Multi-quantum imaging

Constant-time imaging of H in solids has been applied in combination with MAS for line narrowing [Cor3, Cor4]. The images were recorded for a dynamically stressed poly(isoprene) phantom and of poly(butadiene) in two poly(butadiene)/poly(styrene) blends. Spectroscopic MAS imaging has also been tested on deuterated polymers to probe differences in molecular moblity from the lineshape of the rotary-echo envelope 

The use of multi-quantum imaging inherently includes a multi-quantum contrast filter in the sequence. Such multi-quantum filters (cf. Section 7.2.10) can also be combined with single-quantum space encoding techniques. They are used to discriminate coupled spins i from uncoupled spins in liquids and signals from ordered materials from those of disordered materials. 

Formally, multi-quantum coherences of order p are described by irreducible tensor operators Tqp (cf. Table 3.1.2 for coupled spins [Eml]. The coherence order is described by p = mf-mi (cf. Fig. 2.2.11), where m and /n, are the final and initial magnetic quantum numbers of a transition. For double-quantum coherence, for example, p = 2. The total spin coherence q corresponds to the maximum order possible. In this case, p = q so that maximum coherence order is described by T,. 

If evolves under a field gradient applied along the z-direction parallel to the static magnetic field, the evolution of spin coherences under the Zeeman interaction leads to changes described by the transformation 

In NMR, multi-quantum coherences can be excited by just two pulses [Eml, Muni] but for rigid samples multi-pulse sequences are more efficient (cf. Fig. 7.2.26) [Bau2, Muni]. Because the receiver coil in the NMR experiment corresponds to a magnetic dipolar detector, only dipolar single-quantum coherence can be detected directly and not multi-polar multi-quantum coherences. However, the latter can be detected indirectly by methods of 2D NMR spectroscopy [Eml]. 

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Multi-quantum imaging has first been explored on dipolar coupled protons in adamantane (Fig. 8.4.2) [Gar2]. Together with the anisotropy A of the bilinear spin interaction, the duration tp of the multi-quantum preparation period determines the order to which the... 

Multi-quantum transitions can only be observed indirectly by a modulation of the detected signal with the phase of the multi-quantum coherence. This modulation is achieved in an experiment by variation of an evolution time prior to detection. Repetitive detection of the signal for different evolution times provides the information about the evolution of the multi-quantum coherence. The indirect detection of spectroscopic information based on phase or amplitude modulation of the detected signal is the principle of multi-dimensional NMR spectroscopy [Eml]. Thus multi-quantum NMR is a special form of 2D NMR. Also, NMR imaging can be viewed as a special form of multi-dimensional NMR spectroscopy, where the frequency axes have been coded by the use of magnetic field gradients to provide spatial information. 

Depending on the particular pulse sequence used and on the coherence order, the multi-quantum build-up curves can be calculated in the short-time regime for a particular chemical group [Schl2]. From these known expressions, parameter images of... 

Fio. 7,2.30 [Sch 13 Multi-quantum filtered images of a phantom made from Pt samples with different cross-link densities. The cross-link density varies from left to right according to medium, high and low. The top image is a conventional spin-echo image for reference. 

Fig. 7.3.4 Pulse sequences for 2D spectroscopic 2D imaging, (a) COSY spectroscopy [Ziel]. The spectroscopic imaging sequence is preceded by a water suppression sequence of three selective pulses, (b) Heteronuclear multi-quantum coherence-transfer spectroscopy [Zij2]. The hatched gradients are for selection of coherence transfer pathways.

Efficient suppression of water signals is a side benefit of heteronuclear coherence transfer schemes. The heteronuclear multi-quantum coherence (HMQC) method (Fig. 7.3.4(b)) is a broad-band version of the HYCAT experiment of proton detected C imaging (cf. Fig. 7.2.30(a)) [Knii4]. The initial 90° pulse on is used for slice selection. For a heteronuclear AX system, single-quantum proton magnetization is transferred into heteronuclear zero- and double-quantum magnetization by a 90° C pulse after... 

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