Relaxation mechanisms narrowing

The Cua site, common in biology (inset in Fig. 5.42), is dinuclear with two copper atoms bridged by the thiolate sulfurs of two cysteine ligands. One unpaired electron is delocalized over two metals, which are thus Cul 5+. The NMR spectra show narrow lines from the copper ligands (Fig. 5.42) [120,121], corresponding to an electron relaxation time of 10 11 s, as in Cu2+-Cu2+ dimers (see Section 6.3.2). However, in Cua there is no magnetic coupling between the two centers, as they contain only one unpaired electron just as an isolated Cu2+ ion. Electron relaxation of Cua may be fast because the orbital overlap between the two copper centers provides new relaxation mechanisms not available to a monomer (as Orbach or Raman relaxation). 

Watanabe H, Kotaka T (1984) Viscoelastic properties and relaxation mechanism of binary blends of narrow molecular weight distribution polystyrene. Macromolecules... 

At the other limit of correlation times, Eqs. 8.6 and 8.9 show that for small tc, the denominators approach unity, and T2 = T,.The region of Tc< 1 /(o0 is often called the extreme narrowing condition. Note that we are considering here only dipolar interactions. Other relaxation mechanisms discussed subsequently may cause T2 to be smaller than 7), even under the extreme narrowing condition. 

Av is the frequency difference between two anisotropic ESR resonance lines, the resulting spectrum is the superposition of the individual configurations. On the contrary, if r < (2 JtAv), we have an isotropic spectrum the resonance frequency is the average of the anisotropic components of the individual configurations As discussed in detail by Ham , motional narrowing can be produced by three relaxation mechanisms, which are characterized by a different temperature dependence an Arrhenius-type dependence (r" = Voe ) for an Orbach process, and a linear dependence or proportional to T for direct and Raman processes, respectively. Therefore, the temperature dependence of the isotropic spectrum gives information about the relaxation mechanism and consequently on the vibronic level scheme. 

The exploitation of cross-correlation effects in high magnetic fields has introduced a new form of NMR spectroscopy called transverse relaxation-optimised spectroscopy or TROSY. The cross-correlation of the optimised dipole-dipole (DD) and chemical shift anisotropy (CSA) relaxation mechanisms leads to differential transverse relaxation rates for the two components of the l5N- H doublet in undecoupled spectra of l5N-labelled proteins. For one component, DD and CSA relaxation constructively add to produce very efficient relaxation, leading to a broad line, whereas for the other component, the two relaxation mechanisms constructively interfere, leading to a narrow line when the two mechanisms are nearly equal. There is no optimum field where DD and CSA relaxation are equal for all amide bonds, because DD relaxation between the amide protons and other nearby protons differs for each residue.72 Clearly, the overall effectiveness of TROSY is optimized when the non-exchangeable protons in the macromolecule... 

The process of T relaxation can have contributions from a number of different mechanisms, e.g. dipole-dipole, scalar coupling of the first or second kind, quadrupolar, chemical shift anisotropy (CSA) and spin-rotation. The temperature dependence of the T relaxation time depends upon the relative contribution of each of these mechanisms. For example, if spin-rotation is the dominant relaxation mechanism, then the Ti value decreases linearly with increasing temperature, whereas if dipole-dipole is dominant the T value increases with increasing temperature in the extreme narrowing limit. Examples of temperature measurements using T are included in Sections 3.2.5 and 5.1. 

If dipolar relaxation is the main relaxation mechanism, the ratio of15N and 13C relaxation times under the conditions of extreme spectral narrowing provides information on the relative motions of these substituents. 

In order to determine which relaxation mechanism is operating in a given case, you should rely on some estimates based on previous knowledge as well as doing experiments to sort out the different mechanisms. Using common sense and chemical knowledge, you can significantly narrow the number of possible mechanisms so that the correct experiments can be chosen. 

There are a couple of special methods of separating the contribution of dipolar relaxation in solution. One is by the NOE factor which is the fractional difference in the signal intensity of one spin with and without irradiation applied to another spin system. For a sample containing protons and carbon-13 in the motionally narrowed limit, this factor should be 2 if the relaxation takes place through the dipolar and the scalar interactions. Thus, the departure from 2 of the NOE factor is an indication of other relaxation mechanisms. Clearly, any other pairs of spin systems with NOE s can be treated this way, with appropriate limiting NOE factors. See, for example, Noggle and Shirmer listed in Appendix A for more details. 

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