Carbon dipolar relaxation rate

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... 

Carlomagno, T., Sanchez, V. M., Blommers, M. J. )., Griesinger, C. Derivation of dihedral angles from CH-CH dipolar-dipolar cross-correlated relaxation rates a C-C torsion involving a quaternary carbon atom in epothilone A bound to tubulin. Angew. Chem. Int. Ed. 2003, 42, 2515-2517. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

The coupling term, traditionally denoted by cr B (which has however nothing to do with the screening coefficient of Section 2.2), is the so-called cross-relaxation rate and is a relaxation parameters which depends exclusively on the dipolar interaction between nuclei A and B, contrary to auto-relaxation rates which are compounds of several contributions. For instance, if A is a carbon-13, the auto-relaxation rate can always be written as... 

This is the beauty of this quantity which provides specifically a direct geometrical information (1 /r% ) provided that the dynamical part of Equation (16) can be inferred from appropriate experimental determinations. This cross-relaxation rate, first discovered by Overhau-ser in 1953 about proton-electron dipolar interactions,8 led to the so-called NOE in the case of nucleus-nucleus dipolar interactions, and has found tremendous applications in NMR.2 As a matter of fact, this review is purposely limited to the determination of proton-carbon-13 cross-relaxation rates in small or medium-size molecules and to their interpretation. 

It can be noticed that the maximum NOE factor (2 when A is a carbon-13 and B a proton) is reached under extreme narrowing (see Section 6) conditions and if RA arises exclusively from the A-B dipolar interaction. On the other hand, the cross-relaxation rate gab is easily deduced from the NOE factor and from the A specific relaxation rate... 

Finally, it can be noted that there also exist dipolar-dipolar crosscorrelation rates which involve two different dipolar interactions. These quantities may play a role, for instance, in the carbon-13 longitudinal relaxation of a CH2 grouping.11,12 Due to the complexity of the relevant theory and to their marginal effect under proton decoupling conditions, they will be disregarded in the following. 

Figure 6. The proton(I)-carbon(S) dipolar coupling during a C-13 T,p and decoupled Tj experiment are compared. The relaxation rate is determined by the molecular fluctuation at the spin lock frequency u>,c or decoupling frequency a,a-...

In addition to using /-scalar coupling data (see above), several other methods have been proposed to estimating sugar conformations in RNA based on the 13C-4H dipole-dipole cross-correlated relaxation,289 based on the cross-correlated relaxation rates involving 13C CSA and 13C-4H dipolar interactions,290 and based on the 13C chemical shifts of sugar carbons.291... 

It is the "second generation" of solid state techniques, in which the onset of relaxation of magnetization is observed in the time domain, which offer promise for the detailed, In-sltu investigation of early diagenetic processes. For example, Hagaman and Woody (19) showed that the time dependence of cross polarization could be used to Improve the resolution of complex spectra of coal, since different carbon types cross polarize at different rates. Wilson (20-21) has used dipolar dephaslng to distinguish carbon types in soils and resins based on relaxation rates. 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

Eqs. 3 and 4 show the electron-nuclear relaxation-rates for the spin-lattice (longitudinal) and spin-spin (transverse) relaxation-rates. In both of these equations, the first terms reflect the dipolar term, and the second part reflects the scalar interaction. The dipolar term contains a distinct r distance term between the electron of the metal atom and the respective carbon atom in contrast, the scalar term has none. 

As the size of the dipolar interaction depends on the product of the gyromagnetic ratios of the two nuclei involved, and the resulting relaxation rate constants depends on the square of this. Thus, pairs of nuclei with high gyromagnetic ratios are most efficient at promoting relaxation. For example, every thing else being equal, a proton-proton pair will relax 16 times faster than a carbon-13 proton pair. 

By the same experimental technique, the temperature dependence of the nuclear spin relaxation rates was investigated for the radical cations of dimethoxy- and trimethoxybenzenes [89], The rates of these processes do not appear to be accessible by other methods. As was shown, l/Tfd of an aromatic proton in these radicals is proportional to the square of its hyperfine coupling constant. This result could be explained qualitatively by a simple MO model. Relaxation predominantly occurs by the dipolar interaction between the proton and the unpaired spin density in the pz orbital of the carbon atom the proton is attached to. Calculations on the basis of this model were performed with the density matrix formalism of MO theory and gave an agreement of experimental and predicted relaxation rates within a factor of 2. 

The dipolar and chemical shift anisotropy spin-lattice relaxation rates for those carbons bonded to hydrogen may be obtained by iterations of the following steps (1) through (4), followed by step (5). 

Solid-state C NMR spectra of oil shales, obtained by CP/MAS with high-power decoupling are broad because of the multitude of resonances from the different carbon types found in these complex materials. A number of af roaches have been taken to improve the resolution of solid-state NMR of fi il fuels. Such tedmiques include variable temperature studies, variable frequency studies, mathematical enhancements and deconvolution techniques, and relaxation rate methods. The most popular method of enhancing solid-state NMR spectra is a relaxation rate method called dipolar dephasing (DD), which is sometimes referred to as interrupted decoupling. The exploitation of relaxation methods in CP NMR of fossil fuels has been reviewed elsewhere. ... 

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