Relaxation contact time

As shown in this table, the relative intensities of peaks a and increase from 5.5 to 8.0% and 28.7 to 30.2%, respectively, on going from sample (b) doped to sample (c) dedoped. However, the relative intensity of peak y decreases from 53.7 to 49.4% by dedoping. Hence, the relative intensities of peaks a and /3 increase with a reduction in conductivity, but peak y decreases. In addition, the relative intensity of peak 8 does not change with the increase in conductivity. When the N CP/MAS experiment is performed using a contact time of 100 jls, the intensities of the peaks a and )3 are relatively enhanced as shown in Fig. 16.6(b), and the chemical shifts and halfwidths of the observed shoulder peaks are determined accurately. Furthermore, the difference of the intensity enhancement between peaks a, and peaks y, 8 shows the difference of the magnetic environments, i.e, a difference in T h (contact relaxation time between N and H) values between N and H and in Tip, between peaks a, j8 and y, 5. 

In those experiments, the solvent is distinguished from the host material by the huge difference in the transverse relaxation times. The technique to be described here monitors interdiffusion between two sample compartments initially filled with deuterated and undeuterated liquids (or gels) of the same chemical species. Bringing the compartments into contact initiates interdiffusion. Mapping of the proton spin density thus permits the evolution of the corresponding concentration profiles to be followed. 

A number of studies (9,10) have demonstrated that the valence of coordination of vanadium in typical vanadia catalysts changed with gas composition in contact with the catalyst. As we discuss below, changes at the surface are partially offset by transport of oxygen from interior strata of the catalyst. We believe it is the diffusion of oxygen, as an ion, which is responsible for the relaxation time observed. 

Let us first examine the NMRD profiles of systems with correlation times Xci = Tie assuming the Solomon-Bloembergen-Morgan (SBM) theory (see Section II.B of Chapter 2) (2-5) is valid, and in the absence of contact relaxation. We report here the relevant equations for readers ... 

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

The NMRD profile of Mn(H20)g in water solution shows two dispersions (Fig. 10) in the 0.01-100 MHz range of proton Larmor frequency one, at about 0.05 MHz, due to the contact relaxation, and a second, at about 7 MHz, due to the dipolar relaxation (39). The correlation time for contact relaxation is the electron relaxation time, whereas the correlation time for dipolar relaxation is the reorientational time (ir = 3.2 x 10 , in accordance with the value expected for hexaaquametal(II) complexes). This accounts for the different positions of the two dispersions in the profile. From a best fit of longitudinal and transverse proton relaxation profiles, the electron relaxation time is described by the parameters A = 0.02-0.03 cm and... 

Ti, = 2-3 X 10 s (providing Xso = 3.5 x 10 s). The measurement of the transverse proton relaxation rate at high fields, in fact, permits to obtain the field dependence of the electron relaxation time from the contact contribution to relaxation. The constant of the contact interaction is calculated to be equal to 0.65 MHz. 

Chromium(III) has a ground state in pseudo-octahedral symmetry. The absence of low-lying excited states excludes fast electron relaxation, which is in fact of the order of 10 -10 ° s. The main electron relaxation mechanism is ascribed to the modulation of transient ZFS. Figure 18 shows the NMRD profiles of hexaaqua chromium(III) at different temperatures (62). The position of the first dispersion, in the 333 K profile, indicates a correlation time of 5 X 10 ° s. Since it is too long to be the reorientational time and too fast to be the water proton lifetime, it must correspond to the electron relaxation time, and such a dispersion must be due to contact relaxation. The high field dispersion is the oos dispersion due to dipolar relaxation, modulated by the reorientational correlation time = 3 x 10 s. According to the Stokes-Einstein law, increases with decreasing temperature, and... 

Table II reports the contact coupling constant for different aqua ion systems at room temperature. The contact coupling constant is a measure of the unpaired spin density delocalized at the coordinated protons. The values were calculated from the analysis of the contact contribution to the paramagnetic enhancements of relaxation rates in all cases where the correlation time for dipolar relaxation is dominated by x and Tig > x. In fact, in such cases the dispersion due to contact relaxation occurs earlier in frequency than the dispersion due to dipolar relaxation. In metalloproteins the contact contribution is usually negligible, even for metal ions characterized by a large contact contribution in aqua ion systems. This is due to the fact that the dipolar contribution is much larger because the correlation time increases by orders of magnitude, and x becomes longer than Tig. Under...

The NMRD profiles of V0(H20)5 at different temperatures are shown in Fig. 35 (58). As already seen in Section I.C.6, the first dispersion is ascribed to the contact relaxation, and is in accordance with an electron relaxation time of about 5 x 10 ° s, and the second to the dipolar relaxation, in accordance with a reorientational correlation time of about 5 x 10 s. A significant contribution for contact relaxation is actually expected because the unpaired electron occupies a orbital, which has the correct symmetry for directly overlapping the fully occupied water molecular orbitals of a type (87). The analysis was performed considering that the four water molecules in the equatorial plane are strongly coordinated, whereas the fifth axial water is weakly coordinated and exchanges much faster than the former. The fit indicates a distance of 2.6 A from the paramagnetic center for the protons in the equatorial plane, and of 2.9 A for those of the axial water, and a constant of contact interaction for the equatorial water molecules equal to 2.1 MHz. With increasing temperature, the measurements indicate that the electron relaxation time increases, whereas the reorientational time decreases. 

The NMRD profiles of water solution of Ti(H20)g" have been shown in Section I.C.7 and have been already discussed. We only add here that the best fit procedures provide a constant of contact interaction of 4.5 MHz (61), and a distance of the twelve water protons from the metal ion of 2.62 A. If a 10% outer-sphere contribution is subtracted from the data, the distance increases to 2.67 A, which is a reasonably good value. The increase at high fields in the i 2 values cannot in this case be ascribed to the non-dispersive term present in the contact relaxation equation, as in other cases, because longitudinal measurements do not indicate field dependence in the electron relaxation time. Therefore they were related to chemical exchange contributions (see Eq. (3) of Chapter 2) and indicate values for tm equal to 4.2 X 10 s and 1.2 X 10 s at 293 and 308 K, respectively. 

Cross-polarization is based on the notion that the vast proton spin system can be tapped to provide some carbon polarization more conveniently than by thermalization with the lattice (7). Advantages are two-fold the carbon signal (from those C nuclei which are indeed in contact with protons) is enhanced and, more importantly, the experiment can be repeated at a rate determined by the proton longitudinal relaxation time Tin, rather than by the carbon T c (I)- There are many variants (7) of crosspolarization and only two common ones are described below (12,20). 

Ru dihydride [in the absence of (CF3)2CHOH], and the Ti,min (RuH H) is a minimal relaxation time of the hydride ligand that is involved in dihydrogen bonding. The Ti min CRuH- H) value is calculated from eq. (4.11) as 0.0894 s. This time is remarkably shorter than that in the individual dihydride (0.178 s), due to an additional hydride-proton dipolar coupling. Then this additional relaxation rate, 1/ T i min (RuH- H), governed by the single hydride-proton dipolar contact, is expressed as... 

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