Solid-state nuclear magnetic resonance

NMR measurements on immobilized or slowly moving samples, using approaches such as decoupling, sample alignment or magic angle spinning to manage anisotropic interactions.

Dipolar recoupling uses controlled spin rotations to restore sensitivity to NMR dipolar coupling that would otherwise be averaged away, commonly during magic angle spinning. Spinning can narrow spectra by averaging an orientation-dependent interaction; recoupling deliberately preserves a selected part of that interaction so it can reveal spatial information.

REDOR illustrates the experimental purpose. Rotor-synchronized pulses on a second nuclear species change how the coupling contributes during the rotation cycle. A matched reference echo and a dephased echo then supply a coupling-sensitive comparison. Early carbon-13–nitrogen-15 measurements on labeled alanine used isolated-pair calculations and a powder average to choose pulse placement.^[ref]

An original commuting toy model shows how a zero average can become nonzero. Let the interaction bewith dimensionless spin operators and angular-frequency scale $d$. Without control, the integrated coupling over one period vanishes. Ideal instantaneous $\pi$ rotations of the second spin at $T_r/4$ and $3T_r/4$ reverse the sign of $S_z$ between those times. The effective sign $y(t)$ then matches the sign of $\cos ({\omega }_{r}t)$, soHere $\chi$ is the coefficient multiplying $I_z{S}_z$ in the exponent of the interaction propagator $\exp (-i\chi I_z{S}_z)$. It is not automatically the phase of every detected coherence. The model demonstrates controlled sign reversal; it is not a reconstruction of the full REDOR pulse sequence or of all the angular terms in a spinning sample.

Restored sensitivity is not the same as a unique distance measurement. NMR dipolar coupling scales as the inverse cube of separation, but motion, additional spins and the pulse sequence affect the measured echo. NMR pulse errors can also change that echo, which is why reference matching and phase compensation such as XY8 matter.^[ref]

Rotational-echo double resonance, or REDOR, is a solid-state nuclear magnetic resonance method that reintroduces sensitivity to NMR dipolar coupling during magic angle spinning. Rotor-synchronized pulses acting on a second nuclear species interrupt the averaging of the interaction. Comparison with a matched reference echo reveals coupling-dependent dephasing; dipolar recoupling makes a normally suppressed interaction experimentally useful.^[ref]

Write $S_0$ for the full reference echo and $S$ for the echo measured with the dephasing pulse pattern. A common normalized readout isFor invented matched signals $S_0=100$ and $S=60$, the dephasing is0.40. This does not mean that40 percent of the nuclei are missing. The pulses change the coherent echo, and converting its attenuation into an internuclear distance requires an appropriate spin model and experimental calibration.

The early alanine record reproduced in Jacob Schaefer's retrospective is unusually concrete. It compares full and dephased carbon-13 echoes of nitrogen-15-labeled alanine, recorded by Terry Gullion on29May1987 at a carbon resonance frequency of50.3MHz. Dipolar evolution lasted ten rotor periods at3.2kHz spinning. The authors used an isolated-pair calculation and an isotropic powder average to choose pulse placements.^[ref]

An original timing calculation gives $10/(3200{\mathrm{s}}^{-1})=3.125\mathrm{ms}$ for those ten rotor periods. That is a duration derived from the reported settings, not a newly inferred pulse width. The retrospective explicitly says the sample weight and accumulated scan count were not recorded, so those details cannot be reconstructed from its spectrum.^[ref]

Because the dephasing experiment can involve many refocusing pulses, NMR pulse errors can mimic or obscure coupling-dependent changes. XY8 phase routing helped control off-resonance distortions in long REDOR pulse trains. Reference matching, pulse quality and a suitable model remain necessary even when the normalized dephasing is easy to calculate.^[ref]

Cross-polarization magic-angle spinning, abbreviated CPMAS, combines two operations in solid-state nuclear magnetic resonance. Cross-polarization (nuclear magnetic resonance) transfers nuclear spin polarization from a more strongly detected spin population, commonly protons, to a less sensitive one such as carbon-13. Magic angle spinning rotates the sample to average appropriate orientation-dependent interactions. Signal enhancement and spectral narrowing address different experimental obstacles.

The angle is fixed by a geometrical condition:This nulls the relevant second-rank angular factor under the averaging assumptions; it does not remove every interaction or every source of linewidth. Chemical shift anisotropy and sample motion must still be interpreted within the actual experiment.

In their 1976 paper, Jacob Schaefer and Edward O. Stejskal compared carbon-13 spectra of solids obtained with cross-polarization (nuclear magnetic resonance), with and without magic angle spinning, against solution spectra. The polysulfone example showed how the combined method could reveal much more resolved structural detail in a solid.^[ref]

For an original comparison, consider two carbon sites with equal populations but different efficiencies of polarization transfer. Their measured peak areas can differ even when their populations are equal. Changing contact time or relaxation conditions can change that weighting. NMR signal integration in a CPMAS spectrum therefore requires a justified acquisition model before peak areas are treated as direct composition measurements.

Sample rotation about an axis at approximately $54.74^{\circ }$ to the field, averaging appropriate second-rank anisotropic interactions when spinning and pulse conditions are suitable.