24.5 Fourier Transform NMR Spectroscopy 1025
Example 24.15 the population ratio for a 200 MHz instruments at room temperature is
0.9999678.
The vector sum of the magnetic dipoles in a sample is a macroscopic magnetiza-
tion vector denoted byM. Since slightly more of the protons are in the spin-up state
at thermal equilibrium, and since the spins are randomly oriented around the cones,
Mwill point in the positivezdirection. Even thoughMis a vector sum of many
individual magnetic dipoles, it behaves like a single magnetic dipole when acted on
by a magnetic field. A strong pulse of radio-frequency radiation is delivered to the
sample, similar to the pulse of infrared radiation used in Fourier transform infrared
spectroscopy. If the pulse is polarized so that its oscillating magnetic field is in the
xdirection, it imposes a torque onMso that the vectorMrotates clockwise in the
yzplane. The length of the pulse is chosen so that it rotates the magnetization vector
by 90◦onto the positiveyaxis. This pulse is called a 90◦pulseor aπ/ 2 pulse. The
direction of the nuclear spins is independent of the orientation of the molecule, so that
the magnetic moments of the nuclei are rotated without rotating the molecules.
After the pulse the magnetization vectorMbegins to precess in thexyplane as the
individual spins precess. SinceMlies in thexyplane equal numbers of nuclei now have
spins up and spins down. This is a nonequilibrium distribution, and the spins begin to
relax to the equilibrium population given by the Boltzmann distribution. There are two
mechanisms of this relaxation, each of which produces an exponential decay with a
characteristic relaxation time. The first mechanism is interaction of the spins with their
surroundings, and its relaxation time is known as thelongitudinal relaxation timeor
spin–lattice relaxation time, denoted byT 1. The second mechanism is the interaction of
the spins with each other, and its relaxation time is known as thetransverse relaxation
timeorspin–spin relaxation time, and is denoted byT 2. Figure 24.7a depicts the path
of the precessing magnetization vector as it returns to its equilibrium position on thez
axis.
The precessing magnetization vector induces an alternating voltage in a coil placed
in thexyplane around the sample. The coil detects only the component ofMin thexy
plane. The signal detected by the coil comes from the component ofMin thexyplane,
as depicted in Figure 24.7b. The detected signal is called thefree induction decay
signal (abbreviated FID). A simple decaying oscillation is shown in Figure 24.8a,
corresponding to a FID signal with a single frequency and a single relaxation time.
If a substance has protons with different chemical shifts and spin–spin splittings, the
protons precess at slightly different frequencies and produce a FID spectrum that is
a sum of signals like that of Figure 24.8a with different frequencies. Figure 24.8b
shows the sum of two decaying oscillations, one of which has twice the frequency of
the other. The FID spectrum encodes the NMR spectrum as a function of time instead
of as a function of frequency. The Fourier transform of the FID spectrum provides the
spectrum as a function of frequency in the same way as in Fourier transform infrared
spectroscopy. If the signal did not decay, the spectrum would consist of lines of zero
width. Since the signal decays, the spectral lines have nonzero widths.Multipulse NMR Experiments
Several techniques involve two or more pulses rather than the single pulse used in ordi-
nary Fourier transform NMR.^6 These techniques can provide information that cannot
easily be extracted from ordinary NMR spectra.(^6) T. C. Farrar,Introduction to Pulse NMR Spectroscopy, Farragut Press, Chicago, 1989; J. B. Lambert
and E. P. Mazzola,op. cit.(note 4).