Diffusion Dipolar interactions

If the considered molecule cannot be assimilated to a sphere, one has to take into account a rotational diffusion tensor, the principal axes of which coincide, to a first approximation, with the principal axes of the molecular inertial tensor. In that case, three different rotational diffusion coefficients are needed.14 They will be denoted as Dx, Dy, Dz and describe the reorientation about the principal axes of the rotational diffusion tensor. They lead to unwieldy expressions even for auto-correlation spectral densities, which can be somewhat simplified if the considered interaction can be approximated by a tensor of axial symmetry, allowing us to define two polar angles 6 and

symmetry axis of the considered interaction) in the (X, Y, Z) molecular frame (see Figure 5). As the tensor associated with dipolar interactions is necessarily of axial symmetry (the relaxation vector being... 

The fact that dynamic 13C polarization is only possible through the indirect way via tire 1H spins suggests the mechanism of polarization transfer. Since the polarization transfer between the electrons and nuclei are driven by the dipolar interactions between them, and the fraction of the guest triplet molecules was small, it would be natural to assume that the polarization of the electron spins in the photo-excited triplet state is given to those H spins which happen to be close to the electron spins, and then the 1H polarization would be transported away over the whole volume of the sample by spin diffusion among the 1H spins. 

For the dilute aH spins surrounded by a large number of the 2H spins, the heteronuclear aH-H dipolar interaction is dominant, lifting the spectral overlap between the 1H packets. H spin diffusion is driven by the flip-flop term of the 1H-1H dipolar interaction, which becomes secular in the presence of spectral overlap. Thus, spin diffusion would be accelerated if it had not been for the 1H-2H dipolar interaction. In order to confirm this prediction, they used another RF channel of the OPENCORE... 

The Tte of the 3Fe-4S centre in succinate ubiquinone reductase between 4 and 8 K is decreased by interaction with paramagnetic cytochrome b.98 To mitigate the impact of spectral diffusion the relaxation times were measured by a picket-fence sequence with 100 pulses. Analysis of the powder pattern distribution of relaxation times indicated that the anisotropic dipolar interaction dominated over isotropic scalar interaction and a lower limit of 10 A was estimated for the distance between the iron-sulfur cluster and the heme. 

Aside from the question of the precise model by which relaxation times are interpreted there is the more practical problem of isolating that part of the relaxation specifically caused by diffusion. The contributions of exchange processes (see below), spin-rotation interaction (9), and spin diffusion (9) can be identified by temperature dependences different from that which is solely the result of the motionally modulated nuclear dipolar interaction as sketched above, and corrections can be made. The molecular rotation contributions to dipolar relaxation can be removed or corrected for by (a) isotopic substitution methods (19), (b) the fact that rotation is in some cases much faster than diffusion, and its relaxation effects are shifted to much lower temperatures (7, 20), and (c) doping with paramagnetic impurities as outlined above. The last method has been used in almost all cases reported thus far, more by default than by design, because commercial zeolites are thus doped by their method of preparation this... 

The high frequency relaxation is attributed in part to the modulation of intermolecular dipolar interactions by the translational diffusion. The cutoff frequency (60 MHz at 55°C) corresponds to the local diffusive jump frequency that is estimated from measurements of the diffusion coefficient (D 10"6 cm2/sec at 55°) (19, 21). This cutoff frequency also varies in temperature with the same activation energy (Eact 0.25 eV) as the diffusion frequency. 

Self diffusion coefficients of deuterated toluene were measured, rather than protonated toluene in order to minimize the experimental difficulties associated with very long proton spin lattice relaxation times (T- ). Since the value of the T1 determines the length of time between pulse sequences, a long relaxation time leads to prohibitively long measurement times. Previous measurements (36-38) of proton and deuterium relaxation times in liquid toluene have been made as a function of temperature and pressure. The relaxation is due to dipolar interactions in protonated toluene and quadrupolar interactions in toluene-dg. Therefore, the relaxation times can be expected to increase with increasing temperature. However, the quadrupolar relaxed deuterium T. values are smaller than the proton T1... 

Kehr M, Fatkullin N, Kimmich R (2007) Molecular diffusion on a time scale between nano-and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions Application to polymer melts. J Chem Phys 126 094903 Kirkwood JG, Riseman J (1948) The intrinsic viscosity and diffusion constant of flexible macromolecules in solution. J Chem Phys 16 565-573 Klein J (1986) Dynamics of entangled linear, branched, and cyclic polymers. Macromolecules 19(1) 105—118... 

In multidimensional NMR studies of organic compounds, 2H, 13C and 31P are suitable probe nuclei.3,4,6 For these nuclei, the time evolution of the spin system is simple due to 7 1 and the strengths of the quadrupolar or chemical shift interactions exceed the dipole-dipole couplings so that single-particle correlation functions can be measured. On the other hand, the situation is less favorable for applications on solid-ion conductors. Here, the nuclei associated with the mobile ions often exhibit I> 1 and, hence, a complicated evolution of the spin system requires elaborate pulse sequences.197 199 Further, strong dipolar interactions often hamper straightforward analysis of the data. Nevertheless, it was shown that 6Li, 7Li and 9Be are useful to characterize ion dynamics in crystalline ion conductors by means of 2D NMR in frequency and time domain.200 204 For example, small translational diffusion coefficients D 1 O-20 m2/s became accessible in 7Li NMR stimulated-echo studies.201... 

The orientation of electron spins in this manner influences the electron-electron dipolar interaction described above. For strong magnetic fields, the diffusive... 

Different models of CP kinetics have been developed. The simplest model of CP dynamics (I-S) was derived for homogeneous solids where the I-S heteronu-clear interactions are relatively weak and the /-/ homonuclear dipolar interactions are sufficiently strong to provide efficient spin diffusion. For the abundant-dilute spin system, the CP dynamics can be described by equation (6) ... 

Whereas the I-S model is simple to understand and is widely applied, it is not sufficient to describe the CP kinetics for solids with heterogeneous populations of the source spins. The I-I -S model takes into account the efficiency of spin diffusion, which relies on homonuclear dipolar interactions and proceeds through ffip-ffop spin transitions. The I-I -S model relies on the existence of different proton populations, denoted I for the protons directly bound to an 5 spin under study and I for the rest of the proton network. The CP proceeds in two steps. A fast rise of the intensity is observed initially due to the transfer of the magnetization to a dilute spin (I -S) by the abundant spins in close proximity followed by a slow rise of the intensity or damped oscillation. Several equations have been proposed to describe the CP kinetics the simplest... 

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