Chemistry Reference
In-Depth Information
quantum transitions. The enhancement factor is defined as
N
eq
, where
N
Z
and
N
eq
are the nuclei numbers in the polarizing and thermal balance states,
respectively. After solving the rate equations for this system, we can obtain the
following equation for the signal enhancement:
x ¼
N
Z
=
x ¼
1
rm
g
E
g
N
(2)
with
W
2
W
0
r ¼
W
2
;
(3)
W
0
þ
2
W
N
þ
W
0
þ
2
W
N
þ
W
2
m ¼
W
0
;
(4)
W
0
þ
2
W
N
þ
W
2
þ
E
hi
E
hi
Ehi
;
¼
(5)
where
corresponds to the electron transition saturation factor ranging from 0 (zero
saturation,
h
E
z
i¼h
E
0
i
) to 1 (complete saturation,
h
E
z
i¼
0). From the above
equations, the coupling parameter
1.0 to 0.5, corresponding to
pure scalar coupling and pure dipolar coupling, respectively. In liquid samples, the
dipolar coupling is a major interaction leading to a maximum enhancement of 330.
On the other hand,
r
can vary from
o
0
E
and the
degree of molecular motion. This relation is shown in Fig.
2
of the Maly et al
.
review [
13
]. It is obvious to find that the OE process is inefficient at high magnetic
fields. Many scientists (Armstrong and Han, Grucker et al., and Hofer et al
.
)
r
also depends on the electron Larmor frequency
Fig. 2 (a) Population distribution at thermal equilibrium for a general three-spin system. (b)
Saturation of the allowed EPR transitions for one of the dipolar coupled electrons (
o
0
E
1
) leads to
negative enhancement. (c) Saturation of the transition corresponding to the second electron (
o
0
E
2
)
leads to positive enhancement. M
E1
,M
E2
, and M
N
are the spin states of electron 1, 2, and nucleus.
Reproduced with permission from [
13
]
