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Encyclopedia of Physical Science and Technology EN010C-493 July 19, 2001 20:30

Nuclear Magnetic Resonance (NMR) 713

FIGURE 4 NMR powder patterns of nuclei. (a–c) Dipolar coupling. (d,e) Shielding anisotropy. (f) Central 1 – 1 tran-
2 2
sition of a weak quadrupolar nucleus. (g) Scalar coupling anisotropy. (h) Lifetime broadening.

of protons in solids may be obtained from NMR much action so as to remove it from the observed result. This
more easily than from X-ray diffraction. What does one is the quite narrow line inside the broad line. At the bot-
do, however, when a given nucleus is exposed to a num- tom is an enlarged version of the narrow line, where the
ber of anisotropic interactions, all of which are roughly abscissa has been changed from kHz to ppm. In the spec-
the same magnitude, such that the solid state spectrum is trum shown, the resonant frequency was 56.6 MHz, so
featureless and less informative than the information from one ppm is 56.6 Hz. The full width of half height (fwhh)
just the chemical shift plus scalar coupling obtained in a is about 3 ppm, corresponding to about 170 Hz. Thus a
measurement of NMR in the liquid state? spectrum 20,000-Hz wide has been reduced to a spectrum
Fortunately, the introduction of transient techniques in about 200-Hz wide by manipulating the nuclear spins in a
NMR has led to the ability to remove, or attenuate some, manner now becoming available via transient techniques
and in favorable cases all, of the above intractions in a in NMR.
selective manner, such that all but the interaction desired In a similar manner, each of the other broadening inter-
to be seen remains. These techniques are outside the lim- actions can be manipulated to remove or scale their values
itations of the present writing, but may be viewed in de- suchthattheresultingspectrumrevealsfeaturesassociated
tail in some of the references supplied. An example of the with predominantly one interaction. This manipulation of
removal of broadening due to proton–proton dipolar inter- spin and real-space operators is a small branch of science
actions, without removal of shielding anisotropy, in a pow- in itself, and the subject of a number of texts referenced at
dered solid of high-density linear polyethylene (in which the end of this article. An interesting feature of these ma-
there is only one chemical species of proton, the methy- nipulations is the physical rotation of the samples at speeds
lene proton), is given in Fig. 5. Here, the powder spec- about that of dentists drills: about 180,000 rpm. A favorite
trum without (a) and with (b) transient techniques used to angle of orientation of the rotation axis with respect to the
separate proton–proton dipolar coupling from shielding static field is the so called “magic angle,” which is that
anisotropy are shown. In part (a) of Fig. 4 is shown the along the diagonal of a cube with respect to a cube edge:
◦
powder spectrum of protons in polyethylene under a stan- 54.77 . If a sample is rotated at this angle in the static
dard experiment in which the spectrum is a result of both field at speeds large compared to the shielding anisotropy
shielding anisotropy and dipolar coupling. In this case, in cycles per second, the resulting broad powder spec-
the dipolar coupling dominates the spectrum, and the line trum associated with the shielding anisotropy is reduced
width is roughly 20 kHz. Also at the top the narrow line to its isotropic value (i.e., to a sharp line comparable in
is indicated resulting from manipulating the dipolar inter- width to spectra observed in liquids). Thus, for a system