Hartmann-Hahn mismatch

Fig. 42. Comparison of the experimental and calculated Hartmann-Hahn mismatch sideband patterns for polybutadienes with the average molecular weight between crosslinks M = 6810 (A), Mc = 2730 (B) and Mc = 1020 (adapted from Ref. 250>)...

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). 

If pulse shaping devices and linear amplifiers are available, then rapid, phase-coherent changes of the rf amplitude can be conveniently implemented. In this case, the Hartmann-Hahn mismatch that is created by the additional pulse can be further reduced by increasing the rf amplitude of the additional pulse (see Fig. 24D and D ). The offset dependence of the coherence-transfer efficiency of a boosted MLEV-17 sequence (MLEV-17b) with I f = 10 kHz and v = 20 kHz is shown in Fig. 24D. 

The first example, also being the example introducing optimal control to solid-state NMR [40] and further elaborated on later [161], is optimal control versions of the DCP experiment. This experiment was a natural choice for numerical improvements as it is widely used and it is well known that this experiment is sensitive to offsets, rf mismatch relative to the MAS-modified Hartmann-Hahn condition, and rf inhomogeneity. In particular the two latter effects may reduce significantly the performance of 15N to 13C transfers, severely complicate setup of such experiments, and render these critically sensitive to altered tuning/rf conditions in the course of potentially long experiments for biological samples. 

Homonuclear Hartmann-Hahn transfer functions for off-resonant CW irradiation have been derived for two coupled spins 1 /2 (Bazzo and Boyd, 1987 Bothner-By and Shukla, 1988 Elbayed and Canet, 1990) and for the AX 2 spin system (Chandrakumar et al., 1990). In the multitilted frame, Hartmann-Hahn transfer functions under mismatched effective fields are related to polarization- and coherence-transfer functions in strongly coupled spin systems (Kay and McClung, 1988 McClung and Nakashima, 1988 Nakai and McDowell, 1993). Numerical simulations of homonuclear... 

Vj, effective coherence transfer is possible (Davis and Bax, 1985 Bax et al., 1985). This sequence (DB-1) is the analog of square-wave heteronuclear decoupling (Grutzner and Santini, 1975 Dykstra, 1982). For heteronuclear Hartmann-Hahn experiments, a similar sequence [mismatch-optimized IS transfer (MOIST)] was introduced by Levitt et al. (1986) (see Section XII). In order to allow Hartmann-Hahn transfer of only a single magnetization component, the total duration during which the rf field is applied along the... 

Figure 24A -D shows the offset dependence of the corresponding MLEV-16 and MLEV-17 sequences. The reduction of the active bandwidth, which is induced by the additional pulse, can be limited by reducing the flip angle B of this pulse (Sklenaf and Bax, 1987 Bax, 1988a see Fig. 24B and C). For example, for a MLEV-17 sequence with pf = Pj = 10 kHz and B = 180° (Bax and Davis, 1985b), the effective fields for two spins i and j with offsets p, = 0 kHz and Vj = 3 kHz are mismatched by about 13 Hz [psl(f,) = 303 Hz and Psl(f,) 316 Hz], which significantly reduces the efficiency of Hartmann-Hahn transfer for coupling...

Jij/2, in complete analogy to the heteronuclear case (Chingas et al., 1981 Ernst et al., 1991). The concomitant increase of the transfer time by a factor of 2 is characteristic for heteronuclear and doubly selective homonuclear Hartmann-Hahn transfer. During doubly selective irradiation, mismatched spins m are effectively decoupled if c vf and Jim and the three spins i, j, and m approach an effective POO... 

Thus, for a given nitrogen the full polarization transfer can be reached only to the extent that the cross polarization time t is given the appropriate value. Moreover the HARTMANN-HAHN condition [Eq. (3.1)] is less easily fullfilled in the liquid state than for solids since the tolerable mismatch is now of the order of the scalar coupling constants which are at least two orders of magnitude smaller than the dipolar ones. The homogeneity of the rf fields is also a critical condition and in practice probe coils doubly tuned for and protons have been especially constructed. (See also (C 28)). 

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