Carbon-13 longitudinal relaxation

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. 

Table 5. Summary of the methine carbon longitudinal relaxation rates ri( Cm) and the deduced NMR data for trans-[Co(acac)2(XY)] in DMSO and MeOH. ...

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. 

In 2-substituted adamantanes 25 both types of 8-positioned carbon atoms (8syn and 8 ) exist within one molecule (Scheme 37). Early measurements with limited spectral resolution (176) did not differentiate between their signals. Later (124,244), differences of up to 0.7 ppm were detected, and application of various independent methods, including addition of lanthanide shift reagents (245), determination of longitudinal relaxation times T, (246), and evaluation of deuterium... 

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

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). 

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

The experiment is applied for the evaluation of C T, values. T, values are usually used to optimize insensitive C experiments, i.e. to adjust the length of the preparation time in other NMR experiments. To deduce structural information it is usual to interpret the dipolar part of the longitudinal relaxation time (T, ). To separate the dipolar contribution from the contributions of other relaxation mechanisms, it is necessary to perform further experiments (gated decoupling experiments) to evaluate the heteronuclear NOE values. T °° may be exploited in a qualitative way to differentiate between carbon nuclei in less or highly mobile molecular fragments. In a more detailed analysis reliable T, values can be used to describe the overall and internal motions of molecules. 

Phase Structure as Revealed from the Mobility of the Solvent. The phase structure of the sPP crystal in the gel form, which was elucidated by the line-decomposition analysis of the DD/MAS 13C NMR spectrum, will reflect on the mobility of the solvent in the gel. The mobility of the solvent can be examined by the longitudinal relaxation of resonance lines assigned to the carbons of the solvent. Figure 31 shows the longitudinal relaxation for the line at 130 ppm of the o-dichlorobenzene. The open circles indicate the data of the pure solvent and the closed ones those of the solvent in the gel. As can be seen, the relaxation of the pure solvent evolves exponentially with a Tic of 3.0 s, whereas that of the solvent in the gel evolves nonexponentially. This indicates that there are some solvent molecules in the gel that differ in their mobility. We assume here that the longitudinal relaxation of each component of the solvent evolves exponentially. Then the longitudinal relaxation of the total solvent follows the relationship ... 

The spin-lattice relaxation process, designated 7 (also termed longitudinal relaxation), varies widely for different types of carbon atoms. 

The longitudinal relaxation curves for the alkyl radicals monitored at the peak of the six-line spectrum (indicated by arrows in Fig. 6) are shown in Fig. 7. For n-alkanes, the relaxation rate decreases with the increase of the length of carbon chain, and it is independent of the radical concentration. This indicates that the cross relaxation between on-resonant and off-resonant radical spins is not the main source of the relaxation. In contrast, the relaxation rate for cyclohexane and polyethylene is the lowest, and depends on the radical concentration it decreases with the decrease of the radical concentration. This indicates that the cross relaxation contributes to the longitudinal relaxation in cyclohexane and polyethylene. 

Fig. 18. Values of the kc jk-i ratio (evaluated from the experimental efficiencies of formation of the excited state) as a function of the solvent longitudinal relaxation time Ti. Data for 4-(9-anthryl)-V,V,3,5-tetra-methylaniline in acetonitrile (ACN), pro-pionitrile (PN), butyronitrile (BN), propylene carbonate (PC), sulfolane (TMS) and 7-butyrolactone (BL) solutions. Adapted from [153].

On these systems the C longitudinal relaxation times T of the C5Me5 moieties have been measured by means of the Torchia s pulse sequence [48]. The Ti( C) values obtained for ring carbons have been rationalized on the basis of two relaxation interactions (dipole-dipole and chemical shift anisotropy) modulated by the motions involving the permethylated cyclopentadienyl rings. Interestingly, a qualitative comparison between solution and solid state C relaxation data shows that the same relaxation mechanisms are operative in both physical states. 

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