T, longitudinal relaxation time

In polymers one will often particularly be interested in very slow dynamic processes. The solid echo technique just described is still limited by the transverse relaxation time T being of the order of a few ps at most. The ultimate limitation in every NMR experiment however, is not T but the longitudinal relaxation time T, which for 2H in solid polymers typically is much longer, being in the range 10 ms to 10 s. The spin alignment technique (20) circumvents transverse relaxation and is limited by Tx only, thus ultraslow motions become accessible of experiment. 

Mozumder (1969b) pointed out that in the presence of freshly created charges due to ionization, the dielectric relaxes faster—with the longitudinal relaxation time tl, rather than with the usual Debye relaxation time T applicable for weak external fields. The evolution of the medium dielectric constant is then given by... 

The majority of double-resonance solid-state NMR experiments involving spin-1/2 nuclei use transfer of nuclear polarization via dipolar cross polarization (CP) to enhance polarization of the diluted spins S with small gyromagnetic ratio ys and significant longitudinal relaxation time T at the expense of abundant spins I with large y, and short 7 [215]. Typically, CP is used in combination with MAS, to eliminate the line broadening due to CS A, as well as with heteronuclear decoupling. To achieve the / S CP transfer, a (n/2)y pulse is applied at the I spin frequency,... 

Longitudinal relaxation times (T]) and NOE measurements The relevant data are reported in Table III. The T values were measured by the inversion-recovery method. 

The correlation function C(t) is purely phenomenological. Interpretation of its time evolution is often based on theory in which the longitudinal relaxation time, tl, is introduced. This time is a fraction of the Debye relaxation time ... 

Experiments in the picosecond time range show that C(t) is non-exponential in most solvents with an average spectral relaxation time greater than the longitudinal relaxation time tl and smaller than the Debye time td-... 

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... 

Two principles are usually applied to clinical water or fat selective imaging on the one hand, water and lipid signals show different longitudinal relaxation times T and, on the other hand, they are recorded at slightly different Larmor frequencies due to their different chemical shifts. 

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). 

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. 

By spin-lattice relaxation, the longitudinal magnetization Mz increases to its equilibrium value M0 (longitudinal relaxation). T, is therefore often called the longitudinal relaxation time. 

Debye-Onsager model for C(t) and the longitudinal relaxation time Tj... 

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