Off-resonance spin locking

If the condition 7S1 2> 6v is not fulfilled, then the experiment is called the off-resonance spin-lock or T p experiment in a tilted rotating frame . The experiments of this type, employing off-resonance conditions to a variable extent, have actually been proposed as a tool for varying the frequencies at which the spectral densities are being sampled [49]. The advantage of this approach is that it provides a means of estimating the rotational correlation time for macromolecules in solution. 

For large off-resonance frequencies, the angle 9 in (7.2.5) is small enough so that the second 90° pulse in the sequence of Fig. 7.2.4 can be discarded. Off-resonance spin locking can also be seen as a low-power alternative to spin locking, so that the technique may be used in medical applications [Fai 1]. 

Proton relaxation under multiple pulse conditions has also been used to characterise phase composition in, for example, PET [95,96], and polyethylene [120]. The technique is particularly useful in the case of PET because the phases present generally do not show large differences in the decay times of their FID components, so FID analysis would be particularly problematic. Although the problem of assessing the extent to which spin diffusion is suppressed also applies to relaxation under multiple pulse conditions, the available experimental evidence suggests that they may be more effective in practice than the corresponding off-resonance spin-locking experiment [96]. This is almost certainly due to practical considerations rather than theoretical ones. 

The third complicating factor specific to ROESY is the attenuation of cross-peak intensities as a function of resonance offset from the transmitter frequency [69]. Off-resonance spins experience a spin-lock axis that is tipped out of the x-y plane (Section 3.2.1) resulting in a reduction in observable transverse signal in addition to a reduction in cross-relaxation rates. This is more of a problem for quantitative measurements, although fortunately mid-sized molecules show the weakest dependence of ROE cross-relaxation rates on offset. The so-called compensated ROESY sequence [69] eliminates these frequency-dependent losses should quantitative data be required. 

Carbon resonances arising from both nonprotonated and proto-nated aromatic carbons may appear at the same frequency under proton decoupling. Yet these two resonances could possess very different relaxation behavior and in a solid could evolve very differently due to local proton dipolar fields which attenuate with the carbon-proton distances as 1/rcH When the spin locking pulse for proton nuclei is turned off, carbons with directly bound protons such as methines and methylenes rapidly dephase in the local proton fields and their spectral response is rapidly diminished. The rapid internal motion of CH3 groups greatly decreases the effectiveness of methyl protons. Nonprotonated carbons are only dephased by remote and therefore... 

What does this mean for the effect of the spin lock on sample magnetization If the sample magnetization starts on the / axis, for example, the tilted spin-lock axis will destroy the component that is perpendicular to the spin-lock axis and retain the component that is on the spin-lock axis. This preserved component is locked because it is on the axis of the effective field and has no reason to precess around the z axis. So even if the spin is off-resonance, its magnetization does not precess around the z axis during the spin-lock period. Instead, the component that is not on the tilted spin-lock axis precesses around the spin-lock axis until it is destroyed by Bi inhomogeneity, and the component that is on the spin-lock axis is retained. 

A selective TOCSY experiment starts with putting the net magnetization of just one resonance in the x -y plane and locking it with the TOCSY mixing spin lock. After an appropriate mixing time, the spin lock field is turned off and we simply start acquiring the FID. These steps can be summarized as follows ... 

A number of theoretical transfer functions have been reported for specific experiments. However, analytical expressions were derived only for the simplest Hartmann-Hahn experiments. For heteronuclear Hartmann-Hahn transfer based on two CW spin-lock fields on resonance, Maudsley et al. (1977) derived magnetization-transfer functions for two coupled spins 1/2 for matched and mismatched rf fields [see Eq. (30)]. In IS, I2S, and I S systems, all coherence transfer functions were derived for on-resonance irradiation including mismatched rf fields. More general magnetization-transfer functions for off-resonance irradiation and Hartmann-Hahn mismatch were derived for Ij S systems with N < 6 (Muller and Ernst, 1979 Chingas et al., 1981 Levitt et al., 1986). Analytical expressions of heteronuclear Hartmann-Hahn transfer functions under the average Hamiltonian, created by the WALTZ-16, DIPSI-2, and MLEV-16 sequences (see Section XI), have been presented by Ernst et al. (1991) for on-resonant irradiation with matched rf fields. Numerical simulations of heteronuclear polarization-transfer functions for the WALTZ-16 and WALTZ-17 sequence have also been reported for various frequency offsets (Ernst et al., 1991). 

Fig. 5. (A) Vector picture describing the relationship between the rf field strength and offset frequency in off-resonance experiments such as LGCP and PISEMA. (B) A simple pulse sequence (called LGCP or FFLGCP) to set-up the Lee-Goldburg condition. As explained in the text, this sequence can be used to determine the S-spin-lock field strength that matches ileff./for the effective spin exchange between / and S spins.

The particular value of coi can be adjusted by the strength fii / y of the spin-lock field. The range of effective spin-lock field strengths can be increased if off-resonance techniques are applied. In this case, the effective field Beff forms an angle 0 with respect to the z-axis (cf. Fig. 2.2.7), and the effective relaxation rate (T p,efr) is a combination of the longitudinal relaxation rate (7i) and the relaxation rate in the rotating frame (Tip) [Kim2],... 

Although in principle the simple scheme presented in Fig. 5.59 should provide TOCSY spectra, its suitability for practical use is limited by the effective bandwidth of the continuous-wave spin-lock. Spins which are off-resonance from the applied low-power pulse experience a reduced rf field causing the Hartmann-Hahn match to breakdown and transfer to cease. This is analogous to the poor performance of an off-resonance 180° pulse (Section 3.2.1). The solution to these problems is to replace the continuous-wave spin-lock with an extended sequence of composite 180 pulses which extend the effective bandwidth without excessive power requirements. Composite pulses themselves are described in Chapter 9 alongside the common mixing schemes employed in TOCSY, so shall not be discussed here. Suffice it to say at this point that these composite pulses act as more efficient broadband 180 pulses within the general scheme of Fig. 5.60. 

Set against these obvious benefits are a number of experimental problems, principally TOCSY transfers also occurring during the spin-lock and signal attenuation firom off-resonance effects. These issues are further addressed in the practical sections that follow, so it is sufficient to note here that even more care is required when acquiring and using ROEs than is needed for NOEs, so much so that some would regard this only as a specialist s technique. 

The chapfer consists of four sections, which are devoted to theoretical and practical issues of the detection of nitrogen-containing substances. Section 2 deals with theoretical aspects of the two most popular multi-pulse sequences multipulse spin-locking—MW-4 and "strong off-resonant comb"—SORC. In spite of the fact that the development of these sequences has enabled a dramatic increase in the sensitivity of NQR methods, until recently a number of theoretical and experimental peculiarities of these sequences have not been studied adequately. The primary issue concerns the sequence SORC, and also behaviour of both sequences in case of close times of spin-lattice and dipolar relaxations, which is especially important for the detection of such a popular explosive as hexogen (RDX). There are also demonstrated some experimental techniques for the detection of some other explosives (PETN and trinitrotoluene (TNT)). 

The application of various multi-pulse methods in NQR requires a clear theoretical understanding of physical processes first of all behind the simplest "basic" multi-pulse sequences which include such a popular sequence as multi-pulse spin locking—MW-4, and a sequence of identically spaced coherent radio frequency (RF) pulses with intervals between them less than the time constant of free induction decay (FID) —strong off-resonance comb— SQRC. ... 

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