Dipolar relaxation mechanism

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

As anticipated in Sections 2.2.2 and 3.1, the unpaired electrons should not be considered as point-dipoles centered on the metal ion. They are at the least delocalized over the atomic orbitals of the metal ion itself. The effect of the deviation from the point-dipole approximation under these conditions is estimated to be negligible for nuclei already 3-4 A away [31]. Electron delocalization onto the ligands, however, may heavily affect the overall relaxation phenomena. In this case the experimental Rm may be higher than expected, and the ratios between the Rim values of different nuclei does not follow the sixth power of the ratios between metal to nucleus distances. In the case of hexaaqua metal complexes the point-dipole approximation provides shorter distances than observed in the solid state (Table 3.2) for both H and 170. This implies spin density delocalization on the oxygen atom. Ab initio calculations of R m have been performed for both H and 170 nuclei in a series of hexaaqua complexes (Table 3.2). The calculated metal nucleus distances in the assumption of a purely metal-centered dipolar relaxation mechanism are sizably smaller than the crystallographic values for 170, and the difference dramatically increases from 3d5 to 3d9 metal ions [32]. The differences for protons are quite smaller [32]. 

This result suggests, if it is assumed that a C-H heteronuclear dipolar relaxation mechanism is operative, that methyl protons dominate the relaxation behavior of these carbons over much of the temperature range studied despite the 1/r dependence of the mechanism. The shorter T] for the CH as compared to the CH2 then arises from the shorter C-H distances. Apparently, the contributions to spectral density in the MHz region of the frequency spectrum due to backbone motions is minor relative to the sidegroup motion. The T p data for the CH and CH2 carbons also give an indication of methyl group rotational frequencies. 

The methodology for the calculation of the complex relative permittivity for the dipolar relaxation mechanism is founded on the calculation of the dielectric response function, f(t), for a depolarization produced by the discharge of a previously charged capacitor. In Figure 1.29a, a circuit is shown where a capacitor is inserted in which a dipolar dielectric material is enclosed in the parallel plate capacitor of area, A, and thickness, d, with empty capacitance C0 = Q0/U0 = 0(A/d), and E0 = U0ld. In Figure 1.29b, the corresponding depolarization process is shown. 

Carbon-13 relaxation-rates of monosaccharides are dominated by dipolar-relaxation mechanisms,18,22 and primarily give information about molecular motion,75,76 in addition to the somewhat trivial distinction between C, CH, CH2, and CH3 groups. However, by measuring spectra with a suitable pulse-sequence, the differences in spin-lattice relaxation-rates can be used for the assignment of signals from overlapping CH and CH2 groups.77... 

Kinetic studies were performed with allowance being made for both first- and second-sphere dipolar relaxation mechanisms such that ... 

Ti measurements by high resolution NMR provide information about molecular motion of each nucleus of the polymer. Based on the dipolar relaxation mechanism, Tj is expressed as follows ... 

Figuring out the frequency of a given transition is simple. On a 500MHz instrument, the frequency is 500MHz and the frequency is 125 MHz. For the single quantum Wjh transition that involves only flipping the spin of the H, the frequency of the photons that will drive this transition is 500 MHz. If the spectral density function is not zero at 500 MHz, then the Wjh transition will he efficient and the dipolar relaxation mechanism will he an efficient relaxation pathway for the H. For the transition, the frequency is 125 MHz so in this case, having spectral density at 125 MHz will make the single quantum dipolar relaxation mechanism efficient. For the double quantum W2 transition that connects the ota and pp spin state combinations, spectral density at 625 MHz (vh + Vc) is required. For the zero quantum Wg transition (also called the flip-flop transition), spectral density at 375 MHz (vh Vc) is required to make the transition efficient.

A second important consideration to bear in mind when we use the NOE difference experiment concerns competing relaxation mechanisms. If the dipolar relaxation mechanism contributes negligibly to enhancing the overall rate of relaxation for a particular spin because of other efficient and available relaxation mechanisms, then we will... 

There are two basic 2-D NMR experiments that make use of the NOE the NOESY and the ROESY [1] experiments. NOESY stands for nuclear Overhauser effect spectroscopy and ROESY stands for rotational Overhauser effect spectroscopy. The ROESY experiment is also referred to in some of the literature as the CAMELSPIN experiment. The principal difference between the NOESY and ROESY experiments lies in the time scale associated with the dipolar relaxation mechanism. 

Previous sections have exploited the scalar coupling, J, and dipolar relaxation mechanisms for purposes of autocorrelation. It is certainly possible, however, to correlate resonances via other fundamental processes. Some examples include exchange processes. As a group, these experiments are sometimes collectively referred to as EXSY (Exchange SpectroscopY) experiments [54—59]. 

The dipolar relaxation mechanism is unique because the dipolar coupling interaction contains two spin terms involving mutual spin flips - zero quantum t J. J. t and double quantum J J < j j transitions. All other relaxation processes are limited to single spin interchange. While the decoupler is on, the spin population differences between the levels irradiated are equalized as the rate of energy input from the decoupler greatly exceeds the outflow by relaxation. In dipolar coupled systems, the availability of double and zero quantum relaxation pathways (cross-relaxation) produces non-Boltzmann spin populations in the energy levels of the observed nucleus. These perturbed populations are measured as the nuclear Overhauser effect (nOe) effect rj). The relationship is... 

The intemudear vector is usually taken along the diredion of the C-H bond in C-NMR, and in the direction of the proton pair in H-NMR, assuming a purely dipolar relaxation mechanism. The spin-lattice rdaxation times. 

For the dipolar relaxation mechanism, the spin lattice relaxation time is sensitive to the reorientation dynamics of the CH bond vectors. Different orientations of the CH bond result in slightly different magnetic fields at the carbon nucleus and the modulation of this field allows the spin flips to occur. When we define ecn as the unit vector along a CH bond, the second Legendre polynomial of its autocorrelation function is given by... 

The molecular dynamics and dipolar relaxation mechanism of PWH, PMMA and their blends were investigated using the TSDC technique [36]. Two... 

In an A- X experiment (i.e., irradiate X, observe A), the NOE is dependent on the gyromagnetic ratio of A and X nuclei, provided that the intramolecular dipolar relaxation mechanism is the predominant pathway through which nuclei A are relaxing. Thus the maximum NOE factor /a(X) for the A signal in an A- X experiment is given by... 

Although other relaxation mechanisms may be important for some nuclei, the dipolar relaxation mechanism of P that is coupled to protons and the chemical-shift anisotropy mechanism are most important for nucleic acids. In the case of dipolar relaxation, expressions for the spin-lattice relaxation time T, spin - spin relaxation time Tj, nuclear Overhauser effect (NOE), rotating frame spin-lattice relaxation time in an off-resonance radiofrequency (rf) field T°, and off-resonance intensity ratio R are given by (Doddrell et a/., 1972 Kuhlmann eta/., 1970 James eta/., 1978 James, 1980)... 

The spectral densities appropriate for the dipolar relaxation mechanism for this model are... 

---