Page 344 - 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

Nuclear Magnetic Resonance (NMR) 709

C. Electric Field Gradient; Quadrupolar Nuclei interaction for nuclei in the first two rows of the periodic
table.
The electric field gradient is simply the change in electric
To summarize the discussion, a nucleus that is not
field with direction due to the local distribution of nu-
moving has an NMR spectrum that is characterized by
clear and electronic charges at a particular point in space
a number of anisotropic interactions. These interactions
in which the nucleus in question is located. For exam-
may each be thought of as ellipsoids, with principal axes
ple, a sodium ion in a sodium chloride crystal would see
yielding NMR frequencies associated with the axis of
an electric field and an electric field gradient associated
quantization being along that axis. On isotropic rotation
+
−
with the presence of all neighboring Na and Cl ions. In
with a rotational frequency fast compared to the spectral
this special case, the electric field gradient is zero because
width associated with the anistropy of any interaction in
the crystal symmetry is cubic. If this nucleus is magnetic, question, the observed spectrum is a single line at the fre-
1
but has spherical nuclear charge symmetry (spin , e.g.,
2 quency specified by the istropic value of the interaction.
13 C), then it is unaffected by a field gradient. If the nuclear
1
charge symmetry is not spherical (spin greater than , e.g., For example, the two major interactions of protons in solid
2 benzene are shielding and dipolar. The shielding interac-
27 5
Al with spin ), it can orient in an electric field gradient,
2 tion has a spectral width of about 6 ppm, or of 1,800 Hz at
which is to say that its nuclear energy levels that determine
a proton resonant frequency of 300 MHz, and the dipolar
the NMR spectrum are sensitive to the field gradient. The interaction has a spectral width of roughly 20 kHz. On
1
1
spectrum associated with the central, – transition of
2 2 melting, the benzene molecules in the liquid are isotrop-
27 Al in an electric field gradient that has axial symmetry
ically rotating at frequencies much faster than 20 kHz,
for a sample of a powdered solid is shown in Fig. 3f, Sec-
with the result that the observed proton NMR spectrum is
tion IV. Thus, the NMR spectrum of a quadrupolar nucleus
associated with the isotropic values of the shielding and
associated with the presence of a nonzero electric field gra-
dipolar interactions. Because the isotropic value of the
dient is a measure of both local nuclear, and electron-cloud
dipolar interaction is zero, the observed spectrum does
geometries. The ellipsoid characterizing the spatial sym-
not reflect the dipolar interaction at all. It is simply shifted
metry of the electric field gradient is in general completely
from some reference by the isotropic value of the chemi-
asymmetric (i.e., E xx
= E yy
= E zz ). While in general the
cal shift only. The scalar coupling then acts to further split
isotropic value of the electric field gradient ellipsoid is not
the lines in the observed spectrum, as will be illustrated
zero, to a first approximation it may be taken to be so. This
later. If the nucleus in question is a quadrupolar nucleus
fact will be important in considering the effects of motion 23 3
(e.g., Na, with spin I = , then in addition to the effects
on the NMR of quadrupolar nuclei. 2
of shielding and dipolar interactions of, for example, Na
in NaNO 3 , on the NMR frequency of Na, there will be an
effect of the local electric field gradient. However, since
D. Scalar Coupling
the isotropic value of the electric field gradient is almost
At this point we have seen that nuclear resonance frequen- zero, sufficiently rapid isotropic rotation of the molecu-
cies can be sensitive to just the total electronic distribution lar environment about the sodium nucleus, such as would
(shielding), or just to the local distribution of magnetic be experienced in an aqueous solution of sodium nitrate,
nuclei about the nucleus in question (dipolar interaction), will result in a sodium NMR spectrum that again reflects
or to the total distribution of nuclei and electron charge primarily the isotropic values of the shielding and scalar
(interaction of a quadrupolar nucleus in an electric field coupling.
gradient). The fourth interaction to which all nuclei re-
spond has a physical origin slightly different than any of
the previous. It is a type of dipolar interaction, but trans- III. NMR SPECTRA OF LIQUIDS
mitted from one nucleus to the other through the electronic
charge distribution in a molecule. More specifically, it is In Section II we have seen that although the nucleus in
transmitted by just that portion of the electronic cloud a molecule has an NMR spectrum that is a reflection
that touches both of the interacting nuclei. It is therefore of the entire molecular framework and the anistropy of
a measure of a portion of the total electronic charge cloud this framework about the resonating nucleus, in the liq-
in molecules. Because it is a dipolar interaction, its spatial uid state the resonance frequencies are simply a reflection
dependence is exactly the same as for the classical dipo- of isotropic shielding and scalar coupling. This fact sim-
lar interaction between two nuclei, with powder spectrum plifies the observed spectra of liquids relative to those
shown in Fig. 4a, Section IV. However, its magnitude, of solids. In addition, NMR has the capability of yield-
which depends on different physical factors, is quite dif- ing both a quantitative and a qualitative analysis simulta-
ferent, and in general smaller than the classical dipolar neously. The reason for this remarkable fact is that it is