Page 347 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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

712 Nuclear Magnetic Resonance (NMR)

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with spin , which means that the proton acts as a small and of the scalar coupling. It has been previously noted
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magnet lining either with or against the external magnetic that at least six pieces of information characterize each
field. Then, as indicated in Fig. 2b, the methyne carbon anisotropic interaction responsible for nuclear resonance
frequencies. Thus, with four interactions and six pieces
resonance will be split into a doublet, with frequencies f 1
and f 2 , centered about the original unsplit signal shown of information each, there are 24 parameters that could
in Fig. 2a. Indicated at the right-hand side of Fig. 2b is in principle contribute to each observed NMR spectrum.
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the energy-level diagram of the methyne carbon, split For a nucleus in a solid, such as Al in an aluminosilicate
by its lone proton, and the transitions, which are vertical catalyst, all interactions will be present and will contribute
lines with a wiggle in the center. These transitions are at to the shape and width of the spectrum. The resultant spec-
frequencies f 1 and f 2 , and are seen in the high-resolution trum will be quite broad and featureless compared to the
spectrum of adamantane shown at the bottom of Fig. 2b. relatively sharp NMR absorption lines observed for alu-
At the left side of Fig. 2b are shown three peaks cor- minum in a liquid solution. In other words, resolution,
responding to the methylene carbon CH 2 in adamantane, and thus information, has been lost. While there are in
split by its two attached protons. The manner in which principle 24 pieces of information available, they are not
these two protons split the carbon energy levels is indi- separable from each other in this case, and in fact lead
cated at the center of Fig. 2b. One proton supplies the to a loss of information because they obscure each other.
same type of splitting as shown for the methyne carbon, However, in many cases, there is one major contributor
and the second proton further splits that level as indicated. to the NMR spectrum of a nucleus in a solid. For exam-
The transitions associated with this splitting are indicated ple, the major contribution to the proton NMR of hydro-
by the “bathroom tile” diagram, at frequencies f 3 , f 4 , and gen in gypsum, CaSO 4 ·2H 2 O, is the dipolar interaction
f 5 . Note that there are two equivalent transitions at f 4 , between two localized protons. The major contribution
so the intensity of the center line will be twice that of to the NMR of deuterium in perdeuterated polyethylene
the two satellites. This experimental result is found in the would be the interaction of the local electric field gradi-
high-resolution spectrum, shown on the lower left side of ent with the quadrupole moment of the deuterium. Thus
Fig. 2b. the physical information inherent in the spectrum due to
Scalar coupling, or “spin–spin splitting” as it is com- single contribution (internuclear distances from dipolar
monly termed, is thus a diagnostic tool that adds consider- interactions, etc.) may be extractable.
ably to the power of the NMR spectroscopist to diagnose It is therefore useful to examine the powder spectra as-
details of molecular structure. sociated with each of the interactions in a solid. These
Structure determination of molecules in solution is by spectra are shown in Fig. 3. These “powder patterns” have
far the most common use of NMR at the present time. The quite characteristic forms for particular symmetries of the
amount of space devoted to this important application of interactions, and from these forms the types of structural
the technique in this discussion is thus not commensurate information mentioned in the introduction can be derived.
with its present use, but perhaps not out of line in view of For example, the powder pattern associated with the dipo-
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future applications in other fields such as materials science lar interaction of two localized spin- systems, with gyro-
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and medicine. magnetic ratios γ 1 and γ 2 , is shown in Fig. 4a. The splitting
in frequency ν/Hz between the two sharp horns of this
spectrum is simply related to the internuclear vector r ij by
IV. NMR IN SOLIDS the formula
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ν = 1.5hγ 1 γ 2 2πr ij .
In Section II, we discuss the effects of local arrangements
of the electron cloud and other nuclei about a resonating Thus, as stated in Section II, the frequency splitting of
nucleus in a molecule that are responsible for the effec- this famous “Pake doublet powder pattern” is proportional
tive magnetic field seen by this nucleus, and thus for its to the inverse cube of the internuclear separation and is
NMR absorption spectrum. Each interaction is discussed quite sensitive to this separation. For example, the two
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in turn, as if it were the only interaction present, the jus- isolated protons at a distance of 0.248 nm (2.48 A) in the
tification being that many timesthe NMR spectrum of a trichloroacetic acid dimer, (Cl 3 CO 2 H) 2 , in the solid state,
given nucleus appears to be the result of one or two in- yield a Pake doublet with “horns” 11,771 Hz apart, inde-
teractions. A case in point is the NMR spectrum of a nu- pendent of the magnetic field. A change in the interproton
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cleus in a liquid, discussed in Section III. In this case, all distance by 0.01 A results in a frequency change of 80 Hz
information relating to anisotropy of the local environ- in the separation of the horns, and easily detectable change
ment effectively disappears, and the resulting spectrum is by NMR and an almost impossible change to detect us-
simply due to the isotropic portions of the chemical shift ing X-ray diffraction. The separations of localized pairs