Relaxation contact

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 ... 

In the presence of contact contribution to nuclear relaxation, the NMRD profile results as a sum of the dipolar and contact relaxation rates. The profile of contact relaxation as a function of field is characterized by the presence of only one dispersion (Fig. 3), corresponding to the (OsT e dispersion (Eqs.(5) and (6)), in the hypothesis that Xg, = T,e (see Section II.B of... 

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... 

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...

For nuclei other than protons the dipolar term is smaller, due to the smaller value of yjv, a.nd the contact term may be larger, in case of directly coordinated nuclei. Therefore, contact relaxation may more often be the dominant contribution to nuclear relaxation. 

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. 

Analogously, on the assumption that the establishment of magnetic interactions within a cluster does not change the spin density distribution on the ligands nor on the metal ion, the equation for contact relaxation is ... 

The present Chapter deals with the hyperfine shifts which are only due to the average electron induced magnetic moment and therefore are related to (Sz). Chapter 3 will deal with nuclear hyperfine relaxation which, as discussed above, depends on both average electron induced magnetic moment (Curie relaxation) and on the full electron magnetic moment (dipolar and contact relaxation). 

The first term provides the dipolar relaxation the second, corresponding to the limit of the former for r = 0, provides the contact relaxation. 5 indicates the Dirac 8 operator and , represents the sum over all unpaired electrons. 

The enhancement of the longitudinal contact relaxation rate, after extension to the general case S > V2, is given by the Bloembergen equation [29,36]... 

The presence of contact relaxation indicates that a given moiety is covalently bound to a paramagnetic metal ion and provides an estimate of the absolute value of A (Eqs. (3.26) and (3.27)). Sometimes the contact coupling constant can be evaluated by chemical shift measurements, and it is therefore possible to predict whether the contact relaxation contributions to R m, Rim or both, are negligible or sizable. 

When electron relaxation has a field dependence as described by Eq. (3.11), contact relaxation can determine very large values of R2M. as shown by Eq. (3.27), while the contribution from dipolar relaxation can be negligible if r(d,p = ty. 

As far as contact contributions are concerned, the nuclear yi parameter is contained in A (Eq. (2.2)) and therefore the same yj dependence as in dipolar relaxation is introduced in contact relaxation. Again, heteronuclei are expected to be less relaxed owing to their smaller y/. However, heteronuclei can be directly coordinated to the paramagnetic metal ion. In this case the spin density on the nucleus can be very large and thus A can be very large compared with the proton case. Values of (A/h)2 as large as 1017 rad2 s-2 can be obtained for directly... 

The H NMRD profiles of Mn(OH2)g+ in water solution show two dispersions (Fig. 5.43). The first (at ca. 0.05 MHz, at 298 K) is attributed to the contact relaxation and the second (at ca. 7 MHz, at 298 K) to the dipolar relaxation. From the best fit procedure, the electron relaxation time, given by rso = 3.5 x 10 9 and r = 5.3 x 10 12 s, is consistent with the position of the first dispersion, the rotational correlation time xr = 3.2 x 10 11 s is consistent with the position of the second dispersion and is in accordance with the value expected for hexaaquametal(II) complexes, the water proton-metal center distance is 2.7 A and the constant of contact interaction is 0.65 MHz (see Table 5.6). The impressive increase of / 2 at high fields is due to the field dependence of the electron relaxation time and to the presence of a non-dispersive zs term in the equation for contact relaxation (see Section 3.7.2). If it were not for the finite residence time, xm, of the water molecules in the coordination sphere, the increase in Ri could continue as long as the electron relaxation time increases. 

Vanadium (IV) is a d1 ion. The electron relaxation times are long and high resolution NMR is hardly performed. The NMRD profiles of V0(H20)5+ at different temperatures are shown in Fig. 5.50 [139]. The first dispersion in the profiles is ascribed to the contact relaxation and corresponds to an electron relaxation time of about 5 x 10-10 s (Table 5.6), the second to the dipolar relaxation and corresponds to the rotational correlation time of about 5 x 10-11 s. The value of the correlation time connected to the first dispersion cannot be... 

By increasing viscosity, the longer value of zr moves the second dispersion toward lower frequency, at the same time increasing the relative contribution of the dipolar relaxation with respect to the contact relaxation [26]. The nonlinear increase of relaxation rate with zr at low fields provides evidence that zm is affecting the correlation time. When zr becomes longer than the electron relaxation time, the latter becomes the correlation time for nuclear relaxation and the field dependence of zs is revealed by the hump in the high field region. 

Analogously, the equation for contact relaxation takes the form ... 

The relaxation time of the end-to-end vector correlation for the adsorbed chains depends on the number of contacts. Chains with one or two contacts have most of their segments free and thus due to their bulk like dynamics the end-to-end vector can rapidly relax. On the other hand, for the chains with most of their segments adsorbed this process becomes very slow as the segment dynamics are very sluggish inside the solid oligomer interface (Fig. 15). For strong wall attractions ( w=2 or 3) the chains with more than three contacts relax with almost the same time constant. This insensitivity shows that the slowdown of the dynamics is caused by the densification inside the first layer rather than the magnitude of the surface-fluid interactions [38a,d]. 

Observed linewidths of NMR signals in paramagnetic systems vary enormously and the conditions that govern the observed widths are considerably more complex than in diamagnetic systems. Swift (30) reviewed the problem some years ago. Relaxation times of spin-j nuclei are governed by dipolar and hyperfine exchange (Fermi contact) relaxation processes. The dipolar interaction is normally dominant except in some delocalized systems in which considerable unpaired spin density exists on nuclei far removed from the metal ions (e.g. Ti-radicals). Distinction between the two processes can be made by consideration of the different mathematical expressions involved. For dipolar relaxation when o)fx 1 (t = rate constant for rotation of the species containing the coupled pair and to, = nuclear resonance frequency) ... 

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. 

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