202 (327) BRUKER BIOSPIN User Manual Version 002
Relaxation Measurements
verse magnetization to zero is termed transverse or spin-spin relaxation. Both the
transverse magnetization and the difference between the current and equilibrium
z-magnetization decay exponentially, with time constants denoted T
1
for longitudi-
nal relaxation and T
2
for transverse relaxation. Relaxation also occurs while radio
frequency pulses are being applied to the system. Normally this is ignored, but in
the case of spin-locking pulses it is important. During cross-polarization, the mag
-
netization on the dilute spins is increased by transfer from another nucleus, but it
will also decay, since the radio frequency field (weak compared to the static field
B
0
) is insufficient to maintain the resulting transverse magnetization. If the pulse
on the excitation nucleus is stopped, and only that on the detection nucleus con
-
tinued, the transverse magnetization will decay exponentially, with a time constant
denoted T
1ρ
. This rate of decay will be strongly affected by the amplitude of the
spin-locking pulse.
Both of these processes occur via spin energy level transitions. It turns out that
the spontaneous transition rate is very low, and thus relaxation is dominated by
stimulated transitions. Such transitions are stimulated by local magnetic fields,
which fluctuate due to local molecular motion, and the transition rates depend on
the strength, and details of the fluctuations, of these local fields. Since the fluctua
-
tions are random, the rate of fluctuation is defined by the correlation time of the
motion. For efficient relaxation via a particular energy level transition, fields fluctu
-
ating with an inverse correlation time close to the frequency of the transition are
required. Longitudinal relaxation occurs via transitions on a single spin, and thus
requires fields fluctuating with inverse correlation times near to the Larmor fre
-
quency. Transverse relaxation occurs also via flip-flop transitions of pairs of spins,
which have energies close to zero, and so local fields fluctuating very slowly will
cause transverse relaxation. T
1ρ
relaxation involves transitions at the nutation fre-
quency of the spin-locking pulse, which can be chosen by the experimenter. Mea-
surement of these relaxation rates can therefore provide information about local
motions on a range of time scales.
T1 Relaxation Measurements 16.2
Longitudinal relaxation can be measured using a number of methods – which
method is appropriate depends on the sample involved. Here the experiments are
demonstrated on glycine, which has a very simple spectrum and will give results
using all the methods discussed. In general the only setup required is to calibrate
pulses for the nucleus under observation, and to have some idea of the relaxation
time constants involved.
Experimental Methods 16.2.1
The inversion-recovery method is the originally proposed method for measuring
T
1
values. The experiment proceeds as follows: firstly, the magnetization is invert-
ed by a 180° pulse. Then, there is a delay during which the magnetization relaxes,
and a 90° pulse converts the remaining longitudinal magnetization to transverse
magnetization, and an FID is recorded. The intensity of a particular signal in the
resulting spectrum depends on the initial intensity, the relaxation delay, and the re
-
laxation time constant T
1
as follows:
(Eq. 16.1)
)/exp())0(()(
1
TtSSStS
EE
−−+=
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