 12 for (Oq/Itc — 42.3 and... 

From a practical standpoint, the only NMR-active isotopes in the body present in concentrations high enough for detection in a typical MRI scan are and H. As you know, the usual in vitro NMR experiment provides chemists with information regarding chemical shifts, relative numbers of protons in different magnetic environments, and the number of nearest neighbors to a particular type of proton. In contrast, the MRI experiment yields information on hydrogen density and spin-lattice (T. ) and spin-spin relaxation times (T2), which define the rate and mode by which a nucleus relaxes to a lower-energy spin state. 

Fig. 7. Calculated dipolar 7i and NOE dependence on isotropic reorientation time (tc) for a nucleus relaxed by a single hydrogen at a distance of 1.09 A in a magnetic field of 23.5 kG.

For Gd(III) complexes there are several processes that can contribute to this correlation time. Electronic relaxation (l/Fi e) at the Gd(III) ion, rotational diffusion (1/tr) of the complex, and water exchange in and out of die first (l/tn,) or 2nd (1/Xni ) coordination sphere all create a fluctuating field that can serve to relax the hydrogen nucleus. It is die fastest rate (shortest time constant) that determines the extent of relaxation. For water in the second sphere, the relevant correlation time may be the lifetime of diis water, which may be on the order of tens of picoseconds. Water in the inner sphere typically has a much longer residency time (1-10,000 ns), so the relevant correlation time is usually rotational diffusion or electronic relaxation. 

Hydrogen. - The H nucleus has been traditionally the most important for n.m.r. investigations. It has spin-, natural abundance of practically 100%, high gyromagnetic ratio, and relatively short relaxation time, and consequently is the most sensitive of all nuclei. Its chemical shift range is however small (about lOp.p.m.), and in the field of solid-state n.m.r., where homonuclear dipolar broadening is a severe problem for 100%-abundant nuclei, the width of the lines frequently, but by no means always, tends to obscure the important chemical shift information which we have come to expect from 13 C and 29Si n.m.r. 

If there is indirect spin-spin coupling (scalar) coupling between two spins I and S and if the relaxation of nucleus S is short due to other interactions, quadrupolar interactions, it may cause relaxation for for nucleus I, known as scalar relaxation, proposed first by Solomon and Bloembergen [80] and observed it for hydrogen fluoride. 

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