How Fast Should I Spin My Solid Sample?

The choice of MAS rate depends on the interaction to be averaged by the magic angle spinning. If you want to average out the chemical shielding anisotropy then you must spin the sample at a rate comparable to or greater than the span of the chemical shift tensor expressed in Hz. Although the spans of chemical shift tensors, measured in ppm, are independent of field strength they are linearly dependent on field strength, when expressed in Hz. As a result, an appropriate spinning speed in one magnet may not be an appropriate spinning speed for the same sample in another magnet. The spectra below illustrate this point. Both are 31P CPMAS spectra of dibasic ammonium phosphate with a spinning speed of 4 kHz. The lower trace was acquired at 11,75 Tesla while the upper trace was collected at 4.7 Tesla. One can see that there are many more spinning sidebands in the spectrum acquired at higher field despite the identical spinning speeds.One would have to spin the sample at 10 kHz in an 11.75 Tesla magnet to get a spectrum comparable to the one acquired with a spinning speed of 4 kHz in a 4.7 Tesla magnet.

Magic Angle Spinning

The NMR spectra of solids generally have very broad lines due to a number of interactions which are averaged either to zero or an isotropic value in solution. It is the averaging of these interactions which leads to the narrow lines observed in liquids. The rapid random motion responsible for the averaging in solution is not present for solids, however, it can be mimicked by spinning the sample about an angle of 54.7 degrees with respect to the magnetic field at a rate comparable to or greater than the extent of the interaction being averaged. This technique is called magic angle spinning (MAS) and it allows the measurement of high resolution spectra of solids. When the spinning rate is less than the extent of the interaction, the spectrum is split into sidebands spaced at the spinning speed. In the figure below are 81 MHz 31P CPMAS spectra of ammonium dihydrogen phosphate with high power proton decoupling at various spinning rates. When the spinning speed is zero, one can see the powder spectrum characterizing the chemical shift interaction. As the spinning speed is increased, there is a centerband at the isotropic chemical shift with sidebands whose intensities can be used to calculate the chemical shift tensor. When the spinning speed exceeds the span of the chemical shift interaction the sidebands are very small and a liquid-like spectrum is obtained.