Rotating frame, relaxation

Deverell C, Morgan R E and Strange J FI 1970 Studies of ohemioal exohange by nuolear magnetio relaxation in the rotating frame Mol. Phys. 18 553-9... 

AppHcations of soHd-state nmr include measuring degrees of crystallinity, estimates of domain sizes and compatibiHty in mixed systems from relaxation time studies in the rotating frame, preferred orientation in Hquid crystalline domains, as weU as the opportunity to characterize samples for which suitable solvents are not available. This method is a primary tool in the study of high polymers, zeoHtes (see Molecular sieves), and other insoluble materials. 

Figure 4-9. (Ai Precessing moment vectors in field tfo creating steady-state magnetization vector Afo. with//i = 0. (B) Immediately following application of a 90° pulse along the x axis in the rotating frame. (C) Free induction decay of the induced magnetization showing relaxation back to the configuration in A.

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). 

Moreover, precession under selective irradiation occurs in the longitudinal plane of the rotating frame, instead of rotation in the transverse plane, which occurs during the evolution of the FID. The magnitude of the vector undergoing precession about the axis of irradiation decreases due to relaxation and field inhomogeneity effects. 

Bull, T. E. Relaxation in the rotating frame in liquids. Prog. Nucl. Magn. Reson. Spectrosc. 1992, 24. 

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... 

T2 measurements usually employ either Carr-Purcell-Meiboom-Gill (CPMG) [7, 8] spin-echo pulse sequences or experiments that measure spin relaxation (Tlp) in the rotating frame. The time delay between successive 180° pulses in the CPMG pulse sequence is typically set to 1 ms or shorter to minimize the effects of evolution under the heteronuc-lear scalar coupling between 1H and 15N spins [3]. 

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. 

Jonas et al. measured the proton rotating frame spin-lattice relaxation time (Tip) at pressures from 1 bar to 5000 bar and at temperatures of 50 to 70 °C for DPPC and at 5 to 35 °C for POPC. If intermolecular dipolar interactions modulated by translational motion contribute significantly to the proton relaxation, the rotating frame spin-lattice relaxation rate (1/Tip) is a function of the square root of the spin-locking field angular frequency... 

Fig. 3. The basic Hahn sequence for the measurement of the transverse relaxation time T2. Any precession motion characterized by the frequency v in the rotating frame is refocused. This precession may arise either from chemical shift or from Bq inhomogeneity (symbolized by the shaded area, which has been strongly reduced for visualization purposes owing to the fast decay of the fid, it should in fact extend to the whole circle).

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.

Notice the presence of a spectral density at zero frequency in i 2 arising from bz t)bz Q)dt (which evidently does not require to switch to the rotating frame). This zero frequency spectral density will be systematically encountered in transverse relaxation rates and, in the case of slow motions, explains... 

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

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