Spin-lattice relaxation sequence

The spin-lattice relaxation time, T/, is the time constant for spin-lattice relaxation which is specific for every nuclear spin. In FT NMR spectroscopy the spin-lattice relaxation must keep pace with the exciting pulses. If the sequence of pulses is too rapid, e.g. faster than BT/max of the slowest C atom of a moleeule in carbon-13 resonance, a decrease in signal intensity is observed for the slow C atom due to the spin-lattice relaxation getting out of step. For this reason, quaternary C atoms can be recognised in carbon-13 NMR spectra by their weak signals. 

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 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... 

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

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

The DDIF experiment consists of a stimulated echo pulse sequence [50] and a reference scan to measure and separate the effect of spin-lattice relaxation. The pulse diagrams for these two are shown in Figure 3.7.2. Details of the experiments have been discussed in Ref. [51] and a brief description will be presented here. 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

The essence of the ASAP method is based on the different spin-lattice relaxation behaviour of these two types of protons. In the case of a HMBC experiment, the acceptor protons are those directly bound to 13C with large spin-spin couplings they are the spins that give rise to the final spectrum. By contrast, the donor protons have negligible couplings to 13C and are therefore essentially unaffected by this polarization transfer sequence, which simply returns them to the z axis. In their method, Kupce and Freeman have proposed to replace the usual relaxation delay with a short cross-polarization (HOHAHA) interval. This offers a... 

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... 

The second difficulty is not encountered in proton spectroscopy, where proportionality between peak area and concentration of the respective sequence is virtually guaranteed, but is present in caibon spectroscopy where one works under heteronuclear broad-band decoupling conditions. Under such conditions, both the nuclear Oveihauser effect (NOE) and the differences in spin-lattice relaxation time T, can alter the intensity. In this connection, however, Schaefer showed that for the different C nuclei inside the polymer chain, because of the restricted molecular movement, there are no large differences in NOE (121). 

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... 

A solution of cinnamic aldehyde 4 was used to test the two pulse sequences, the results of which are shown in fig. 6. Three frequencies were selected to simultaneously perturb Cl, C3 and Cl for experiment IVa and Cl, C4 and Cl for experiment IVb to correlate directly and long-range coupled spins respectively. To minimize a decrease in sensitivity due to relaxation effects during the pulse cascade, the frequencies in the pulse train were ordered according to their estimated spin-lattice relaxation times. The... 

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.

Fig. 3. Proton-detected carbon-13 spin-lattice relaxation for the pentasaccharide p-trifluorao-acetamidophenyl-2,6-di-0-[/3-D-galactopyranosyl-(l 4)-0-2-acetamido-2-deoxy-/3-D-glu-copyranosyl]a-D-mannopyranoside. The measurements were performed with the two-dimensional method proposed by Skelton et al. [21], modified to obtain a one-dimensional pulse sequence. The figure shows the measurements for Cl in the 2-acetamido-2-deoxy-glucopyranose residue attached at position 2 on the mannopyranose residue.

Isotopes in low abundance have long spin-lattice relaxation times which give rise to poor signal-to-noise ratios. Sensitivity can be improved by using a technique known as cross polarization where a complex pulse sequence transfers polarization from an abundant nucleus to the dilute spin thereby enhancing the intensity of its signal. 

Now it will be necessary to elucidate the location of the butyl isopropenyl ketone unit in the polymer chain. The spin-lattice relaxation time, Tj., of the protons in the polymer and oligomer was measured. The Ti of methylene protons adjacent to the carbonyl group was nearly the same level as the T of methyl protons in the terminal butyl group or terminal methine proton (Table ) but much longer than the T of the protons in interior sequences of polymer (13). These indicate that the butyl carbonyl group in the polymer or oligomer locates at or near to the forefront or the end of the chain. 

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