Rotating frame relaxation processes

Sefcik et al. [3] studied quenched and annealed PET films with different crystallinities varying from 3-50%. They measured rotating-frame relaxation times of protons and carbons, Tip and Tip These parameters give information about molecular motions in the tens or hundreds of kilohertz range, which is a characteristic frequency range for many important motional processes in solid polymers. Sefcik et al. were particularly interested in relaxation times. Tip which, in principle, can provide information about molecular motions at specific sites within the polymer. A multiexponential behavior of the magnetization decay was observed. 

The process of relaxation of M to a value proportional to the applied rf fields in the rotating frame is called spin-lattice relaxation in the rotating frame. The mechanisms available for this form of relaxation are entirely analogous to those available for simple spin-lattice relaxation as described above. Similarly, rotating frame relaxation is characterized by a time constant analogous to T, and is called Tip, or the spin-lattice relaxation time in the rotating frame. Typically, Tip values obtained from protons in solid samples are not of much use, since communication between the abundant protons tends to average the relaxation process, so that individual proton relaxation mechanisms cannot be observed. For C, however,... 

Measurement of relaxation is usually easier then but also time consuming. It should be borne in mind that spin-lattice relaxation of is bi-exponential [86] unless protons are decoupled during the relaxation delay. at natural abundance and nuclei are often used as probe of dynamic processes. Parameters such as and spin-lattice relaxation times and Tj), carbon and proton-rotating-frame relaxation... 

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Trott and Palmer used perturbation theory to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy. 

A detailed analysis of the cross-polarisation behaviour showed that quantitative results can be obtained. The amount of unreacted units, typically 0-15%, was found to depend on the polymerisation parameters. Conditions favouring mobility, i.e., higher temperatures or increased solvent quality, resulted in lower content of residual double bonds. Bromine addition values are 2-3% higher than the NMR data. The reactivity toward bromine further indicates that the mobility is reasonably high. This has also been confirmed by measurements of the rotating-frame relaxation time constant, Tj ( C) Most likely, Tjp is dominated by spin-lattice processes i.e., it can be interpreted in terms of molecular dynamics. The values obtained for C=0 and >C =CH2 in unreacted units are about twice that of C=0 in reacted units, indicating increased mobility. The reactivity of the remaining double bonds in a radical polymerisation with a chiral monomer was also demonstrated. 

Vibrational broadening in [162] was taken into account under the conventional assumption that contributions of vibrational dephasing and rotational relaxation to contour width are additive as in Eq. (3.49). This approximation provides the largest error at low densities, when the contour is significantly asymmetric and the perturbation theory does not work. In the frame of impact theory these relaxation processes may be separated more correctly under assumption of their statistical independence. Inclusion of dephasing causes appearance of a factor... 

Luminescence lifetime spectroscopy. In addition to the nanosecond lifetime measurements that are now rather routine, lifetime measurements on a femtosecond time scale are being attained with the intensity correlation method (124), which is an indirect technique for investigating the dynamics of excited states in the time frame of the laser pulse itself. The sample is excited with two laser pulse trains of equal amplitude and frequencies nl and n2 and the time-integrated luminescence at the difference frequency (nl - n2 ) is measured as a function of the relative pulse delay. Hochstrasser (125) has measured inertial motions of rotating molecules in condensed phases on time scales shorter than the collision time, allowing insight into relaxation processes following molecular collisions. 

Temperature-dependent lineshape changes were observed in an early study of the fluo-renyllithium(TMEDA) complex. A detailed study by lineshape analysis, which was also applied to the TMEDA complex of 2,3-benzofluorenyllithium(TMEDA) (Figure 29f, yielded barriers AG (298) of 44.4 and 41.9 kJmoD for the 180° ring flip in these systems, respectively . A second dynamic process, which was detected via the temperature dependence of, the spin-lattice relaxation time in the rotating frame, is characterized by barriers of 35.1 and 37.6 kJmoD, respectively, and may be ascribed to the ring inversion process. For the fluorenyl complex, a barrier AG (298) of 15.9 kJmoD for the methyl rotation in the TMEDA hgand was determined from temperature-dependent NMR spectra of the deuteriated system. 

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