Efficient relaxation

In the oxidized form, the weak coupling of the high-spin Fe(III) ion to its surroundings amd the very large ligand-field energy of about 10,000 cm (12) are not liable to give rise to very efficient relaxation processes (see Appendix). However, the S = 5/2 manifold provides a set of transitions for multiple direct processes that may be efficient... 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

One other (very rarely encountered) situation is that of the stabilised free radical. It is possible for certain conjugated multi-ring heterocyclic compounds to support and stabilise a delocalised, free electron in their pi clouds. Such a free electron again provides an extremely efficient relaxation pathway for all... 

Quadrupolar nuclei Those nuclei, which because of their spin quantum number (which is always >1/2), have asymmetric charge distribution and thus posses an electric quadrupole as well as a magnetic dipole. This feature of the nucleus provides an extremely efficient relaxation mechanism for the nuclei themselves and for their close neighbors. This can give rise to broader than expected signals. 

Manganese(II)-A/, A/r -dipyridoxylethylenediamine-A/r, AT-diacetate 5,5 -bis(phosphate) 75 (DPDP) is clinically used for enhancing contrast in the liver (detection of hepatocellular carcinomas) (312). Some dissociation of Mn(II) appears to occur in the liver, and enhancement can also be obtained in functional adrenal tissues (313). Manganese(II)-tetrasulfonated phthalocyanine also shows tumor localization properties and is a more efficient relaxation agent than the analogous Gd(III) complexes (314). 

Using a simple kinetic model, Solomon demonstrated that the spin-lattice relaxation of the I and S spins was described by a system of coupled differential equations, with bi-exponential functions as general solutions. A single exponential relaxation for the I spin, corresponding to a well-defined Tu, could only be obtained in certain limiting situations, e.g., if the other spin, S, was different from I and had an independent and highly efficient relaxation pathway. This limit is normally fulfilled if S represents an electron spin. The spin-lattice relaxation rate, for the nuclear spin, I, is in such a situation given by ... 

In the more general case where there may be surface interactions, i.e., a chemical exchange with surface sites where more efficient relaxation may occur, a term is added to the relaxation equation that is proportional to Ijd. The relaxation may generally be written as the sum of contributions ... 

MHz relative to the protons in Mc4Si at exactly 100 MHz. The effect of quadrupole line broadening is attenuated to some extent by the magnitude of / (/= 9/2), and the line widths are among the narrowest of all quadrupolar nuclei studied to date. One would expect efficient relaxation via the quadrupole moment, giving very short T2 times and consequently broad NMR signals. Also if the electronic distribution around the nucleus is symmetrical, sharp resonances can be obtained. 

Neutral hydrogen in the magnetic fields in interstellar space may have excited state life times that is measured in years—in contrast hydrogen in liquid water at room temperature display excited state lifetimes of 3 seconds. Why is this How come that the liquid water can lead to a more efficient relaxation of the proton... 

This is based on spatial nuclear magnetic resonance of water protons within the body. For a contrast agent to be effective, direct coordination of water molecules to the lanthanide is necessary to impart efficient relaxation of the water protons. Therefore, whilst this has been covered comprehensively in a number of recent reviews... 

A second difference from the continuum model is that large stresses near the reaction center should undergo thermally activated relaxation. According to the molecular mechanism of stress relaxation proposed above, such irreversible, or plastic, deformations occur in UP when the two decyl radicals back away from the reaction center by rotational translation along their long axes. In the process of making more room for the two new C02 molecules, each radical chain is driven into the adjacent interface between two layers of peroxide molecules. Introduction of a defect or a hole at the end of the peroxide chain should facilitate this motion and allow efficient relaxation of the stress. 

Mechanisms analogous to those illustrated in Fig. 3.1 apply also to electron relaxation (see below). However, electrons have other more efficient relaxation mechanisms which overcome the former ones. They are based on the presence of spin orbit coupling. Molecular motions modulate the orbital magnetic moment and then affect the electron spin. Several possible mechanisms for electron relaxation... 

Since t(2E) is essentially independent of temperature for Cr(teta)(CN)2> it is clear that thermal population of low lying electronic components of the higher energy doublet state do not provide an efficient relaxation pathway in this system. 

If levels in two electronic states are mutually perturbed, the electronic wave function associated with each level is essentially a mixture of the wave functions for the two pure states, and it becomes of doubtful value to assign these levels to either electronic state. If these levels are formed as a result of recombination, they may be able to radiate to much lower levels in the ground state and hence to stabilize. Moreover, collisions will tend to repopulate these levels from those where this mechanism is less probable, and an efficient relaxation pathway may result. Alternatively, in cases where the levels in different states lie close together, but do not perturb one another, it may be possible for collisions to induce transitions to the state from which radiation can occur. Both mechanisms become more likely with complex molecules since the manifold of levels in each state grows accordingly. 

The electron spin(s) of a given metal ion may relax faster if coupled to another metal ion experiencing more efficient relaxation mechanisms. This electron relaxation enhancement depends on the electron relaxation time of the more rapidly relaxing metal ion and on the magnitude of the coupling constant. In the case of isotropic coupling between two metal ions, Eq. (11) has been proposed, which describes the increase in the electron relaxation rates of the more slowly relaxing metal ion (Banci et al., 1991),... 

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