This appendix is designed to introduce the reader to solid state nm r
spectroscopy at a simple level involving theory, technical procedure and terminology. Acknowledgements are d ue to Dr Patrick Barrie and his lecture course.
N m r spectra of solids are not recorded in the same w ay as liquids due to the num ber of anisotropic interactions occurring in the solid state. The three m ain interactions are (direct) dipole-dipole coupling, chemical shift anisotropy and quadrupolar interaction. These effects are averaged out in solution by fast, random molecular m otion bu t in the solid state, they lead to broadening of peaks in the spectra and obscurém ent of most of a spectrum 's information.
Dipole-dipole coupling arises from neighbouring nuclei (which have a magnetic moment) exerting a magnetic field on other nuclei. The Hamiltonian is proportional to the m ultiple of the gyromagnetic ratio (y) for each nucleus coupled to a spin geometry term (for either homo- or hetero-nuclear spins) and to the specific orientation (0)
between the two nuclei. It is inversely proportional to the cube of the internuclear distance (r), thus consideration is only needed for nuclei w ithin a short range.
H o = ( 1 - 3 c o s ^ 0 ) • [sp in g e o m e t r y term ]
To remove dipolar broadening from the spectrum, the term involving orientation must be averaged to zero, thus imitating the behaviour in solution nmr. The method most widely used is magic-angle spinning (MASk If the solid is set to spin at an angle to the magnetic field, (3, then an expression can be set up for the average values of ( 1 - 3
cos^G) linking it to the angle betw een the vector joining the spins and the rotation axis. This can be varied and if (1 - 3 cos^p) can be set to zero then the orientation effect, ( 1 -
3 cos^G), m ust also be zero. This angle is then the "magic angle" - 54.7°. Thus, if the sample can be spun so that is averaged quickly w ith the m agnitude of the dipolar interaction, then the effect can be negated by magic-angle spinning and a higher resolution spectrum be obtained. By spinning quickly, the anisotropy effect can also be removed.
In reality, machines are capable of spinning speeds to remove the interaction except for where coupling to hydrogen or fluorine exists, due to their high gyromagnetic ratios. To counteract coupling to hydrogen, high power decoupling m ay be used which involves a strong radiofrequency pulse (at the frequency of proton) being applied. This makes the proton spins change so rapidly such that the influence of their magnetic moment is averaged to zero. It is termed high power decoupling because the strength of the pulse m ust be of the same order as the undesired interaction. Another w ay to
record spectra w ith hydrogen and fluorine coupling is to use a multiple-pulsing technique w hich will resolve the spin p art of the H am iltonian to be zero.
In solid state nm r spectra, the signals are w eak and spin-lattice relaxation times are generally long, leading to long times between pulses. Cross-polarization ('CP') is a technique that transfers magnetization from neighbouring hydrogen nuclei to the target atom (usually C). This allows a shorter time betw een scans and enhances the signal. It is possible to regulate the orientation, timing and strength of the irradiation of the nuclei so that the two nuclei have the same quantization axis and the energy gap betw een the energy levels of the carbon and hydrogen atoms is identical. The dipole- dipole interaction that exists between them is used to transfer energy betw een the two nuclei, i.e. the excess m agnetization of the hydrogen nuclei becomes ^^C magnetization and the populations of the tw o C levels are changed. After allowing time for this transfer, the irradiation of the carbon nuclei is stopped and the ^^C signal is measured. This effect enhances the signal intensity by a factor of four for carbon; in general, the enhancem ent is the ratio of gyromagnetic factors, Yh/Yx (^or any nucleus, X).
N ot only is the signal enhanced bu t as the time betw een scans is determ ined by the relaxation time of hydrogen nuclei, not the target nucleus, then the time taken for the n m r experim ent m ay be significantly shortened. The rate of cross-polarization depends mainly on the num ber of hydrogens nearby (available for magnetization transfer), the distance aw ay and any molecular motion. For nm r, the CP rates are observed to decrease in the order : C H2 > CH > CH3 > Cq^atemary This follows the num ber of hydrogen nuclei available except for methyl groups whose high mobilities reduce the rate of cross-polarization.
The reliance of cross-polarization on the dipole-dipole interaction seems contrary to the action of MAS averaging out these interactions. However, the strength of coupling betw een the nuclei is such to allow spectra to be recorded at speeds up to 12 kHz. The exception to this involves the quaternary carbon w hen spinning speeds over 6 kHz will lead to intensity distortions in the spectrum.
N on-quaternary suppression (NQS) is possible, usually accompanied by the total supppression of sidebands (TOSS). The dipolar dephasing suppresses CH and CH2 signals, b u t leaves those for Cquat and CH3. Spinning speeds achieved are ~ 4
kHz. The final nm r experim ent used in this work is FLIP, which is essentially the technique used in solution nm r spectroscopy.