Inversion spin-lattice relaxation

It is possible to monitor relaxation times by modulating the microwave amplitude at a rate close to the inverse spin-lattice relaxation time, Tj (Misra, 2004). This is due to the fact that if the microwave amplitude is changed faster than that which the spins can follow as governed by the electron SLR time, the EPR signal is determined predominantly by T. This modulation technique permits measurement of relaxation times in the interval between the values that are slow enough to be measured by the recovery techniques and the values that are too fast to have any significant impact on continuous wave (cw) lineshape. These latter relaxation times can be as short as 10 s, which is substantially shorter than those that can be measured by the saturation/inversion recovery techniques. 

Figure Bl.13.4. The inversion-recovery detennination of the carbon-13 spin-lattice relaxation rates in melezitose. (Reproduced by pemiission of Elsevier from Kowalewski J and Maler L 1997 Methods for Structure Elucidation by High-Resolution N R ed Gy Batta, K E Kover and Cs Szantay (Amsterdam Elsevier) pp 325-47.)...

Canet D, Levy G C and Peat I R 1975 Time saving in C spin-lattice relaxation measurements by inversion-recovery J. Magn. Reson. 18 199-204... 

The technique for measurement which is most easily interpreted is the inversion-recovery method, in which the distribution of the nuclear spins among the energy levels is inverted by means of a suitable 180° radiofrequency pulse A negative signal is observed at first, which becomes increasingly positive with time (and hence also with increasing spin-lattice relaxation) and which... 

Figure 2.27. Sequence of measurements to determine the C spin-lattice relaxation times of 2-octanol (42) [(CD3)2C0, 75% v/v, 25 °C, 20 MHz, inversion-recovery sequence, stacked plot]. The times at which the signals pass through zero, xo, have been used to calculate, by equation 10, the T values shown above for the nuclei of 2-octanol...

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

Selective, spin-lattice relaxation-rates are measured by the inversion-recovery technique. A rather weak, 180° pulse of very long duration (10-50 ms) inverts a multiplet (single-selective) or two multiplets (double-selective) in the spectrum of asperlin (1 see Fig. 2 ) and the recovery of the... 

Inversion recovery A pulse sequence used to determine spin-lattice relaxation times. 

Fig. 30. Hydrogen spin lattice relaxation time T, in a-Si H against temperature for flake samples removed from their substrate (solid line) and for a-Si H on quartz substrates two weeks after deposition (triangles). The circle data points are for the quartz substrate samples ten months after deposition. The magnitude of the 40 K minimum of T, is inversely portional to the number of H2 molecules contributing to the relaxation process (Van-derheiden et al., 1987). 

FIGURE 31. Typical data set for measurement of the spin-lattice relaxation times of the sp2-hybridized carbon atoms of, 6-carotene at 11.7 T. The chemical shift values are shown across the bottom of the figure. The t-value for each spectrum is the delay time in the inversion-recovery pulse sequence. Reprinted with permission from Reference 49. Copyright (1995) American Chemical Society... 

Spin-lattice relaxation times were measured by the fast inversion-recovery method (24) with subsequent data analysis by a non-linear three parameter least squares fitting routine. (25) Nuclear Overhauser enhancement factors were measured using a gated decoupling technique with the period between the end of the data acquisition and the next 90° pulse equal to eibout four times the value. Most of the data used a delay of eibout ten times the Ti value. (26)... 

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. 

Polymer Dynamics. 13C spin-lattice relaxation times (Ti) were determined with either an inversion-recovery sequence (16) (for carbons observed by direct polarization) or with a modified cross-polarization experiment (17). 13C rotating-frame relaxation times (Tip(C)) were derived from measurements of the carbon signal that remained after a Tjp(C) hold time of... 

Selective inversion experiments for the determination of slow exchange rates are analogous to the saturation-transfer method in that they involve selective manipulation of one of the exchanging sites, while observing the subsequent effect on the second site as a function of time [48, 69, 70]. Chemical exchange, if present, will provide an alternative route to normal spin relaxation processes which a spin system undergoes, if perturbed at the start of an experiment. The rate of relaxation will depend on both the exchange rate k and the spin-lattice relaxation rate (Ti) (fig. 5). 

Fig. 1. Pulse sequences for determining spin-lattice relaxation time constants. Thin bars represent tt/2 pulses and thick bars represent tt pulses, (a) The inversion-recovery sequence, (b) the INEPT-enhanced inversion recovery, (c) a two-dimensional proton-detected INEPT-enhanced sequence and (d) the CREPE sequence. T is the waiting period between individual scans. In (b) and (c), A is set to (1 /4) Jm and A is set to (1 /4) Jm to maximize the intensity of IH heteronuclei and to (1/8) Jm to maximize the intensity of IH2 spins. The phase cycling in (c) is as follows 4>i = 8(j/),8(-j/) 3 = -y,y A = 2(x),2(-x) Acq = X, 2 —x), X, —X, 2(x), —x, —x, 2(x), —x, x, 2 —x),x. The one-dimensional version of the proton-detected experiment can be obtained by omitting the f delay. In sequence (d), the phase 4> is chosen as increments of 27r/16 in a series of 16 experiments.

The NMR spectra were taken on a JEOL JNM-MH-100 (CW) spectrometer using tetramethylsilane as an internal standard. 13C spin-lattice relaxation time of the polymer was measured by the inversion-recovery Fourier transform method on a JNM-FX100 FT NMR spectrometer operating at 25 MHz. 

The dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

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.

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