Multi-pulse excitation

To measure high-resolution spectra of disordered samples, the anisotropy of the chemical shift must be eliminated in addition to the homonuclear dipole-dipole interaction. This can be achieved for abundant nuclei by combined rotation and multi-pulse spectroscopy (CRAMPS), which is the combination of homonuclear multi-pulse spectroscopy and MAS [Bur2, Ger2, Sch6]. In Fig. 3.3.13, H spectra of monoethyl fumarate are compared for different NMR techniques [Brol]. Only the combination of MAS and multi-pulse excitation produces a high-resolution spectrum of the polycrystalline powder. 

Fig. 3.3.13 H NMR spectra of CH3CH202CCH=CHC02H at 187MHz for different excitation techniques, (a) Single-pulse excitation of the nonspinning sample, (b) Single-pulse excitation and MAS. (c) Multi-pulse excitation of the nonspinning sample with BR24 sequence, (d) Combination of BR24 and MAS. Adapted from [BrolJ. Copyright 1988 American Chemical Society.

In combination with multi-pulse excitation, rotating-frame imaging can also be used for imaging of solids [Choi]. A time-suspension multi-pulse sequence (cf. Table 3.1) is applied to the sample by use of an rf coil with a homogeneous B field so that both... 

In terms of instrumentation the less demanding approach is multi-pulse excitation for averaging of the homonuclear dipolar interaction by trains of repetitive magic echoes during space encoding and acquisition of the spectroscopic response. Two such magic-echo... 

In the following, some aspects of multi-pulse excitation are reviewed which are relevant for space encoding. The effects of time-invariant and pulsed gradients are addressed as well as methods to increase the line-narrowing efficiency through second averaging and CRAMPS (cf. Section 3.3.4). 

Multi-pulse excitation in time-invariant field gradients... 

Fig. 10.3.1 [Hepl] F chemical-shift spectra of PTFE. The dipole-dipole interaction has been removed by M V8 multi-pulse excitation, (a) Isotropic molecular orientation, (b) Uniaxially drawn sample. The drawing direction is parallel to the magnetic field.

Two areas of signal processing research in cochlear implants are coding strategies for multi-electrode excitation and the development of noise-suppression systems. One of the problems in cochlear implants is that there is a large spread of the electrical stimulation within the cochlea. Because of this, simultaneous electrical pulses at... 

Equation (4.2.11) describes the response to three delta pulses separated by ti =oi — 02 >0, t2 = 02 — 03 > 0, and t3 = 03 > 0. Writing the multi-pulse response as a function of the pulse separations is the custom in multi-dimensional Fourier NMR [Eml ]. Figure 4.2.3 illustrates the two time conventions used for the nonlinear impulse response and in multi-dimensional NMR spectroscopy for n = 3. Fourier transformation of 3 over the pulse separations r, produces the multi-dimensional correlation spectra of pulsed Fourier NMR. Foinier transformation over the time delays <7, produces the nonlinear transfer junctions known from system theory or the nonlinear susceptibilities of optical spectroscopy. The nonlinear susceptibilities and the multi-dimensional impulse-response functions can also be measured with multi-resonance CW excitation, and with stochastic excitation piul]. 

A solid-state variant of the DANTE sequence (Fig. 5.3.15) is obtained by replacing the rf pulses and the free precession periods of the original sequence by line-narrowing multi-pulse sequences [Carl, Corl, Flepl, Hep2J. Such DANTE sequences can be used for selective excitation in solid-state spectroscopy (cf Fig. 7.2.8) and for slice selection in solid-state imaging (Fig. 5.3.16). 

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]. 

The measured responses to the combinations of multi-frequency selective pulse excitation can be unscrambled for each volume element by transformation with a super-Hadamard matrix. The dimension of this matrix equals the product of the dimensions of the Hadamard matrices used for encoding each space axis. 

Fio. 9.3.4 Excitation with a surface coil of 9 mm diameter in a Bo gradient of the order of lOT/m by the NMR-MOUSE (a) Series train of CPMG echoes from a carbon-black filled SBR section of an intact car tyre with a steel belt. A fit of the echo envelope with an exponential decay function yields a transverse relaxation time Ti [Eidl]. (b) Variation of the pulse duration in an a — te/l — Ta — ts/ i- pulse sequence for different rf frequencies. For each frequency maxima and minima are observed which define the nominal 90° and 180° pulse widths. With decreasing rf frequency the distance of the sensitive volume from the rf coil increases. A frequency of 17.5 MHz correspond to depths of 0-0.5 mm, 16MHz to 0.5-1.0mm, and 16.5 MHz to 1.0-1.5 mm into the sample [Gut3], (c) Hahn- and solid-echo envelopes for a sample of carbon-black filled cross-linked SBR. The Hahn-echo decay is faster because of residual dipolar couplings which are partially refocused by the solid-echo [Gut3]. (d) Multi-echo excitation. 

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