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Second-order dipolar order in magic-angle spinning nuclear magnetic resonance
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Image of FIG. 1.
FIG. 1.

(a) Jeener-Broekaert sequence used for generating dipolar order. A 32-step phase cycle was used to obtain the indicated coherence pathway (Table I), allowing all odd-order operators during τ1 (effectively ±1Q) and filtering out up to 8Q during τ2. This ensures that the experimental data only reflect the generation of dipolar order, as described in the theory section. (b) Corresponding sequence for generating dipolar order using ADRF-ARRF.

Image of FIG. 2.
FIG. 2.

(a) Simulated buildup of second-order dipolar order λDO (black) and three-spin ZQ operators (red) during the JB experiment as a function of τ1, in a three-spin system at 20 kHz MAS. A distance of 2.5 Å was assumed between all spins and a random orientation of the dipolar tensors with respect to each other. (b–e) show simulated results for JB in a linear seven-spin system at 30 kHz MAS as a function of τ1 and τ2. The distance between neighbours in the chain was taken to be 3 Å, the orientation of the dipolar tensors was randomized. The second-order dipolar order constitutes a constant of the motion and converts efficiently into observable signal. The residual three-spin ZQ operators not only decay rapidly during τ2 but also do not convert efficiently into observable signal. (f) Simulated decay of second-order dipolar order in a four-spin system as a function of the MAS frequency caused by higher-order terms in the AHT expansion.

Image of FIG. 3.
FIG. 3.

(a) Simulated ADRF experiment for the three-spin system of Figure 2(a) at 33.33 kHz MAS, as a function of the length of the Gauss pulse τADRF. The various operators generated at the end of the ADRF are shown in different colours: one-spin SQ operators (λSQ1), double quantum (λDQ), triple quantum and higher (λMQ), (purple, λSQm), ZQ operators with one, two, three, or more spins (λZQ1, λZQ2, λZQ3, λZQm), and finally second-order dipolar order (λDO). (b) Simulated ADRF experiment for a six-spin system at 33 kHz MAS.

Image of FIG. 4.
FIG. 4.

(a) 1D 1H spectra of four compounds under static conditions (black) and 10 kHz MAS (red). (b) Buildup of second-order dipolar order during JB as a function of the spinning speed, normalized to the Zeeman order. The curve for camphor at 20 kHz MAS is shown despite minor effects of the impending chemical-shift resolution in the spectrum, the curve at 25 kHz was strongly affected and is not shown (c) Decay of second-order dipolar order as a function of the spinning speed. The curves were approximately normalized to one to allow direct comparison and the colours match those used in (B). Black dots indicate the sampling points for τ1 or τ2.

Image of FIG. 5.
FIG. 5.

(a) Second-order dipolar order measured with JB on camphor, at 12 kHz MAS, both far above (room temperature) and below the rotational transition at 208 K (Ref. 33) showing the importance of higher-order terms of the AHT expansion. (b) Complementary static measurements of second-order dipolar order, indicating the dramatic change in the proton coupling network upon freezing of the dynamics. Due to proton background signal the absolute efficiency was not determined.

Image of FIG. 6.
FIG. 6.

(a) 1D 1H spectra of adamantane at 850 MHz and 20 (black) or 64 kHz (red) MAS. (b) The effect of chemical-shift resolution and offset under the same conditions on the efficiency of JB at generating dipolar (DO) or Zeeman order (ZO).

Image of FIG. 7.
FIG. 7.

(a) 1D 1H Spectrum of camphor at 500 MHz and 40 kHz MAS. (b–c) show the buildup of “dipolar” and “Zeeman” order, respectively, for the JB experiment as function of the carrier offset. Note: “dipolar” denotes the echo signal obtained in the imaginary buffer at times t FID = τ1, while “Zeeman” order is the signal obtained in the real buffer at times t FID = 0. The resolution in the 1D spectrum makes it impossible to be on-resonance for all lines simultaneously. These offsets induce modulated Zeeman and dipolar order that is large compared to the case where the homogeneous linewidth is larger than the isotropic chemical-shift dispersion. The Zeeman order can be minimized but there is still a remaining modulation present, caused by the chemical shifts, which is not present in the other experimental data presented here. (The presence of a strong Zeeman component would be a good reason to discard the data).

Image of FIG. 8.
FIG. 8.

(a) 1H spinlock efficiency (90° pulse, cw spinlock, detection) as a function of the applied rf-field amplitude for adamantane at 16 kHz MAS (5 ms spinlock) and (b) the corresponding 19F spinlock efficiency for CaF2 at 25.5 kHz MAS (2 ms spinlock). (c) Efficiency of the ADRF-ARRF sequence as a function of the maximum applied rf-field amplitude for adamantane at 12 kHz MAS (red) and CaF2 at 25.5 kHz MAS (blue). The effect of the HORROR condition at κ = 1/2 is readily observed. Note that the rf calibration is only approximate, explaining the 10% shift from ideal ratios for CaF2. (d) Buildup of second-order dipolar order for the ADRF-ARRF sequence as a function of the length for CaF2 and adamantane under static and MAS conditions (25.5 and 12 kHz, respectively).


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Table I.

Phase cycle for generating dipolar order as shown in Figure 1.

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Table II.

Homonuclear resonance conditions up to third order in a 6-spin system.

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Table III.

Experimentally determined relaxation times T1 and TDO (s) under static conditions and at 10 kHz MAS (in units of seconds) and at room temperature.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Second-order dipolar order in magic-angle spinning nuclear magnetic resonance