Spin-lattice relaxation times in rotating

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... 

Recently, Lipton et al. [25] have used zinc-67 NMR to investigate [Zn(HB(3,5-(CH3)2pz)3)2] complexes which have been doped with traces of paramagnetic [Fe(HB(3,4,5-(CH3)3pz)3)2]. The low-temperature Boltzmann enhanced cross polarization between XH and 67Zn has shown that the paramagnetic iron(II) dopant reduces the proton spin-lattice relaxation time, Tj, of the zinc complexes without changing the proton spin-lattice relaxation time in the Tip rotating time frame. This approach and the resulting structural information has proven very useful in the study of various four-coordinate and six-coordinate zinc(II) poly(pyrazolyl)borate complexes that are useful as enzymatic models. 

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>. 

Table 5.33. Selected Carbon-13 Spin-Lattice Relaxation Times (in ms) and Rotational Correlation Times (in ns) of Ribonuclease A(H20 [41]).

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). 

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)... 

In the first case, the energy is dissipated within the lattice as phonons, that is, vibrational, rotational and translational energy. The mechanism by which this dissipation occurs is known as spin-lattice relaxation. It is characterized by an exponential decay of energy as a function of time. The exponential time constant is denoted Tie and is called the spin-lattice relaxation time. In the second case the initial equilibrium may also be reached by a different process. There could be an energy exchange between the spins without transfer of energy to the lattice. This phenomenon, known as spin-spin relaxation is characterized by a time constant T2e called the spin-spin relaxation time. 

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. 

The miscibility of poly(methyl acrylate) (PMAA, Mw= 150,000)/PVAc (Mw= 167,000) blends at various mixing ratios was investigated by both Ti and Tip measurements. C CP/MAS NMR spectra of PMAA, PVAc and the PMAA/PVAc blends are shown in Fig. 2. Figure 3 shows the plots of the spin-lattice relaxation times in the laboratory (Ti , A) and in the rotating (Ti, B) frames against the molar ratio of PMAA (xpmaa)-The ll relaxation times from the CI 12 (O) and OCH (A) carbons for PMAA and PVAc, respectively, can be observed because these two carbons are observed separately even in the blends (Fig. 2), so that it is possible to obtain each relaxation time for PMAA or PVAc in the blends independently. 

Fig- 3. Observed spin-lattice relaxation times in the laboratory (Ti, A) and in the rotating B) frames against the molar unit ratio of PMAA/PVAc blends... 

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