Page 352 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

P1: GNH/FEE P2: GPJ Final Pages
Encyclopedia of Physical Science and Technology EN010C-493 July 19, 2001 20:30

Nuclear Magnetic Resonance (NMR) 717

important to chemists, materials scientists, and others who
may have an interest in analyzing the properties of matter
3
7
on a microscopic scale. Examples include Li, with spin ,
2
Li being an important part of the current-carrying species
5
in Li batteries; 27 Al, with spin , Al being a critical part
2
3
of catalysts used for oil refining; and 11 B, with spin ,
2
boron being an important species used in production of
new glasses for use in fiber optics.
Each nucleus with spin S can have 2S + 1 quantum
statesthatdescribeitsangularmomentum.So,forexample
27 Al has four states describing its angular momentum,
and it is possible to produce three-quantum coherence in
ensembles of such nuclei, no coupling being present.
The importance of multiple quantum coherence in such
systems lies in the fact that use is made of such coherences
FIGURE 9 Multiple quantum spectrum of coupled protons in a
to produce high-resolution NMR of these species in solid.
C n H m fragment resulting from the adsorption and reaction of ethy-
Until these techniques were developed in the late 1990s,
lene on a supported ruthenium surface. The plot is of intensity
high-resolution NMR of quadrupolar nuclei in solids, with
versus order of coherence. The highest order, k, observed, is 5,
meaning that in this case there are six coupled protons in the the resultant power of the chemical shift as a fingerprint,
sample. The inference is that the fragment being observed could was unachievable in a manner that was technically simple
be (Ru) CH 2 CH CH CH 2 (Ru), where the (Ru) indicates the enough to be used by the average NMR spectroscopist.
metal surface.
This “holy grail” of solid state NMR has now been found,
87
and spectra of species such as Rb in the solid state have
selectionrulesoftheexperiment,therearesixcoupledpro- been obtained with a resolution of a single part per million,
tons. This figure is not a plot of intensity versus frequency. as illustrated in Fig. 10. The conditions under which the
Rather, it is a plot of intensity of each k quantum coher- bottom spectrum of Fig. 10 was achieved involved spin-
ence versus the order of the coherence, k. The method of ning the sample at 1.2 million rpm, at the so-called magic
obtaining this information from the data, which in pulsed angle to the static field, and, simultaneously creating, and
experiments are always represented by a plot of intensity detecting multiple quantum coherence. The experiments
versus time, is beyond this article. It must be emphasized, have been labeled MQMAS, for Multiple Quantum Magic
however, that the observable in NMR experiments is al- Angle Spinning. This is, in the author’s opinion, a stunning
ways single quantum coherence. The implication is that achievement with implications to be developed far into the
to obtain the information in which the multiple quantum future.
coherence is contained in the observable, it is necessary
to convert from multiple to single quantum coherence in a
two-dimensional NMR experiment, one example of which VIII. MEDICAL IMAGING
was given in Section VI.
A rather lovely aspect of this experiment is that there is The precession frequency of nuclear spins in a magnetic
a sense in which time is reversed, in that the experiment field has been alluded to now a number of times; it is
starts with the system being in a state of Zeeman order (all ω eff = γB eff . A physical result of this statement is that if
spins aligned along the external field), is caused to develop B eff , the effective magnetic field at the nucleus, can be
multiple quantum coherence, and then caused to reverse its made to vary in space, then the resonant frequency will
evolution back into a state of Zeeman order again. NMR is vary in space. This fact is the basis of imaging of nuclei
a wonderful tool for the study of time-dependent quantum in the human body, and for that matter, in any region of
mechanics. matter. In an imaging experiment, coils of wire are placed
about a subject in a magnetic field, and pulsed current
is run through these coils to produce gradient magnetic
B. Quadrupolar Nuclei
fields that vary with space and time. The nuclear reso-
A second case in which it is possible to have quantum nance frequencies of nuclei in the subject in turn vary
states that differ by greater than unity in angular momen- with space and time. Since different tissues (e.g., mus-
tum quantum number is that of nuclei with spin greater cle compared to bone) have different concentrations of
1
than . Almost 70% of the nuclei in the periodic table nuclei such as protons, as well as differing relaxation
2
have this property. Some are quite common and therefore times T 1 and T 2 , for these nuclei it is possible to convert a