Introduction to Nanotechnology

i 3.4. SPECTROSCOPY 69
NMR involves the interaction of a nucleus possessing a nonzero nuclear spin I
with an applied magnetic field Bapp to give the energy-level splitting into 21 + 1 lines
with the energies
E, = fiyBappm (3.15)
where y is the gyromagnetic ratio, sometimes called the mugnetogyric ratio,
characteristic of the nucleus, and rn assumes integer or half-integer values in the
range -I < m < +I depending on whether I is an integer or a half-integer. The
value of y is sensitive to the local chemical environment of the nucleus, and it is
customary to report the chemical shift S of y relative to a reference value yR, that is,
S = (y - yR)/yR. Chemical shifts are very small, and are usually reported in parts
per million ( ppm). The most favorable nuclei for study are those with I = i, such as
H, 19F, 3'P, and 13C; the latter isotope is only 1.1% abundant.
Fullerene molecules such as C,, and C70 are discussed in Chapter 5. The wellknown
buckyball C,, has the shape of a soccer ball with 12 regular pentagons and
20 hexagons. The fact that all of its carbon atoms are equivalent was determined
unequivocally by the 13C NMR spectrum that contains only a single narrow line. In
contrast to this, the rugby-ball-shaped C,, fullerene molecule, which contains 12
pentagons (2 regular) and 25 hexagons, has five types of carbons, and this is
confirmed by the 13C NMR spectrum presented at the top of Fig. 3.34. The five
NMR lines from the a, b, c, d, and e carbons, indicated in the upper figure, have the
intensity ratios 10 : 10 : 20 : 20 : 10 corresponding to the number of each carbon type
in the molecule. Thus NMR provided a confirmation of the structures of these two
fullerene molecules.
Electron paramagnetic resonance (EPR), sometimes called electron spin resonance
(ESR), detects unpaired electrons in transition ions, especially those with odd
numbers of electrons such as Cu2+ (3d9) and Gd3+ (4f7). Free radicals such as those
associated with defects or radiation damage can also be detected. The energies or
resonant frequencies are three orders of magnitude higher than NMR for the same
magnetic field. A different notation is employed for the energy E, = gpBBa,,m,
where pB is the Bohr magneton and g is the dimensionless g factor, which has the
value 2.0023 for a free electron. For the unpaired electron with spin S = on a free
radical EPR measures the energy difference AE = - E-1,2 between-the levels
rn = *$, to give a single-line spectrum at the energy level
(3.16)
Equations (3.15) and (3.16) are related through the expression gpB = Ay. If the
unpaired electron interacts with a nuclear spin of magnitude I, then 21 + 1 hyperfine
structure lines appear at the energies
(3.17)