= Cross-polarization magic-angle spinning
= CPMAS
{c}
{synonym}
<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:
$$
3\cos^2\theta_{\mathrm m}-1=0,\qquad \theta_{\mathrm m}=\arccos(1/\sqrt3)\approx54.74^{\circ}.
$$
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.<Carbon-13 nuclear magnetic resonance of polymers spinning at the magic angle by Jacob Schaefer and E. O. Stejskal>[Page1031 and Figure1: CP/MAS, static CP and solution comparisons]{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.
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