Phase-twist lineshape

In conventional two-dimensional Hartmann-Hahn experiments, only the transfer of a single magnetization component a is used. In order to avoid phase-twisted lineshapes, the orthogonal magnetization components B and y are eliminated with the use of trim pulses or other filters (see Section XII). If two magnetization components can be transferred with identical transfer functions 7) (t) = the sensitivity of multidimen-... 

If the phase cycling used selects only one coherence transfer pathway, a two-dimensional spectrum with phase-twist lineshapes is obtained. However, the experiment can be easily modified to ensure that pure absorption (pure phase) lineshapes are obtained. The most commonly used modified acquisition schemes that allow pure-phase MQMAS spectra to be obtained include amplitude-modulated experiments, with hyper-complex (States) acquisition, and phase-modulated experiments, with delayed acquisition such as shifted echo or antiecho and split-methods. 

Figure 5.22. Contour plots of (a) the phase-twist lineshape, (b) the same following magnitude calculation, and (c) the same following resolution enhancement with an unshifted sine-bell window and magnitude calculation.

One problem with the gradient approach described above for COSY is that it necessarily precludes the acquisition of high-resolution phase-sensitive data sets by selecting only one pathway in ti. Since this leads to phase-modulated data it provides only phase-twisted lineshapes. Recall that phase-sensitive ac-... 

Absolute-value (magnitudemode) COSY-90 Simple and robust, magnitude processing well suited to automated operation. Phase-twisted lineshapes produce poor resolution which require strong resolution enhancement functions. Crosspeak fine structure not usually apparent. 

This is a single line at = (+Q +Q2) with the phase-twist lineshape,... 

The phase-twist lineshape is an inextricable mixture of absorption and dispersion it is a superposition of the double absorption and double dispersion lineshape (illustrated in section 7.4.1). No phase correction will restore it to pure absorption mode. Generally the phase twist is not a very desirable lineshape as it has both positive and negative parts, and the dispersion component only dies off slowly. 

This is a two lines, both with the phase-twist lineshape one is located at (+Q1,+Q2) and the other is at (-f2j,+f22). As expected for a data set which is cosine modulated in tl the spectrum is symmetrical about co] = 0. 

This is two lines, located at (+X21,+f22) and (-f2,+f22), but in contrast to the above both have the double absorption lineshape. There is still lack of frequency discrimination, but the undesirable phase-twist lineshape has been avoided. 

Few two-dimensional experiments naturally produce phase modulated data sets, but if gradient pulses are used for coherence pathway selection it is then quite often found that the data are phase modulated. In one way this is an advantage, as it means that no special steps are required to obtain frequency discrimination. However, phase modulated data sets give rise to spectra with phase-twist lineshapes, which are very undesirable. So, it is usual to attempt to use some method to eliminate the phase-twist lineshape, while at the same time retaining frequency discrimination. 

The quantity in the square brackets on the right represents a phase-twist lineshape at F = +Q, F2 = Q... 

Perspective view and contour plot of the phase-twist lineshape. Negative contours are shown dashed. 

This lineshape is an inextricable mixture of absorption and dispersion, and it is very undesirable for high-resolution NMR. So, although a phase modulated signal gives us frequency discrimination, which is desirable, it also results in a phase-twist lineshape, which is not. 

This corresponds to two phase-twist lineshapes, one at Fl = +Q, F2 = Q and the other at F, = -Q, F2 = Q the lack of frequency discrimination is evident. Further, the undesirable phase-twist lineshape is again present. 

We will see in later sections that when we use gradient pulses for coherence selection the natural outcome is P- or N-type data sets. Individually, each of these gives a frequency discriminated spectrum, but with the phase-twist lineshape. We will show in this section how an absorption mode lineshape can be obtained provided both the P- and the N-type data sets are available. 

The greatest drawback with data collected with phase modulation is the inextricable mixing of absorption and dispersion-mode lineshapes. The resonances are said to possess a phase-twisted lineshape (Fig. 5.21a), which has two principal disadvantages. Firstly, the undesirable and complex mix of both positive and negative intensities and secondly, the presence of dispersive contributions and the associated broad tails that are unsuitable for high-resolution spectroscopy. To remove confusion from the mixed positive and negative intensities, spectra are routinely presented in absolute-value mode, usually after a magnitude calculation (Fig. 5.22). 

Figure 5.21. A stacked plot illustration of (a) the phase-twisted lineshape and (b) the doubleabsorption lineshape. Clearly the resolution in (b) is far superior, and for this reason phase-sensitive methods are preferred.

---