Chemistry Reference
In-Depth Information
discussed this phenomenon and show the determination of the coupling parameter
r
in their articles [
12
,
14
,
15
]. The leakage factor
m
describes the nuclear spin
relaxation by electron spins. The value of
m
can be assumed to lie between 0 and 1.
The
m ¼
0 represents no relaxation caused by the electron-nuclear coupling,
1 means no other relaxation mechanisms (
W
0
m ¼
¼
while
0). The saturation factor
¼
1 when the electron transitions are completely saturated. This condition is
important in the application of polarizing agents based on nitroxide radicals,
although it depends on the number of hyperfine lines in the spectra. For concurrent
time-dependent spin exchange, an additional factor
s
can be introduced to describe
the attenuate contribution on signal enhancement by scalar coupling. Generally, the
value of
can vary between 0 and 1, corresponding to no contribution and large
contribution of the scalar coupling, respectively [
13
].
s
2.1.2 Solid Effect
The solid effect (SE) is a DNP mechanism which requires states mixing caused by
the nonsecular component
K
PSE
of the hyperfine coupling [
16
]. The pseudosecular
term
K
PSE
contains the form
E
Z
N
þ
and
E
Z
N
(E: Electron spin operator, N:
Nucleus spin operator), which leads to a mixing of the states of the system. In SE
polarization, the new mix states are generated from the original states with
a coefficient
p
, which can be calculated by the first order perturbation theory and
is given by
3
g
E
g
N
e
if
p
¼
sin
y
cos
y
(6)
o
0
N
R
3
4
where
R
,
y
,
and
f
are the polar coordinates describing the electron-nuclear vector.
The irradiation probability of zero quantum or double quantum transitions is
proportional to 4
p
2
[
16
]. Furthermore, this transition probability and sensitivity
enhancement will be scaled with
o
2
o
0
N
. Therefore, this
correlation has restricted the application of SE in high field DNP experiments.
Practically, the SE requires the use of polarizing agents with a homogeneous EPR
line width and an inhomogeneous spectral width smaller than the nuclear Larmor
frequency. These agents can ensure that only one of the forbidden transitions is
excited at a time. However, the Differential Solid Effect (DSE, [
17
]) simultaneously
exists and leads to partial or complete cancellation of the polarization effect.
0
N
, since
p
is proportional to
2.1.3 Cross Effect/Thermal Mixing
The Cross Effect mechanism is based on allowed transitions and involves
the interaction of electron spin packets in an inhomogeneously broadened EPR
line. A similar effect, found in a homogeneously broadened EPR line, is called
thermal mixing. Wollan proposed a method to process the intermediate case of
