Probably the most widely used experimental technique used in solid state NMR is magic angle spinning [32], more commonly known as MAS. In liquids rapid molecular tumbling averages out many of the internal interactions, however this is not possible in solids. The large majority of samples analysed are polycrystalline in nature and there-
fore consist of many crystallites with random orientations. The internal interactions, chemical shift, dipolar coupling, scalar coupling and the quadrupole interaction all have components that are dependant on crystal orientation and are said to be anisotropic. Therefore solid state NMR spectra contain broad lines caused by the slightly different frequencies arising from the many different crystallite orientations. While it is possible to analyse such spectra and determine structural properties, it becomes increasingly difficult to interpret and analyse such spectra if they contain more than one chemically inequivalent crystal site with overlapping resonances.
Fortuitously the molecular orientation dependence of the internal interactions dis- cussed in Chapter 2.5, all involve the same 3cos2 θ - 1 term, and in a powder sample
effectively all values of θ are represented. If the sample is rotated, the angle θ will vary with time as the orientation of each crystallite changes. This angular dependence 3cos2 θ - 1 is proportional to the 2nd degree Legendre polynomial
P2(cosθ) =
1 2(3cos
2θ−1) (3.6)
for the angle 54.74◦ P2 = 0. The angle 54.74◦ is called the ’magic angle’ and it is
found that by rotating the sample at the ’magic angle’ it is possible to average out the 3cos2 θ - 1 term from the internal interactions, provided that the rotation rate is fast enough compared to the size of the interaction. Therefore it is possible to simulate the rapid molecular motion in liquids and in theory reduce the line width of solid state experiments to that of liquid state experiments. However this is generally not the case, there will in most instances be significant narrowing of the line widths, but residual effects from dipolar coupling can still cause broadening and the chemical shift anisotropy can be significantly large enough that it is not possible to average it out completely. Disorder can also be a problem in solid state NMR, in liquids slight differences in frequency will be averaged out by molecular tumbling, but this is not the case in solids, even under MAS, and manifests as broadening of the lines. Similarly, quadrupolar nuclei that have large CQ’s are still broad under MAS, as the second order
perturbations have a second angular dependence, and the line width is only partially narrowed (by approximately a third)by MAS [51], however it is possible to overcome
this and will be discussed in the next section.
In order to average out the anisotropy of the interaction the rotation rate (ωr) has
to be a factor of three or more greater than the anisotropy (∆ω) and it is not always possible to achieve this, if the rotation of the sampleωr <<∆ωthen it will not be much
different than the static spectrum. If the rotation rate of the sample ωr ≈∆ω the line
width will still narrow significantly with a narrow line at the isotropic chemical shift but will also be joined by what are called spinning sidebands (see Figure 3.3a) which are shifted from the isotropic peak by ±ωr. The isotropic peak will not necessarily be
the most intense peak or the central peak as overall shape of the spinning side band pattern will reflect the shape of the anisotropy, and the only way to determine what peak is the isotropic shift is to spin at different speeds, as the isotropic shift is the only one that will not move, if the spinning speed is increased the number and intensity of side bands will decrease.
Despite improving resolution, several factors have to be taken into consideration when using MAS, the anisotropies are field dependant and this can provide complica- tions at higher magnetic fields and requires even faster spinning speeds. The presence of spinning side bands can make interpretation of spectra difficult when there are mul- tiple sites, however sometimes it is desirable to have spinning side bands as they can be analysed to give information as to the anisotropies and asymmetries in the sample. MAS probes come in many different configurations, these range from high sample volume (several grams of sample) with slow spinning speeds 2-4 KHz, to very small volume (tens of milligrams of sample) and very high spinning speed greater than 60 KHz, speeds of up to 80 or 90 KHz are possible but not quite routine yet. They all work in generally the same way (see Figure 3.3b), with the sample holder (otherwise known as a rotor), sitting on an gas bearing, the rotor has a turbine cap at one or both ends which is also driven by gas, the gas is usually compressed air or nitrogen. Due to the incredible forces involved when the samples are spun, the materials that the rotors can be made from are limited as they have to be strong and light enough, the most common materials used for rotors are zirconium dioxide (ZrO2) and silicon
Figure 3.3: (a) MAS spectra showing how changes in the rotation frequency ωr ωr
affects the line shape and width, when spun at various speeds relative to the static line width ∆ω (b) a schematic representation of a MAS probe head.