Relaxation times in the rotating frame

Different solid-state NMR techniques CPMAS NMR, the second moment of the signal, the spin-lattice relaxation time in the rotating frame T p) were combined to reach the conclusion that in the case of por-phine H2P the double-proton transfer is followed by a 90° rotation within the crystal (see Scheme 2). 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

The frequency scale detected by 13C-resolved H spin-lattice relaxation time in the rotating frame Tq) 1 evaluated from the 13C CPMAS spectra42 is similar to that of the 13C T2C values and line-shape analysis16 for 13C (or 15N) or 2H nuclei, as illustrated in Figure 3. It is demonstrated... 

The main NMR interactions in solution of interest to chemists are the chemical shift relative to some stated standard (6), the indirect coupling constant (7) and the relaxation times T1 (spin-lattice) T2 (spin-spin related to the line width) and T p, the relaxation time in the rotating frame. In the case of solids and oriented samples both the direct dipole-dipole and the electric quadrupole interactions assume greater importance. We shall confine our attention in this chapter to diamagnetic compounds so that we may neglect nuclear interactions with electron spins. 

Any modification of the magnetization thus arises from relaxation phenomena. The transverse magnetization spin-locked along must end up at its thermal equilibrium value, that is zero. The corresponding evolution is exponential with a time constant denoted by Tip (relaxation time in the rotating frame), very close (if not identical) to T. In practice, the signal is measured (and subsequently Fourier transformed) for a set of x values, in successive experiments, and obeys the equation... 

Fig. 5. Principle of a spin-lock experiment leading to the determination of the relaxation time in the rotating frame (Tip). (SL)y stands for the spin-lock period which corresponds to the application of a rf field along the y axis of the rotating frame.

Finally, concerning the so-called spin-lattice relaxation time in the rotating frame (Section I.C), one has... 

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. 

However, relaxation times can be used as well as the chemical shifts to provide information on the dynamics. Especially, the spin-lattice relaxation time in the rotating frame of 3H ( ll T,p) is very sensitive to the... 

As an NMR methodology for elucidating miscibility in the PLA/PLV, PLA/PLIL, PDA/PLV and PG/PLV blends, the proton spin-lattice relaxation times in the rotating frame ) for homopolypeptides and their... 

T, Tlo nuclear spin lattice relaxation time in the rotating frame. 

Figure 3. Log of the inverse of the spin lattice relaxation time (T 1), the spin-lattice relaxation time in the rotating frame (T lp 1), and the line shape as a function of time for the HP sample after the sample was heated to 460°K and brought back to room temperature.

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

Complementary NMR measurements, such as rises of carbon polarisation in a spin-lock experiment and determination of 13C spin-lattice relaxation times in the rotating frame, Tip(13C), support these conclusions about the correlation times of the side-ring CH and CH2 motions in the various poly(cycloalkyl methacrylates). 

Another way of using JH NMR to study the dynamics of phenyl protons in BPA-PC consists in selective deuteration of the methyl groups (BPA-d6-PC) [32]. Thus, the temperature dependence of the JH spin-lattice relaxation time, Ti, and spin-lattice relaxation time in the rotating frame, T p, has been determined, and is shown in Fig. 38. 

The temperature dependencies of the ( 172)0/ 1/2 ratio, where ( 1/2)0 is the 1/2 value measured at room temperature, determined for the CHOH - CH2 - O and CH2 - N units of the hydroxylpropyl ether (HPE) sequence (Fig. 92) in the HMDA network [63] are shown in Fig. 97. It is worth noticing that the 1/2 values of these two types of carbons have the same temperature dependence. Up to 60 °C, the 1/2 values are constant and equal to the rigid-lattice values, indicating that the HPE sequence does not undergo any local motion at a frequency equal to or higher than 105 Hz in this temperature range. Above 60 °C, mobility develops, which leads at 100 °C to motions in the tens of kilohertz for the whole HPE sequence. These results are qualitatively confirmed by data on 13C spin-lattice relaxation time in the rotating frame, Tip(13C). 

Io is the maximum intensity, TCp is the cross polarization time constant and Tiph and TlpC are the relaxation times for ll and 13C in the rotating frame. The cross polarization rate (l/TCp) depends on the square of the dipolar interaction while the relaxation time in the rotating frame provides... 

In order to probe lower frequency motions, some relaxation measurements are made in instruments designed to allow relaxation to occur at very low magnetic field, where the Larmor frequency is a fraction of a MHz. Alternatively, it is possible to define and measure a spin-lattice relaxation time in the rotating frame, given the symbol Tlp, Which is sensitive to motions in the kHz range. We shall return to Tlp in Chapter 9. 

Tj (Tlp) Spin-lattice relaxation time (in the rotating frame)... 

Time period of forward CP in DCP - see text and Fig. 14 Depolarisation time period in DCP - see text and Fig. 14 P spin-lattice relaxation time in the laboratory frame Cross-polarization time constant for the I-P-S model H spin-lattice relaxation time in the rotation frame H spin-spin relaxation time in the laboratory frame Recycle delay... 

Chang et al. reported the miscibility of poly(vinylphenol) (PVPh) with poly(methyl methacrylate) (I MMA) Figure 1 shows the C CP/MAS spectra of pure PVPh, PMMA, PVPh-co-PMMA, PEG, and PVPh-co-PMMA/ poly(ethylene oxide) (PEO) blends of various compositions with peak assignments. VPh contents of PVPh-co-PMMA is 51 mol% and Mn of PEO is 20,000. The spin lattice relaxation time in the rotating frame (Tip ) was measured to examine the homogeneity of PVPh-co-PMMA/PEO blends on the molecular scale. 

---