Magnetic dipole relaxation

It is known from nuclear structure theory that nuclei with I > 1 also have an electric quadrupole moment Q, which is a measure of the asphericity of the nucleus. Nuclear quadrupole moments affect the rate of magnetic dipole relaxation, and nuclei with Q 0 are candidates for NQR measurements (see Table 3.3). 

Nuclear magnetic dipole relaxation interactions may occur with other nuclei, or with unpaired electrons. These processes usually dominate the relaxation of spin - nuclei. Both intra- and intermolecular interactions may contribute to dipole-dipole nuclear relaxation times. The value of due to the intramolecular dipole-dipole process is proportional to the sixth power of the internuclear separation. Consequently, this process becomes rather inefficient in the absence of directly bonded magnetic nuclei. However, it follows that a measurement of can be provide an estimate of internuclear separation that can be of chemical interest. The nuclear Overhauser effect (NOE) depends upon the occurrence of dipole-dipole relaxation processes and can similarly provide an estimate of internuclear separation. 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

There is arbitr iriness in describing phenomena as either physical or chemical, but in some sense the nuclear relaxation mechanisms we have discussed to this point are physical mechanisms, based as they are on rotational motions of molecules, magnetic dipole-dipole interactions, quadrupolar interactions, and so on. Now we discuss a nuclear relaxation mechanism that is chemical in origin. 

Here, is the magnetization of spin i at thermal equilibrium, p,j is the direct, dipole-dipole relaxation between spins i and j, a-y is the crossrelaxation between spins i and j, and pf is the direct relaxation of spin i due to other relaxation mechanisms, including intermolecular dipolar interactions and paramagnetic relaxation by dissolved oxygen. Under experimental conditions so chosen that dipolar interactions constitute the dominant relaxation-mechanism, and intermolecular interactions have been minimized by sufficient dilution and degassing of the sample, the quantity pf in Eq. 3b becomes much smaller than the direct, intramolecular, dipolar interactions, that is. 

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

The story is even more complicated than we have suggested, because carbon can relax by more than one mechanism. Protons rely on dipole-dipole relaxation, which also works well for protonated carbons but badly for non-proton-ated carbons. But carbon also for example makes use of spin-rotation relaxation, which is particularly active for methyl groups. And the magnetic field dependence of the various mechanisms also differs. We realize that relaxation is a very difficult subject, and if you want to know more then there are plenty of textbooks available ... 

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. 

Figure 1. Schematic representation of dependence of the T, and Tt relaxation times on isotropic correlation time (tc) of motion for a C-H fragment assuming dipole-dipole relaxation and 7 T magnetic field.

A.A. Jones, Clark Univ., Mass. I would tend to agree with the dynamic picture you presoited. The idea that the high frequency motion in the sulfone hexene type polymers doesn t cause a net relaxation of dipoles but moves the magnetic dipole-dipole interaction around to cause nuclear relaxation is, I think, the crux of the matter. 

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

The rotation of the molecule causes a magnetic dipole-dipole interaction between the protons in the molecule, which is a function of the distance r between the two dipoles. The relaxation rate, varies linearly with the rotation... 

Figure 16-9. a) Spectral density J(oo) of the local magnetic dipole field at various temperatures and b) relaxation time T, (spin-lattice relaxation) as a function of the reciprocal temperature. 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

Another mechanism of relaxation is associated with the magnetic interaction between nuclei and paramagnetic electrons (the so-called magnetic dipole interactions). This process is known as spin-spin relaxation time (T2). 

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